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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/9_with_messages_without_nonce.txt
{"block_hash": "0x34e815552e42c5eb5233b99de2d3d7fd396e575df2719bf98e7ed2794494f86", "parent_block_hash": "0x3ae41b0f023e53151b0c8ab8b9caafb7005d5f41c9ab260276d5bdc49726279", "block_number": 1, "state_root": "0x74abfb3f55d3f9c3967014e1a5ec7205949130ff8912dba0565daf70299144c", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "version": "0x0", "contract_address": "0x30b81d3f0f4e2af48e211d9914d611422430cd6fac6a9df64136a6a879c1dc5", "contract_address_salt": "0x6030390b01fe79d844330de00821c68206959c389ef744b2d315e27078f0ad", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x782142c3526899d48e6f1ce725f56b11cb462586c9f1340e4cfbcbebdd174f2", "0x7dee1fa95f31fd5ffb0ad1c3313aa51d82d66adfbb65efb982eae696c4309b7"], "type": "DEPLOY"}, {"transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "version": "0x0", "contract_address": "0x703283db9c320db759d02c5255af47be11ac2e2dca4a27bca92b407e25e063b", "contract_address_salt": "0x13b7e67ff6b2e1a5aac25134cc2765ea2a1bf36a7b94c92aa3fc4690978d1c5", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x26a1e7e74188cbc724a793c972ad09d5aba110c4c06dfae51ae078b321e957", "0x461226574f9663500fc330295cea93b295389618c9eab30c3362fa14975d54c"], "type": "DEPLOY"}, {"transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "version": "0x0", "contract_address": "0x3cafce8a34c9796e8f71209bcfcc2903dcad24b8d924944e88466b0cafd352", "contract_address_salt": "0x25c239a162c5a7ace888ca39f295aad52b75174952f4ea8f3afed13cde4490a", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x1a315d6be5adafdd493b45672137525190b23b7f3a0ec91feafaa6ab48b0828", "0x24740a6b71ae76d658a1ec1efb6f201ba9794ebeed49ca59c0efe63f4a3cca2"], "type": "DEPLOY"}, {"transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x64ed79a8ebe97485d3357bbfdf5f6bea0d9db3b5f1feb6e80d564a179122dc6", "0x4e23b03fa17cab92b1fbcf15b4f6583736b7bef4be4d87559618265095adf32"], "contract_address": "0x7b196a359045d4d0c10f73bdf244a9e1205a615dbb754b8df40173364288534", "type": "INVOKE_FUNCTION"}], "timestamp": 1638978017, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/1_with_transactions.txt
{"block_hash": "0x42553deb16a14de4153f28312971f825e83d924e0f2883c1178de86a64a398f", "parent_block_hash": "0x315571f683fadc29bccd6bc6b666562d3fee101b6dcb8b12cf62821ecba9b62", "block_number": 100, "state_root": "0x4be6496e74b3877db0b958a197b32ad797b3d2b1045e0697c01c1481501ea39", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x2cce6f468d865bf93476c7a96b7ce0ca3d26a6ffbb4ba93a027a67f0d2e2773", "version": "0x0", "contract_address": "0x3272141143bc48b691d2037401c6957aef95f8e5ac0228b8d4518c8a0ef4b9f", "contract_address_salt": "0x7388987d7b2b134b2607a5bcb16cf4d2a746c5b195cceb3bd642109a3c111f0", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x733f7cf7e65348e0de5e7da675c243254fb225031575efa12b3baf9528cec6c", "0x600139c4376cff21a74f59f76bd2ffbd834e3944efcd9b712887bdd73b025db"], "type": "DEPLOY"}, {"transaction_hash": "0x2258d22b67b91625a4fa0b382787d3d22497c941a4cfe5839f14dddf9bc2dcc", "version": "0x0", "contract_address": "0x51e85932cee8a876fad5406e260d8b35c7ec181c9ce921f0cd1c8539d187e2a", "contract_address_salt": "0x7186ad1959aaf89e6c4a7835ba2eb8a89704018b9f339835b6c771b5a00e4df", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x145269486f7776d82292863ab8ca51e5b75de049a1a0d24926ba76a42eed5b9", "0x57d1eb0164ab13261149136d825b9968f7af98b11cc3f0d3c8345b26d3a61c1"], "type": "DEPLOY"}, {"transaction_hash": "0x6c26da8c26aa61dc40ed36b9078536f3b5b0532e884a8f0b7488480580bf3c9", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x27c3334165536f239cfd400ed956eabff55fc60de4fb56728b6a4f6b87db01c", "calldata": ["0x1b16ae63c8a3ca48ad7df4b7699750d1dbb1570f528628384e7ae76fa9b18dc", "0x33ce93a3eececa5c9fc70da05f4aff3b00e1820b79587924d514bc76788991a", "0x1", "0x0"], "contract_address": "0x12d1e51756ee5642f08f32d6a63f661e0af3ad44f8f253ae8060368712029b1", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x26699471faacb1f3a4f1da4b0dacb16b2e7b7fe0019d84f5971efe50c3bcded", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x3d7905601c217734671143d457f0db37f7f8883112abd34b92c4abfeafde0c3", "calldata": ["0x29b0cd7db5834d7db252fc218d1c6e22b3d7270dd28a699e2d718ba5a3af795", "0x65d6725ca6901828f58a45d340e51a59f373302a504dcf2f55a6acd4f6dbfbd"], "contract_address": "0x53f3bb33d1690fb40f108e76dfa2e2df8d71d575588426a4b0f6d882c4313ac", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x39fe0e1e4a3311850fc6aa3fab4fcb3a4534b04d338a00d5a5a576ce3bc161", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x12ead94ae9d3f9d2bdb6b847cf255f1f398193a1f88884a0ae8e18f24a037b6", "calldata": ["0x645a5ced0a6ea39b08298daead96bfa5ada4bbff"], "contract_address": "0x1b16ae63c8a3ca48ad7df4b7699750d1dbb1570f528628384e7ae76fa9b18dc", "type": "INVOKE_FUNCTION"}], "timestamp": 1638987140, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x2cce6f468d865bf93476c7a96b7ce0ca3d26a6ffbb4ba93a027a67f0d2e2773", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x2258d22b67b91625a4fa0b382787d3d22497c941a4cfe5839f14dddf9bc2dcc", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x6c26da8c26aa61dc40ed36b9078536f3b5b0532e884a8f0b7488480580bf3c9", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 63, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 1, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 1}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x26699471faacb1f3a4f1da4b0dacb16b2e7b7fe0019d84f5971efe50c3bcded", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 25, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 4, "transaction_hash": "0x39fe0e1e4a3311850fc6aa3fab4fcb3a4534b04d338a00d5a5a576ce3bc161", "l2_to_l1_messages": [{"from_address": "0x1b16ae63c8a3ca48ad7df4b7699750d1dbb1570f528628384e7ae76fa9b18dc", "to_address": "0x645A5CED0A6EA39b08298dAEAD96Bfa5ada4bBFf", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 31, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/5_with_class_hash_and_actual_fee.txt
{"block_hash": "0x34e815552e42c5eb5233b99de2d3d7fd396e575df2719bf98e7ed2794494f86", "parent_block_hash": "0x3ae41b0f023e53151b0c8ab8b9caafb7005d5f41c9ab260276d5bdc49726279", "block_number": 1, "state_root": "0x74abfb3f55d3f9c3967014e1a5ec7205949130ff8912dba0565daf70299144c", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "version": "0x0", "contract_address": "0x30b81d3f0f4e2af48e211d9914d611422430cd6fac6a9df64136a6a879c1dc5", "contract_address_salt": "0x6030390b01fe79d844330de00821c68206959c389ef744b2d315e27078f0ad", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x782142c3526899d48e6f1ce725f56b11cb462586c9f1340e4cfbcbebdd174f2", "0x7dee1fa95f31fd5ffb0ad1c3313aa51d82d66adfbb65efb982eae696c4309b7"], "type": "DEPLOY"}, {"transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "version": "0x0", "contract_address": "0x703283db9c320db759d02c5255af47be11ac2e2dca4a27bca92b407e25e063b", "contract_address_salt": "0x13b7e67ff6b2e1a5aac25134cc2765ea2a1bf36a7b94c92aa3fc4690978d1c5", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x26a1e7e74188cbc724a793c972ad09d5aba110c4c06dfae51ae078b321e957", "0x461226574f9663500fc330295cea93b295389618c9eab30c3362fa14975d54c"], "type": "DEPLOY"}, {"transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "version": "0x0", "contract_address": "0x3cafce8a34c9796e8f71209bcfcc2903dcad24b8d924944e88466b0cafd352", "contract_address_salt": "0x25c239a162c5a7ace888ca39f295aad52b75174952f4ea8f3afed13cde4490a", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x1a315d6be5adafdd493b45672137525190b23b7f3a0ec91feafaa6ab48b0828", "0x24740a6b71ae76d658a1ec1efb6f201ba9794ebeed49ca59c0efe63f4a3cca2"], "type": "DEPLOY"}, {"transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x64ed79a8ebe97485d3357bbfdf5f6bea0d9db3b5f1feb6e80d564a179122dc6", "0x4e23b03fa17cab92b1fbcf15b4f6583736b7bef4be4d87559618265095adf32"], "contract_address": "0x7b196a359045d4d0c10f73bdf244a9e1205a615dbb754b8df40173364288534", "type": "INVOKE_FUNCTION"}], "timestamp": 1638978017, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/13_without_entry_point.txt
{"block_hash": "0x34e815552e42c5eb5233b99de2d3d7fd396e575df2719bf98e7ed2794494f86", "parent_block_hash": "0x3ae41b0f023e53151b0c8ab8b9caafb7005d5f41c9ab260276d5bdc49726279", "block_number": 1, "state_root": "0x74abfb3f55d3f9c3967014e1a5ec7205949130ff8912dba0565daf70299144c", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "version": "0x0", "contract_address": "0x30b81d3f0f4e2af48e211d9914d611422430cd6fac6a9df64136a6a879c1dc5", "contract_address_salt": "0x6030390b01fe79d844330de00821c68206959c389ef744b2d315e27078f0ad", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x782142c3526899d48e6f1ce725f56b11cb462586c9f1340e4cfbcbebdd174f2", "0x7dee1fa95f31fd5ffb0ad1c3313aa51d82d66adfbb65efb982eae696c4309b7"], "type": "DEPLOY"}, {"transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "version": "0x0", "contract_address": "0x703283db9c320db759d02c5255af47be11ac2e2dca4a27bca92b407e25e063b", "contract_address_salt": "0x13b7e67ff6b2e1a5aac25134cc2765ea2a1bf36a7b94c92aa3fc4690978d1c5", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x26a1e7e74188cbc724a793c972ad09d5aba110c4c06dfae51ae078b321e957", "0x461226574f9663500fc330295cea93b295389618c9eab30c3362fa14975d54c"], "type": "DEPLOY"}, {"transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "version": "0x0", "contract_address": "0x3cafce8a34c9796e8f71209bcfcc2903dcad24b8d924944e88466b0cafd352", "contract_address_salt": "0x25c239a162c5a7ace888ca39f295aad52b75174952f4ea8f3afed13cde4490a", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x1a315d6be5adafdd493b45672137525190b23b7f3a0ec91feafaa6ab48b0828", "0x24740a6b71ae76d658a1ec1efb6f201ba9794ebeed49ca59c0efe63f4a3cca2"], "type": "DEPLOY"}, {"transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x64ed79a8ebe97485d3357bbfdf5f6bea0d9db3b5f1feb6e80d564a179122dc6", "0x4e23b03fa17cab92b1fbcf15b4f6583736b7bef4be4d87559618265095adf32"], "contract_address": "0x7b196a359045d4d0c10f73bdf244a9e1205a615dbb754b8df40173364288534", "type": "INVOKE_FUNCTION"}], "timestamp": 1638978017, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/4_pending.txt
{"parent_block_hash": "0x101f1bbeecabb9afa027412df8f6224b21f66633891cffa798c7ab9dbb987e9", "status": "PENDING", "eth_l1_gas_price": "0x3b9aca0c", "strk_l1_gas_price": "0x5f5e101", "transactions": [{"transaction_hash": "0x47b4000598758d1746ec2174d2ef9b1ab7f610fc1866e7af06b795ef1d018fb", "version": "0x3", "signature": ["0x416249e3679975127dce51b754a277be0663d61bc7ae5c014f782007dda6a08", "0x4a8ebcc83d587605781b93b93326099c084bc453d716ebc35ffcfb7259b7dfe"], "nonce": "0x2343", "nonce_data_availability_mode": 0, "fee_data_availability_mode": 0, "resource_bounds": {"L1_GAS": {"max_amount": "0x186a0", "max_price_per_unit": "0x5af3107a4000"}, "L2_GAS": {"max_amount": "0x0", "max_price_per_unit": "0x0"}}, "tip": "0x0", "paymaster_data": [], "sender_address": "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "calldata": ["0x1", "0x47ad6a25df680763e5663bd0eba3d2bfd18b24b1e8f6bd36b71c37433c63ed0", "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "0x2", 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"0x42bf85a3a716d499c6e4bd598583a042360a8347ac0dabce490b40073aeec49", "0x2f62a9b2ee4ef077153f08c32ac2690aa9c41219d98cd492558ddcf77a0688", "0x4f15bd9ba25dac9596e29a58c84bd5d637ebeef4b54bb1019b1be5c28460b78"], "account_deployment_data": [], "type": "INVOKE_FUNCTION"}], "timestamp": 1702110166, "sequencer_address": "0x1176a1bd84444c89232ec27754698e5d2e7e1a7f1539f12027f28b23ec9f3d8", "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x47b4000598758d1746ec2174d2ef9b1ab7f610fc1866e7af06b795ef1d018fb", "l2_to_l1_messages": [], "events": [{"from_address": "0x4718f5a0fc34cc1af16a1cdee98ffb20c31f5cd61d6ab07201858f4287c938d", "keys": ["0x99cd8bde557814842a3121e8ddfd433a539b8c9f14bf31ebf108d12e6196e9", "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "0x1176a1bd84444c89232ec27754698e5d2e7e1a7f1539f12027f28b23ec9f3d8"], "data": ["0xacbcafb7fb", "0x0"]}, {"from_address": "0x4718f5a0fc34cc1af16a1cdee98ffb20c31f5cd61d6ab07201858f4287c938d", "keys": ["0xa9fa878c35cd3d0191318f89033ca3e5501a3d90e21e3cc9256bdd5cd17fdd"], "data": ["0xca46d96b37266650e0a8b79938d9300037337cad82ea4f45a921ad68b6a5f9", "0x4a05f6bcf69cf21", "0x0", "0x4a060188c19871c", "0x0"]}], "execution_resources": {"n_steps": 850, "builtin_instance_counter": {"range_check_builtin": 15}, "n_memory_holes": 1}, "actual_fee": "0xacbcafb7fb"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x1a8bf22d7f9745c97eb37f7ac8a374cdbed5260af38cf1e71b77c5704cba2ca", "l2_to_l1_messages": [], "events": [{"from_address": "0x47ad6a25df680763e5663bd0eba3d2bfd18b24b1e8f6bd36b71c37433c63ed0", "keys": ["0x623f05ab950f48f4c7de96ada26e6ef575b83094cf09c69317ea7228afc4271", "0x79bf37f3c3b3d202aaaae8d01158839c06da467f7b6c0437e819ef91ac86c3d", "0x3452b9f33bb0f17c137423f9951d2f39092ce81406121deb2ba192ba4289900", "0x2edf461da90078be0eb9fa962e4a13d8646abde903b1154f78c09b6d8c94969", 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["0x99cd8bde557814842a3121e8ddfd433a539b8c9f14bf31ebf108d12e6196e9", "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "0x1176a1bd84444c89232ec27754698e5d2e7e1a7f1539f12027f28b23ec9f3d8"], "data": ["0x3ab84aa3da", "0x0"]}, {"from_address": "0x4718f5a0fc34cc1af16a1cdee98ffb20c31f5cd61d6ab07201858f4287c938d", "keys": ["0xa9fa878c35cd3d0191318f89033ca3e5501a3d90e21e3cc9256bdd5cd17fdd"], "data": ["0xca46d96b37266650e0a8b79938d9300037337cad82ea4f45a921ad68b6a5f9", "0x4a060188c19871c", "0x0", "0x4a0605344642af6", "0x0"]}], "execution_resources": {"n_steps": 1520, "builtin_instance_counter": {"range_check_builtin": 34}, "n_memory_holes": 1}, "actual_fee": "0x3ab84aa3da"}], "starknet_version": "0.13.0"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/3_with_events.txt
{"block_hash": "0x5f73a3f0d5f241b791a29dfa84eb6ed525963948a30b355a1d961016c81e589", "parent_block_hash": "0x1d2fbcba52c72cc6d0da86403990c87041f3389f29e767b162fc92f130516b8", "block_number": 70000, "state_root": "0x737ad6b017450d6ff7df697398cedbe0677dfa7e3dcafc889591b432b8ea2e9", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x45480d68c7c77a7356702c4e4fe143e549db81cc3172533e5485d45f9d097c6", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x3d7905601c217734671143d457f0db37f7f8883112abd34b92c4abfeafde0c3", "calldata": ["0x1779a6bbf5cfb4466ca61556a0598eee6f1954e91d79e63900d7af2a686f155", "0x56ece85bd20a9fc563c56fe92fa641af0534eb57f56b134a97ef5d81afa7bcf"], "contract_address": "0x7228ecef5152a55b25e80c934421ee119679050ebf7ed67eeee160787b1d9d6", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x783f5f53d8be9f373c04c190d0681359a64af59dd3fe3017e0410ea524e3187", "version": "0x0", 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0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/7_with_declare_tx.txt
{"block_hash": "0x2d55a37a13f6e2e5be94e01b5b35f16c676ff88d0b71522ac2c0d4138f4de69", "parent_block_hash": "0x3899fc79d4688863df959f68c424183cd478e4b8cd7be6dc40da90bea583e58", "block_number": 209679, "state_root": "0x60eac244530e1b9d04edaa567ffa2ac442e8e1304b177e7011c9cb1d6512880", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x3b9ac9ff", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x9e0be0faeeb9263ab079e23a3ab6adf27a89a7ea834bed58619ea0e5d3572e", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x27f4e1fcd5966cfe509ef0ea11a4a9ec9e9009305181cb963e6a387b3be9cd3", "0x577e3fcc120737f8ed4395baba2d36ce65a15eb3039c3ad99985262f9bb0376"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x34ad9fd64124f06bb18e31140a4c8285679da1bd97351a53fba96b075717fda", "0x2913ee03e5e3308c41e308bd391ea4faac9b9cb5062c76a6b3ab4f65397e106", "0x0", "0x5", "0x5", "0x2", "0x76ca73d1301beb9ef1869f59817a65769d6e39c6625405aaac13fc04e27e0be", "0x74129dcbe52686ae8770c2c9d53dae1139cd0f8b76467eb65a6e157c90d65c4", "0x1", "0x767ca036ead9c447478e13a7618967d099e432179ae7cd2c8dc6281ac8952b7", "0x2a"], "contract_address": "0x396fd5a266e97adeb75c2fde397b746a64eece8476966da8b96b58dd37016bc", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0xe9e8350ccc7bad6ba8a45e2ba112db726f8b5f1149c8a55a0c607bfa353992", "version": "0x0", "max_fee": "0x0", "signature": [], "nonce": "0x0", "class_hash": "0x44e64d6959e027a274c96d2a410dd17aba3fd6596f22253fb3a4dce44417dd2", "sender_address": "0x1", "type": "DECLARE"}, {"transaction_hash": "0x52ccaacb9d2353d305ca44dd40c1012fea081811a099881794bcb73553150b7", "version": "0x0", "contract_address": "0x93dbb5d019c022e0edd010ac209d0cd21f3aaadbf561a5c8657cd28325726b", "contract_address_salt": "0x37b699265cb801b7933e5801aa0d8809262410b3e62020dd4c91f8b593adb88", "class_hash": "0x44e64d6959e027a274c96d2a410dd17aba3fd6596f22253fb3a4dce44417dd2", "constructor_calldata": [], "type": "DEPLOY"}, {"transaction_hash": "0x7690e22efd0195cc901ee9e89e53fb1ca8eff6e5d9c1f0c66c39d53f1f0125b", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x26eebb296aa1ee22828e12d84035e0793dcb15cc49786ef4cc0a383a4a60507", "0x7c08a0bc690c4b5641939f702c1f75574b28d5d54552ad0582ac50a8d8d08cc"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x15d6d329847e14894b9938053ed81ba9771998ce6de85454fe6eb1429831bdd", "0x7772be8b80a8a33dc6c1f9a6ab820c02e537c73e859de67f288c70f92571bb", "0x0", "0x3", "0x3", "0x266e70822e3e819a27a70324d63ba44ef216a36718f5ee21ed11dc7ab839a42", "0x772a8ef0d78e68eadff8c470d89f4aced3f20a5fdafef08ba98eb80b3c36c8f", "0x64826b48d7a1b280318da7a7ae91ac3ba1f8dbf5c38de031dbb97e24d10a70e", "0x2b"], "contract_address": "0x396fd5a266e97adeb75c2fde397b746a64eece8476966da8b96b58dd37016bc", "type": "INVOKE_FUNCTION"}], "timestamp": 1660295244, "sequencer_address": "0x46a89ae102987331d369645031b49c27738ed096f2789c24449966da4c6de6b", "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x9e0be0faeeb9263ab079e23a3ab6adf27a89a7ea834bed58619ea0e5d3572e", "l2_to_l1_messages": [], "events": [{"from_address": "0x34ad9fd64124f06bb18e31140a4c8285679da1bd97351a53fba96b075717fda", "keys": ["0x76ca73d1301beb9ef1869f59817a65769d6e39c6625405aaac13fc04e27e0be", "0x74129dcbe52686ae8770c2c9d53dae1139cd0f8b76467eb65a6e157c90d65c4"], "data": ["0x767ca036ead9c447478e13a7618967d099e432179ae7cd2c8dc6281ac8952b7"]}], "execution_resources": {"n_steps": 276, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 4, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 3}, "actual_fee": "0x37e11d5f100"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0xe9e8350ccc7bad6ba8a45e2ba112db726f8b5f1149c8a55a0c607bfa353992", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 0, "builtin_instance_counter": {}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x52ccaacb9d2353d305ca44dd40c1012fea081811a099881794bcb73553150b7", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 0, "builtin_instance_counter": {}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x7690e22efd0195cc901ee9e89e53fb1ca8eff6e5d9c1f0c66c39d53f1f0125b", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 409, "builtin_instance_counter": {"pedersen_builtin": 2, "range_check_builtin": 8, "bitwise_builtin": 2, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 25}, "actual_fee": "0x6d884292899"}], "starknet_version": "0.9.1"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/12_l1_handler_without_nonce.txt
{"block_hash": "0x2a70fb03fe363a2d6be843343a1d81ce6abeda1e9bd5cc6ad8fa9f45e30fdeb", "parent_block_hash": "0x47c3637b57c2b079b93c61539950c17e868a28f46cdef28f88521067f21e943", "block_number": 1, "state_root": "0x525aed4da9cc6cce2de31ba79059546b0828903279e4eaa38768de33e2cac32", "status": "ACCEPTED_ON_L1", "gas_price": "0x0", "transactions": [{"transaction_hash": "0x2f07a65f9f7a6445b2a0b1fb90ef12f5fd3b94128d06a67712efd3b2f163533", "version": "0x0", "contract_address": "0x327d34747122d7a40f4670265b098757270a449ec80c4871450fffdab7c2fa8", "contract_address_salt": "0x3a6b18fc3415b7d749f18483393b0d6a1aef168435016c0f5f5d8902a84a36f", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x4184fa5a6d40f47a127b046ed6facfa3e6bc3437b393da65cc74afe47ca6c6e", "0x1ef78e458502cd457745885204a4ae89f3880ec24db2d8ca97979dce15fedc"], "type": "DEPLOY"}, {"transaction_hash": "0x214c14f39b8aa2dcecfdca68e540957624e8db6c3a9012939ff1399975910a0", "version": "0x0", "contract_address": "0x6538fdd3aa353af8a87f5fe77d1f533ea82815076e30a86d65b72d3eb4f0b80", "contract_address_salt": "0x90677b5114f8df8bb7dd5e57a90cceabe385540cb0ca857ed68e22bd76e20a", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x10212fa2be788e5d943714d6a9eac5e07d8b4b48ead96b8d0a0cbe7a6dc3832", "0x8a81230a7e3ffa40abe541786a9b69fbb601434cec9536d5d5b2ee4df90383"], "type": "DEPLOY"}, {"transaction_hash": "0x71eed7f033331c8d7bd1a4dca8eedf16951a904de3e195005e49aae9e502ca6", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "calldata": ["0x327d34747122d7a40f4670265b098757270a449ec80c4871450fffdab7c2fa8", "0x0"], "contract_address": "0x6538fdd3aa353af8a87f5fe77d1f533ea82815076e30a86d65b72d3eb4f0b80", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x1059391b8c4fba9743b531ba371908195ccb5dcf2a9532fac247256fb48912f", "version": 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"0x327d34747122d7a40f4670265b098757270a449ec80c4871450fffdab7c2fa8", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x169d35e8210a26fd2439207d77ef2f0abe77471acbc2da8d5eeab5127d8d57b", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x12ead94ae9d3f9d2bdb6b847cf255f1f398193a1f88884a0ae8e18f24a037b6", "calldata": ["0x9c47c96a115dad3a7dbbdafb2369fdaa2835d0d4"], "contract_address": "0x6538fdd3aa353af8a87f5fe77d1f533ea82815076e30a86d65b72d3eb4f0b80", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x68a8426d72bcac7dc3c84c52d90f39f64ffdc10e50b86f8d6f047ee243e2ba1", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x317eb442b72a9fae758d4fb26830ed0d9f31c8e7da4dbff4e8c59ea6a158e7f", "calldata": ["0x2c4301154e2f60000ce44af78b14619806dda3b52abe8bc224d49765a0924c1", "0x2", "0x2b36318931915f71777f7e59246ecab3189db48408952cefda72f4b7977be51", "0x7e928dcf189b05e4a3dae0bc2cb98e447f1843f7debbbf574151eb67cda8797"], "contract_address": "0x6538fdd3aa353af8a87f5fe77d1f533ea82815076e30a86d65b72d3eb4f0b80", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x7eff4524ae42c2ffa72ff228cee4729bf7f31c2a0aefe3ee1c8abe546442158", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x6538fdd3aa353af8a87f5fe77d1f533ea82815076e30a86d65b72d3eb4f0b80", "0x1aed933fd362faecd8ea54ee749092bd21f89901b7d1872312584ac5b636c6d"], "contract_address": "0x327d34747122d7a40f4670265b098757270a449ec80c4871450fffdab7c2fa8", "type": "INVOKE_FUNCTION"}], "timestamp": 1637072695, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x2f07a65f9f7a6445b2a0b1fb90ef12f5fd3b94128d06a67712efd3b2f163533", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, 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"transaction_index": 3, "transaction_hash": "0x1059391b8c4fba9743b531ba371908195ccb5dcf2a9532fac247256fb48912f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 209, "builtin_instance_counter": {"pedersen_builtin": 2, "range_check_builtin": 8, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 24}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 4, "transaction_hash": "0x73fe0b59ac28a2c3c28b4d8713f4f84d4463c48245539644838cf1e8526b536", "l2_to_l1_messages": [{"from_address": "0x327d34747122d7a40f4670265b098757270a449ec80c4871450fffdab7c2fa8", "to_address": "0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 332, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": 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0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/10_with_l1_handler.txt
{"block_hash": "0x1474d03859dc30b43a447451c17fdee793bda9cb14abeb82d45aca354797a86", "parent_block_hash": "0x22180db9352fe1c389547d5b7b4bc339068a084551b21a90c7224928cde6a97", "block_number": 77881, "state_root": "0x4b59f41718eeeb75576a375393ab2b9ec710bf02721d48fc54a2f36c0afaee1", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x4861a1e73e730dee2108d51e94dac5e24bdfa38d5143e31f2526e1ead8cf755", "version": "0x0", "contract_address": "0x824ecb6cf460f89d415542e90928eaae78cb9353e02c3005c699b77a720c2d", "contract_address_salt": "0xe4518980ea5d9088853bf5298332a33d3358e2535e3992ce6b2393e812dbd2", "class_hash": "0x48498ebae1afc22157322db4bb7814b668c7ee20237cc8be64d934649679da1", "constructor_calldata": ["0x21c8e8c97fab810f6d2d4f36d984718508f8eed337a8b7e7095e16f8c72c4c8", "0x326e2488fa5982d4319c6f3c8f86f6bd9c5b57e9d70a658eddd07e0d2f6529d"], "type": "DEPLOY"}, {"transaction_hash": 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"0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 332, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 26, "transaction_hash": "0x22377e31d75ae74f4ae3889bd59f9575f232d4d573632cbc7c4d0e76e669f9f", "l1_to_l2_consumed_message": {"from_address": "0x0552D0AE6ac009C771c308A9e853c43a76A19167", "to_address": "0x7e829edae4832b140c73ba615e02f2d593122d43724352e21716daff98bd1da", "selector": "0x2d757788a8d8d6f21d1cd40bce38a8222d70654214e96ff95d8086e684fbee5", "payload": ["0x587a8075a2b0bfd4d7b99164b300f744f65d4fdf14ca7f0c268d1c3318476c5", "0x5dc", "0x0"], "nonce": "0x0"}, "l2_to_l1_messages": [], "events": [{"from_address": "0x7e829edae4832b140c73ba615e02f2d593122d43724352e21716daff98bd1da", "keys": ["0x221e5a5008f7a28564f0eaa32cdeb0848d10657c449aed3e15d12150a7c2db3"], "data": ["0x587a8075a2b0bfd4d7b99164b300f744f65d4fdf14ca7f0c268d1c3318476c5", "0x5dc", "0x0"]}], "execution_resources": {"n_steps": 575, "builtin_instance_counter": {"pedersen_builtin": 2, "range_check_builtin": 12, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 24}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 27, "transaction_hash": "0xd6db9d9d838d38597643774cea8d35449671fcc4b988a1133cc4fad732ae83", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 28, "transaction_hash": "0x420bce5822d57c169d78bb50b110c2da47021c00d3976935e8519b34f7282c2", "l2_to_l1_messages": [{"from_address": "0x11dc7fccce1df61b183927614739c3ce238fbe5a5cc24167a7fac9b25622b01", "to_address": "0x424f5Ddd7A91dFFFd11CDc0be9D1e54caD362a05", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 31, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 29, "transaction_hash": "0x1d47ff55b0d6d0953e4dcd7779f325cda30ed9bd8d03262e9c3c9951871a3e6", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 25, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 30, "transaction_hash": "0x5bc57f14b4eef0f72119b694b3e98fc2422431f0ae9778068651fdd3b185aab", "l2_to_l1_messages": [{"from_address": "0x6b61859ec13599f94dc858a78d5f162f04ba5e626a698792f15b9d58144d937", "to_address": "0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 372, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 1, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 2}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/8_with_starknet_version.txt
{"block_hash": "0x19b67b0aa0d29ed45352f113df69d4ed41ecf29d04368bd2a25e9ddb356669e", "parent_block_hash": "0x6cbc5f75688917d1a150eb913edf313d5a520856eb9bba23fd328c39cfe0509", "block_number": 200000, "state_root": "0x212073e6eab4a5cc4269e2638eefd9ce153a9ae100f17337005280beda5a2bf", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x59682f07", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x31430dd19eff308adca90182f1bfa0209185d0664c13b465dc4c2c8e1ea41eb", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x56ed338ad5ec0849ad9635ca68a9b2b2b62552d3f4f69648655a27c1707e29", "0x5904be5d6ed06cf902ac6451cfe7f8c1c3dee2e6f6c20174a0461bae4af778e"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x223951c7eb0638baf432631f05a2fe72ae96c25be1a1b9c7f81b6e3adaa19f", "0x12ead94ae9d3f9d2bdb6b847cf255f1f398193a1f88884a0ae8e18f24a037b6", "0x0", "0x1", "0x1", "0x60b1cec296e0cddad1e976bdef7a0ec495ee1c1c", "0x1b3"], "contract_address": "0x2e2ed6c28ff10eef7391edd6f3151ebc3528ccb55dd78f9babfc89a40ac6148", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x5a69b18074cdf81c0802e125f45fcba712dc00d418752387cf24597f5251be", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x2aab5123fe61803c6ad5a463f39b9ba62d802860d08ff6554aca32eb2bb068e", "0x57ba06c79c306bcdfb9c66c4cee1de0fe8eff9f83f204609bb56422afc1d5cc"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x219d65d795fb8f32d6c9f604f049c2e256d322334802e0311f26b896e093a60", "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "0x0", "0x2", "0x2", "0x676340aaad0380a56111f48160587d8f09cbccb6ec82553cbcb4720dacdde1a", "0x0", "0x18f"], "contract_address": "0x396fd5a266e97adeb75c2fde397b746a64eece8476966da8b96b58dd37016bc", "type": "INVOKE_FUNCTION"}], "timestamp": 1658297240, "sequencer_address": "0x46a89ae102987331d369645031b49c27738ed096f2789c24449966da4c6de6b", "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x31430dd19eff308adca90182f1bfa0209185d0664c13b465dc4c2c8e1ea41eb", "l2_to_l1_messages": [{"from_address": "0x223951c7eb0638baf432631f05a2fe72ae96c25be1a1b9c7f81b6e3adaa19f", "to_address": "0x60B1CEC296E0Cddad1e976Bdef7A0Ec495Ee1c1c", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 264, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 2, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 4}, "actual_fee": "0x2ba354ac07a5"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x5a69b18074cdf81c0802e125f45fcba712dc00d418752387cf24597f5251be", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 471, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 2, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 5}, "actual_fee": "0xc1114a0d4db"}], "starknet_version": "0.9.1"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/6_with_sequencer_address.txt
{"block_hash": "0x19b67b0aa0d29ed45352f113df69d4ed41ecf29d04368bd2a25e9ddb356669e", "parent_block_hash": "0x6cbc5f75688917d1a150eb913edf313d5a520856eb9bba23fd328c39cfe0509", "block_number": 200000, "state_root": "0x212073e6eab4a5cc4269e2638eefd9ce153a9ae100f17337005280beda5a2bf", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x59682f07", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x31430dd19eff308adca90182f1bfa0209185d0664c13b465dc4c2c8e1ea41eb", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x56ed338ad5ec0849ad9635ca68a9b2b2b62552d3f4f69648655a27c1707e29", "0x5904be5d6ed06cf902ac6451cfe7f8c1c3dee2e6f6c20174a0461bae4af778e"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x223951c7eb0638baf432631f05a2fe72ae96c25be1a1b9c7f81b6e3adaa19f", "0x12ead94ae9d3f9d2bdb6b847cf255f1f398193a1f88884a0ae8e18f24a037b6", "0x0", "0x1", "0x1", "0x60b1cec296e0cddad1e976bdef7a0ec495ee1c1c", "0x1b3"], "contract_address": "0x2e2ed6c28ff10eef7391edd6f3151ebc3528ccb55dd78f9babfc89a40ac6148", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x5a69b18074cdf81c0802e125f45fcba712dc00d418752387cf24597f5251be", "version": "0x0", "max_fee": "0x2386f26fc10000", "signature": ["0x2aab5123fe61803c6ad5a463f39b9ba62d802860d08ff6554aca32eb2bb068e", "0x57ba06c79c306bcdfb9c66c4cee1de0fe8eff9f83f204609bb56422afc1d5cc"], "entry_point_selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "calldata": ["0x1", "0x219d65d795fb8f32d6c9f604f049c2e256d322334802e0311f26b896e093a60", "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "0x0", "0x2", "0x2", "0x676340aaad0380a56111f48160587d8f09cbccb6ec82553cbcb4720dacdde1a", "0x0", "0x18f"], "contract_address": "0x396fd5a266e97adeb75c2fde397b746a64eece8476966da8b96b58dd37016bc", "type": "INVOKE_FUNCTION"}], "timestamp": 1658297240, "sequencer_address": "0x46a89ae102987331d369645031b49c27738ed096f2789c24449966da4c6de6b", "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x31430dd19eff308adca90182f1bfa0209185d0664c13b465dc4c2c8e1ea41eb", "l2_to_l1_messages": [{"from_address": "0x223951c7eb0638baf432631f05a2fe72ae96c25be1a1b9c7f81b6e3adaa19f", "to_address": "0x60B1CEC296E0Cddad1e976Bdef7A0Ec495Ee1c1c", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 264, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 2, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 4}, "actual_fee": "0x2ba354ac07a5"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x5a69b18074cdf81c0802e125f45fcba712dc00d418752387cf24597f5251be", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 471, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 2, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 1}, "n_memory_holes": 5}, "actual_fee": "0xc1114a0d4db"}], "starknet_version": "0.9.1"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/11_without_execution_resources.txt
{"block_hash": "0x34e815552e42c5eb5233b99de2d3d7fd396e575df2719bf98e7ed2794494f86", "parent_block_hash": "0x3ae41b0f023e53151b0c8ab8b9caafb7005d5f41c9ab260276d5bdc49726279", "block_number": 1, "state_root": "0x74abfb3f55d3f9c3967014e1a5ec7205949130ff8912dba0565daf70299144c", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "version": "0x0", "contract_address": "0x30b81d3f0f4e2af48e211d9914d611422430cd6fac6a9df64136a6a879c1dc5", "contract_address_salt": "0x6030390b01fe79d844330de00821c68206959c389ef744b2d315e27078f0ad", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x782142c3526899d48e6f1ce725f56b11cb462586c9f1340e4cfbcbebdd174f2", "0x7dee1fa95f31fd5ffb0ad1c3313aa51d82d66adfbb65efb982eae696c4309b7"], "type": "DEPLOY"}, {"transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "version": "0x0", "contract_address": "0x703283db9c320db759d02c5255af47be11ac2e2dca4a27bca92b407e25e063b", "contract_address_salt": "0x13b7e67ff6b2e1a5aac25134cc2765ea2a1bf36a7b94c92aa3fc4690978d1c5", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x26a1e7e74188cbc724a793c972ad09d5aba110c4c06dfae51ae078b321e957", "0x461226574f9663500fc330295cea93b295389618c9eab30c3362fa14975d54c"], "type": "DEPLOY"}, {"transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "version": "0x0", "contract_address": "0x3cafce8a34c9796e8f71209bcfcc2903dcad24b8d924944e88466b0cafd352", "contract_address_salt": "0x25c239a162c5a7ace888ca39f295aad52b75174952f4ea8f3afed13cde4490a", "class_hash": "0x10455c752b86932ce552f2b0fe81a880746649b9aee7e0d842bf3f52378f9f8", "constructor_calldata": ["0x1a315d6be5adafdd493b45672137525190b23b7f3a0ec91feafaa6ab48b0828", "0x24740a6b71ae76d658a1ec1efb6f201ba9794ebeed49ca59c0efe63f4a3cca2"], "type": "DEPLOY"}, {"transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x64ed79a8ebe97485d3357bbfdf5f6bea0d9db3b5f1feb6e80d564a179122dc6", "0x4e23b03fa17cab92b1fbcf15b4f6583736b7bef4be4d87559618265095adf32"], "contract_address": "0x7b196a359045d4d0c10f73bdf244a9e1205a615dbb754b8df40173364288534", "type": "INVOKE_FUNCTION"}], "timestamp": 1638978017, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x782806917e338d148960fe9d801cabdf41c197d144db73cde4a16499321e2a", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0x7e845e48e9e9350f4f638ab145ab58346e767396aa84a5f9b695a27332f301b", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x5b99cc55d38c5dd909eeda916a2564364577a8d348b05c00de1419e1ff318e2", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 29, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x53028e485df33f22d4a6cd3a539759bce78e940314906c3057d206b57d4ce3f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/2_with_messages.txt
{"block_hash": "0x74cfd4248411f1c1f9a772dfab593d8567903409cd28d53b9999b075be7fde0", "parent_block_hash": "0x5b346e034baaadbd76fdcdc1cd2c66a952d8c2c0a5c13efd6f870cb598a790a", "block_number": 102, "state_root": "0x7f99e1098cf1bce26d5ba04ebdf6359d223d85c564c3dbd463bc1b86be8e519", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x0", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0xbf7dc15a05a3a20af67cede6d6b01dc51527a66c76d62e65e3786f6859658d", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x12ead94ae9d3f9d2bdb6b847cf255f1f398193a1f88884a0ae8e18f24a037b6", "calldata": ["0xfe6bfff9cc3a865e6a4c5a32f1ce6c1edaa8a20c"], "contract_address": "0x3e591c0f03fa44890270a10afcc20cd2955c230d3a5f23e9e878472d30de894", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0xaf6a0198fb059b6191567251ea91289401e3b21c30eaae80b14fd488296d3f", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x19a35a6e95cb7a3318dbb244f20975a1cd8587cc6b5259f15f61d7beb7ee43b", "calldata": ["0x838154919880a519aa34274066150498421b0e457a29e402fdc031b42e57c1", "0x5a81ca3fe1e5124d3213a3d954c720f58fee76e67a4865375e9f510776dff32"], "contract_address": "0x6eb02b1b1de08371b4040fed26cd4bc7e0e20869e4101d5805b55de928c9a30", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x21d1eee03dd6d65dd21566f7cdb9d9adcdf19ab348e7dec69c1f3fe3b30d6d8", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "calldata": ["0x428bb1b6ccf6d6f453d1bc541e979cbdebc430a8b88bb9ef609124778189662", "0x1"], "contract_address": "0x43c33f9fd75b39e85e2e5be148af0789509e2dff3d27c190ba968899e7e0eca", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x69acd104e3e67a279ff97a7888267338e49079e5f285554c6615e0330607171", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x27c3334165536f239cfd400ed956eabff55fc60de4fb56728b6a4f6b87db01c", "calldata": ["0x32abe45df04186f254d536dc09ff417552f4f6ce56aa98e566844a46ed27f88", "0x317eb442b72a9fae758d4fb26830ed0d9f31c8e7da4dbff4e8c59ea6a158e7f", "0x4", "0x27f0e2d287cfd186965790e011f6ed645a2a187b856d454d910dada87df8ce0", "0x2", "0x6023a97527d85b7ac20137432157ca417bac994d482148b3f9a14756f4c55dd", "0x7566eaa8a44e269354271a238b066b13a5614530ddbd8be5f6859677ac91a63"], "contract_address": "0x79631f37538379fc32739605910733219b836b050766a2349e93ec375e62885", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x7d6be64ce22c9336649c18c1007cfeac5a3ae1c0c70d752378c93b68740d874", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "calldata": ["0x267d07be3b4a438180cb8e6f5b738afab61b802afd2d7e9cc1b940ca42c103", "0x2"], "contract_address": "0x7bd521e81062d3b6033a38ee88e3072600e3a5bed2b5c8cf05e4ed0463e37c9", "type": "INVOKE_FUNCTION"}, {"transaction_hash": "0x4859ce9a202e89cdcb420f5a8ea28e185196a5aaf9db4426aea71fc456c5c4d", "version": "0x0", "max_fee": "0x0", "signature": [], "entry_point_selector": "0x218f305395474a84a39307fa5297be118fe17bf65e27ac5e2de6617baa44c64", "calldata": ["0x3886f6f7afa7f499b90d16131f34eee70e0422a10fca83f1bde2bfcc44afce8", "0x2"], "contract_address": "0x838154919880a519aa34274066150498421b0e457a29e402fdc031b42e57c1", "type": "INVOKE_FUNCTION"}], "timestamp": 1638987334, "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0xbf7dc15a05a3a20af67cede6d6b01dc51527a66c76d62e65e3786f6859658d", "l2_to_l1_messages": [{"from_address": "0x3e591c0f03fa44890270a10afcc20cd2955c230d3a5f23e9e878472d30de894", "to_address": "0xFE6bFfF9cc3A865E6A4c5a32f1CE6c1EDaA8a20C", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 31, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 1, "transaction_hash": "0xaf6a0198fb059b6191567251ea91289401e3b21c30eaae80b14fd488296d3f", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 178, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 2, "transaction_hash": "0x21d1eee03dd6d65dd21566f7cdb9d9adcdf19ab348e7dec69c1f3fe3b30d6d8", "l2_to_l1_messages": [{"from_address": "0x43c33f9fd75b39e85e2e5be148af0789509e2dff3d27c190ba968899e7e0eca", "to_address": "0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 332, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 3, "transaction_hash": "0x69acd104e3e67a279ff97a7888267338e49079e5f285554c6615e0330607171", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 209, "builtin_instance_counter": {"pedersen_builtin": 2, "range_check_builtin": 8, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 24}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 4, "transaction_hash": "0x7d6be64ce22c9336649c18c1007cfeac5a3ae1c0c70d752378c93b68740d874", "l2_to_l1_messages": [{"from_address": "0x7bd521e81062d3b6033a38ee88e3072600e3a5bed2b5c8cf05e4ed0463e37c9", "to_address": "0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}, {"from_address": "0x7bd521e81062d3b6033a38ee88e3072600e3a5bed2b5c8cf05e4ed0463e37c9", "to_address": "0x0000000000000000000000000000000000000002", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 426, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}, {"execution_status": "SUCCEEDED", "transaction_index": 5, "transaction_hash": "0x4859ce9a202e89cdcb420f5a8ea28e185196a5aaf9db4426aea71fc456c5c4d", "l2_to_l1_messages": [{"from_address": "0x838154919880a519aa34274066150498421b0e457a29e402fdc031b42e57c1", "to_address": "0x0000000000000000000000000000000000000001", "payload": ["0xc", "0x22"]}, {"from_address": "0x838154919880a519aa34274066150498421b0e457a29e402fdc031b42e57c1", "to_address": "0x0000000000000000000000000000000000000002", "payload": ["0xc", "0x22"]}], "events": [], "execution_resources": {"n_steps": 426, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "actual_fee": "0x0"}]}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_block/14_deploy_account.txt
{"block_hash": "0x357dd542a2df5a5a85c22eca3eea3303fcd02b460efabda5cb6db2874f88164", "parent_block_hash": "0x723291afb02722d20718992790f5f5957793da26e80b558ea8f9106eac95a47", "block_number": 228457, "state_root": "0x6e31e5f1af729acdb4454e9f9af70ac91783b39bcd576bc66de24a4e7ab2c39", "status": "ACCEPTED_ON_L1", "eth_l1_gas_price": "0x14f93ca8", "strk_l1_gas_price": "0x0", "transactions": [{"transaction_hash": "0x1d6f35c0239183ebd25e3e878227d4c0247c31b62811cad8d6f3143c54a9aea", "version": "0x1", "max_fee": "0x1c8482b480e", "signature": ["0x6325a9678f7601a6ea05f0bb96e474e0e2be447bf4762cd64194f29f23aed73", "0x36562c1f8f6775c29004395604f702f80bbea6f6653391867286f2d18f93777"], "nonce": "0x0", "contract_address": "0x39696a0665e4c9806a709c7872030c63ca82b551925b2f517ed1985066217b8", "contract_address_salt": "0x6ccdf35bc37d9c5030215e2fb39b97de8f755c8ed43dd52a4c30e5ab96e61b", "class_hash": "0x1fac3074c9d5282f0acc5c69a4781a1c711efea5e73c550c5d9fb253cf7fd3d", "constructor_calldata": ["0x539f848975104309396ee8ebaee0a45acb0238e0b13da9df0f855c082a3b7f3"], "type": "DEPLOY_ACCOUNT"}], "timestamp": 1665044362, "sequencer_address": "0x46a89ae102987331d369645031b49c27738ed096f2789c24449966da4c6de6b", "transaction_receipts": [{"execution_status": "SUCCEEDED", "transaction_index": 0, "transaction_hash": "0x1d6f35c0239183ebd25e3e878227d4c0247c31b62811cad8d6f3143c54a9aea", "l2_to_l1_messages": [], "events": [], "execution_resources": {"n_steps": 41, "builtin_instance_counter": {}, "n_memory_holes": 0}, "actual_fee": "0x19ecd3e9e98"}], "starknet_version": "0.10.1"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_trace/1_with_messages.txt
{"function_invocation": {"caller_address": "0x0", "contract_address": "0x3e591c0f03fa44890270a10afcc20cd2955c230d3a5f23e9e878472d30de894", "calldata": ["0xfe6bfff9cc3a865e6a4c5a32f1ce6c1edaa8a20c"], "result": [], "execution_resources": {"n_steps": 31, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 0, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 0}, "internal_calls": [], "events": [], "messages": [{"order": 0, "to_address": "0xFE6bFfF9cc3A865E6A4c5a32f1CE6c1EDaA8a20C", "payload": ["0xc", "0x22"]}]}, "signature": []}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_trace/2_with_events.txt
{"function_invocation": {"caller_address": "0x0", "contract_address": "0x49672cf4a6780b060f57d49b26634de69d3fa463e6428e060a35ef5e5f453d6", "calldata": ["0x8", "0x5310ba60cc041e1257880106159e014acd7f2db250577bfb95bf9a83936f127", "0x1cb4b3d6d873d4e399a0dd19e455cacf0614a944ca61c85496b9b20d5f51dd5", "0xbd65265d8c7afe085be7c3daefb875bbb2fc5cde9b97ea5ade799660ab360f", "0x62806861a4ba85af8d328ee0b7f1adec629232b873d66b94919d3e3ec503e62", "0x3434892122606509e984778cd29b30a200536b7e84e37f128f3ac8c74418c87", "0x72af1bff57cf5e0e888814c2a22faa7d20ecf71f2b976de4c871d609ebdc587", "0x547a1d7b3939ee1e0e2161ba091f7d2502163e0cef20c05408e13faa730e804", "0xd49e57e8597ea10b2c48dd26a46bc79fd6cd7bd14c50b77fa39e586bb13f7b", "0x0"], "selector": "0x2913ee03e5e3308c41e308bd391ea4faac9b9cb5062c76a6b3ab4f65397e106", "entry_point_type": "EXTERNAL", "result": [], "execution_resources": {"n_steps": 43, "builtin_instance_counter": {"pedersen_builtin": 0, "range_check_builtin": 2, "bitwise_builtin": 0, "output_builtin": 0, "ecdsa_builtin": 0, "ec_op_builtin": 0}, "n_memory_holes": 8}, "internal_calls": [], "events": [{"order": 0, "keys": ["0x5310ba60cc041e1257880106159e014acd7f2db250577bfb95bf9a83936f127", "0x1cb4b3d6d873d4e399a0dd19e455cacf0614a944ca61c85496b9b20d5f51dd5", "0xbd65265d8c7afe085be7c3daefb875bbb2fc5cde9b97ea5ade799660ab360f", "0x62806861a4ba85af8d328ee0b7f1adec629232b873d66b94919d3e3ec503e62", "0x3434892122606509e984778cd29b30a200536b7e84e37f128f3ac8c74418c87", "0x72af1bff57cf5e0e888814c2a22faa7d20ecf71f2b976de4c871d609ebdc587", "0x547a1d7b3939ee1e0e2161ba091f7d2502163e0cef20c05408e13faa730e804", "0xd49e57e8597ea10b2c48dd26a46bc79fd6cd7bd14c50b77fa39e586bb13f7b"], "data": []}], "messages": []}, "signature": []}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_trace/4_with_validation.txt
{"code": "StarknetErrorCode.INVALID_TRANSACTION_HASH", "message": "Transaction corresponding to hash 1 is not found."}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_trace/3_with_call_type.txt
{"validate_invocation": {"caller_address": "0x0", "contract_address": "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "calldata": ["0x2", "0x4d0b88ace5705bb7825f91ee95557d906600b7e7762f5615e6a4f407185a43a", "0x169f135eddda5ab51886052d777a57f2ea9c162d713691b5e04a6d4ed71d47f", "0x5", "0x772164c9d6179a89e7f1167f099219f47d752304b16ed01f081b6e0b45c93c3", "0x2e0a0b7625be9e2727125166351da8b9f43ad6e4f78f26f4d6fa6daa6f282d4", "0x2", "0x41110247563d500ef76776594d148aa6a9f16fe258cfc274db4f3cef96aa3bc", "0x2202a556642afd1cbb50cc29d520c8d2152017213a89829bb361aa058229bf", "0x3fe8e4571772bbe0065e271686bd655efd1365a5d6858981e582f82f2c10313", "0x1136789e1c76159d9b9eca06fcef05bdcf77f5d51bd4d9e09f2bc8d7520d8e6", "0x2", "0x6aa87a8dd4f10ae5694223e8167a06e4", "0x577669320375d903569e370ca02272be"], "call_type": "CALL", "class_hash": "0x2338634f11772ea342365abd5be9d9dc8a6f44f159ad782fdebd3db5d969738", "selector": "0x162da33a4585851fe8d3af3c2a9c60b557814e221e0d4f30ff0b2189d9c7775", "entry_point_type": "EXTERNAL", "result": ["0x56414c4944"], "execution_resources": {"n_steps": 1131, "builtin_instance_counter": {"ec_op_builtin": 3, "range_check_builtin": 28}, "n_memory_holes": 63}, "internal_calls": [], "events": [], "messages": []}, "function_invocation": {"caller_address": "0x0", "contract_address": "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "calldata": ["0x2", "0x4d0b88ace5705bb7825f91ee95557d906600b7e7762f5615e6a4f407185a43a", "0x169f135eddda5ab51886052d777a57f2ea9c162d713691b5e04a6d4ed71d47f", "0x5", "0x772164c9d6179a89e7f1167f099219f47d752304b16ed01f081b6e0b45c93c3", "0x2e0a0b7625be9e2727125166351da8b9f43ad6e4f78f26f4d6fa6daa6f282d4", "0x2", "0x41110247563d500ef76776594d148aa6a9f16fe258cfc274db4f3cef96aa3bc", "0x2202a556642afd1cbb50cc29d520c8d2152017213a89829bb361aa058229bf", "0x3fe8e4571772bbe0065e271686bd655efd1365a5d6858981e582f82f2c10313", "0x1136789e1c76159d9b9eca06fcef05bdcf77f5d51bd4d9e09f2bc8d7520d8e6", "0x2", "0x6aa87a8dd4f10ae5694223e8167a06e4", "0x577669320375d903569e370ca02272be"], "call_type": "CALL", "class_hash": "0x2338634f11772ea342365abd5be9d9dc8a6f44f159ad782fdebd3db5d969738", "selector": "0x15d40a3d6ca2ac30f4031e42be28da9b056fef9bb7357ac5e85627ee876e5ad", "entry_point_type": "EXTERNAL", "result": ["0x2", "0x1", "0x59cc87201a08025619d0dedaa2092d36bc5c9484116036344089d38f8387b19", "0x0"], "execution_resources": {"n_steps": 1632, "builtin_instance_counter": {"range_check_builtin": 36}, "n_memory_holes": 18}, "internal_calls": [{"caller_address": "0x35acd6dd6c5045d18ca6d0192af46b335a5402c02d41f46e4e77ea2c951d9a3", "contract_address": "0x4d0b88ace5705bb7825f91ee95557d906600b7e7762f5615e6a4f407185a43a", "calldata": ["0x772164c9d6179a89e7f1167f099219f47d752304b16ed01f081b6e0b45c93c3", "0x2e0a0b7625be9e2727125166351da8b9f43ad6e4f78f26f4d6fa6daa6f282d4", "0x2", "0x41110247563d500ef76776594d148aa6a9f16fe258cfc274db4f3cef96aa3bc", 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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/10_deploy_account_v3.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/9_declare_v3.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/3_not_received.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/4_failure.txt
{"finality_status": "NOT_RECEIVED", "status": "NOT_RECEIVED"}
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/7_reverted.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/2_deploy.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/1_invoke.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/6_declare_v2.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/8_invoke_v3.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction/5_declare_v1.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/1_success.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/3_with_declarations.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/2_pending_block.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/4_with_nonce_changes.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/6_with_replaced_classes.txt
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_state_update/5_with_declare_v2.txt
{"block_hash": "0x67d24961077de7a1f49b6b1da78903ee80217662d026c155e14d7abedc04034", "new_root": "0x16faa4c43f71b49facab6b0585094195c989ea6168e69f235fdcef86428cd42", "old_root": "0x5e40123c30cfecb5284c041a703c2b542de91a8c29c69af2e37e12496fa88a", "state_diff": {"storage_diffs": {"0x24dbaeb7bf551b2e6c403957a5e4c1b19596c2d6b9c77d677ed85af73007fc": [{"key": "0x5", "value": "0x65"}, {"key": "0x1469414c13009d9841e8cf4d8abd32ae6d59fe66c8e555271dc2231f45c7a6d", "value": "0x1c0f34928344fecbeed32e6087bd0c8ec049c1f33b6b115568f2b11c94a9ab6"}], "0x22fa2a6e1854e136bca7a60fa841bd0e7ae9f86320ea941db6da2ec53145265": [{"key": "0x6bfbb0f2bdec6f6e4a6eb5de2bfad5722a48bbcf7db16dbb361edf1b15eaa65", "value": "0x5a887e8eea583dd5ffa62dff9a127c2b851c63d40d6694932143fa7d30ee"}, {"key": "0x5", "value": "0x22b"}, {"key": "0x212a9e2c79c5bed28bca6740bae5babb6e2ec02c8e63d19e18027080b41bd31", "value": "0x69deb1aaf37c520b687dfa5e23b60d10822ac65875446c2f3a26d9251f12e93"}, {"key": "0x212a9e2c79c5bed28bca6740bae5babb6e2ec02c8e63d19e18027080b41bd32", "value": "0x1c65c2f72ab9a8589d1594e4c367a499d663af5de0184d387af8f5009048a31"}], "0x49d36570d4e46f48e99674bd3fcc84644ddd6b96f7c741b1562b82f9e004dc7": [{"key": "0x42328937f66f0427ca9e66a9b2b0e471a361ff0524b2676d4dc9546aff531a8", "value": "0x69d296d2ba457ca"}, {"key": "0x2d782db90efbf9b41bf6bdf47cfe2ad71e4f2cb31532a827f98260725f854c9", "value": "0x1e1731bd604ae0"}, {"key": "0x48e3426cfff518cb97998a29da47874171880da2a5b5da4e1b91d6f91dd59ce", "value": "0x8c264c2a2f178746"}, {"key": "0x31bd9ebcad63b29b6ce51df0b9978b7f5b1c158b0ee90b6d44024f225603e28", "value": "0x99655dab499a330"}], "0x60de99e2ba100ea02799ed692306ff5e209edc3a2be30c5c7e00e789f74771c": [{"key": "0x633cce43561d71b1f82035f5f0af626da6b22bea7a0ff9f942a6fd4f039fe51", "value": "0x126a5919e999f9195ae166f349429f050380f691fc4ea5b2f4d8585d050bf12"}]}, "nonces": {"0x2fd67a7bcca0d984408143255c41563b14e6c8a0846b5c9e092e7d56cf1a862": "0x3", "0x52125c1e043126c637d1436d9551ef6c4f6e3e36945676bbd716a56e3a41b7a": "0xf", "0x733dead6027a46717d7e79be28bf059bb8f5b02db2854c742ff652392d94506": "0x6"}, "deployed_contracts": [{"address": "0x60de99e2ba100ea02799ed692306ff5e209edc3a2be30c5c7e00e789f74771c", "class_hash": "0x4631b6b3fa31e140524b7d21ba784cea223e618bffe60b5bbdca44a8b45be04"}, {"address": "0x390a7973fd96e03d16ff669cee465dec765920c66d6e63ee4901270f4930e97", "class_hash": "0x4e70b19333ae94bd958625f7b61ce9eec631653597e68645e13780061b2136c"}], "old_declared_contracts": [], "declared_classes": [{"class_hash": "0x4e70b19333ae94bd958625f7b61ce9eec631653597e68645e13780061b2136c", "compiled_class_hash": "0x711c0c3e56863e29d3158804aac47f424241eda64db33e2cc2999d60ee5105"}], "replaced_classes": []}}
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repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_status/3_failure.txt
{"tx_status": "NOT_RECEIVED", "finality_status": "NOT_RECEIVED", "execution_status": null}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_status/2_not_received.txt
{"tx_status": "NOT_RECEIVED", "finality_status": "NOT_RECEIVED", "execution_status": null}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_status/1_accepted.txt
{"tx_status": "ACCEPTED_ON_L1", "finality_status": "ACCEPTED_ON_L1", "execution_status": "SUCCEEDED", "block_hash": "0x42553deb16a14de4153f28312971f825e83d924e0f2883c1178de86a64a398f"}
0
repos/starknet-zig/src/core/test-data/raw_gateway_responses
repos/starknet-zig/src/core/test-data/raw_gateway_responses/get_transaction_status/4_reverted.txt
{"tx_status": "NOT_RECEIVED", "finality_status": "NOT_RECEIVED", "execution_status": null}
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo0/generate_artifacts.sh
#!/bin/sh # Deterministically generate contract artifacts docker run --rm \ -v "$(pwd)/artifacts:/artifacts" \ -v "$(pwd)/contracts:/contracts:ro" \ -v "$(pwd)/docker_entry.sh:/entry.sh:ro" \ -v "$(pwd)/scripts/generate_hashes.py:/generate_hashes.py:ro" \ --env "USER_ID=$(id -u)" \ --env "GROUP_ID=$(id -g)" \ --entrypoint "/entry.sh" \ starknet/cairo-lang:0.12.1
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo0/docker_entry.sh
#!/bin/sh set -x set -e compile () { starknet-compile-deprecated $1 --output "$2.txt" $3 python3.9 /generate_hashes.py "$2.txt" > "$2.hashes.json" chown $USER_ID:$GROUP_ID "$2.txt" chown $USER_ID:$GROUP_ID "$2.hashes.json" } # Ugly hack to make contract artifacts compact sed -i "s/indent=4/separators=(',', ':')/g" /usr/local/lib/python3.9/site-packages/starkware/cairo/lang/compiler/cairo_compile.py # Ugly hack to send the internal hinted class hash to stdout sed -i "s/return structs\\.DeprecatedCompiledClass/print(f\\\" \\\\\\\"hinted_class_hash\\\\\\\": \\\\\\\"{hex(compute_deprecated_hinted_class_hash(contract_class=contract_class))}\\\\\\\",\")\\n return structs\\.DeprecatedCompiledClass/g" /usr/local/lib/python3.9/site-packages/starkware/starknet/core/os/contract_class/deprecated_class_hash.py # ./artifacts/event_example.txt compile "/contracts/EventExample.cairo" "/artifacts/event_example" # ./artifacts/deployable.txt compile "/contracts/Deployable.cairo" "/artifacts/deployable" # ./artifacts/emoji.txt compile "/contracts/Emoji.cairo" "/artifacts/emoji" # ./artifacts/oz_account.txt cd /contracts/openzeppelin/src compile "/contracts/openzeppelin/src/openzeppelin/account/presets/Account.cairo" "/artifacts/oz_account" --account_contract
0
repos/starknet-zig/src/core/test-data/contracts/cairo0
repos/starknet-zig/src/core/test-data/contracts/cairo0/scripts/generate_hashes.py
import json import sys from starkware.starknet.core.os.contract_class.deprecated_class_hash import ( compute_deprecated_class_hash, ) from starkware.starknet.services.api.contract_class.contract_class import ( DeprecatedCompiledClass, ) print("{") file_path = sys.argv[1] file_content = open(file_path).read() contract_definition = DeprecatedCompiledClass.load(data=json.loads(file_content)) class_hash = compute_deprecated_class_hash(contract_class=contract_definition) print(f' "class_hash": "{hex(class_hash)}"') print("}")
0
repos/starknet-zig/src/core/test-data/contracts/cairo0
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/deployable.txt
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[cast(fp + (-4), felt*)] = __calldata_actual_size;\n","autogen/starknet/arg_processor/6a1a539ae30d2e62b23ed0bb735b8c83307bbbe2a0921f8d1bc90561bfef7d31.cairo":"let __calldata_arg_contract_address_salt = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/6a5e642bec1f7526308a73478077ef051a66625a56a9015e448ad8b892166ca8.cairo":"let __calldata_arg_class_hash = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/6e0504637d5a47a76258d886576965ed87e8e4420080f3d8c89fc4dd4a97244c.cairo":"let __calldata_arg_arg = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/c31620b02d4d706f0542c989b2aadc01b0981d1f6a5933a8fe4937ace3d70d92.cairo":"let __calldata_actual_size = __calldata_ptr - cast([cast(fp + (-3), felt**)], felt*);\n","autogen/starknet/external/__validate_deploy__/3f2c77ab4e9866f148094b3f3c2497496b7ce8700b8370e7f1bc10658a33d640.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt*)];\n","autogen/starknet/external/__validate_deploy__/6f34f106e51e90104887bfff49bfbca1479ee73c25a71ba5300198abb2b5a03e.cairo":"let ret_value = __wrapped_func{}(class_hash=__calldata_arg_class_hash, contract_address_salt=__calldata_arg_contract_address_salt, arg=__calldata_arg_arg,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate_deploy__/93099bea078b47105ec080392b498d5fa602cf51e6076f4584216f16f5b4c273.cairo":"return (syscall_ptr,range_check_ptr,retdata_size,retdata);\n","autogen/starknet/external/__validate_deploy__/fd099223670ab5d428127810c2328d37c65c29951c7abc7cebaa651b40be0a6a.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 1, felt*)];\n","autogen/starknet/external/constructor/3f2c77ab4e9866f148094b3f3c2497496b7ce8700b8370e7f1bc10658a33d640.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt*)];\n","autogen/starknet/external/constructor/719e201a810faa7c21d8b38a891b9c244d6abe8fbeb299073dbb8068feb181db.cairo":"let ret_value = __wrapped_func{}(arg=__calldata_arg_arg,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/constructor/93099bea078b47105ec080392b498d5fa602cf51e6076f4584216f16f5b4c273.cairo":"return (syscall_ptr,range_check_ptr,retdata_size,retdata);\n","autogen/starknet/external/constructor/fd099223670ab5d428127810c2328d37c65c29951c7abc7cebaa651b40be0a6a.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 1, 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[cast(fp + (-4), felt*)] = __calldata_actual_size;\n","autogen/starknet/arg_processor/1e685535e26ead7c7414f5feeeb2e28bc52d93f40700caef24a3ce3ebdd87114.cairo":"let __calldata_arg_signature_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/2cf747b33fafe4b7e0f1cfb0079d61cecba83ef4f51af2d9bea36803bc3f4e9f.cairo":"assert [__return_value_ptr] = ret_value.publicKey;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/5c10028f67364b153272aa9b4cbc0fb78920a40fab821ac7257b0069e0773b49.cairo":"assert [__return_value_ptr] = ret_value.success;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/60a1d0127411d0a1f9a364f5245ae52da8e752ea42edf6ddaf5217c8bdeb8bad.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_calldata_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_calldata = cast(__calldata_ptr, felt*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_calldata_len * 1;\n","autogen/starknet/arg_processor/6a5e642bec1f7526308a73478077ef051a66625a56a9015e448ad8b892166ca8.cairo":"let __calldata_arg_class_hash = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/708f2877a5fc05dca278266df4d8e2025597a78068ffd64385f0ef27ab208871.cairo":"let __calldata_arg_interfaceId = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/7dc21e5febb3934461e79e32b9e043909f57ea5d5d88047175f79be259d9fdd5.cairo":"let __calldata_arg_call_array_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/81481b77e98c23bf09409bf36feae804b99043d0f280564ccb359aeee5de8778.cairo":"assert [__return_value_ptr] = ret_value.isValid;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/8442669a24c29ff6d5063db132f71e228356ef131c5c70fde623342799c14bb2.cairo":"let __calldata_arg_newPublicKey = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/8dcade045a914a94bd6d8ab9c7927a671c36ad8cecedb9f9ea763d7da696f3ef.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_signature_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_signature = cast(__calldata_ptr, felt*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_signature_len * 1;\n","autogen/starknet/arg_processor/b07888c526f97925bd7037f4dcde235d5ffb2d92354828348c217678c2166713.cairo":"let __calldata_arg_hash = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/b3680ca562908399dc897f0a23ed55686e0fba9ab4a18330c139e561aa7b41d8.cairo":"let __calldata_arg_calldata_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/b929869545548e90b3e0972d942496bfe6c38d7ef8c117fc5015fd8f5ae5ede3.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = ret_value.response_len;\n// Store the updated range_check_ptr as a local variable to keep it available after\n// the memcpy.\nlocal range_check_ptr = range_check_ptr + 1;\n// Keep a reference to __return_value_ptr.\nlet __return_value_ptr_copy = __return_value_ptr;\n// Store the updated __return_value_ptr as a local variable to keep it available after\n// the memcpy.\nlocal __return_value_ptr: felt* = __return_value_ptr + ret_value.response_len * 1;\nmemcpy(\n dst=__return_value_ptr_copy,\n src=ret_value.response,\n len=ret_value.response_len * 1);\n","autogen/starknet/arg_processor/ba1d9ba0c2820d7cb2df6f2f4aeae34ef8b189c7149c4a757e99674aa5743013.cairo":"let __calldata_arg_salt = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/c2f1fff90123af1ac991a5f7ea9000b626c118903b694b399e02806d44fb5def.cairo":"assert [__return_value_ptr] = ret_value.response_len;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/c31620b02d4d706f0542c989b2aadc01b0981d1f6a5933a8fe4937ace3d70d92.cairo":"let __calldata_actual_size = __calldata_ptr - cast([cast(fp + (-3), felt**)], felt*);\n","autogen/starknet/arg_processor/e0103dcf78458048e6a2fbe82ac74a16ee35839175ed068cc53ace2ff3c8d843.cairo":"let __calldata_arg_publicKey = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/f5400fee6fdbca52ac7f13a8db039513b257d76f3d002ecd8e6ef16039a7d47d.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_call_array_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_call_array = cast(__calldata_ptr, openzeppelin.account.library.AccountCallArray*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_call_array_len * 4;\n","autogen/starknet/external/__execute__/14203d9b4e0dcdb2fae0cfadacffb50de6a91057e77d7d8f2555840ed4167b4d.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, starkware.cairo.common.cairo_builtins.BitwiseBuiltin**)];\n","autogen/starknet/external/__execute__/2b6f94bd80770e05a0280a2684c74ec7cd726551cc04b16ccd7c3801383a9fd0.cairo":"func __execute__() -> (syscall_ptr: felt*, pedersen_ptr: starkware.cairo.common.cairo_builtins.HashBuiltin*, range_check_ptr: felt, ecdsa_ptr: starkware.cairo.common.cairo_builtins.SignatureBuiltin*, bitwise_ptr: starkware.cairo.common.cairo_builtins.BitwiseBuiltin*, size: felt, retdata: felt*) {\n alloc_locals;\n}\n","autogen/starknet/external/__execute__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__execute__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__execute__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__execute__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__execute__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__execute__/fda2b8aa49b29c30228f00b8e9823863453031a1abe9ca64b44c8468cfa74e87.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, bitwise_ptr=bitwise_ptr, range_check_ptr=range_check_ptr}(call_array_len=__calldata_arg_call_array_len, call_array=__calldata_arg_call_array, calldata_len=__calldata_arg_calldata_len, calldata=__calldata_arg_calldata,);\nlet (range_check_ptr, retdata_size, retdata) = __execute___encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/__validate__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate__/883be30acb6a1330d51bfd10cbcbff897d747444eaacd9630821b0430bd22dc4.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(call_array_len=__calldata_arg_call_array_len, call_array=__calldata_arg_call_array, calldata_len=__calldata_arg_calldata_len, calldata=__calldata_arg_calldata,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__validate_declare__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate_declare__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate_declare__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate_declare__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate_declare__/aeb171d2cc305f87c40b0407565ecdd1a4c396c46cd94f15ca0069e15eab01ed.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(class_hash=__calldata_arg_class_hash,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate_declare__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate_declare__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__validate_deploy__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate_deploy__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate_deploy__/848b6f2a8b49060747719a7d39d6d2fa962bc14d0633409ac194aa41364c7768.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(class_hash=__calldata_arg_class_hash, salt=__calldata_arg_salt, publicKey=__calldata_arg_publicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate_deploy__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate_deploy__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate_deploy__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate_deploy__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/constructor/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/constructor/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/constructor/85878491738bbe4da46aa469fbd2786d48e333915f5f6757828b7b21676593c8.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(publicKey=__calldata_arg_publicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/constructor/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/constructor/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/constructor/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/constructor/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/getPublicKey/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/getPublicKey/43a9d1274d92c1a4aee1843a7b473645245807418483fb76dcc5c8cdf673e692.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}();\nlet (range_check_ptr, retdata_size, retdata) = getPublicKey_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/getPublicKey/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/getPublicKey/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/getPublicKey/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/getPublicKey/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/getPublicKey/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/isValidSignature/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/isValidSignature/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/isValidSignature/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/isValidSignature/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/isValidSignature/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/isValidSignature/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/isValidSignature/dc25ac1b979358bf96523ef3405d0b0d9c7820971d203cff2e2c75e545e055cc.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(hash=__calldata_arg_hash, signature_len=__calldata_arg_signature_len, signature=__calldata_arg_signature,);\nlet (range_check_ptr, retdata_size, retdata) = isValidSignature_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/return/__execute__/372012ab0384bb7289ee5ea400e8c2c07e9056ce02e109689ce1ae824183c43b.cairo":"func __execute___encode_return(ret_value: (response_len: felt, response: felt*), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/getPublicKey/3b684397f6604a19c1ca2d5c5582ea20120aa5ea9a960892c6c6ecfc1b12fe56.cairo":"func getPublicKey_encode_return(ret_value: (publicKey: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/isValidSignature/788c6a8b6b18c5871daf6f002535597a864dc3acd6177843eee7ab2e36e975c5.cairo":"func isValidSignature_encode_return(ret_value: (isValid: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/supportsInterface/40b33230f82887d6ee6ba7936c0fcb15006d084631250a62d0c39394fb5b7629.cairo":"func supportsInterface_encode_return(ret_value: (success: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/setPublicKey/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/setPublicKey/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/setPublicKey/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/setPublicKey/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/setPublicKey/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/setPublicKey/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/setPublicKey/f8713c73f8d22af1d0a9d32b90c808ff9a49c6ffa2faf2712a70740d1450c1be.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(newPublicKey=__calldata_arg_newPublicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/supportsInterface/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/supportsInterface/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/supportsInterface/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/supportsInterface/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/supportsInterface/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/supportsInterface/bca8209c591df9f65b13800fe22999fe396aef7f2e9ee72505ad6a9793c5916d.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(interfaceId=__calldata_arg_interfaceId,);\nlet (range_check_ptr, retdata_size, retdata) = supportsInterface_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/supportsInterface/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/storage_var/Account_public_key/decl.cairo":"namespace Account_public_key {\n from starkware.starknet.common.storage import normalize_address\n from starkware.starknet.common.syscalls import storage_read, storage_write\n from starkware.cairo.common.cairo_builtins import HashBuiltin\n from starkware.cairo.common.hash import hash2\n\n func addr{pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (res: felt) {\n let res = 0;\n call hash2;\n call normalize_address;\n }\n\n func read{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (\n public_key: felt\n ) {\n let storage_addr = 0;\n call addr;\n call storage_read;\n }\n\n func write{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}(value: felt) {\n let storage_addr = 0;\n call addr;\n call storage_write;\n }\n}","autogen/starknet/storage_var/Account_public_key/impl.cairo":"namespace Account_public_key {\n from starkware.starknet.common.storage import normalize_address\n from starkware.starknet.common.syscalls import storage_read, storage_write\n from starkware.cairo.common.cairo_builtins import HashBuiltin\n from starkware.cairo.common.hash import hash2\n\n func addr{pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (res: felt) {\n let res = 550557492744938365112574611882025123252567779123164597803728068558738016655;\n return (res=res);\n }\n\n func read{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (\n public_key: felt\n ) {\n let (storage_addr) = addr();\n let (__storage_var_temp0) = storage_read(address=storage_addr + 0);\n\n tempvar syscall_ptr = syscall_ptr;\n tempvar pedersen_ptr = pedersen_ptr;\n tempvar range_check_ptr = range_check_ptr;\n tempvar __storage_var_temp0: felt = __storage_var_temp0;\n return ([cast(&__storage_var_temp0, felt*)],);\n }\n\n func write{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}(value: felt) {\n let (storage_addr) = addr();\n storage_write(address=storage_addr + 0, value=[cast(&value, felt) + 0]);\n return ();\n 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repos/starknet-zig/src/core/test-data/contracts/cairo0
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/emoji.txt
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0
repos/starknet-zig/src/core/test-data/contracts/cairo0
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/oz_account.hashes.json
{ "hinted_class_hash": "0x1c139c3c572b30282301f28d682ae0a408a696cdb5bb433e5d796ed09b7440c", "class_hash": "0x4fda56652f3dfe9c59904dd0fdc0fa5965b1e560e1641a06e132fdf90a96424" }
0
repos/starknet-zig/src/core/test-data/contracts/cairo0
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/event_example.txt
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repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/pre-0.11.0/event_example.hashes.json
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0
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/pre-0.11.0/oz_account.txt
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[cast(fp + (-4), felt*)] = __calldata_actual_size;\n","autogen/starknet/arg_processor/1e685535e26ead7c7414f5feeeb2e28bc52d93f40700caef24a3ce3ebdd87114.cairo":"let __calldata_arg_signature_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/2cf747b33fafe4b7e0f1cfb0079d61cecba83ef4f51af2d9bea36803bc3f4e9f.cairo":"assert [__return_value_ptr] = ret_value.publicKey;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/5c10028f67364b153272aa9b4cbc0fb78920a40fab821ac7257b0069e0773b49.cairo":"assert [__return_value_ptr] = ret_value.success;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/60a1d0127411d0a1f9a364f5245ae52da8e752ea42edf6ddaf5217c8bdeb8bad.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_calldata_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_calldata = cast(__calldata_ptr, felt*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_calldata_len * 1;\n","autogen/starknet/arg_processor/6a5e642bec1f7526308a73478077ef051a66625a56a9015e448ad8b892166ca8.cairo":"let __calldata_arg_class_hash = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/708f2877a5fc05dca278266df4d8e2025597a78068ffd64385f0ef27ab208871.cairo":"let __calldata_arg_interfaceId = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/7dc21e5febb3934461e79e32b9e043909f57ea5d5d88047175f79be259d9fdd5.cairo":"let __calldata_arg_call_array_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/81481b77e98c23bf09409bf36feae804b99043d0f280564ccb359aeee5de8778.cairo":"assert [__return_value_ptr] = ret_value.isValid;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/8442669a24c29ff6d5063db132f71e228356ef131c5c70fde623342799c14bb2.cairo":"let __calldata_arg_newPublicKey = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/8dcade045a914a94bd6d8ab9c7927a671c36ad8cecedb9f9ea763d7da696f3ef.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_signature_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_signature = cast(__calldata_ptr, felt*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_signature_len * 1;\n","autogen/starknet/arg_processor/b07888c526f97925bd7037f4dcde235d5ffb2d92354828348c217678c2166713.cairo":"let __calldata_arg_hash = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/b3680ca562908399dc897f0a23ed55686e0fba9ab4a18330c139e561aa7b41d8.cairo":"let __calldata_arg_calldata_len = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/b929869545548e90b3e0972d942496bfe6c38d7ef8c117fc5015fd8f5ae5ede3.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = ret_value.response_len;\n// Store the updated range_check_ptr as a local variable to keep it available after\n// the memcpy.\nlocal range_check_ptr = range_check_ptr + 1;\n// Keep a reference to __return_value_ptr.\nlet __return_value_ptr_copy = __return_value_ptr;\n// Store the updated __return_value_ptr as a local variable to keep it available after\n// the memcpy.\nlocal __return_value_ptr: felt* = __return_value_ptr + ret_value.response_len * 1;\nmemcpy(\n dst=__return_value_ptr_copy,\n src=ret_value.response,\n len=ret_value.response_len * 1);\n","autogen/starknet/arg_processor/ba1d9ba0c2820d7cb2df6f2f4aeae34ef8b189c7149c4a757e99674aa5743013.cairo":"let __calldata_arg_salt = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/c2f1fff90123af1ac991a5f7ea9000b626c118903b694b399e02806d44fb5def.cairo":"assert [__return_value_ptr] = ret_value.response_len;\nlet __return_value_ptr = __return_value_ptr + 1;\n","autogen/starknet/arg_processor/c31620b02d4d706f0542c989b2aadc01b0981d1f6a5933a8fe4937ace3d70d92.cairo":"let __calldata_actual_size = __calldata_ptr - cast([cast(fp + (-3), felt**)], felt*);\n","autogen/starknet/arg_processor/e0103dcf78458048e6a2fbe82ac74a16ee35839175ed068cc53ace2ff3c8d843.cairo":"let __calldata_arg_publicKey = [__calldata_ptr];\nlet __calldata_ptr = __calldata_ptr + 1;\n","autogen/starknet/arg_processor/f5400fee6fdbca52ac7f13a8db039513b257d76f3d002ecd8e6ef16039a7d47d.cairo":"// Check that the length is non-negative.\nassert [range_check_ptr] = __calldata_arg_call_array_len;\nlet range_check_ptr = range_check_ptr + 1;\n// Create the reference.\nlet __calldata_arg_call_array = cast(__calldata_ptr, openzeppelin.account.library.AccountCallArray*);\n// Use 'tempvar' instead of 'let' to avoid repeating this computation for the\n// following arguments.\ntempvar __calldata_ptr = __calldata_ptr + __calldata_arg_call_array_len * 4;\n","autogen/starknet/external/__execute__/14203d9b4e0dcdb2fae0cfadacffb50de6a91057e77d7d8f2555840ed4167b4d.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, starkware.cairo.common.cairo_builtins.BitwiseBuiltin**)];\n","autogen/starknet/external/__execute__/2b6f94bd80770e05a0280a2684c74ec7cd726551cc04b16ccd7c3801383a9fd0.cairo":"func __execute__() -> (syscall_ptr: felt*, pedersen_ptr: starkware.cairo.common.cairo_builtins.HashBuiltin*, range_check_ptr: felt, ecdsa_ptr: starkware.cairo.common.cairo_builtins.SignatureBuiltin*, bitwise_ptr: starkware.cairo.common.cairo_builtins.BitwiseBuiltin*, size: felt, retdata: felt*) {\n alloc_locals;\n}\n","autogen/starknet/external/__execute__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__execute__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__execute__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__execute__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__execute__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__execute__/fda2b8aa49b29c30228f00b8e9823863453031a1abe9ca64b44c8468cfa74e87.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, bitwise_ptr=bitwise_ptr, range_check_ptr=range_check_ptr}(call_array_len=__calldata_arg_call_array_len, call_array=__calldata_arg_call_array, calldata_len=__calldata_arg_calldata_len, calldata=__calldata_arg_calldata,);\nlet (range_check_ptr, retdata_size, retdata) = __execute___encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/__validate__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate__/883be30acb6a1330d51bfd10cbcbff897d747444eaacd9630821b0430bd22dc4.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(call_array_len=__calldata_arg_call_array_len, call_array=__calldata_arg_call_array, calldata_len=__calldata_arg_calldata_len, calldata=__calldata_arg_calldata,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__validate_declare__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate_declare__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate_declare__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate_declare__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate_declare__/aeb171d2cc305f87c40b0407565ecdd1a4c396c46cd94f15ca0069e15eab01ed.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(class_hash=__calldata_arg_class_hash,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate_declare__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate_declare__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/__validate_deploy__/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/__validate_deploy__/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/__validate_deploy__/848b6f2a8b49060747719a7d39d6d2fa962bc14d0633409ac194aa41364c7768.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(class_hash=__calldata_arg_class_hash, salt=__calldata_arg_salt, publicKey=__calldata_arg_publicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/__validate_deploy__/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/__validate_deploy__/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/__validate_deploy__/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/__validate_deploy__/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/constructor/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/constructor/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/constructor/85878491738bbe4da46aa469fbd2786d48e333915f5f6757828b7b21676593c8.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(publicKey=__calldata_arg_publicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/constructor/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/constructor/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/constructor/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/constructor/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/getPublicKey/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/getPublicKey/43a9d1274d92c1a4aee1843a7b473645245807418483fb76dcc5c8cdf673e692.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}();\nlet (range_check_ptr, retdata_size, retdata) = getPublicKey_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/getPublicKey/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/getPublicKey/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/getPublicKey/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/getPublicKey/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/getPublicKey/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/isValidSignature/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/isValidSignature/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/isValidSignature/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/isValidSignature/972efe4adb0e1cedbdf0f0747cf1e121111a6180229de74773d49a6e595c4f3d.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, starkware.cairo.common.cairo_builtins.SignatureBuiltin**)];\n","autogen/starknet/external/isValidSignature/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/isValidSignature/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/isValidSignature/dc25ac1b979358bf96523ef3405d0b0d9c7820971d203cff2e2c75e545e055cc.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, ecdsa_ptr=ecdsa_ptr, range_check_ptr=range_check_ptr}(hash=__calldata_arg_hash, signature_len=__calldata_arg_signature_len, signature=__calldata_arg_signature,);\nlet (range_check_ptr, retdata_size, retdata) = isValidSignature_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/return/__execute__/372012ab0384bb7289ee5ea400e8c2c07e9056ce02e109689ce1ae824183c43b.cairo":"func __execute___encode_return(ret_value: (response_len: felt, response: felt*), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/getPublicKey/3b684397f6604a19c1ca2d5c5582ea20120aa5ea9a960892c6c6ecfc1b12fe56.cairo":"func getPublicKey_encode_return(ret_value: (publicKey: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/isValidSignature/788c6a8b6b18c5871daf6f002535597a864dc3acd6177843eee7ab2e36e975c5.cairo":"func isValidSignature_encode_return(ret_value: (isValid: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/return/supportsInterface/40b33230f82887d6ee6ba7936c0fcb15006d084631250a62d0c39394fb5b7629.cairo":"func supportsInterface_encode_return(ret_value: (success: felt), range_check_ptr) -> (\n range_check_ptr: felt, data_len: felt, data: felt*) {\n %{ memory[ap] = segments.add() %}\n alloc_locals;\n local __return_value_ptr_start: felt*;\n let __return_value_ptr = __return_value_ptr_start;\n with range_check_ptr {\n }\n return (\n range_check_ptr=range_check_ptr,\n data_len=__return_value_ptr - __return_value_ptr_start,\n data=__return_value_ptr_start);\n}\n","autogen/starknet/external/setPublicKey/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/setPublicKey/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/setPublicKey/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/setPublicKey/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/setPublicKey/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/setPublicKey/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/external/setPublicKey/f8713c73f8d22af1d0a9d32b90c808ff9a49c6ffa2faf2712a70740d1450c1be.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(newPublicKey=__calldata_arg_newPublicKey,);\n%{ memory[ap] = segments.add() %} // Allocate memory for return value.\ntempvar retdata: felt*;\nlet retdata_size = 0;\n","autogen/starknet/external/supportsInterface/2e2c5536af4c3ea88b562852f6f3740af166f645e0f066972184481010fe04da.cairo":"let bitwise_ptr = [cast([cast(fp + (-5), felt**)] + 4, felt*)];\n","autogen/starknet/external/supportsInterface/741ea357d6336b0bed7bf0472425acd0311d543883b803388880e60a232040c7.cairo":"let range_check_ptr = [cast([cast(fp + (-5), felt**)] + 2, felt*)];\n","autogen/starknet/external/supportsInterface/9684a85e93c782014ca14293edea4eb2502039a5a7b6538ecd39c56faaf12529.cairo":"let pedersen_ptr = [cast([cast(fp + (-5), felt**)] + 1, starkware.cairo.common.cairo_builtins.HashBuiltin**)];\n","autogen/starknet/external/supportsInterface/b2c52ca2d2a8fc8791a983086d8716c5eacd0c3d62934914d2286f84b98ff4cb.cairo":"let syscall_ptr = [cast([cast(fp + (-5), felt**)] + 0, felt**)];\n","autogen/starknet/external/supportsInterface/b363de5c884e054e373732fa94161084d4128000eba968c31dbb40d4ab78ae25.cairo":"return (syscall_ptr,pedersen_ptr,range_check_ptr,ecdsa_ptr,bitwise_ptr,retdata_size,retdata);\n","autogen/starknet/external/supportsInterface/bca8209c591df9f65b13800fe22999fe396aef7f2e9ee72505ad6a9793c5916d.cairo":"let ret_value = __wrapped_func{syscall_ptr=syscall_ptr, pedersen_ptr=pedersen_ptr, range_check_ptr=range_check_ptr}(interfaceId=__calldata_arg_interfaceId,);\nlet (range_check_ptr, retdata_size, retdata) = supportsInterface_encode_return(ret_value, range_check_ptr);\n","autogen/starknet/external/supportsInterface/c6c4d3a7a58c6b37d5fdd51b25e5ab9f3e75174b411ab503db3ce03636ed6e2a.cairo":"let ecdsa_ptr = [cast([cast(fp + (-5), felt**)] + 3, felt*)];\n","autogen/starknet/storage_var/Account_public_key/decl.cairo":"namespace Account_public_key {\n from starkware.starknet.common.storage import normalize_address\n from starkware.starknet.common.syscalls import storage_read, storage_write\n from starkware.cairo.common.cairo_builtins import HashBuiltin\n from starkware.cairo.common.hash import hash2\n\n func addr{pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (res: felt) {\n let res = 0;\n call hash2;\n call normalize_address;\n }\n\n func read{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (\n public_key: felt\n ) {\n let storage_addr = 0;\n call addr;\n call storage_read;\n }\n\n func write{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}(value: felt) {\n let storage_addr = 0;\n call addr;\n call storage_write;\n }\n}","autogen/starknet/storage_var/Account_public_key/impl.cairo":"namespace Account_public_key {\n from starkware.starknet.common.storage import normalize_address\n from starkware.starknet.common.syscalls import storage_read, storage_write\n from starkware.cairo.common.cairo_builtins import HashBuiltin\n from starkware.cairo.common.hash import hash2\n\n func addr{pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (res: felt) {\n let res = 550557492744938365112574611882025123252567779123164597803728068558738016655;\n return (res=res);\n }\n\n func read{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}() -> (\n public_key: felt\n ) {\n let (storage_addr) = addr();\n let (__storage_var_temp0) = storage_read(address=storage_addr + 0);\n\n tempvar syscall_ptr = syscall_ptr;\n tempvar pedersen_ptr = pedersen_ptr;\n tempvar range_check_ptr = range_check_ptr;\n tempvar __storage_var_temp0: felt = __storage_var_temp0;\n return ([cast(&__storage_var_temp0, felt*)],);\n }\n\n func write{syscall_ptr: felt*, pedersen_ptr: HashBuiltin*, range_check_ptr}(value: felt) {\n let (storage_addr) = addr();\n storage_write(address=storage_addr + 0, value=[cast(&value, felt) + 0]);\n return ();\n 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repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/pre-0.11.0/oz_account.hashes.json
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repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts
repos/starknet-zig/src/core/test-data/contracts/cairo0/artifacts/pre-0.11.0/event_example.txt
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0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo1/docker_entry_hashes.sh
#!/bin/sh set -x set -e hash () { python3.9 /generate_hashes.py "$1" > "$1.hashes.json" chown $USER_ID:$GROUP_ID "$1.hashes.json" } hash "/artifacts/abi_types" hash "/artifacts/erc20"
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo1/docker_entry_compile.sh
#!/bin/sh set -x set -e compile () { starknet-compile $1 "${2}_sierra.txt" starknet-sierra-compile "${2}_sierra.txt" "${2}_compiled.txt" chown $USER_ID:$GROUP_ID "${2}_sierra.txt" chown $USER_ID:$GROUP_ID "${2}_compiled.txt" } compile "/contracts/abi_types.cairo" "/artifacts/abi_types" compile "/contracts/erc20.cairo" "/artifacts/erc20"
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo1/generate_artifacts.sh
#!/bin/sh set -e # Deterministically generate contract artifacts docker run --rm \ -v "$(pwd)/artifacts:/artifacts" \ -v "$(pwd)/contracts:/contracts:ro" \ -v "$(pwd)/docker_entry_compile.sh:/entry.sh:ro" \ --env "USER_ID=$(id -u)" \ --env "GROUP_ID=$(id -g)" \ --entrypoint "/entry.sh" \ starknet/cairo:1.1.0 docker run --rm \ -v "$(pwd)/artifacts:/artifacts" \ -v "$(pwd)/docker_entry_hashes.sh:/entry.sh:ro" \ -v "$(pwd)/scripts/generate_hashes.py:/generate_hashes.py:ro" \ --env "USER_ID=$(id -u)" \ --env "GROUP_ID=$(id -g)" \ --entrypoint "/entry.sh" \ starknet/cairo-lang:0.12.1
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/scripts/generate_hashes.py
import json import sys from starkware.starknet.core.os.contract_class.class_hash import ( compute_class_hash, ) from starkware.starknet.core.os.contract_class.compiled_class_hash import ( compute_compiled_class_hash, ) from starkware.starknet.services.api.contract_class.contract_class import ( CompiledClass, ContractClass, ) from starkware.starknet.services.api.contract_class.contract_class_utils import ( load_sierra_from_dict, ) base_file_path = sys.argv[1] sierra_class_json = json.loads(open(f"{base_file_path}_sierra.txt").read()) compiled_class_json = json.loads(open(f"{base_file_path}_compiled.txt").read()) # Tricks cairo-lang into thinking we have "pythonic_hints". It's not used for hash calulcation # anyways. compiled_class_json["pythonic_hints"] = [] sierra_class_hash = compute_class_hash(load_sierra_from_dict(sierra=sierra_class_json)) compiled_class_hash = compute_compiled_class_hash( CompiledClass.load(data=compiled_class_json) ) print("{") print(f' "sierra_class_hash": "{hex(sierra_class_hash)}",') print(f' "compiled_class_hash": "{hex(compiled_class_hash)}"') print("}")
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/erc20.hashes.json
{ "sierra_class_hash": "0x6d8ede036bb4720e6f348643221d8672bf4f0895622c32c11e57460b3b7dffc", "compiled_class_hash": "0x18f95714044fd5408d3bf812bcd249ddec098ab3cd201b7916170cfbfa59e05" }
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/abi_types.hashes.json
{ "sierra_class_hash": "0x1f2ed0d6d6bbe273ba53092c303851bd11ff61a0c6664ea3e98717dd086d6b3", "compiled_class_hash": "0x5047109bf7eb550c5e6b0c37714f6e0db4bb8b5b227869e0797ecfc39240aa7" }
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/erc20_compiled.txt
{ "prime": "0x800000000000011000000000000000000000000000000000000000000000001", "compiler_version": "1.1.0", "bytecode": [ "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffffe548", "0x400280007ff97fff", "0x10780017fff7fff", "0x69", "0x4825800180007ffa", "0x1ab8", "0x400280007ff97fff", "0x48297ffc80007ffd", "0x482680017ff98000", "0x1", "0x4824800180007ffe", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x6", "0x480680017fff8000", "0x0", "0x10780017fff7fff", "0x4", "0x480680017fff8000", "0x1", "0x480680017fff8000", "0x1", "0x48307ffe80007fff", "0x20680017fff7fff", "0x41", "0x1104800180018000", "0x1272", "0x482480017fff8000", "0x1271", "0x480080007fff8000", "0xa0680017fff8000", "0x9", "0x4824800180007ff4", "0x0", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007ff47fff", "0x10780017fff7fff", "0x24", "0x4824800180007ff4", "0x0", "0x400080007ff57fff", "0x48127fff7fff8000", "0x480a7ffb7fff8000", "0x1104800180018000", "0x786", "0x482480017fde8000", "0x1", "0x20680017fff7ffc", "0x11", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffe7fff8000", "0x48127ffd7fff8000", "0x1104800180018000", "0x7ac", "0x48127ff77fff8000", "0x48127ff17fff8000", "0x48127ff17fff8000", "0x480680017fff8000", "0x0", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x48127fff7fff8000", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482480017ff28000", "0x1", "0x48127fef7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x480a7ffb7fff8000", "0x1104800180018000", "0x78f", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x48127ff57fff8000", "0x48127ff27fff8000", "0x48127ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482680017ff98000", "0x1", "0x480a7ffa7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffffe548", "0x400280007ff97fff", "0x10780017fff7fff", "0x69", "0x4825800180007ffa", "0x1ab8", "0x400280007ff97fff", "0x48297ffc80007ffd", "0x482680017ff98000", "0x1", "0x4824800180007ffe", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x6", "0x480680017fff8000", "0x0", "0x10780017fff7fff", "0x4", "0x480680017fff8000", "0x1", "0x480680017fff8000", "0x1", "0x48307ffe80007fff", "0x20680017fff7fff", "0x41", "0x1104800180018000", "0x11f5", "0x482480017fff8000", "0x11f4", "0x480080007fff8000", "0xa0680017fff8000", "0x9", "0x4824800180007ff4", "0x0", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007ff47fff", "0x10780017fff7fff", "0x24", "0x4824800180007ff4", "0x0", "0x400080007ff57fff", "0x48127fff7fff8000", "0x480a7ffb7fff8000", "0x1104800180018000", "0x741", "0x482480017fde8000", "0x1", "0x20680017fff7ffc", "0x11", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffe7fff8000", "0x48127ffd7fff8000", "0x1104800180018000", "0x72f", "0x48127ff77fff8000", "0x48127ff17fff8000", "0x48127ff17fff8000", "0x480680017fff8000", "0x0", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x48127fff7fff8000", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482480017ff28000", "0x1", "0x48127fef7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", 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"0x48127ffd7fff8000", "0x48127ffd7fff8000", "0x48127ffc7fff8000", "0x1104800180018000", "0x6cd", "0x48127fd77fff8000", "0x48127fd77fff8000", "0x48127fd77fff8000", "0x480680017fff8000", "0x0", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482480017ff28000", "0x1", "0x48127fef7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x480a7ffb7fff8000", "0x1104800180018000", "0x617", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x48127ff57fff8000", "0x48127ff27fff8000", "0x48127ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482680017ff98000", "0x1", "0x480a7ffa7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffff736a", "0x400280007ff97fff", "0x10780017fff7fff", "0x86", "0x4825800180007ffa", "0x8c96", "0x400280007ff97fff", "0x482680017ff98000", "0x1", "0x480a7ffc7fff8000", "0x480a7ffd7fff8000", "0x1104800180018000", "0x689", "0x20680017fff7ffe", "0x6c", "0x48307ffc80007ffd", "0x4824800180007fff", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x6", "0x480680017fff8000", "0x0", "0x10780017fff7fff", "0x4", "0x480680017fff8000", "0x1", "0x480680017fff8000", "0x1", "0x48307ffe80007fff", "0x20680017fff7fff", "0x48", "0x1104800180018000", "0x1077", "0x482480017fff8000", "0x1076", "0x480080007fff8000", "0x480080007fff8000", "0x482480017fff8000", "0x0", "0xa0680017fff8000", "0x8", "0x48307ffe80007fd3", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007fed7fff", "0x10780017fff7fff", "0x28", "0x48307ffe80007fd3", "0x400080007fee7fff", "0x482480017fee8000", "0x1", "0x48127ffe7fff8000", "0x480a7ff87fff8000", "0x480a7ffb7fff8000", "0x48127fee7fff8000", "0x1104800180018000", "0x694", "0x20680017fff7ffd", "0x13", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffd7fff8000", "0x48127ffd7fff8000", "0x48127ffc7fff8000", "0x1104800180018000", "0x646", "0x48127fd87fff8000", "0x48127fd57fff8000", "0x48127fd57fff8000", "0x48127fd67fff8000", "0x480680017fff8000", "0x0", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x48127ffb7fff8000", "0x48127ff87fff8000", "0x48127ff87fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x482480017fea8000", "0x1", "0x48127fcd7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x480a7ffb7fff8000", "0x1104800180018000", "0x58d", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x48127fef7fff8000", "0x48127fd27fff8000", "0x48127ffa7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f2073686f727420666f7220617267756d656e7473", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x48127ff87fff8000", "0x48127fdb7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x482680017ff98000", "0x1", "0x480a7ffa7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffff566e", "0x400280007ff97fff", "0x10780017fff7fff", "0x9f", "0x4825800180007ffa", "0xa992", "0x400280007ff97fff", "0x482680017ff98000", "0x1", "0x480a7ffc7fff8000", "0x480a7ffd7fff8000", "0x1104800180018000", "0x5ee", "0x20680017fff7ffe", "0x85", "0x48127ffb7fff8000", "0x48127ffb7fff8000", "0x48127ffb7fff8000", "0x1104800180018000", "0x5e7", "0x20680017fff7ffe", "0x6f", "0x48307ffc80007ffd", "0x4824800180007fff", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x6", "0x480680017fff8000", "0x0", "0x10780017fff7fff", "0x4", "0x480680017fff8000", "0x1", "0x480680017fff8000", "0x1", "0x48307ffe80007fff", "0x20680017fff7fff", "0x4b", 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0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/abi_types_sierra.txt
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"0x221065b061706c30217065b06021502025b061506cd0215065b06301807cc", "0x41065b063b06ce021a065b063406c7023b065b062106c20234065b060c0634", "0x2414206020c184206020c0209070602414206020c184206020c47411a0706", "0x47180209180207d1021142074206d00602110907092107cf210602a0090706", "0x2110907094907d4070602490207171e0209d3060248180209180207d20602", "0x9180207d8024d18071806d70602110907091707d60602110907090707d506", "0x2110907091507db0602110907091107da0602170207070207d906024f1802", "0xdd06024f0207070207dc06" ], "sierra_program_debug_info": { "type_names": [], "libfunc_names": [], "user_func_names": [] }, "contract_class_version": "0.1.0", "entry_points_by_type": { "EXTERNAL": [ { "selector": "0xb417e2a96017dfa99a52d94474fd9aacef98f2e3eea3ab43f8637f8ca74bb4", "function_idx": 1 }, { "selector": "0x324977dffe970a83394d59b0a08099eee0d2065143979eb36bb6c909c9e510c", "function_idx": 0 } ], "L1_HANDLER": [], "CONSTRUCTOR": [] }, "abi": [ { "type": "enum", "name": "abi_types::abi_types::AbiTypes::ExampleEnum", "variants": [ { "name": "variant_a", "type": "core::felt252" }, { "name": "variant_b", "type": "core::integer::u256" } ] }, { "type": "function", "name": "example_view_function", "inputs": [], "outputs": [ { "type": "abi_types::abi_types::AbiTypes::ExampleEnum" } ], "state_mutability": "view" }, { "type": "struct", "name": "abi_types::abi_types::AbiTypes::ExampleStruct", "members": [ { "name": "field_a", "type": "core::felt252" }, { "name": "field_b", "type": "core::felt252" }, { "name": "field_c", "type": "abi_types::abi_types::AbiTypes::ExampleEnum" }, { "name": "field_d", "type": "()" } ] }, { "type": "function", "name": "example_external_function", "inputs": [ { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [ { "type": "abi_types::abi_types::AbiTypes::ExampleStruct" } ], "state_mutability": "external" }, { "type": "event", "name": "ExampleEvent", "inputs": [ { "name": "value_a", "type": "core::integer::u256" }, { "name": "value_b", "type": "abi_types::abi_types::AbiTypes::ExampleStruct" } ] } ] }
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/abi_types_compiled.txt
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"0x324977dffe970a83394d59b0a08099eee0d2065143979eb36bb6c909c9e510c", "offset": 0, "builtins": [ "range_check" ] } ], "L1_HANDLER": [], "CONSTRUCTOR": [] } }
0
repos/starknet-zig/src/core/test-data/contracts/cairo1
repos/starknet-zig/src/core/test-data/contracts/cairo1/artifacts/erc20_sierra.txt
{ "sierra_program": [ "0x1", "0x1", "0x0", "0x1", "0x1", "0x0", "0x2c1", "0x13f", "0x3f", "0x52616e6765436865636b", "0x0", "0x4761734275696c74696e", "0x66656c74323532", "0x4172726179", "0x1", "0x2", "0x536e617073686f74", "0x3", "0x537472756374", "0x1baeba72e79e9db2587cf44fedb2f3700b2075a5e8e39a562584862c4b71f62", "0x4", "0x753332", "0x2ee1e2b1b89f8c495f200e4956278a4d47395fe262f27b52e5865c9524c08c3", "0x456e756d", "0x3288d594b9a45d15bb2fcb7903f06cdb06b27f0ba88186ec4cfaa98307cb972", "0x7", "0x4275696c74696e436f737473", "0x53797374656d", "0x2f528e3c691e195fca674982b69c0dc4284f206c3ea4d680220e99b59315a92", "0xb", "0x5", "0x19b3b4955bdcfa379bfc5a4949111c4efdd79128f8676f4d0895419b22e2ad7", "0xd", "0x7538", "0xf", "0xcd9deb349f6fb32e657baec1ad634c533f483d4a7d58d9b614521369f9345a", "0x10", "0x75313238", "0x25e2ca4b84968c2d8b83ef476ca8549410346b00836ce79beaf538155990bb2", "0x12", "0x13", "0x3e7e8f96dca87f227717f10d0bef2c534e695d83e025ee7952c3addec8a0295", "0x14", 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"0x16ae8021e00627c06ae407018021dc0201c2008002026b801c060087700807", "0x9af00600811024070242501ebb0300901c060089f19c06024201ec4919c06", "0x6008a9008070802000809af8022780629c06af4070180201c7501c8a01c75", "0x2c001c06008a9008070802000809afc07" ], "sierra_program_debug_info": { "type_names": [], "libfunc_names": [], "user_func_names": [] }, "contract_class_version": "0.1.0", "entry_points_by_type": { "EXTERNAL": [ { "selector": "0x83afd3f4caedc6eebf44246fe54e38c95e3179a5ec9ea81740eca5b482d12e", "function_idx": 6 }, { "selector": "0x16d9d5d83f8eecc5d7450519aad7e6e649be1a6c9d6df85bd0b177cc59a926a", "function_idx": 2 }, { "selector": "0x1d13ab0a76d7407b1d5faccd4b3d8a9efe42f3d3c21766431d4fafb30f45bd4", "function_idx": 9 }, { "selector": "0x1e888a1026b19c8c0b57c72d63ed1737106aa10034105b980ba117bd0c29fe1", "function_idx": 5 }, { "selector": "0x219209e083275171774dab1df80982e9df2096516f06319c5c6d71ae0a8480c", "function_idx": 8 }, { "selector": "0x2819e8b2b82ee4c56798709651ab9e8537f644c0823e42ba017efce4f2077e4", "function_idx": 3 }, { "selector": "0x31341177714d81ad9ccd0c903211bc056a60e8af988d0fd918cc43874549653", "function_idx": 0 }, { "selector": "0x351ccc9e7b13b17e701a7d4f5f85b525bac37b7648419fe194e6c15bc73da47", "function_idx": 1 }, { "selector": "0x35a73cd311a05d46deda634c5ee045db92f811b4e74bca4437fcb5302b7af33", "function_idx": 4 }, { "selector": "0x3704ffe8fba161be0e994951751a5033b1462b918ff785c0a636be718dfdb68", "function_idx": 7 }, { "selector": "0x3b076186c19fe96221e4dfacd40c519f612eae02e0555e4e115a2a6cf2f1c1f", "function_idx": 10 } ], "L1_HANDLER": [], "CONSTRUCTOR": [ { "selector": "0x28ffe4ff0f226a9107253e17a904099aa4f63a02a5621de0576e5aa71bc5194", "function_idx": 11 } ] }, "abi": [ { "type": "function", "name": "constructor", "inputs": [ { "name": "name_", "type": "core::felt252" }, { "name": "symbol_", "type": "core::felt252" }, { "name": "decimals_", "type": "core::integer::u8" }, { "name": "initial_supply", "type": "core::integer::u256" }, { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "get_name", "inputs": [], "outputs": [ { "type": "core::felt252" } ], "state_mutability": "view" }, { "type": "function", "name": "get_symbol", "inputs": [], "outputs": [ { "type": "core::felt252" } ], "state_mutability": "view" }, { "type": "function", "name": "get_decimals", "inputs": [], "outputs": [ { "type": "core::integer::u8" } ], "state_mutability": "view" }, { "type": "function", "name": "get_total_supply", "inputs": [], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "balance_of", "inputs": [ { "name": "account", "type": "core::starknet::contract_address::ContractAddress" } ], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "allowance", "inputs": [ { "name": "owner", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" } ], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "transfer", "inputs": [ { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "transfer_from", "inputs": [ { "name": "sender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "approve", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "increase_allowance", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "added_value", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "decrease_allowance", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "subtracted_value", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "event", "name": "Transfer", "inputs": [ { "name": "from", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "to", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "value", "type": "core::integer::u256" } ] }, { "type": "event", "name": "Approval", "inputs": [ { "name": "owner", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "value", "type": "core::integer::u256" } ] } ] }
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo2/docker_entry_hashes.sh
#!/bin/sh set -x set -e hash () { python3.9 /generate_hashes.py "$1" > "$1.hashes.json" chown $USER_ID:$GROUP_ID "$1.hashes.json" } hash "/artifacts/abi_types" hash "/artifacts/erc20"
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo2/docker_entry_compile.sh
#!/bin/sh set -x set -e compile () { starknet-compile --single-file $1 "${2}_sierra.txt" starknet-sierra-compile "${2}_sierra.txt" "${2}_compiled.txt" chown $USER_ID:$GROUP_ID "${2}_sierra.txt" chown $USER_ID:$GROUP_ID "${2}_compiled.txt" } compile "/contracts/abi_types.cairo" "/artifacts/abi_types" compile "/contracts/erc20.cairo" "/artifacts/erc20"
0
repos/starknet-zig/src/core/test-data/contracts
repos/starknet-zig/src/core/test-data/contracts/cairo2/generate_artifacts.sh
#!/bin/sh set -e # Deterministically generate contract artifacts docker run --rm \ -v "$(pwd)/artifacts:/artifacts" \ -v "$(pwd)/contracts:/contracts:ro" \ -v "$(pwd)/docker_entry_compile.sh:/entry.sh:ro" \ --env "USER_ID=$(id -u)" \ --env "GROUP_ID=$(id -g)" \ --entrypoint "/entry.sh" \ starknet/cairo:2.3.0 docker run --rm \ -v "$(pwd)/artifacts:/artifacts" \ -v "$(pwd)/docker_entry_hashes.sh:/entry.sh:ro" \ -v "$(pwd)/scripts/generate_hashes.py:/generate_hashes.py:ro" \ --env "USER_ID=$(id -u)" \ --env "GROUP_ID=$(id -g)" \ --entrypoint "/entry.sh" \ starknet/cairo-lang:0.12.1
0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/scripts/generate_hashes.py
import json import sys from starkware.starknet.core.os.contract_class.class_hash import ( compute_class_hash, ) from starkware.starknet.core.os.contract_class.compiled_class_hash import ( compute_compiled_class_hash, ) from starkware.starknet.services.api.contract_class.contract_class import ( CompiledClass, ContractClass, ) from starkware.starknet.services.api.contract_class.contract_class_utils import ( load_sierra_from_dict, ) base_file_path = sys.argv[1] sierra_class_json = json.loads(open(f"{base_file_path}_sierra.txt").read()) compiled_class_json = json.loads(open(f"{base_file_path}_compiled.txt").read()) # Tricks cairo-lang into thinking we have "pythonic_hints". It's not used for hash calulcation # anyways. compiled_class_json["pythonic_hints"] = [] sierra_class_hash = compute_class_hash(load_sierra_from_dict(sierra=sierra_class_json)) compiled_class_hash = compute_compiled_class_hash( CompiledClass.load(data=compiled_class_json) ) print("{") print(f' "sierra_class_hash": "{hex(sierra_class_hash)}",') print(f' "compiled_class_hash": "{hex(compiled_class_hash)}"') print("}")
0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/erc20.hashes.json
{ "sierra_class_hash": "0x442b7bf0e8517b040e8a63af4e749958611317510f908bc14366f4bbaa4f919", "compiled_class_hash": "0x4a0197fa1cd6cde6c1c2aa30319c83ac73dc9cec5f297ea89773b823d3a4e69" }
0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/abi_types.hashes.json
{ "sierra_class_hash": "0x16197dd41cfcf33993ffce9ef107cd50f707315eea88394f939fca238fb0f52", "compiled_class_hash": "0x24c23011777822949ba7da73033d587cf74e1727f45e585b358d9425dc8b933" }
0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/erc20_compiled.txt
{ "prime": "0x800000000000011000000000000000000000000000000000000000000000001", "compiler_version": "2.3.0", "bytecode": [ "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffffe2f0", "0x400280007ff97fff", "0x10780017fff7fff", "0x5b", "0x4825800180007ffa", "0x1d10", "0x400280007ff97fff", "0x48297ffc80007ffd", "0x482680017ff98000", "0x1", "0x4824800180007ffe", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x10", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x48127ffc7fff8000", "0x48127ff97fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x1104800180018000", "0x129d", "0x482480017fff8000", "0x129c", "0x480080007fff8000", "0xa0680017fff8000", "0x9", "0x4824800180007ff7", "0x0", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007ff77fff", "0x10780017fff7fff", "0x24", "0x4824800180007ff7", "0x0", "0x400080007ff87fff", "0x48127fff7fff8000", "0x480a7ffb7fff8000", "0x1104800180018000", "0x6f2", "0x482480017fd88000", "0x1", "0x20680017fff7ffc", "0x11", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffe7fff8000", "0x48127ffd7fff8000", "0x1104800180018000", "0x6fc", "0x48127ff77fff8000", "0x48127ff17fff8000", "0x48127ff17fff8000", "0x480680017fff8000", "0x0", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x48127fff7fff8000", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482480017ff58000", "0x1", "0x48127ff27fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482680017ff98000", "0x1", "0x480a7ffa7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffffe2f0", "0x400280007ff97fff", "0x10780017fff7fff", "0x5b", "0x4825800180007ffa", "0x1d10", "0x400280007ff97fff", "0x48297ffc80007ffd", "0x482680017ff98000", "0x1", "0x4824800180007ffe", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x10", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x48127ffc7fff8000", "0x48127ff97fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", "0x208b7fff7fff7ffe", "0x1104800180018000", "0x122e", "0x482480017fff8000", "0x122d", "0x480080007fff8000", "0xa0680017fff8000", "0x9", "0x4824800180007ff7", "0x0", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007ff77fff", "0x10780017fff7fff", "0x24", "0x4824800180007ff7", "0x0", "0x400080007ff87fff", "0x48127fff7fff8000", "0x480a7ffb7fff8000", "0x1104800180018000", "0x69d", "0x482480017fd88000", "0x1", "0x20680017fff7ffc", "0x11", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffe7fff8000", "0x48127ffd7fff8000", "0x1104800180018000", "0x68d", "0x48127ff77fff8000", "0x48127ff17fff8000", "0x48127ff17fff8000", "0x480680017fff8000", "0x0", "0x48127ffa7fff8000", "0x48127ffa7fff8000", "0x208b7fff7fff7ffe", "0x48127fff7fff8000", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x482480017ff58000", "0x1", "0x48127ff27fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ffa7fff8000", "0x482480017ff98000", "0x1", 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"0x48127ff67fff8000", "0x48127fda7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x1104800180018000", "0x10dc", "0x482480017fff8000", "0x10db", "0x480080007fff8000", "0x480080007fff8000", "0x482480017fff8000", "0x0", "0xa0680017fff8000", "0x8", "0x48307ffe80007fd7", "0x482480017fff8000", "0x100000000000000000000000000000000", "0x400080007ff07fff", "0x10780017fff7fff", "0x28", "0x48307ffe80007fd7", "0x400080007ff17fff", "0x482480017ff18000", "0x1", "0x48127ffe7fff8000", "0x480a7ff87fff8000", "0x480a7ffb7fff8000", "0x48127ff17fff8000", "0x1104800180018000", "0x5c9", "0x20680017fff7ffd", "0x13", "0x40780017fff7fff", "0x1", "0x48127ffd7fff8000", "0x48127ffd7fff8000", "0x48127ffd7fff8000", "0x48127ffc7fff8000", "0x1104800180018000", "0x580", "0x48127ff27fff8000", "0x48127fef7fff8000", "0x48127fef7fff8000", "0x48127ff07fff8000", "0x480680017fff8000", "0x0", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x48127ffb7fff8000", "0x48127ff87fff8000", "0x48127ff87fff8000", "0x48127ff97fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x48127ff97fff8000", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x482480017fed8000", "0x1", "0x48127fd17fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4661696c656420746f20646573657269616c697a6520706172616d202331", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x48127ff87fff8000", "0x48127fdc7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x4f7574206f6620676173", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x482680017ff98000", "0x1", "0x480a7ffa7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", "0x208b7fff7fff7ffe", "0xa0680017fff8000", "0x7", "0x482680017ffa8000", "0xffffffffffffffffffffffffffff68de", "0x400280007ff97fff", "0x10780017fff7fff", "0x91", "0x4825800180007ffa", "0x9722", "0x400280007ff97fff", "0x482680017ff98000", "0x1", "0x480a7ffc7fff8000", "0x480a7ffd7fff8000", "0x1104800180018000", "0x535", "0x20680017fff7ffe", "0x77", "0x48127ffb7fff8000", "0x48127ffb7fff8000", "0x48127ffb7fff8000", "0x1104800180018000", "0x52e", "0x20680017fff7ffe", "0x61", "0x48307ffc80007ffd", "0x4824800180007fff", "0x0", "0x20680017fff7fff", "0x4", "0x10780017fff7fff", "0x11", "0x40780017fff7fff", "0x1", "0x480680017fff8000", "0x496e70757420746f6f206c6f6e6720666f7220617267756d656e7473", "0x400080007ffe7fff", "0x480a7ff87fff8000", "0x48127ff67fff8000", "0x48127fbb7fff8000", "0x480a7ffb7fff8000", "0x480680017fff8000", "0x1", "0x48127ff97fff8000", "0x482480017ff88000", "0x1", 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repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/abi_types_sierra.txt
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{ "name": "variant_a", "type": "core::felt252" }, { "name": "variant_b", "type": "core::integer::u256" } ] }, { "type": "struct", "name": "abi_types::abi_types::AbiTypes::ExampleStruct", "members": [ { "name": "field_a", "type": "core::felt252" }, { "name": "field_b", "type": "core::felt252" }, { "name": "field_c", "type": "abi_types::abi_types::AbiTypes::ExampleEnum" }, { "name": "field_d", "type": "()" } ] }, { "type": "function", "name": "example_external_function", "inputs": [ { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [ { "type": "abi_types::abi_types::AbiTypes::ExampleStruct" } ], "state_mutability": "external" }, { "type": "l1_handler", "name": "example_l1_handler", "inputs": [ { "name": "from_address", "type": "core::felt252" }, { "name": "arg1", "type": "core::felt252" } ], "outputs": [], "state_mutability": "external" }, { "type": "event", "name": 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0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/abi_types_compiled.txt
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0
repos/starknet-zig/src/core/test-data/contracts/cairo2
repos/starknet-zig/src/core/test-data/contracts/cairo2/artifacts/erc20_sierra.txt
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"0x2819e8b2b82ee4c56798709651ab9e8537f644c0823e42ba017efce4f2077e4", "function_idx": 3 }, { "selector": "0x31341177714d81ad9ccd0c903211bc056a60e8af988d0fd918cc43874549653", "function_idx": 0 }, { "selector": "0x351ccc9e7b13b17e701a7d4f5f85b525bac37b7648419fe194e6c15bc73da47", "function_idx": 1 }, { "selector": "0x35a73cd311a05d46deda634c5ee045db92f811b4e74bca4437fcb5302b7af33", "function_idx": 4 }, { "selector": "0x3704ffe8fba161be0e994951751a5033b1462b918ff785c0a636be718dfdb68", "function_idx": 7 }, { "selector": "0x3b076186c19fe96221e4dfacd40c519f612eae02e0555e4e115a2a6cf2f1c1f", "function_idx": 10 } ], "L1_HANDLER": [], "CONSTRUCTOR": [ { "selector": "0x28ffe4ff0f226a9107253e17a904099aa4f63a02a5621de0576e5aa71bc5194", "function_idx": 11 } ] }, "abi": [ { "type": "impl", "name": "IERC20Impl", "interface_name": "erc20::erc20::IERC20" }, { "type": "struct", "name": "core::integer::u256", "members": [ { "name": "low", "type": "core::integer::u128" }, { "name": "high", "type": "core::integer::u128" } ] }, { "type": "interface", "name": "erc20::erc20::IERC20", "items": [ { "type": "function", "name": "get_name", "inputs": [], "outputs": [ { "type": "core::felt252" } ], "state_mutability": "view" }, { "type": "function", "name": "get_symbol", "inputs": [], "outputs": [ { "type": "core::felt252" } ], "state_mutability": "view" }, { "type": "function", "name": "get_decimals", "inputs": [], "outputs": [ { "type": "core::integer::u8" } ], "state_mutability": "view" }, { "type": "function", "name": "get_total_supply", "inputs": [], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "balance_of", "inputs": [ { "name": "account", "type": "core::starknet::contract_address::ContractAddress" } ], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "allowance", "inputs": [ { "name": "owner", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" } ], "outputs": [ { "type": "core::integer::u256" } ], "state_mutability": "view" }, { "type": "function", "name": "transfer", "inputs": [ { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "transfer_from", "inputs": [ { "name": "sender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "approve", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "amount", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "increase_allowance", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "added_value", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" }, { "type": "function", "name": "decrease_allowance", "inputs": [ { "name": "spender", "type": "core::starknet::contract_address::ContractAddress" }, { "name": "subtracted_value", "type": "core::integer::u256" } ], "outputs": [], "state_mutability": "external" } ] }, { "type": "constructor", "name": "constructor", "inputs": [ { "name": "name_", "type": "core::felt252" }, { "name": "symbol_", "type": "core::felt252" }, { "name": "decimals_", "type": "core::integer::u8" }, { "name": "initial_supply", "type": "core::integer::u256" }, { "name": "recipient", "type": "core::starknet::contract_address::ContractAddress" } ] }, { "type": "event", "name": "erc20::erc20::ERC20::Transfer", "kind": "struct", "members": [ { "name": "from", "type": "core::starknet::contract_address::ContractAddress", "kind": "data" }, { "name": "to", "type": "core::starknet::contract_address::ContractAddress", "kind": "data" }, { "name": "value", "type": "core::integer::u256", "kind": "data" } ] }, { "type": "event", "name": "erc20::erc20::ERC20::Approval", "kind": "struct", "members": [ { "name": "owner", "type": "core::starknet::contract_address::ContractAddress", "kind": "data" }, { "name": "spender", "type": "core::starknet::contract_address::ContractAddress", "kind": "data" }, { "name": "value", "type": "core::integer::u256", "kind": "data" } ] }, { "type": "event", "name": "erc20::erc20::ERC20::Event", "kind": "enum", "variants": [ { "name": "Transfer", "type": "erc20::erc20::ERC20::Transfer", "kind": "nested" }, { "name": "Approval", "type": "erc20::erc20::ERC20::Approval", "kind": "nested" } ] } ] }
0
repos/starknet-zig/src/core/test-data
repos/starknet-zig/src/core/test-data/serde/broadcasted_invoke_v1_non_query.json
{ "max_fee": "0x1", "version": "0x1", "signature": [ "0x2" ], "nonce": "0x1", "type": "INVOKE", "sender_address": "0x3", "calldata": [ "0x1", "0x2", "0x3" ] }
0
repos/starknet-zig/src/core/test-data
repos/starknet-zig/src/core/test-data/serde/broadcasted_invoke_v1_query.json
{ "max_fee": "0x1", "version": "0x100000000000000000000000000000001", "signature": [ "0x2" ], "nonce": "0x1", "type": "INVOKE", "sender_address": "0x3", "calldata": [ "0x1", "0x2", "0x3" ] }
0
repos/starknet-zig/src
repos/starknet-zig/src/crypto/pedersen_hash.zig
const std = @import("std"); const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; const Felt252 = @import("../math/fields/starknet.zig").Felt252; const CurveParams = @import("../math/curve/curve_params.zig"); const ProjectivePoint = @import("../math/curve/short_weierstrass/projective.zig").ProjectivePoint; const AffinePoint = @import("../math/curve/short_weierstrass/affine.zig").AffinePoint; const pedersen_constants = @import("./pedersen/constants.zig"); const SHIFT_POINT = ProjectivePoint.fromAffinePoint(&CurveParams.SHIFT_POINT); fn boolsToUsizeLe(bits: []const bool) usize { var result: usize = 0; for (bits, 0..) |bit, i| { if (bit) result += @as(usize, 1) << @intCast(i); } return result; } fn addPoints(acc: *ProjectivePoint, bits: []const bool, prep: []const AffinePoint) void { // Preprocessed material is lookup-tables for each chunk of bits const table_size = (1 << pedersen_constants.CURVE_CONSTS_BITS) - 1; for (0..bits.len / pedersen_constants.CURVE_CONSTS_BITS) |i| { const offset = boolsToUsizeLe(bits[i * pedersen_constants.CURVE_CONSTS_BITS .. (i + 1) * pedersen_constants.CURVE_CONSTS_BITS][0..4]); if (offset > 0) { // Table lookup at 'offset-1' in table for chunk 'i' acc.addAffineAssign(&prep[i * table_size + offset - 1]); } } } /// Computes the Starkware version of the Pedersen hash of x and y. /// pub fn pedersenHash(x: Felt252, y: Felt252) Felt252 { const x_bits = x.toBitsLe(); const y_bits = y.toBitsLe(); // Compute hash var acc = SHIFT_POINT; addPoints(&acc, x_bits[0..248], &pedersen_constants.CURVE_CONSTS_P0); // Add a_low * P1 addPoints(&acc, x_bits[248..252], &pedersen_constants.CURVE_CONSTS_P1); // Add a_high * P2 addPoints(&acc, y_bits[0..248], &pedersen_constants.CURVE_CONSTS_P2); // Add b_low * P3 addPoints(&acc, y_bits[248..252], &pedersen_constants.CURVE_CONSTS_P3); // Add b_high * P4 // Return x-coordinate return AffinePoint.fromProjectivePoint(&acc).x; } test "Pedersen hash" { // Test case ported from: // https://github.com/starkware-libs/starkex-for-spot-trading/blob/master/src/starkware/crypto/starkware/crypto/signature/test/config/signature_test_data.json const in = [_]std.meta.Tuple(&.{ u256, u256 }){ .{ 0x03d937c035c878245caf64531a5756109c53068da139362728feb561405371cb, 0x0208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a, }, .{ 0x58f580910a6ca59b28927c08fe6c43e2e303ca384badc365795fc645d479d45, 0x78734f65a067be9bdb39de18434d71e79f7b6466a4b66bbd979ab9e7515fe0b, }, }; const out = [_]u256{ 0x30e480bed5fe53fa909cc0f8c4d99b8f9f2c016be4c41e13a4848797979c662, 0x68cc0b76cddd1dd4ed2301ada9b7c872b23875d5ff837b3a87993e0d9996b87, }; for (in, out) |i, o| { try std.testing.expectEqual( Felt252.fromInt(u256, o), pedersenHash(Felt252.fromInt(u256, i[0]), Felt252.fromInt(u256, i[1])), ); } }
0
repos/starknet-zig/src
repos/starknet-zig/src/crypto/poseidon_hash.zig
const std = @import("std"); const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; const Felt252 = @import("../math/fields/starknet.zig").Felt252; const field_constants = @import("../math/fields/constants.zig"); const poseidon_constants = @import("./poseidon/constants.zig"); const CurveParams = @import("../math/curve/curve_params.zig"); const ProjectivePoint = @import("../math/curve/short_weierstrass/projective.zig").ProjectivePoint; const AffinePoint = @import("../math/curve/short_weierstrass/affine.zig").AffinePoint; /// The PoseidonHasher struct represents a hasher based on the Poseidon cryptographic primitive. pub const PoseidonHasher = struct { /// The type alias for the current struct instance. const Self = @This(); /// The state of the hasher. /// Initialized with the default value of Felt252 and repeated 3 times. state: [3]Felt252 = [_]Felt252{.{}} ** 3, /// The buffer for storing the input message. /// Nullable, initialized with null. buffer: ?Felt252 = null, /// Updates the hasher state with a new message. /// /// This function updates the state of the Poseidon hasher with a new message. If the hasher has a /// pending message buffered, it combines the buffered message with the new message and applies the /// permutation computation (`permuteComp()`) to update the hasher state. Otherwise, it buffers the /// new message for subsequent hashing. /// /// Parameters: /// - `self`: A pointer to the current struct instance. /// - `message`: The Felt252 message to be incorporated into the hasher state. pub fn update(self: *Self, message: Felt252) void { if (self.buffer) |*previous_message| { // Combine buffered message with the new message and update the state. self.state[0].addAssign(previous_message); self.state[1].addAssign(&message); self.permuteComp(); self.buffer = null; } else { // Buffer the new message. self.buffer = message; } } /// Finalizes the hashing process and returns the resulting hash. /// /// This function finalizes the hashing process by incorporating any buffered message into the /// hasher state. If there is a buffered message, it combines it with a one (Felt252.one()) and /// updates the state before applying the permutation computation (`permuteComp()`) to obtain the /// final hash. If there is no buffered message, it treats a one as if paired with the last /// element of the state. /// /// Returns: /// The resulting hash as a Felt252 element. pub fn finalize(self: *Self) Felt252 { if (self.buffer) |*last_message| { // Combine buffered message with a one and update the state. self.state[0].addAssign(last_message); self.state[1].addAssign(&Felt252.one()); self.buffer = null; } else { // Treat a one as if paired with the last element of the state. self.state[0].addAssign(&Felt252.one()); } // Apply the permutation computation to obtain the final hash. self.permuteComp(); return self.state[0]; } /// Performs the Poseidon permutation computation based on the HADES design strategy for hashing. /// /// The HADES design strategy incorporates different types of rounds within the same permutation /// construction, utilizing both full S-box layers and partial S-box layers. This strategy aims to /// provide a balance between computational efficiency and security against statistical and /// algebraic attacks. /// /// The permutation consists of three phases: /// 1. R_f rounds at the beginning and end of the permutation, applying S-boxes to the full state. /// 2. R_p rounds in the middle, containing only a single S-box in each round, while the rest of /// the state remains unchanged (i.e., identity functions are used). /// 3. R_f rounds at the end, applying S-boxes to the full state again. /// /// This approach enhances security against statistical attacks by utilizing full S-box layers at /// the beginning and end, together with the wide trail strategy. Meanwhile, the use of partial /// S-box layers in the middle rounds increases the overall function's degree, providing additional /// protection against algebraic attacks. /// /// For further details, refer to the paper "The HADES Design Strategy for Hashing." pub fn permuteComp(self: *Self) void { var idx: usize = 0; // Apply full rounds at the beginning. for (0..poseidon_constants.POSEIDON_FULL_ROUNDS / 2) |_| { self.roundComp(idx, true); idx += 3; } // Apply partial rounds in the middle. for (0..poseidon_constants.POSEIDON_PARTIAL_ROUNDS) |_| { self.roundComp(idx, false); idx += 1; } // Apply full rounds at the end. for (0..poseidon_constants.POSEIDON_FULL_ROUNDS / 2) |_| { self.roundComp(idx, true); idx += 3; } } /// Performs a single round of the Poseidon permutation computation based on the HADES design strategy, /// incorporating AddRoundConstants (ARC), SubWords (S-box), and MixLayer (M). /// /// Each round function consists of three components: /// 1. AddRoundConstants (ARC), denoted by ARC(·). /// 2. SubWords (S-box), denoted by S-box(·) or by SB(·). /// 3. MixLayer (M), denoted by M(·), which represents the linear layer of the construction. /// /// In each round, the operations are applied in the following order: /// ARC → SB → M /// /// During the permutation, the following pattern is observed: /// - The first and last rounds (R_f + R_f = R_F) have full S-box layers, each consisting of 't' /// S-box functions. /// - The middle rounds (R_p) have partial S-box layers, with one S-box and (t - 1) identity functions. /// /// The MixLayer operation (M) involves multiplying the state with a t × t MDS matrix, which applies /// the wide trail strategy to enhance security against cryptographic attacks. /// /// For more detailed information about the HADES design strategy, refer to [GLR+20]. /// /// Parameters: /// - `idx`: The index indicating the position of the round within the permutation. /// - `full`: A boolean indicating whether the round contains a full S-box layer (true) or a /// partial S-box layer (false). pub fn roundComp(self: *Self, idx: usize, comptime full: bool) void { if (full) { inline for (0..self.state.len) |i| { // AddRoundConstants. self.state[i].addAssign(&poseidon_constants.POSEIDON_COMPRESSED_ROUND_CONSTS[idx + i]); // SubWords. self.state[i] = self.state[i].powToInt(3); } } else { // AddRoundConstants for partial round. self.state[2].addAssign(&poseidon_constants.POSEIDON_COMPRESSED_ROUND_CONSTS[idx]); self.state[2] = self.state[2].powToInt(3); } // MixLayer. self.mix(); } /// Performs mixing operations on the state as part of the Poseidon permutation computation. /// /// Mixing involves combining the state elements and applying arithmetic operations to achieve /// diffusion and non-linearity, enhancing the security properties of the permutation. /// /// The mixing operation consists of the following steps: /// 1. Summation of the state elements 'self.state[0]', 'self.state[1]', and 'self.state[2]'. /// 2. Doubling the value of 'self.state[0]', then adding the computed sum ('t'). /// 3. Doubling the value of 'self.state[1]', negating it, and then adding 't'. /// 4. Multiplying 'self.state[2]' by a compile-time constant Felt252.three(), negating it, and then /// adding 't'. /// /// Parameters: /// - `self`: A pointer to the current struct instance. pub inline fn mix(self: *Self) void { // Summation of state elements. const t = self.state[0].add(&self.state[1]).add(&self.state[2]); // Doubling and addition for state[0]. self.state[0].doubleAssign(); self.state[0].addAssign(&t); // Doubling, negation, and addition for state[1]. self.state[1].doubleAssign(); self.state[1].negAssign(); self.state[1].addAssign(&t); // Multiplication, negation, and addition for state[2]. self.state[2].mulAssign(&comptime Felt252.three()); self.state[2].negAssign(); self.state[2].addAssign(&t); } /// Hashes two elements and returns the resulting hash. pub fn hash(self: *Self, x: Felt252, y: Felt252) Felt252 { self.state = [_]Felt252{ x, y, Felt252.two() }; self.permuteComp(); return self.state[0]; } /// Hashes a single element and returns the resulting hash. pub fn hashSingle(self: *Self, x: Felt252) Felt252 { self.state = [_]Felt252{ x, .{}, Felt252.one() }; self.permuteComp(); return self.state[0]; } /// Hashes an array of elements and returns the resulting hash. /// /// This function takes an array of Felt252 elements and computes their hash using the Poseidon /// permutation. It iterates over the input elements, combining them in pairs and updating the /// internal state accordingly. If the array length is odd, it treats the last element as if paired /// with a one (Felt252.one()). /// /// After processing all input elements, the function applies the permutation computation /// (`permuteComp()`) to the final state to obtain the resulting hash. /// /// Parameters: /// - `self`: A pointer to the current struct instance. /// - `messages`: An array of Felt252 elements to be hashed. /// /// Returns: /// The resulting hash as a Felt252 element. pub fn hashMany(self: *Self, messages: []const Felt252) Felt252 { // Initialize the state with three Felt252 elements. self.state = [_]Felt252{.{}} ** 3; var idx: usize = 0; const messages_len = messages.len; // Process input elements in pairs. while (idx + 1 < messages_len) { // Combine pairs of elements and update the state. self.state[0].addAssign(&messages[idx]); self.state[1].addAssign(&messages[idx + 1]); self.permuteComp(); idx += 2; } // Handle the case where the array length is odd. if (@mod(messages_len, 2) != 0) { self.state[0].addAssign(&messages[messages_len - 1]); self.state[1].addAssign(&Felt252.one()); } else { self.state[0].addAssign(&Felt252.one()); } // Apply the permutation computation to obtain the hash. self.permuteComp(); return self.state[0]; } }; test "PoseidonHasher: Poseidon hash two elements" { const test_data = [_]std.meta.Tuple(&.{ Felt252, Felt252, Felt252 }){ .{ Felt252.fromInt(u256, 0xb662f9017fa7956fd70e26129b1833e10ad000fd37b4d9f4e0ce6884b7bbe), Felt252.fromInt(u256, 0x1fe356bf76102cdae1bfbdc173602ead228b12904c00dad9cf16e035468bea), Felt252.fromInt(u256, 0x75540825a6ecc5dc7d7c2f5f868164182742227f1367d66c43ee51ec7937a81), }, .{ Felt252.fromInt(u256, 0xf4e01b2032298f86b539e3d3ac05ced20d2ef275273f9325f8827717156529), Felt252.fromInt(u256, 0x587bc46f5f58e0511b93c31134652a689d761a9e7f234f0f130c52e4679f3a), Felt252.fromInt(u256, 0xbdb3180fdcfd6d6f172beb401af54dd71b6569e6061767234db2b777adf98b), }, }; for (test_data) |d| { var hasher: PoseidonHasher = .{}; try expectEqual(d[2], hasher.hash(d[0], d[1])); } } test "PoseidonHasher: Poseidon hash a single element" { const test_data = [_]std.meta.Tuple(&.{ Felt252, Felt252 }){ .{ Felt252.fromInt(u256, 0x9dad5d6f502ccbcb6d34ede04f0337df3b98936aaf782f4cc07d147e3a4fd6), Felt252.fromInt(u256, 0x11222854783f17f1c580ff64671bc3868de034c236f956216e8ed4ab7533455), }, .{ Felt252.fromInt(u256, 0x3164a8e2181ff7b83391b4a86bc8967f145c38f10f35fc74e9359a0c78f7b6), Felt252.fromInt(u256, 0x79ad7aa7b98d47705446fa01865942119026ac748d67a5840f06948bce2306b), }, }; for (test_data) |d| { var hasher: PoseidonHasher = .{}; try expectEqual(d[1], hasher.hashSingle(d[0])); } } test "PoseidonHasher: Poseidon hash many elements" { const test_data = [_]std.meta.Tuple(&.{ []const Felt252, Felt252 }){ .{ &[_]Felt252{ Felt252.fromInt(u256, 0x9bf52404586087391c5fbb42538692e7ca2149bac13c145ae4230a51a6fc47), Felt252.fromInt(u256, 0x40304159ee9d2d611120fbd7c7fb8020cc8f7a599bfa108e0e085222b862c0), Felt252.fromInt(u256, 0x46286e4f3c450761d960d6a151a9c0988f9e16f8a48d4c0a85817c009f806a), }, Felt252.fromInt(u256, 0x1ec38b38dc88bac7b0ed6ff6326f975a06a59ac601b417745fd412a5d38e4f7), }, .{ &[_]Felt252{ Felt252.fromInt(u256, 0xbdace8883922662601b2fd197bb660b081fcf383ede60725bd080d4b5f2fd3), Felt252.fromInt(u256, 0x1eb1daaf3fdad326b959dec70ced23649cdf8786537cee0c5758a1a4229097), Felt252.fromInt(u256, 0x869ca04071b779d6f940cdf33e62d51521e19223ab148ef571856ff3a44ff1), Felt252.fromInt(u256, 0x533e6df8d7c4b634b1f27035c8676a7439c635e1fea356484de7f0de677930), }, Felt252.fromInt(u256, 0x2520b8f910174c3e650725baacad4efafaae7623c69a0b5513d75e500f36624), }, }; for (test_data) |d| { var hasher: PoseidonHasher = .{}; try expectEqual(d[1], hasher.hashMany(d[0])); hasher = .{}; for (d[0]) |msg| { hasher.update(msg); } try expectEqual(d[1], hasher.finalize()); } }
0
repos/starknet-zig/src
repos/starknet-zig/src/crypto/ecdsa.zig
const std = @import("std"); const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; const Felt252 = @import("../math/fields/starknet.zig").Felt252; const big_int = @import("../math/fields/biginteger.zig").bigInt(4); const field_constants = @import("../math/fields/constants.zig"); const CurveParams = @import("../math/curve/curve_params.zig"); const ProjectivePoint = @import("../math/curve/short_weierstrass/projective.zig").ProjectivePoint; const AffinePoint = @import("../math/curve/short_weierstrass/affine.zig").AffinePoint; const Hash = std.crypto.hash.sha2.Sha256; const Hmac = std.crypto.auth.hmac.Hmac(Hash); /// Number of bits required to represent an element in the ECDSA field. const N_ELEMENT_BITS_ECDSA: u256 = @floor( @as( f128, @floatFromInt(std.math.log2(@as(u256, field_constants.STARKNET_PRIME))), ), ); /// Upper bound for elements in the ECDSA field. /// Calculated as 2^(N_ELEMENT_BITS_ECDSA). const ELEMENT_UPPER_BOUND = Felt252.fromInt( u256, std.math.pow(u256, 2, N_ELEMENT_BITS_ECDSA), ); /// Represents an error that can occur during ECDSA signing. pub const SignError = error{ /// The message hash is invalid. InvalidMessageHash, /// The value of `k` is invalid. InvalidK, }; /// Represents an error that can occur during ECDSA verification. pub const VerifyError = error{ /// The public key is invalid. InvalidPublicKey, /// The message hash is invalid. InvalidMessageHash, /// The value of `r` is invalid. InvalidR, /// The value of `s` is invalid. InvalidS, }; /// Represents an error that can occur during ECDSA signature recovery. pub const RecoverError = error{ /// The message hash is invalid. InvalidMessageHash, /// The value of `r` is invalid. InvalidR, /// The value of `s` is invalid. InvalidS, /// The value of `v` is invalid. InvalidV, }; /// Represents an ECDSA signature. pub const Signature = struct { const Self = @This(); const EC_ORDER: u256 = 0x0800000000000010ffffffffffffffffb781126dcae7b2321e66a241adc64d2f; /// The `r` value of the signature. r: Felt252 = .{}, /// The `s` value of the signature. s: Felt252 = .{}, /// The `v` value of the signature, if it's provided. v: ?Felt252 = null, /// Initializes an ECDSA signature with `r` and `s` values. pub fn init(r: Felt252, s: Felt252) Self { return .{ .r = r, .s = s }; } /// Initializes an ECDSA signature with extended `r`, `s`, and `v` values. pub fn initExtended(r: Felt252, s: Felt252, v: Felt252) Self { return .{ .r = r, .s = s, .v = v }; } /// Signs a message using the provided private key and nonce (random scalar) in the elliptic curve digital signature algorithm (ECDSA). /// /// This method generates an ECDSA signature for a given message using the provided private key and nonce (`k`). /// The signature process involves several cryptographic operations to ensure the integrity and authenticity of the message. /// /// # Arguments /// /// * `private_key` - A pointer to the private key represented as a field element. /// * `message` - A pointer to the message represented as a field element. /// * `k` - A pointer to the nonce (random scalar) represented as a field element. This nonce is crucial for security, and its uniqueness for each message is essential to prevent key recovery attacks. /// /// # Returns /// /// An ECDSA signature containing the `r` and `s` values. The signature represents the cryptographic proof of the message's authenticity and integrity. /// /// # Errors /// /// Returns an error if any error occurs during the signing process, such as an invalid message hash or nonce. It's essential to handle these errors to ensure the security and reliability of the signature. /// /// # Remarks /// /// - It's crucial to use a cryptographically secure random number generator for generating the nonce (`k`) to prevent predictable signatures and key recovery attacks. /// - The uniqueness of the nonce (`k`) for each message is fundamental to the security of the ECDSA scheme. Reusing the same nonce for multiple messages can lead to the leakage of the private key. pub fn sign(private_key: *const Felt252, message: *const Felt252, k: *const Felt252) !Self { // Check if the message hash is valid. // Message hash must be smaller than 2**N_ELEMENT_BITS_ECDSA. // Message whose hash is >= 2**N_ELEMENT_BITS_ECDSA cannot be signed. // This happens with a very small probability. if (message.gte(&comptime ELEMENT_UPPER_BOUND)) return SignError.InvalidMessageHash; // Check if the nonce `k` is zero if (k.isZero()) return SignError.InvalidK; // Compute curve point r = k * G const full_r = (comptime CurveParams.GENERATOR).mulByScalarProjective(k); const r = full_r.x; // Check if r is zero or greater than the maximum field value if (r.isZero() or r.gte(&comptime ELEMENT_UPPER_BOUND)) return SignError.InvalidK; // Compute s = (k^(-1) * (z + rd_A)) mod n const s = Felt252.fromBytesLe( r.toBigInt().mulMod( &private_key.toBigInt(), &comptime CurveParams.EC_ORDER.toBigInt(), ).addWithCarry( &message.toBigInt(), )[0].mulMod( &(try k.modInverse(comptime CurveParams.EC_ORDER)).toBigInt(), &comptime CurveParams.EC_ORDER.toBigInt(), ).toBytesLe(), ); // Check if s is zero or greater than the maximum field value if (s.isZero() or s.gte(&comptime ELEMENT_UPPER_BOUND)) return SignError.InvalidK; // Calculate v = (y-coordinate of full_r) mod 2 const v = Felt252.fromBytesLe( full_r.y.toBigInt() .bitAnd(&comptime Felt252.one().toBigInt()) .toBytesLe(), ); return .{ .r = r, .s = s, .v = v }; } /// Verifies the authenticity of an ECDSA signature. /// /// This function verifies whether a given ECDSA signature is authentic by checking against the provided public key and message hash. /// /// # Arguments /// /// * `public_key` - A pointer to the public key represented as a field element. /// * `message` - A pointer to the message hash represented as a field element. /// /// # Returns /// /// Returns `true` if the signature is authentic, `false` otherwise. /// /// # Errors /// /// Returns an error if any error occurs during the verification process, such as an invalid message hash, `r`, `s`, or public key. /// /// # Math Behind the ECDSA Sign/Verify /// /// How does the above sign/verify scheme work? Let's delve into the mathematics behind it. /// The equation behind the recovery of the point R', calculated during the signature verification, can be transformed by replacing the pubKey with privKey * G as follows: /// /// R' = (h * s1) * G + (r * s1) * pubKey = /// = (h * s1) * G + (r * s1) * privKey * G /// = (h + r * privKey) * s1 * G /// /// If we take the number s = (z + r * privKey) * k^(-1) (calculated during the signing process), we can calculate s1 = s * k as follows: /// /// s1 = s * k^(-1) = /// = ((z + r * privKey) * k^(-1)) * k /// = z + r * privKey /// /// Now, replace s1 in the point R': /// /// R' = (h + r * privKey) * s1 * G = /// = (z + r * privKey) * G = /// = k * G /// /// The final step is to compare the point R' (decoded by the pubKey) with the point R (encoded by the privKey). /// The algorithm, in fact, compares only the x-coordinates of R' and R: the integers r' and r. /// It is expected that r' == r if the signature is valid and r' ≠ r if the signature or the message or the public key is incorrect. pub fn verify(self: *const Self, public_key: *const Felt252, message: *const Felt252) !bool { // Check if the message hash is within the valid range if (message.gte(&comptime ELEMENT_UPPER_BOUND)) return VerifyError.InvalidMessageHash; // Check if the 'r' value is zero or exceeds the maximum field value if (self.r.isZero() or self.r.gte(&comptime ELEMENT_UPPER_BOUND)) return VerifyError.InvalidR; // Check if the 's' value is zero or exceeds the maximum field value if (self.s.isZero() or self.s.gte(&comptime ELEMENT_UPPER_BOUND)) return VerifyError.InvalidS; // Attempt to convert the provided public key to an affine point const full_public_key = AffinePoint.fromX(public_key.*) catch return VerifyError.InvalidPublicKey; // Calculate the modular inverse of 's' with respect to the EC order const w = try self.s.modInverse(CurveParams.EC_ORDER); // Check if the modular inverse of 's' is zero or exceeds the maximum field value if (w.isZero() or w.gte(&ELEMENT_UPPER_BOUND)) return VerifyError.InvalidS; // Calculate 'zw * G' const zw_g = CurveParams.GENERATOR.mulByScalarProjective( &Felt252.fromBytesLe( message.toBigInt().mulMod( &w.toBigInt(), &CurveParams.EC_ORDER.toBigInt(), ).toBytesLe(), ), ); // Calculate 'rw * Q' const rw_q = full_public_key.mulByScalarProjective( &Felt252.fromBytesLe( self.r.toBigInt().mulMod( &w.toBigInt(), &CurveParams.EC_ORDER.toBigInt(), ).toBytesLe(), ), ); // Check if the sum or difference of 'zw * G' and 'rw * Q' matches the 'r' value return (try zw_g.add(&rw_q)).x.eql(self.r) or (try zw_g.sub(&rw_q)).x.eql(self.r); } /// Recovers the public key from a given ECDSA signature and message hash. /// /// This function attempts to recover the public key used to sign a message from the provided ECDSA signature and message hash. /// The ECDSA signature scheme allows the public key to be recovered from the signed message together with the signature. /// The recovery process is based on some mathematical computations (described in the SECG: SEC 1 standard) and returns 0, 1, or 2 possible EC points that are valid public keys, corresponding to the signature. /// To avoid this ambiguity, some ECDSA implementations add one additional bit v to the signature during the signing process, and it takes the form {r, s, v}. /// From this extended ECDSA signature {r, s, v} + the signed message, the signer's public key can be restored with confidence. /// /// # Arguments /// /// * `message` - A pointer to the message hash represented as a field element. /// /// # Returns /// /// Returns the recovered public key as a field element if successful. /// /// # Errors /// /// Returns an error if any error occurs during the recovery process, such as an invalid message hash, `r`, `s`, or `v` value. /// /// # Note /// /// Public key recovery is possible for signatures based on the ElGamal signature scheme (such as DSA and ECDSA). This feature is particularly useful in bandwidth-constrained or storage-constrained environments, such as blockchain systems, where transmission or storage of the public keys cannot be afforded. For example, the Ethereum blockchain uses extended signatures {r, s, v} for the signed transactions on the chain to save storage and bandwidth. pub fn recover(self: *const Self, message: *const Felt252) !Felt252 { // Check if the message hash is within the valid range if (message.gte(&ELEMENT_UPPER_BOUND)) return RecoverError.InvalidMessageHash; // Check if the 'r' value is zero or exceeds the maximum field value if (self.r.isZero() or self.r.gte(&ELEMENT_UPPER_BOUND)) return RecoverError.InvalidR; // Check if the 's' value is zero or exceeds the maximum field value if (self.s.isZero() or self.s.gte(&ELEMENT_UPPER_BOUND)) return RecoverError.InvalidS; // Check if the 'v' value is greater than one if (self.v.?.gt(&Felt252.one())) return RecoverError.InvalidV; // Attempt to convert the 'r' value to an affine point var full_r = AffinePoint.fromX(self.r) catch return RecoverError.InvalidR; // Adjust the 'y' coordinate of 'full_r' based on the 'v' value if (!Felt252.fromBytesLe( full_r.y.toBigInt().bitAnd( &comptime Felt252.one().toBigInt(), ).toBytesLe(), ).eql(self.v.?)) full_r.y = full_r.y.neg(); // Calculate 'full_r * s' const full_rs = full_r.mulByScalarProjective(&self.s); // Calculate 'G * message' const zg = CurveParams.GENERATOR.mulByScalarProjective(message); // Calculate the modular inverse of 'r' with respect to the EC order const r_inv = try self.r.modInverse(comptime CurveParams.EC_ORDER); // Calculate '(full_rs - zg) * r_inv' const rs_zg = try full_rs.sub(&zg); // Return the 'x' coordinate of '(rs_zg * r_inv)' return rs_zg.mulByScalarProjective(&r_inv).x; } const noise_length: usize = 32; // Description: This function returns the elliptic curve order as a byte array. // // Returns: // - [32]u8: The elliptic curve order represented as a byte array. // // Notes: // - The function computes the elliptic curve order at compile-time. // - The elliptic curve order is converted into a byte array with big-endian representation. // // Reference: EC_ORDER - The order of the elliptic curve used in cryptographic operations. fn getEcOrderAsBytes() [32]u8 { comptime { var q: [32]u8 = undefined; std.mem.writeInt(u256, &q, EC_ORDER, .big); return q; } } // Description: This function computes the number of leading zeros in the binary representation of the elliptic curve order. // // Returns: // - u64: The number of leading zeros in the binary representation of the elliptic curve order. // // Notes: // - The function computes the number of leading zeros at compile-time using the @clz intrinsic. // // Reference: EC_ORDER - The order of the elliptic curve used in cryptographic operations. fn getEcOrderLeadingZeros() u64 { comptime { return @clz(EC_ORDER); } } // Description: This function generates a deterministic scalar according to a secret key and optional noise, // following the process described in RFC 6979. // // Parameters: // - message_hash: Felt252 - The hash of the message to be signed. // - secret_key: Felt252 - The secret key used for signing. // - seed: ?Felt252 - Optional additional randomness (noise) to enhance security. // // Returns: // - Felt252: The deterministic scalar value suitable for ECDSA or DSA signatures. // // Notes: // - The function uses HMAC-based Extract-and-Expand Key Derivation Function (HKDF) for deterministic scalar generation. // - The provided secret key and message hash are converted into byte arrays. // - The function initializes V and K according to the specified process. // - If noise is provided, it is incorporated into the HMAC computation. // - The function repeats the process until a proper value for k is found. // - The resulting scalar value is returned as a Felt252. // // RFC Reference: https://datatracker.ietf.org/doc/html/rfc6979 // Section 3.2: Generation of k fn deterministicScalar( message_hash: Felt252, secret_key: Felt252, seed: ?Felt252, ) Felt252 { // Check if noise (seed) is provided, convert it to bytes; otherwise, set it to null. const noise = if (seed) |s| s.toBytesBe() else null; // Convert the message hash to bytes. const h = message_hash.toBytesBe(); // Convert the secret key to a 256-bit unsigned integer and store it in a byte array. var private_key: [32]u8 = undefined; std.mem.writeInt(u256, &private_key, secret_key.toU256(), .big); // Initialize V as a sequence of octets of value 1, with a length equal to the hash length. var v = [_]u8{0x01} ** 32; // Initialize K as a sequence of octets of value 0, with a length equal to the hash length. var k = [_]u8{0x00} ** 32; // Determine the index of the first non-zero byte in the noise array, if noise is provided. var first_non_zero_index: usize = 0; if (noise) |n| { for (n, 0..) |elm, i| { if (elm != 0) { first_non_zero_index = i; break; } } } // Iterate twice to compute K and V. inline for (0..2) |i| { if (noise) |n| { // Initialize HMAC with K as the key and update it with the concatenation of V, 0x00, private key, h, and noise. var hmac = Hmac.init(&k); hmac.update(&(v ++ [_]u8{i} ++ private_key ++ h)); // If noise is provided, update HMAC with the non-zero part of the noise array. if (first_non_zero_index != noise_length) hmac.update(n[first_non_zero_index..]); // Finalize HMAC to compute the new value of K. hmac.final(&k); } else { // If noise is not provided, directly compute K using HMAC with the concatenation of V, 0x00, private key, and h. Hmac.create(&k, &(v ++ [_]u8{i} ++ private_key ++ h), &k); } // Update V using HMAC with K. Hmac.create(&v, &v, &k); } // Repeat the process until a proper value for k is found. while (true) { // Update V using HMAC with K. // Compute V = HMAC_K(V) Hmac.create(&v, &v, &k); // Convert a portion of V to an integer, considering leading zeros based on EC order. const k1 = std.mem.readInt(u256, &v, .big) >> comptime getEcOrderLeadingZeros(); // If k1 is within the valid range and not 0, return it as a Felt252. if (k1 != 0 and k1 < EC_ORDER - 1) return Felt252.fromInt(u256, k1); // If k1 is not suitable, update K and V and repeat the process. // Compute K = HMAC_K(V || 0x00) Hmac.create(&k, &(v ++ [_]u8{0x00}), &k); // Compute V = HMAC_K(V) Hmac.create(&v, &v, &k); } } }; /// An ECDSA key pair. pub const KeyPair = struct { const Self = @This(); /// Public part. public_key: Felt252, /// Secret scalar. private_key: Felt252, /// Computes the public key corresponding to the given private key using the elliptic curve parameters. /// /// This function calculates the public key corresponding to the provided private key /// using the elliptic curve parameters. It performs scalar multiplication of the base generator point /// by the private key, following the ECDSA key-pair generation process, and returns the x-coordinate of the resulting point as the public key. /// /// # Key Generation /// /// The ECDSA key-pair consists of: /// - Private key (integer): `privKey` /// - Public key (EC point): `pubKey = privKey * G` /// /// The private key is generated as a random integer in the range [0...n-1], where `n` is the order of the base generator point `G`. /// The public key `pubKey` is a point on the elliptic curve, calculated by the EC point multiplication: `pubKey = privKey * G` (the private key, multiplied by the generator point `G`). /// /// # Arguments /// /// * `private_key` - A pointer to the private key represented as a field element. /// /// # Returns /// /// The x-coordinate of the resulting point after scalar multiplication, representing the public key. pub fn fromSecretKey(private_key: *const Felt252) Self { // Scalar multiply the base generator point by the private key and return the x-coordinate. return .{ .private_key = private_key.*, .public_key = CurveParams.GENERATOR.mulByScalarProjective(private_key).x, }; } }; // Test cases ported from: // https://github.com/starkware-libs/crypto-cpp/blob/95864fbe11d5287e345432dbe1e80dea3c35fc58/src/starkware/crypto/ffi/crypto_lib_test.go test "getPublicKey: test with precomputed keys" { // Precomputed keys can be found here: // https://github.com/starkware-libs/starkex-for-spot-trading/blob/master/src/starkware/crypto/starkware/crypto/signature/src/config/keys_precomputed.json const private_keys = [_]u256{ 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0x800000000000000000000000000000000000000000000000000000000000000, 0x800000000000000000000000000000000000000000000000000000000000001, 0x800000000000000000000000000000000000000000000000000000000000002, 0x800000000000000000000000000000000000000000000000000000000000003, 0x800000000000000000000000000000000000000000000000000000000000004, 0x800000000000000000000000000000000000000000000000000000000000005, 0x800000000000000000000000000000000000000000000000000000000000006, 0x800000000000000000000000000000000000000000000000000000000000007, 0x800000000000000000000000000000000000000000000000000000000000008, 0x800000000000000000000000000000000000000000000000000000000000009, 0x2e9c99d8382fa004dcbbee720aef8a97002de0e991f6a8344e6dc636a71b59e, 0x8620458785138df8722214e073a91b8f55076ea78197cf41007692dd27fd90, 0x1b920e7dfb49ba5ada673882af5342e7448d3e9335e0ac37feb6280cd7289ce, 0x704170dbfd5dc63caef69d2ce6dfc2b2dbb2af6e75851242bbe79fb6e62a118, 0x4b58bf4228f39550eca59b5c96a0cb606036cc9495eef9a546f24f01b1b7829, 0x2e93226c90fb7a2381a24e940a94b98433e3553dcbf745d3f54d62963c75604, 0x4615f94598cd756ad1a551d7e57fd725916adfd0054eb773ceb482eef87d0b2, 0x6ade54b7debd7ca1d4e8e932f9545f8fa4024d73be1efcc86df86367fc333f8, 0x618e7467dd24c2a3449c4df640439c12cdd0f8ea779afcee6e252b2cf494354, 0x7eae185e1f41ec76d214d763f0592f194933622a9dd5f3d52d0209f71619c1a, 0x178047D3869489C055D7EA54C014FFB834A069C9595186ABE04EA4D1223A03F, }; const expected_public_keys = [_]u256{ 0x1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca, 0x759ca09377679ecd535a81e83039658bf40959283187c654c5416f439403cf5, 0x411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20, 0xa7da05a4d664859ccd6e567b935cdfbfe3018c7771cb980892ef38878ae9bc, 0x788435d61046d3eec54d77d25bd194525f4fa26ebe6575536bc6f656656b74c, 0x1efc3d7c9649900fcbd03f578a8248d095bc4b6a13b3c25f9886ef971ff96fa, 0x743829e0a179f8afe223fc8112dfc8d024ab6b235fd42283c4f5970259ce7b7, 0x6eeee2b0c71d681692559735e08a2c3ba04e7347c0c18d4d49b83bb89771591, 0x216b4f076ff47e03a05032d1c6ee17933d8de8b2b4c43eb5ad5a7e1b25d3849, 0x5c79074e7f7b834c12c81a9bb0d46691a5e7517767a849d9d98cb84e2176ed2, 0x1c4f24e3bd16db0e2457bc005a9d61965105a535554c6b338871e34cb8e2d3a, 0xdfbb89b39288a9ddacf3942b4481b04d4fa2f8ed3c424757981cc6357f27ac, 0x41bef28265fd750b102f4f2d1e0231de7f4a33900a214f191a63d4fec4e72f4, 0x24de66eb164797d4b414e81ded0cfa1a592ef0a9363ebbcb440d4d03cb18af1, 0x5efb18c3bc9b69003746acc85fb6ee0cfbdc6adfb982f089cc63e1e5495daad, 0x10dc71f00918a8ebfe4085c834d41dd22b251b9f81eef8b9a4fab77e7e1afe9, 0x4267ebfd379b1c8caae73febc5920b0c95bd6f9f3536f47c5ddad1259c332ff, 0x6da515118c8e01fd5b2e96b814ee95bad7d60be4d2ba6b47e0d283f579d9671, 0x7a5b4797f4e56ed1473876bc2693fbe3f2fef7e050717cbae924ff23d426052, 0x1ff6803ae740e7e596504ac5c6afbea472e53679361e214f12be0155b13e25d, 0x5967da40b90d7ca1e36dc4024381d7d4b403c6ac1a0ab358b0743984934a805, 0x78c7ab46333968fbde3201cf512c1eeb5529360259072c459a158dee4449b57, 0x534bd8d6ebe4bb2f6992e2d7c19ef3146247e10c2849f357e44eddd283b2af6, 0x1097a8c5a46d94596f1c8e70ca66941f2bb11e3c8d4fd58fdc4589f09965be8, 0x369f0e8c8e984f244290267393a004dba435a4df091767ad5063fece7b1884c, 0x1ee5b8d612102a2408cde59ce52a6498d2e38fe8789bb26d400dea310684ec9, 0x37de3bf52412b2fb9b0030d232ca9dd921cd8f71fd67975cdc62546826e121, 0x71c2b578c432f2d305d3808bb645ecc46dd670cb43d4f4a076f75ccbff74fbc, 0x2b0160052e70176e5b0ff2a6eff90896ae07b732fc27219e36e077735abd57e, 0x1895a6a77ae14e7987b9cb51329a5adfb17bd8e7c638f92d6892d76e51cebcf, }; for (private_keys, expected_public_keys) |private_key, public_key| { const k1 = Felt252.fromInt(u256, private_key); const k2 = Felt252.fromInt(u256, public_key); try expectEqual( KeyPair{ .private_key = k1, .public_key = k2 }, KeyPair.fromSecretKey(&k1), ); } } test "Signature: verify valid message" { // Define the public key for testing purposes const public_key = Felt252.fromInt( u256, 0x01ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca, ); // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000002, ); // Define the `r` value of the signature const r_bytes = Felt252.fromInt( u256, 0x0411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20, ); // Define the `s` value of the signature const s_bytes = Felt252.fromInt( u256, 0x0405c3191ab3883ef2b763af35bc5f5d15b3b4e99461d70e84c654a351a7c81b, ); // Initialize the signature with the `r` and `s` values const signature = Signature.init(r_bytes, s_bytes); // Verify the signature against the provided public key and message hash try expect(try signature.verify(&public_key, &message_hash)); } test "Signature: verify invalid message" { // Define the public key for testing purposes const public_key = Felt252.fromInt( u256, 0x077a4b314db07c45076d11f62b6f9e748a39790441823307743cf00d6597ea43, ); // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0397e76d1667c4454bfb83514e120583af836f8e32a516765497823eabe16a3f, ); // Define the `r` value of the signature const r_bytes = Felt252.fromInt( u256, 0x0173fd03d8b008ee7432977ac27d1e9d1a1f6c98b1a2f05fa84a21c84c44e882, ); // Define the `s` value of the signature const s_bytes = Felt252.fromInt( u256, 0x01f2c44a7798f55192f153b4c48ea5c1241fbb69e6132cc8a0da9c5b62a4286e, ); // Initialize the signature with the `r` and `s` values const signature = Signature.init(r_bytes, s_bytes); // Verify that the signature does not verify against the provided public key and message hash try expect(!(try signature.verify(&public_key, &message_hash))); } test "Signature: verify with invalid public key" { // Define an invalid public key for testing purposes const public_key = Felt252.fromInt( u256, 0x03ee9bffffffffff26ffffffff60ffffffffffffffffffffffffffff004accff, ); // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000002, ); // Define the `r` value of the signature const r_bytes = Felt252.fromInt( u256, 0x0411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20, ); // Define the `s` value of the signature const s_bytes = Felt252.fromInt( u256, 0x0405c3191ab3883ef2b763af35bc5f5d15b3b4e99461d70e84c654a351a7c81b, ); // Initialize the signature with the `r` and `s` values const signature = Signature.init(r_bytes, s_bytes); // Verify that an error is thrown when attempting to verify the signature with the invalid public key try expectError(VerifyError.InvalidPublicKey, signature.verify(&public_key, &message_hash)); } test "Signature: test message signature" { // Define the private key for testing purposes const private_key = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000001, ); // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000002, ); // Define the nonce (random scalar) for testing purposes const k = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000003, ); // Sign the message using the provided private key and nonce const signature = try Signature.sign(&private_key, &message_hash, &k); // Derive the public key from the provided private key const key_pair = KeyPair.fromSecretKey(&private_key); // Verify that the signature is valid for the provided public key and message hash try expect(try signature.verify(&key_pair.public_key, &message_hash)); } test "Signature: test recover" { // Define the private key for testing purposes const private_key = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000001, ); // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000002, ); // Define the nonce (random scalar) for testing purposes const k = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000003, ); // Sign the message using the provided private key and nonce const signature = try Signature.sign(&private_key, &message_hash, &k); // Recover the public key from the signature and message hash try expectEqual( KeyPair.fromSecretKey(&private_key).public_key, try signature.recover(&message_hash), ); } test "Signature: test recover with invalid r" { // Define the message hash for testing purposes const message_hash = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000002, ); // Define the 'r' value for testing purposes const r = Felt252.fromInt( u256, 0x03ee9bffffffffff26ffffffff60ffffffffffffffffffffffffffff004accff, ); // Define the 's' value for testing purposes const s = Felt252.fromInt( u256, 0x0405c3191ab3883ef2b763af35bc5f5d15b3b4e99461d70e84c654a351a7c81b, ); // Define the 'v' value for testing purposes const v = Felt252.fromInt( u256, 0x0000000000000000000000000000000000000000000000000000000000000000, ); // Initialize a signature with the provided 'r', 's', and 'v' values const signature = Signature.initExtended(r, s, v); // Attempt to recover the public key from the signature and message hash try expectError(RecoverError.InvalidR, signature.recover(&message_hash)); } test "Signature: generate deterministic scalar padded" { const data = [_]struct { message_hash: Felt252, private_key: Felt252, seed: ?Felt252, k: Felt252 }{ .{ .message_hash = Felt252.fromInt(u256, 0x010b559a3b4dc1b7137d90521cb413b397ff07963214d128a92d65aec7182f68), .private_key = Felt252.fromInt(u256, 0x07e3184f4bef18f371bc53fc412dff1b30dbc94f758490fb8e2349bae647a642), .seed = Felt252.fromInt(u256, 0x03fe27199aaad4e700559e2436a919f4de70def585a6deb2f4c087fdf6a27c1b), .k = Felt252.fromInt(u256, 0x00514de5048c11bf01f3dc98a131e0a3fde03d6269cdfab69d944c8281149184), }, .{ .message_hash = Felt252.fromInt(u256, 0x058a8fc2bed05af3ae202f0ea4f6e724b6d3b1034382c7a2e1a3a06bd48bf7ea), .private_key = Felt252.fromInt(u256, 0x00efacf45682998e4748e853f13a789b4729be197353eb1b8063fd425e0576f8), .seed = Felt252.fromInt(u256, 0x05a595cc1e2dcdb26e2ee3964aaa55090bff0c02be6980f098669bc8c87fb994), .k = Felt252.fromInt(u256, 0x0610bd4aec3a26b00331daee8baefc2ad9c94eab42d21384851a1c4fcd5c0483), }, .{ .message_hash = Felt252.fromInt(u256, 0x02de2f0d139af136ef15a5ccf8139724131ff6000034be37e281b37a33b06ed7), .private_key = Felt252.fromInt(u256, 0x01d2cb8a451ddbe6d0d2f193cf384c275e919e18aeb4aa09e39c2236dd5d4121), .seed = Felt252.fromInt(u256, 0x033fe7b36cb79df110f92739f13fcf9c1a9ed9f80dba80a724f73055d763eb94), .k = Felt252.fromInt(u256, 0x06019bb42abee70ad655cf5135f35a6fa38ccfa7823abd238e5742d979dcd470), }, .{ .message_hash = Felt252.fromInt(u256, 0x05379d4cabb167483ffeeec5463452a021092773ae2d3c9fa639e501cbd337cb), .private_key = Felt252.fromInt(u256, 0x062465a3562e57a73e4fbdbc3dc4c7b14138258639a276410fbc553d951f498e), .seed = Felt252.fromInt(u256, 0x0603a421b6a665a83efcba9bff5361d728ae96096e3305b0a17df896b54c3832), .k = Felt252.fromInt(u256, 0x00c1bc03501b4c521310a5f47f020899f63079d20268126ebf5237c4fe40cc06), }, .{ .message_hash = Felt252.fromInt(u256, 0x0605b776d195609f6ed6ebacb20efb1859b7c827abfa9743c4541e1eb48f1c2d), .private_key = Felt252.fromInt(u256, 0x00a13a4fa63b534583089df4d6f5ff74ca3cbc2679c4161e076969803cae1aac), .seed = Felt252.fromInt(u256, 0x0104c78975779c741a5a5c0a6f5edc8841f570ded6a1c5c519ab0f963ec64c0a), .k = Felt252.fromInt(u256, 0x07badb8d84631f6bd418e5eaa46e9b09c083fa607c879e881cf5c31923520e3a), }, .{ .message_hash = Felt252.fromInt(u256, 0x01856e6d1c3ce0a34ab04992b4a8d8d9ef756a4044bfc0a5f8068013f829ee17), .private_key = Felt252.fromInt(u256, 0x01e20f779df440c3fca66a3ede6f43c68ba60222b23f893854f55c5138c77a1c), .seed = null, .k = Felt252.fromInt(u256, 0x01bdbdc2db77b6dad0c9bdaca20acb5a78a61200c711cc2dcaeebcb86f9ef1ca), }, .{ .message_hash = Felt252.fromInt(u256, 0x0438e872bae2e39e148ab372c6aa4506602d9d0f0acca48dfa853e858e38a8aa), .private_key = Felt252.fromInt(u256, 0x02d50c10d13ecf299d6bccea372efd6b0212208fd5f04cca66e5072d89b9bc2f), .seed = null, .k = Felt252.fromInt(u256, 0x051a3dd43ef8e85094c95ca1d6d5f4cbd5a2c8253466d558a815dde2bae17b76), }, .{ .message_hash = Felt252.fromInt(u256, 0x0470d8bd5f6640bbae27a997f5da4493953a2f6c2aacb7ac3a26cfe810738470), .private_key = Felt252.fromInt(u256, 0x01af592805ccb005eed4ce5b1997193c7446786b1d8c3cdc9fb30b84ea084cd6), .seed = null, .k = Felt252.fromInt(u256, 0x004e29ac94c51097d4ee87d4bf9bcfc33ca29518f73e972e725f851ada274a57), }, .{ .message_hash = Felt252.fromInt(u256, 0x04d85b6e736dd4aa07a8b1222819585f99e122a09f7e9c77e22da288f9c893b0), .private_key = Felt252.fromInt(u256, 0x046dda98ddd7337b4f6248795aedbc2e1b192466356ab8f61ee25317500e3a22), .seed = null, .k = Felt252.fromInt(u256, 0x014ee0f4a9e8b4f98d48d47993788d8485ded1eca3c894c8501b31dbcd8190e5), }, .{ .message_hash = Felt252.fromInt(u256, 0x03fcafdbc49c1b8ff00ad5884db731a643899a2010169481203e9a4aab0545f3), .private_key = Felt252.fromInt(u256, 0x02bb48d586e127c86a3a4e6b831a99bac5a9adf0e3974bc629c43a12f52fb488), .seed = null, .k = Felt252.fromInt(u256, 0x0052218bd1d5447347793972e5d40800a45cc91794746533164827e6f3ce8250), }, }; for (data) |d| { try expectEqual( d.k, Signature.deterministicScalar( d.message_hash, d.private_key, d.seed, ), ); } } test "Signature: generate deterministic scalar non padded" { const data = [_]struct { message_hash: Felt252, private_key: Felt252, seed: ?Felt252, k: Felt252 }{ .{ .message_hash = Felt252.fromInt(u256, 0x0080977da1148412a7976215729d396b72aec9e955498757a7b859281354b4b1), .private_key = Felt252.fromInt(u256, 0x03fa56dcdbe2fb6769a83786469faf589a3d1e31c66db8b0432f741a38cdeed1), .seed = Felt252.fromInt(u256, 0x0776cc1aa4c66417a4923768b9d4a7cfca731e862e4972ed930d8f2ad45d352b), .k = Felt252.fromInt(u256, 0x0013480c97bb5861404aa16e1f97a99411ba8f4039b2d54de839dea5c9f0af47), }, .{ .message_hash = Felt252.fromInt(u256, 0x00acf1ce22cb1f49d4fc7a6df93cd290d28f4c5a27888c9624b07cfa193de992), .private_key = Felt252.fromInt(u256, 0x06ad6342c62315862f51722808d2764a60824f9c5894105dffbb6478cfb06a95), .seed = Felt252.fromInt(u256, 0x01314de4fcf69889ea0cdf4aefd1cc7732d1dfbdc6476066e3132c1609756bd0), .k = Felt252.fromInt(u256, 0x0687b462764b919fabefcb84fe77a4eae838f45b97f49b2d24fec995ff482c04), }, .{ .message_hash = Felt252.fromInt(u256, 0x0020791e67f0d6083d406a3a0fdaf8f4008fc1c6616dc97c1e1fdda352030e2f), .private_key = Felt252.fromInt(u256, 0x06e18a4a890962776c397e3ddf659b07275995a341e32bb75cd5a3bff55cfe7b), .seed = Felt252.fromInt(u256, 0x0506b182cf3d46d6a7918ed4dfcced8f46c09a44c68067b3b40f2d82bee65e1a), .k = Felt252.fromInt(u256, 0x02cc9d2484afa0569b44487cf1705906db0a4cb78d9f73426efaaa572a5d47bb), }, .{ .message_hash = Felt252.fromInt(u256, 0x006243fd868f3e5b1852a9bda7a93780405cd05e5809904837398343c649c863), .private_key = Felt252.fromInt(u256, 0x0752543710a5075733d597329ff9ef354a2d4a36dbf769a6293a4fd0082026be), .seed = Felt252.fromInt(u256, 0x06a7c98da9ea1f2abd105b5cf6722f0d03efadb60891b8d58c79c7a9fc2649a2), .k = Felt252.fromInt(u256, 0x02e701fb8707ecd930bea12f9761cfedd9f559d1706a104d3f529d4f7b43223a), }, .{ .message_hash = Felt252.fromInt(u256, 0x00b3b40642edd4d2e4c7c60310c55b9e99bcb64b57b05ccd3d4062b6caa10bfc), .private_key = Felt252.fromInt(u256, 0x05a1e54cd91afff6b1797ad6244a93380cd530f05eda201b9b25d52da61fbcb2), .seed = Felt252.fromInt(u256, 0x00343ace243e3236520d132a07a6bdd757f743e5a4901e7b5d60b72c3f9450af), .k = Felt252.fromInt(u256, 0x05bb9f6160e41bd0887b58c40c90060a32569de14dcab341426b16bdf4d9dd94), }, .{ .message_hash = Felt252.fromInt(u256, 0x006c663dc46f1f680f32ef5f3f4fe71c5a0488c7fd2500eeee29cbaa3e4231e3), .private_key = Felt252.fromInt(u256, 0x013a6f2b21a9344b51635f16da58573f69c7d09ec20769ec9b481629ea9ec485), .seed = null, .k = Felt252.fromInt(u256, 0x02d59476386604375e958f2ee7f07446d1861a4ceb92eb393009b1c72db308a7), }, .{ .message_hash = Felt252.fromInt(u256, 0x006c846f23ae7941f843c53cf86004e0addb8974bdfc5d051035edbfd3dcf836), .private_key = Felt252.fromInt(u256, 0x0562bb91276d2463e3186631dcff433169e99592639e0df9f358c56437e90c9a), .seed = null, .k = Felt252.fromInt(u256, 0x076e1465a3753e7b1139223d9f68880c6192cd19f68b2a1c43b34b7aaa8cab16), }, .{ .message_hash = Felt252.fromInt(u256, 0x00539c45625f25004f965082e1e7f5a837f4eee253c915a95f00503fcdfb2c35), .private_key = Felt252.fromInt(u256, 0x05f4dddfc752dd28e72f498c7c0298a42fa6cfef14db2c3bdd798c6ca5b1497b), .seed = null, .k = Felt252.fromInt(u256, 0x06054d0413882a9798127d5760d61dc9e3e940b11ccc353deb33ef4ca58ccf34), }, .{ .message_hash = Felt252.fromInt(u256, 0x0050b1346abe44d73084f557fc88f209ae4aadff253bb23b4212f859076f8755), .private_key = Felt252.fromInt(u256, 0x0580cf0b0db0ffb7b792b61d6d3da583210b320337a9222ab4208aae78ce4963), .seed = null, .k = Felt252.fromInt(u256, 0x052b8601d62662702ed36ee1440d1f76ef814193d206218e436ccd3aae25451e), }, .{ .message_hash = Felt252.fromInt(u256, 0x0054077f197503c09c1265254398f57fb79f3a4f6a5a143cf871d58eeb5a5729), .private_key = Felt252.fromInt(u256, 0x07e69dd5b7cf548d598650be2ab3a8ebc038a5877a592d35a1cafa7249ef7fc4), .seed = null, .k = Felt252.fromInt(u256, 0x07af7d6cf50798dd5fa6e5731394d7d33f16dd57cca4169d63256a2b42179649), }, }; for (data) |d| { try expectEqual( d.k, Signature.deterministicScalar( d.message_hash, d.private_key, d.seed, ), ); } }
0
repos/starknet-zig/src/crypto
repos/starknet-zig/src/crypto/pedersen/constants.zig
const AffinePoint = @import("../../math/curve/short_weierstrass/affine.zig").AffinePoint; pub const CURVE_CONSTS_BITS: usize = 4; const big_int = @import("../../math/fields/biginteger.zig").bigInt(4); const Felt252 = @import("../../math/fields/starknet.zig").Felt252; pub const CURVE_CONSTS_P0: [930]AffinePoint = .{ .{ .x = .{ .fe = .{ .limbs = .{ 3602345268353203007, 13758484295849329960, 518715844721862878, 241691544791834578, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13441546676070136227, 13001553326386915570, 433857700841878496, 368891789801938570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16390798442227108542, 4459397208487568853, 6299111438052962557, 275749452099435948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1280036789011951735, 2792097536409196339, 3069182914186845479, 267809665474690740, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8711763012873219356, 15212051297345004119, 15657862152792686007, 214317678238552735, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4038507203023017298, 17358917237117523672, 4455506067486657930, 162545576806579736, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1852679819546688474, 11720024525106607284, 18226840214477480010, 224249572646532941, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14528472358788883832, 12527404634214091799, 13962287978638919074, 169068292311512341, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15214088468263405539, 3559423045572230351, 3184424227475712789, 103430309885895176, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12869265880755710427, 3511222980989122603, 12903947816958939347, 177279687877508316, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13211871192819116456, 10809268444910089765, 8878359780384627180, 350129966603299180, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4650282840312315554, 3265519857896300114, 15102414183311453733, 393380294749450461, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9171957005886420615, 9643680970633651735, 8822141692482650274, 126495145115287155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17861343015994099006, 10140539152342220432, 3879648526602712757, 55095909773933446, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11906898082339326253, 14005401007936979841, 13677815028167526775, 177482561045637325, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7065046784534526604, 3506666571320247296, 9271671314531910510, 566393519956473124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1518591804341898852, 956597588755387711, 1805245447396855305, 391954315416768955, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17781375865510360639, 7922224446276556716, 844718631158327664, 396029403368518300, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4476019200402823375, 9825995460605393760, 13174469346514093990, 441775390247344554, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13094069499501189423, 1573940960550025409, 9840395016474282647, 169487119810640561, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14383797733352935760, 3171630772217731434, 17645676251522158707, 316295448545948615, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9751763788229254174, 4382192863250216803, 2524913917774084055, 423700107029885243, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13194744713866251983, 3387955117091920413, 6363340760762704566, 291308922126839382, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1764158491160504527, 701884549056726103, 11512699319987153493, 287942167579412813, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4336456974200001888, 2274629446203318996, 8364534601289982408, 102090168344724923, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9322738930526443635, 13055154325629333709, 16547453342713402629, 216911479390450336, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12153227620020974266, 14929886557088916865, 4435525574255891220, 12988420136645424, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7210887971207390714, 15363277620054676875, 12921942274014928074, 346559003089286051, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7328466191650696302, 684370724249540386, 5564325476911563807, 540409505057587724, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8202103542525242123, 14398378930883516937, 11851174246641875209, 351347611245334432, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7879889331196042675, 8000735345716179736, 11134029773577570755, 503285931539484467, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14876474552510719042, 15598122510424452671, 5018335632706699354, 349769894069483658, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 653276751355607085, 11259700290765893389, 13830639676898841818, 204522125873064042, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9626716605176161895, 16626139821296225206, 4579439747184432007, 141183858941918366, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10485437032003524620, 10930649594744069904, 5948030865144806067, 96901653810601525, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9863778039483782340, 14747489419204569813, 78762043355937542, 485095069754417327, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17163721246494031414, 307925883507963363, 10272768818414436805, 482751593414405607, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1024802959735579860, 3046971371285477088, 10877521220947970745, 444242034992266334, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12595265386059141377, 12626919543395926730, 7630502977220179456, 79783986660298659, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10298354662955237215, 12420119573814167918, 1902039845517891242, 220610523081332186, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17626034728057686656, 16580974831448020868, 8077538761201346809, 549620908174315673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6135740512412730233, 129227947519444969, 9271184133604862130, 203063184638157300, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 985986073134248295, 1446457351568910116, 12350699564918472961, 108371117431586732, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13878341331433930873, 18014449569544058732, 16740381689525165224, 303334238143720833, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12730042055084817937, 12476999969825171350, 12355484085776270052, 487566253557281299, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11547336601790713784, 9973037301616234078, 14222534170599023155, 195411302354089278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10518946748575493087, 6791903136623225605, 17373439233882695728, 54269271686175405, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1484037119436401804, 16280202647972111981, 5591596206904822096, 211888694370786840, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18102456494158242733, 3367627634806672903, 1911722120048685244, 491130375551095654, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9682028239964295346, 9592387205871247869, 7508193566177001522, 428800518395631260, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 418085488572984998, 6017588782875043836, 12933677495041445192, 22388036998696773, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12476961836240321015, 1327902338171908762, 12128348805325558367, 90042007091290288, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9489741093134142126, 8506106585676368070, 4189004977614296426, 267561180807569332, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1850799197612542023, 4719997532011195156, 17313427308898645468, 287883235595424743, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12637661580127209614, 17702390452432631016, 4164098421702675237, 313599012336836678, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8489847918383293494, 11490472591559985634, 17573648577728391042, 162418870325251249, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15660411076744189499, 6292274883204292029, 6278815633635017002, 192861546724130437, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9561581251893321929, 3135784756464764180, 6245648995936351067, 192890173834752649, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4692393387592895353, 414391643269739445, 14152698039882216395, 401673740304678934, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12046506823132763756, 3234157638347867820, 17401111255645365177, 381589981843949843, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7200790303955253061, 15209533175674975866, 4381798968221265549, 31675635315559417, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9420091276869746871, 10274463214433000784, 16775012250691393906, 289063893118852068, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7869312440415945038, 7356016458822800971, 6329271451033404927, 508914159409384251, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8501653249920261961, 4080959950196165769, 17960053602043590125, 351728216655448434, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17126937514457159299, 17505140531391789733, 13813923338920436259, 144742573435284770, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6066603023928396825, 14457690111900383647, 13282550725526680069, 481715782648943196, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18427926721256346350, 3567143268310080114, 12525317430438125368, 7784072475426566, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5801246551762253451, 8619453051075142426, 8313902311863875549, 313970070543329332, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17396670322575641772, 6430280777153441121, 13670513367778078843, 78213827799493902, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17470571363422781792, 5638273805874955995, 988962332810065868, 95991719508860008, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1034736289995622754, 11259465955427621302, 17319353756070682977, 389604592535571842, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16478265298902386495, 9005485185873900614, 10794843634783329684, 511884649862734238, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16632283853334655992, 3192732360221339529, 18253954765701578239, 303861953755268263, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10729045205746393015, 3276012746047648832, 11622658952196644298, 423904001570829987, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16682506297868074312, 1837229207514263972, 994663108085692373, 434154725049279505, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2283834683149236436, 14904205134878077080, 18181549957384076174, 477608883777572440, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10080220434584570989, 5428706801612446884, 9056309831112437671, 20812591211950158, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11491422990335102471, 7348721724153008378, 8122640892952613222, 421093941629618889, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8113887107662498397, 6350419700606419440, 3524560597777366623, 363187919452754914, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17058264639888931669, 9929983051847313666, 3772492605768664937, 468843028064622168, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3523142510669458877, 17383213962841914123, 582183908446944352, 329372581631322786, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5213596096943757671, 1091648439335845255, 9889449079371637980, 316292687043913574, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16908031086780524220, 10181596244608699082, 14107485739084409109, 211489715399482143, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9183611595369016522, 9577369529746510824, 17862110582331468233, 108650764475235368, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8828245744855157098, 14825872836798126950, 14125681420462848309, 319096444591541689, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10334272569223557645, 2345177696610951472, 1500706279889330465, 486372832253700053, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8619219679823773312, 16276213895872879502, 8553150866189881940, 327661558517655380, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11015550170485136085, 7311047300292896052, 4158017305649611709, 180844003266927783, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12412988310051911008, 9427725146780907652, 10295216533765998648, 33555543215400689, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1850827504635753958, 4795757300505758885, 9854527139340062373, 326205190918517827, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14458180765091909135, 17451155129104877172, 3742734177224041592, 137213313135484019, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17256371805640170240, 10058659326592183485, 6996861471191699793, 119742132085792934, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9076552185096894072, 16541014821168959001, 1037329421855342321, 413045073197596438, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12082811518378424088, 9258299774773102359, 2279728337945128666, 467864340500869470, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1077741099594007522, 12489172984922862137, 8478812851001621990, 154868610479683812, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15614847751435332530, 11176359012443608095, 2618610733238682608, 246233805833182306, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18233287364623409716, 6804217814828077591, 15801199887910276905, 130443767372573034, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9201353037335203391, 8141401633290272594, 5332263747479939355, 433038581364109356, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3463809294636174610, 9756815165052383548, 2825724785833355362, 127894071404878621, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14836064080829646585, 6031256168782042493, 10697996316306551875, 116187726117348856, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18079692840424048470, 18419938381812824832, 16153484037005049501, 413450868310354288, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2306362329621014719, 13799578092466973489, 10834157994553319041, 189194202336427485, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10335862500219817987, 1454524471528159827, 939039826082779145, 367514103911997091, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6390326966812689699, 1059916741636172146, 13336483312398383982, 186080958982558421, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13799264192008471703, 1187520579288929996, 12702779378300893097, 217079714445177370, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2212578741384904734, 4806706565746900290, 2704628919463158494, 60886810077518570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13170245504239287878, 2374795225572610837, 10215936245644586926, 378417543974004049, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7278092934067240258, 12498354252788846457, 2592900819030657859, 485027336962581786, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3486610038182848683, 5507722579912502634, 7061971123531903704, 494226451557154181, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9995093720053631955, 13918987056718192958, 7075284882389103142, 397963692118798990, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1067978670642003937, 12991090513434338663, 16030902844863584833, 17851378233766609, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12162202303663568437, 5239925287003155115, 7728776327716700068, 129543114384690222, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3533700974891833559, 18029495568064467355, 17447814818193362404, 568236207502922600, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14019999753364177637, 3803128667653880832, 6687452163000985517, 14772468399993896, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11666078877063244397, 6238070875062318961, 16372474862291668114, 127636539524287727, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11450145605873749597, 10567588338322066161, 16811172538506674506, 485292272468332620, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4206270073127487629, 6083237010335756208, 17205771432083388508, 4178223523061854, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10487190104286056782, 13459074958584590233, 5085310847245977605, 523461435051647389, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 657912764705470149, 6172657488391719992, 12452161276590418858, 41688432582074279, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1819484726583317367, 2307989762504891108, 716757963983250719, 429648425130610750, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13569759248702400487, 2219552815915070740, 2636166335352343354, 213050779561936545, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9073947389847755861, 559357678535476130, 18099944371932180273, 253430567175118780, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9166168240307809179, 7267626630440466821, 15022720599423388079, 536102861170205948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10099787400322536555, 11276077462458361480, 9634798254100573497, 249831897942739757, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14162204948625768291, 10535453725699069018, 13433207965169628366, 519788384120393415, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1630580183198827774, 18037624509608989885, 14034503073400668851, 289770606020500331, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7158238976582520500, 17466084711122018011, 18060375523204348512, 358348714844911249, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8701747240537723073, 16953879228633010936, 7057426244380936039, 199595536999590349, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9404145827263967040, 13277978819204674685, 7855598430081726087, 364356992611561938, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15144596314549588447, 3431297115228846141, 16297364010151361441, 42172657580077696, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15216255010112511294, 11011706007525913172, 8192161061906388560, 285739262761682200, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14772737085393469786, 6369395316455826088, 16500506819882804848, 246802185769551234, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7291720882098277244, 4136636837972663676, 14346589887702417867, 560033584735657478, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12131511905809073883, 14090926442679353756, 16668122267287215719, 130042540004640855, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9217391733185198099, 7148386638145606627, 17015291173345553941, 397857137442521601, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11476005373020982955, 17627504251231419175, 3998789151281029048, 384545833702617226, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8967431386265105513, 2868384530557921647, 5120127995071388611, 435567842721136126, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15548781562717506603, 15809952009853449332, 16092980841101803426, 50397560917196697, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5239374851322936021, 8706751466102956520, 16253679747842063305, 311426608491740598, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2244545014136652310, 11898055382208726314, 463249067177630355, 355019080150017493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5804090390913183160, 9236591192728846259, 11073322230124378501, 571654701983379284, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12790276434540415848, 18312264727420897883, 10813275157679536884, 344657180722254699, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13618061957426024675, 16932622430180060409, 3470000664175873591, 261833822788696505, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5210936284446086710, 7322838476534304687, 17773782935471847354, 182140455800677752, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9667686233119689003, 10316679532209331717, 9451745333322688482, 318615112461755648, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17714376296024452575, 14294467910055320018, 16869473377640117913, 455508079568585209, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3800905245684872448, 2647269798387460783, 18148584526973943651, 64188603887238403, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17604292232481254661, 7166983434666241087, 2242153109347397384, 112430125490659947, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2114489305717479879, 8034180912422610240, 12653080198662082596, 430134219659226085, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4638101242187574369, 2026052174060993094, 12538090475175146686, 1394134534672430, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15272905515130758396, 7740754165781175316, 15470496122609710705, 534007628833544654, }, }, }, .y = .{ .fe = .{ .limbs = .{ 710225575955586974, 13407343815744315291, 3254436521040483667, 346280093760703561, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17079541752746566530, 13730452703559725824, 17931434868352436716, 383514479022666140, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9471628783225343082, 6272822550145160680, 6859234081031584521, 214174023519907468, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2783188059635271612, 10965920886060238852, 16731812255241285179, 16886674654441045, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1905787542523088626, 5802830335615593075, 3560676423738883110, 252073613535976637, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1813671267290589542, 12588905877195042878, 5174488200993815280, 72930295283924155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3067056268266272642, 14833002999999732525, 14096999927433355402, 64851436340147665, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12187940806294464184, 13288094559345448931, 1245486123087444228, 185697263741093633, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4587198761115290198, 11970335968245118886, 663575796995062619, 432260670371425858, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8477263657783388088, 831622444443718415, 18052976516489205818, 64644666853167791, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14162215436135154817, 10977523439699896756, 10355938033089606678, 378856180733477383, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14482191439109196608, 14337309791275181677, 6979773212817711638, 459054462839911070, }, }, }, .y = .{ .fe = .{ .limbs = .{ 990972127060855155, 9190518823010448209, 4543965389459629607, 302298783459303396, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12671228573221303968, 3494283571362176810, 15585474110873877231, 218880947954351707, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17898294007534907461, 4773402326540918158, 8577778116697972430, 257103111306324518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11256138271387609316, 3567835614282567372, 3809835818768412517, 231229292308142374, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12408945525774464516, 4028614156859850345, 12743720999248653872, 64350759342654473, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13660559998827312525, 3748714980285709109, 15079032396802772787, 49029358268563674, }, }, }, .y = .{ .fe = .{ .limbs = .{ 472430178059514691, 15919217113829500687, 12671921168853551982, 366659818500234263, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 818848960565390553, 6070681590954279536, 3323789200917376928, 428807348764694131, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7414948941682198282, 1579608988577211890, 15590503003068860529, 461548509092487842, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15170836834461085911, 13351769557789774399, 9422133345910645158, 272766658371506731, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11681620253279042667, 3026865197808032764, 12692690490059351860, 368456683252739290, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6088651875418321649, 10577445542485516929, 6055326290758320462, 6200049121300161, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9499107221541914949, 12498151551376394047, 537560004912635468, 161743085733251095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7975803846682331345, 10999921910600315146, 3639161056915604498, 370765723758935195, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3684013848851153395, 14862672119676577974, 12391240590458208995, 496678911871006829, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4094657149920876235, 11173100326529686616, 9691877320559344282, 33413423991871204, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15493285259959772657, 8940066418090471503, 13123920345854615265, 250159258766826695, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17921018486802185000, 10275967818454321187, 6360999267560649145, 59264255986447108, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15349607240485667589, 12596791154569934910, 16983909124382038436, 459825745399754997, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14656240340652604805, 10731029630487021311, 54847742754962833, 98185677124292390, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7940387477249587438, 14359186495577803846, 18237511232545007725, 421894057901392536, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5233000449446180149, 17881820251730286224, 8992462628101412456, 140338872492312788, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12412583743738071850, 15914463618703219387, 2975669310551158142, 476670892281967195, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10799811216760477868, 11046605544841105187, 5852468610628505773, 48110907016750771, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4653058373231656286, 7517982747425905193, 5297946035701942196, 513151702806833011, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17719159782554552366, 11681295816293043107, 12893100648597619127, 382209558018408039, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9141869935115456617, 9136499170976908420, 11289415291351038624, 238827726725650731, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1103447682771463252, 7933565780397002559, 4261531873996211787, 177996842804332150, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17288130455644544793, 9731526375696130968, 12347025719585918808, 130011803985364124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3089382768959958579, 12773267431485254127, 11197064427408184940, 484129773566792039, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17006385672008882597, 15327375025484816170, 13469122484845017973, 281825440877299259, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10247406360036252715, 11965212112825588083, 6099679692325535471, 323677023013733627, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8333619703929593581, 8207992107231956404, 3530441989962429380, 22116685361087526, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8461971943621530779, 8356946144434177193, 10870389576642472873, 183191915575715647, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15857465816442432451, 3646810366767692992, 8058030439921833902, 284237594171960401, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6628592469974089427, 15949817365541463260, 12713758201774357508, 228775763103681116, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7878932413053605840, 10146281402556682560, 13345021732957448190, 288063334413447124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17154783571354485489, 2542205157494276548, 1640123881584042045, 22044476162281917, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4332792172067821828, 11433733217679561658, 10545838301615042660, 460692360383884181, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5538893628069080616, 1569759772385988728, 6042989628128099325, 151900228063078662, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2709044034702006029, 18168294905944890394, 15319942225743994643, 113276614685223173, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16789945964570010342, 17218838798776708311, 13992879790000943760, 484347014321891318, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5039617540246648992, 8255754775293949607, 6391910160718315561, 464643228680235913, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13146622383900841440, 3063662349463757781, 8515564177845669057, 224180128854190126, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3585979060967842131, 12322280569532246344, 16287864921930252224, 527190946910415026, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6619905083056538540, 13033234920062376163, 17710756897791072972, 311696024509889411, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13046678352476503129, 10061452088102737909, 7153770766785927513, 59509633550250340, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3896398529683574377, 543012859046617575, 11476112527032425197, 140967205199186677, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5425850598289979450, 12211525764575191919, 8296253755316238556, 554439000035166180, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7288473212619386100, 14962866603698149592, 9372723512555966679, 536101499886137495, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1147358802397217279, 10330937526810921942, 7091883305167706050, 536687317112996568, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6676900183135822289, 7560277405735299263, 14168858996243081946, 96260391431528032, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3898061367588749417, 3426813637818024563, 16986800465374190204, 564991061519280518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11957874130445520696, 10289982057970345434, 8380836065924262500, 135592431801785330, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1471537469710252672, 3453284586479349747, 13386357964884612210, 143915832139081063, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9877176842661004019, 2493212190578959097, 17771425703362309528, 322094216952057240, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2762002861246862264, 15297861835030548686, 11811909654349884438, 321812099855284593, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17921377929085711714, 17694416529977303489, 12089546345251940425, 398171687221339419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5283652764849580390, 14955070304943943337, 16633980500250794592, 106215700698067344, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11617619371071812266, 12374140856063088500, 13077690855874054984, 328841814859027704, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12620792904103817751, 13473293446465023523, 17617212336850291381, 332673211580660485, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15910526439729959780, 13874544930631926961, 5917908358698128987, 103039962672229059, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11370249872274582093, 5561058890300023453, 12480158063391185747, 268541099266450327, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1416681474569494234, 12766382276237347404, 2593157902821360076, 110368499774069803, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4682668308198539740, 11875190337178151115, 7196121822058986202, 229111184455562434, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2574226666604156923, 1938185814959683607, 11800031831237682191, 58361089837049912, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17076182864201161271, 17518163642290245595, 11133752026981918790, 190142974525657863, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7259820380518794556, 2447183564138537633, 13319460615492520678, 37073012344714067, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15151776912475023667, 4936943346217763179, 5773420235847001167, 562488657130213526, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17259995648375514267, 5113245305044049382, 16847695358518702150, 289624152342283813, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6360726860509293159, 3829794896577990968, 7429511242843817138, 270743256527066374, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17977135278781556535, 11014743808675892057, 1210028597454819311, 481434075164399434, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10821187454156603974, 8428078575679784762, 3482804123222685162, 373661272976350907, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3442959158086084614, 9843057499396278937, 4365712337176902003, 238246484767757169, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5592325730444277915, 6467576624146470760, 16182931413643092301, 276763981300896137, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4384358567460786141, 4809420605113050024, 2114999194317898808, 285185797634226809, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18372250830587245869, 6842817587915912106, 16984639347724462430, 211699887861405674, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13799513050911057536, 2590461638578316014, 2573376572269647066, 452206322665487360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4508436034176327072, 1008471363573869062, 13299994836133739894, 219890763093474184, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6832649820950921050, 3845329417976282843, 2087265403479195490, 501053833642518431, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6459621523945686825, 446496192313891417, 1614780136269823264, 557429596652436998, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15870105195985582449, 15196291145586648235, 15552398151134021743, 9204348470612425, }, }, }, .y = .{ .fe = .{ .limbs = .{ 326455116620545585, 9342677737527285423, 3266068801153203351, 384965668587845109, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2896970725654075560, 2285627418290468350, 9027264029241134938, 206302728219480560, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5510260442138664896, 18025825627762704350, 2430206568310609586, 292778177636133066, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3385575925550146282, 16430102864774845199, 17920886836503862891, 133220872063990776, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13646327798137753240, 5450797926919126132, 15626440047933840311, 497912906421357071, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3739100411825964965, 5061200887972958999, 11214607972752638320, 390239545273543370, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13183636395155455688, 4024212394381546699, 15114575797106607930, 347455649364349198, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13067242252360510324, 484574253151613643, 9433581162354479516, 145104778235164208, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15420715916036495407, 5336867442851446172, 6424609668649088170, 394919721509123518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10544622534701546458, 646011323718272588, 18089435352177355886, 79526626245867688, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10450970989559943468, 17072536393588987109, 49166172402521561, 162611064265716495, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18290036167376435835, 5697518241936083252, 15094751735616872564, 237344791305647517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16134859735782091091, 6033176468565442777, 12170132112886153355, 572766275609942201, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17667314761096453108, 17271169269607830432, 15041285127360055276, 304046531747451843, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12434671690347908565, 1489506626083714877, 6296589168202809778, 151161960725330007, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4568516592108948177, 9180660256382589780, 911926500323113416, 84627093858335434, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12805294138683548225, 6965458906094209125, 2142976982549625445, 444566758742179065, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8794234332340252385, 4913972877346638379, 14667634447114138719, 301205100290705458, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1371277708236544672, 8225404409290003685, 17597288429828495676, 206167311585992832, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7592169179174618393, 12347913780381280539, 12428473817897356978, 476961083088832218, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5235574574356954642, 158275061369121530, 15175537501929119794, 576121255022780647, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16642043327919550611, 4034959082451630621, 13489716091716111606, 9422258277943427, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7029000670346792125, 9987837392227349008, 17088710614869672159, 479663276936738569, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10546294782813134492, 5615022822002760853, 12412807534230330666, 106225827798018484, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3050200286562715170, 1380331087389840848, 2464131262298216813, 329619839031527189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1054090983649635360, 6004253059590525804, 2302829353319702604, 320509615373624280, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14648240380002564070, 484291375586655955, 1994112388829928839, 209149462471398749, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15782968248884197313, 4609012873316991629, 2462152325477134116, 84106938519964878, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13271806123330742684, 17958526290807196937, 5075341967615373348, 132611931834713473, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 302071270258883775, 5411169406551059859, 8595078007693022667, 308234838324561828, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7953653599683852675, 7045508786824303994, 1420198532828507552, 461346643044001267, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6543813269245120105, 14561760611881389881, 7837494635680727646, 413769022697702487, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12088399683109640096, 4106774314920530676, 3562830684587061932, 73382270209894611, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12869599128105061105, 3788548413040138993, 17746057490059799725, 393499377026082826, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17443462718056955939, 7842847213371421837, 6862193875625710028, 564925960789172579, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6886893540427542623, 7900120655872771283, 10789409119488501334, 39257430123854148, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17137677894307952179, 16854361597904605033, 14851547120338662113, 373628622595128505, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13498142790003015476, 16729313217685200027, 10392141278258578264, 395763229794316915, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15365979635396295763, 8944638775834302036, 18003544920056806131, 473193451601551770, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11882930742831947147, 2213839430776654055, 13327019724138311116, 516681140542515321, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5965659035671138086, 6287714994863192111, 17181116718404094060, 336508315875698017, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5375436822007346508, 2799906133869159224, 13817602380257379231, 367082678776161128, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7761086908172825879, 1423241667776120676, 17378566098122852060, 124021301934884569, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17202247621856916605, 1303879953725013311, 3625648138219134059, 319843718940262678, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3316593044432927626, 13637605945596930694, 9213547739939381523, 136106234032311506, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8897238597103463764, 16178745319453788160, 12882148517137647770, 411234465979990512, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5832750894523063151, 5157342471313516017, 2122716964666591681, 534818818983599539, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16491040555268884797, 11224439492631287769, 3622378006242194495, 49699746879445870, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4497245591130483478, 1699010666105527886, 2401508689659918055, 456771749889001825, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6204992572296352741, 5596772244083804784, 16901133267707975307, 186320927733335820, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7973050515889345157, 9070282857461353563, 3954983096236921231, 508979677415251308, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17021239526239625992, 4370140285525565030, 9038449869112344436, 505727395415348782, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10019531165662585123, 10391513370990080823, 14446348530412321039, 420009497691987787, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4026362766475546294, 1949779769025198049, 18263726428496896898, 42799062236729097, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12921741003782674393, 2015162489538751377, 16710775422486346855, 346036647265087500, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7322028907819632210, 7161255128298438498, 7120076457254366165, 448130405614126254, }, }, }, .y = .{ .fe = .{ .limbs = .{ 271656601376895222, 9119004566807573867, 6404368715254509889, 371928118998619433, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11715730728876465889, 16218355608055007684, 13743311805152321149, 365267327391268003, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7534977821016117787, 8494530260183690881, 116251399733521489, 112982519360990904, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 962826936156701600, 12842641005189975855, 1808842135951986533, 298563196556894090, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3345193589916201287, 16794548358698763243, 10984494370431464723, 375393505012850918, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4702474481306201537, 9122467655642606453, 12124866968565114794, 571613406245503016, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14747128198648099174, 15064844111245440778, 1830881278598814544, 23565427985806540, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7437147145054142142, 5578438522592985422, 6801289436643042135, 146550132274368991, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12981536858939672265, 16553964491164311378, 1889499143893926654, 374873445147428356, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16246140381046272756, 17986662018521918796, 9361620852713256276, 178642477504854685, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6939147760689555296, 2206993353298275671, 4586306247239302599, 337206639278996397, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11397493698290519272, 15084673241253065444, 1847929781874658086, 143034366951934117, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16497593951413383285, 11529874131705347715, 14990545136298061079, 516254795766666848, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1886337949885197020, 7016602582562894302, 18414803792406312627, 166063419248330156, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3583479262715210845, 9482038000324759275, 12364377785373064427, 43964259694757601, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5152842313865605402, 7623123219612055796, 6650548770026129214, 376597448788802360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11551069313307129723, 14778641677810329796, 2653441791244679650, 564412379462782811, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17179417533192628416, 3187161622319893341, 14679566881691209129, 455178666403901631, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14719238922493898839, 4298143347571710259, 5839597452201148241, 142840847210790622, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9712826182351353172, 4602599909750896901, 10229598282576224146, 264023829326456155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2318295924658029030, 6844048233638772470, 11195233699327384351, 137509404946369863, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17833211693221784182, 17345655250303165516, 5782398434760353274, 566309060461286624, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18304231978593571258, 7359980812817647752, 7302897918464907292, 30338490126884975, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10521648299231327125, 6158131428640798883, 4123393187132551332, 501085079265595442, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4266370388643386733, 11617059511822165168, 14116703655149696458, 337787152278164474, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 742759477757114215, 7924464445198608169, 14463246818796703833, 573612785920202613, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15845165102833080990, 7009187323778817718, 8337193447670907691, 493321628017591581, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17548209006934079353, 4504171499705412645, 13246775540775956708, 499316120942848174, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3113414052311265098, 370209004098029782, 2035116459943969540, 167344206445886133, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3400883644215877870, 438073050201204844, 2598804240949688361, 347142865581529916, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10480735680020753267, 15388346495819576972, 10648668583798333778, 238178445802524448, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1210268042755441864, 7419302776314326295, 15253920230305207381, 128374678267994362, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7215610759578900948, 18263365918160079652, 5294662902052230190, 477645686741602334, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13251604400501946139, 5445230013590417288, 7901323446774742705, 500869579816008163, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3447009755292656954, 9053563642101696771, 12381129423555761549, 333478036466329362, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14061065521891010000, 1691402205321715114, 11022998248114253814, 320750783981591575, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11576749888991901334, 3065262215201501852, 2155626467997346784, 357007685209114575, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3017103907050510651, 8934494066423825284, 642249118915844959, 519650147803127043, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14071649707137919146, 15641880407831564909, 16583613209127465449, 33689084853214753, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14779088055182458029, 3130956182394565903, 10782919918375415404, 50746365843156915, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6235145504477058030, 17553187279770596024, 2327759728675713388, 194345937038787535, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13887784054423248459, 4499952561254748377, 17128922621296976575, 367305420996450693, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8662448969075778140, 5792692313834565258, 6475221495861822227, 381519338935906449, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14181197660082525198, 11451630337216023699, 17447499578112715485, 48450585911187848, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7032657413002962530, 1313676039183782072, 4402721190648767289, 309711320909115316, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4378893475162963554, 12829553711135310844, 12931328814461071026, 133377263001018647, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11680884260584623460, 6597256861072187830, 555220470298159500, 84458068268198704, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10279317357672493175, 14818524521743790590, 16224425916644208756, 81849637811466774, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12529605950802299462, 4472637034397135596, 9957225946405514768, 206788636908939240, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10346569574486712585, 11145952962317949224, 9101250499502574886, 156765306934548705, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11751201311680843403, 3824007793514802286, 4300206360930590927, 415673954626888390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8155178997308467151, 10114244833478610876, 5632945156650059272, 345504904387907386, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7490201073995444012, 7847421866758944684, 6806194879237239658, 431389814602602462, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8341081377069111059, 1849857853023616987, 13919363092132121675, 398994952890695852, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17596185798054137545, 2347353832890425061, 7247490340193768955, 354801293534796959, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16648947085487939379, 17753291905926701747, 11522781239953050459, 474042875574542840, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17889867458243410233, 10954180372441273663, 11862699163873514388, 191661450716927311, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15332565256579659650, 8854674155359752606, 12536344614023792408, 391658282087624816, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17913914406286001178, 17767845382721654525, 17088882754062688170, 88689624786396691, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11883231574900606121, 16223549695635614257, 447958398919072520, 321189065519287307, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2004270137514057696, 5331561290597267412, 11310833820772996477, 409708817703036417, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3362080833133643325, 16133774404000462478, 9496091996058837871, 470618418148336817, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8679118905789611662, 3880823876137801707, 14496338141970514027, 444568589973067928, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17275010612009932854, 15309558692939439181, 9806309884227463200, 96531783044483341, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3051760658572433383, 13958033867171029236, 10800414558817428807, 557107417520419246, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16169193868986078958, 15000798996576289975, 1361386290427294538, 249253837169774056, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4551364382968481725, 535500790612828601, 2667625530766304088, 187268953956285495, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13158039525982990142, 10307779620630145793, 11188925368142595426, 175924951529991521, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4910881750925358550, 2598139467540220225, 17574519683874490083, 358361663959496839, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3585571415968032499, 13282790873993706754, 13955105667030010911, 384953540042837254, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6769454961424613229, 10843089127784307527, 2731041284244913534, 200527829589847342, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18062733057981211903, 8993470607816699110, 8145374684148802025, 271537324411506120, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17846336480417568314, 77375440258155033, 14754562302280565294, 319307231133151808, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12279580901711110572, 2792774237375615203, 5260032083983335945, 488778531554923937, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8259824629472910723, 3361224972619721967, 16132590763255747488, 279754914735674544, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1618484410929438678, 7774090198359306408, 16499495212273942193, 37053105652856501, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4552973249391240832, 12328065633848892904, 13971793281975698400, 361988487386751819, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4332942289343579077, 6500945240602321777, 9866483590564674807, 296696804704584968, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10785365952251318102, 1817879224838994115, 17371880994342108330, 238107844943526323, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4406565875171968169, 8341729089088005271, 10477723397585731496, 437884248171936103, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1130177751932364923, 13904406886520656116, 16423970734792065986, 562792846090285792, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6938034585260058107, 10062890980811805814, 6366538639807541162, 378350154998928189, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4553734865131907141, 13240965581473812816, 14252700966351773893, 273764638692671108, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13177435363973566544, 13882298789326237046, 489092277148458351, 138689453855581124, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14129668811015098299, 17960018623650456531, 615476088137510990, 110670777560967147, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9838635039415562956, 2468352163575661723, 2351480023122781526, 393070095812862879, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8430968733870201685, 2188420886382760088, 16128148584182339871, 8616031474102853, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8667750312205721222, 330040945125475840, 7781808076571566719, 304917943146247619, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3673161591421587223, 17648915608890420742, 1202986806207449155, 74529715307851268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8560047375414405155, 16022580704369903734, 5448037743102349300, 524368077596924996, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13449550207333999331, 3144275334487652983, 13786101926110235807, 233283234195069937, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15192640977218456683, 7642830312317606619, 15497366919002118929, 499733053510738730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5454785631366687934, 8178147644786657163, 10900568974354213235, 158216029962083002, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3387472154715752571, 12251432187319768584, 18003579430082991322, 360665583387882832, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10104778859243835515, 17069495997647322467, 17322744862319552548, 115254888524604621, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7693974263721678629, 33579516692986597, 17599822775049162749, 17075818186494760, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7218684602289109853, 13625679128197645979, 11367334528124202222, 11027673750127095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10845181445429504940, 15918313605051391727, 2063915491664134710, 363490787497123202, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16130949961218543358, 4121750380406223927, 11080012123398019991, 410374756180643032, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1951612839643817407, 16803804550761020767, 4258565536726969147, 215289940453340561, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12217793646097918884, 9468239637552779068, 8330919068754264897, 357901566498319100, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 164778104826855993, 321508845688829556, 16749084605372366783, 45628221949300156, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6676717686726500654, 9493760103108196808, 5315660196733217567, 315055773559426859, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3099026458133313775, 424581470853922619, 15952295062938682260, 304297957625763670, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8879238221844920221, 8972687194310210698, 16937266460226410503, 219879306648196614, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18287983524161124137, 11519155379021259903, 2961064715392553992, 431115804397153992, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12526982872223846415, 8590820089100462641, 5020845103476367449, 292849345855443241, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6645094037637039426, 4840242258302774954, 3252645424280600731, 317818804160745785, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16868908404782584996, 16255476469239851855, 7960176611959698497, 474016109291764811, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10416582008565586250, 4763865685962808578, 2449973517710133290, 308352662036045836, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13019963208008955255, 7654220594267882124, 9188130438088749859, 88615401937751310, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16399701700354136372, 11319296735627748715, 15937467159797045094, 386096940047541435, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15621439681881463775, 9347452677162580795, 11477572655269988295, 425260523763117830, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7946172231941701644, 11154757750204738447, 10587612014789242536, 483453846612885712, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3251550140043005359, 7460299523411100032, 11810071048003648734, 259543516102122538, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16242684722187745975, 11761544596793948156, 12212939885078564712, 530880152374408210, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10323447639648725662, 7284677702720746619, 4022738276111528679, 400003187964915925, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1017763025475098688, 1722769082722144801, 8505337335100773180, 524524869682664426, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16433589241172543483, 14691824876969174172, 14628503564028006170, 434436150147148465, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17516859832988759066, 6238034585368941619, 6588434719544249897, 469627567803424542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9598725994029629750, 1979045562949683681, 8338798724027460554, 315588695211050178, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16743026603249202090, 17837588755517845739, 12439831911057999975, 85973201853148044, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16163833704074865011, 7209731268798336169, 6958074705137452833, 163095955740426852, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2492623358599966869, 13775036893164634053, 8835752708761277770, 327532302877043920, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8967465493069407513, 17677325906633175988, 16183318956608745599, 168499353996625353, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8903525461006129974, 10700825485841907034, 4850838800683690291, 555898555351515227, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11732571318979429518, 17248797879810637498, 1310982071081128858, 156024184040076018, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1452207247371218543, 1487402757956331171, 16498464669592406052, 311263151331928966, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5892431030826768068, 10201159998730982633, 2100420282776814480, 552606882397142219, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8265683647023886592, 8828583890052498477, 14240726955799604071, 440987703621843799, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2707069755039256871, 17718324916943110659, 15280293724324786296, 12801162424664526, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1031024804103653153, 12404465784308256106, 1721056621794553844, 560397858124569255, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1272368900520713162, 1423225082658803901, 15586469632321566227, 397050029510556799, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8852988789146884907, 17141669279513341774, 8354465433411050453, 6780555028457037, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3356787538837995884, 9726772538279380663, 15513070064991610091, 398557541829672687, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7089948823017866941, 10759143190388377971, 5573904031189126225, 486012874927841306, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2062281257633071695, 15011350123262823634, 15119613598918961540, 57347136892796589, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17186414569529823616, 3333514848075315682, 1650135900299352559, 527320748548279955, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3323525013179003183, 10350533905515764475, 10738040509005724059, 52658888880998624, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9338503405079570482, 10547742759710574202, 1533251289157499888, 377869308954513366, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1843717550840319890, 8676524530043184491, 7199322384280770945, 211281119465125882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15605780094917162762, 1254079408833659125, 15933414018241701440, 274231003128302409, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8644276852918571025, 3945300354729102916, 7697582069205927570, 344105700127112927, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3949470543563863211, 10239432404489875923, 6173812469680117655, 426779965670913208, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7152813859404957034, 4584486019445055784, 16268688761904500780, 324585966341354699, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13486358379900695014, 18300019305994357449, 1676744090773243040, 371626977813700839, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4442432293263725806, 10504479973294757868, 830434410923652406, 346323085455756876, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9297829631503583551, 5756202224624367808, 11807404236848666982, 449469966433364303, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11840462487245744217, 16475676514290398395, 967862074764420065, 532927259985647163, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10775011944647074859, 7176623126845579881, 1631354793754077874, 312893274476288444, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9519008589719918764, 1511026744223622587, 10998936462083593265, 354153526501355339, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 700181679368528816, 1756698401865861304, 2822811639568753494, 148691439043986168, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9381786898783059186, 7929272233967252941, 10937408741249787935, 500003736865782672, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1516105926241558333, 11177729025499609901, 9730198679419131846, 306135881319352645, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10405119986103005164, 9463457674509028076, 15694464394928498341, 347463575586027473, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1933801535469622521, 3712380893878257966, 12425082442529672157, 331062443199657687, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16747969358087982133, 8509566951526415754, 18208819781495656840, 105701115436545039, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14527172600281556537, 14760694585795594485, 16535500481906822391, 197686927518691064, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5384877355952821392, 6094520071288229436, 1458411049381943760, 178461788641212784, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15148884544054262031, 17835123790447925755, 15977013183731180607, 228930692689968643, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7789070192825031999, 193527619124898501, 8405201860516888188, 411688668138810153, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12347923122162213674, 9252768163088763178, 2633883746737865337, 10119019525748806, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4217839633525681650, 16553850181866204455, 16518358755262303654, 240702953037510037, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14972014998466054540, 3589789253194742926, 18150210762642607793, 543921334353196588, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7857095322523310287, 15788232889368777924, 9247150144248226242, 235339098311715732, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15019501136600652418, 6957586065247869594, 8630794721336203402, 424756050061469694, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12701715986692734965, 1672492196813358181, 14921756224956139558, 514963232038461941, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15720490833890385013, 11796842461324997934, 15988968706500284590, 43077691219704257, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3546077153218011824, 2545061996939847991, 13228415401660345259, 460645244557728337, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2006063536729200235, 11933529345402380244, 17998772046796378677, 502119717368425529, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5828060251630833082, 4242040339399200419, 5537762046540518014, 98777633520009834, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14058315176337395292, 6902946088673460454, 13220076103560516250, 248866099284600557, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8582901022071143805, 7494253247974065715, 15207015825328454031, 26574223449994574, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17598079942691484272, 3122723129589928484, 865872693307105335, 277140801665858436, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18064514587537332835, 1068418936230891396, 9105758566791042162, 183265284198144421, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10346994579178953780, 2535411822176089536, 4302026194997545840, 323487033959170112, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13938148667058799844, 530966867294664946, 6182666154334192422, 393017274641372303, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11461810883681012502, 969296708473555972, 16065417290254807163, 442542738520476015, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17841652895279614963, 15563574363679706293, 13556114024215608230, 407767933475255036, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4592817347608487007, 14742329847762694342, 15170650491078806162, 193875288668540329, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18250700015699792540, 449615038283984863, 12928343420146784537, 499645801065168444, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2449667921754092398, 7430448426418535434, 8889100052400200074, 70999054235248090, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15465834881143636401, 1068240842072932261, 5921489543585279995, 255277221207698011, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5547766345426898863, 7454002990666525669, 15025858443366003898, 62390046395057417, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12089404586506629267, 12049620732402343214, 9586315088979536083, 562201937945940544, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8902884160856772127, 4424571130823441212, 12381176845462668753, 317705438485502925, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7629981971989240847, 7599929965411195109, 5283724663227839607, 57104477992113534, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 895455514719609365, 12409069073442647135, 15606348428225469083, 310559651988683510, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15842111680279382819, 5020692775729352379, 8413033767817883766, 567165879570270095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3434877860254641006, 7147080038950088792, 11328321126907732798, 567160744551489339, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3316206772231981973, 6163757933058019121, 445223816317259012, 87532490560058911, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6624403451993836795, 2663179279604686927, 11228747352737445376, 91306942150639183, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1333942423152346044, 3658416987701631907, 6387630511097732352, 525947020671081363, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13119040227704065872, 10283296353837464260, 14363684659976267214, 499979166720530848, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16951964807540994336, 17753642707540836407, 13662921661781501837, 244506428088691314, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18286588436953453724, 15784433409935521410, 12412459337690903522, 204687763782616877, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8165693520746800969, 6148086108827940365, 9391895016798958319, 186393141674280857, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14702858033796855326, 9893351114446777340, 11328070595078620873, 407897065069091930, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5192978873332007384, 7580687773087616758, 2524441879673879694, 209510025355692092, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17819780007140367746, 14285946814722724052, 603983225301862716, 101458199834350188, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2720864736431739151, 826585506947670293, 5138830491232664443, 186728371240031437, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2542523291028390625, 12797582513551494798, 8410825624288279999, 408264880030734310, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1286947473741195596, 5365026244745929139, 5085632248841929931, 365259946357077958, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10318443300084758415, 16814129589342467945, 8921191065941759510, 468202364498239443, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7935653029597411107, 15934937921545835233, 16499455106444327643, 403453169832482429, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 139932788166681856, 2584348449226764018, 9548292530736478460, 91307828244512091, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4278852509947851057, 15226405418560825716, 11307665667783175491, 47713075941973145, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4982805232388651728, 3267823923491293833, 8413905575552083860, 181951949930722270, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15915561203007933311, 16229126486737786182, 5212680583465461400, 266672671137380625, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2330644698460047022, 1830510293903313505, 17877305671018396902, 16195386937125093, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18159289292975818913, 7441120343547617276, 18343586738739149244, 4887408480870904, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13172788340609719151, 1289891628020538798, 12762181985307371009, 529209329644583473, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8389496564379993821, 11140433081507496282, 9380951155602491721, 312143834611925540, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6911972181952037456, 5251626075521301195, 7835325749923234122, 225405645744080420, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11372135349847286575, 2222892036840637250, 9710122672004140468, 4882361334407472, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13509779570389574930, 7753622119491471523, 6694865129924265764, 267412576436445610, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14116580225365636619, 4038322236551546133, 14863238782715306097, 43561020554620025, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14195951030037122807, 12970933161065187340, 8788922280221423103, 212786906992143582, }, }, }, .y = .{ .fe = .{ .limbs = .{ 115659089583209164, 13694920124793076520, 18122410625591098334, 122382481978301050, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16638561509661425354, 4501138184628701725, 284987821376258557, 93229949273487504, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6936379066464999394, 11228624214192992999, 15951514899555202108, 256088782527961123, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8460871833073329643, 578573575109327669, 7000828846209463965, 548673288093010905, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10009808129927334036, 10321974449403089158, 17539397174096355485, 447284859420710351, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8076391972439179468, 4357745794691188852, 17053898628138057414, 399895273542924220, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17442982684457476557, 3892735810442876540, 17130774802490019614, 246975151415353660, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5063265591616655225, 4141484735329507592, 4814730896618582657, 326140102688018955, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10030725824244561124, 9567925599727793820, 10515759630313255177, 2900017181647301, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12736476279851936551, 17408404223440570592, 14398677452418903268, 237891115485148181, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11663009722319540395, 54803221150519506, 3344271157654422454, 408436564205249930, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15651395678138674794, 12415852777537312168, 15671464940208083906, 570782102503974892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2612746995254321122, 13154359073489652552, 15912817457503655043, 50590132705440403, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8792182905818319553, 14920907534780151844, 17968098188871531007, 243091546286024345, }, }, }, .y = .{ .fe = .{ .limbs = .{ 102257238285393067, 17539526180638628026, 14229325505386184849, 515043410571031006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6420392003535654022, 2990733376918921273, 10654421944236200981, 536904800839329063, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7250444053133256470, 16528774657064077840, 3280861071419986167, 482750341493893157, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17138309748422861031, 7130694021550976239, 10848433001588836463, 262961699791269215, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1913556156547728947, 6643642499282330560, 3289948086812649389, 522705325463464635, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16629601929336639060, 6248455088143190890, 6690618813624305210, 534565555709773, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17097626003999817648, 10022935785738625523, 14968836350689836889, 552855690075983298, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2390104098425371137, 9945308228606926081, 1395867215002504847, 489647687861586856, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12459532955446872825, 12293588985156667683, 1669349282542356604, 3749475715606478, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4505878729237813674, 11308354624271000004, 8071140592441449412, 132330371007849282, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14638335848418816456, 10159912428009088438, 1309992775604269677, 402496683909843969, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 124743728134860226, 2805357933776208938, 14953912399315797591, 128977671488224042, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10317206590323800992, 595075568603036325, 8111508218619686342, 314582175833885869, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11614242505459576253, 9472374006962441620, 14723855232257010900, 520895631921259865, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16704829518855134347, 7154349547776324306, 8147447318436438885, 515742600615698696, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18310378591233186225, 17044958429562850333, 5543692464854250733, 304537319156861629, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17079463945779561684, 16785839048682683122, 11695375954752553626, 14516272941585094, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3936503034718399732, 3089984681271668763, 16489155455366531045, 408995872923089370, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6393564762873268922, 6245568971774888408, 17969153330714992149, 76393626610104949, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17988840237315490012, 3955447440533093375, 15645745270776806629, 293183847952480647, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17998522835873887494, 3073852167622620853, 6099355819735920077, 387397484165825601, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1494103255496409199, 1833103195045654228, 1035858880403276751, 530400299808819972, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7298043057810195885, 14246255964843745779, 17139453508280255864, 353334076548866156, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4040357360693096219, 684046132956235616, 13911804675569252841, 200723450921813105, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3343438896786227613, 3772097761910247923, 668574746165175759, 433547789867961538, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15433147095417010929, 11588686596740022784, 1797455940284220530, 261453668069596988, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8395736245137817619, 1379361797736650769, 11793364897943440782, 488194946170261084, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9496827393987278381, 166629601513809179, 728210306545005999, 531483631878974628, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1680905899707095378, 4387576555033223193, 2125189972639208489, 166883483858584587, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4587094060503779957, 12845537250359427887, 4401445455629648292, 282818257729363897, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13289643885996445381, 4793338286521729787, 7343399098175866617, 391222083855014634, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10042147541890936005, 16566767979290091164, 5599781911046954850, 92176637036065697, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13010651042970098053, 7307791912509386223, 13272386663330295686, 554168107796581483, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9894484328210103550, 13867022138285170297, 12926502421348664550, 300210158399643022, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7519969814446784467, 1891449579261282684, 16756304586319730700, 434378873350660016, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17557907043690250836, 15698537203321909100, 14537204971581685916, 132385770999712087, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11093093430440911886, 13183667688783122261, 7678024513844017340, 458632894119665993, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13038559325097185469, 11351095728630010, 240802986846089113, 213908569028525759, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8509191973541416372, 3910657279966792056, 6093832316634416151, 236668352762800074, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 967218525833742881, 1136316969114429212, 13128268772737294023, 426815242763361236, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9360244320066251843, 13011030080610242722, 12873789004603274616, 36143564688053898, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6686704063995796946, 2983915449309750136, 1812978004237783673, 256684317616990273, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4886101414626677746, 16537409949997952886, 15046678497732690913, 412803575712423518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9752170768778345500, 11180044155633572216, 11872786344253847789, 299080937492323965, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17254355361905261904, 18203631627400306173, 1398538151822892843, 53714286108068438, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7621965980487315598, 3741208530835332397, 6300600476713147994, 131919433401203222, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1837136917184104627, 18142347019301949970, 6382382821469022747, 290762432412797679, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 289478378848778779, 257155352213256131, 11411877684055047929, 137499308302040942, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3829554633656006882, 3894241112289567732, 17759873243898700608, 135826428924531724, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 532116386886743631, 16723169348526859092, 17396892239224826550, 194114322124379452, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8398376515213863161, 4864250479466407305, 7758085918649227866, 175025689670907393, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 145789625051514116, 15782134208422813407, 9071555193436007934, 507326532528965581, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11530096351702965666, 12120575009656285941, 4133205172504107270, 202916114882836319, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8479650087953427358, 8860431307502076948, 11259877849808046461, 466332737029545270, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8189408365985814370, 11476008193156260807, 7268880139804833857, 212909043006814317, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9018720977878382574, 8448922113682954920, 8809862759509290817, 309711761312063517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5731186948469318817, 6591786705679543417, 6903224924156327313, 476728314301355435, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 202363917821940434, 11583122820182257813, 7107311340921021033, 210530293861638828, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4923913661828916056, 12935496607987345084, 4428699262293250342, 126529887480342947, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16290368400617341303, 8971459927863749595, 4948589187755493594, 302475126357209430, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11654426897101284069, 10799991410790485470, 17467322000745496683, 297804800079278570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6861834376078716557, 14731592329738423058, 2611963263863611022, 558059346178304766, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15035649640867656573, 14587748043114371654, 2290529692408967300, 179832655574233742, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2905988145011696500, 11075993732004674915, 10525335736543431503, 418683985329496057, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14415584286339936280, 8875329143470808219, 17480886239105395103, 34638119009159382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8902178952151800429, 16732486124447813017, 16668768007366301149, 100070702816669096, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3611323137728402816, 1746948313341967468, 9502293243350253896, 289220759780954883, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17919061668989773686, 13853400680836806791, 7854263792235764840, 531782439867869095, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8520214047303206198, 11131868616357434243, 10416889588935473209, 281180751064184735, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1334966233672052404, 763075755257353384, 858047609947322495, 456010617206580992, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15029168489695912970, 16061000862077962287, 12153818666505441495, 34187170633509, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15278789428183256839, 9020905677767918216, 15722971160474516729, 57786633473306933, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11078753602184273943, 15565822918874379862, 13228546750612368054, 482685128949304606, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4886582634726344081, 15181396214845717169, 10724385652388673003, 572987508707849248, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7334783459842195829, 15430442587294048823, 13126837005697000529, 246528081039036012, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8988364235028863202, 3216863376686787281, 15186503749294598134, 423210184188788867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11310169756886336603, 8117375767998892182, 1273304899782309490, 49147599370237079, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5484244370560436848, 3958648025184365989, 10489936996013518166, 55969710116235920, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17639466187712847670, 12751606774227589432, 9285624556280285718, 181926657658404339, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2313797998286597106, 12090537579642234865, 15957023247027872140, 238277159261113280, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12450753943853082143, 16092289479686836377, 16259393158054941991, 134711724644015565, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5376947007269021547, 13493838916795384424, 9336402165137425410, 36872673599820590, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2476134706282283258, 12489094348400102778, 13306608086187957291, 422406633011890298, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8676953657334967785, 2010200023397320169, 2446714125304474893, 443540839728952559, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4792926573440732670, 7138534009784323610, 432119429910576538, 339883042695209175, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7151440158049856132, 8095842386775383882, 9905255190782592286, 282796168328666498, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15630932698786826674, 10691490925766589080, 15646845396103289558, 459773636080332095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15789159260878419013, 1743621234356135671, 17008973860148395529, 446902304660854092, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5333269304732094207, 14277102321461303209, 14502442579885089053, 84679431686085236, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15183206142545544434, 17827595557277252209, 7834462098137773058, 457208286015950647, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9125826578125690661, 11051282602697627826, 4729658207512851227, 346243768569800716, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11267314304027460383, 14325709587170925963, 6782622053681843694, 462130339431387899, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5784985717888349778, 17050155358259896857, 4593980303102786335, 192390762371316939, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1238276057408554409, 4122773329070549167, 9307574684580026864, 525535586847467521, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4845278901916638312, 16617853608374235151, 536648239866162799, 282554522720880267, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7200734421907215345, 6179259202649354135, 5648600331874971871, 361274296153194274, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3635360849799242409, 17437325352225209918, 2409360026661281400, 111264240263112739, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16432322289735054978, 18296385176598609743, 9297997617944796979, 326234133386458269, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11897673851106252857, 751096831053490661, 12827735826681475752, 306558043952101516, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10170641401404508761, 17251647014520625770, 2643983109571370005, 376194831781826943, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5606010442685547214, 7631644504934561046, 3842587197901473212, 309243061265980051, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13706419512220487534, 7730890572780454241, 14219333936993352672, 462701829682973231, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17628469733636277446, 6648756779423638594, 15712128182827308295, 514293175182273840, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 134155876155516448, 14575831303031746204, 8504233501803794766, 215629862781527478, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11129816728130743269, 396415422762080200, 9934583962199416195, 27051703109047419, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14325792560454986498, 9683637225269353764, 1204240954226598913, 361049930332344876, }, }, }, .y = .{ .fe = .{ .limbs = .{ 983723155099106373, 5203780633989225382, 3357898919818004254, 496890268592997878, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3210730393218536228, 17660790045128266226, 7342066308938536990, 195060850208423813, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16692032986795351189, 15025987063467235365, 17463215200133254698, 107448742927772682, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9172550208485755132, 8482395390036979510, 5824950583381923949, 51146786252514083, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2794443902178059178, 4035773739512910706, 3015433183903607605, 360166072051426005, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1335881449167631373, 8710322815721430650, 6726802862353884244, 489485674574068075, }, }, }, .y = .{ .fe = .{ .limbs = .{ 105616352865536158, 3962771408512779596, 14214319687463426729, 95646330057395518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7591212388339657256, 9121102077368480849, 2911980386760377247, 412842561044340958, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1994224935946171205, 11199433467288776140, 5514951616491846196, 113667406281924918, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14164291676734890285, 5774346516447586624, 13923325803820923969, 504594358866708703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1627369329316025136, 2821593604806692363, 6123125842750867601, 329113431266679840, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10847191959361738578, 5476286868618574660, 6663003206117850905, 385953381634494310, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4182986128104639154, 10078804858850526537, 16121663172400537990, 432420461142497011, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7854438356149178907, 12204905527118532561, 6792595249686266977, 306188055371775796, }, }, }, .y = .{ .fe = .{ .limbs = .{ 683026606570789265, 8371994182004836299, 7125890144391840901, 505839406532069672, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12372921130621943013, 4574634628837725063, 2051494479699346199, 327581011522879532, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13721271171735302053, 4522758099145902463, 8791095337294027054, 423533960740809566, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4884379123163256317, 10278720033895413903, 9235180988230947200, 249185680882095686, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1230301427095937517, 9658044912762456069, 2782758526039687999, 245877564838469168, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5851290811503812968, 11274525744995829902, 2827081814216245137, 13215688709336361, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11550862360795904692, 5752908756616628232, 13261087847591328873, 239112865024951245, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8134523757326269567, 255526369733009320, 12267202951657834367, 554849430280130605, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8102334165802025247, 7429322867866944346, 3465250103573596013, 105415556413769114, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5492625370727322536, 3044218968107244210, 1188001632903757431, 25221852176162532, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12222341538640439889, 8628111399284251846, 11952394791631126764, 240617246108342532, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9269148183367794941, 8261275545691884590, 2801504136297005336, 18412723075361909, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17721039924420666044, 9884284161369432950, 14404930608305946193, 62005185243810407, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14606832075259989213, 16294199378437151709, 8265978101596113958, 163807491695819456, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6995212312285730558, 7921882884667617599, 15844091655329880542, 106832211625345449, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4931005770423247849, 15849472667713925541, 16417266148512721900, 122973567154146028, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1877736378684709991, 14504094083480213700, 5050112738040824728, 508168095789505454, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15564522477562510774, 15326481055011642283, 4950130920174108428, 497043356417393994, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3536081489019583885, 18320006774203456887, 5050893860282893304, 46324436664632297, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4630704306924828335, 7150583486998454236, 2395406688882936209, 257137892717984317, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2825029728574367238, 10590998438606594315, 14547182980540392968, 392324313611121817, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2337751993962490504, 6040535464251733688, 763646832736087053, 472349104877501374, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5596495012769861640, 2212677261683476870, 7051358955600887902, 21724790662830649, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5345444381146606900, 11876620573042881879, 5975996645283373617, 134452847517613583, }, }, }, .y = .{ .fe = .{ .limbs = .{ 895685418374343283, 13485338915368957031, 3676806345439518026, 452910745595386258, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14315663896972871159, 8205992606867765264, 2947401526528745101, 39861205606850758, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5745600841630269256, 13101297741273406979, 12505162238292934876, 432663199856232949, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7472176253029032067, 7005174586160923733, 17180839913290472573, 149268648268741109, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11946637487024388819, 13827197502003823532, 16420575964050354424, 277037843666613610, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1927015130764044324, 10175904795048173707, 930156150436276771, 552983898253384142, }, }, }, .y = .{ .fe = .{ .limbs = .{ 590420870592787952, 15116727102717644120, 9709592281650696248, 233270084040254068, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15806550933555488531, 3320870280875626282, 2951935784799405180, 340888198788378782, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9299748908910756016, 14969083182682118162, 5156114991865508041, 426812510389166936, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4437194390515815391, 16894669623635539966, 16834234452649974602, 177527319337614630, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6536041097478749053, 1815031378085055554, 9489878012190698221, 223366037738372293, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7877550543258574167, 1684908776331898737, 3393286611704221604, 248126766067043173, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5194370619730304474, 190058116772893345, 10706983399827016468, 493224861935670708, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 244619060966139928, 6401726426533477060, 5968352505330421714, 420184572650523090, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11426262605485642624, 15391592949836763688, 10817141973652761747, 518168817854833498, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17356096619281294545, 16523465360670256312, 8866001777138695073, 459758345396446502, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17004485719530804042, 3981633652020794432, 14144443077399734295, 234157971865107130, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3129653687694061641, 12242950525384883089, 11728515177718648310, 492576130605853386, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15166209663086194392, 16588671303110115159, 9054411566457058340, 217692292438558222, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9425582818516945220, 13731072446765678892, 2324869055281691620, 502504131342798245, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8778750868932492419, 16804357535936135897, 15515065042948091732, 250735731791777476, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17667819074908035602, 4480354656245540563, 8440332499923152213, 155722518492258373, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14013019778359402987, 6348968571091189330, 15921345032224479876, 5010832160447887, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8596119526074215130, 13161775635158222729, 17084678836752587614, 405880591048174893, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2656894527814645007, 2306150089038840228, 5271563036803546584, 240293705558122500, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9016267369017037144, 11264558797337898298, 6983039962033501194, 142027663459596371, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14229352349632578768, 14299181914274298700, 11471892939958068597, 172060654853017591, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16994385524496918929, 1328905471200221429, 12423539549555354617, 527929049798784004, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15199183883927334678, 15634993139935310126, 14479065401679620789, 96413763495364255, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4991903370331228909, 60823352510895887, 9481427288537623513, 516823065710427793, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17041194172184820016, 16318409490353459667, 14680871283393659650, 106646740225132489, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17288210034667356405, 17619721238237795026, 16910296092939145092, 247247971837079955, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16675079714667000856, 9435311628712832063, 6582847542575458841, 252356590254475046, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15593889424775447385, 15453199119218166215, 7858332394052824797, 512679174964847699, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8409149623219026466, 5621843873174041903, 8863956792192432570, 418002853086151035, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7818213189521162211, 5645315459493759253, 3221954559673087516, 25232549387661978, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10091390881188896454, 11862036600333902231, 1624689289604152188, 416161296017471660, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13095857706763948339, 4458966194192654723, 10219720230990675669, 253991934856988778, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1060519498325367316, 15553498036094090953, 3271447503263055001, 562171954351461040, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12544708156847805658, 12384080604762116420, 1926822513874882099, 209718900198895130, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8648628426981660421, 4025539082609079261, 6245135606120744994, 398506415140811008, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12302122151347251719, 10245790945051634608, 2460937046520772545, 19566214290367088, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11712335278834498519, 12569266737222098612, 12244192941173581389, 199325744596478079, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11365661652186370507, 9994401749068072126, 16224176484344262509, 263177691213175430, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10611804742895505820, 6644555376850244134, 17105546798029537591, 498602179579602889, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2484481554015266223, 3663595951226664960, 17984339978864891726, 333539390301460872, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12776241091320747019, 669473748787706401, 8618088917443140856, 467621856182734835, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5113678788621693104, 40393738649514646, 2612365556299800304, 59714838245749828, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5769662086744568837, 15540441663016436416, 11948920782420693497, 175211150523075084, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17661075986696061434, 17854256601651174284, 5722938464375939861, 138620941784445325, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14132267469484754481, 13966332644392180393, 2664650878308297088, 402412833758015335, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15103451817137807210, 8635842717748394350, 14075372492543320063, 180218009901861432, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4946800625957070143, 7089679580246020000, 17709154991498044997, 540056280576021791, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5351746220688346369, 11809274194141762724, 712639723496426342, 92896065892201492, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16020052038198179980, 13443227223633995340, 6356610618953340826, 23710603666480742, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17144476229303561642, 7602935946554310303, 9956887881603910955, 51594265075118849, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3484591383728461820, 15236896440845310194, 10829875640546401033, 478150259928653547, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17712484864251020702, 1587162055552445255, 6166722578773756460, 313895873722621558, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13830739940146531531, 10788705257831400942, 6304978859718149797, 575052832510801824, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3747461379003138803, 775861772203281893, 7844901370488642055, 366583207509794951, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17771549349570032640, 7520608345968498504, 1567472846142804435, 173560867905162790, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5891614012178356642, 1602669879912010073, 18018215362308249137, 90764997909499159, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13864590986259240160, 11237560084523912701, 535316474965458727, 78152453376192146, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14138783540582838793, 18020824522183847972, 15857442270223021981, 85561170138760548, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3476511338052394640, 9104481017522902950, 12634838202204949970, 221380102346254303, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3791398642501740415, 4586821820816363734, 10043067716804866734, 27352390523084621, }, }, }, .y = .{ .fe = .{ .limbs = .{ 395591315833816677, 11734809879740416019, 1950700147565908714, 392504701747728197, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11565222406407848361, 2833166196184738354, 7028581220804623018, 73184413263731584, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4294705887748655452, 11896498254657034952, 13873457349857949298, 362819963117603576, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6479290487172391743, 17832138787528692990, 8725113130622213183, 58025165992060622, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9833720788236060528, 4325901629300076588, 6763099032689003438, 467766157279326893, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5202110108756710607, 5594293543829930475, 2383760987447691829, 45742680669607520, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11716331455457298560, 7958792645754503850, 7174693647312580898, 54225837495589981, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18399565408825599651, 16518074045410860203, 1893765454510512039, 271111389849242798, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10053633847952730422, 7714447575603653467, 2756349928458999372, 270329928865335171, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16038626309837663374, 7012530695332564432, 9589781214450957218, 572617296474043202, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9127146432760815629, 14086134191359107205, 2463507588422798924, 165091165068216868, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 804220701966965652, 236494879572312361, 10966531543068780431, 253654943899772130, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3990341361244643416, 7354094915517564908, 3879188150600327075, 414642497831001816, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13985630428809375675, 16487742374437159709, 4542062440145060061, 210512807913540837, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18273454285301447149, 15216751216643835665, 4322347883528474316, 463703191869454057, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14691146721746282531, 10553004980653212440, 9790990159625472377, 414257175701287673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16093238293552304595, 1137617585879768392, 183713853238814250, 454837553299621027, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4951315171247731455, 15158662478133541737, 9606428746424327575, 119169153487651715, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3829704824115492015, 4945686100017886019, 1833626963508014760, 347067360372386863, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6090177281099432486, 4682872152417742727, 14628454879788830679, 292563933654759359, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1320197411086132956, 7222038375630107144, 3423824686745102820, 59006054409310414, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2535637427905739826, 1571513156827155573, 4407286054919505936, 457963007291964222, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4074392579498500601, 13456627644321958639, 10662147884793965648, 173752680864842496, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1469619891744611209, 2473774399524373416, 1841317190211097308, 230450668299459258, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5956340211954596445, 2470855371346883687, 2228221222103786125, 238386617801279539, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16754933912686472213, 16892309882302011493, 12000379363560664801, 4538696333747246, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15501316319139966416, 12932422678599184442, 6824341662373761345, 315040745080426324, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5953378382686237775, 5344605192805508236, 5799151864488234711, 514646100815497598, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12793558164302802944, 17030933840857865487, 7087426927710242911, 149161071707707517, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4273602379865813916, 16456028159780441818, 1269969152903733386, 233958368162906119, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17783589166939707157, 11161350242709167102, 2864306935585810589, 408757510456599570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3557853494806504841, 7744933704306205134, 3311579299846254412, 336122106500328719, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14018518449368551508, 5157887038489360291, 18047376658491585251, 6190323639800833, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16850634571598660846, 18117692483338105765, 5176318145628439610, 111908509632036951, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4048654053044830643, 3927727248071728799, 6696176801071235949, 233461995263725127, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7092646038082003034, 4990618119812796250, 12927906062208862312, 514882454853872122, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1335332280640958688, 1741300376197522358, 10064937598103540409, 279908403578010431, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12469774989881252017, 866097597963545530, 10732479511320836682, 462643199167550013, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7627712991033596914, 16330440016985382086, 12074951984339934478, 501231161657059137, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10128158549849454172, 11010387839536264039, 7613123186699564510, 415054113000771586, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11643248213644457672, 4689092476059774497, 15818616880052031545, 323953146539842448, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2574938034964911405, 410062209408340349, 15500523566938924455, 7678806534097955, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4083784972826594954, 15589452967990788554, 262963223069617537, 241540140754242006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 538990576728195536, 14102923768786963683, 3055233878241230906, 69997352423662507, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7841948534137543462, 15407746549128073000, 1082114685193124976, 175395067746405640, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12849025151050332636, 7638885882254052895, 13965729318662929257, 372907898107196976, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2003524822942960708, 5125146614205187614, 17817407328331395895, 228171554923977549, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7527167587467169807, 5722477335407464113, 11232600175313032312, 183517854742835354, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16872233400612775360, 7158777060480653468, 6229859326351971511, 537275040141305172, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16600600989496198909, 7547939349930173521, 2664300148039038132, 330471075004142574, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11249828593445762172, 16421236729525781461, 14311868096243684555, 324816132362940549, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13530751588527169008, 10542759246992781880, 7357038664125905031, 144826003128799065, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8928733852601831157, 14145257517615518806, 60729517505011370, 506856813147187047, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14843740340057895163, 1500606146225819340, 15030000321092990253, 60246384080790618, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3548043486529634833, 11697351617993782009, 3203926741860115557, 327475816801124885, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 498287153286731836, 15367170161147112513, 9574467903476810092, 510100728182573447, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10251264395305625159, 4119951910016545855, 18018239481200485042, 307208279494890984, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7972550706500165163, 11065766713266812263, 11697664302682572715, 74365442362175528, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6488325827238796236, 5733515266882209785, 10838524732287033334, 46760788344232691, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8060869782608898184, 15182708356286909823, 4886143974228680442, 370779243405412513, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18259910375381449289, 3330850108946267129, 9561787823524792078, 536163075138951493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17426682848108306561, 6991011124221403496, 3709066404425826467, 382350086748642379, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8488122845172472578, 4847191557821720483, 4617102298198491144, 133960204503957621, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9214302315990353152, 15145245678303849155, 10142986885919990716, 74545214459782048, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3067847475039086882, 13313037129142238620, 11048652009575420974, 117631462308096091, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 779015807205680088, 10497277813890014759, 6642778808300765419, 543227635341187145, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15372990812215929574, 14403187659949443312, 8166336946826133526, 421821900197898514, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18115051000921170996, 3527925097048878406, 9266115721712107641, 234750317397617756, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7631285761276878361, 14900159627544918026, 13308325384068056761, 431564953490003371, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7435279372874967985, 18226890801233452010, 18406291562550309318, 151022888285273361, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3124187200430113854, 8644054424843224014, 18284369440676258056, 365801622501588413, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7661796819237773681, 12113483713291611506, 6946095850198375193, 273479206802928711, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7376917106043561253, 18244827489894424376, 17453273873739712466, 35749751482601146, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13603321821984318279, 2750070338154541100, 990235234491700239, 303314030096025937, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8790374109741602060, 15187371092671659598, 11084309726693655515, 54336266909119549, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12551578553651964540, 14764362385928074525, 1501460408903868059, 236725485847305923, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11278613210812797608, 2337630688974703144, 7158157766721604397, 24819859245086667, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15255280833389634410, 17672918342479789259, 6169478875171769550, 285610617600430942, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1874079169715868794, 7429696505007384009, 2833480966625076732, 235902824897401821, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11619245080423508581, 7540955642566300535, 15436740492111576158, 547965633070042700, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11047738180290599831, 6941714400696158560, 12899393831343228496, 260977547406414789, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5830384142561664243, 12770134929230740651, 2345663200045122422, 504758467548277786, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4411525612878979931, 15543082942669492244, 2179816696928912726, 380656306899167077, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16214145039620388997, 16713829520400641332, 2122173493106174987, 531284159094290868, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2563145066501966490, 11597226037119046616, 6396519071604382734, 262457177315850006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10800358242426637148, 6872153937232628075, 16865217080561864809, 158654895329120433, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16194101152046926010, 8449103213969621871, 13624954889022132435, 379773303857649774, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11632843848586528182, 15658092125024411159, 869174640166332832, 63744346606959523, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5615267675567887916, 14024586190944761408, 16590795781733275305, 318585248947235609, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6786803914206436792, 13118538901920335149, 3269883725534306932, 535719744338244348, }, }, }, .y = .{ .fe = .{ .limbs = .{ 237018986824314202, 3330800635979008440, 7002789590340478802, 200993618407152382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3629413177819177071, 16870007959576405702, 27006708743505938, 287894632790305133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13507912530134830396, 4697805971711370278, 8850505952218840940, 542937156612529882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14752423326564617079, 3843751558002193456, 9068752558270401736, 69630193079978703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7802333754092547737, 10645156655288389362, 10335597119744163418, 494758956777014160, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14102963079996004862, 8629362317446144912, 14305516897004835863, 425691109512923245, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10889274362304242030, 13849769570028792724, 16167117903704857059, 538846980725263789, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17334543668032931058, 16911054702318348791, 13532561619646325101, 553491181071872350, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9462010092576310620, 4553411141191639771, 10759674381090180892, 365935101593748312, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10511043541834115430, 10478079506959655127, 1237021275689355396, 431057335163084112, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15061337941293490322, 12472099119037014855, 145415907028114147, 388161871263457260, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1112918384550145281, 13244585843409137209, 10993541264039105845, 9694947786864600, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11282605962408960658, 4659876380939792960, 2234167282319026140, 225765227738040318, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11623744774981271010, 1357497067044047617, 11884048844220422456, 409303809025784608, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1202850075206547479, 256619431186292072, 8296841001347083933, 160593416850576038, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10904862448204947197, 18067848270151701575, 5486020908361610735, 413609267626696951, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12676077127976364378, 11207077039352292287, 158947493186869103, 513519599509357410, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3577005431475534477, 16359751269261362273, 10592963442827789715, 373785787869843917, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6475226550587519904, 15607656451448877916, 9919046080876323180, 428640575629891668, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4167993965440778624, 15093874104618635172, 714607128193734458, 13937935438717206, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11293526008155695249, 12915673126454280770, 13576279959896959459, 46818962806216632, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14813151783169135977, 10443301082515561028, 18123720055423325668, 510263745088843542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1236787054572124974, 16135621355168499579, 2294672442039976755, 222200574473426497, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6998974213025442079, 3390762463810533871, 14910089454349431825, 482138918180160731, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4190719071065631351, 15104690931574948366, 7088303047329769001, 199301333894574352, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8583713658266542754, 17902674145902419496, 15081156392689818930, 54475431980643798, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6459036789864340799, 7847243238482762120, 16172795005769397705, 484608031245969219, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2896852294200945267, 15459206815445311145, 17189145441032926111, 526493137641373239, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16312688023892120870, 13993463721456894696, 17835436725313683531, 345912521550968014, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5966754772577039970, 15493174457073191086, 6248071053433179892, 576288532362372666, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16282612858162085552, 8189444789763132549, 10936997242955637574, 87267959386725051, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8082335851294997545, 17163353335947165569, 13758668253821337250, 10828091169471412, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11669353912489771828, 17179148265143520275, 15338235477407034333, 200320715513245306, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 338246751666423864, 1918376852963324569, 7545521651111186275, 38338478716867233, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5705593736750520163, 3762223855043197740, 14842585641089445346, 236835283498584096, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6777869927816656617, 8578393850977172018, 14248424316578226824, 252921818218674014, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11195483035155608035, 4864533557503920264, 6222991957896901219, 388339960429625324, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 644002279831188687, 13735331836547151896, 12479800292920035406, 573337745634677698, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3227839212644946555, 6516063515228542442, 5267858760903773846, 182132708422391642, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2373078539314638601, 3852557190792210663, 7617819964230254183, 403185164921237793, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12740383102263731921, 14364090994900049580, 7879967815275667689, 289714912619127028, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15461847898716210681, 12787106617787549751, 282440805981120189, 511720116949133935, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8953568860298435742, 12076694356240278068, 2550676646168056960, 318181622722361145, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13655983463093243119, 18236648021999646032, 11514411727091157552, 536679593940513517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14754900532905372879, 15448124078751903227, 17063159489718049105, 126813911367203175, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18365287936435734671, 17320173181348885945, 10145659133660316516, 495690165614325833, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2943514134546246595, 263251756583184111, 7125733705626383026, 248804763925626882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9337193552738710809, 14564300333525632329, 482771104342968018, 298545797768655627, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11710587111935962791, 1344139875512383167, 16286897729503732543, 447459471381905111, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14208674740094672012, 4777626370417796877, 11757607107287885302, 292871365035324682, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16522028236749954331, 5417352191686906741, 3673974872760290852, 402984412118075764, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12870905268268394906, 1805898204000558358, 8556765064549345144, 374876371059697362, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15358638857795014087, 15270253832929685859, 1536318336316218349, 220039352722168050, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12227727897609126949, 15526283981376112062, 17993368208787705879, 434344467905483552, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13128113073246463845, 10083965062458043711, 288688768050501382, 405305384466393089, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15232867826030668989, 10112882991344903154, 3702738388401099285, 211739978336039565, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1328780807095537635, 10988152272970145586, 184210245611435448, 396114213881006074, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17132542882281081758, 17015095901398017202, 3939255297568229689, 76955155588224678, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5381347436623683182, 1065742288775047335, 2274906038405210980, 393378683310668739, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11661820223682920698, 189272106335537036, 15213314748185669642, 315866420053070613, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17594011333762806061, 6827465886133818997, 1007298644828807644, 193731222025024487, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5991892643207774998, 1401031002280183290, 14465888016074728035, 422330624704850718, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13630525621008076198, 16224801011424447988, 6841360225681464594, 391320885797034000, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7389921116828476327, 2507283233007451728, 15462415124323080803, 42431328309473996, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3338793200483633090, 10053976619674914144, 17931093422817580703, 333029696362434502, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15228374511674296836, 14878184254771897296, 1083783095669111257, 368013244562826094, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1071316441524766881, 15337625456484810015, 15224449137839250112, 554006555146707775, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5478723962717773018, 4490812538134409335, 2567264034984559516, 194086955378754785, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2897239334845019211, 10917127349059079800, 5601898179844417222, 146559883192998917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16230913515947001106, 17631437482230222375, 5785159737172670855, 553859161035087737, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18166633604760002077, 13798048477301234648, 4375425371852646811, 51139672229695983, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14237681218144005589, 7860775980721450032, 10705071451753929525, 396684469445333784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2157946505918873948, 1065386615164863356, 4060529072241957664, 420087261034252768, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1072359028268289744, 13138432463654194571, 5567929968335765618, 157764338488226411, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1467193499778253509, 15010382220482997017, 5016546830729717925, 551255918340537516, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5620789670736009690, 2022697419215959773, 2288070345064394534, 561366440011920107, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9537789622343437808, 10461671556970056326, 14505488977822281778, 151264485541292891, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2777613057365740913, 5727656959189707047, 3500010381890674009, 432648802156772587, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5725798491380011704, 13755502141492075904, 16946451036054844307, 65613411609827398, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9250435315338952816, 4225336159932463776, 12129270304990918780, 19885508964480342, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2477507529520889693, 10855491035521753320, 5417810934297575973, 372316036911025617, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 809323524305395051, 4704070610733443370, 10616001601420289813, 502592729394957789, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17493680503304954231, 11384350398148860309, 193949441328840525, 375010189885276183, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16872980894946227021, 7952293830186827774, 14362326143107486857, 523191306660526794, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9252604113480227405, 7157056303808651292, 7670501432549613919, 470314919777810880, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18403536133933301385, 4031654189011485679, 18342866390787945338, 70419797492651134, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18394966102607502370, 13402210325150036532, 4931050615184375214, 451921553618247601, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11873036322181954107, 4861484461308503370, 17648091575158954757, 289815410441694472, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4424227810197229254, 711880324583671860, 4897733516253566343, 108723819688179893, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2384981170335139634, 11424735511271099870, 8597710404200231290, 301754545896105425, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17304562601318542427, 10662688705585517430, 11482846365182317908, 437542941772623133, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6348249744527015134, 17287632609550022372, 15251032452214078593, 266059119513945945, }, }, }, .y = .{ .fe = .{ .limbs = .{ 922361927219705915, 10203920619988920188, 9314249056581450124, 348152236029383980, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15419070373542303239, 941633763167096027, 7673791549328195934, 260954066476439615, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3924906068105111856, 1790149685716452078, 13097221412965448829, 527848589487237045, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17220139704233756577, 10568962430222686479, 10830404691584513875, 393250898710998094, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4723120196925683605, 7530229464971145268, 14456017429849186842, 410632113418094392, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8665436316118001416, 6117501295443337589, 11534998452234622246, 273106287877653804, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4175362859048275677, 17997605516846051341, 4789721124471043947, 112345379785014317, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3011060968239530068, 12808819234879166535, 10289574962044709656, 394308209892823912, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3499439693518959150, 2030722215710256412, 803513232011510314, 308339387148358272, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15286174392289182218, 15690568336393773123, 6004696803999506440, 560537664596171927, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16594847487309709056, 16285917427646476341, 6793178330062295656, 37789185088243977, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10542399942827970555, 590372914652150013, 14373627630183172001, 477233110106096912, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2157416490804534204, 548227982672236241, 9774406785970013584, 243822531470742269, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9268000976121457294, 6748935706269819858, 17179487091875439702, 249280004336097730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1022522897750657045, 10211961570799810901, 12589420081930959427, 230613325705743219, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15926076202806315779, 5246253592078554496, 14788525632576961630, 190829403185313253, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2695462915291909631, 9405284910227357736, 4448178223752006537, 37207349135102806, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4694391813079524673, 4923047957824346068, 12198573704936283610, 439653237357886380, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7984506540719423369, 485264540828492450, 9302593865710645794, 510878789264886410, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8289403597623420010, 13029343221565205496, 1801475514233593199, 537612955392475867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7353281141657213798, 13337293696664853734, 424250686025692703, 346253676516206424, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6228541841607485428, 4285334297093722905, 6054134711662038038, 383680791466475669, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9597847251807687221, 8788723282910593016, 5335498069689059525, 72916802912978999, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9714251619005831603, 8125421497481535626, 606520335686302328, 493393376968953765, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8284152346100716698, 15113665545888920602, 9346580085453636685, 18080808520148223, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8941558754943480565, 1095008668076020185, 9399558209460898866, 78609995222724625, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8987699710958786629, 7539753907455440031, 9720122021666270347, 207668426998151009, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11580632530270255547, 1206120419676539044, 14350060538158065257, 553857953881110826, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12875328530809245381, 9544134044618747954, 12040776998321330473, 307004891029508354, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2963264702473618481, 8287602827572563800, 3069604845485998915, 373827034415620716, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10063805341366516341, 15344360332696418676, 9438594538071053574, 393209063175941270, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16814937762234740383, 16100158846387180292, 10743531642096124455, 120833120163098681, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6530424859185038987, 10830865338779180283, 1337776463138759501, 491155246502573693, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12619826107266959340, 15027850664766769941, 15934855597893364690, 409577661124230673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8612695557752536404, 14071642921628884316, 1914926121695266894, 321509823868184210, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 136831164515923804, 16810986275110407785, 3163660453014028213, 339936961563555143, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12526844112680709762, 13235329398990264879, 10038257275471356838, 235124269251175164, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1910642465716184360, 14556943149823291370, 5719028315596668785, 249881208996684382, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11250533748317242478, 14005599986075101279, 8097485251456747199, 539854810372757001, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14037058215293025493, 3257385979073763759, 2704192406375213970, 375917930167416022, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4301778294784643365, 5130761496258052830, 5284328761423272483, 247059961833566538, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10608222311809381381, 14179433633019075125, 11256310891371979014, 262677872992317907, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6632078925922428516, 14679359364920141922, 953723237741944717, 125590304547819409, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1901746464047172592, 7789953790308982096, 14603382904094778930, 30884285480967973, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14641518999846846552, 10100351557304914722, 7463550638152480472, 313173581788238994, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5217067902931255948, 1019211347976093591, 9757172576804720682, 211233871037512911, }, }, }, .y = .{ .fe = .{ .limbs = .{ 758655969246139093, 38450446389316438, 7032787821589921524, 206946931160451570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12663860457660024047, 7425349667638388260, 13774635371193117690, 428274459267594340, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8727030534920404056, 3813382556715809188, 8323148359686656611, 506346227305681413, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13500111691772391375, 8512799794009394824, 14885897624710275801, 185963613400294651, }, }, }, .y = .{ .fe = .{ .limbs = .{ 379715276789126110, 6534487519887391969, 4157246768915837287, 314587597118699733, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4533275510353438156, 16958747756938507589, 15077318968859470365, 525600853367670435, }, }, }, .y = .{ .fe = .{ .limbs = .{ 451409688568450865, 3174418407830541201, 14042053951671350739, 167732188386482692, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3188475704425066986, 2841324871749893455, 12140647056980990068, 140779607414809689, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12639151724039171957, 6160299407687175611, 4308808999392023437, 280648384175513131, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10811103517824653202, 1939950283107099148, 17569127139914987331, 335998330449409774, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5334762413907028171, 17546096405078536028, 8215625338862507731, 378944930315303266, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13064815186363563392, 16556942980937362175, 5317132678694557496, 222207667050765721, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8716532645216527788, 88264913938640226, 5611966876497801965, 209145759586427896, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11580611547058882141, 3212811943996087882, 11365186567603879406, 32543246589965656, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7229952084403909011, 11755873541830045142, 8190960148677940456, 133198518538902871, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7277951515249681362, 10379822178588985519, 4194742428596351352, 110959776211225873, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13577893061238343294, 6685686437652449075, 10116744599847723697, 387366475453964403, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2335114469225796859, 14721245077334451825, 6644792305823809644, 232138439556594017, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17808093523517193964, 845602800840971740, 3986076346215013273, 176106639622676839, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3264908415189251806, 11422953681466030595, 14024560267423056588, 72331871602943357, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16078367816931195631, 14553111481444685397, 2152768413580614042, 28300039516454012, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16706641624231704655, 11664708879297745768, 8344197858231819307, 91799935532730435, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9387694040460984930, 9978521908328014625, 18126620314925552562, 260155361243785161, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7355877437672409816, 11429702290957673738, 108516570189997464, 526700129473617695, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15128492162464890413, 11137289845674319093, 14847421247758580160, 509304255294529414, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11243754114777387816, 5838103412275798623, 8666232391384627543, 555095665109939594, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1857389687863111345, 13368733306475672092, 17175583235835054114, 9231067757765364, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12121265599019905776, 4848356166237452019, 12322757462475629811, 275751044747756897, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6669298621040418444, 15682591618080336214, 6964436091389806582, 244635209369586893, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10961935860574213587, 11724686046258324928, 544158089945378250, 302564344424581853, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15752063914795665046, 2303300373219702138, 14488925119281111224, 108399995779735501, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5630888881379876816, 7534788104607572923, 16925269276744998841, 348343058372430923, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11661793898236225816, 5702309030322158456, 12374017309056592782, 524645750468223673, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8308402773642324888, 3409541566090676351, 16125591727034643130, 401401638836444851, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1966670471760719295, 6613447727123585845, 4813415959631926161, 359748896798023575, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8244779939433154820, 10560569113116835031, 855099938610034917, 15547705806975139, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11729257375978626650, 11754530715570629034, 3801009435041894261, 358953784206259304, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4780878983660457282, 14893843231088469831, 706010516460809081, 410123372405878304, }, }, }, .y = .{ .fe = .{ .limbs = .{ 985117770124637157, 5936367029676603674, 5711651917094809748, 47447118801768275, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7096658196412507033, 11131161607364516507, 12359607501095402482, 79142243588325753, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9081069837026315724, 7358657028208157439, 11888371738799452733, 432260147707768306, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18218419781734958517, 11505893422202214714, 4017717730009935039, 547783846801513557, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10970314299806012297, 8877709073609870406, 4684759849317639216, 467960722152350905, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11208265668187477246, 1591843059309061422, 14383098632025562491, 56907081061410441, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12959734635963027359, 12160838255222374229, 9015157520819675746, 255187589970213753, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6540696587141777144, 10101623788562059052, 8718893131626843887, 96835583829889141, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2342455622065247175, 13856460966317814933, 7413925600458807127, 278574711937562608, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3272636082904075524, 17023498973294180429, 6289903295898724940, 116565296120489184, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1978803561660197575, 100715463386252109, 11296506604540167687, 6210739382917537, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 708896399396278435, 1257845322872047028, 9460875284062196607, 512152541830737988, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11480745051599530291, 9444920357129943631, 4401680877429808649, 2982624683426796, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13180795591816971948, 15857779886151579403, 2229523854259548924, 486164765377466142, }, }, }, .y = .{ .fe = .{ .limbs = .{ 777216931967977958, 12879538836437814927, 6158373272121243117, 11991703002644569, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14731722845400063527, 16808763357379967083, 523569040968505290, 569727280860017254, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15519807550737692275, 15533104138327414974, 3605298489313360123, 308736699849397321, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8402157611736153321, 12335186267036144886, 17316730951123558377, 8053615448287280, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2464097699444445709, 15278422141801232680, 1264055437976230394, 62987966580156524, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11906765971041174577, 4904314976939900735, 2323528508094724743, 229245958268862337, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10374373696667693464, 14156656339221603545, 15161315185034556204, 31998828523023068, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15493996712189256493, 8003743452920250323, 46817852390186857, 532686145944113756, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10589202952894845526, 7647216732226872840, 2812027809692146986, 248628752491637791, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17729050606626425909, 13960179788055019103, 15721001196712736950, 396247213581664949, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12681468492532660773, 10011574997039835880, 9492381527587476030, 175837127245622302, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12198605505843418430, 9756008664939354985, 5936924970562939714, 6498497365826016, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5558641056603022813, 17991767787230375375, 17906345391172924895, 538209777795255418, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15564752163688964845, 3532397975308930256, 9536361127652243771, 429105980952523559, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6434879541049101897, 14131375934449979737, 13286700063678432862, 140648086631455802, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12103130033338415694, 16483241259333571253, 7102253938717453365, 153492797811060015, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12457036057359878962, 6523809874917124025, 747911101758653911, 337331280801514081, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14572688967617578292, 7902381354499906069, 17768396035543064388, 342288285669239154, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17344992593953973049, 842096858123853783, 11503668830173057092, 244118383642880168, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7128192822068580287, 9753355421120678550, 5564039137317013056, 127961721065339506, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3434802148276232851, 15766408410759307818, 12307311456104845458, 278781804967694346, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4501537342491628094, 3937869100901724905, 5548621437958950967, 168374953474974443, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8458616616167393841, 3964316461018986389, 7680445528896300597, 175605426526901467, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3059242938583319588, 6975875198730913718, 8114532542440727784, 25500146114154602, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2021804179971149150, 15914864515146745609, 650981212831424302, 290947372338985850, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15809927383800258005, 15015095527411699235, 3286311532938581293, 72213750736898658, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7536650316492986750, 17434434451849617741, 6148616840925828132, 435933679332998271, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13134707106823702043, 2843837219609411296, 17994654589179648951, 493169306145082553, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11042055168968920200, 10349048052365087618, 12614820822989161390, 89460090451275419, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7791804133280658954, 922078076538637905, 14731719312686968225, 396369340745182023, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13797921473021274853, 2791770430008581056, 2844146837912131569, 98723152217632408, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10617905221193062373, 5475459939089702304, 11825728031061841034, 272522316697683360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16030979659611702984, 4979785187387034590, 2980284069341175415, 8588765100100470, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6472264319659489411, 3231213189151302125, 16587209062023579090, 312921449783430664, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1002776544285412258, 8246934484225054403, 5615883167395766737, 295373842487976195, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3111991392178299502, 83618171148214428, 9093653213497523312, 375456957395115125, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5355172018136510259, 13865985324998566882, 4120806731665089074, 229659890304680712, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9377680120309639785, 11808659327985277352, 9362701792939503750, 340865316749527182, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12569603833539533256, 12732435060275726470, 9866395690083199597, 551560162828947815, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1281807810734772487, 5557285537229937599, 14054407055514043978, 561626688557802447, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6870114136612589612, 9958650456606217606, 5717621367868785235, 114171889722406617, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6860791923844561081, 5831092704677644340, 9746977715349181364, 27167211911534587, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1854555982018145717, 15261343543029843852, 3154401055387652624, 425222568442199390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4117540852079187136, 13003349855161851814, 18073274689800713338, 104132027140405991, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11655456477527678773, 10888974192983698909, 10317906052670687866, 342149695850905519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4368626347506469479, 11142298346611969138, 10010604492298688291, 482925093730542796, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3893515702742788152, 15629881421900784242, 8898552952623703674, 217423363270209759, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1127506450418840622, 154601121892408756, 17361490288053835289, 35761225487394128, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10895667689925530398, 4699907956086855292, 3682929027438900235, 56152336184024874, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12251652453799522070, 13136948957521123059, 1461680952899273693, 71767718490255028, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8262123316169142781, 10662272227942319767, 17169959487258048543, 203799261436608880, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3742154698247796556, 17533971287018838470, 13615929908639915700, 189940005969722602, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7030152037682733907, 2417780219791302963, 14986802879833051101, 30354904275255548, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13259299100189473364, 16986796905329930576, 3218033448788384908, 493723669600038765, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12784562790890497839, 10382738960654623475, 75854193486377699, 425582404773023013, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7096445958532860987, 12821916217496213991, 11298405856651010801, 60556678299213976, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1291957632489929441, 18305420337150562244, 11942356429426757850, 111809280498015327, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18001610369031558777, 17091515170629564191, 2877091952323592572, 304379368005493536, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15080117622445519104, 944218815546559792, 628426811882548163, 281043949284091115, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13088353800358089468, 1745052294860312042, 6068180167252425666, 393531985698082290, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15556075500828778758, 4263175994807684683, 11431395934602022778, 445854057210330680, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14047795444169607301, 10927753923875026796, 16468662532682598956, 158455782187269751, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9404312645502328367, 2391581424686660157, 241550256756009447, 350072880368558710, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16029426644127340417, 10184579717973737816, 17843762345008793927, 414554522635220327, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16888356682348000956, 7482363278252515629, 17380396166849998795, 39322888921945738, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15994392865259640893, 6670612506451094368, 11566549683148626257, 390087388287212163, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16028525559023338584, 11805753427416835894, 16403560602819256851, 563390918688047680, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7882045287164437615, 1037193050981455358, 7307907162644468826, 433807253551625802, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8104268392407740988, 7271340508495448220, 5875448742202298505, 178516267161972847, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12396338133332133162, 13278337483266896070, 1830038486096285402, 149667973043076968, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14656512991050895153, 17226766796091157063, 9240302315662670711, 45148168977262190, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16013672712243861708, 13790751235038461360, 10568076726745988815, 515262176496879545, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6507201697546135224, 18134177081234882269, 13722375632466820687, 123196566603481422, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8318131261602585271, 6217917880241174724, 9178920676798261089, 147747243012265962, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3347909043587813717, 9480780573427545424, 2966013745085196629, 349134209855315476, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9705735393624894157, 13836311364477005452, 3009431592538806268, 298546507034901743, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4652637300703199545, 15201599396206084221, 17697752872287524508, 358437263926329398, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14729047276829065681, 14872841611917641814, 3187755402283889535, 282324218415438731, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6228080721671078261, 7128455435808129180, 7884420133363843739, 50703567788488001, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4366751413687309944, 8961757443136819787, 15261287458401843408, 332421078328963245, }, }, }, .y = .{ .fe = .{ .limbs = .{ 494751444998195829, 1109050200095604290, 2412724168068631528, 476397250762054095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15031832016613629340, 11993584551752128966, 13799356808111512021, 158723353784134988, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4381949835710488643, 588350007631615403, 17907758462553865898, 333379622041018550, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3307544366964709366, 16401339697824789966, 10468306833682043083, 535532196314598734, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3875374707000900686, 16211421939034922418, 12288610420512124735, 565189929954463917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12660600601070444226, 820930815059993510, 9490210824889961635, 438582468127349007, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10044249209820070112, 5734248060742708440, 7958300757595099043, 65960422333870751, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 758531547533047503, 459183603099826642, 14271742281513549074, 425465980735416238, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12980299993199744540, 4916556264330731297, 3445106964200483514, 525790169876068178, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1106194410999596065, 6317913819282829218, 11356527832155890312, 298635218702921741, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2090853079871076161, 12726859410897068806, 8161960669074187695, 527293911128169762, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15528902546749637627, 11880119289227504118, 7590331755447659140, 212391786856085647, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4686615191741203954, 12301329486059876889, 2898461165772327064, 488306509126144735, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16557023692184351851, 7865680122713837496, 13079132544721090183, 181202208652469430, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1659506928266911655, 16355170968599813449, 8941011659121980265, 169211867839228909, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 775656885741871503, 16696809857148531399, 13055894456241314742, 487413827698246772, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6539571797058345979, 16580425210499948779, 17674950350467109771, 112645387744122714, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2096969368233526990, 12564989920568552978, 10471706250077691021, 57400432028155528, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7999844791167600455, 7218354321303465620, 9689499147595730497, 149175212112844942, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18222674570543281559, 11124042305889944611, 115989448480774132, 307964230629416784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15216892031997542988, 3698497996830378295, 13500925266932728830, 207800423331926590, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9406931071366291336, 13175103936484489529, 18322587499551175929, 534537357303350681, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4465628233556958367, 10060438184036970433, 14490399162870703911, 352524018477681730, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5725497718462496482, 4747301589709979744, 12811925324744471444, 75988327500774896, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12445274623742169693, 1163757277988888044, 8347414670398616850, 245613582748970990, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2828383810627426023, 1906655211873591652, 15341522601447281430, 371225567205938542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9682022232064236854, 3783822359497716848, 10708769434082648602, 26099032578612511, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1439068760011242122, 5228115716237429493, 13517982620192145987, 121035771874935084, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13710831753090057923, 15560280613003795597, 11014260890226075622, 326092322994364285, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10960262280189074875, 592119394186389484, 13153952817323059064, 128868398623624867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17866649848876035280, 17408617125065432650, 1205157829535160002, 271254531364260555, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2994316464927881245, 13036605199810981869, 837057750021131264, 553806264933736419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16326681266031747804, 2748045696434691875, 7178314978066862345, 302439115302154827, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4768196947345566069, 15252017338294152077, 18252373168565216157, 90692171255692292, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7980766838227315519, 13483495198396481654, 2802632918606786081, 327585913187015594, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3111407480646536532, 8426329325902239580, 2930505150712314752, 139232395716159106, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15264580823319865692, 2965069581554337825, 2643989965271778947, 337597530659059550, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9730027592101619160, 12215034973040072680, 2784528108857453981, 198340614856105913, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7077027699253107711, 18114895854995819818, 1824520488724554572, 438375945396273890, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6145674211479154129, 3098015548950002075, 13271228464591993772, 408448348513910072, }, }, }, .y = .{ .fe = .{ .limbs = .{ 722727602561250029, 15342867024249394301, 2807540378779594019, 246939295579839958, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5815916529134507479, 2038522691076050451, 339274293754828524, 159406817174830273, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12623000395788161661, 11852318580808105127, 6499204809435376384, 27387143744661325, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13492250709766747546, 7400045911623455814, 8134958691825671606, 515091327758929861, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10350398634801270121, 15631861619143203679, 10736345461478212303, 323411644309543220, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4573128656646417356, 12942551796197595140, 10991408819281342053, 172329982608461458, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15889621348541647864, 6320988485539637830, 15045583135734952794, 50162061232930120, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10642219718002625125, 5579239263490918164, 14124033023191512441, 107937757857369950, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4165638932427847199, 7845825122144222133, 11669609033102207855, 121336643135222504, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8744590309253372902, 13309939428127977456, 12920495560204587365, 470939412421879182, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15596583111150235352, 358562117240114046, 9409005095123290057, 449185084060760492, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4986082465807994211, 10353010652298595453, 11617497720722258700, 192279945422258506, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17398474295664292529, 11137104669066257229, 3733279452612220688, 62419042617675039, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14751887434219872588, 201048437290442430, 10143304973867035807, 394012913056510661, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14302411739606013960, 1381138149746384905, 1003026079641470315, 562929533156438906, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7325173584661975613, 15635419163173521037, 9230175697472895225, 350764608315351142, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3011075534966671255, 13057743981822803468, 18091568413369754753, 304368475596535754, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11099242636866223758, 12304019402857975465, 5739631396388129428, 43889470664634570, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12689449736197829367, 16622530435575006931, 10226583181813905297, 572132393227256366, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8299245280814356321, 10632578639153086358, 2731832868612646879, 33563904066246231, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2061834391117153294, 5739278602998678806, 617769518003240770, 42967515311786476, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13264730078459764846, 1330179900875861256, 23248554618335228, 406763533126134346, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12901669287130371581, 10464863202424236638, 17985332641701054186, 303774582432122075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 506661788494664639, 11347289098085379276, 6900642142882699609, 511970383777318815, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16683281132874950049, 2082451386620300058, 15642038367766442591, 50379214052797680, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6663630600505130156, 8336167285785379954, 395400236797732223, 258780643896358388, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5509080511188478983, 7671164824748860955, 2263626985088223519, 294782300116567199, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9489223912964735547, 15104726661184384261, 17788233693599527264, 35998351051279211, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5960730528601242113, 11002676821432343783, 15348984501708057104, 17181746840746590, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17640957236446203512, 2210107972092869895, 7128710576917723543, 216336057114834304, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6343018666715351730, 16081330940823314448, 13576379594602947588, 439807765742239779, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1851295853241772759, 15104192761666176254, 668323658832129659, 38968209127338249, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11089006479287186573, 9274294894687444723, 7589241052270625794, 196713849411599478, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1361370824204395646, 13483521734955727885, 8150454932358589975, 281606196573890998, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6219312218857985288, 17963676052017338175, 14010478768091307949, 200331343178595072, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 797380002912259532, 16280302577739705011, 5355249657143934487, 551882519196317967, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10355406852782557290, 12650365430499245663, 9421938389007003644, 530777022201536983, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6513804908458472001, 3421221284272090975, 4306322825012766510, 506840671897569164, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10114501768224219549, 6354778948419715939, 15903446823112515713, 255579366405234566, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17991546209972753958, 16348238513077036688, 18116602323778727934, 408288904452213171, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6891378373748028021, 8291097220007514947, 14455371732173378100, 121550491900328945, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15438446297514460390, 17032966975211894336, 3841843279034546541, 423337252401880885, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7329497251450685884, 12090379961462146007, 3336710957094255530, 217242997587919462, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8295802864409377579, 5499586646208558965, 5172644871745281525, 493830130345542106, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8922884806938275703, 15783429920950061876, 16650952069645278451, 567060746023666790, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8229171880767991992, 5288144753704277739, 2534759872531689018, 261246631855495239, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4458217755921795043, 17410820512917188390, 17170505487887222923, 266436325987580108, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12733335049437088015, 14289366864053854551, 15016823125938001158, 265316029589809984, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3020203238698957154, 16194908471247299765, 16910689232738961207, 477936131965647916, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12227364492251033007, 17534321770835763745, 7049318302708538236, 417200079392068577, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6575472935264208513, 1670190961973867881, 3917441617503054661, 424382304743575124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1376979204477718268, 4087434322796567667, 1037263690842298138, 53256529580124688, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12203288664175236573, 10423860455808417525, 14529919869445312526, 575103197751273166, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5132752260986568220, 1839810498694636480, 9885507614411049935, 14321714761030124, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17797806571313603169, 16393569622519057070, 6966512584830678682, 272434133186094239, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9575965705745796223, 3032335282516528316, 11040946510024996214, 32024750503196476, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17739004311519960254, 16639088937425913825, 6174720542736443116, 398080779816220162, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16745882171464841579, 10658292892824484473, 3059184099864899556, 153183194401346972, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5613343074447207716, 9295684051748634178, 16277757831229595725, 7101825607747348, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6229567867847666925, 1807524163326209062, 4726356763157123700, 533664522186978360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15780145896319512050, 2385308022048617756, 10936154524366669572, 349956995856181634, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11647508002171952981, 8729096082108875588, 16447073621404140258, 435247614436260256, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16969255939732930720, 3863337178725646715, 17872193456681798492, 256679096779561146, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11714852470340901665, 3147009520299589153, 9852368598529821726, 212218677264847658, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4738170221930133460, 3847026265682816488, 7440643047645777594, 29457193993010268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1871329348548027210, 2891090993320780797, 17956447994849822508, 15704696836928324, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6614119493990727281, 1602162943954730719, 17633924596636045871, 455469949118581552, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6750515533349606121, 15820440363928931151, 14981566423255533729, 511199765910546784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11481888021465966729, 11403716550234868715, 16328936802357349983, 554593123452664033, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7030946345392469477, 2265701518055024870, 9291442591980952964, 160697064495901427, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13515489574572624411, 1967540407654071557, 17123759146330618534, 268604787403184550, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3786288411850223455, 1746706807658652980, 17795921954500836387, 321815082459798442, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12741972633789513602, 267803094534303914, 12698034810646660228, 541843421354023549, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11818965955913867066, 15699656486716705958, 6874476651780457818, 454006905652299155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14812641244261314497, 2359487956894109567, 10588553242957432773, 440146598776293214, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17043286424374465826, 7558608690536515593, 4883948470081081025, 356950405088328385, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17873899509738894177, 739031107680494717, 17379703133407047237, 13157686797713661, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10530611865596430515, 13103904825478137213, 2228982312958657147, 447127761522345728, }, }, }, .y = .{ .fe = .{ .limbs = .{ 602667626983383686, 17289974012073002359, 10987679825131330028, 62889156612917962, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10108072206624752670, 16301135523908278156, 435124368488585191, 313645237060520031, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3650472388549532092, 9339996712203481143, 923090254981826780, 370771542920400187, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16931600820990289756, 4978561324408042476, 99840856835462459, 388718486262640260, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9865078094327428222, 14060594831492560822, 18188877797310798413, 39675492463236546, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13323293089640339511, 12294176089101143140, 11742737147419071616, 282553784136690876, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5992792213877925176, 6292258959033002232, 844415449210488634, 407248947459790240, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 804292030956390284, 11901181598577117265, 8139289797414126855, 291603869496892865, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6967453449066513950, 12140714129529186869, 9511847599753515714, 441952578307132004, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16580854510585889834, 11196234461955923989, 247971481089233032, 518665588792808387, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8647638347794175823, 7551666826937235718, 4159708779623378719, 469305779948736636, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2611263139759804988, 3174734521080511442, 2199051040687827344, 550406108122284645, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10450416012750774327, 3146156932228588803, 4399284191781729365, 191419974604693912, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16390490295221872317, 364249580276344418, 3946817112293166977, 68551176692870168, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13321178650959799865, 4788374542483874817, 15090627966988685174, 267450173368457736, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16458312103783902567, 5779962888289717401, 2883491317319571577, 210979363913019892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 560567698729560715, 13081846537406059126, 11290497454349353239, 256831559272546882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16477961950834862782, 15653705609641937346, 14100189892425566732, 144864666876901542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13021790991268837118, 15685648383202217743, 3531626773114729874, 492465175501089494, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18248114942376125340, 6502948260159687285, 8146379529161247840, 295997938617736676, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15446510383956896172, 503288772313800000, 18146897612179389318, 10397191491403901, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7679714386516868119, 14835947115493674887, 1943742043368379856, 182374927050564167, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5008060805500416988, 13006581734623688401, 399039732555207804, 425452078778166020, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18174940165004999168, 14966248565481959713, 7378604443218153458, 307993428744154448, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8465126678475924851, 10359806679670448976, 16953656517191420752, 276352942582452883, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16929222690082561369, 1066524941225911467, 5174573803474570462, 366517703219096466, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13650281098997264492, 13576929178065757748, 3696375952559268623, 175374458309695098, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6538908372082895041, 13753584369296177299, 9693713021264638725, 182850373936568512, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11451434305757667764, 18170471375568105860, 3718153783072250750, 168666578356678702, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17302049506210333926, 14706103293389561546, 3131855153381365232, 489545566458381867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 967641953739331124, 10009907123721993341, 10695546175607429053, 480792966270890596, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16354687980736167595, 17703153696944593524, 9626760217775878756, 61663084690212458, }, }, }, .y = .{ .fe = .{ .limbs = .{ 526200972348044520, 8627917522674288640, 2407008191691701329, 149046924224227177, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6148680273850811003, 15955198759147357142, 1915715758649771902, 87230526885733317, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9941895349558456528, 10736738262890297016, 16556303349807123633, 93119434638863029, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5472326562200860482, 1620337444867949820, 15816089781271967344, 222819468510007557, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7121726107269151243, 2245181310040444682, 12516949842905280246, 316347366255571488, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5101042474122929830, 9010829457507764239, 7858498061437346013, 273549287286092026, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5763449550594362194, 7288909042244500871, 1702581078487268405, 542853098305180048, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7676759006209912020, 3294725159977817138, 12281440218235764646, 269450821540315230, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10193297116292592179, 14857493344419219241, 6106683643911059443, 454899511600863998, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17581641449495038418, 12730349614658523553, 4843841585370460425, 121728478032258646, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15747602723528905436, 344009447128273655, 3484025125463625005, 64003040796192826, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12856209401739586490, 1159017103802318099, 14376868251403921145, 177402852985300053, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2279342982411165338, 17357520947277689958, 9992011520390620976, 420451384061392164, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12274606366406724126, 15897051182823707203, 2539862158204248656, 562185936986224385, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17403623151486016909, 16051343824230167821, 17639402735184720612, 72022773033645857, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15970805067105903555, 6695064896459872809, 4446198333967940043, 7557875721864127, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3939811072245882588, 13598197579603452825, 10497592932510155157, 36619252925678160, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12158278733008939597, 12132953045783716290, 149784675758701375, 574485159635632981, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8759872002042121940, 17274207760378015395, 4874417942501800316, 450981838926730683, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7047732094024507421, 3501740668061675000, 4921849839455384100, 16838672363475036, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9755991836584729612, 4882733825856273499, 12469413810519595992, 451817429908552493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1480236847444370591, 12523897909941099590, 2633247211013389502, 468054788133905164, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17795674711960172116, 11650699922306226012, 16408914621544430119, 69242211573197922, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2775459284222928839, 18258661115477628842, 7524556504781294581, 361957911165583059, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2850945593057626764, 15545256155514171078, 4591017382679495673, 535647751708015925, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8948340813219068882, 7543149992934968955, 1031905097037227142, 516830988218467319, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5836339274780471786, 12788966344379758997, 11774435807998042662, 392852980229480827, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16071255444632459671, 18066858618276461722, 3304958526151377164, 301395426947632606, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4789805395881099895, 12857779802038532270, 8403844105713923560, 403878236472907652, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17554026590794928895, 14492275581220742089, 16236761360745167773, 27917801890742240, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16792199290760227448, 5677614769299220166, 17408544781323138850, 292104021194186806, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8011170714645162784, 12679938176260867373, 14688893908954670673, 425394407991693594, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7512518378872264273, 9860459568725671367, 9582204337333121191, 34798402539814994, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17465016472598203878, 6001091660106057950, 1621428139447247106, 364278690456801287, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6386263777262860555, 7008324967813008329, 7654736559468742759, 466985962854534095, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6369454618819442560, 4244200161284134625, 13164272715361322305, 408139182455221010, }, }, }, .y = .{ .fe = .{ .limbs = .{ 851785672034390345, 7804639303650873373, 460665502960260381, 280541600730134440, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6368793144266809024, 761786927526076528, 3805850703911443173, 359289313277239654, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12266932720587593550, 10514882262831143997, 2837256050446630134, 279192922787016516, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11142599733742018729, 17201388155953090181, 2319639297610168666, 219541310719037068, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12563550622894940893, 17566492279679949936, 15938574214067195170, 415730570958364226, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9794927431642504498, 14948103469093938254, 6920785697275476734, 389738759858516303, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1231484524699875966, 17782057677753960955, 16387781949666889729, 162524203263850572, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16187072451935530343, 15048190779630214432, 257074834876729815, 230836902507631283, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7333510673902487948, 3006188685406634356, 16810531798356823974, 2869689415980320, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1983029191674847134, 13827836557688767028, 15131959353489489323, 563236686531755323, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6956006720813914959, 4256219206749358328, 8908165999439896257, 432941331628633148, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10172409055674961415, 2991643425275108332, 2604144548500327641, 211300538066325775, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14228456204483524738, 13896637556135639458, 5201465525550127949, 106698571045294182, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15117717963795132445, 6625359303238549974, 17356605540503598055, 217045358317277220, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17732954795184226060, 8488903871223844205, 482726664149736777, 470899391725262082, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13273030398223281084, 16101035855993042487, 2788971191874441780, 553612962680403642, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4469790749812286895, 14789543976582959262, 9185235127892411200, 49344726918831192, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17971517253466150779, 17533888757222795070, 1932525174799485230, 50253542355173081, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3850584319102794502, 16043516747461499412, 4611702560316070649, 421243111302763838, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6778224735795496263, 4138001164126903948, 699241902910269985, 83738503424378473, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9685194965374994881, 4245946521085138724, 3181965640295537584, 138678700040218761, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9152476036764314754, 3716669615448453669, 9544525870199996894, 556246414575342844, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13702334055431027819, 12261816102019939813, 701431582021906922, 453743575839221565, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13928437418588696541, 10310977386307986239, 7313978071613450899, 212289750622954635, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13724201507731037036, 14423432184839441416, 5123610393460631817, 535728502353306972, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11805474405405033922, 15731186868046392024, 11767251508365021414, 538536494581978721, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9771162049032468144, 3973337511258548697, 11106744195588274150, 160705997326554880, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11655957402900014828, 6897632922774411406, 9447655464091763024, 223660424415898577, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10634691786769152222, 1297911444560694983, 4712131668695850647, 120598689576899917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13075395845005026217, 10207564455191527778, 561193316160189957, 497697777244859339, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16706300397220768504, 12482845757517665624, 17547939847960011920, 482453425181888428, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14750467008014031114, 3508534097219244340, 8626446483785541335, 318650520754548843, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11952101272201875296, 8763240670433842850, 13733361674789614784, 334064537258281079, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9802963960090844167, 16479141900475593394, 13593064822682323056, 135486696133799394, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9931520924878555823, 4924127156972097670, 9522042530527738798, 22909858984959122, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7340662397248909576, 3544129621932354863, 12854930591591696742, 22231499320137719, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9379396662135460370, 5807634136013219552, 16027446640877305688, 100264491418489459, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6991715099466909826, 14725428464397014929, 10740850060083389918, 416609077927722201, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12354588195886169591, 17031162387890805201, 7995504203645933944, 397263989011163644, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9309654085235182528, 9355903745052814455, 3775323213197160382, 431994330589920540, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4973341212311959236, 3990983795377220086, 16570498405848869579, 244432505182713242, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16799827637869355568, 17867291562092318189, 8116298505583832067, 375238979282479174, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10604958694777322258, 12435219654107797861, 10709097673951509946, 110584013582577924, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 200041902229076688, 7720682185152763014, 14862120859429147539, 537036309671738230, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9411419029978731005, 3490780876696751468, 11197604063124729825, 43633620017640515, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10859785726629222592, 1526398368145170403, 11042235489459303935, 37780158557494936, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11431621366692840492, 17603860459562666680, 4717098704930563603, 270517451965618795, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9185293150387633677, 2841462147255091591, 10131199200212860937, 389858634839621511, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9734373645107459262, 16522605902261066416, 8759380845828337940, 389538639006989627, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8665633051084320401, 13844036922304098598, 14279621299215254505, 161812991764265039, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13276282294908732508, 8439515456973525890, 11802180493719618365, 175332828671666075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1597602493452300091, 12360174065380600900, 14761852859082831137, 364307041777008899, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10158488418799560864, 13272671824035112966, 4637751150364534009, 88030278406812886, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5881349174673715653, 13203574425191755691, 15543913143608470700, 280829392558151223, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9050039357246961471, 17356135193867884853, 4530594212477272819, 130434008949460199, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1172934139738815846, 3921053270172997083, 2180994751442803586, 417757033415262188, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7833863279366022076, 14815648434042726159, 3069234065241894480, 433448015835396692, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13861762188650227562, 11583127390409286207, 10954365989506609354, 98085666048447336, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7321806517273213272, 11144496328969987542, 8668117221605212293, 288499415411959197, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8330187583621549297, 5748146285424897370, 10245851208202899329, 89156122096407823, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12640650145334322992, 6839521006286079957, 16044600529541741214, 265003688152012598, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4944412574004450784, 4851430994021934800, 2099276135391467291, 349323538955432971, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14866145299589666450, 4261271311411930614, 9475576747816015115, 66826930892205220, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15666046498637727731, 11181074789572514355, 4767783739153979567, 89129404051844505, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11344314057597569935, 7919454436760059576, 7304483190455579842, 287799244771945065, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5190497011092042296, 4929406500615055357, 15348112481565197094, 321333260896357438, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15450239161480202154, 1385408206251546821, 14086704522672761080, 363097870197186731, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16433811279249904959, 7086984708921448708, 5167436367061529492, 73475606789490951, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1571733773272134592, 12381475135472533610, 15028960760715224049, 48184146056438305, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3304958075414462307, 4994798233459185715, 12991455251592484072, 246340722961270793, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3199376419804453782, 15322171618696205502, 13587637700436628936, 241457640752671685, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1737893813571152331, 9386542412591238829, 7683481463662700285, 417800748027073779, }, }, }, .y = .{ .fe = .{ .limbs = .{ 924096204756435432, 13820964774173289145, 4775877940336928306, 554310898298781524, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14181124907559851480, 3085631853410802113, 2991932878566387488, 35709350045923479, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4561775337722490161, 11215805500850519935, 394779798915910449, 277261226855561511, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5648411079012792777, 4376010857817046739, 8706103991222609636, 281206748491699650, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6052627847062799750, 13296037268575343088, 11841252775980332826, 308325384807731866, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 149420943841418506, 6295429524037323307, 12195124866403294657, 57890824629005316, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1198162378377260962, 18341045859138217648, 13502574376522185510, 374512037572407256, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3937787611301091197, 12717910990669395679, 7367795626272597670, 64320808453848998, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9969632024857835160, 1167636333753597053, 13328951389018639469, 269376767806039499, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5294790234062841868, 7920982726320314052, 6889991390569942879, 210361691773625475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13873671451837291322, 4008136330459125402, 323314392742383476, 79786523359369196, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1546808111424868771, 1761772331115036353, 12214778737851263245, 115205816268837453, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16452919507854867111, 7282391135262747531, 9758334574700977060, 283674554130526761, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3574036737051276993, 1719953581154871330, 10455517955710780401, 384114362866811722, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6726690548787287363, 4312728732448530883, 12685767475592637295, 141419403006272773, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8902157280935545104, 7719405538515506074, 10989493644028249310, 18351956213680312, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9283835284121198368, 943938507519782051, 15130076497215356962, 95498180816152778, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10114004174370946590, 18050548702668634626, 1871333831370871246, 545312343311345848, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3920357249501580193, 9018680810564119680, 8172559844508228384, 152551141700024483, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12794626968241555664, 11711491641780648770, 14633631094054916685, 447064766421475099, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17426687197344703899, 16215203824090643298, 3478396992233592857, 240324376017891597, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17643356679698056295, 18399428145572557529, 7647039638189862099, 101566820621912399, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10107628778968633576, 17383635559020258324, 9649706261672271194, 35422021867937336, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12133212925630504582, 3723089923635977872, 6265613199621874421, 318701462291929985, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16958577888888224970, 16932102334624302993, 293736299231229942, 341194542468498522, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11559886251105433454, 17186606228802779267, 2431977333365014617, 109639571278761210, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10855097225347243097, 11733121288198076284, 18238760613635130259, 543557968663167321, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16539032320242915068, 10218754528365377288, 8967516112864350083, 501102676833374563, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14450770285992238921, 13286681525123145544, 12749613388422254349, 565690355097784879, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7272085800563009137, 17972382423623778511, 8209284046764436453, 30067457235044779, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7853281693934912274, 14513994875985553926, 2682843633047383505, 313754963470059060, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9454427692713035939, 14912509897615001851, 1933564020944221598, 398636632743316987, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13879093631600764092, 11466424831101468923, 8217284579753390834, 338252609559718217, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11238867163057683299, 5808077196128614210, 8364426491777018134, 221456232709100535, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15025574857405747940, 16628731178295865702, 13419436956814138877, 194439919675318431, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1975188119851929823, 2363764417715134133, 6294301169247279667, 25978791885203688, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15653489783764618508, 8795132233920850601, 17176478576111113010, 492522191766089279, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17786569108088572940, 16984010761518653209, 12308618492272021178, 486164050318626948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 22513582848160544, 9372800566274642772, 3626013193059266650, 289450451006740832, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17445538837406337875, 18086909248718461996, 5338907091733665809, 560826938328629480, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9547419267779629710, 3125567996960047534, 3478174769564621301, 30271410953483155, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8866885630482044743, 16482933764299708161, 7042493938067864354, 48510676952042254, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12160488006104483148, 4040132027952934810, 14868245764106624933, 535341167796005833, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5065272616408803453, 16299527390538425035, 7079920589228077829, 477160551531458702, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5375896691248945988, 16085547482342435295, 1268982406592904227, 573508487155201869, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12759692333788343966, 14846083953693366859, 4977013191440388499, 447827145371660873, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13474687474240928658, 11251570402917043340, 124007504181557106, 300623946615153597, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14179078046700206022, 15186620040343286186, 5241292994119559165, 534320472411442105, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4073280361354857862, 126566919189616390, 12970079126685707161, 177893495674240580, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17252826193886556840, 8589832681528040857, 16970194297404196966, 34002253200577722, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1035309274313171069, 2603478352520222827, 4863120998813269881, 144687764677021706, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10295476321363210491, 3625145492656539140, 3513003497831059656, 467988068807659789, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12357314458705616119, 13778496724634716822, 8227130650002066397, 214790013228005807, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11762736605299448270, 2311031577694056988, 15747333290155525225, 325981086772104362, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6616251212466177537, 1909328121035368221, 9509742222736389076, 249449307149525383, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3328392306994323119, 5259999797723798274, 12049097987999081621, 220982074382311952, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10698249923976059505, 4370438099917108940, 1247165368049755097, 285080681862924049, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5329026840274972526, 4663347639090431429, 15617961871433800315, 83165464189669772, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15175150950241264831, 12177450133467501322, 14407424660320827985, 94534288859822382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3048978111797709485, 4715510511098382686, 7960114294969759840, 563926079786427272, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13724872202510742133, 9562487148381734068, 6184839089557033610, 111500071154665252, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8102971140500437396, 17524149036564761679, 10940159180868698546, 100454836386250281, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3113186315951796790, 18010313745287735407, 8324453530433566656, 461253026521162594, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8495783952081927737, 1709836487296406932, 9172707527258279756, 408703306467735078, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15811357372413711015, 13091183759372238065, 16937779855692048917, 380870141606475453, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15092227164410554563, 16105933972295050793, 8557021528994275204, 565446457761077754, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16017364389594366208, 11819236266645282425, 13033659011745315888, 463689196449908171, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11975955138140884276, 11547211367367149696, 11654234708619878414, 400557865305116440, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4165499845911196500, 3533101300741829206, 16122722608605164280, 110754761024059512, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10507489988504496214, 18295834738443458837, 10535011355886924419, 514075237861113429, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10068521830556494492, 13262382603421551544, 4856849201339363694, 242012883110482279, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14792846743138337614, 12167399334675777844, 10699449603640769653, 400129504139182931, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5411855163111102106, 6107134897107453584, 15293397281939776589, 94980827349323693, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 919716973460550607, 2460309756854636729, 3582613312158299240, 280431406951995410, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15889035618838389137, 17897682738635242507, 17038882754175988505, 138845026082699390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7368641368297677166, 5083956399604504468, 2154215204858199566, 57756671851463758, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1238042691099011822, 6627414523830672719, 337486065711405976, 525416334042451434, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15991345059073839519, 9989678028461637270, 12174397435840288056, 103261262353682615, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6558649282940236733, 312336291888741357, 6794442436321987121, 269823928363960609, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15726994596783322683, 8247866281533054456, 14192637346600102858, 284760244673326112, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15183494392712078920, 17040525274191257121, 7685058392900688452, 92426014015140538, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4918459491712695251, 10120940870911272273, 13120632251561933857, 276448582486424934, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14499890789862895062, 7288331104768315147, 14199925101961878501, 126970279039908647, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11897826589287269084, 2706823104083490170, 3897230911384360389, 462000485672558995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8881156418881293510, 15445401724412315384, 9985163920881845053, 350022001268414825, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9149953810672039699, 4622756430478875867, 8068745132905623127, 510805860011364729, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17670811551804007797, 1135678465962954420, 13270885876924453388, 545664696913563523, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1343301083888659518, 16889449507502244655, 16387609799488744145, 518182466532248292, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4102990564890189688, 6839359364628745143, 4721219220326338544, 336939367774611310, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3631198185513589540, 6642621808423228248, 17020258205888443454, 144285119512900236, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8604831561268156954, 7748206776616699341, 6040173851512212312, 438851356306865397, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12969485909760294296, 9798348213824502528, 6465415368425839759, 522089319837246511, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2035802976833739243, 12144446087646897729, 4357408357618663942, 296801074021329515, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7417282378538254270, 4383636143421165937, 5566408632592297036, 45079343803115713, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17232236075366926187, 8164413096464104608, 448214952328417696, 159799920231155540, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11566149442880474789, 16173353115307156522, 4779317396672590193, 393525396265008434, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12356013882876946254, 8196300041640515761, 7685463742727756297, 420108079165376094, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13236374787143583621, 12512034881711105985, 5730482461533131485, 117937234116183715, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9879728890605924579, 14463984689166138433, 3143429225214783972, 185377413737369347, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7273850360135135267, 1634672364737073461, 15822710011791910888, 490487378741630419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12603675882092945789, 11885809053795347530, 3054052041359488720, 99597343955930145, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2236974331837337797, 18212194329035352728, 11150970233476136752, 241086276732391816, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16525337574447230906, 5524535950819018460, 8808028032865126648, 275775596422679403, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10203571199953604212, 7707524028197668546, 16836754749812952242, 101072024718258575, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8724039542818024967, 745336549374782430, 13329414072845068904, 568921046257863480, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4658550808298123894, 12776850585352289047, 569730529793611656, 288368365426636134, }, }, }, .y = .{ .fe = .{ .limbs = .{ 61937436062784718, 2713090689714739277, 2661922882171221784, 399658995378903189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12044130464691105737, 9645070831357769039, 7507682003002629693, 152687194898083271, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10581006478916348298, 6300038032443182054, 16614889523702422118, 485834052189713612, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13963470620381389899, 9101278341108140297, 18031144259344201351, 12429266471677088, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13739711682143482188, 9707593906826947438, 10346588841455281514, 63704210996060073, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12526627402056720077, 588601529408570821, 11439378291698366929, 95337787652137668, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6205471781703851746, 5053143366101574035, 16249838791516723498, 377345633845088541, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5782235309747857533, 3133560651282012750, 1653617675983024290, 45370759214685573, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4760562704979276767, 16084254347861224991, 15760470741663856740, 456391558923743749, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1168189529741924532, 1018044325913320669, 1016045262208019044, 524300600492218536, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14699203080697400340, 1945052594507894327, 11770042110123183459, 102318937376993431, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11849678206774688476, 13622165796220481049, 1705244792061863054, 319343898173510783, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10055590353992490618, 3816853177774237029, 11439712191670234654, 119558480338938989, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4362254566925097729, 9070062631196492197, 5007705134631208753, 288710930223221845, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14403278579841757216, 707369095345287576, 17972514663638347044, 446873312653793269, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15830903983743751664, 9396891716656748997, 283231381981522476, 471871463521080088, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10628530968580773120, 16880707277229042321, 7885705365238975, 124989905723366006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12116033367663076372, 3470259911810594241, 14160453000850120099, 358181449834515934, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11556147533489309254, 11725489541474395397, 8485886532941891329, 52574242542986227, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17621041448442594135, 1482023962432591125, 6258342158793668436, 222473929675393714, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8857433472154035663, 2600399106498818634, 10787917331706556707, 8253749367290765, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3663697637684332680, 809649279051418068, 3933681715155301489, 527580758106681837, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2127664572814193614, 2035673671773843381, 17260573978827802009, 217520144326102359, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4666691847137778303, 10119715469750701378, 11503069771321514634, 562931864745687558, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3282822845566643532, 14893272043016304756, 12368309728587972064, 186284033509414523, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10351844876871426056, 11800995050608954935, 7819400177652015951, 254269164252901499, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7360505881093896132, 4129121451282015688, 2246136900361118385, 477672322552675985, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12226589931753417856, 3484632845808646860, 10579596961968429200, 329018977694913929, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14032020210674920606, 13229374818065054905, 8768894248269846585, 537504398154998941, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15128643695187757237, 2560513759208295344, 7840907473356514882, 488079631256520819, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13466772511031325598, 5916390754291114312, 7077726083291700669, 295741746048353462, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18175728133415231025, 7845719146715255708, 2435248290545547349, 112155022551820926, }, }, }, .y = .{ .fe = .{ .limbs = .{ 117327006500508175, 3489776052217200572, 10604120804903795102, 186604037374674414, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5779751893738974761, 11512153353161513675, 13794975767839571723, 119674857350121935, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2011837134899333989, 14892884071315447583, 1358058814466308728, 106661031684965528, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4156397349792154267, 4603245393324435159, 16199598564045677554, 475085788717010252, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5713855811876607098, 1826138546504624517, 14917483246990529833, 69541826791714128, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11086295739698349294, 9109011864707766768, 11118244175597693144, 183307306948889574, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3016562234877805094, 15222062310375573289, 828411657039211418, 258472315440406360, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 621488382954208082, 2646863641801027142, 10538367733152418199, 39303425993967869, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8905158940124390632, 7803936009770958294, 10972848335467613162, 217943749314268080, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7684646099365173711, 16497990930643201133, 16451144896627150873, 558304622573798713, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10497664452622934326, 3660278907638904100, 5616574795812469202, 518034965299226140, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14407724815464097913, 17828714840180502036, 5346602009994162231, 368027971489950597, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11058705855166959503, 16424794811095627159, 10858936986343386573, 475785948242823593, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15867824325490034455, 11488917430108751690, 13245068941471813228, 563694520253099707, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12826143747590015457, 17648877115733036083, 10948165927966242589, 123571912400350619, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11751015231858051737, 3170359556645183871, 3273567676664756043, 417385285389990177, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14872362272893479241, 11919460821984518973, 8014212803191269688, 252483601662548267, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9707982026062557407, 3551139781695295836, 17325877250293903898, 308611913314078149, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7145821063572106979, 1353631305254499854, 7192804988885076775, 512816069643066085, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15140894124972741108, 12045849607819072641, 6443646791505703862, 11153260311942480, }, }, }, .y = .{ .fe = .{ .limbs = .{ 275835998137983524, 1578721592860241338, 9382928764499306613, 254856360571791352, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14141921951633966254, 17198810434706233197, 2296355166861628709, 20484243594897863, }, }, }, .y = .{ .fe = .{ .limbs = .{ 48287898521215870, 16994504592824535124, 14745825070315473207, 297782192010831240, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11849009020106690022, 8958822716773017978, 17231125848481136910, 147341870184465709, }, }, }, .y = .{ .fe = .{ .limbs = .{ 460580449663912228, 11725232547109069458, 7470090670349389847, 533278238767805017, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5006430009295692328, 9990056751862071445, 10422790138372531108, 13949431895511034, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6437043904833404183, 5380748395050161285, 15264355879902975456, 499957185742842896, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10632109032154559665, 1295117565487781475, 6287411909914131698, 407182210624537334, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8883115435837886855, 1390137155717281670, 9838205380776148603, 509746117612233657, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13275958606422078484, 7707487654697955428, 10305897939495567863, 212400532971855502, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2974705545898916673, 11707610121082525209, 111757789381676762, 118207203311304637, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3381784168725619831, 16360097307464365303, 11264532860825507394, 162169292321568445, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11276567789049727735, 4591360072278675351, 10240396252905975079, 541178780489114250, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3139213119357725255, 5797806538769470649, 2472536069406004400, 418565518828471666, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10108447492632772607, 730246137776371394, 12258739082858956766, 29848569586661399, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8931613213080284135, 16070897387569037577, 8906495825450752605, 249572219585236861, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14458654658089706129, 16170292075638674456, 581457232766655722, 361944838793323559, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14400209750893056464, 15777990434865703674, 11309205313776743715, 557488721348937664, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4862045216342869293, 16898912275283107178, 9129127564733789741, 560525248087001699, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6560699576131992037, 9983002480153057702, 14783785067181810948, 16069554353349525, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10918640250762794318, 9873301549043777026, 18383610931550331298, 71717865490410572, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16658083607667804658, 6228087053217029080, 13379095443937847815, 414364438563134019, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14699223188762325027, 5618232198039295620, 3936762493856493947, 56647760813028448, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5932586022644877328, 17778174293330630345, 17190033232939996823, 532549340229841711, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17123954557672927162, 11995511971376762430, 8120729849227757440, 537589036611087554, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13620606671819440054, 2293461951157862326, 13876369548903568396, 73580829890807121, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1689004207492928984, 11067590234527758407, 15944335950684725268, 507599781479092195, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16769462892706640030, 1227135382632476775, 6302041938843007123, 2011903356843015, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13616353758333199133, 2754526337379806291, 11913088616234653131, 446271048908618056, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3297735205345154674, 9108691790451152584, 13506286348388175741, 87688574279428472, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17045835315125239165, 14246155604100882247, 16571209095253861417, 494559611430050316, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3653098252352865038, 10455566684272718214, 8418066718273437222, 120350849958247424, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8694101212995046253, 7576992982512062766, 9225949311325675202, 279511102344789970, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11745382476259278633, 15409454901356594128, 14368518298581941901, 411286796186061004, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12827635051356092221, 1693500739779838879, 13537254139438275060, 66533698614401492, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2679785517626369599, 7938687530404523078, 6356296659912377075, 39752652140596204, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16156042477270853091, 11779649452084241412, 9971592991249204631, 83456000731602197, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6199329195812069642, 5615599415754042074, 7995433433070231941, 222545995349272097, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3362482742830969076, 9415896192927204643, 17802879901109437827, 402921961164327362, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6183670889501506807, 14929949655935807893, 10746978839506518184, 418040965860403837, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12735902781583167786, 12077630616309622764, 9737479135323597583, 200181596482371064, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17591521296901105893, 12404686964748341124, 16918898165939355601, 144266983152436449, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15586993577781855484, 15786406818279517416, 2384876608872714222, 23972084191998603, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6165893318328860846, 3229347573809196850, 4891641964783683488, 314852056850898355, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9452737625110992855, 17392404311913977631, 9410316213732600360, 383811917634594266, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1670806249140876624, 18441172415941889062, 8222603783076631871, 329521087524830734, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4985024301264898070, 14537592030051973592, 3022674935184313456, 451358475432119562, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6568104028731200737, 14778661774954642672, 16691125442072352143, 246031442145734748, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18025568220083534801, 12018258184356668311, 4074320775417950489, 569779547400121978, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18225296419128310010, 1093388705436681989, 4501759228627949785, 315523380031258767, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10134415180464838026, 8291020451587129420, 7675478897332627061, 283531774923404977, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7489441938719029336, 8816897393674897523, 134084689780073854, 535734325414897568, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1441027238558598116, 3036693634250354872, 1812453649045981382, 123340408339708918, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13755861381938774312, 17022454447008097565, 6277117758274515404, 15621506785875883, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11266614337355170173, 411361284296643548, 122310397053483211, 189626499957885422, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13477531670388832379, 8489865535122039257, 14734864397735535355, 338140013273052208, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1283349149088131578, 2847056090076939427, 9765083767768104130, 109854094868901503, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14961200183920015613, 7938811605384865150, 11951538916295057999, 244976778568481768, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16469746423624914810, 2833140652627128785, 5116764439868923672, 356115398293772239, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8947534344801189923, 9475486042927740496, 1277827644245251313, 295717789309604261, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7997181771860096556, 205389760971681075, 6765619741631155407, 277183761682661344, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16468426873498999547, 11259223887045672246, 8871149428611020889, 191201058212783227, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16322802617133010690, 3486137618317063527, 12747683708096059830, 463503190297594983, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8137912718641699780, 12397193597570838801, 7100206756389396616, 72124363855384393, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7417148662841540751, 14654864970643719828, 15965393317055658670, 493127328370538553, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10010574445664966285, 4611732769625963181, 809019605171345381, 516075013945231663, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5467706186840609580, 5198849972497580320, 4479639792190725138, 102064888990104923, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10218158494400743015, 15048865846442916533, 12051713715736300140, 489276275891072965, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12948265703162751240, 2021785692517951413, 3277834868671990415, 428887939092422332, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3208762759688274691, 4357841556879139103, 17115633256720904364, 312514012199301134, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5271195748536717707, 4746804876176029251, 4890221399264900336, 85468628464872340, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4967036524536971233, 7213750927117510670, 17758105526768540374, 107092096465527455, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13282338155734019322, 2575645881663771038, 14607646786182116934, 339803237083203588, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7819729337853175945, 1435593715037803404, 8089811598393168144, 340053405861316572, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13916877862624578360, 3100978227986113278, 9676192589687498121, 254173657386311535, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5381449990226873561, 6951786952405887696, 7905386323528582895, 500719463505385261, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13441034113130847652, 2405464070254100724, 3734141506008128506, 535624259165175575, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16781080913845109139, 7676593103937500093, 9155269117838795917, 24462395882177241, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10703378207651699954, 16268959549802434252, 2791116719827215164, 433848107973669367, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12974286938220612934, 15902844761471748870, 18150183229412305164, 413980886252046674, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4938792914648188245, 6321977483887289991, 10822404994119911834, 474519933548181641, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2048263490472815650, 14369328720254783119, 7466262286569898029, 301769599692379997, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1897055742080578345, 12154878186438128309, 10297697706893431557, 473143665390727814, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13542399002179649094, 3986806875251493364, 1460218508107537073, 14673433828528542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8504423420120998818, 4630845725076236089, 8614843534419390865, 528964370671122750, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15708717873978064824, 15510848298007970620, 13452528395607112638, 449124958643970246, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6774088475254890960, 12316821175953168563, 17884517130824402993, 385187075228189458, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12076504233661866927, 14889702058658659372, 13640815879901513720, 27539114207307866, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13434524288701918803, 2727622831259075381, 14631431026815851268, 435123434741168962, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4979753371406926740, 15551302772156541291, 10233113917291200758, 566119977581238916, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17886085361560530158, 5703523019282292780, 7322743561961827655, 131675699588234310, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8430051161412515997, 18309912704058408913, 4866091858234590227, 196950546235277866, }, }, }, .y = .{ .fe = .{ .limbs = .{ 133320928173724283, 6313424694317008107, 14173759000889547549, 404016948703988418, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3100033765006288408, 15019165551052847390, 1998897392502657328, 253954049308892913, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16315819431809147558, 9076381052318973038, 3555372711943877014, 464617245111367034, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7986993942391136549, 1833291970128318385, 3314574680524159985, 210961748850827995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11533548722277738852, 4649993604812857796, 18409223970751844623, 548720754734820218, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5157000027371209163, 13507170806370115698, 11194121737283100431, 7375996874321540, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11237946922051444758, 17082617181418983959, 8886252076677772306, 191764480415053644, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12018089798084153138, 13975692024986532203, 4093273171412775525, 360504607129996916, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1392489608958188911, 15018245955002045466, 11329974107739854286, 464052914918731619, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4047326850563393331, 6177798478851142798, 1400681922057892086, 201506254653962973, }, }, }, .y = .{ .fe = .{ .limbs = .{ 792933640528599406, 15061655018525231938, 11708263865111648365, 84217931566502375, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15736602844985500543, 6723285059332691415, 4325899300364218184, 110577467236216818, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2217131729482454714, 7060138456138434044, 1655003283006890247, 538261628507298344, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18024130190612103844, 2566530974407587585, 1280922572569090070, 302127438399157224, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2721181013135329908, 8086141000044589117, 2244608069938844743, 478535658210553467, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13965462113982013795, 14915150977981408670, 12499992547544019930, 555288739253636442, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2270360718904190365, 9815350544565011395, 9992325067695882610, 160532779296307751, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17190353605867473540, 11521961333129101630, 11133012171003982044, 571904030365568444, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5747685566264221358, 2261602182790665426, 1595761676651838537, 349221841790888029, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15263301430218958707, 8509759570925086934, 15561409298078283905, 473704232530424505, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14720218043436572909, 1583726251965168810, 11743411718489588820, 458998176938894107, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7108721630121717401, 1439146523303723301, 12569981628062481262, 229884429593596035, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11909713324048624793, 15707311749718875496, 9975559061487174965, 333113001503422215, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5371716470121092036, 9314699551728066567, 14677827299569536765, 29414761220989933, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15762395648468139579, 14651703553544274701, 2353811260073221382, 163356346661442399, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5256901798729246953, 2420772358706335079, 10824288394722989698, 2140379704816778, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17235610839277005612, 2545686963591762795, 6659720382663210180, 322048339447937782, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8412016397751024652, 15969034870093978018, 2372686766427032356, 399393048412130842, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11536642136242973611, 15305830497515163505, 14621613801414781028, 8898730103337179, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7626397940109903894, 7229748298861740298, 16233287803958184149, 504158942886747349, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8071906170084309212, 14719333560253833413, 18025041161348964232, 141308522540643343, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8660565327157884157, 14302436085642647249, 2883151584064081078, 92952160143735374, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3911337531966865510, 14892208453307367101, 2935410405873876550, 204143629343782539, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4084831677849026934, 2191414620920061719, 12097307227800404854, 317031904627027847, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13957000452424288317, 2253898268322432332, 5705667200523582064, 52044879628154608, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13425797188849095905, 15212108399267728095, 18404498717183344676, 391295707486415358, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17808888321177891262, 5952605236337642275, 6011710291539943949, 86109932111176550, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13801865446645691618, 4743670785615481445, 7194723738339436332, 49677573681230132, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8964235889745705209, 6234205315861951602, 9998251648454280089, 424402701845650995, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 739971396204429101, 6448621088734913743, 1449192989266726711, 112807682574679249, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8905957916438398312, 712927843974457387, 2224471455689899494, 467404184361749242, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10901702809044943843, 6094885859877862475, 15333604971016503761, 501105976024719011, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12346759469560666748, 13643419175632994887, 2012369215750170500, 541443270804196867, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4032376807879129029, 9784499480286808927, 3440914809529433820, 223291640407733948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13604952893852443643, 6941109902661292269, 3241428592004194990, 426687913889924353, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2757526926961026714, 7191459980271489595, 18128967034013859477, 183516383410071640, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10144659095025531537, 10087325094538304882, 11432547631744575705, 368793430781503166, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16052188366688595552, 2651597497585160756, 2351158209322731942, 556365873460785263, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11133089406208555689, 14174517319744588753, 14903374649569102692, 277345409324094721, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18244306352784415650, 4287955035277117182, 1057469681808491653, 195729315047835570, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13112025723375573653, 10892322617773164246, 16577392760205370658, 193171537713376083, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4964196228580680894, 9754144630989931070, 13821786885452681648, 252939514907651003, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13352311291665725247, 13245520389576248130, 6980183088269297087, 327942926043687947, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10651639001692414851, 5400692718993021708, 5782862557637824061, 25154207474696679, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4065282256443120035, 15445582423914111411, 14054835361100901010, 458802369122533557, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14932206955750419551, 11114460190190857354, 16938287287457722865, 275263517375755629, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13491370044291658898, 2322663963719935818, 10496541192964209487, 481232150672155742, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 255720463934108580, 9516009794930900716, 17096892933483499703, 488302092737744312, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10690192745490775763, 581549797662458114, 1555598961754613425, 127668204096877594, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14013347484192874695, 8213152819602000245, 10446542455822150226, 6866865321364123, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11437876746360571998, 7312786154396489447, 4518712813620008654, 376264381578537092, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7690806294590586864, 5629068265921058966, 12807938174505401547, 12543737700153160, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6184858247510785374, 7165898071471397480, 7577539791191385487, 362084204646857399, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4656155754467439739, 6079894181677872112, 8429036680658432108, 113893079242030379, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5636379438375036303, 11729254821639109471, 8343239503585656442, 107788624577736882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2174721648936244353, 4634321183585690648, 5063408972877770653, 304832425762297928, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9327446310508165895, 15875987312542204848, 11792668147964773580, 341414176115572041, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17805079119926312526, 887838249770583667, 10293021889696387363, 407504184791719526, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16766444765927205182, 4282630696483638094, 14154821013090872547, 1812089111990290, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17689552409800180999, 1265010834569091099, 14200825045741703569, 256772570433488696, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6810293181747256161, 214919174201509857, 10277096960575601591, 425559134640641563, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3496901205178417649, 425858392712039442, 14471477808846313668, 160046101428854686, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2299073917513339559, 2356704355151087191, 8736683974166376157, 79627970197033217, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13307167365012580398, 5752602177304618312, 14357633617183903309, 44704331521847142, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14378306013228075978, 5279689627359972860, 6722526987200312807, 1159804649160044, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6860255188838407470, 802214380535420620, 8002662016999687488, 344309483786527040, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12219865927685036619, 17604936858247789984, 1283124990707657971, 506822930972572946, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1270414495909320742, 9937213143839974679, 13785876477861883718, 452998474559296676, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6699513982196983227, 7097467473425931634, 480041265061287687, 24233641456902437, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4752744159485803472, 15637240134959553373, 6013497089959222623, 231745516298039275, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13476015582157885330, 244991095391033794, 17350187805410849072, 499106517810512999, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16110048347066007377, 3981706135792243025, 9554564696873814658, 362889199812178604, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10735772812802386041, 6722340271420998662, 14957719606574085958, 344843522651623373, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14933192035863659860, 5525349372374584463, 5742526426877063840, 240008601825297210, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10300036157557114409, 7269065963473665273, 3019121771136495053, 171959522534598068, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14805573146570340375, 17020555876625985134, 5980081597951286521, 553692991041067436, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7381900073241321707, 13243108841303473055, 3613493642281964392, 279550588957193738, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10253300995092027992, 3107716887535972269, 17335247695946219796, 461156204609024547, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15604544241202357024, 18242684940595854210, 9595546402718670426, 436923009631099777, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2345828709915333814, 145768556992398959, 14209584050291925061, 252570214110633127, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2633389065738632510, 5702635991869175265, 4026013792647103028, 198022731236063420, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5705785658820415000, 9511114054025041463, 12597360729756222071, 349746796240654114, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12880123809997962586, 2159005698450463889, 12434537471676678620, 293895549424602139, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5599184261672971931, 1957489519997873373, 6939755571750289857, 23202266284282199, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17136182287091683884, 2105092032507745423, 13530242036024827764, 344558963450723864, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8620369252225072065, 14815574483729179189, 233865748536670243, 474772968901987998, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18392720107385865507, 710862615227869016, 8845279650616113350, 470771218931880474, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18079916048212058803, 8269723711109248497, 11144440681148542714, 11290784725431166, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9320777662855589896, 11490649620539631467, 16526423244961466933, 212303308027866703, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7009928818298858389, 17625415588366038364, 8637377457114245720, 13823137547887919, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14613355080229069816, 14312616303126646339, 11132740818203011698, 398376578612362375, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7110979356275275608, 9441718658416534483, 4776876745138358757, 523371297192344494, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9519352183019614823, 1325861907511984150, 6390473478913151624, 233399747113693568, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14300243960372143311, 6814809881936557373, 5761749331497479005, 268579459117389865, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9233048121491868856, 17363986484154469616, 17523092139380940095, 491919943950972931, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16129023590172024790, 17643423826668730069, 12121999140105417717, 539315219417688425, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18390091812810584103, 18341619854599938681, 16798870358456352976, 369061244648076409, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13746932369554354884, 11027905138219304542, 5025097144320287537, 126725351786361350, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7044943387549395904, 10354352732949914839, 17502309380529040400, 60607984664582680, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4992484778740639487, 5378866648315718308, 5835547576106348351, 198251689277592961, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4446015548724859310, 16213823472738342436, 11977607649541896634, 303358611620371161, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11947305993111246642, 12333938959580736244, 323784528416490798, 1935759770392935, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9366068875955489686, 4716623639111762506, 7730097695248441535, 407490586287713248, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16973574915745230104, 9706577183604242436, 10210855763474299624, 200361784145119292, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4515530402814893747, 15443827297939366589, 13026634577948134711, 149455162059474258, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4673143993860248268, 14417631479560976203, 2695559728763034512, 262033002133785005, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17920094120053529521, 12181421051193326892, 11971296823770497533, 43878208941552072, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7162960248233859077, 11572333746263654562, 4850448240858756375, 322957098267132464, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5508812385879292742, 3071681223404808982, 14784658127125320346, 412910102668036950, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9669510390628514018, 518366262218420120, 4515916936684873488, 293952536054427783, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15076529385204383966, 3903369164223447524, 2167240783994725538, 286842934220131134, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14615100334888361723, 18299693827000641791, 500831163655522903, 367941966903771302, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1357905036535080688, 15902482718950808092, 4364879675108160118, 315487986289265923, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5586722552049384059, 13623660895211412395, 6624795531951403304, 568335863647933619, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14387645160964397205, 5694293162139263499, 14586684700458022021, 239075005482550639, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17874437631973327005, 5027530416027043593, 10953606866494717869, 253023470464864700, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15042840810390528138, 3418606280652229174, 5776581558478224155, 388868637648247251, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4004068416263034716, 2449570571085819562, 15061550474290773709, 45328159972269422, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4548508872634524741, 11136615910366080438, 11959491123827933889, 73748979700252151, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4125942086077854170, 1604649793631231444, 11436961635852716096, 412736028287697493, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2748875764258552579, 11371547600093232995, 11221346668337247249, 420215995306611843, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9510136727882449185, 17863362470608308729, 7144021917113524760, 430563862068830890, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13142902354989611860, 2890670151583143098, 11666236673409585405, 276352265946371337, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1647698555380031703, 1181579810472553097, 4186843795419677548, 327328907284531736, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6747173941338366184, 4178743517145648016, 14919975937446321993, 451927184797539632, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17287139846538294746, 16686695244766760179, 10284615777151624177, 334488397000002222, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13031964000894244577, 9537093216040758297, 8895232130077400562, 18994595545268315, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2919358864320178839, 10450125907849555854, 17472740845225954305, 69041609888241551, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2901938673777531854, 9578010631779007100, 13803046638319652382, 226779884139862286, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9566485048630570395, 15693959041084496051, 4849004766168643435, 413388717749060557, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3934835637439336863, 14895763314552624816, 13990564919486393087, 313074959602822073, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14493086873108589871, 14870285631004672483, 2034618807826177390, 135069143438284823, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4975658756792553712, 4362313640841755671, 5046232952126846013, 195152167024685794, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4789354227815325805, 9206709033499752385, 4459854662591583593, 280749794945725559, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10894066390187635337, 17647096458287523986, 18237159025991386072, 336051190108695460, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10796042849081589566, 538392285139981624, 18134413243297594953, 326862553321216872, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14746387574397519555, 10392440214079543608, 17393237450568334451, 359739458194331775, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4908682943669007225, 9826759808959592010, 4557278517171734219, 493273461770170783, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5631534604946592675, 934632775895395267, 14601246466263925671, 202957104168987867, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13321640943246864142, 94041930563864261, 25784120270502333, 368792868206129408, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9872682134522200137, 3730482451424249535, 16383909528521367870, 482490057655071662, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10108284879207803467, 9811506661751168569, 17175687496065785305, 244737068187871693, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12863968671940472693, 10424754166367106984, 15648927859655015110, 229883407798099900, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16401031819099941510, 18434272842562763006, 5010031743276176040, 138421830463569698, }, }, }, .y = .{ .fe = .{ .limbs = .{ 538408833160292304, 14154945327485610844, 3552649321813971497, 71803852390449404, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11181851375765255549, 5027955704866918034, 10565918529228563199, 35609357206484785, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9922228953971631078, 6184567742482150257, 6670583405944129711, 77463206975240123, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3745423615480654041, 4372847132687507756, 3463813804147862240, 346968751294899329, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9401962901141734446, 3959627827985227698, 13390518749794574610, 222426317645168963, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9788434229196749584, 10489723112571215242, 460273068713390813, 533395573513075331, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9802486039403419125, 2270375425411584259, 17586555381670512874, 269653199159913669, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18214632729013051386, 8997063168444278621, 1015575293178221365, 177161231816396412, }, }, }, .y = .{ .fe = .{ .limbs = .{ 93106128138410501, 17131249959468074242, 7993081275592213076, 37629607382796655, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4636223503227177601, 2464939789034411823, 7686760613566445527, 480074899216236110, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18264855966302194157, 6797289201040177409, 310644370040059921, 192614496415760376, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16802858842074144581, 10342221802107361991, 12250117468155035705, 517489011124412342, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1649912860221579378, 1314862049551661778, 1978587138406660855, 163925702398028782, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5610568387465630736, 6390145634352937267, 14513301662396517938, 541960092046248644, }, }, }, .y = .{ .fe = .{ .limbs = .{ 942969415144644292, 9390362347835621941, 8541731111188543200, 358305107585398237, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11211131681792974838, 1617754137439136096, 14443167264210226948, 75591610168134884, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7286436509879101387, 8708795501978046178, 16567585430864300093, 231248055181210138, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7396002768356793585, 10368643152831505313, 6238374730107111948, 377423699151149475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17637990490760646284, 6293581161876483258, 13794291581197185640, 493843434188659046, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2626467900455692681, 12297954090690963465, 9176425970861521134, 364142640937441011, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10668371955606046552, 16224930432081093556, 15101217706388543227, 177343909738396875, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17103567391824299238, 590796823881591277, 13841165662543700301, 92443034935637948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5125452145599508627, 15749902656990406213, 2060811872904130246, 439212203649170408, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7561610546305260305, 6832522165754571119, 9850373079770005981, 155287329268315002, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10186078682357995885, 15188887382357417960, 13523178270444134359, 455278421964626029, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6292041172003140045, 11965524993427265435, 12001146827628021806, 20274078350505048, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3857482831153733264, 18373111979531174581, 1234956660792605098, 217546830513541417, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5845414940037954048, 17989052014804382661, 14338589475090287335, 416131236214867406, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13811674729645374910, 15745208838899306815, 18070979630565845043, 1214307732481053, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 302613719772844395, 15417944818831825786, 3115336494358087643, 430984560258530422, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8393308440027214805, 3917463684232158485, 16892368904930356612, 546798629424121566, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1189178056846160179, 12696854140898336893, 10193657805797782887, 170837906656566943, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8067689289474660825, 347809793251344526, 16258956993971894544, 94817568475107958, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8696500678982395485, 16973083858862416908, 7854900864836988051, 339701027926478638, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15792768842453353876, 1708112572975155666, 870688971207419541, 274940834472357268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11426340209947729679, 10988295194895161098, 11078363991418424245, 189529276497579703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2372843215201609613, 10994661414371606664, 15424234127047379767, 563118476761863894, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18082288706437783685, 2553173234217236118, 823754585825398983, 267808412667396273, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8319875148482989612, 16078615400489464511, 10496423823228002048, 261473280981545727, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8638230971016444690, 5923630740230683750, 16294491518027926742, 60378094078325587, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4047687787765280085, 1435324595389031592, 8860434014077100142, 453276431621461440, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10899143524327592376, 15992403363206066270, 6619497642734630154, 254142841280139630, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15972732590914228907, 17222329883529041203, 3005797965811099943, 309091412112179158, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12036194637833031619, 2379303379255952707, 2630336218941137341, 298175830238978986, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13171469358708341999, 13196585620091293416, 8257272955190657882, 388914669063319699, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10328309366621259750, 5454926528070195112, 17731537590827173175, 327021129936797796, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7868956650287668505, 12785798021418153359, 16435051716649347987, 211404435594729570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10576928998843757465, 989157184734866190, 17741227432106058012, 336604306040293250, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6865165019935508991, 14597826293168970216, 18146706013039855632, 381477149933295543, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3788958514657322496, 1720267394626859242, 10268099430882688532, 289832053436412517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15155569815652640375, 17105973759644686887, 25840029934239676, 129484347589022359, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9876919522235318077, 10104877085235490146, 2026995131509070127, 42983157427931494, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14272061022403468179, 12182452420357273923, 7531387754082376953, 560981026126723917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 895348506556772034, 2088662670155154532, 4100384691701088187, 118331820743624354, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1515739780943815411, 15705045312727447202, 12671920733466894496, 193418494501900489, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16295813339819324397, 13781926157540095521, 11958051703046497887, 198386389444023478, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14492003295087073091, 1611879114407472283, 8662577261999597600, 385706849199577112, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2373210466998759390, 13547044256612177695, 5123784120649478454, 456534975777491859, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17069156226186802169, 816643307504062968, 5181047180488339929, 24518947261369526, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9203161470367135221, 13803730103302398735, 18344843198250269508, 15404830802761848, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3992722049103750800, 13717717798571085297, 7710518942761485631, 26529649247957757, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 861071028229496582, 9491680939126806142, 3153597581704396349, 531960569777661979, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4251694744348130128, 9907225376936138349, 11580390143858527912, 439210714454879552, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15533924168298474151, 10042345841237415598, 5692726781804769094, 92376090663120792, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17188262595283081855, 11601342192401398595, 7519507816861600034, 454014487387083345, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8314179267094922057, 17345653539452352342, 2707996882135495187, 459986843507034216, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6751652014689900370, 15786325194295001178, 1232411735780654384, 324949853189496278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 253204653997020391, 13634849423589072893, 289646135178180077, 142228686469517046, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3205003758965163655, 17940112966543666827, 13601374019370391866, 245748326994978881, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7919243201171087398, 328744557580713385, 14851367221746048677, 316986519909444349, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15027537819551927666, 166859269291811531, 13913529788892065393, 419341022343096226, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6946555333959605500, 17573739714520887829, 6505681845766920336, 431336256611928730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11125165741161468404, 17297011662888341903, 8579395432347856658, 541324963088810708, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 136265960984831561, 8207441829275277875, 1892030722167265206, 563328861823135854, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15440487217136914299, 1095182597512473380, 8305004945903143772, 373535485957299261, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2588728369407481016, 13538453131358431149, 16918160027680409942, 137348513744222739, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7020936461153791767, 12692796035223792207, 5070979669608804000, 386494452033523208, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2525757447241144585, 8756776521960423719, 1119981648404318050, 507966936085919935, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3481690368320993958, 17015066674789883424, 18366743642625868442, 385729921795896215, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9916850050137652701, 14048980784611428891, 4475658530188988792, 53535436865516590, }, }, }, .y = .{ .fe = .{ .limbs = .{ 555998226639081285, 613365300294049728, 917172586749574979, 461080807293372951, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8081431858984918208, 17047884394786627468, 5528566566992183401, 144571361363562763, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9563162472246259642, 13983811715563513828, 16154518557311293252, 453789802263618261, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15539943076511310806, 9166182266795354422, 10291651914239286702, 425236043869135087, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11554867051245886565, 6000855836246266799, 4233640170081634321, 175551015217140403, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17277824195282819483, 1621196452087874800, 14301201708901958323, 425193901570209682, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18000860777510985535, 552710767032127796, 10886708803322474824, 44410906107456116, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7587896678687174833, 17566217706765128934, 15109765370145287564, 60457347465409493, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11249052900494205343, 11978211093226085242, 5189466695619615573, 501403253096508334, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1745081325534918985, 13211628247636436189, 8878843234670803930, 223439795398915022, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8628235860806102668, 17613774559641129405, 11892017700852691680, 255938175162978297, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16058906889274468314, 779166878837244601, 2956100287325541055, 41932576404304123, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3338375109516799531, 3310032567156376994, 513326651141779316, 363057361196386409, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9709678815693505290, 4407278592274442812, 2237612510659541333, 438438947689393942, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11350571480193392691, 2423946501414975782, 18421264792322256321, 218276125186622026, }, }, }, .infinity = false, }, }; pub const CURVE_CONSTS_P1: [15]AffinePoint = .{ .{ .x = .{ .fe = .{ .limbs = .{ 16491878934996302286, 12382025591154462459, 10043949394709899044, 253000153565733272, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13950428914333633429, 2545498000137298346, 5191292837124484988, 285630633187035523, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6463962446053846451, 14430568257409928677, 9187326482496096674, 208396807325653186, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17860876644931008024, 3803101314126340344, 9229715523658973561, 80369650009776185, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6712128255430143474, 4770188062141855115, 14951224421815048307, 77143148444844727, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5398663745784422238, 18095941582675483462, 7555917152234253346, 465850654197259287, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15831341733893438986, 8883505792511323749, 242482662763259194, 518955820148905663, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2848161037228033143, 1520492901145416824, 2443405453077752063, 480557872201742673, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7542490450320915912, 9456360783083301346, 2603009309005222564, 525453672380471331, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14763904340635211585, 3427363245122249150, 14410386308123012825, 54840548304474616, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10023935369527771768, 16028607403407734046, 16259473967539312552, 448070589960979328, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2458941206956413583, 8025896525494588220, 13086767854682703606, 546980762845271413, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11306888859174766380, 2004905152912729891, 6327540279154554110, 523583081610922332, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16961872383941761658, 14503096654793354853, 12039402248687729593, 450445378482230846, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16698091693130522299, 12107933722389162588, 9016461946955294728, 272303042582027915, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10408200759674877169, 16030055603026960932, 1561064571423254615, 7653304533470566, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8650693611198002178, 612127249560419755, 1190428918750247414, 97091516589008686, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4806408829007321317, 11441569991382132807, 580538530836370126, 457267932630758801, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4600845270560160624, 3957465378020598329, 16402663618100332653, 376590812920727983, }, }, }, .y = .{ .fe = .{ .limbs = .{ 886147601517176501, 11588587433155761386, 12962654286132727780, 198783228375597715, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8160567980241006, 15176685359146049227, 4314945499737422762, 60138587324010827, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11303474150831854734, 17117016490365949071, 17850207449975232537, 323864078728088253, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2180679908132969045, 8310103971707992134, 115544662574283160, 470917846575098069, }, }, }, .y = .{ .fe = .{ .limbs = .{ 844416858368742674, 5730886031761495885, 4357062748692292036, 349235734896451611, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9592326848255749216, 12335243100793985957, 9577192663987490643, 283208905826564738, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2056415999306806995, 3834019799261530811, 3390701471764778118, 102989077854836511, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2736532516828634425, 17098495743187088299, 7222285897754351037, 491426249574472186, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4040263960547694198, 16045607449588802773, 7887317340725789875, 460411380476297970, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6409402878107370040, 15802393048347231884, 12419631264456661885, 437287425058588466, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9403760497679966090, 12196936726317213183, 644376337283239687, 504962547047992432, }, }, }, .infinity = false, }, }; pub const CURVE_CONSTS_P2: [930]AffinePoint = .{ .{ .x = .{ .fe = .{ .limbs = .{ 1203723169299412240, 18195981508842736832, 12916675983929588442, 338510149841406402, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12352616181161700245, 11743524503750604092, 11088962269971685343, 161068411212710156, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16206597911164544875, 8940610334877524311, 4324324088700867929, 279325506684784493, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16878149387482290976, 1949347436593853961, 5949151032934683222, 359469617183095565, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4834942204790228933, 7288783544256345124, 4781413845828464900, 59495576925982832, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10305751015375621443, 15428068101663458065, 15608280936903204915, 457827904089161247, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7022228567775850879, 10329258034226928552, 1703052278349618722, 476102324495024251, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2199108980814885527, 4931193453068540143, 13970399783286747847, 179324820269248035, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8696643645045584359, 14664609412897304912, 1479427412652191979, 571853308251672780, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16859483774431370246, 13525543119372655764, 16710817791565586968, 443957923954761328, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14093782800956210245, 5697065167330374357, 1297653758204149718, 508279389989758055, }, }, }, .y = .{ .fe = .{ .limbs = .{ 751650123438225459, 2640511804595475459, 15504622481353135837, 142591664733950181, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7696979716968940028, 16100837618159392545, 223358165164141116, 556724107698767668, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1964695618188260764, 2509579924608368060, 13230039750101998464, 86446786339454867, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11243440153023765290, 1789876198932802503, 17834332769464155514, 531058128923271343, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3921232398029854446, 14012986149159567220, 6097926305949627162, 501932170068436254, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12745379464026225717, 277985131316856660, 2553707364271104520, 454163372723475526, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9272526899244166969, 1208708408952323363, 7086223223385736824, 305228593904071325, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15722280378952625561, 15327501428653716374, 14242725627825109905, 232269400405041171, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2269606931069868381, 15653426346045155460, 15216406404619233490, 319407800235594332, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5617762107955738260, 1410416541557237907, 16562636490482106372, 90519150949163920, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12390958366491389121, 14176935611477402671, 6192195770765915389, 554386859652143094, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7195481167042271649, 4107244950396664629, 6922388157368099210, 270487271650740579, }, }, }, .y = .{ .fe = .{ .limbs = .{ 158309199458366453, 11764735114858832834, 6278857363228201403, 187937732150364519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10243737345155841376, 7506523484187819095, 2524284564729682801, 94288881744964703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1176389513061062343, 17364289529689797779, 4859065375079299818, 288300655424187350, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 891159761834565011, 4205604760521161369, 10520072704571759397, 48445367187189703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6291816516781345129, 9800562812601074167, 10806270116540350410, 51131023934619677, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 847968392712829343, 18397745778123261083, 15363829902684647282, 174579314758084653, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12734832307651078010, 13325911587474964282, 17099327262122601275, 111936261713248485, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14838443063773320160, 16710252711599145335, 17945306320549534264, 76811625825759535, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11720675390566820844, 14918093534596212493, 17314003876674700972, 139263666878290189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1322752058299681290, 7923757124884113552, 6033513753206410029, 527792593940076758, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10989002742953490061, 949749897773842789, 9733302531175209937, 182954887998424600, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12073220364766169982, 17835067532627326487, 10843221867234803219, 509054922106834876, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6525534809169314248, 10533543236131359705, 3595709794389290059, 495696694677563697, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18026144224540159195, 6245137875232955419, 3829147013857086866, 426348740010882454, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11047360515902103567, 4702317337830252156, 17255393190617378035, 138053845144745406, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1443288183626932582, 14971970768210879972, 4825545849925091112, 43041514118303376, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6006118042402621042, 3723569649046500214, 16796882214745433572, 26235083094035383, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12185968910948821405, 18401672857626740527, 2155265118493697509, 98391214822422612, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11592910965287241679, 8421249382210464202, 16819836630764435318, 220806650050913714, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8917592261197068943, 15864603013562968497, 8237023460921940208, 488635861043524508, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15145747228630291627, 14461055788326395420, 16719877471350490136, 60122978161802953, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7174338020030566009, 14570153911939996782, 10701711782391361838, 426575898341538033, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5246636203510122662, 10215357914370585678, 18010091894035667462, 505608081124223164, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13382774420691377478, 17710556398397600604, 5512574772345108911, 158742265949613144, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8485498290761680035, 17614766784926065600, 9143807639511001001, 182731414199546936, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10381437919887238461, 7318953335711340674, 1398671388753422008, 42480638582781721, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2939729861908147055, 14697281894557051517, 10075070738643187959, 459132731154742136, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13723981191237752905, 2850948002865600517, 12740308013649414741, 399517953951425756, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7837019661803016005, 6675671497334041889, 14553065585702119224, 443831158217917353, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11455343121831522548, 3733574799638780718, 5053022962612127539, 501451216319345251, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9908240632538652775, 17056847784507851045, 14455526516069768672, 179244854220381530, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7239043091204049440, 16697099335168557020, 17513752923214776569, 310979030502864046, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11714914995921493976, 2780874661497550179, 15755965039911661783, 136928547551094796, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6905715472003603506, 18028156573215717641, 5522034274755497544, 88037232094416590, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4665890478970053064, 11631883937117070589, 14199581439014811666, 186037247150860259, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12273372004284493558, 1123767436101381487, 16356136770357406355, 467243796988002323, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17119223569790418457, 589954154852195712, 1704960444017029787, 362995863686242149, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16672246377086627268, 6353000081561509174, 8100658857046171299, 452725968905692702, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4915279297148803046, 4403875857317786376, 1140901361702823038, 46869080662534805, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12362868579703983155, 15821352995118212048, 8856211213555252611, 517258288912438288, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10500158890360687066, 13080488544732039946, 9059047779683466369, 528622236894263371, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11769415216961381188, 661123151106951938, 7104976106293130521, 435623882257585055, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9823180793794584992, 234184886235441505, 4238030306256190960, 373200374628286769, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12720555563177514859, 17486604138575998684, 11925833450855511864, 567445771490975360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17429860060875375527, 1351298251518459818, 18438183459390574999, 540401485361172459, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9902679654947095412, 18145625327979444738, 18331625177461936529, 564626614335712314, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17217815902554836808, 8234470765723201475, 15640548296836514094, 458305299800047368, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2147949509670356421, 13363701374575032360, 4530827237277412622, 63403375334059837, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2720045186129986943, 8741787738880470546, 8924706150872876962, 209761895545701741, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14652162831549207466, 15441168428482590589, 446347298457556201, 315720418970042999, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13082740297593746144, 16460823965313187705, 16861312276555070893, 12736401350733032, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11616534159956634504, 16722814574794513320, 2889076253716488818, 59754493411286699, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13373425833337493222, 6366298088280924466, 5372834431557611827, 567308876849607880, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4814869045686507470, 6522102457168539684, 17743709617933713757, 231379791628437631, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3819732471133868644, 14594448222488992235, 13908543681654067683, 271400398609009631, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14210794839076259007, 17565533533167329657, 3424595166374542132, 54561428315751361, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17868117353061616982, 11080031570490171306, 14152194613948819363, 265909342228080151, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4563747008090561624, 3179170566203750609, 15578052478750892785, 314125378081389165, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17804359979046857405, 9705193531661921345, 13779910270917003102, 4534251633807491, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15729184346923292829, 13609603978480984664, 15209681169079703430, 473093045533105554, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13349460850255048179, 17745498272002653690, 12060847758134143382, 558209063198896843, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14713247852825326338, 8810320845839867809, 3128421173474117575, 552592605113099809, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14496934169463775971, 7670885121303690379, 17163943050855332188, 183686108605509099, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15002779127559751878, 3164929740008288781, 9768001162438272266, 99092861611453320, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18176382246532359992, 17820595285105359667, 14208100779692243865, 490249674663281955, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5831981062222632923, 323498880836147723, 9955435295321203166, 243762846326082378, }, }, }, .y = .{ .fe = .{ .limbs = .{ 734721852344308973, 13815135318068321249, 11830061666363686816, 87529693169183913, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17404412181423674314, 7966576523026450310, 8135733281769410251, 511498817730517335, }, }, }, .y = .{ .fe = .{ .limbs = .{ 169299464981970391, 333181084061654415, 4687294117808735727, 455749250811184126, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 731886730405166556, 9896381575888562602, 7171452274880892718, 201125484774721657, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1023679711322620073, 10360731086374274590, 11305448541803876282, 71861375091136310, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9392920889551320515, 4520025766927978253, 286734105208918978, 321839961979279867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4031160967626465117, 12949795169965565811, 6814015996115020526, 564448456910562364, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5209961393719129219, 5284278488239799570, 2130762765890188682, 375212848424962071, }, }, }, .y = .{ .fe = .{ .limbs = .{ 527772649588985418, 782896302418720129, 2151042335418576166, 186959036037028928, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1589038938120360984, 11702269619538231927, 1896749191956833056, 229390695873057322, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2679085110662814722, 3845199795095650877, 2692937069557244066, 171286736364929765, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15456475352434365286, 14692592223323370813, 10157645945336494423, 388227434569112730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5655274013465675609, 4284765836645981544, 6559543552212123249, 366970260870985519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10177793759636143948, 4160945013333756901, 18433787030874606655, 330955387195900784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18342732316202808734, 8502416317461980606, 9076196671502014988, 19881648948420812, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17590842741580820831, 15324767428705036849, 4209896162849446240, 341670581222164663, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2885933588078995043, 10918333094075878794, 14435915678599530600, 175245814178764150, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8169583411606313854, 11164021220951826703, 8307221558985377897, 366192743081141416, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17538402512716693431, 10907191182987384177, 13947779235849236314, 184557924726781595, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3151480502111413864, 4591744211193486408, 15201208708367156083, 191667389027395538, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9213820439160636078, 8276992850429378843, 1255691612475922097, 561829217361002075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17217494090484775184, 637014367297953376, 15762526944265671446, 401419635890404148, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1416555225145593598, 5801628765287521535, 13227378469759875226, 432720333315189332, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4614883962388280012, 4713212769805736721, 15867601953719454881, 59372008955326758, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2520755549268580179, 3405598097599833543, 13271019308395966979, 478073626184527370, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17240485679919430293, 14327125536221320613, 5142504282035134352, 35473382009942658, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1035826000034784894, 18418247166098904505, 6784110537080598681, 364466268755229352, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15866815790493826622, 6494651410430266998, 4395134600840286031, 31841191892059076, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10720155900897271307, 8940738805131157517, 14048099448652792805, 556510365980239602, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16265850323406252800, 18440488820218148439, 3753384311107508085, 373848123401813376, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4549086349791826086, 5696146414807640841, 4428284739799840019, 87246809519085370, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12084458700134416126, 7844111579283711962, 3332292414630780664, 18437409126174468, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8258392078718472149, 11211798505470449209, 9893617473140085262, 557747506431403565, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3227480538530392332, 4439292535456864960, 10310049646897244015, 265280314952254962, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1718311869394526916, 5181020718861927266, 4569170168461110359, 57618821385534629, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5373451265022399287, 6792547505537400200, 8476027221607708525, 460928900577897562, }, }, }, .y = .{ .fe = .{ .limbs = .{ 131694598029382240, 10526366921214561104, 13857487153671651939, 95495661878034437, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11236398728524880686, 10104841605073712848, 15607876152202882748, 551961090742197369, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5852244156499479037, 4472092360333270710, 16794685541884394100, 358900036181400765, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2714261989959506256, 13565337595984336656, 7268994520690468331, 542987604746335689, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6174214484388448613, 14834261377120562653, 3831554375952192233, 363954203735553279, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5675660162394990127, 521644432511710917, 6084366193041956842, 449403612993091204, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8254687708142224730, 8614066788702232521, 5715984936001202101, 210416359488204549, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7452326583579690659, 9225281487410177199, 16982410920297393762, 115628435687076274, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8184909147729363857, 11998140515552081705, 17379197921743971513, 72957775590298845, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4774145490411147762, 13127903127999769550, 11277627102803743226, 235148251443942663, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14156519415049463082, 9054483809072845524, 16714213598661724075, 469193504319899993, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14288008843891022347, 10848786708659251522, 2678096517409598260, 304936350366618493, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17328108407268081701, 18189070230986963596, 17184351428108907372, 539254347980439134, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3976805707422585627, 12887601985198338703, 13409233582658504420, 219165088883463669, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17550349962127791327, 14741735850186645333, 3681775228027793835, 36419750637095544, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11543308266967101242, 13979911936147800685, 14847975525066587356, 250016766030748401, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16826188800097840166, 1631700129146342777, 4762832900252316802, 396617798145412284, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1747087034830682344, 17598002964405167357, 15846026584110971197, 7854336735982642, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3944710869258020278, 14016084671746845138, 5012348198783267454, 544569922028145219, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15681382965835645256, 18282273994209634716, 12850856952140201412, 206636674545333044, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3725780383991404799, 14882468663680818671, 15032824683974994718, 24852029678145934, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6910547438376405729, 5612851836347194895, 10492802228125139133, 498189579030737211, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7083437741625243379, 4465080153507657658, 10834092486449340362, 226531676690823048, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9959564117741132179, 16364796178513731701, 8365219473822961582, 543987673431455629, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5261646919874068625, 6500357258424481764, 16432742537871049799, 570997046780609636, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5673069023486392075, 12864332027556200040, 13916718992017486068, 466390140541033304, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6573455038650096299, 6580442945826520776, 14552446313069595036, 543278308992281463, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5135017788578227063, 323506796849334345, 11037947464907239272, 255781696017314165, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16879667462922161539, 347389521605954793, 9940068406568377628, 317329481844399659, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 260679114464911183, 4186712169179170741, 834940305585158227, 201155825221869925, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16571530282378892913, 4344690914709476087, 1023317258935927338, 180948171244227321, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18224124866030251396, 453977930038507609, 13557192346628713618, 576406756880392577, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3452823965499366217, 788921136283795853, 17633092892361324949, 7168479961305423, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10955132725522244757, 9509642034918307570, 8993204497533937284, 154310668279968756, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9006800467123210563, 2211958052695088758, 2602463515421274670, 27225501206841278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12752196479097124607, 13998093195326818230, 10112859759330453136, 55511182891763869, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5502088082133272445, 3585463428365447231, 7283578986835197779, 238332597774803730, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14731293934087546452, 14516352279038357093, 1906045450265850904, 40383003655332318, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3205350757834588363, 9453839077643906515, 16721307156774279669, 114648874698846355, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16772603845758566192, 10921450701526971858, 2198291817450155210, 343734166089051427, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16077205716922728700, 2583731099684016212, 6183985881507314219, 499101114543859785, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6935091754883371162, 3460912408145189215, 12298941390152976038, 226307313523591146, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14982264133826581039, 6139708237407942247, 2130028205423055664, 562103201307536234, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3675714709529762250, 15234150409223736655, 9296867787399629460, 100382355436976661, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15775622839725242864, 15620218092863836706, 2583547587413846108, 441626593062808260, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10035714327374098879, 2827861748500879207, 2300594293083601655, 34122497036852703, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17444640712223032775, 1274793623792730766, 5529061611694583150, 27626856440962883, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15211614575823848459, 16886162860632647413, 7064982952591004241, 56522112674447470, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10454752267697522972, 7102824787851182689, 13657396709549088811, 553421261683296881, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2061254765486759232, 18247830106574912755, 18340207239940232898, 446109838024593475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16443975784052641925, 11818916142731083815, 3191668235488243629, 309484196154936492, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3621607820268591545, 10318097800769505422, 17040756850614235634, 501832681401516183, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15708824791013079449, 2687541509675344922, 15619845943374987899, 492128937621311117, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10949471026580795394, 2686382193099934654, 1800034632295108999, 327020652373925913, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5489075357437374392, 5752007147714714808, 17312587883311194276, 275158864570468128, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7339749078242119467, 7957137267824257723, 18088514965247358942, 331193789354464337, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12207933696055740882, 7423223746328732132, 3437367668847046609, 408454618295249803, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2839515777038704446, 16001961253316166312, 11220590730574329529, 409733521798220342, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9333120865577044736, 6218467434333842391, 8259131009540080910, 132779812754605327, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4831514198294432128, 4523149417603496121, 17557010879590134770, 399692677742806250, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13145411060972027543, 16178129545963861186, 668702951862766293, 510793757983230730, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4077024628754917778, 14427355612785039270, 6563710728848879036, 506922712814611500, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15623306815561288647, 10504738673380845172, 11414831788575352552, 517842391382685808, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1583282882988042870, 12164431138602196143, 15374397032168965828, 481143032416830919, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9428102188165937750, 17461698785027512800, 4104866467779585813, 75812344700439006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13162191141593364892, 6433437866982515633, 528361227164070782, 73385314597342424, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11507927230078466793, 5742425888582077681, 10648408168316990372, 575371444538974778, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6961827359100178176, 4034902637327644260, 1802669663286140679, 90904369529554491, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9614242274505313443, 10513439444078450861, 18242919944547077450, 49277703899626107, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17028219446000709338, 17567158562455857051, 2758703658821819091, 213732076351795447, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7251101412042715998, 16114020711963602115, 18277422374611945423, 359243008477352493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1175183407716547814, 13007696844103449412, 2204159536599612363, 190073302868306987, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4794239037983202470, 5496530626051460726, 16081586201273717035, 562875007871816200, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10485781706676953423, 11301365929720386691, 3820682241141404338, 461951088668777506, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16084605962382695673, 11356574118675364631, 10990909488640520545, 337133692994741871, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12080030062829989546, 18116028454796747053, 4787249037255388294, 134334861530927818, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2469729301484263323, 13075808737267942781, 8813051406556896781, 541660243442581687, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3219889812681315333, 4113765763727321024, 17775514962935150119, 449406601663880746, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17607615265772880022, 6311520649071893847, 18315429961652729287, 489078467522903975, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11035801941259865905, 10260622795427780927, 195198747902691373, 69785775095216630, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13135570296880168999, 4401988956219555602, 18117572995702273314, 142928361235862422, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12522348894852514037, 5252739356108200688, 5652556309135580757, 350798317444062877, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6058614600430991253, 5961421757893207767, 10343441684782607086, 563962695287779212, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4971099418138586410, 11804698112418733644, 7071191662008286347, 162317806754312374, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11477950719236658629, 4964736566723298048, 15837117190743359664, 546471114936857501, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9236878685047878759, 18007037676600022675, 12376814584931511447, 271790055913009674, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6285785841193527390, 16483851880227029826, 1552847757620835129, 470529358289623734, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7887482583213929561, 3208427846802767765, 9009848723754308388, 355067369987459012, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7942953522008196712, 5630400415273757789, 13156762823073962815, 489481362333262942, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9067880864418693113, 3433808706629256465, 688763968899046146, 494907540395883548, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1568767399079089532, 13092375629567269154, 10214802673738012541, 457136040527770308, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12422701497637169255, 1992196375358266211, 8661827688838160477, 458113163731139409, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4386140732463411829, 14065558494019899424, 6653158639003281, 376891302738947454, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17305328471029820826, 16732656915551416282, 2431979775815662086, 236533140844827812, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3771917530112490921, 4336972497414950694, 14304384449340454685, 542307422494749985, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15406330830589185368, 14569796840851350586, 12143132142675922500, 13776054219483215, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8483317987843868925, 16375870271514810350, 3967058012729008110, 422552018950475565, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10672167727783803986, 10537865264984463112, 12015851086889257295, 295867698225563419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7391717495255518117, 17886740063613641895, 13001826555876226177, 563109772400707718, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5607511041427582434, 1348834769651990107, 12868539997965496402, 72772633124473019, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15310020519658267859, 1159358669589866802, 1214354492451389128, 371099108024755586, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11992412342947721687, 8512924863775225731, 8719885772821044352, 444604386752718036, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7899427588603921172, 2753648543116628611, 9855271178775132664, 4778729813203220, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2719551904470675166, 9066641535899360912, 7907720238578626806, 317819353574780847, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1046022113071569871, 10100341760513926055, 4248079697367985897, 544599133763381252, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 517536338807426693, 10275096057147070332, 14141731517031034479, 320610536096327257, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16340514502244500075, 17190343612311038851, 2832770982624874417, 238559994285102682, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 961482805974844199, 15885805522119738162, 10592717473678559692, 322457246290940423, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15103946335174355857, 7092344105483256032, 3990912679596986362, 506094688846324207, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7276972732528462472, 4863182333244736232, 17204926761316047212, 356772232642425465, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5273638390389716258, 10580174913962641504, 5457517500519296022, 76536983781951860, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14948795677998234208, 7959186641024733036, 9215135217208897918, 67357899789842949, }, }, }, .y = .{ .fe = .{ .limbs = .{ 810687351111099639, 4104983721819495759, 10759982069460148067, 490668611685360683, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9606186253916740565, 726009893624347310, 11732337768036318137, 101036238415312386, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2305766630157652718, 17684727179198597355, 2751756456495369092, 238406071543715758, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2756905179141425686, 3133335710504403357, 4500613145856368676, 252474049909353662, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16074985417759112033, 17128911667084157855, 6049360868498404861, 75781676816399384, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9307719978454287270, 17041593009235267904, 13263424063019013329, 8045776814983259, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13737040200308644149, 7651329849377990573, 17867910536372816111, 96718528219914960, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13427618482533251240, 8633642204229608209, 13182340086103525116, 435061429350028676, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8599401331582818337, 13982019157550882017, 14317541852619098864, 300532359411986348, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10307994582074671920, 4445286378781641328, 6404078615447150102, 528871182893749286, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3326311014671384880, 8367030795812240869, 17292161759346240176, 39457300988013528, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1942764660040494548, 7524730407964824114, 10404462238752866645, 539013097781126476, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11532166235831966234, 16874891211321432598, 18176616469798334354, 536497929095701268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17877347712484550703, 4821628185728896253, 1478296328204896057, 465367920051032850, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14325196123106721028, 16257091679563067050, 1055753687796194228, 146523387832129292, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8054767769887154042, 16508716851973674359, 16520369598763781266, 472569326504798828, }, }, }, .y = .{ .fe = .{ .limbs = .{ 903294711484219164, 3861975831013918390, 10414028254831399034, 138633353337565725, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11078006341477042174, 6762098204481222304, 13294722464535747396, 66658400764561635, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6328278366860566003, 17798481388582655812, 3766995566962483382, 411434844972318541, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10920894104698583963, 8704813489483798315, 1316043304170809813, 395263436317490634, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16785529659709723553, 6629393433244439603, 7220845358162053196, 411722250259483542, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13965191912996467797, 15991905193466572766, 2400913798929545851, 284599817704553636, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15291714821263084317, 10007820433293591109, 13409478720750009878, 546093762753632025, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2536928174580643688, 1880994155892914795, 12755686068269462340, 24667474028485047, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6925392332430894968, 1657469192479452078, 17644223512207058959, 190252474982991533, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9909708269694573254, 7051943722405491705, 9022173861823115959, 549604833319177192, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1887687595169924300, 5636884779691360702, 8068775953880567040, 122712923508497557, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1168203652087719934, 5329687281880457487, 11671877677683448477, 179051240305100517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13620239518282911400, 9973428241613090397, 17073076932134280666, 143191575222294943, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18398768358987860112, 10455148401115149528, 11234346391270162301, 265376687066151179, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2956145797742163299, 2837327227610102360, 809175406908866368, 439321587380790735, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16034948431265093549, 8140062974788878657, 7183276582014096143, 64402714030893733, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17118239125182070736, 13418904382745747779, 8961759481597400367, 294117956503625912, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11786256235238224893, 11645169027648556650, 11230711685097837962, 76659294106286144, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7685854018064471220, 18048115386403378905, 17723476362721014664, 311916392467384906, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17366578917858484605, 1717770967725674280, 14474914663253375255, 566539205564187050, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8276569751740898445, 15816105282308016792, 7084572236641807057, 53821200917297225, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11601065239506221447, 18066547670520362231, 2866603635183029338, 122663631631813264, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15981123250706934951, 16053056368289178928, 12714530752158937226, 228509339465374121, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8520772710025538550, 10924699020812479322, 11371218488286307383, 470243171616285670, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2503327895871834326, 156168686658738506, 13360617893910389756, 288068105903187140, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8272747160739178034, 5086242350210539592, 17531317689190435329, 323582687294961944, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11185771284992139106, 5540980542859933473, 16805661641312002170, 168636800548767090, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15244436711203341462, 15042636549383476073, 52076088286466324, 192638026557697930, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4123703759485755584, 11883412825940717447, 5313869743285663586, 183478157807709990, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5031744182811641703, 7734456972174592385, 16242039279680721620, 172809236014615250, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11780759338158100636, 2336735051314396301, 15468027019190797603, 89133568506868801, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3624827355380207862, 15921695405753811117, 11266559104607477283, 461527973497783386, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12099465311549470147, 14258238854429517686, 15668357117839208674, 374881083695883204, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6275493163059378793, 16290092049344023289, 11896729570376846321, 224336096049092246, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14625358393853636533, 4597655155247263302, 3858590929265696020, 337976977323030472, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 449997877534208665, 3286526141965098759, 12130455460265332938, 354364514423598671, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14551530149143219431, 10057285989600213316, 13238484736996842707, 492091655622197071, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16297518627287277189, 2935101547028333626, 16745847909061542922, 502035459365784498, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8238398944051998145, 12856028230323450348, 17119175816289007628, 204036836891607278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2401161906960183298, 13619314541673810635, 2068303044546904597, 322583580893070700, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16927937794714599207, 2446848829677624677, 15233095996766709041, 295764703440354239, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12350593359124675021, 9320070286805907903, 14217138817263676723, 92188819171198252, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13681765618797567913, 5767140675043617614, 13395004808825635147, 187086611901451508, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7276768603446691047, 14268294839411073651, 8072253252240609902, 105478989935763709, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2289026076151175273, 8690940994932560662, 12327933368601328378, 554299494681227671, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1809617673163953887, 7374015381564544169, 17001829378616471692, 461300799229538069, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15973126785440807699, 9592946528764426036, 16602563930339212517, 11521790839834514, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4256184226718774420, 6852511805210056558, 17701186314033161420, 281531113761579495, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2440038242050236835, 4991228921006769339, 16513604386869306354, 264378554104667663, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17723322183891255297, 16410831451288443106, 1335837529449664262, 315786722959209631, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7509949925949223271, 84479538486798215, 8206768419022732753, 116965745018876345, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2804460327885465882, 17435980920962017725, 11328379217400619141, 544115847118260606, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3713762075021957050, 1324732139289153281, 8146497925493761466, 131632606128654005, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1802438404742958368, 3664285059540291052, 5725532500122706430, 294592645989192129, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1141181356376487128, 15123349460048384397, 2061043080463964615, 422243394187161318, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16499216108886337462, 7751512256333671812, 7881104398766302059, 126007178232346898, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8758962774896403082, 6510638666868963156, 10030111834216140862, 540729687507317798, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10385371929055805127, 4908256719954155000, 17352426550287132040, 312549508164826542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13277514327015896054, 18385544174314996629, 7549641823266862647, 7193970179483321, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3845165277091222929, 1704747155306252032, 8549731982255922990, 225065560142345035, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18196195801961640334, 8440648953861962413, 12968320292924861420, 439256243678694283, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8565651758217688881, 13423481242862215416, 13705917146848369140, 433977292504202345, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8700269926680051968, 9203377436915277423, 1659610852728880090, 333292145651662104, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9803498188028924424, 5654134177530988743, 17536610083513478957, 548478926911079799, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3285352620657892588, 6984447753925456117, 16021260629994970692, 77787860894030609, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7715347970122265894, 4479496192241287637, 15871532663940050136, 187879925147264838, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4860202407761629941, 2317710903997111191, 3704849177456333204, 44616356874401876, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8755219799125680335, 13661116432819092927, 14182914436890478654, 316267994896331840, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8955129570478255875, 3995859817112111629, 9586682927801163464, 193745929614105134, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8712238529565101858, 7864806487192059785, 12109239763700633829, 451470314947804025, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10566310373256674926, 1344930332651942690, 8000850824132476086, 409554869408946765, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10576583813078310135, 15177641535528633644, 17908318112251726282, 73722088962071706, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2414638479971907242, 1642803749955354382, 11572027825086193985, 207325713501715886, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5801180137529477268, 4299292940518599558, 5452340712645004333, 272566279893656434, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3846643757462617152, 5799488698150951750, 8663600431335130838, 358864297910862098, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11733190937914166668, 3987716509085125021, 3087461666530739376, 131994131576257864, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2865590441458299590, 13815302039031134159, 1394207564084489915, 193033591507446461, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6732836224389524156, 4518006703994927970, 12054019969160156684, 122785166855336866, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13967075683165046090, 4561313760311917776, 18007116456325534472, 282893757779717129, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 246532098857264882, 17998261805825378973, 3476211317241834547, 428046224595742634, }, }, }, .y = .{ .fe = .{ .limbs = .{ 649727115778233895, 16731426157550838354, 3726878036768350539, 406778917211711382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4976063983327661406, 13191440705192158940, 10809015951591914866, 182420113504246946, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3814019912281063726, 16234204948438672156, 13299120030987249382, 481220128060896684, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9881433614937340882, 3380725499905132571, 3131861050505050318, 206599875182610405, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14259899808703900342, 6082037330554009563, 391594675012373014, 304125610851859023, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17991806067757089721, 16235224324200786380, 1225288280691607607, 434889684483945261, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16380893474443851962, 6557954832345598980, 15928158742630822877, 327821641881992057, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1613554738224794181, 17037499236069416943, 2549152661212883563, 132694675937525135, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2987378688706442415, 15760795352737560862, 10490289391462361950, 423982987158185857, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17905408019797504787, 3951702164926614989, 13800727652428172117, 473366545132646985, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17815349775582299917, 11921317439417938961, 10661776444352018302, 35608235589227955, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11373081815259512498, 13906161232648126915, 8588621811217588537, 499016827548097636, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1893356518097047493, 18369049928644909865, 7518892908221843829, 405215950267312523, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8133277889279435872, 15051304413641835854, 9573307554630496754, 313736738226167800, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6638506169960550532, 11370600465404842355, 6790521908879565325, 40833590616783675, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9732330044251616685, 18355402082192112581, 14738654694570586931, 362894249990438764, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14849808111409976228, 12834564330735336831, 1489376574776348418, 549023029462282094, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6039921069243725786, 11041533816629361383, 9784401816875940787, 481353246025393485, }, }, }, .y = .{ .fe = .{ .limbs = .{ 611244550930570709, 16782763698932303015, 14136828677299324393, 35460836011845306, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3108261703661330575, 8648539030890011450, 11838163451272785835, 295140693023347890, }, }, }, .y = .{ .fe = .{ .limbs = .{ 382168167390143049, 4522501819740669341, 6011245708678889771, 235350033245754524, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8253555429673539408, 15169094351917032546, 8092205065583734918, 50738158849467825, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8380467237695809622, 17903376136400559580, 684079321857948436, 430324319782946255, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13275667871234208515, 8388927866671689582, 16651044765280124210, 242822546955477521, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13537586019111002433, 14750902423194856640, 12385405778279657087, 136623512177451141, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13249414768798606826, 10252548313139133985, 550773185085779032, 472982131815085715, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8656109035893349698, 11964275593111981442, 17641042254392890176, 331097697223929249, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6851762306891818372, 9412021843550090283, 2447398175069565109, 95860981851075509, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2602377303734826936, 15958288803996563791, 13373278944840253873, 128638733705717926, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14976511855781141063, 4427835946581924526, 7448557476832191839, 273992488640954148, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12544506415563449991, 817277441590717289, 13558460244721680033, 248831926714888614, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3675585881549450187, 871065214283425990, 14670362520114299035, 129696810076464378, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15309160303420482634, 1056789735379687314, 5953553248266994298, 289565390761463157, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11075768572886603007, 621316485811508008, 12102222266913173758, 76824465812577215, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10524353059766593622, 810111463984664197, 16777373361347305284, 84641244783946169, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8953086994174468980, 11050670044068185180, 11551895413943381305, 408626133962041901, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5039216991617322425, 304409763616803035, 6035463069372251683, 305642824546060804, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8646242898717313766, 15076856719697783118, 1903693847637396235, 34446169911603056, }, }, }, .y = .{ .fe = .{ .limbs = .{ 336973864206811580, 10840593466343261142, 17098170728832524104, 144752606996863933, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17096310110385237932, 10141449298085693050, 8993132159723714767, 291944687502004978, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15743448466821369681, 18091799245335981120, 12727135340308765707, 310152879208449395, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 582739359213836381, 11644144213261202213, 2198922838900445545, 3387194022637747, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13346111132263665973, 12607805917584446936, 13267001229778227620, 274214372079691927, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2113957425984454952, 5047950501357357835, 1132944873442532758, 306586729700921998, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12602356095559500314, 11448730679894384163, 17470421410188320765, 54019706994506730, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8122023100104712432, 2054976008113638123, 18114382107191303974, 409770761236784343, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5467372435788876105, 2704888906111420378, 10109313506045506799, 211320969258244398, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3388907200638534258, 9911262340817659323, 2520622382331660287, 405093932417660344, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14039076146854657440, 6098589010699673033, 11841402703362634650, 200678173467425625, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1856039755972977840, 1198829078594497093, 4943076902298803388, 496928205438187799, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8479824918277241251, 4300260446265203287, 16984365383122031973, 164363195158109983, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1265948781753915634, 8997371845902794890, 2352555409069634889, 31646123565682602, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17408416991719996041, 3799873389580414566, 10972168070571058740, 529619035906168803, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5861682335199296318, 10284161169946385803, 1551724996652003190, 473467799200056728, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13838427050630320099, 11676419756658700970, 9239812470318832332, 150207059213310191, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6857229182907051813, 14191538212120208918, 9152994194088556577, 548457563648897580, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4023596101708205644, 1491959352935954650, 14197715703337499706, 172860515790666654, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6171641737699989862, 6902452568648477918, 4756785069314406103, 520799548469401877, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3623316121938399613, 7061623719358229991, 11909992090926706314, 533799638810386345, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4795246998181201386, 54023997139942349, 8402010728091644553, 377352481099902475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4907609926904758100, 3689277681042788007, 10226048395345793670, 228769663960902193, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2817760216721694151, 12492596960913350405, 2023351365527973856, 108433527174137039, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15488529810139206671, 6034026781295941761, 6502631495435158509, 567681805073130274, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14676651858140718876, 13122925373941521545, 1152496919912870536, 390090166680618189, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6820636359101957899, 16728643740872694625, 3956100645716122086, 30744973451037175, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4331846480006547073, 17408708806091510843, 7899516460411093698, 33434056805248947, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1394932607371605982, 6345850343322098462, 1414419605193276599, 499526726460108277, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7998142049129524848, 11511705460521538498, 15702124071628219039, 288498978945211136, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11373804963283515331, 8464246100499908691, 7635508113608781054, 347713580396803951, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12475083240600804756, 485781228165767704, 3824824862642467333, 72712433311530041, }, }, }, .y = .{ .fe = .{ .limbs = .{ 411945565823589470, 7242440432668940372, 9240679836921882605, 270032149984735626, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11644070534242586731, 16322625832910066246, 82883473557100437, 134914190807561770, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18036635693638857172, 6265027665773050897, 10569416937273902173, 10440470568011461, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17136322162503628369, 7089961470935634658, 7396834545886417976, 50164524763522392, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9214287651387666414, 12821006856729488265, 9963370564101885514, 32732449632376719, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16645859689941117621, 6362138023380430002, 359766867353506329, 212302670555997956, }, }, }, .y = .{ .fe = .{ .limbs = .{ 977080536263700394, 2948363392757580762, 10978625147620434446, 60794714817587201, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7191066553883201218, 13442917711374520172, 7381653529303790708, 153992151643425539, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6299699792542581737, 5790681849741533400, 14365828877642878535, 321426328874486627, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4072474680379511158, 17224922207028686113, 8300379133754153170, 5362761071762590, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17217595822806100662, 103073678799646291, 17212036523475951873, 336571295046659345, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9465996420942434942, 8771645377221260825, 14132155122590858231, 408527371352738957, }, }, }, .y = .{ .fe = .{ .limbs = .{ 789465945821089750, 17820347643032978363, 8378992465886351469, 574618757949760240, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11400246448630650035, 5588768913346655200, 12051654771766887976, 198538805522511111, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3284613343277762546, 8561282108783937167, 11725380292024892020, 366726845356366731, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9004407102594028988, 12068321698022602414, 12788657018967981030, 387664161795064572, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11929899222303615401, 16971263449546362007, 5273613076856418383, 402310900124463574, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12022995556337256464, 2344059118455704353, 2195855902615100148, 323521908947813224, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13342816939823754123, 9263811610080513192, 10744358474196066628, 117316280982091847, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7647288356084509710, 12463060049845584638, 8245903081099922622, 201670405799775405, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10473113807765868190, 17809672230860068418, 6443888495972381498, 338680182684826112, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11930084981843493960, 14718557075462823500, 3836735706521149394, 131467959675558624, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8868667053866076501, 10447736101944882051, 13226643423153766414, 262800590471467532, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6565496123231237593, 4963005566598223231, 5486413358570719549, 526675958405450820, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1150958825257931249, 5171700457508790709, 11104738759003770265, 208185155926901765, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3571184670149884782, 45121584733683764, 10874830375050461238, 246873758671632913, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3976882291881968884, 5713604667469346994, 8352085593736961975, 572883329394805912, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12735533806311608009, 7918528800782094122, 5625268641580137364, 376801129150827701, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12495105271804861178, 13048775850444238496, 11742125104306931437, 572119184219169194, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10626504203423128374, 12623364617853285181, 1786659498358314067, 355861318714153765, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1124671421168944122, 18004851141172905190, 17021810599598287732, 175041682589476848, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10823870676385615215, 5471510065195732312, 5660935716935298417, 230119002981379303, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2401349690260204784, 10701303539803752075, 17642376617613560520, 393285578156622904, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14587840579939464885, 9889084481454354919, 232086214106491176, 59689487362126595, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6141390797485558315, 4424400401380414751, 10215261025676436565, 35803539393086067, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8611203597672389584, 13826430993518889963, 12496410351615970545, 27761748839997128, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10661143618994020775, 15320637236911772300, 4901025882057317615, 572983045810470162, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8898331500182303121, 6673489542088592966, 597933341850350605, 347177396091537214, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1290981088026486925, 13718828945908187981, 15191777880431659576, 360858631964231501, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17421499823534068644, 13606801507803223213, 10722192172909942330, 366944507447717868, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12513009789261730812, 6274021351875197059, 3802573914626766276, 215430749288362685, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17608924616904795186, 15427498099050710666, 449122513564885917, 281605757675938113, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8635101657996861111, 18249425665890758073, 15783577608654073057, 318393359621748137, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13584323167897636775, 11301840305858162134, 14839484973478588119, 252143521864719661, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13016606817625529215, 10375949892046037169, 12464632630418855536, 342702203094281107, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1425901831022343206, 991194030146116047, 7211467861959945378, 195898457428170601, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7601183325229934054, 2490116013206419965, 3048279425331977833, 161874144049110946, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17822248695004747325, 7475761931252657159, 12544656043275823447, 550225123858085155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8201381396541553620, 7231203252279238206, 14826814534775172064, 283959669520053460, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17805343612507515319, 13938871879194511315, 7496409983224377339, 231613778449273826, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6130263343748875264, 10525653983063560692, 9062017858386112899, 238092163502687376, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12908133593626432836, 8884993558391398348, 12850844961645229798, 352527291246186014, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2097665786537873898, 1341989030642883744, 10557479951853597183, 470286416734894113, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11038388873072048708, 17731078118464411358, 2484296110612659931, 91189458235159369, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17744320341380517913, 443882574585260343, 15030910262251641310, 145684532671451550, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17037873222560866413, 18081060587557147284, 13728812702942952743, 380567630316785180, }, }, }, .y = .{ .fe = .{ .limbs = .{ 524352996599653006, 11459619083674438438, 738360516698908956, 162539022490046543, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4236142512903113294, 11645199203955415983, 5387932701250372899, 9318021393914933, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12829439648180956891, 3779866771412800891, 10438698038696999836, 120277964883689876, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15268391422179492747, 14485811192504470019, 12994163993851065115, 280883158089438660, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13877951330164859544, 3507558696565085752, 8618440986122824617, 371507423316078671, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12320418356180694622, 14640626387171276544, 15444302674147017018, 156908777344867673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1601015206550185206, 12099143037357448776, 2135284930578267455, 326963384929741370, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6961324150379012232, 13346258887428214510, 703912215125812720, 165053445857002072, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18167009099994179599, 6519225489386934147, 5035435835454092950, 484694084999622692, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10717020647595596121, 2135409494020154654, 8287618798193104067, 317730207376372243, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7723946524912617064, 14261510464881225543, 5789968080044826341, 255649984825977372, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16650879905317566363, 12060343983746751335, 667556831664310094, 137866350996097263, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16409730236290371362, 7075211273321234944, 7426766825289966439, 506298024877934681, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17082699288042626169, 8663086108058760071, 16155443657621143300, 477079645269076816, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9664605332956960115, 3286621494530239664, 14043132510112930304, 501182723629064201, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8973122646181016532, 6025739682334630146, 2198556372415393867, 527415408485412708, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5296711486572570057, 6462178782668131252, 11367940067783628842, 463813496750372432, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5785753421814987832, 10674551266504189321, 6238033956855131975, 344724840284239074, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12596581483680123507, 2118454038888159948, 3981371846952999677, 110663395752675605, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4741363256566270477, 4287342729252839086, 1162995647611678915, 380840872450999910, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6512824173788976801, 14178258166467640201, 624918380083123152, 112609144138762622, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9021438618221074345, 17785103655538609993, 18268247573201971308, 497236087135775220, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14303474569721182855, 13848421539308857611, 3475532281695354583, 150605393850498802, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5456760287045512662, 4509341029414279571, 1788804520052288067, 361352483302194035, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16316401506538389810, 5693407011294825580, 4647318193066779272, 574395939556221486, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6563392640774778665, 10910812237124019412, 15407536914662793987, 9374000689339147, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6417710594005126723, 9112892936425074570, 1260873643693461439, 247482655867104388, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3298361759933006316, 6104830304433525377, 17349177831857033348, 470033223207186601, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1551930902325411509, 12741687413451801060, 1258067186321670431, 86436448525338390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3858014496395946678, 15567376387120007860, 10938712665603272578, 161232722136647673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 555032047570731652, 4051388503611982558, 16957489159035828158, 530859916087870748, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11031627403643706952, 11448052125542620406, 1985331767070302917, 499288371078601240, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15832610436193809867, 9316733139919986380, 12614669347690338337, 96299325055196439, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7509410864113099412, 647734932078080375, 7965541450348775288, 427166140775587784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15719944576647130418, 4633850622088468979, 73095322375933016, 320331876052273274, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1205656894151720335, 10106125084091068839, 775526666452095698, 562446870152572262, }, }, }, .y = .{ .fe = .{ .limbs = .{ 700348033266211136, 4352937164361901311, 10500368940309431405, 211739694357921409, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15863749970874908259, 16088001725285565178, 15960867384228707507, 396050470620292147, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1214441194834537240, 10790750466234364017, 17588273437876173428, 66225273156741737, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17529879335299076311, 5788732568443767556, 12359854935726202028, 293661051001435509, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12229124900959858322, 7749997258371697738, 7802559933686042614, 62013924025960189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9902935618454440041, 63754175787750735, 5107048933038098128, 350708291691761709, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5969810742274771942, 9633595892440918659, 16229123829117569464, 83906161751450033, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6057867456435683679, 16950963440474570596, 685358037367384205, 350121734534020452, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7344976308536415152, 14751195639298394966, 17851689374205421461, 291927262604220304, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3662700162603924272, 10230675352594392999, 13924228188329406510, 245509428931232077, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6479949029094011910, 8418096432144188667, 5155081268900480720, 267707653373302065, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13601177414727912661, 18075453444095914259, 5125975838626760223, 14188961874489902, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13748754107512076144, 14323361634636886798, 12157129589169971715, 450273109019325822, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17248635263857618755, 11940117519997370689, 10387166543051449332, 442059026596999799, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16489012576702980715, 9312936454180027567, 9143963650170915780, 237074831324025371, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17783008139017695518, 11096971405888362203, 11295722523100695694, 530208926590155433, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6250823245902572966, 9364987334418935280, 10510801984070834595, 529541379019563042, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16586934936214300964, 2564626492232232266, 13870501495021318818, 436031463476838575, }, }, }, .y = .{ .fe = .{ .limbs = .{ 535796895276217497, 18211154658038248030, 6251071747185309546, 433941231891271110, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14907522313046261497, 4230981837136627281, 18100463409595520425, 398645411453675486, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3878188349430947116, 6087564632258829524, 7594615847836889728, 68227579563598081, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16628687685975957928, 9802295565032245629, 8332150126405849839, 193584590332140667, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9315858643875011544, 3667606598458157052, 12315222360514019899, 229830426378001624, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1041189424706356596, 11093439459798672069, 13783469434601437576, 474748917310970298, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16683693333846168409, 6116653723456016906, 1319785642110021354, 486691308331893824, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3927095314580472761, 9957691451785126694, 11608985679388982527, 423434321443741875, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16326213748505492229, 6096062081071015418, 552052526628094652, 268220893979594609, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8856042164696071656, 12332011950729996515, 11704879020361910737, 553596926270416006, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7241746018105472545, 702348972881724050, 10194247834109835100, 116895894871745587, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15778547920966600169, 11339589343991848282, 7369811034412371966, 478031103546862924, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17726296287756391659, 13707461451001346166, 17966969747884365962, 121193434210323967, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16685343478775158627, 1248539042142179623, 10349462775771229508, 562488352852584701, }, }, }, .y = .{ .fe = .{ .limbs = .{ 566771668855241263, 9989737970877506583, 895873046700594834, 555522645998853173, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7143376571807946832, 18094405580160874372, 2519776456848783841, 490284586349698010, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16777110555874917987, 7037898064211887633, 16182993809245365204, 26013291144501337, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7912543089668539445, 13036188023761666711, 4257036096868449337, 326575041262607736, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9584109427482271823, 13601454321611175394, 5322404843389955909, 153194362568310272, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13339809463021738485, 3107461697466453653, 3526582565486190507, 353431789312457945, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17408121070606504072, 9294815371810541552, 5116311037888716455, 50522301731260488, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2959021536086078843, 14815026056988173661, 2501833392236098277, 366502150439728158, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16214349167678526742, 13737459598562364689, 846703913331247128, 30651585660657065, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16572664232820859703, 11407088955067735971, 6268371743264022471, 513647806506499744, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3991596482469005945, 3427879966866773241, 1510952784293783907, 429240854179624711, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16893169139817172806, 5878006096116243750, 16626788810732515883, 161614713663348172, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11926664909296668344, 14374679442783077973, 3817768894929257792, 469964743898356767, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5434672280224499242, 18432141254108275269, 15250574208872477314, 114927594084852109, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16076661204613385758, 4613749341115192207, 3545601273780608457, 346877953513864468, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15032323673524560838, 11447728440406948191, 3771740486488437188, 302272800759118133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12305458692419204949, 3205828710141864078, 2064544481018110471, 561366715095927080, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10649536838661574436, 2233396435427204417, 7784005606386365398, 204040440459197008, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5099285667715874260, 5205523575118506895, 1341991808878343928, 65458291303431521, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4912379664905777175, 10906069331150484321, 4086194328425738661, 116891995057611629, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3705132698640473125, 10852349932620661306, 17393589209808412547, 216885226625430446, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11331962697811094739, 17784573249348414327, 17213001586381882144, 373120941742277588, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6720587761660957594, 9787054245803661623, 7460520403236254297, 322974538015583605, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14282510253334937469, 9847200582187755845, 7523358376698447303, 62922460435087315, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9894129524918793471, 11107409818118724922, 8361815247218805411, 111077091128035974, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9117696473702537205, 11863911138112401159, 9888568233547930263, 571725158441734114, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11310839555405550973, 12559588152166100390, 3825070422263013169, 573403217923570078, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12724880653151393619, 13990680356177537723, 16908872305310689721, 287138380996125967, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1072029209579751760, 15385293229174108330, 4716967368626135553, 554875133570567987, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9015418596638165573, 8520803551518301483, 4097683185200939277, 463781787782712981, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2045015215382697758, 16534997324993793233, 5798474653290757769, 183772101702545968, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17128556718922405816, 1085671990762097641, 17529038445506610567, 343797926212115472, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11698057714735275693, 2715933619629222586, 7041839074685022185, 400573401948438854, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11730574816191151677, 951739195419625469, 13291157736893718966, 126890057041085921, }, }, }, .y = .{ .fe = .{ .limbs = .{ 518924765475089509, 8185904688210289765, 2399087521363746151, 39277187942594826, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2759358512067235382, 15189688014601521132, 12689826244101920979, 16324873705636068, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15240814158994763317, 3000759020705354219, 7418928144543397281, 155463159076873617, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13621896992922094695, 2386372498450296966, 7685381128572789046, 565387118839765282, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14375152113735663021, 15520943661896606176, 11162370071198071715, 548951291365960964, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14328936461742711164, 11296259215177114321, 15361621549926240051, 479638919226985615, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14146667741881493012, 1495033659502128479, 10623448179596480853, 233663559184996489, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10313843973322761486, 7364433260304385775, 17500432408991112873, 20077292873239307, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2233462079551712259, 14123460036102184701, 457652196567923094, 477260084709732694, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3731861941306416557, 17624492170927776915, 15956892850927746099, 425276773485436293, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11188532497623385006, 16296294883079930694, 9464330098828911605, 105024280192702032, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17731892157012034600, 6002071936853169678, 13197386501591348985, 432592373764698442, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10646596484724745009, 74166784136941165, 2494592489308431815, 68361252247441529, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18144897286907654154, 14172867864593998440, 18084334830058463561, 170542040660449192, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5560180760667093107, 5186671549969203963, 6679813822790875255, 10423789383119618, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17729702459160037401, 10994506068399459370, 2304124147942670230, 171055966996966401, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17748206762134949475, 18015145561976693638, 16172133880327575609, 412481180477980608, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16509383961023541671, 14144989375573402154, 3653399385380022711, 290440734090226187, }, }, }, .y = .{ .fe = .{ .limbs = .{ 48856473252645574, 5745015787710566956, 1639482262392226508, 77703555851155995, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15267669029834017974, 6196412753668342357, 16106544574532788575, 266026939178546244, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7635238132388646090, 6584982739835049374, 13733891454724628232, 305724464834150112, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6690479314526791986, 6232023270327428587, 9050529727441957591, 316956169422615037, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14999165607540250592, 8125454665193577555, 4672421910689918971, 290820864178125487, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14177808238652911318, 11274309249612841525, 3342063615874787230, 289271937250912569, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6551398310949235322, 17148960732743480491, 8402271080303557053, 8898021422061493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2289078808098738191, 4531427704016105313, 5585329201639524953, 236165963397195616, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10078875915520915531, 6490357465645249168, 1563862460000067668, 556817448797047973, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3529014276712526554, 15446217511946953655, 4820858478484380585, 533418433822870516, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15995313572794497395, 9919388112218748115, 12108665053895969071, 357739137322109804, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3945430513461938581, 1050343859367033237, 16078962335606463652, 165393723738837900, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11317579865437055033, 2136697718090069816, 9019585349213020521, 566403963218988940, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16530425026348489594, 11629102774612249015, 13557748615822230458, 440269570043526824, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13345150595262156110, 15441385966260938487, 6483734251098685353, 454027816283472278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 573441490290728794, 3221557541450791057, 9412024468569351350, 341844381707454799, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2114160910906940939, 563545636260911629, 5892092074060293176, 386228164870853090, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5260297001163545189, 5026386141718563979, 5625023770856399155, 195258522599372967, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15034228617670174360, 496719791666953585, 3227787708498206696, 133373669459479804, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8850115884542226216, 6939732002210097922, 8223115870290483714, 507192826575180651, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8936191093374773492, 4551436715562256220, 7433347071734904253, 232840974340620773, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13733296087414963921, 17278797162061312231, 16221057106363498940, 338626756143413724, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6547896372791692730, 5909353643406106090, 14057499310825565743, 397232939914585265, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 849644728839957297, 13700735315594159606, 2194303567187815613, 133312305758355783, }, }, }, .y = .{ .fe = .{ .limbs = .{ 781061615943569701, 14925871369910003217, 12413105907321183041, 502318348846933735, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5926672478215771658, 5908947514413427087, 9121766768726831861, 70984617540245762, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4638265200999217000, 6895679056759389182, 14710177043577362715, 491860490720162188, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13084785013910048594, 7196594000996252647, 16052664519732213276, 286364712119666871, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2662444251182038550, 11877051448162508067, 3195611327174001085, 92145645670663046, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8938823848377010020, 11601620049784049207, 8870829314962724320, 290359864444503635, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6258464226290786229, 847728948377181120, 4295629155101155998, 321177536989332080, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5632057400908908172, 15011364182653609615, 4336194663782770260, 220072980347654762, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10271206811961671234, 639226472370536018, 11091091335683139085, 79480281491658379, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5106320509391676408, 11166398332708880904, 6672006004341143832, 571962766899786016, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1130011344505755574, 9262654007365044425, 8740125741549230577, 399615542243107345, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8734715481801540655, 339040080379589117, 4303485093181139334, 291280492379409153, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16298908000356187435, 13143941211260270809, 17267651334148577063, 66787194204303811, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14454226023798835769, 8008441568137952395, 11612494726773456785, 368804031064720150, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3026593417216436216, 12813320793223745096, 2245761647565117891, 125702849813236924, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3827135775759872844, 13580194486269501134, 16203189230293512383, 266679370668594592, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12444508824908406203, 6424256132955658828, 7270783920445614531, 472341263283940102, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17753351750243945563, 7594877622416374834, 2308705524363665273, 191608753435890507, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18249117885435795050, 76731169126791038, 17908931919536639684, 19950226814992508, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4001438063014813018, 2148944314446762337, 7706225611269520141, 252576773301688107, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14855758109453722251, 6537922212180390404, 9187304012488670148, 476161311375827122, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5328080859188359553, 16087049196515245737, 9033286855791648302, 73094011301413679, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10854188193705190244, 15343577843610056690, 8004374347068185678, 551798431017463520, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16570734699107257068, 11379172471300007532, 1050754825906775579, 48817693402361233, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5983752480356316059, 13969663358283669336, 18348271332285829109, 393100068372580472, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14709222960182647420, 1143294625229445585, 15189565191182467661, 409407498564480310, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17443935985166542501, 11160702580281991622, 11435604120592860942, 480720961369546944, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9400721159317018595, 4077070414584804646, 706515853745837242, 555060695318262335, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11059509483470714509, 11566729770833039751, 4433418423617208693, 305015225717125932, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1775046804002609329, 2948459924481175894, 13093970669346509081, 560096171466616983, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9744980286805192591, 17013849838059266947, 5848645956283592711, 443158621979450132, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5727305565974932747, 14403055235546365549, 13918187873192329493, 32800273075343809, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17417868403161553471, 4478713408331057806, 5498835351596356700, 123753352532968991, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4465580985391627182, 4793424103564463020, 4891854145223714299, 541326379550668894, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13299893362222862588, 1535465812800894600, 5855820476999104169, 385694741243482265, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13547144675003547406, 18156603694260675970, 5928811381655476725, 514234934418274962, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6434121336741949923, 7096311990182546926, 16223203255389142560, 319868289164356134, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3932420677316781838, 6192067719759180399, 12191910985719204227, 333781304924928365, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14389905269366987625, 3458899414742488068, 5129606138824836965, 511961520884733076, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17584870100419883413, 17398848335532997524, 12735562586826013646, 318489050180614694, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12849003037700630554, 16647416650483351986, 17964418267896894713, 408205799435252890, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14432122325493150947, 16058410332649200089, 16096527561902758955, 440446752344733153, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5581103934908177393, 17108025484262865919, 13050722346081432537, 562042333715689868, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1052086792251750215, 2764557618616957707, 5160815583773215413, 323837339861343698, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12050404592471381085, 16782553288874056897, 10309003677924364586, 253885802948422772, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3981729737432428474, 1193500026890858289, 2620957193419373278, 477262713576645614, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3435867314575255322, 3235784462744221731, 4776515305025191598, 385648755656798959, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17172987476284745625, 8941862825795640253, 7833287814030173146, 428668625642232038, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5930372161432292293, 9573853078779394420, 11842363369362915829, 491459911579842831, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6503861576360300678, 12148214960252234727, 12646107601944075979, 250819987898516223, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11500014823138625562, 18291022500753786219, 13230152228505574747, 297332608162815109, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5479716955475841083, 16373426310301306356, 13829781097824523817, 570224424745724941, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7864192970911032094, 2577988239612462372, 6997365086880569386, 423558822493883823, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5195750444928544410, 4495518314023875412, 15011965107347099010, 280203546740317006, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12268480781925810257, 9284449372269031071, 8708433224082719415, 463956825067502935, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16741390579714346745, 561194089846379607, 12576381420562184447, 139886976057928708, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9743297796520326909, 17399176042213963735, 12482638230381305545, 524192089089938521, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3987749099002836191, 17865934125376497687, 12404075972017281430, 44934446591502488, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8244866552228525428, 12664206844437640780, 3760562397366417949, 512235259261622203, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9655658583435451129, 13347384847190474959, 447013173484508868, 415959664607711369, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13416580453919399187, 5996376912545743050, 15305448047656270577, 238946472715209853, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14653959084728534985, 12097696886424878089, 16443206872140451793, 9548603066281023, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4616317586090518769, 11647101014721254357, 18202438170913612112, 257484708147141142, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5119966680142736257, 1703409068592521907, 11110154969778677880, 127891635888057910, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14094164203753951686, 15360303232412793369, 2656841195701029282, 444604569947189171, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1105489476901493269, 16301575813929145417, 12950086683890696393, 506000115369778135, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14359102428199988896, 9787468968515825923, 9059644492244152646, 308668106521011156, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17670954792208004175, 8869725341302771294, 8090654764197398143, 268913530704766960, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8522308177005888371, 10411534903293675441, 1544442550812002608, 313143009772604235, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10145338996718545722, 17133439793743677669, 12631299064538597842, 81953672720239794, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18006450469033399712, 6218384465335169896, 5823278847849426814, 249331894898507455, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1875970481417459887, 2793034784560015157, 3044108791317691054, 485320461745848805, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14531746536790857125, 234125666162144045, 9543181833713040550, 115481097531243118, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8173607765316663867, 9957411259710117591, 8852601805860351492, 415127849927260185, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16548861186244420273, 17616610298673904855, 7434140994213430469, 61314578267926722, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13109163895768237032, 12563200736482706608, 794615180395034969, 374702880605038990, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2423131533614408810, 10248559071950499694, 6097071689059816388, 223263742620736104, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1305578365870022747, 12647284402365074359, 14258697513649633083, 100349073571013267, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15246727590209264800, 2273609503134828841, 5439464232156904741, 200557449959388851, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7784152265790031752, 8241903387785668131, 8413992722257661856, 265287267869017548, }, }, }, .y = .{ .fe = .{ .limbs = .{ 556421926255477155, 15383156438994281652, 7211305454813086037, 25236548660467964, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17733024125182535442, 559441693527798530, 16536309706083896192, 470496501248528283, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5732571449893072579, 5886263015298536347, 3499382087884445374, 420894403184936743, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1730465751167476726, 3896894302244568091, 11114204682602205155, 269466570103668209, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17881743854701996858, 15643145055354119891, 3042979364389980800, 158817147422736796, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6325539589683323289, 4957530617163147522, 6555471448482403254, 145690442420273747, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17300020746593429176, 6198424847966400583, 3808608318483999999, 51786088977618422, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3158471564009805246, 1793123099847760108, 13322763276541584362, 554792179108593846, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14266509962501729083, 8521676774882401387, 13806316945676114464, 400480203102636798, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17138476595150605441, 7209773032311799246, 14205785666254680643, 308631139399033283, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13686935080609099501, 10984309095500269756, 11435878317203328119, 560982273635548489, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5357323542809784409, 12287622562544929783, 17922494808296152066, 27597636917700145, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10828065759115401602, 12684336469854161729, 1633440134922380966, 29291241377296289, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10685639500742306044, 14485776635116333771, 924703680558009110, 440495004148151662, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7581782791030863827, 4786095101319477483, 14460195222036491263, 58230835803575441, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13384393027035697849, 3968945691029602554, 7635824616304425567, 20996930284446552, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8644019293931003038, 8270263735965375994, 3171925317670762717, 233817475241177346, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6306422806986721836, 13217103470330640027, 1927845591668334081, 258040630468539403, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14193144194476325743, 8489324515884035437, 16507474657768210792, 51345246744797072, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1651898543933098654, 18091631568653670992, 11958207952213118732, 171464707138813688, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15201476434492203654, 6479675468375761750, 7509819729429289671, 68871681592573296, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6431243980832365496, 4478532805743836424, 2446048894886291934, 24575825641315317, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8184408455710612455, 18364703900399582829, 12091212605853750617, 198477950150354304, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8587987413726752529, 15928515859165613513, 4649238980023362297, 51275333177805271, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12126053494418118611, 477021522851638250, 16344169490710094634, 424131094583659446, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10502690358799624835, 16849604525134220966, 12660153211332620432, 530585395461843680, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17493060254827604146, 7312367647968831227, 17385335001356016006, 558637891006483512, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13597652510899144624, 5346798433789399876, 7352261890641605087, 123663527999404768, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1542811512111310953, 10383946453298027039, 9171100048298581378, 84915654774362015, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7056996132874904564, 4592138961820627718, 3840407833201033264, 123254178038005533, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14624122301190835596, 18369991210234014805, 17997277412285095442, 453169658253486502, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8715229057109345895, 14829873775613715983, 7725521090861050973, 444508626653082842, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16518301753969494613, 3167833567349310581, 9257713836852251074, 141988814764011418, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11167563719677552727, 14404814950439209710, 7074377004485073462, 223480427328339119, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12446269523147314079, 404278363765214255, 18001080029044768582, 572983369038684285, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2076639192737228193, 11053289268798385185, 4104188947955404911, 428225207193753235, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6649718598758733779, 15570115563286107394, 1804591873446179320, 478199700632343099, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1089831364442904897, 14889791584836681870, 2406540131190227162, 540462581410917183, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17903458382136402339, 15693334332794378860, 2686083396185613439, 7038474017635159, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2517157007851737609, 10558694907419379688, 15818452585998685322, 70228533120376078, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1132675433369409289, 8058131989721075921, 15589881888810333553, 64556852519238641, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9047056631761562423, 14343371457540217362, 9612638663330659356, 363263922392386422, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11559964518579359046, 6277139239965362284, 13773965662031080040, 101987809458842068, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15876791795417774538, 7444448127266305819, 8618350842866090041, 402062932511360295, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1307578500484379585, 14687609892951080675, 2417529131274787169, 331983070639569958, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1105927585422481505, 15464978511734168789, 9788798557757018416, 103444483930086784, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3689127388562520901, 12112836071625661410, 10412635640903605034, 484492481253071218, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14189910168152501409, 12233100216832998620, 2606133649887433169, 42921446239217373, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14114454103313530905, 9539608226210717564, 5460429279881957782, 136276755321241645, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2793918991076879201, 2572092399862008049, 12585621452370069934, 90494324368554218, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12842188419945632920, 13358524565273996312, 10211991061501695033, 341239844171029697, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9172778933809682090, 1840315808323446401, 6599346241004845901, 280046381703917730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16645096325333531877, 16833974567698277741, 12128762441688561255, 507699928878756181, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15340008566487295, 16035972332247680511, 17307679662120684113, 391498941765799554, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3241848964285057398, 13177563864554634325, 14840614694340365231, 542500987896330227, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15346967577407608292, 14479583303456062391, 17278910257202290278, 316959741636263171, }, }, }, .y = .{ .fe = .{ .limbs = .{ 482284822557508501, 12483373052739088700, 7386940713252148756, 452900665783553952, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11257774460301413529, 8752008137281504432, 1844243492932067668, 80125265779848995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3567294795113827821, 14534894465888508788, 16637856476195175046, 242848379899301356, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13646232227299313498, 4363618540527887856, 2562404749075351790, 567829110670227395, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17260551552926225911, 5478518424175353299, 7273519271701486554, 375782083182935516, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1589470408258701842, 18132724912636547000, 2144419323677847884, 43181086017959158, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10986628414090533755, 767023258693864009, 2537857436397186490, 561495535911247898, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12141702268420126867, 12523336537899468376, 14503477873101089251, 238213665566600326, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9399790473934452658, 12682703654683222027, 18436756125913084050, 63395455518127265, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8320319618629300281, 16314677816485029971, 56303949943905617, 401855567026832043, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18329790855477338151, 3943539482168310051, 15803779574637180824, 556706014781287560, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8426305303737382682, 18130077054010002837, 6334814640241489792, 117225391939605192, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10641206425095158002, 16057072306970159344, 11608603756727974377, 169055517345185928, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17657210995732179022, 9446344136936120727, 13394765295061502120, 204244881687263056, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10021303717239125815, 8833123220408368821, 14924127634101052778, 494170249638449746, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12549170519549457227, 13994286334835155493, 5147439332505774123, 502052374410687954, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15206653380242479490, 4473396381684003034, 6194435824784376766, 487212554231352045, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3298492280922146026, 6007210937459832607, 1612043948323700510, 67242807801086430, }, }, }, .y = .{ .fe = .{ .limbs = .{ 500071627009791434, 16517036773184781028, 14672414878021224510, 75237822984509056, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11929308324024285481, 14676101036637607258, 10289250085278154077, 93687973924909287, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10445543549206756338, 12642557013870071544, 5113090288235636335, 516962997699565278, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8058864339533164293, 15204443261301858138, 5729170696005217231, 483394826644823463, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9124289819464231238, 3119360496895091256, 17535442225632678216, 407293940241087726, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8154272241756888152, 199348977702237439, 10415430634734121373, 407089158350445159, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5900167380926144250, 8738192765103916368, 11712195963910640529, 281969753711518355, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14304935148967812431, 14980960725657775481, 15379001809456985963, 318319288629456739, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7023589402862818551, 16366758419879503489, 7730152574554244223, 508653974308490702, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3514977654546626564, 11954268399533720588, 7327001350027349006, 340798525159873611, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4407637016247036541, 4295237514218909455, 16834296860349523462, 204276450174111983, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14993382472940413433, 15613497043736854907, 13812838140863031932, 425256803351983970, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10038339062961118369, 10011893833782188696, 11318604532152142029, 378620278241676970, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16411236792448671798, 3402331780009755677, 7592113612951215307, 66097262817744845, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7706032963916026160, 1089436071825834137, 1034374917942975322, 516302107581671032, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8055881189638012385, 12982411775987837033, 9107191051168999964, 188000036268081797, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2381927584589119373, 9407599912581035053, 15065134042787286025, 302202984770640492, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2244126983655976103, 11059445143556253447, 3823707468594567772, 152324387406467560, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3107972459034355550, 9033237406443495643, 11633728392426989872, 226016058499469419, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13550145820127249498, 145068642265714200, 17653739729311542272, 528977077045640771, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5675044563102694208, 17456223916996599410, 4512520964766110223, 6639334864686226, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18030326742020893844, 12843014188292148056, 7632928029171294913, 205492629808203912, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7413087641189818333, 10942611535146191722, 2769654356274562759, 511803426447727464, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8501765741421691365, 503706688947025310, 14659786907411418670, 187238697465916290, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2197057060879017315, 12133312767591795251, 11988822896113573846, 486175074097388139, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6260024531384898710, 10100954950382021859, 17636329448877012823, 376367150218344340, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13035203577109763866, 14854312947356244577, 15811761355077864667, 356609941574440982, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5371815061989520128, 2468662136793038946, 821218598950879521, 547845577809693706, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3708537800851838039, 1133283292875395481, 6626304304965170058, 281776926709911854, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5867383977628735594, 1776720431392393188, 12657734449422953106, 130432865185967477, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9850882568511449021, 14300875070852711820, 3539960286933834028, 78673748095592375, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16169257859325217697, 11217427653836939850, 2283359101215750334, 573215617620519252, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9392717287787917344, 13432725232581058600, 8905814446535897878, 238607597815089221, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12395168052869784470, 8455649083402927474, 738154629521398175, 464799107661920210, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10796951488736465916, 14173544443669058872, 11699673139496556482, 409536268034285133, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2531483199735168697, 14999405110984428187, 7781535517965745551, 323819005595464058, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8319754606912295694, 1180129864299252098, 9570108201838561564, 136782080959561355, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1043140102377452363, 639378427116434914, 14152948625845756166, 187016201822395862, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7103377280294527344, 3374661943167442691, 624254033649162138, 300918557055961261, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2851523359853407852, 3924722166878862308, 15265142292501979481, 465856348662682696, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6393026910844076722, 8622453878688676034, 5572415522603617772, 172381851632314140, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1362640387462842932, 10687160571938831306, 9065294459125386514, 72407209158856540, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15164285438732840954, 959523532095665048, 2585236356377860291, 106976973374215712, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2813324363274571541, 9698236840032155927, 1836121555985430044, 284296349832673495, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4967416097680506096, 884810886682522574, 1726324106723531763, 59487107052624954, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3402494628686734492, 2065893728424868210, 2394760691444073147, 348613147203476882, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15711240330872669611, 17532278809367561168, 50180877583396932, 478864156795314988, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9211002992255789661, 9558169101676866639, 12131366525942071315, 368506122749226326, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6263151707131033764, 8604906641610772389, 12456276834166933988, 273461086849602957, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13066579823660760941, 16489435037237223108, 17273027640939630481, 57647093937145360, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3956332803987770520, 2442467977718069552, 17828869862094446483, 544524702008420508, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13785563684539753830, 5823095043957632795, 244776027929820084, 502926645535172976, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1635523490594195974, 8935946737773078250, 10059219414392107475, 125817019178978995, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13175826941427594249, 8880895657559511844, 7163608198335762451, 481018164077151939, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17559948938430655678, 7961906466640488481, 5408809725287538729, 516340417054812719, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5218651634505424441, 4159611364261109291, 15597470373335692898, 264504328028346578, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11568688706820218785, 1292164547033361457, 11069299744028039225, 104201206267445718, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6311031674679809905, 5494151316951832980, 11923198895390548812, 350076935229342511, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7206426983705132489, 8043462389944820137, 1927522595421692753, 516851150328912554, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3657564013567248985, 7019260972203769853, 15770258399945732533, 370361389211001656, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2580486121968534967, 111232627562498080, 15664300219273378795, 514156901669149781, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18354990218841927828, 12124673859874010976, 6257326105880524236, 1924827517271836, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8295483686575368520, 7494809115000016330, 7344104827554555482, 158679709091733431, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10763312863397843890, 831724104452471762, 16786225723495942804, 275092446772866374, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2383738308589638760, 12784819199453661836, 532789638460250452, 351070918492493124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10471808402073719799, 5373829378693027896, 15477502303897051241, 569267289253180059, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13984375376972200419, 2378688902292948739, 11670374147029109424, 324278967422932795, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8572351362020366978, 7930722276802902015, 8506127096686451777, 222481287364467761, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10203775226401887353, 7780035509681815207, 912779036131669132, 471235630503905097, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2681035477908578591, 4499478189029097122, 13503485638213786333, 56731297572806, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2239486483614057530, 14866741861245720060, 3019396952785098074, 278707767883983161, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2606848652814301233, 5493873802062592576, 9577700854489651004, 203770989365697032, }, }, }, .y = .{ .fe = .{ .limbs = .{ 730940444348137243, 1240732430023965369, 11522725477869094379, 130117911289239801, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13173909163078295772, 6712961890932409314, 8798782231626965156, 345460129523136195, }, }, }, .y = .{ .fe = .{ .limbs = .{ 676774854529576552, 381094988477302982, 1125410455753487770, 445321302099166268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3791906969155111247, 4991173091407337502, 12296707025187565252, 185929631121654034, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5070182493364374016, 13516455503924643901, 8247898136682314595, 322000233198637160, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12815720756301988892, 12467052346750947753, 12844342981465703588, 452620989870731961, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1556959842811324859, 6648507737014391540, 7445023760275624308, 18361925630330188, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12388654348652988690, 14787331142275887322, 366289983784316485, 15158852237605238, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13504675049906003641, 13721899556840847496, 15957812980592904679, 290558274301922289, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6068195768669248457, 17940488438160336995, 17542970513786781341, 473063262556893700, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16935151097776679584, 11357822297234743109, 13203577204569928864, 267409697193649948, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 344819309305349969, 2968414457405683133, 12926603497605598069, 221831235585571669, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10987892547488535159, 5671238896979987153, 9697939013104138897, 487183255211936487, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6318007045377106819, 1822062885819396552, 3893871081455579688, 500589289267194884, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8387032282476514110, 8074936776682476355, 8984946087871534685, 153747871641555050, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3565969342873546670, 680313313444367639, 1984111681432200515, 152661486057421396, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3552056568378983976, 17103488057092963941, 11187538813208027176, 480504399457126329, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13048786572982944352, 8059256127282015542, 11604380541618141292, 110452696588327718, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2270102226051461923, 5577272961330688914, 9445826936662017148, 541214655187622709, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3573256582925715531, 4169697976485516391, 16501878507367972950, 31212192317780037, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6398388989041955845, 14553498484983698883, 11937104451591293092, 495775394393192155, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17279644497984444473, 12718005564293281177, 168361443140536642, 362737528435205892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2291455245576530650, 3571679363974088968, 6577397500719130375, 444254232730632648, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1422298175244319989, 10425590092395099902, 12913834460179631929, 186115541738455391, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1486054841366483232, 15347412289024349145, 16908897508929735891, 358157084944819915, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11665010446160766531, 4955445418069469624, 3157336321535447499, 129960930346874736, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14585661383427210196, 8174909810175488268, 12201953471797500545, 379190099497205331, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1781881134451444771, 17830116165400574873, 6633806321407299820, 572222499934657929, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8667063789860164468, 3570557087845865269, 14968837590068591879, 378420617655272092, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16476055918306619793, 8454657271996832927, 17417192027673056234, 494087655678936225, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10919574237127074361, 7592839516223644374, 11641615748316511537, 490879898121062785, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15354844889314849562, 11256687508260223606, 15042680057830446476, 371402147744698149, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8733810807403908813, 6859189963196584214, 17777553161040131614, 155794164306881391, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5828044571705369154, 1673448727510990398, 12646248502728502817, 405208572150493475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5913449158196945893, 13163458351842201732, 10331563128778174744, 77456153265131353, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9699978253111131277, 1662520592520584669, 566599435364498275, 139789001597743971, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18114584874826411992, 9656712573082002098, 5002361968289377510, 112445621774999414, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4974058660629644096, 14419515235238714142, 15967811710588462523, 433507758132586774, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5694138871215591446, 16849124529510714412, 2375700860423719190, 460121673139521846, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8633181646620357856, 18109839383561042405, 4247379351214278004, 19043624477408486, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6754285013632745089, 13247230515919442002, 4520200409205088605, 113390597050005185, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11976716929757721004, 9223082867989329343, 534717287986156423, 343754104938516175, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17839802822440028647, 8566467114473855773, 4098139870256334152, 409611917920946925, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6520656434365733171, 3244180940908962275, 10994168598533767024, 226630638231353879, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9343856908911323867, 4062435140761504781, 1699968548585521613, 15865551453877491, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12182713657959302239, 12566096949848536392, 10663923399201213975, 336227594091988138, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12245554620317011632, 7724747540818691811, 12434971630276622249, 45486594676664539, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2361093931112906926, 6965576966431782233, 54138342077173314, 250860870696456443, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14581746869893639227, 6787815930022556393, 5481171770720593037, 480144439049555055, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6349127044052574155, 893861556660244292, 13907401107632963788, 26366589612563215, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10564381008670948979, 11116647491816251966, 10665990137215891589, 57610505509517513, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8743656828623130906, 4325062520181892186, 3302464270082445850, 304977677751868825, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14529342560033549088, 17174367823735296109, 9987338876503422852, 213313943166993078, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10236690967721597589, 14463225549116811272, 13085313423827246995, 492652406312510620, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3048559373842544511, 12226077039095477013, 11153921552625112646, 317514675871565392, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18015483733537880655, 889118439400348035, 2358291389855949485, 95561500163888073, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7430850267964076746, 2221494547586478072, 9934362845047076788, 489367048407216619, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17241072207355781877, 13922818854755833158, 12165372268146784131, 85616530957748612, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6943524476743941477, 6855316101478887713, 4226199831913460585, 507063589722981834, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7423294131604550871, 17998978773073053602, 13957230467645028968, 57836454657304769, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1507739142064562742, 3687549919207219828, 978623822900435388, 166337843074949085, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11971549865573527797, 918369398912445571, 16635334634075497893, 415752366786790135, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17262805183211439431, 9017716850012204832, 17274042101110171875, 313896046126044834, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 561946217572041114, 4274240445149176299, 5029331338856000767, 495157520987803099, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16935328183809683417, 12614521737251629747, 1459970056941361052, 217262534947185010, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2718359931598675249, 15198794988856745783, 8395221763544361259, 172683462483252277, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11306563086975729358, 5539048811607777409, 13430825289315188586, 25697738098449599, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11768142505974244601, 8850623158923103008, 16448156115369318364, 501407614539922133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8472412472463913234, 5187939727769411047, 14044467000243286189, 563947977187162441, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2139411548325651687, 17366123489522975582, 4802680064829028728, 38124942340438299, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1467370731153280567, 1883244610618611848, 12363524586557905637, 375669641447620826, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9424694683887606054, 3097831961310514033, 975321448982469016, 401170158055093569, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16324022569589068820, 14114356466852456064, 14902678661993802498, 89941899843604575, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7655216619403680101, 4501396528660459108, 9735677635605561944, 190039553920337390, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1035671209874900585, 14942147933039345916, 7094146394016399629, 339184548829361757, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8671143389099881836, 4672821303741838794, 6066999771575866746, 240929847980761956, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11291888867933507001, 14822879639035337244, 15371911610268689226, 15870373993911481, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15266375863156785795, 8949703910419710657, 15533046803185592964, 315839883962078074, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14675129824438027043, 2923897158331291875, 5442232034211780569, 419878203088088482, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4733387180339332913, 2504392160149285274, 8932528462228827229, 105287190256744917, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8260038613219730764, 6727694922110533465, 13260371028968207907, 274165282651803259, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7403592300513205584, 5081468184987310002, 4188790789820040812, 253467496821597422, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13422901122364382750, 6573030412261845167, 8240016888069222945, 291760508868541166, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11407858338011852109, 15145064337602608855, 14112464448450481013, 184126303173077346, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1743879083192807287, 16636976115762968232, 13015045631419255955, 246436737934160792, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3723701767963263224, 12629222953006573283, 10720805288151989553, 555306736955407227, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11337070857775377922, 6703105556930173765, 702558586005898557, 136909206725750830, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9063349398535344732, 7518636360592128547, 2789788137421153827, 419934088817431810, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16265365808518560096, 10240578311012445832, 2249037465479424296, 496736249286597131, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16895333596144923260, 17737637858009560668, 1445212596976669994, 393356961629850764, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16407836368707329781, 1272043421760790673, 13977226252626454803, 557454144208582773, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5907005931414981497, 8009245913933862281, 6214603671611019535, 374713552536842401, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9984436264670107928, 7321190637637209380, 6485356729460767783, 208873746702159928, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2941910918779144653, 1693464160272674829, 4617301657512558274, 177382062927038, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8893296553075838233, 5796194889127553536, 6223487001437819048, 104548988419219525, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6302602488920755501, 7462055348850744590, 9922584207482930410, 374614728963010512, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14495696438487966328, 15145794258682646392, 9105424635436783127, 502610166058517766, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9251435162898486880, 8326228889881164422, 2184368350944571922, 525187676442617367, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12550051984458918133, 11607703112263209233, 8164831727875090397, 309988439809119136, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3068129884767188641, 17877066788879585170, 3041229004793346281, 309200762645509678, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14440952855894200146, 15047009765942190132, 11234733190037493110, 46671119497018782, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5478610592844872968, 13320033584590754934, 17615821565614659679, 132461183702960268, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4799084462178766976, 3541193913147432684, 10261976149450561868, 715095599329055, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9910122334161865148, 5350913141075891689, 4835775280641195265, 215907387106182459, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11377295752937180898, 6920810960240203065, 4956596693465850698, 528616938449215084, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 159819142669024419, 2438493579882725354, 14849570675165756193, 398535532915915168, }, }, }, .y = .{ .fe = .{ .limbs = .{ 26303328925766857, 5569911651805133153, 16954405031177930790, 562319916127784502, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13320858219802612547, 14207020933257739477, 3175396038859554082, 21291960717261742, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12364031321922584677, 17501953390597884675, 262297542921321355, 216384541216589051, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3282761725670566532, 794556573304439701, 11638143548552924581, 396244063785373658, }, }, }, .y = .{ .fe = .{ .limbs = .{ 130994415139626873, 5735343376106712730, 18079534363578370674, 171356759822795930, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7413821513214327552, 7114063415507898764, 17021922701931660905, 24002260449639188, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11499185486654313702, 5358275821581760828, 7035783611686380785, 233659880425797873, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9793164158831539728, 3053297612471000334, 1794629051446742906, 488541167997880673, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14033731749129009295, 11362468931541695920, 16313737240298581497, 174755176859569873, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13727702362156122665, 70961646111312120, 7865961781218182054, 330439284734813389, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18043530963062160194, 6137352399219553066, 14745886874893331626, 499381120252426958, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13374968879888799989, 16402530414096466689, 10189590027500111122, 335867249213028811, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4230089476746770528, 17805795284784846568, 8086489395517632004, 550588195562360546, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5143166050644797127, 1410628480270039247, 2444783058165533594, 201687183733651994, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15961089485387246247, 8164843142479611741, 14545328105267453671, 545137441209207627, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13778108880655487421, 348087261119178106, 6306957684825183762, 86940290612661196, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6401777069131070650, 5368350761339918391, 11882267894497807432, 321668584205090341, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15338085445822238786, 2695408786255042002, 17912601967459779921, 336741861471060021, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8363339404813506692, 17373998769633227689, 10266201865972443685, 2646355090472795, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17520471066188695236, 11290831749710265197, 9181705432830158051, 317226239104479698, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9598367935775904634, 12288608279164924359, 5104448847921998297, 401046367092205029, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6011994111777019565, 3774793710938097614, 11366372814813899730, 403747020946658894, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14956876097976908901, 8713796839839536866, 1407327153052998985, 332977992767296427, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8238276359722496678, 16495301957648362470, 12687016382425486024, 510032705270478107, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18365786828107446714, 9963924654641567107, 14225302234564584119, 1037129271733482, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17061025189398091512, 886113663711705943, 15443603342763062915, 232091703316292198, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5303889263984910724, 17613091898685389095, 7382743180413114140, 249736613730603211, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10910235695891978737, 7205498351228331900, 4679752981420098713, 38808745983757385, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12553255447634801671, 9193949174395394080, 3954074243502563036, 122778242515681415, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15532924173426276414, 14497021951554257182, 5673299852420829584, 50094874131580906, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17469760428251550173, 18090525994230140872, 8359499916381625947, 189652776703630854, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1518817506498892633, 269625989053359877, 2726807844425056038, 101012623232029121, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16574070345616950571, 5434333801757979003, 6237042918135214550, 292586769877343376, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14029511119181391700, 13100783652894562108, 15000790354853183196, 86638162139583317, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5398189556311643677, 16759891916750270446, 5751472405075522858, 542869774074891128, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2054184086083755971, 14172728097572269891, 7351741817099864824, 510537980428646076, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12189956582405712954, 2343238985948904440, 17114821984444143679, 88669303366597975, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5990445798562015985, 12799500893204103627, 3824012384867494050, 181611511521869116, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4763471894402758990, 7352798717370411644, 14745431791103573768, 544807097514969036, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1920287456720821076, 13791086407489574349, 4522435272691686488, 443428001859426459, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3995560914468968758, 678598398747825814, 12091444822279224564, 56609729348272686, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 987766062892024373, 13835043710954222908, 628937179935840526, 133387996223013388, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13588873707010806293, 10363161633582859764, 1446875545367016693, 50976294860320064, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3220940351552358495, 10846278179865571253, 14169023025521553017, 146411625942236059, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12458851758780822959, 17761838645626272063, 2480649643336112405, 229793791986595161, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14007815467916280668, 2981813863626379408, 15149495533172916495, 83287867299974042, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17127874069833402328, 4944394393436431962, 15973278418215126548, 536407304217545237, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12449511939955193094, 10073651709744963486, 13347610415530563296, 75721245425690494, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15426068173908991104, 405449259711434949, 17460294701061907129, 353451246706160915, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12645976853879404255, 6142583270982743689, 8641043173046392187, 430798834028199637, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7854918056033238126, 7086652334567227256, 2443807730941185653, 450780475682942037, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10824112235587187459, 2962248578104951746, 2804190840635349094, 491445080743615611, }, }, }, .y = .{ .fe = .{ .limbs = .{ 85779268508408802, 10273749760967287574, 7495513389054278304, 345579613973017986, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16221493058710773032, 16835070557686148609, 17426695288867210942, 285412634827457688, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10888751384004181003, 17753865609205832600, 12853353878827757882, 398437909672142384, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6152554412144059804, 13145693863509861451, 1162457178479233894, 221501977969027375, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2848574631820124545, 10747556400203935425, 7559080812448865088, 555988169418732948, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3238325442093757130, 12215522436588032834, 7846770475084498466, 534933974731487918, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2003239678767390891, 13638729618903946464, 12380198179623465904, 408741794418703433, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8406248281287867048, 7183569861816228821, 3177183575027231288, 82147122115841090, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7066499098384192547, 5369633233991551372, 7202523039703824018, 566743831457370053, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14132007411735974706, 5224591249512401918, 11516733743736549806, 548897223551249253, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11661507805521170953, 11685753642706251585, 10190677760895242902, 57151116953089165, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5059770294111793989, 4601821011777917124, 16957491232463794302, 252229142120629133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8966357096579774986, 9129148094866196387, 12000123679517588919, 163185463545138206, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1920573576616223998, 8927332885411239943, 14571435146623146062, 230327530577943652, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12199208813624790389, 3789463208005467738, 13098526913496638957, 488140676775901026, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10821605988121755911, 14394915655278969987, 3651234951003967766, 119750814775790186, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18058209903544916046, 2584378722267451235, 11341632367072239225, 469674049782655349, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6257073345714734150, 14582967507676642190, 4383155215561157707, 277864475105342133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5907926049311089992, 3374201633224902079, 8876247973152743390, 512806070635025876, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4014780556879232872, 4161534852069541035, 12788302248668774027, 343401004714420614, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7921654379398010663, 16022418336610204155, 15003468883185078606, 24339087731097141, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5520692601941083562, 4914384619797758233, 12544988541855111791, 267231247300320537, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11607816758706419019, 11171599255455315259, 7185473124469626760, 136669506783734996, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9702719537186925376, 5273622851841113784, 15467587526440073346, 71592440345357971, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9349150698589565113, 18240467901736752571, 14831192922647066936, 287016492587689559, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11097560166397981421, 3295813825630568903, 5398639755380022402, 152988176312564885, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10724628363081766359, 1199867209591249603, 6515982143998511448, 129378923969835122, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17637223024573694608, 6345673511845527424, 15936787042243877161, 154943552884419543, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6722939677625022709, 11566032261179876385, 9944769883435675534, 238958265227368960, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17908981482235635766, 597702959528542605, 9823219286003566700, 201380741892380995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 102211542361958422, 4943316676009252665, 88411649408882466, 401815364958596195, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 604759052388140955, 3529725616718084876, 3525787800435694445, 127794288275491498, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2442620942124034651, 5593581112620390841, 12597086385499531992, 371125864215641059, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12984836281563856641, 2428882102286591468, 7728113201908286195, 19401500113107235, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6839219126487678208, 1546339768785082364, 8405876235314565634, 17337319058972488, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11817122520451988338, 15745810523446209801, 10579407147064519667, 477333504471065811, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11632856045634812534, 18396725509391870109, 7416782301070834413, 56308210964751701, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13528632763048794489, 338944619417464374, 2644967664095411072, 265786783369884260, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11287068586555068208, 16442891415156952468, 209237622810559823, 421373694506716305, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13891623794390714632, 8845817209352371918, 2281817030465748067, 383048364601035084, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12588139107830038047, 2446473954641412431, 14376030540248570153, 168898906222150237, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4204732626810049046, 103266040554187484, 4788933839439068737, 473392170615389031, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7201582664291491250, 663884193926884828, 16620782182825245026, 522938701519778675, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5741356872110258733, 12426286022435211175, 13037478620493511240, 317854687051794867, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15861888939157626582, 16448258675619429361, 3174055315690394085, 149964040085961899, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 268154152525458500, 2424340084192212632, 8208565411825598015, 481862029157790968, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17849263807176783223, 6835327307310104141, 1850454026284377628, 453311206173683538, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16676586247543241699, 6686387192985942199, 14363051028656278458, 105940040242367003, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17295620835461780206, 7122730320831643771, 8214064716383795376, 537433061610452293, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18305646029935442438, 4810835030681871149, 17601026698029429554, 551210968004649833, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13461431228356806287, 8902572577695419093, 15279242053136490168, 307907225572495917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17059908625899444404, 15686479696520832531, 16475055754900329434, 13831247939660106, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17962528576964971378, 4035046039698492514, 15110578380835671857, 397386765548224716, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7526295034490009451, 4666503974132596691, 4039476925114137344, 489044838342949142, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15396342345240387470, 11217965798947950212, 4555080427491746721, 540343731796122645, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7836696528252644968, 6941385114590732865, 16050200019770718580, 535289473346239013, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11234278433685780503, 15578752593082085716, 16335834321329428987, 306943829507444453, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 778829136761980340, 3670365011738322334, 12999681027825976252, 146135931082593826, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5078646440035683208, 6042157840957385457, 9661420264174361015, 537615971865486647, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1303062706269930153, 15580749584732012199, 490028556841869423, 543284308106104735, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12855882728128491292, 8235784961658994585, 11759983044006834980, 100839149594789639, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16802949731754198250, 683059206625423557, 14228691649521102738, 404861288389548164, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5880557092472980215, 6795332984903013254, 18378134975036679560, 6138881350371818, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2915020090602733338, 9957713024428996078, 7776830330609918046, 357567935675879208, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13993725596302616580, 9416911875258985471, 13922879217618647317, 252176986851496516, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15277177264453420487, 12828768231000461935, 5240804593474551536, 397019784796029616, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9428050715011192280, 9551846057163945780, 16649871814009275870, 155293317639165902, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5444969079707361684, 18199015783421515955, 14112642647263230094, 101358106561394320, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11777295896963152411, 16128309594702362612, 7228928028931536337, 470116049435027614, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1390500508310211942, 6306080318041758169, 9565588941287517797, 79375670868228660, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12837049299756760184, 18242790827024798435, 11508879313902233969, 172952957033553616, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9999190257022847009, 703770013506401418, 17842859489042386669, 294443478520055759, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8211436079883655347, 10748381652522324239, 5158553815605477530, 233100212787934889, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10436721971540509176, 3382936176093064775, 8301547829664704729, 288958235230331611, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1929433535282586732, 15273735035742601422, 11207561419118767994, 191743505736155939, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 870661521545447299, 7869213537942473874, 14554143608734420263, 355347820914782511, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4767523449734054354, 17337055114077236477, 3711125443646367489, 99995442726223408, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8815851020211401807, 2478721697004604254, 3831499314331868823, 446107412291039541, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13565968628112977581, 7286864243007834753, 3555482595628687466, 89530573138535850, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15937689409926649781, 2435179769137017636, 12862769833710191597, 205618064998165421, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11831578868729845282, 14753818160990389561, 8834946395421227142, 81313157328605967, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1251768636805470360, 3906118843047057915, 12163364084980303430, 747616433467333, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11419161751030715393, 8100270675196731686, 17864069622992311874, 445431827412369865, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6828187854451781602, 16205638442746001125, 5128786680262164946, 394871813338901721, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11035944020282611500, 5613579525076928209, 1086474851425610754, 383705646725123763, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17528180621911207398, 17752691065368992398, 11505477764237498798, 184423106614312806, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3436329111283779354, 11544232168023480435, 3145404176197759267, 434886002847277917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1857760910090183947, 3765374781002721299, 2368637860126193444, 107667691680755521, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5683430122912528113, 7853508564489860548, 847718824114052695, 24384075456797562, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6079373064131092404, 1605465022330076399, 14769820073621503209, 435502598075751991, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11904613030353848030, 1115001334519284840, 6868084068826157852, 499177049001549145, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16081487189983739039, 15875606112131074485, 10206051842061338876, 327735631645678103, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18148934549735238929, 13028776102779503990, 11193355005524635935, 336366414402179621, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15181377015370884435, 1508136496340538472, 9900184356203636979, 295578792558778668, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4269735265507115794, 3482842809343010257, 1983627293255470506, 297552210749449031, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7175040633539505687, 8580429300992070866, 15851665168201501113, 157826570249764197, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11632330650694560144, 6475332278346276584, 14167167633211062756, 364280790603241981, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5554356563994142582, 7550768593814156363, 4827346846174517692, 150321769614740321, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7419028025814266819, 8291753402302597955, 14436296731454463791, 142788078934239445, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5854298671654981850, 2603050858391981342, 16955642161078048956, 173193831654601401, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3758895612759721855, 17589366244203528298, 15375459681785896218, 89178075667343046, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17663261730253936316, 16128521904201896579, 1688514549667038483, 574908107608161693, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5890739117197109990, 6772249408190586324, 17356138650205381561, 371795820211745204, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7650206667036929904, 1160658896390241504, 14086019631979156648, 486206160159234237, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16722794190388340727, 10902266012530306218, 2437502932825591810, 167913555891476664, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1629695070352883615, 6305678086011886260, 5567486968269631172, 201048717846388481, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9643782320505057684, 11606740746479090808, 16328278538185943187, 253333006785155222, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15609204914361644222, 8348522517925583793, 7394946334433359136, 271261460294125201, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15734559541962465970, 7599594752704098753, 5024776015391104194, 12483760393970229, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13097128453332467029, 3398377340463255813, 16485458552741357955, 565971449159410573, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7798889831361165892, 14950356537420157149, 10292794352304568871, 335719404521444905, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14188261447014205998, 17579381747892796882, 1087887232299390174, 489444763906828694, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18268523581437835712, 17500254699598283523, 12667947098450557793, 500834625915655429, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13932658395684340007, 8859111581080983146, 6289134076793889534, 99150351428574570, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3849831661111572181, 5307029322986110677, 17960943602069060220, 281764863590650289, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8399408547332663237, 1985350988134509605, 2276447196639799400, 291461588013772364, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7548351029404190159, 18341121619894501689, 3164742886724355902, 504595067579787758, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11390506405586236109, 11557767405097541141, 14362955574834838020, 1340286643746362, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1084530316766349571, 1515738555990224667, 4908572522288113516, 178709668031227962, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14746703321491349055, 17331060267179340893, 1070919602213974150, 41895146469233678, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8255624513687311286, 1029710607650884878, 9555114541180587395, 121389360984241610, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7706685011455003745, 509801552572645975, 17025018439084229752, 64580001560569927, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9385817159503553448, 2918794997584248337, 11836450080217786909, 39480048297323916, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14911086081754423478, 15135502186392426803, 16452400237579806743, 345511442512899250, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15782614899590612607, 14532649122302115845, 17054526072415273823, 329880703128530385, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11003392236279749115, 3465522475331769750, 2281986075583823438, 430968508833341028, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17370122605443411793, 15943221587796156425, 17046671372916903515, 326711119186766189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4946676541248040461, 5821104259729426616, 15335054674341817040, 40767050203196981, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14561770765090304457, 4151773467717336134, 1168989608151051513, 68973402161156293, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17705783402503246007, 277577571039887952, 16402793195125420514, 259825372168940898, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4444982292063044242, 5079036889414898453, 35521945531046005, 162091738678526020, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 144868230629860009, 16244487074079651800, 2419137539424416448, 352261442643453925, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13199091984230185237, 3098593821835888708, 15691256732404853922, 178716572843140272, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13885967558395652572, 8578158100867077740, 17543546515403466953, 395619649693365718, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6756894619204178073, 12834841782569866654, 12730318732527624190, 168141355665791539, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11641486345817104067, 11842098383980195683, 6140077725764752049, 321278687436882159, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6443660938633326248, 12363696360848125240, 7427450230591663954, 506880031389382879, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18229172836492089006, 9252302760144191960, 13994416448905911570, 225054788044723136, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14077683056616080325, 8536530013937179464, 17103569668194492605, 415932575317679484, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1591284087687978930, 10717701927173873008, 12155582864520537589, 84577602503392907, }, }, }, .y = .{ .fe = .{ .limbs = .{ 529214897346431257, 290287758796092204, 14023372626950078793, 269007280365631554, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15896238013218303156, 1840722016462304821, 15703557114346104830, 77956671062862183, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10185006904724425132, 2952242233624867861, 14860087341755783370, 181018433645354394, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10799260634723010072, 9391814083421394646, 4782957243648972300, 336002721886599892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6548663624281805785, 4086152955003638697, 1513352913667294416, 29681093360583073, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17000986663523944695, 5538061290319621012, 2849163254509453907, 270074837385955406, }, }, }, .y = .{ .fe = .{ .limbs = .{ 940841787960356389, 18159327680172639017, 3405282674749429127, 141717695024952372, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14116165523166486675, 7589421982632549515, 6171631842327857407, 349121880335153198, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14008455627103813275, 1868773876769220315, 7596735941833140867, 268750667796581741, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11295861504767909922, 18125031313640913057, 7539200547493906955, 297208190513073798, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8882532230474605549, 10848449155366322198, 11532630819408598460, 221122048626349729, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8067361166951604457, 5274936583325047890, 833815361710024832, 277811350087543349, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4104376776247427056, 6377128600863535476, 14222838615082779210, 365102898627578973, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4275944215705565304, 12606562696433932395, 10487343234032195634, 502262312917438022, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2586708907573857594, 1713779116608368475, 6100212630170505299, 430702742656992172, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14338917801275937038, 15487410149956537392, 17146307107671338475, 154895689362794398, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16263429686275683735, 4624680514730044587, 4401142035872137865, 330425453226020149, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15613952649868705310, 16091070281548246133, 16248016095793534295, 194880820034126552, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3598359288371138248, 7914143726860207784, 9986842742113505863, 298647863785280604, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2898309675232378528, 11545032280876770700, 13828358075043340593, 207683507143026975, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1159730774127087667, 2624253871370178952, 6583409774781102196, 157812878589085202, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13625407473485960853, 12730011760406535103, 15869726900544072995, 406968864267037168, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6291571541913541887, 16534000050973135297, 18058595447198145198, 335778280271484696, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3346110371971074353, 8828800540366779077, 7589877885719747085, 151157557378563181, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3204863726218192448, 546660101944819100, 355387960511667400, 98375213641027472, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13080049012882541416, 16916424886730135278, 13719535322712779407, 328255053425457757, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9030079216824564602, 11463139523570877289, 6027068371602873200, 418954257835050861, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1080805853324151795, 7220702879171694034, 10951306289861328044, 102537762651692403, }, }, }, .y = .{ .fe = .{ .limbs = .{ 479420502856408062, 15043502221570863225, 1370256142611672242, 555858091045069390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9269500156552038592, 16648189207390148933, 10702648599991818623, 314380205881758272, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17099915981441034313, 13711566753585440553, 7497430875159633607, 77111157663052355, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1746029637943587215, 9589343444685439058, 8108008839111548165, 220586343664680978, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13381374437850135142, 14867442619671068615, 7019332972957363231, 379262153738753038, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12665690812985531068, 3011521736371638574, 6017931187594626461, 189949677282821652, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8014795530705245147, 2246078120125913284, 14865704335241829351, 97219889936088879, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10615205221795192374, 13658616906790819937, 6987382512101229033, 7214987112009414, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2742069135335362593, 6823313708316487328, 13869872909478264868, 328621970476665946, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10949338633159753937, 5119040219301927520, 14662930781982394516, 448075496488678439, }, }, }, .y = .{ .fe = .{ .limbs = .{ 582413304061450425, 1995693926045973852, 16169202968883474096, 67901473695068503, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6605324863898837097, 3254409872519918363, 8070173357298298564, 262834950384185143, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14830046197199007414, 10206213773789761702, 10438044835710407108, 499822147102253917, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5204119873303022577, 5729152581054675248, 4616078415029375294, 351284780555369823, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14381772210330737575, 3148101407293938668, 15808399110717068424, 190876571462654325, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13746603949095546892, 666460957140740539, 7508887035220309352, 497564073429118642, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9495177525556096639, 1927284725375911816, 132024444528558534, 305144088311983809, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3970579964179834641, 7190676784543543934, 16456650687519201347, 270400996789239658, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12961811188559254923, 1508009173224952110, 2847105059336016269, 430915277946714172, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5731975324082239634, 13623551838390224039, 5185472293277170377, 102679111185952560, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6810790355351594238, 3388739681653719923, 6669564451505271278, 498469974238439122, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 36887440463561452, 5342615970722986822, 5805560158956249562, 482394272865856296, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15471398243252902688, 14817277360865054717, 15835805884864546289, 252134350061091618, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6203677175917840362, 12032260790414932434, 14189331478503101501, 400898190351636399, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12897595387430398227, 17825211252776054076, 6030115774415108321, 414146705779475596, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3057416509935364137, 18248027629710486947, 10825755086970095811, 144768626969564312, }, }, }, .y = .{ .fe = .{ .limbs = .{ 283781603448918756, 8500172766212491771, 3761835573376496866, 422501086534778149, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18176082647054252053, 6398669984262652388, 18320691854215961545, 482039148813502735, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14055569384794862629, 1642878311914406339, 7980923634665529073, 89909429845983018, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1858560050681586192, 7931404410831752771, 17414951126328551106, 59329801869834522, }, }, }, .y = .{ .fe = .{ .limbs = .{ 193469233085030086, 15041596940195816447, 14624180478715447327, 132063743460421947, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18379625292860938107, 10239776653013744877, 14159302963412113279, 469680938850908346, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16236035871202246021, 6566881361336208387, 7013590034704470574, 490499451292157364, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5619346973881398611, 16297332077436498487, 13619519023237076004, 436940463439016014, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14582282421569238157, 5610883971754571357, 9582285504089997322, 51189110089000118, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1024813006933750805, 8377166344206175962, 9031993628635924789, 51817486880384774, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7171541631468213367, 4938405501100100661, 6495044770204147495, 433274692422712027, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17496147733223076303, 13119705111081677740, 7955811525816164621, 159831777072566509, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12226969911203074533, 9889904008643645658, 15045787088284710738, 331746050392694683, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 107256720559629532, 15363213035621978572, 14924383024147158317, 447147092359353912, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10231865075739729020, 13514160784520531157, 17788678847891723964, 409673202952768488, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7745872276050507871, 4093199186366582190, 12501963030076606040, 454337386759407042, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7444190662467695888, 18418385727690075920, 5652081638249767406, 552228466463893519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6414408513210848827, 16339374537240026939, 7617980299460944207, 347881067241681730, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4539881687250230280, 10658764374152883363, 15207436420468792879, 97561181738641659, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15385291907438445662, 3882360028725811247, 8306106077666599042, 372378687234457400, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8734351852605498320, 11277571003177728387, 7104918860738928630, 134818152683126382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 79717126109356460, 507209053559872093, 14899369881549592115, 20809212881700724, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17667054066422956063, 14975974887554579666, 10565432657007823419, 184636641534296601, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13065541850954895924, 353738540671540100, 18106590401164146504, 53095420466901816, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18439631854476249354, 17099014781917824555, 5415994781738244646, 529182757038524030, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1683641258133765407, 6977319476115888895, 10906546669766765340, 225533503733386623, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2299198946570052714, 13076905236851572945, 12199716447762363842, 157807047853273704, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13817307242793581316, 11691430129265838474, 287693394894785208, 178914874110401340, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7646436552752588768, 17742013811705953306, 5417502397605622023, 131178429845457608, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14317806539981028417, 12209883859676248285, 5735255372249808645, 411098155285829774, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12571477045661943714, 18100197718718374400, 678182483977420828, 502179945263329019, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2985715665377970775, 10221586185699579906, 9925011211634034170, 389196260621732676, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16245285800492063142, 6678107731232404153, 17298088310349703773, 68280487771082313, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1134677397300590381, 4193515887447484402, 6003761858783734319, 150757782587207372, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9550585303225703743, 2890918335505291629, 9623859664064061427, 43989400056561490, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2708096254382099319, 8306548668325377200, 6865526779522954695, 452436411525559456, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11936012544657183336, 8934771306586680096, 3822055702812762375, 501503418864182531, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7174900967588792577, 12794600832110767767, 7461869308176243069, 343513655732605382, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6887004907753948549, 4187418143372857172, 8478117486708271606, 486671303456969668, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8648830498253174229, 5814117423228200951, 3442638714457640113, 457500273967177864, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4523992209470942524, 3136593018890180747, 7426926813045496032, 96190169296734213, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11374202898103422683, 1970792111761777635, 13082097801173702152, 293627695746156991, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8734378302976346015, 1425002397319614193, 10465890340782263952, 273099769102833918, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5626416362130906660, 478818414046207143, 10721427292721396326, 424838331334599646, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3059725090224466306, 17122661222944117250, 13860143608356791197, 140841302430107967, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12871263523012128413, 13683648066018309617, 4801548717948523934, 571541492461422648, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11228424232633156673, 16650273340741236143, 17754689644924193377, 23746862535076029, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9877132255326544541, 7094167189151323965, 6839004381977648140, 374890094597959520, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14384480948771764092, 2788338138453772248, 10454255067714162309, 559231593291296513, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15258438116404590173, 18038506997713490616, 12732057364319131904, 462842522522769544, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6901893379945993403, 939492627251959292, 17134333384830982400, 38415444106311751, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1258312071003118935, 14438651943721032142, 16562716595269289216, 461747526584110475, }, }, }, .y = .{ .fe = .{ .limbs = .{ 120207300927897980, 3182368288693332378, 13749792996062845752, 385788498177739340, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2633061753761500518, 972379475801950672, 380806098126239994, 398272042471333704, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8085446823542218678, 1546168132360138719, 12747395250500258177, 418631655124757301, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8968763058375768517, 16170327167732022696, 18272208567709613488, 454286199332092890, }, }, }, .y = .{ .fe = .{ .limbs = .{ 426911519480961539, 875033581313429289, 8628385886977174949, 489359249177583716, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4499648144896388304, 17724822892233325032, 9490939770524771521, 132512467973723585, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14762435972556644664, 16142250455820678330, 17667728951326815598, 361154944133328773, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17906538438337612910, 1847425507496773221, 11383858271584354481, 302227485510107437, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8463715841845050913, 2232439326788864068, 14642661688575391699, 388822857480650640, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10595363369249360623, 7740461228626535219, 16037613761156535541, 490472953288350352, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12379178698623881368, 556730435647283529, 9596758001968668165, 382947913298689137, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3247626786576125811, 2400662828492243965, 961782861299252094, 201572424784851599, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2613129736506654235, 17731311222214104272, 15499375203570144816, 550071407731443106, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15064181330499553243, 14991921473550665959, 2154485415540583146, 405974386524014076, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12260196538489456573, 7036515865014919518, 8676507704365864291, 145273212104728046, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5372318705800864535, 11180190109913677595, 10305017127758531375, 115042852687784024, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18381878356201278973, 12144305354701888200, 4173366768959779020, 530096612662738423, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16730483708642117252, 7869799901218299079, 13873680747285340636, 491227660342473781, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15882096381507879018, 15041639937881513588, 10582617997254985120, 22608920143423910, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8226711409325257223, 2420585059397998595, 17474845625162071905, 246425098861730167, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14715846640672849261, 4870616093073398237, 10524879170604874170, 574999680734579966, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7046075010086598307, 5816076425564823469, 7000410671949393568, 41697533245338056, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1658391065599973194, 5915676390396598003, 16452159834325214398, 59663986337172248, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2408496236517569908, 1828339038276753664, 7028324401999711399, 64304715892127889, }, }, }, .y = .{ .fe = .{ .limbs = .{ 61783821832657132, 11046424629513366322, 8936635590621237888, 164365009155559838, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4033605281950674498, 3141569916371133141, 15159338612943909082, 421196806436768625, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13612228142126194132, 7859611849291515879, 10237691696478718742, 262857159588468896, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5247731466961314226, 9831644786339250281, 13456211675601252159, 557670336443095344, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13414281083715876914, 17864355679725064909, 5496239960427611730, 108293728536490123, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5112316221780401497, 5700258338997971089, 16766189057480497632, 413854124355572957, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7513682147932359340, 16020872473812027390, 10720418877027763719, 516554313188489194, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10094654760743847590, 10395242790549504363, 6942226160625128735, 43304467319825633, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15916066343559526742, 13088384890535190813, 12790680669058027284, 223329561157077383, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 645787320905593903, 14778238478662711939, 15645679378233909266, 391419017115368192, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10441952064874059145, 14528965008711565347, 10941812042733761855, 342198146399181126, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14332499483166055874, 17727309795225632284, 13869077516546691970, 59952937252990740, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5046044500547225799, 4553155249040555436, 13107725554829663767, 228037128330889246, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6290483542300019263, 5759765633076122478, 7661288514708326519, 517094099031576068, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3852387144110722433, 7999691521932365112, 5719999710420003712, 245198500985412222, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2235332925320673636, 12883298826095363172, 9012670855818000843, 266857876958374505, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11354733132089333624, 17723767180387415792, 7447950871123269786, 64080798816024976, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3507049242943428735, 13066578561221990831, 15194592416318964188, 15024052613920738, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16591199301208853401, 2491532553021847727, 8251456345148475907, 76235160060237399, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12080819170877836370, 14343859778831451862, 7959879100425415547, 62157661562441489, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2575932466165507018, 2576821847378321313, 2028191291775705042, 73627715429741351, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10651677496515157188, 10443062406348740496, 8205608808825333270, 349307159983190228, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1532532235998289891, 607435915900307885, 14088932773534005382, 186205012183932349, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14968994023540151634, 4094970074335288873, 11297407601835457946, 317728172042816481, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4868081625699440058, 12389420462711713794, 4960785899528490416, 260012199970668141, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11843684346465590397, 11375705578306759834, 11442245629403635000, 559104464680391656, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16149546320138436928, 3372602069717044939, 18250652598407255568, 28439393451099087, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5182480415916833407, 14114337857560522736, 8061344949145315132, 481434105835515833, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3151612752991873850, 4499825140509565662, 7607632141020159535, 508057844572958627, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14989965326479272802, 12039818943948534379, 4032720075185402608, 305328440113853819, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9659135662592135773, 17484226751916870246, 11292028939680877522, 113115289354650285, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9755958532003047581, 9628838737296462951, 17041574364028704779, 118537673356989097, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17431253231803058330, 5399931780426754021, 3233257711245535858, 396350842493064311, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15106292802837036795, 9012922041233019983, 16819782412188270872, 79677597441928037, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7209652096458706970, 4831648716231546225, 13477963960890839496, 227737951469363364, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4018150707202124406, 8355229729033988138, 11006078815400331201, 482758340569698568, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10894289540187919079, 5540571978542463316, 8622557468625648853, 565803237231933511, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6653078077555884912, 14192503480532333361, 10032319770855583423, 412916686848298187, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9718061534442456568, 11943879498990811883, 9737009027321041040, 85143110374393341, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14440818837803235285, 11847614200046646737, 11411821153640347966, 425407124373954211, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2859626629192856277, 349947605792809740, 11911152937487335485, 527066251373288944, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4839476752907116239, 10275113159160480009, 14976457624185473089, 110256141389002517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8445987666209158108, 14203863015043867464, 3741225108423630615, 185300316492214963, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2891753915386849096, 9115213665152035503, 1906935134633209675, 537431469182979253, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3132739630489985535, 1314989548166647555, 3319595620988718244, 252062165502332999, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14155245236574226644, 15939103005291611400, 9880316340895827992, 246865346551031365, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17677389190103548830, 13912933848941138641, 6940135854713993692, 390245568770518259, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7080945026909207699, 7689410790278185128, 11485220864903983338, 555597137892707249, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16693506622933875626, 4770352187802334197, 15124386868278054854, 572366242110084309, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10038348685245185951, 3159575397503763582, 8748555531481780437, 106333296949627198, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7261398236573219958, 5747283102620694353, 5867289942272043775, 202217475333796288, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14337791442768382616, 4040967205080542525, 202634951323454584, 365081846734523575, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15760587503513542789, 8110558577250856770, 14259608565568092662, 476113459911200492, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16601704240911744269, 13550334630366772982, 5586575103159360834, 401356489054159812, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2275693229445028766, 3084582565585435726, 8585853343213020659, 231037949228451398, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1762783598121660761, 10921167926887126956, 257687643604979523, 137755865662301122, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4373052662993206468, 4258851470777670250, 12426247840356713500, 24228693640311473, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8324519617464652951, 8668492369925913610, 2984641807938280094, 497016940392170011, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15370215866755248918, 13999327033431618814, 6768097642197159055, 35735502172342794, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15229756500349633721, 3745433281323996898, 6785976501659732706, 60560786002115780, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11756556113912741626, 17418892003197057488, 15710337661047386082, 394379187769059873, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9873612779970426742, 12298186659728097050, 2005354988137978370, 548969972519995781, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11711269023377174602, 17198075272721941313, 4905014985665813004, 143478424552294077, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15848854110303821105, 4536095595098585980, 4596573434384222419, 461224187124259234, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1221646741520227442, 10543956953676524482, 9920394792378972864, 446339222761004352, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11553190330156661934, 5757315501022944108, 15056144989354052195, 416724099885172221, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11723939321748321328, 17578247873052177077, 18242871004768522150, 62122761012909368, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12002725252770017751, 14202234928769023471, 8242849215117544398, 338027413476375937, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3615049415698539037, 11208392596845093586, 7979520348744177970, 394356706346376794, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6478559569395345536, 9974908348566476203, 1398380117473491485, 431283514769162019, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13018466981311823345, 2771809877577257735, 14605325202086642638, 380243092112123209, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11576028215534556087, 4932160750189451235, 8339185916437170970, 75362447738775272, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16428464006270615463, 6091971851468957045, 9849819683303647065, 48453033370756054, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 524263869268856877, 15929332078635005985, 16300028956322602833, 110882852379510707, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17059049768098955558, 2530822328328585584, 2791143445579456027, 28941060192384064, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12308529696526732167, 4037422779843770800, 17573884986420457695, 299406760595050224, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7897282121350691135, 9302021342923431026, 6944783755895460592, 349295089931177827, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14470245552138802686, 5755488868957240494, 13252576520196390708, 82171913340765685, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12395302804366305347, 12930756102140980741, 17203736554114359874, 150030422708463594, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3420605864470494011, 9659225818993361194, 11391497520274074422, 400460520316303330, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11979235887652447136, 8214690344858989791, 7475386891647752388, 518420781302892092, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17296562025240043580, 9486739130290066273, 15895931042242530457, 132179016782420236, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13396046820338153563, 8539397985752815099, 5792759298169247885, 319466294746010499, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8280585144861826180, 13676509156935136572, 7558356479052335505, 28188003040898862, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11660729103035378801, 18153037726626486664, 9633945967120477980, 496564204862554664, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4680172183032352460, 12643171262099941875, 9620479309724850750, 24279564696999586, }, }, }, .y = .{ .fe = .{ .limbs = .{ 426233697989432903, 12861990988171824859, 12038743351476595282, 136109527245123006, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8739163149974668971, 146756511451833506, 4512284209637982886, 253398674982648300, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3396347414570039119, 6247970701227126508, 11521114518856958172, 215009321704909049, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11507141615914957900, 2015229289728222291, 16860669709490436519, 495709903392362019, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4994304981674957593, 5791394873989909761, 17790454950214093070, 183789788383045059, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13290580230870471981, 4212587348322572492, 12284333957476844588, 32851952226732995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8997733995955954520, 15129582844645231783, 7273010214585821992, 43401521282609075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8243785709504524403, 474185816568567380, 3605643496512114512, 495670432775211825, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10809528025305308081, 3568312868994181729, 14584782412471278198, 495241533015539328, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1235335442306023901, 11111755556137315851, 13250014733661256810, 16425284542109133, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17562183668029479298, 2606685276129404076, 12066998374110943790, 335385594385980827, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8085575724581542105, 683624629839521553, 17053539765784811762, 246479183098430396, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15417826066981241333, 704075228981910196, 6792181984694589847, 440536353364886585, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9666926929075817550, 18120737219285579138, 7118553555525567386, 546447312849504561, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4221685470963748701, 6818706316399004797, 846200614860812836, 481423982176378757, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 797040810179446372, 9538077163188074175, 6028422717811593513, 291060164128295650, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11424801931281979328, 10316081177563367762, 4988671238472999227, 244722176581829875, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9223599948253504020, 5050108808589047451, 11834107416893748447, 369305978493756416, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5411423703821168992, 4802738361544008519, 17786023572380710542, 122331481313860242, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14801068879024840570, 13775439905369406974, 6426075347370136329, 25356141659443840, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3023093813545982852, 53303819207183053, 14259977087948010819, 466643142725004451, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1574162774401534574, 2708736407639521201, 10376321105985860117, 497586069436033203, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10038118487286600407, 15261341416440927458, 708772000418965181, 78147145475846399, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8587037106578456278, 2770130585192343255, 8698141539339252733, 505815013895217063, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9689936908296829258, 9455159721320889899, 3777282801069044890, 363131338718801870, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14360737790798303086, 7495226598580485180, 2340316839939288679, 219855780472831173, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7733984384422798312, 14437869469509076848, 17176288491227011363, 199866219381399663, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10505277388698558611, 56760947924912679, 16283513458364728798, 210033192419111894, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4171530892048631869, 15378352483901707199, 14749928776290903939, 544074966568820710, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6828175251984104562, 12334119633037528507, 2424002570426013031, 130697765176373645, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1230697147658232436, 2297527604378151539, 4438736934030647548, 384783038195574187, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10592424435738675937, 16624248706939501598, 6841689411194931989, 153183732868792277, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11361756295294207549, 3080187129448524553, 15602650078157547393, 30091990806493145, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15046093821279410271, 4541833526201860747, 15447105736934925735, 164113615068356277, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5202497135284982964, 6659554314720060666, 10334233180065738170, 114467563004061846, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2809638408120392820, 11387617184643515502, 12738564915427906694, 297229638223233161, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11167869978338673924, 8238248888130242432, 12501970296859722857, 565946749488351291, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12988025649359556111, 5009026958914357564, 13574919329609531002, 513948455669884233, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8747878262514614719, 12173697654564271229, 14610530018662911408, 22135218460538730, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12301172003794774599, 3967119023043419558, 16713834295775564540, 524955902891024551, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5878079341557157485, 16813367762692985604, 17569992248448694097, 249158196698132893, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15877306722938877070, 3371003103930709807, 14741398427697806386, 173757619508378538, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15392527034034909662, 8664509413127700483, 13771044418973459073, 347167853222630736, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 518146898067292296, 2248074692387169688, 2657299228659231542, 568515867000543630, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15351732301905147814, 16280203938304506736, 17194642866963844189, 465847824089953285, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8681395063048461490, 18120389701257278435, 15650698416372001093, 467554420056981610, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5252416221862066892, 17494639646212282477, 7478678991922980656, 447358043659173883, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13891637335494618611, 14818889135610961541, 12059175867140771706, 23052721337379723, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4369045092640694534, 15101308487412590321, 14089900632609790253, 466301050069368615, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6074162697813086072, 16765580816547266112, 1629021136591630630, 191854687905469442, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12843399407788487825, 8517503316109173617, 15652589749176471029, 40819919150191851, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14247255255253445150, 3820836798735960073, 1950826298434435686, 2950806273745405, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15019642684217194011, 12941398413896596663, 16711085795629152180, 322302971826997701, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17260330650168645268, 6254689788329231374, 4186759755645252906, 30659268311129435, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16788842800815803701, 2676139879515013613, 467772074348741554, 18729427524211371, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12571263624255032878, 677410624612493739, 14065684367889487006, 124385829504669551, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15214007281602547283, 16366953082763812663, 1765160602368841767, 339646762488552519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7941961334420585253, 14582165212936337267, 13919903411812684244, 487943765496545173, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17087237395979611752, 10259151871950510785, 10358655315918353962, 428581246264853772, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9877198601047663653, 7224604761275848798, 1232411118056735015, 348245834738161909, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8721751125541596750, 7725062540869248441, 13943218755964410479, 304484745907162267, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3499988880045586274, 9407253984122440116, 18300628516084777232, 7677989850824054, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15403037696278385691, 4405844647404295288, 8808495302135856132, 536492741197711464, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1252085681245099, 15071026324988151846, 17504991906910419759, 192405460148324621, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11351252794223302157, 5977665481902238955, 15352517475824976092, 54900727241497103, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6868352912229191832, 6401067699271392367, 8457015303244955907, 280230737271270564, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10779784064853163184, 15139730469688451783, 17797992792581955792, 77539045481706697, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14585982445005228090, 198672071629538099, 17546951703005208125, 572574161127237278, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1629886431852893549, 8973507643332712986, 15299943430322473098, 186806578320190772, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7817837166794619643, 9315110057369785406, 5375906068556293981, 107474457865281439, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1841453378003823714, 16724775312148873785, 13744605350127689486, 233415516206555796, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13753569669319847583, 17390458418371967337, 10737022172049938831, 407348764377573535, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4666800113468601939, 10670746658174693033, 14192503562407482510, 226035662827470331, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7758728640422406128, 796521536524490121, 16885153808024887046, 285319445267307747, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14551646828479029357, 1365757586562440267, 8380515939304998327, 4892288835522279, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9840843869805558520, 4563685848302104776, 3507437303772743869, 486085376450979779, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17953229590993025292, 599727678359333121, 10410877742170612807, 9363032973954177, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8640685765675131292, 6083650763958748721, 9576262334459896262, 545801065833600268, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8208902788899107429, 544759771517435413, 15472854507872090438, 474844829016834525, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8052859243143105767, 6416617475308295847, 1289396518684021051, 43437809915892348, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1922350806766495080, 8593194554368174403, 6124184532515405092, 271196936110127834, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7430622010620235258, 4970198750964407489, 13974941411926656420, 100131763431392666, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6837441885313515460, 13816505818515068510, 373197060581702458, 191990543289811887, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4433350534690753093, 899470387847466297, 10557286231574482600, 402274495697838563, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3316060266571412667, 14870437503391776235, 13839962939756000218, 384289355431538343, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12693510570385615663, 12682272743565666685, 7323018752633225041, 414544743162572310, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9830687907491771378, 4917592521082259053, 4505727198772762051, 574026749273111889, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3062974456818253591, 17148726761047239183, 8305796223715047904, 338702396317515109, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7945023335465500849, 7789156541237777723, 14909055586863575608, 46686845274919093, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1744226106325826224, 12814431226476302424, 2890939373329340869, 239644069846085850, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8106541355329842481, 18161037464880767253, 14865983898003911654, 374397434949519467, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14304775275817989323, 6677063982409190134, 13229980409827091401, 373825128756636916, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6653060902953694166, 12011096402959962943, 13496688940066886804, 390263238666594210, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 600548945343475983, 14851363947364887052, 3287433643326730511, 115615258457421395, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5591386489072326909, 16229476436749091469, 17188417829618385799, 267858106755289776, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9061238148539387152, 12993785523515236229, 3379131203396737497, 306577059637653002, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8215040379188626123, 5954942423368691244, 16515136331502970933, 475016156609040295, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18437019180653662889, 13392523598446862518, 2907206517971915847, 231728242841152892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16654104916052672754, 12306180244197425233, 5274439948333276197, 32851725992309602, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5510099258841671003, 17261268512434063429, 497300181954567668, 375715449459796143, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9178384089790853266, 14431512108578340379, 12854703768576298871, 525036541510169083, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7697289245365325757, 11918834895386989966, 5950475634644304486, 93348330108244151, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2978866196605580085, 6570470752139647021, 4616417128920020048, 65964095371663969, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4227748965603254548, 9693028997523349187, 16608129201572709800, 503904383962490185, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10089671221749982677, 9560595569487996177, 12066339054973389249, 168934191764826305, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9168642552301005772, 154937262895256696, 5709620646126493019, 391744082565923892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2117255232082005777, 13592027109356880379, 2789348110720611598, 422824548432003077, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14665769041238277768, 14816198652030512928, 14700654822897760665, 438884722318167102, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8078907936271967818, 3344758152738695776, 13683881471891022582, 272523635656286689, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11230464897834310984, 2837849704946508899, 14889313522725058678, 81251890586681006, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8684861158831556510, 6445307674112105261, 16469087085357666015, 124536066635205129, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12103307310608976272, 4150634247107719141, 11163861903781095441, 283834286517508294, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13308119177513258620, 16594753890618283171, 1655434269833737410, 172230507251234085, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15422019327089364403, 5966293786460686013, 3015488386594963236, 210758130037853648, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17245205993320753620, 7395681485412751442, 5772954558313893633, 214790951147386018, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8175228267080835800, 5863191045613440061, 8753169855652638309, 446880129078584798, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11717942093789500997, 14330021920438130599, 13944386009959290826, 556007008933737556, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17231371779760603770, 16716094849872873314, 7604666335865434721, 242837589462615346, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1442472086428857945, 8380662603358558541, 8620992061031902018, 137971953863021297, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12224274187805127086, 15986302122892303429, 1379062916324481435, 462949156870708624, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1027103442847290480, 16215494834505002970, 13719406990866135475, 344094370542066187, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12114272812597546695, 7549166163364777989, 11282412892130498454, 55456972545849965, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17629242808212248785, 12699923115884434439, 5714548806027038088, 260995999927826518, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5008726892339989298, 13560140033185315212, 11280441451767529104, 494361981484822388, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8193675846984288511, 4364361946593678213, 9972260929652704985, 35422383576441375, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10976537516019769749, 5245698705241649127, 4542644180690403318, 486836245881052216, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1768184120023964141, 12946486218239810813, 4900568906337401667, 564137538109628870, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10403441704667581873, 10574167203947908829, 2876003293127996913, 444569062727777696, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16363230043643063475, 3024656593999190274, 14315671728187803703, 353657043522024286, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6353887283610988092, 7056938630138488587, 11527800414795906391, 362471119982054035, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1961509923397506517, 13429760365363621857, 12150264346852950177, 250699394146528027, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7890638428576835798, 12921696595112681058, 1357078566803628857, 69417285443566937, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14703181678198049595, 10126817033043491758, 3544613803120901203, 431417348481359849, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17778342123713763364, 4255278387813246262, 17804576640378001077, 532724678106277451, }, }, }, .y = .{ .fe = .{ .limbs = .{ 322243735974790940, 15096146991319939378, 4797795729725299328, 77456833141857926, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5267696678627751465, 5069420766087223606, 11901658526318321902, 151419609860632006, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7086258874326391484, 9348709082148962377, 7976904974351297683, 233597159205188881, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3704227011190757808, 9430708428609656287, 2347647012019736190, 221633605251345220, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13305029872109579847, 9045295389767187059, 8875786243512247042, 565301752277888169, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10561133211190225344, 12883922412235838793, 17473844286407666880, 528727694726470329, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1116731079122878940, 1936962754848175834, 9718463900786319556, 52786950874667824, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3641395519200054831, 1072966581104001068, 3478953918844988767, 571511610111545818, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17771728991549552825, 18353408171746270342, 11479616706223138932, 385354335546327276, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14698174674374487905, 2683294746379278508, 9985551610156098880, 147215940742070440, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7319979533930711982, 12583695797383501685, 7982224361814911472, 111319856436129602, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14202257978351722187, 7117406675643217341, 15897344402042652688, 228483308205641290, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3847963983484716939, 1247597444052063096, 3740246904475144443, 221913978970885143, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14673279452359043134, 4090936371634109164, 16039797143405064264, 398612878150122062, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18163801894681251155, 8588283626765924327, 11305849163035098647, 249670343614958810, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11944501631926340076, 9208826584546644847, 13750145900665283882, 335769326605871564, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17335857320270619515, 4245930489971118007, 17491826858494689365, 118156175506009750, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13374304628563255841, 11055337087899319917, 6970882995538874161, 350418972870846240, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18000493871904695499, 10151331925362204772, 5692491868947803364, 204374854947245408, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12104655779966779857, 5359531232729695436, 2254358471367979846, 84709916510959630, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16788631963802419277, 6361887810688044107, 13625632499034323077, 380416945006588978, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 85596007597722130, 9252773835288103441, 3410220306928795500, 313138653848676713, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17953275526435705832, 16456518075080788584, 15068264570366906212, 376700212941112444, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14075321674933148384, 2501246698272762168, 15470114517029783554, 275167804455619335, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18257660108863867286, 2593662368933003880, 11518156799492681400, 548372544754800329, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17613712260568001466, 4198129525377111004, 978383959314494836, 425664914078458147, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3865695964279949856, 4324035907964656271, 3558414694851634505, 275269726340540508, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11209066352254436679, 13887762799300063798, 17993699936319373384, 484354646633298532, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2947618422445490060, 4845229699726328076, 18016683283877181805, 379523564879607930, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12258456446514062244, 14387402866623529465, 2743078695760563363, 268710036186084668, }, }, }, .y = .{ .fe = .{ .limbs = .{ 56994963449520364, 9626178854779614309, 17451830536981471584, 393351803104937075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4736429211277396354, 2980527600363234322, 7392477315391444615, 22633391101377419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1855176679787088336, 8722391309294764400, 7887263211343875986, 180876361963381690, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14926954261419046322, 17916376609598621093, 3044856193103039175, 60421656853562092, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7986088098414453970, 12926722244763271774, 16801825035216911020, 505138400601614419, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3291217884728113214, 11020616226052180876, 8496143781406214580, 468082441140054508, }, }, }, .y = .{ .fe = .{ .limbs = .{ 309470793473325240, 16186886822909239572, 10221869440191219640, 522520209240824198, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10769177638537811003, 16780080528114699220, 11037487612381920321, 30047261322693951, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7609197623156579964, 14482523763921817667, 17855825302829249979, 373627764991503488, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13596374215452281307, 7545977917478482608, 11812244675605405175, 309989419262843717, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4082635585351139043, 2144101667919341105, 7152096057323438943, 13178407575317332, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1146890125962093909, 10169179825549489395, 3894426871683535771, 11787318558335451, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9573833393697528745, 10333735217905488025, 10076320604544025976, 270375479215784985, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4717945469243567286, 748651048912532530, 4233755278440767004, 217000600443445665, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15704663771040079531, 17800138180985522911, 5272187337321589535, 258932052777918067, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13397023580989104513, 13824715029374829386, 3462940003907814170, 171081647184235755, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8857169852535110288, 11906553079263835861, 1776831253225292081, 220426173839863920, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14801526368971118079, 11407324856284291134, 1454029124856686974, 488491676445785044, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11876918932062804758, 2103889710589591369, 6339964853087973362, 507168026333035589, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10302127109356875700, 17027911423189226827, 3428670216681397453, 314038180171437117, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9060090197372746367, 1504951342649030394, 10061134343922742076, 394813619563042815, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9118934925477951524, 3101309607268974642, 3006998042810539580, 555198030211226213, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3223349820007347712, 8264912975061224061, 290117021549992536, 513601544162186328, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13351129655076507677, 4277463485099678805, 8467367138186667844, 452259795974748962, }, }, }, .y = .{ .fe = .{ .limbs = .{ 616130436087951197, 4193532927902387630, 5649535538170355400, 262617981808243981, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 279709663008999028, 12507689957030925382, 11888561282044005599, 68154963329255367, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2661730559213819797, 6522271503202021305, 3691257636233880297, 127310403544928344, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5368777521414421180, 3794295880029948433, 4768357381125361662, 488010939839821419, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16212691468400451622, 6197499968998563796, 3265231341140667201, 157604214015558390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1897827064850209811, 9643727680150094447, 14188535082124095388, 196276293605083110, }, }, }, .y = .{ .fe = .{ .limbs = .{ 483070721904426634, 13103198557817361291, 14371858343712315217, 199650888600861503, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12273426717906676808, 10139274625824515423, 4563047834813026670, 487317289760722534, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12403975101499147031, 13876231967934644114, 10425458155534820442, 148957550468801080, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12409446462587489310, 2627726042276438111, 677679593043772923, 320606870554498792, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14450226692613773853, 8372191144021932473, 4187661414602776432, 119670949480538778, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16563149206735350845, 14675746198364767890, 13968334088041404816, 299858859585054859, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16161569864308108745, 17551719674722533989, 1697267303241846406, 317906702016505493, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6065693026642363140, 3160951849269624578, 2839729783127978392, 71521757589485517, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15328347252123374944, 6925042689129950912, 15590861805843912508, 176784741105996383, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8889903625111285184, 130744733463109725, 3397866618753225333, 431848005795963964, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1003720006533721938, 6913093795572658753, 17037871032182188658, 569252256529452946, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17460799545004473184, 17411315992856190724, 5118114124043520484, 439038477970147050, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13019841563476956862, 9896892593379984513, 1983044130655057562, 105427217505345495, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14135918627889463302, 4179290753395004402, 8183550901338251129, 393851581048588388, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4549810886728312890, 3533081427331275537, 10847000648610127948, 408690731107118138, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8095793053405725149, 12948825956834283082, 13087304556500972341, 668971424582311, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16963618481801952689, 2036098495927342796, 16667021370490167713, 574938431249902880, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2152167919400274623, 2542225547463368469, 8968134295956678321, 287432429264749773, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9670871274945367924, 3318092898777702081, 9014057485482047493, 372825333756930923, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9778593345420739573, 9280114840195223050, 14455096711536094755, 430553979110962184, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9805900214831218184, 18197783805856943779, 7276295024250270245, 402071850286774490, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14661027331306799066, 15643902565797923143, 16754623718149320425, 528783105955623014, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8124948435246315284, 9535040075583385644, 7670460914959718270, 200001701796807828, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12964661786638403837, 9575711964941225100, 9369692645755283370, 52361618245645946, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11903250713258171780, 14092618525189630517, 6232481594677168576, 439866229395151250, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7766183031462565625, 9004345570312347839, 6268468955883801567, 460848979244728247, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12866386101723757443, 2174707024593505047, 9711433516045720646, 521757201278388423, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1619203917691182353, 16019443268997276012, 10208129960962407090, 435753651348079609, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3470692288122099726, 5450631634655688507, 16854866169665767237, 497352480502921440, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7930778217763891336, 18423157633692957772, 874642802164691656, 503223430610767585, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5973356817289490809, 1221651673080531855, 9753207946376483710, 1864060223823126, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14067851712599988981, 7591572619851767862, 4659742222384521405, 478437914794623102, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5873698633664960628, 16972929139185781701, 2743463952670794354, 315394267666033450, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10114230326377833161, 16917182048987776725, 2546492703119505376, 315906485266701711, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8118772775761335048, 8697000855438074283, 7742657226757417661, 252294259014522882, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16246790112071056915, 5957552838050321395, 14553643602867786637, 77489931621797820, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16693422809025231181, 14173467481350050298, 10619503296512928376, 432086266892459950, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4141506869309552433, 6364454242204334599, 15765985108041501687, 82412544116844462, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14401613537660224336, 10335769637674129604, 11201933276159346613, 81073272925302655, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4547739147132455135, 693524728726866347, 2749724420387254739, 543487178638516230, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1075509315556294230, 15080089531177893694, 15793511719713540509, 229584196420424624, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13759344704803705303, 1948846354619675494, 330691958993395370, 533993841965323595, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3515938649226064397, 9715755700703353979, 4865800021893121889, 418875736392951258, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17662505430577369218, 12540271994364083829, 18283413990442049823, 420163342955879092, }, }, }, .y = .{ .fe = .{ .limbs = .{ 832850847358922165, 11039580936552726289, 17849982031727544081, 352656379362035070, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 549206084735996570, 3552674888349934492, 11740520831715496136, 314337420390143851, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14087494845861735134, 10866659165703511810, 17506033578596041432, 165541849717939794, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7490518438112157982, 4764142008670598731, 12742452441106662893, 312338300675559493, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5114344684284701083, 9067421814345110566, 13506998112859272906, 426273337015926877, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2871271157868290755, 16050568517668154632, 2477598446383287188, 251070079750720346, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3155852929638256144, 1447795759618792402, 3944946569518243034, 532158678288539704, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12896979886428321172, 381060653017551402, 1145415438387412735, 47538072375098498, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14718369791634263711, 15624386405183698330, 11776525891349743795, 52269923648473434, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15660983250402598548, 10402484439329412130, 11197391937028195660, 538873752399512101, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17236033709571761631, 7265472080927672423, 1754984069483772519, 449381713376735237, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14710878511359079919, 8353720723329861388, 16572230255322543519, 114363990289084712, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7987047735803137257, 5906299520000885787, 18083779518308535850, 107732161617645304, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17354583471341560963, 6870939211234616046, 9238829442038426667, 297561184245312625, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18089575107080192209, 18384302827443886725, 4176701343388305329, 411341815551141477, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1900031311401103699, 13326259718269156386, 5639651525125240537, 281971515656772138, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16395209097930809337, 4042824281061623206, 7051147007607445601, 71427766272982114, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7836242046087448955, 220937850209137949, 105551302360029338, 373078217740206265, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15232436256309530633, 13433099756181507117, 2082429988004467687, 1188058359783617, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3045578883241142251, 8221965940915546500, 6946998109260795940, 274976906555480432, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2348553132696815710, 5962661028563252784, 268064282780476935, 330265293024774135, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2217397208502707176, 5991731684812596851, 11942998484514212530, 286841864494836326, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15657694612050861077, 9103309183709078119, 16237374840663465755, 564860791886366613, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1670376543524458695, 11419498626399387314, 8397650375231849942, 210398658802446330, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3460709239890511540, 8822789709388520282, 11062742972033374142, 306817424538187015, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4804990041282433722, 5793727742299513659, 12103314109489690003, 53214912941727674, }, }, }, .y = .{ .fe = .{ .limbs = .{ 658850379219447019, 13959075762888684738, 10462409061285409068, 355137648594064507, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11793591896271773678, 10214825458389463544, 1775728144843022272, 512519196394785161, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14449964147992901088, 1887836893816201280, 6186122271428357634, 57576435540431997, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5420162762886053790, 14008245385300036859, 15077229446403249423, 27275924101604896, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17993049380368409938, 17943295500278836656, 1134723637279812612, 303251808172955280, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16801670639880259006, 5456752430360001163, 2238084330481913784, 413470006597432074, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14584537184463415182, 16265403581011937171, 10433222510862963458, 515822421493560182, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13712125105735538374, 13903403041118074086, 96505660631466281, 44274353777457470, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15732031189497241525, 9754790896535049842, 15885965194376010987, 486068813174626173, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17881321080671613328, 9956262013592168062, 17038111966600756214, 43620862035064233, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13502443245849520975, 16331086594779771845, 3825000154621994749, 211567378431142206, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17137560816062132847, 5814722288720035518, 14352298279015680818, 249565549634575920, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5221926842463633175, 7623760820014489915, 29592034278642625, 558759256899221787, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 934121626408230946, 7896869399995619568, 12595243204620007433, 179301683962657542, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5015239846010255794, 12083317366839782445, 6657970985038849695, 315047983968559422, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1416450438709464612, 67940503068777401, 15315560750189671062, 546308955007286724, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11581127087085809420, 12011122748845641211, 5621234528463139322, 575331932023154260, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12205279534786828948, 18213019356539044551, 11349005139408049311, 513298083100704194, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8753945660566985619, 11659843905913621464, 14315938584733719633, 207368801283480734, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5636760667714289145, 1373429219795553308, 12549175961509238350, 299605822835265540, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15138539278535056113, 478318137282569541, 17219567614465028574, 532348025354832001, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16200186453073307745, 8274053065252170458, 17121213225927411005, 52186267418657928, }, }, }, .y = .{ .fe = .{ .limbs = .{ 347912624403137280, 1061392544002760383, 5239764237593484104, 218789243664623783, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10607003334377424382, 14811119289754761347, 14253237348698768035, 278594969959600199, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2072129436520944203, 2853170416504403304, 14051746269728859585, 233220141794286800, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7620768565750578307, 1364093755867564876, 9218694304867193065, 482858950435008081, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16571415010931737193, 2134130467936825567, 5055907902993781847, 80980724114460122, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8409150197086307097, 16931944160884182664, 6275883682528868557, 133538196719669438, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1845120852621539148, 15348693542521782859, 11968605373248629100, 406962478696494189, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17587789008348084642, 4678922791936851679, 10347991876120240864, 6128798999373418, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15338142654658939579, 1752337650145512321, 687739507871476464, 156687948360039166, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16583748745906864816, 7130318907398518765, 8629135462041740482, 244832058301943117, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7012610763493009315, 4399656097547043067, 13680121368600944054, 303667122717639843, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7907789184035305776, 7009697376668270206, 1175157124488225234, 188579168461740144, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2837657023091481660, 11718626991775519969, 6440348123476798399, 380350154211711013, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8719018781063486191, 6188104999803092783, 8311756648263672978, 422387587486088868, }, }, }, .y = .{ .fe = .{ .limbs = .{ 561204100023697279, 5192227392208791172, 4494039982038717771, 518234761683015507, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18068328453727261427, 7004636116242876334, 10273845863164309046, 454860057130231037, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1481027190661876478, 3354402044691356183, 6999851228172977026, 248549410287190070, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12675301436230910099, 8283941690062695490, 15271482178508683708, 346779407346447200, }, }, }, .y = .{ .fe = .{ .limbs = .{ 673576368182267462, 2110304562442383031, 13361779860928415512, 371122063993776354, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12901096441613569, 10340791952348164118, 2881371631889455808, 235035099049043684, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18027743050559485471, 12285763513079871352, 84744244607507487, 344751888099960268, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14185947217949825701, 5010342401050414791, 14123069740116646500, 164969510693113095, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2276921955143805854, 13246370003501732670, 643472492051970444, 113864074467143713, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10970160076366329758, 2916135496588817368, 16229654711727027574, 500426818795878316, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2358200834018776478, 593480757298359652, 6067042020830469612, 95511287139578914, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3616382248069561007, 1788901121633530659, 14458766329990520527, 235770711264821385, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17195196187117560905, 10954038219867658913, 8010982710377435242, 66126984292879517, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9455456404606643879, 12931288204009585322, 4787362211952065733, 308858193052246921, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4251934237744710751, 8402608294922603797, 4377708456450113504, 394405784670838679, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 187850624316550169, 7240476376625133938, 16715515970038211389, 529574532013536107, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11029475161870846471, 4931529966148644406, 12567237158027969197, 194331418391513986, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9558875529952358227, 1848662510473517581, 10848773332358926946, 90264253448518184, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8068933202475539342, 15587707386653431457, 16220912945040869202, 166236200372712121, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2080301506683628556, 13102228142613557753, 3532218469687071734, 553104009927069026, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11633317058636424961, 6934083358709574018, 5565906677976569206, 310751912089087297, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13258844156362517711, 628385690168985600, 17263780487228935875, 226595175138350254, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8042803312398837811, 2922331045715080944, 14634354108985410822, 143042839520932440, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15164415102684723297, 18254580754392847828, 12137217460329440315, 186257602315321948, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16388013644711580484, 5878090138839544123, 8611776155989797173, 430269871718474022, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13903418463832894911, 16181836586051474058, 3964611100135042174, 311604933964746810, }, }, }, .y = .{ .fe = .{ .limbs = .{ 109830881711186723, 7838554497160591997, 11470204000352195572, 136548326832259667, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1563705049965817228, 12506233984480754268, 8630712230732999576, 50615396432676833, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2803613870327741747, 11890387974664707336, 2858073329055610143, 297303082761669985, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1809669202774713901, 16765778371917368782, 12457208193978543641, 467061147740914145, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5352726136657724928, 16104978212626603421, 6179159820338525573, 359405101690455447, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 328190237566581091, 10007028535655831420, 744102094744553411, 483565849367228421, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8675058365206014537, 14063812120211475278, 11198703379252001749, 519080077826658957, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13518916405040156144, 13153747986451091125, 11584402977035311285, 338571086417979559, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10424102603051449265, 10326067688347712186, 16240612959258834146, 251751608521858680, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2214025236628910082, 1433891565464277695, 17291358060670433901, 530919913480328882, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5995421988953651051, 7789902425971617543, 8561859369014823080, 421993831898836710, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13025219255990344851, 17316223664915053281, 4452627535709274543, 275515545871079547, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13027795301275799593, 420021899533874885, 8785206538125142209, 440914603856486857, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12154577045664408983, 14363405383898262225, 13352044609422229271, 482288004119544269, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3721397734679631128, 12459948098909991458, 13508594259712699230, 284727899981076237, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5712942609362910420, 9284863059441744625, 1137901523393121618, 471395052226192968, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9481824003088610016, 16820310578579564826, 10803891342645155212, 162851052500996239, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16592450971748357861, 10021360702098368024, 17474309136804786066, 85496619644508122, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3800986846025008685, 9551266843728128833, 16050299152708176044, 89164366792103310, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16091385642254030628, 7648677094817024569, 3941779933184392960, 313769622730117230, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2220726550856459138, 10176710951044729308, 11594612410540947100, 470267021160012695, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8844428949546079348, 12478413327002397847, 17137242335158180347, 258761136566374092, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2050335592366045766, 17899489279029829158, 10197839234201969007, 149312458823810301, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2427284891097907162, 15754868792673671280, 14056933277315642188, 425955419555682899, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16486059282515823900, 812429349572801863, 15031779704433538931, 480379343839549127, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16126748563067231745, 12528732246634104929, 14920875261462983273, 418493843493403280, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2193637998972505618, 9001198731542420361, 1395704756039437917, 94391354986904795, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9888729751838648135, 16522331073699592015, 17198082016307212129, 502087487336447057, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2471342487501544186, 6473210347736199114, 9772484025692827115, 96725947456081240, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2069013344522935076, 17555886826836510573, 15666912785938846663, 155501425976554361, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2808487660433152161, 16425900402190281983, 14500646634099620489, 566856064061807382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1684394439425633569, 13989295055028277153, 12441369556577944896, 414863332522621723, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3286578267581268893, 14675135945767644104, 13756175464892115495, 116668651185733674, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11114280055338189122, 15720517114300439003, 9938656242365256080, 131136663042666941, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16243764460743968389, 15116838293499816817, 15168584374158586829, 288898846180453177, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2086321184358738714, 16468992716054975151, 18265947098965687526, 108559297039938136, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4144775971611394594, 4682997069251732866, 2289023159338568557, 177205934793335886, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17453196988507755650, 28293792976210135, 13270444381359354944, 118687837715117403, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10588734172597719102, 2698402122108934978, 6377574925490793817, 239661095812883927, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15085897862082342769, 13443902080252791510, 9158152040820005356, 414609686205933117, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2706869698324239300, 16943151303751775191, 12108438590274627204, 569626078520689824, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9380857104510392806, 5302565390090361450, 17589949722785525542, 55870219846436949, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5443635770042569578, 7687079740380076971, 16726151958320821769, 514632326997885175, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8617586357479591341, 1250374355168217814, 5507639866197778591, 300570382544534394, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10823051926415090361, 13004627554533334989, 9053281694009687469, 165278174015332273, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14620116865333507227, 6397608325175174348, 14118433558294263384, 266995424474175914, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13981670386754665139, 9328768654934012383, 9552312529378390830, 228591487666120455, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9565464517208522714, 1339384034684243714, 14162047252707817515, 458940889823578835, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16708856869596549065, 2788189332860027282, 3072679998871692767, 422851326114668507, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18229475436368636568, 11937513365884454702, 5956505305665443883, 30284789747425157, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12005198074879590451, 8984627327699265389, 6529533759392399063, 273259587996472151, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14523053366371533413, 2261028334043624993, 3107197236790959340, 523061337538479875, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6226490468346091544, 17631091997653568974, 12419084400885234241, 25626626200081435, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11766256670662474204, 6247607242224836229, 12682863019849353283, 49443202318716441, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17219280140604158530, 7549386308302924815, 1582931783347413299, 378901082116422392, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18180460886918598509, 3946029057202664081, 5892830778371198561, 508888333917298699, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13143611165137326044, 16151332792113259267, 1893393030858147658, 28884724970164380, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13747484524928067277, 8724426621224459589, 851409030592767475, 31727844287166396, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2998462104098156117, 3452768502262018326, 620857720343548016, 483578809557308647, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14073398054047539517, 13206286292797125685, 5973471206391590598, 339101820953865147, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17445352875824004293, 4468019344879637626, 8350140664488139534, 567309438086462514, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1892883606819136520, 16194690942048158938, 15093599025370553398, 169433753675018269, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14303721402468307880, 7391648831311518674, 18303783933958648195, 243845332890050872, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1240303887446344658, 14220318314613751885, 15553342515231710294, 116308767056745995, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15797579600466321742, 17213151378894538364, 5348253159391920045, 192083874267482404, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3673484962879814205, 14011447463838409037, 6230851714037097011, 339203101540541816, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8044537855437974383, 9664366175204651369, 18260799282178084895, 281735902413791889, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6400644089301302706, 10689513541100755703, 1924858372149146486, 28869617070397781, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12777460685289080443, 14528205938857624476, 8784653032075997852, 453728095718983461, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13940760447156604684, 8413714706060510567, 10648039930041827391, 453478579319951880, }, }, }, .y = .{ .fe = .{ .limbs = .{ 119388938914899555, 2359216550396791421, 4614288163815284280, 11204811046451708, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16362775868834879509, 11901331990923004907, 12834276146139578306, 328396816433990862, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17435711050266343102, 3400830027034864585, 2308033403262721797, 202172518005573546, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9257879706626510681, 17453559082046096352, 2398850445760259751, 295544891071901240, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12705167853087924899, 15282656689687214165, 10124148258786757823, 544203819992435873, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5731573884056666525, 8179349887913827115, 686901985947660649, 421867985809987229, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3053716327770862747, 5189759597400145591, 15826731203567209226, 432990578320346055, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9027991911867520026, 14714909264331641706, 11488950716135756368, 54698836723073439, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8948673254984783813, 2066404193461706982, 13438028521195248310, 428598737361523663, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12160056608706513199, 13762785654809993689, 434385602449705925, 533700031503202962, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15976802799973978461, 7221950576134656342, 10722547835576422069, 111196508131841327, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1554827315190685241, 16608645047876195976, 18142316856268969074, 45857987061019200, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11645235241436765287, 655218664346672046, 6368686074688964241, 223569280387688774, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 506363730525572499, 15884305759123086606, 7767048678626644872, 106258804143872501, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10322248217597563849, 2603720130756381757, 11008950603887778358, 310856873143578820, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9955623072303337894, 14028382008395831053, 17555443170527522854, 523900000033069680, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12448424009103692961, 11947414388350725521, 7622772856415729982, 65176019549211652, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4058512771437134659, 16568352404795546638, 16082748340063280050, 462159895771280984, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16561774596053800572, 14414297372137724875, 12670494281094732737, 464121105118414444, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15349261759679829658, 14941738735552258553, 9275045736345939426, 28693524991607620, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17852230034098182645, 14355289414443486043, 367075719686197950, 311668193580309583, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13058187993137386173, 5056192100872525146, 8575359975265526018, 161707841161341711, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16109859484534382417, 3911016352856416230, 12156178682505377668, 114408700675740248, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14391799364387013377, 6397415938996643709, 15822880028486592478, 142134480498915355, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17896847805093980389, 14709682788110185926, 13792964223573451205, 357143517834634939, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9186289104367306905, 17371411915467340044, 12749176259341625326, 213185605116874207, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8041596648537002306, 17689130692324659624, 8894853932027528319, 239228585975963812, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12820179162992000481, 12062494974170708727, 7131205658440283807, 572551880356760492, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16813297895732348639, 12887147512287260069, 11433753175400347412, 281484096638073688, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18437299620515822751, 8279349169408991726, 4840238974358962780, 331547024411665978, }, }, }, .y = .{ .fe = .{ .limbs = .{ 535452016012642359, 15987295809449633048, 14594038677944222184, 38686509670720580, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10400472064756933500, 691824391024966168, 582991234413051985, 499374174307001842, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3214101675932254428, 11212800701979611056, 12740015340285180828, 84225247214660426, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17636946168820419227, 16494412483753172709, 14850539248777814640, 284543202082711458, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12221259682156683251, 18198622885790044981, 1838626496418888371, 518425307232708390, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16539407682741087544, 15775836030218729271, 17083081409299080336, 215532252712901270, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3386026371946407723, 16103858373169379210, 7567935241720264253, 278464894649632562, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9155324594709292315, 6395060803422329026, 6100367147183249657, 253619021086009257, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10535132696728506157, 2702583007776750755, 15332972873314629846, 373905537670595524, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7004264179400611959, 11619051352479725172, 2524691527324322987, 297795900153520851, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2055110466058414532, 2362889879380568753, 5768806478398224368, 156183632330058328, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 5595084946171378307, 4173609074525204326, 5068435517511237006, 284429284313171201, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2830448858540849054, 9309374891512572612, 14562573433828663029, 482983443491674883, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16427275824388593536, 12928655580940900644, 13590124917215693469, 445128891727874856, }, }, }, .y = .{ .fe = .{ .limbs = .{ 544053979479015321, 53101184160398705, 10782967325921873488, 80185302986119794, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 2238515610254432963, 16739951160545853158, 12899127005022235116, 565000233765475754, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7379244967497858722, 2412709966698251680, 2586570065439487385, 575955511870651470, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11737011731342647921, 3140042683940674525, 18384157165498206069, 373418901080402303, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10214688331686343897, 10990521015677056952, 4603776599722857245, 532675171259064287, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16250544094693523003, 12809028699708399043, 4558590090700503672, 62411715222673565, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5517704015566578251, 1223226560191985581, 10003537197890500888, 285952579827213925, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14140406581780320423, 14547110061750898612, 1338426671872833206, 321701104433084979, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8567695978295159011, 10673783184682488943, 16833687712797285122, 518957907553444726, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11738818994112213822, 7482043154120374088, 412765162397971752, 561204900146389559, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2752807110402055265, 3704782759558645148, 2757232505665655405, 564382658622506664, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10378985575713051002, 10561529542323393156, 5032848802306564995, 232496740034183155, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15731351362111584708, 1454866856163934026, 3055210758460144590, 342982361567833612, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11213879811639071043, 5035780765659392661, 16479932683040722908, 118142170585727492, }, }, }, .y = .{ .fe = .{ .limbs = .{ 18334262345224520292, 12716471189087453246, 12881628021255410386, 483704936068783615, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17293721666271332067, 7587175278647029040, 14483011113884117756, 540165583266750860, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7927907764594134355, 11273815643614334301, 9360867795141492654, 510184310420957206, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10641866985761655145, 12293552661847462729, 3175744936059412125, 397679083606635256, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14348383227874225009, 1598151160167265105, 4671101103980733322, 158532755892682146, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14118903182191052648, 698544334000708965, 12311702198802079357, 17695414050832231, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3811623782123607444, 8930798556998222922, 4733961234003485204, 178120220827674597, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16699777270408595566, 3364667916373714494, 1811990211219498758, 52815702466460599, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2654786000272920890, 18109904725937137453, 14487344101630543274, 102692475946357995, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15415085803115572098, 2766850601065928800, 6148819602543512167, 67405550348413892, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1886097090431661783, 6345826096330714901, 7635346947322175946, 23781457131834471, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15010744627078959299, 6958038085931568530, 11064996004135161211, 490234243901829395, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4544651838755578194, 15072263674365419732, 17709504872812890129, 244375020092919911, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13328187545939501246, 12748132301011691768, 18365888731359713833, 303179930157738537, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17473361359894333937, 18417332136202133437, 16747996058184049267, 229747444742280126, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14738585775480717395, 10816191175338419522, 13081424825019016133, 218698166251618372, }, }, }, .y = .{ .fe = .{ .limbs = .{ 16962441250766213110, 14697047872982753924, 3302638598349769791, 330186710856156899, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 814619082844308353, 10160861292661440470, 3786535366304155364, 464567783930329611, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1635913908673389844, 4943522600713389453, 8900655012801070824, 391515532899251213, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 9477610335334769300, 1312971793569468504, 3605372515991415712, 127988409405668602, }, }, }, .y = .{ .fe = .{ .limbs = .{ 15245094982419405855, 16278487774745672375, 13452314021549889546, 502832121595381821, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8818421487432520060, 361271722107556840, 2983854872535698481, 551358400495884569, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13644074906165400667, 17138675496985166301, 12341429169523868571, 364367239489502519, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15197522759698695901, 2336375784161052814, 2463904031972219787, 313463932363007472, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1966121274651576858, 7741415033617889052, 1622741858752309531, 530659602909903907, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11053959937585926491, 17770926358225405742, 7479160423705264633, 404842092599013270, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12563085897260307975, 6058273057892065251, 11889981975003353024, 83195398001688811, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10900848478340193637, 830722860985107251, 9182432329937578648, 276890183879525692, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17489199376977222947, 2291549134060579689, 10173284267130749217, 179728261227797590, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13329192065512066221, 7723834314161080691, 7969996112683804692, 471454020548470024, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10640520040619954928, 9790837825815935609, 18298488866836746285, 373777289034583989, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1972815996428239605, 15790695197949677736, 11966190616281522549, 205480662977746413, }, }, }, .y = .{ .fe = .{ .limbs = .{ 10914216074029976670, 10268957089124202954, 15172256727559088672, 139412515952646124, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13454376011737206491, 5064566368613728776, 11832604952308335355, 139873594266530443, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17147812321939107233, 6319868525512174977, 2759762309828948572, 145660839555701779, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13000080645585133337, 9541286594793063870, 9449699044042301704, 549681461776504141, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8597416247852816744, 18371129239015595313, 2159482658725339963, 412701800672881751, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10489378027153615072, 69292430450207972, 18015434062942614650, 200447278139506985, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5765786942842087822, 12017435311142179917, 1384764810107317994, 447044166075567510, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 15450335754366174545, 15828637278204507088, 11070547364744837603, 19242423372801070, }, }, }, .y = .{ .fe = .{ .limbs = .{ 17168549325991183173, 8255546675340056711, 8361358523274868100, 336058816922200926, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12247097571993293024, 9943017326733904321, 8672032470351984543, 345960355047784219, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11361267399121319522, 5749950087200260276, 103894843890538442, 307961561419094173, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7629936019519124265, 4619973658705919422, 8587516426151084713, 216896723701039524, }, }, }, .y = .{ .fe = .{ .limbs = .{ 7887756041964331902, 18359112858934762996, 6615974538008427563, 389735774022199394, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3272414982536269862, 1574264469491542342, 16480134157482269745, 485263443019556796, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2291362366667606640, 7655023906228354738, 4893771067430999506, 68583435043890342, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7091134114958095952, 8641253707668174298, 8132597455979939273, 329333577321739246, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11095766071089727193, 16871764254641945857, 7405720161091649529, 539840722972881109, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 8584309101344385048, 16408092362616494763, 5197905725202317400, 50319322418249216, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4024909368244809736, 1693447234417628007, 9452749411481539959, 130192845415052905, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 3086314602541433454, 2392599643933782985, 6021799368299313905, 507712877632812174, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8813852213211790893, 2186615512791797468, 3528161878511175671, 61209330650074986, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 1639358554960631740, 10194285330472023620, 826763558032956071, 457560146889809197, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6125398114541705785, 7871439687091130398, 12845573432215598943, 359157689894991838, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14789530082931895160, 2827135772793024692, 7226308389509576598, 446799049072267701, }, }, }, .y = .{ .fe = .{ .limbs = .{ 14307792495800016623, 5003954322580072425, 287964429828501886, 182849110899357910, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 17727394896316137064, 5012868394231277094, 5328380972755152470, 151720447461405725, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5745704408208896256, 16536543253865212818, 13178227296131783303, 513552148692505230, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 12535126292784620290, 15449761602763135418, 15410673360911857152, 379703927919833497, }, }, }, .y = .{ .fe = .{ .limbs = .{ 5178801651495190065, 4315065419925020523, 12082233553484451017, 561694713630408843, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 7212548029705605292, 16969554260482740182, 5946908157127670814, 356553184462113447, }, }, }, .y = .{ .fe = .{ .limbs = .{ 11364574027013587675, 3164083755889347628, 407238236263446854, 45265090146730268, }, }, }, .infinity = false, }, }; pub const CURVE_CONSTS_P3: [15]AffinePoint = .{ .{ .x = .{ .fe = .{ .limbs = .{ 1145636535101238356, 10664803185694787051, 299781701614706065, 425493972656615276, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8187986478389849302, 4428713245976508844, 6033691581221864148, 345457391846365716, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14807655417810256081, 263464501051676032, 16241977131397442068, 452866674941489585, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9197973842096023338, 17580531949438829174, 6809894974694247587, 293328979442974782, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 13439676882460918674, 5474631779512118081, 6315119708992242340, 505973191052936193, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12171284446998082275, 10845464097478324537, 13158297055950616119, 391282402673382635, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6850712713867447272, 7951893333866029523, 12858461884921570835, 64421709466714210, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3251661854802183134, 16050197233468026580, 16923030445524869826, 252830043392634833, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16379007224910497852, 2665326632692125321, 7532354609298733974, 314960176288741620, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9267589567689898015, 14990651870468887653, 8052102760056601696, 517219027484158075, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6023201272200092866, 16009182788934079051, 17448043034741196995, 498807766334700922, }, }, }, .y = .{ .fe = .{ .limbs = .{ 1758638701270774278, 16026754444684556229, 5466827901019907874, 454140695926075570, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 6877053431871769932, 11024060766975624269, 15311618249752295579, 548243873079642150, }, }, }, .y = .{ .fe = .{ .limbs = .{ 4920180316151553042, 2177351210638010638, 16343882837533282781, 280805501848641475, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 18186352353606695923, 4132509120571385051, 6326854277291134925, 129596621152995520, }, }, }, .y = .{ .fe = .{ .limbs = .{ 3844428830551561895, 11807944473604199932, 1546122216302533604, 566909196302369191, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 10148249458970282650, 7392659404631872269, 9759764444142623947, 326025630337245552, }, }, }, .y = .{ .fe = .{ .limbs = .{ 13735365474946416195, 18367227446542783855, 5227858094742815408, 239056039278781382, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11089849058141487548, 7350448409955704483, 10450025450045932310, 401640599521668471, }, }, }, .y = .{ .fe = .{ .limbs = .{ 2831579575042320187, 2560022868958493881, 6322979822222200515, 279988202990344759, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11008622789114420148, 11758073652558676227, 3008341285907336806, 382865487952099866, }, }, }, .y = .{ .fe = .{ .limbs = .{ 8747240399593070444, 11328999080080036592, 2295626978093021891, 458034822066084613, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 4967556667503679719, 3395405092036421092, 2225865490770469547, 536162948997388487, }, }, }, .y = .{ .fe = .{ .limbs = .{ 68857247440009336, 14285355709627174310, 16438818017529017902, 350656928564634281, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 16411882153701270287, 3633095812298464969, 13114520944851473622, 190471035982669529, }, }, }, .y = .{ .fe = .{ .limbs = .{ 9217769605438560895, 15961315065771321173, 11030254221618720518, 520507472344175674, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 11475331534030911675, 3124065595198259863, 2708790722269589721, 31125297967563749, }, }, }, .y = .{ .fe = .{ .limbs = .{ 6208626431960528169, 11519033879672300283, 14604016228441028552, 38637104234292515, }, }, }, .infinity = false, }, .{ .x = .{ .fe = .{ .limbs = .{ 14232503138734639567, 4094760952218555445, 9827625571275805004, 150262419811769509, }, }, }, .y = .{ .fe = .{ .limbs = .{ 12644979670524768470, 11925693850524930194, 10449795063715396588, 494216056688380304, }, }, }, .infinity = false, }, };
0
repos/starknet-zig/src/crypto
repos/starknet-zig/src/crypto/poseidon/constants.zig
/// based on https://github.com/starkware-industries/poseidon/blob/5403dff9ff4eadb07deb5c0a43e88bedb011deb8/poseidon3.txt /// /// /// This file is autogenerated by poseidon_consts_gen.zig /// /// const Felt252 = @import("../../math/fields/starknet.zig").Felt252; pub const POSEIDON_COMPRESSED_ROUND_CONSTS: [107]Felt252 = .{ .{ .fe = .{ .limbs = .{ 9243643933561577962, 18087611126302680282, 7098098609281275249, 289757450055368158, }, }, }, .{ .fe = .{ .limbs = .{ 7853535095351734343, 10850711010770646915, 12570458558381957509, 325478872510666341, }, }, }, .{ .fe = .{ .limbs = .{ 14487852855283887204, 5186719240138179095, 8414109922749085282, 400708606768273790, }, }, }, .{ .fe = .{ .limbs = .{ 3280395077118373336, 17795901222489795490, 2641423859640672268, 77297546474262716, }, }, }, .{ .fe = .{ .limbs = .{ 8106789448329946608, 5622576456418619364, 917099606739132255, 531983052745549445, }, }, }, .{ .fe = .{ .limbs = .{ 595196979161159364, 13104152156623721627, 11543764507410437138, 296030771607252997, }, }, }, .{ .fe = .{ .limbs = .{ 7816701695378368721, 3357934764826603292, 15403608342128707689, 450788015873872442, }, }, }, .{ .fe = .{ .limbs = .{ 636799349004279181, 6138586124645004146, 9427309254075631876, 241320328808721095, }, }, }, .{ .fe = .{ .limbs = .{ 17291774529514094747, 5039440405858006990, 9298428421172181112, 506951390701988816, }, }, }, .{ .fe = .{ .limbs = .{ 11806696651894481589, 1092083221520939347, 14414850501582138681, 221101813663738384, }, }, }, .{ .fe = .{ .limbs = .{ 13829429898061010046, 2611422711440939737, 15408727842397286736, 507284792967663799, }, }, }, .{ .fe = .{ .limbs = .{ 13083162048600272883, 8232965923506882345, 10342036084285918913, 4246917344608281, }, }, }, .{ .fe = .{ .limbs = .{ 14120941658239655251, 2642188447246846335, 6420128711794491484, 387738584202674747, }, }, }, .{ .fe = .{ .limbs = .{ 4557515129132896247, 12925333772434149495, 8021291067466006291, 359812401200365725, }, }, }, .{ .fe = .{ .limbs = .{ 1890170602709420465, 10101417316275735447, 14228475625622468342, 213055788422889429, }, }, }, .{ .fe = .{ .limbs = .{ 17718807227125703766, 3165015027285286767, 17001522267729424593, 193938768174500364, }, }, }, .{ .fe = .{ .limbs = .{ 11967566541251349, 8042878571206807946, 12035959970295095627, 392852226019534694, }, }, }, .{ .fe = .{ .limbs = .{ 14702858513363496537, 1891459712461864795, 11108523323717023107, 156261542945214132, }, }, }, .{ .fe = .{ .limbs = .{ 1945929902309569324, 12703913861703223537, 18026399617460967320, 552659386849285670, }, }, }, .{ .fe = .{ .limbs = .{ 15676691957102339301, 7305794071419508305, 15605369973884503830, 279124040567655554, }, }, }, .{ .fe = .{ .limbs = .{ 6878414542634060631, 6806916028752188971, 6743346892345011852, 209421398668690776, }, }, }, .{ .fe = .{ .limbs = .{ 14451878242532315248, 280667558436689575, 7481193996043836595, 102898977772584225, }, }, }, .{ .fe = .{ .limbs = .{ 10099174071678455934, 10050300413654558496, 15460796480957384300, 326260635675691414, }, }, }, .{ .fe = .{ .limbs = .{ 12189485177509053284, 18189503908521730582, 2742965211333049654, 246759231813836949, }, }, }, .{ .fe = .{ .limbs = .{ 17131884891365868725, 4126475231607707865, 4142744258917121527, 517354668301661021, }, }, }, .{ .fe = .{ .limbs = .{ 9321360184240157338, 8642907823639066926, 4815888288973513717, 387266619660887473, }, }, }, .{ .fe = .{ .limbs = .{ 9877712865958333042, 172887203519774060, 14912001171503456000, 379922462175671594, }, }, }, .{ .fe = .{ .limbs = .{ 5253862319821606646, 3112421893979476452, 12476994431456066104, 503867426189678810, }, }, }, .{ .fe = .{ .limbs = .{ 6459833828500045091, 8544893956421165385, 4198699220078046017, 361247795501724706, }, }, }, .{ .fe = .{ .limbs = .{ 15367072576308287971, 11136955306523718350, 1150777808545574589, 569094971639990703, }, }, }, .{ .fe = .{ .limbs = .{ 938972551523044539, 14766818754575560648, 14214531273441880096, 519370339044767210, }, }, }, .{ .fe = .{ .limbs = .{ 8541051058482254568, 15415072429245325504, 14957220415534017748, 76536527755312734, }, }, }, .{ .fe = .{ .limbs = .{ 2465712523883598144, 6511341599113654315, 6309081263114838229, 393450888402641516, }, }, }, .{ .fe = .{ .limbs = .{ 940821186092154852, 8192839842351846874, 5396406749139750234, 288112524550260818, }, }, }, .{ .fe = .{ .limbs = .{ 18013945796863515455, 14414340112335121757, 8020715533944075007, 378547930620493071, }, }, }, .{ .fe = .{ .limbs = .{ 10882040312752948163, 13534318422278561025, 16239338703176780807, 315921785019971079, }, }, }, .{ .fe = .{ .limbs = .{ 11804152077864610443, 10711845104699761001, 2579945555704418307, 407428959149964045, }, }, }, .{ .fe = .{ .limbs = .{ 3599124979175311464, 12397382694363857548, 2441162789755772647, 519829512759629210, }, }, }, .{ .fe = .{ .limbs = .{ 1122008851702936351, 2255313605192201584, 9526529507379911735, 297026039684882166, }, }, }, .{ .fe = .{ .limbs = .{ 1993625032903604531, 596810388162793045, 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298970159691700591, 12014891315505021636, 5642896886612387367, 320523276021081874, }, }, }, .{ .fe = .{ .limbs = .{ 2161827243834369197, 6529000939326479156, 3360240309062894342, 423278556197684001, }, }, }, .{ .fe = .{ .limbs = .{ 17922407737483631270, 10846304006776507478, 4814020835957029095, 558105788237772190, }, }, }, .{ .fe = .{ .limbs = .{ 14309821559636775821, 5191281667707819629, 7991629750293746597, 55044774064780458, }, }, }, .{ .fe = .{ .limbs = .{ 4475858853850722769, 4126326734531744171, 14548036495158561611, 569399000276545969, }, }, }, .{ .fe = .{ .limbs = .{ 17137171742635080032, 13734979251366108230, 733658667004231380, 393850665517739074, }, }, }, .{ .fe = .{ .limbs = .{ 18207273213375707676, 9125832381882861274, 13182372482997690796, 374441752858986998, }, }, }, .{ .fe = .{ .limbs = .{ 11725146126629035967, 2224508228469132237, 1606247714594998930, 162358740541808928, }, }, }, }; pub const POSEIDON_FULL_ROUNDS: usize = 8; pub const POSEIDON_PARTIAL_ROUNDS: usize = 83;
0
repos/starknet-zig/src/crypto
repos/starknet-zig/src/crypto/poseidon/config.json
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0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/curve/errors.zig
pub const EcPointError = error{ SqrtNotExist, PointNotOnCurve, };
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/curve/curve_params.zig
// code ported from starknet-curve: // https://github.com/xJonathanLEI/starknet-rs/blob/0857bd6cd3bd34cbb06708f0a185757044171d8d/starknet-curve/src/curve_params.rs const Felt252 = @import("../fields/starknet.zig").Felt252; const bigInt = @import("../fields/biginteger.zig").bigInt; const AffinePoint = @import("./short_weierstrass/affine.zig").AffinePoint; /// Represents the order of the subgroup generated by the base point on the STARK-friendly elliptic curve. /// /// The EC_ORDER constant defines the order of the subgroup generated by the base point on the elliptic curve used in the STARK scheme. /// It is a crucial parameter in cryptographic operations, including ECDSA, as it determines the size of the cryptographic group. /// The EC_ORDER is a large prime number, ensuring the security of the elliptic curve cryptographic scheme. /// /// # Description /// /// The EC_ORDER constant is represented as a field element (Felt252) initialized from a hexadecimal integer value. /// It defines the order of the subgroup generated by the base point, ensuring that the discrete logarithm problem is hard to solve. /// /// # Value /// /// The value of EC_ORDER is derived from the hexadecimal integer: /// 0x800000000000010ffffffffffffffffb781126dcae7b2321e66a241adc64d2f /// /// # Remarks /// /// - The EC_ORDER ensures the security of the STARK-friendly elliptic curve by defining the size of the subgroup. /// - It is essential for cryptographic operations, including key generation and signature generation. pub const EC_ORDER = Felt252.fromInt( u256, 0x800000000000010ffffffffffffffffb781126dcae7b2321e66a241adc64d2f, ); /// Represents the coefficient 𝛼 in the equation of the STARK-friendly elliptic curve. /// /// The ALPHA constant defines the coefficient 𝛼 in the equation of the STARK-friendly elliptic curve. /// It is a crucial parameter in defining the elliptic curve equation, which ensures cryptographic security and efficiency. /// The value of ALPHA is typically chosen to meet specific security requirements and compatibility with cryptographic protocols. /// /// # Description /// /// The ALPHA constant is represented as a field element (Felt252) initialized to the value one. /// It serves as the coefficient 𝛼 in the elliptic curve equation: 𝑦^2 ≡ 𝑥^3 + 𝛼⋅𝑥 + 𝛽 (mod 𝑝). /// /// # Value /// /// The value of ALPHA is one, representing the identity element in field arithmetic operations. /// /// # Remarks /// /// - ALPHA is a fundamental parameter in defining the equation of the STARK-friendly elliptic curve. /// - It is typically chosen to ensure the security and efficiency of cryptographic operations. pub const ALPHA = Felt252.one(); /// Represents the coefficient 𝛽 in the equation of the STARK-friendly elliptic curve. /// /// The BETA constant defines the coefficient 𝛽 in the equation of the STARK-friendly elliptic curve. /// It is a crucial parameter in defining the elliptic curve equation, contributing to the curve's shape and cryptographic properties. /// The value of BETA is typically chosen to meet specific security requirements and compatibility with cryptographic protocols. /// /// # Description /// /// The BETA constant is represented as a field element (Felt252) initialized from a hexadecimal integer value. /// It serves as the coefficient 𝛽 in the elliptic curve equation: 𝑦^2 ≡ 𝑥^3 + 𝛼⋅𝑥 + 𝛽 (mod 𝑝). /// /// # Value /// /// The value of BETA is derived from the hexadecimal integer: /// 0x6f21413efbe40de150e596d72f7a8c5609ad26c15c915c1f4cdfcb99cee9e89 /// /// # Remarks /// /// - BETA is a fundamental parameter in defining the equation of the STARK-friendly elliptic curve. /// - It contributes to the curve's shape and ensures cryptographic security. pub const BETA = Felt252.fromInt( u256, 0x6f21413efbe40de150e596d72f7a8c5609ad26c15c915c1f4cdfcb99cee9e89, ); /// Represents the base point of the elliptic curve, which generates a subgroup of large prime order `n`. /// /// The generator point `G` is a fundamental point on the elliptic curve used in various cryptographic operations, including ECDSA. /// It generates a subgroup of large prime order `n`, forming the basis for key generation and cryptographic operations. /// /// # Description /// /// The generator point `G` is defined by its x and y coordinates on the elliptic curve. /// These coordinates are provided as field elements (Felt252) representing the x and y components of the point. /// Additionally, the `infinity` flag indicates whether the point is at infinity or not. /// /// # Parameters /// /// * `x` - The x-coordinate of the generator point. /// * `y` - The y-coordinate of the generator point. /// * `infinity` - A boolean flag indicating whether the generator point is at infinity. pub const GENERATOR: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca, ), .y = Felt252.fromInt( u256, 0x5668060aa49730b7be4801df46ec62de53ecd11abe43a32873000c36e8dc1f, ), .infinity = false, }; /// The shift point 𝑃0 was added for technical reasons to make sure the point at infinity on the elliptic curve does not appear during the computation. pub const SHIFT_POINT: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804, ), .y = Felt252.fromInt( u256, 0x3ca0cfe4b3bc6ddf346d49d06ea0ed34e621062c0e056c1d0405d266e10268a, ), .infinity = false, }; /// Constant representing the Pedersen hash point P0. /// P0 is derived from the decimal digits of π and is used in the Pedersen hash function. pub const PEDERSEN_P0: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x234287dcbaffe7f969c748655fca9e58fa8120b6d56eb0c1080d17957ebe47b, ), .y = Felt252.fromInt( u256, 0x3b056f100f96fb21e889527d41f4e39940135dd7a6c94cc6ed0268ee89e5615, ), .infinity = false, }; /// Constant representing the Pedersen hash point P1. /// P1 is derived from the decimal digits of π and is used in the Pedersen hash function. pub const PEDERSEN_P1: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x4fa56f376c83db33f9dab2656558f3399099ec1de5e3018b7a6932dba8aa378, ), .y = Felt252.fromInt( u256, 0x3fa0984c931c9e38113e0c0e47e4401562761f92a7a23b45168f4e80ff5b54d, ), .infinity = false, }; /// Constant representing the Pedersen hash point P2. /// P2 is derived from the decimal digits of π and is used in the Pedersen hash function. pub const PEDERSEN_P2: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x4ba4cc166be8dec764910f75b45f74b40c690c74709e90f3aa372f0bd2d6997, ), .y = Felt252.fromInt( u256, 0x40301cf5c1751f4b971e46c4ede85fcac5c59a5ce5ae7c48151f27b24b219c, ), .infinity = false, }; /// Constant representing the Pedersen hash point P3. /// P3 is derived from the decimal digits of π and is used in the Pedersen hash function. pub const PEDERSEN_P3: AffinePoint = .{ .x = Felt252.fromInt( u256, 0x54302dcb0e6cc1c6e44cca8f61a63bb2ca65048d53fb325d36ff12c49a58202, ), .y = Felt252.fromInt( u256, 0x1b77b3e37d13504b348046268d8ae25ce98ad783c25561a879dcc77e99c2426, ), .infinity = false, };
0
repos/starknet-zig/src/math/curve
repos/starknet-zig/src/math/curve/short_weierstrass/projective.zig
// code ported from starknet-curve: // https://github.com/xJonathanLEI/starknet-rs/blob/0857bd6cd3bd34cbb06708f0a185757044171d8d/starknet-curve/src/ec_point.rs const std = @import("std"); const Felt252 = @import("../../fields/starknet.zig").Felt252; const CurveParams = @import("../curve_params.zig"); const EcPointError = @import("../errors.zig").EcPointError; const AffinePoint = @import("./affine.zig").AffinePoint; const TEST_ITERATIONS = @import("../../../main.zig").TEST_ITERATIONS; const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; /// Represents a point in standard projective coordinates over a given field. /// /// Standard projective points extend the concept of affine points by introducing an additional coordinate /// (z-coordinate) to accommodate "points at infinity". /// /// In standard projective coordinates, a point on the elliptic curve is represented as (X, Y, Z), where Z ≠ 0. /// /// The actual point is (X/Z, Y/Z). /// /// This structure encapsulates the x, y, and z coordinates of a point in projective space. pub const ProjectivePoint = struct { const Self = @This(); /// The x-coordinate of the projective point. x: Felt252 = Felt252.zero(), /// The y-coordinate of the projective point. y: Felt252 = Felt252.one(), /// The z-coordinate of the projective point. z: Felt252 = Felt252.zero(), /// Initializes a new projective point with the given coordinates without performing curve validation. /// /// This function creates a new projective point with the specified x, y, and z coordinates without /// performing any validation checks. It is the responsibility of the caller to ensure that the provided /// coordinates represent a valid point on the elliptic curve. /// /// # Arguments /// /// * `x` - The x-coordinate of the projective point. /// * `y` - The y-coordinate of the projective point. /// * `z` - The z-coordinate of the projective point. /// /// # Returns /// /// A new projective point initialized with the provided coordinates. /// /// # Example /// /// ```zig /// const point = ProjectivePoint.initUnchecked(x_value, y_value, z_value); /// ``` /// /// This creates a new projective point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and the z-coordinate `z_value` without performing any validation checks. /// pub fn initUnchecked(x: Felt252, y: Felt252, z: Felt252) Self { return .{ .x = x, .y = y, .z = z }; } /// Initializes a new projective point with the given coordinates after performing curve validation. /// /// This function creates a new projective point with the specified x, y, and z coordinates and /// performs validation to ensure that the resulting point lies on the elliptic curve defined by /// the curve parameters. If the provided coordinates do not correspond to a point on the curve, /// it returns an error indicating that the point is not on the curve. /// /// # Arguments /// /// * `x` - The x-coordinate of the projective point. /// * `y` - The y-coordinate of the projective point. /// * `z` - The z-coordinate of the projective point. /// /// # Returns /// /// If the provided coordinates result in a point on the elliptic curve, it returns the newly /// initialized projective point. Otherwise, it returns an error indicating that the point is not /// on the curve. /// /// # Errors /// /// Returns an error of type `EcPointError` if the provided coordinates do not correspond to /// a point on the elliptic curve. /// /// # Example /// /// ```zig /// const point = try ProjectivePoint.init(x_value, y_value, z_value); /// ``` /// /// This creates a new projective point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and the z-coordinate `z_value`. If the resulting point is not on the curve, it returns an error. /// pub fn init(x: Felt252, y: Felt252, z: Felt252) !Self { const p: Self = .{ .x = x, .y = y, .z = z }; if (!AffinePoint.fromProjectivePoint(&p).isOnCurve()) return EcPointError.PointNotOnCurve; return p; } /// Constructs a projective point from an affine point. /// /// This function converts an affine point to a projective point, setting its coordinates /// accordingly and preserving the infinity flag. /// /// # Arguments /// /// * `p` - A pointer to the affine point. /// /// # Returns /// /// A projective point constructed from the given affine point. pub fn fromAffinePoint(p: *const AffinePoint) Self { return if (p.isIdentity()) .{} else .{ .x = p.x, .y = p.y, .z = Felt252.one() }; } /// Returns the identity element of the projective space. /// /// This function returns the identity element of the projective space, which is the zero point /// represented as the point at infinity. The identity element serves as the neutral element /// in projective space arithmetic. /// /// # Returns /// /// The identity element of the projective space, represented as the point at infinity. pub inline fn identity() Self { return .{}; } /// Checks if this projective point is equal to another projective point. /// /// This function checks whether this projective point is equal to the provided projective point. /// Two projective points are considered equal if their corresponding affine representations /// are equal. If either point is the point at infinity, they are considered equal if and only if /// both are points at infinity. /// /// # Arguments /// /// * `rhs` - The other projective point to compare against. /// /// # Returns /// /// `true` if this projective point is equal to the provided projective point, otherwise `false`. /// /// # Example /// /// ```zig /// const point1 = ProjectivePoint.initUnchecked(x1, y1, z1); /// const point2 = ProjectivePoint.initUnchecked(x2, y2, z2); /// const result = point1.eql(point2); /// ``` /// /// This example checks if `point1` is equal to `point2` and stores the result in the `result` variable. /// pub fn eql(self: Self, rhs: Self) bool { // Check if either point is the point at infinity. if (self.isIdentity()) return rhs.isIdentity(); if (rhs.isIdentity()) return false; // Check if the x-coordinates, y-coordinates are equal. return self.x.mul(&rhs.z).eql(rhs.x.mul(&self.z)) and self.y.mul(&rhs.z).eql(rhs.y.mul(&self.z)); } /// Checks if this projective point lies on the elliptic curve. /// /// This function determines whether the given projective point lies on the elliptic curve defined /// by the curve parameters. If the point is at infinity, it is considered to be on the curve. /// /// # Returns /// /// `true` if the projective point lies on the elliptic curve, otherwise `false`. pub fn isOnCurve(self: *const Self) bool { // Check if the point is at infinity. if (self.isIdentity()) return true; // Convert the projective point to an affine point and check if it lies on the curve. return AffinePoint.fromProjectivePoint(self).isOnCurve(); } /// Checks if the projective point is the identity element. /// /// This function returns true if the provided projective point is the identity element of the /// projective space, which is represented as the point at infinity. Otherwise, it returns false. /// /// # Returns /// /// `true` if the projective point is the identity element (point at infinity), otherwise `false`. /// pub inline fn isIdentity(self: *const Self) bool { return self.z.isZero(); } /// Doubles the projective point. /// /// This function returns a new projective point that represents the result of /// doubling the given projective point, effectively performing point doubling /// in elliptic curve arithmetic. /// /// # Returns /// /// The resulting projective point after the doubling operation. /// /// # Remarks /// /// This function does not modify the original projective point, but instead /// returns a new point representing the result of the doubling operation. /// pub fn double(self: Self) Self { var a = self; a.doubleAssign(); return a; } /// Doubles the projective point in place. /// /// This function doubles the given projective point in place, effectively performing /// point doubling in elliptic curve arithmetic. /// /// # Remarks /// /// The point doubling operation doubles the given point in projective coordinates /// and stores the result back in the original point. /// /// # Errors /// /// Returns without performing any operation if the projective point is the identity element /// (point at infinity). /// pub fn doubleAssign(self: *Self) void { // If the point is the point at infinity, no operation is needed. if (self.isIdentity()) return; // Calculate t = 3*x^2 + a*z^2 with a = 1 (from stark curve). const t = Felt252.three().mul(&self.x.square()).add(&self.z.mul(&self.z)); // Calculate u = 2*y*z. const u = self.y.double().mul(&self.z); // Calculate v = 2*u*x*y. const v = u.double().mul(&self.x).mul(&self.y); // Calculate w = t^2 - 2*v. const w = t.mul(&t).sub(&v.double()); // Calculate uy = u*y. const uy = u.mul(&self.y); // Update the projective point with the new coordinates after doubling. self.* = .{ .x = u.mul(&w), .y = t.mul(&v.sub(&w)).sub(&uy.square().double()), .z = u.square().mul(&u), }; } /// Multiplies the projective point by a scalar represented as a bit slice in big-endian format. /// /// This function performs scalar multiplication of the projective point by a scalar represented /// as a bit slice in big-endian format. The scalar multiplication is computed using the double-and-add /// algorithm, where each bit of the scalar is processed sequentially, doubling the projective point /// at each step and conditionally adding the original point if the corresponding bit is set. /// /// # Arguments /// /// * `bits` - A bit slice representing the scalar value in big-endian format. /// /// # Returns /// /// The resulting projective point after scalar multiplication. /// /// # Remarks /// /// This function does not modify the original projective point, but instead returns a new point /// representing the result of the scalar multiplication operation. pub fn mulByBitsBe(self: *const Self, bits: [@bitSizeOf(u256)]bool) Self { // Initialize the product as the identity element. var product = ProjectivePoint.identity(); // Find the index of the first set bit in the scalar. const first_one = std.mem.indexOfScalar(bool, &bits, true) orelse @bitSizeOf(u256); // Iterate over the scalar bits starting from the first set bit. for (bits[first_one..]) |bit| { // Double the projective point. product.doubleAssign(); // Conditionally add the original point if the corresponding bit is set. if (bit) product.addAssign(self); } // Return the resulting product after scalar multiplication. return product; } /// Multiplies the projective point by a scalar. /// /// This function multiplies the projective point by a scalar value represented as a Felt252. /// It internally converts the scalar into a bit slice in big-endian format and performs the scalar /// multiplication using the `mulByBitsBe` method. /// /// # Arguments /// /// * `rhs` - A pointer to the scalar value represented as a Felt252. /// /// # Returns /// /// The resulting projective point after scalar multiplication. pub fn mulByScalar(self: *const Self, rhs: *const Felt252) Self { return self.mulByBitsBe(rhs.toBitsBe()); } /// Adds another projective point to this point and returns the result. /// /// This function adds the coordinates of the provided projective point (`rhs`) to the coordinates /// of this projective point (`self`), without modifying the original point. It returns a new /// projective point representing the result of the addition operation. /// /// # Arguments /// /// * `rhs` - A pointer to the projective point to be added to this point. /// /// # Returns /// /// A new projective point representing the result of the addition operation. /// /// # Safety /// /// This function assumes that both `self` and `rhs` are valid projective points. Passing invalid /// points may result in undefined behavior. /// /// # Note /// /// The addition operation is performed according to the formulas derived for standard projective /// coordinates. For more information, see the source reference. pub fn add(self: Self, rhs: *const Self) Self { // Make a copy of the original point var a = self; // Perform point addition in place a.addAssign(rhs); // Return the resulting point return a; } /// Adds another affine point to this point in projective space. /// /// This function adds the coordinates of the provided affine point (`rhs`) to the coordinates /// of this projective point (`self`), without modifying the original point. It returns a new /// projective point representing the result of the addition operation. /// /// # Arguments /// /// * `rhs` - A pointer to the affine point to be added to this point. /// /// # Returns /// /// A new projective point representing the result of the addition operation. /// /// # Safety /// /// This function assumes that `self` is a valid projective point and `rhs` is a valid affine point. /// Passing invalid points may result in undefined behavior. /// /// # Note /// /// The addition operation is performed according to the formulas derived for standard projective /// coordinates. For more information, see the source reference. pub fn addAffine(self: Self, rhs: *const AffinePoint) Self { // Make a copy of the original point var a = self; // Perform point addition in place a.addAffineAssign(rhs); // Return the resulting point return a; } /// Returns the negation of this projective point. /// /// This function returns the negation of the current projective point, where the negation is /// defined as the point with the same x and z coordinates but the negated y coordinate. /// /// # Returns /// /// The negation of this projective point. pub fn neg(self: Self) Self { return if (self.isIdentity()) .{} else .{ .x = self.x, .y = self.y.neg(), .z = self.z }; } /// Subtracts another projective point from this point and returns the result. /// /// This function subtracts the coordinates of the provided projective point (`rhs`) from the /// coordinates of this projective point (`self`), without modifying the original point. It returns /// a new projective point representing the result of the subtraction operation. /// /// # Arguments /// /// * `rhs` - A pointer to the projective point to be subtracted from this point. /// /// # Returns /// /// A new projective point representing the result of the subtraction operation. /// /// # Safety /// /// This function assumes that both `self` and `rhs` are valid projective points. Passing invalid /// points may result in undefined behavior. pub fn sub(self: Self, rhs: *const Self) Self { // Make a copy of the original point var a = self; // Add the negation of the rhs point to this point a.addAssign(&rhs.neg()); // Return the resulting point return a; } /// Subtracts another affine point from this point in projective space. /// /// This function subtracts the coordinates of the provided affine point (`rhs`) from the coordinates /// of this projective point (`self`), updating the coordinates of `self` with the result. /// /// # Arguments /// /// * `rhs` - A pointer to the affine point to be subtracted from this point. /// /// # Safety /// /// This function assumes that `self` is a valid projective point and `rhs` is a valid affine point. /// Passing invalid points may result in undefined behavior. /// /// # Note /// /// The subtraction operation is performed according to the formulas derived for standard projective /// coordinates. For more information, see the source reference. pub fn subAffine(self: Self, rhs: *const AffinePoint) Self { // Make a copy of the original point var a = self; // Add the negation of the rhs point to this point a.addAffineAssign(&rhs.neg()); // Return the resulting point return a; } /// Adds another projective point to this point in projective space. /// /// This function adds the coordinates of the provided projective point (`rhs`) to the coordinates /// of this projective point (`self`), updating the coordinates of `self` with the result. /// /// # Arguments /// /// * `rhs` - A pointer to the projective point to be added to this point. /// /// # Safety /// /// This function assumes that both `self` and `rhs` are valid projective points. Passing invalid /// points may result in undefined behavior. /// /// # Note /// /// The addition operation is performed according to the formulas derived for standard projective /// coordinates. For more information, see the source reference. pub fn addAssign(self: *Self, rhs: *const Self) void { // If the point to be added is the identity point, no operation is needed. if (rhs.isIdentity()) return; // If this point is the identity point, update it to the provided point and return. if (self.isIdentity()) { self.* = rhs.*; return; } // x0 * z1 const u_0 = self.x.mul(&rhs.z); // x1 * z0 const u_1 = rhs.x.mul(&self.z); // slope = (y0 * z1 - y1 * z0) / (x0 * z1 - x1 * z0) // Null denominator the slope if (u_0.eql(u_1)) { if (self.y.mul(&rhs.z).eql(rhs.y.mul(&self.z))) { // Perform point doubling operation. self.doubleAssign(); } else { // Set this point to the identity (point at infinity). self.* = .{}; } return; } // y0 * z1 const t0 = self.y.mul(&rhs.z); // y1 * z0 const t1 = rhs.y.mul(&self.z); // t0 - t1 const t = t0.sub(&t1); // u0 - u1 const u = u_0.sub(&u_1); // u * u const u_2 = u.square(); // u * u * u const u_3 = u.mul(&u_2); // z0 * z1 const v = self.z.mul(&rhs.z); // t * t * v - u2 * (u0 + u1); const w = t.square().mul(&v).sub(&u_2.mul(&u_0.add(&u_1))); // Update the coordinates of this point with the result of the addition operation. self.* = .{ .x = u.mul(&w), .y = t.mul(&u_0.mul(&u_2).sub(&w)).sub(&t0.mul(&u_3)), .z = u_3.mul(&v), }; } /// Adds another affine point to this point in projective space. /// /// This function adds the coordinates of the provided affine point (`rhs`) to the coordinates /// of this projective point (`self`), updating the coordinates of `self` with the result. /// /// # Arguments /// /// * `rhs` - A pointer to the affine point to be added to this point. /// /// # Safety /// /// This function assumes that `self` is a valid projective point and `rhs` is a valid affine point. /// Passing invalid points may result in undefined behavior. /// /// # Note /// /// The addition operation is performed according to the formulas derived for standard projective /// coordinates. pub fn addAffineAssign(self: *Self, rhs: *const AffinePoint) void { // If rhs is the identity point, no operation is needed. if (rhs.isIdentity()) return; // If self is the identity point, update self to rhs and return. if (self.isIdentity()) { self.* = Self.fromAffinePoint(rhs); return; } const u_0 = self.x; const u_1 = rhs.x.mul(&self.z); const t0 = self.y; const t1 = rhs.y.mul(&self.z); if (u_0.eql(u_1)) { if (t0.eql(t1)) { // Point doubling operation self.doubleAssign(); } else { // Point at infinity self.* = Self.identity(); } return; } const t = t0.sub(&t1); const u = u_0.sub(&u_1); const u_2 = u.mul(&u); const v = self.z; const w = t.mul(&t).mul(&v).sub(&u_2.mul(&u_0.add(&u_1))); const u_3 = u.mul(&u_2); self.* = .{ .x = u.mul(&w), .y = t.mul(&u_0.mul(&u_2).sub(&w)).sub(&t0.mul(&u_3)), .z = u_3.mul(&v), }; } }; test "ProjectivePoint: initUnchecked should return a projective point (even if not valid)" { try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 10), .y = Felt252.fromInt(u256, 20), .z = Felt252.one(), }, ProjectivePoint.initUnchecked( Felt252.fromInt(u256, 10), Felt252.fromInt(u256, 20), Felt252.one(), ), ); try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, ProjectivePoint.initUnchecked( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), Felt252.one(), ), ); } test "ProjectivePoint: init should return a projective point and throw an error when not valid" { try expectError( EcPointError.PointNotOnCurve, ProjectivePoint.init( Felt252.fromInt(u256, 10), Felt252.fromInt(u256, 20), Felt252.one(), ), ); try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, try ProjectivePoint.init( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), Felt252.one(), ), ); } test "ProjectivePoint: fromAffinePoint should return a projective point based on an affine point" { try expectEqual( ProjectivePoint{}, ProjectivePoint.fromAffinePoint(&.{}), ); try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }), ); } test "ProjectivePoint: identity should return the point at infinity" { try expectEqual( ProjectivePoint{}, ProjectivePoint.identity(), ); } test "ProjectivePoint: addAssign of P + 0 should return P" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }; var p = ProjectivePoint.fromAffinePoint(&a); p.addAssign(&.{}); try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .z = Felt252.one(), }, p, ); } test "ProjectivePoint: addAssign of 0 + P should return P" { var p: ProjectivePoint = .{}; p.addAssign(&ProjectivePoint.fromAffinePoint( &.{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }, )); try expectEqual( ProjectivePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .z = Felt252.one(), }, p, ); } test "ProjectivePoint: addAssign P + (-P) should give 0" { var p = ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262).neg(), .infinity = false, })); try expectEqual(ProjectivePoint{}, p); } test "ProjectivePoint: addAssign P + P should give 2P" { var p = ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, })); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1007300233009797052089600572030536234678420387464749955693412487829103372971), .y = Felt252.fromInt(u256, 1628094014246951319213922206675864072767692386561452886899658728389307097247), .infinity = false, }, AffinePoint.fromProjectivePoint(&p), ); } test "ProjectivePoint: addAssign should give the proper point addition" { var p = ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePoint.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451), .y = Felt252.fromInt(u256, 78981980789517450823121602653688575320503877484645249556098070515590001476), .infinity = false, })); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1732660995762076585664239316986550513074833679175460014337184483203739567080), .y = Felt252.fromInt(u256, 2212051391075121985157657306991376790084194366385999148123095336409007912683), .infinity = false, }, AffinePoint.fromProjectivePoint(&p), ); } test "ProjectivePoint: isOnCurve should return true if the point is on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expect(ProjectivePoint.fromAffinePoint(&a).isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }; try expect(ProjectivePoint.fromAffinePoint(&b).isOnCurve()); } test "ProjectivePoint: isOnCurve should return false if the point is not on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 10), .y = Felt252.fromInt(u256, 100), .infinity = false, }; try expect(!ProjectivePoint.fromAffinePoint(&a).isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 5), .y = Felt252.fromInt(u256, 30), .infinity = false, }; try expect(!ProjectivePoint.fromAffinePoint(&b).isOnCurve()); } test "ProjectivePoint: fuzzing testing of arithmetic addition operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Generate another random affine point 'b'. var b = AffinePoint.rand(random); // Generate another random affine point 'c'. var c = AffinePoint.rand(random); // Convert affine points to projective points. var a_projective = ProjectivePoint.fromAffinePoint(&a); var b_projective = ProjectivePoint.fromAffinePoint(&b); var c_projective = ProjectivePoint.fromAffinePoint(&c); var zero: ProjectivePoint = .{}; // Associativity try expect( a_projective.add(&b_projective).add(&c_projective).eql( a_projective.add(&b_projective.add(&c_projective)), ), ); // Identify try expect(a_projective.eql(zero.add(&a_projective))); try expect(b_projective.eql(zero.add(&b_projective))); try expect(c_projective.eql(zero.add(&c_projective))); try expect(a_projective.eql(a_projective.add(&zero))); try expect(b_projective.eql(b_projective.add(&zero))); try expect(c_projective.eql(c_projective.add(&zero))); // Negation try expect(zero.eql(a_projective.neg().add(&a_projective))); try expect(zero.eql(b_projective.neg().add(&b_projective))); try expect(zero.eql(c_projective.neg().add(&c_projective))); try expect(zero.eql(zero.neg())); // Commutativity try expect(AffinePoint.fromProjectivePoint(&a_projective.add(&b_projective)).eql( AffinePoint.fromProjectivePoint(&b_projective.add(&a_projective)), )); // Associativity and commutativity simultaneously try expect(a_projective.add(&b_projective).add(&c_projective).eql( a_projective.add(&c_projective).add(&b_projective), )); try expect(a_projective.add(&c_projective).add(&b_projective).eql( b_projective.add(&c_projective).add(&a_projective), )); // Doubling try expect(a_projective.add(&a_projective).eql(a_projective.double())); try expect(b_projective.add(&b_projective).eql(b_projective.double())); try expect(c_projective.add(&c_projective).eql(c_projective.double())); try expect(zero.eql(zero.double())); try expect(zero.eql(zero.neg().double())); // Operation with an affine point try expect(a_projective.addAffine(&b).eql( a_projective.add(&b_projective), )); try expect(b_projective.addAffine(&c).eql( b_projective.add(&c_projective), )); try expect(a_projective.subAffine(&b).eql( a_projective.sub(&b_projective), )); try expect(b_projective.subAffine(&c).eql( b_projective.sub(&c_projective), )); try expect(zero.addAffine(&a).eql( a_projective, )); try expect(a_projective.addAffine(&b).addAffine(&c).eql( a_projective.add(&c_projective).add(&b_projective), )); try expect(a_projective.addAffine(&c).addAffine(&b).eql( b_projective.add(&c_projective).add(&a_projective), )); } } test "ProjectivePoint: fuzzing testing of arithmetic subtraction operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Generate another random affine point 'b'. var b = AffinePoint.rand(random); // Convert affine points to projective points. var a_projective = ProjectivePoint.fromAffinePoint(&a); var b_projective = ProjectivePoint.fromAffinePoint(&b); var zero: ProjectivePoint = .{}; // Anti-commutativity try expect(a_projective.sub(&b_projective).add( &b_projective.sub(&a_projective), ).isIdentity()); try expect(a_projective.subAffine(&b).add( &b_projective.subAffine(&a), ).isIdentity()); try expect(a_projective.subAffine(&b).addAffine( &try b.sub(&a), ).isIdentity()); // Identity try expect(zero.sub(&a_projective).eql(a_projective.neg())); try expect(zero.sub(&b_projective).eql(b_projective.neg())); try expect(a_projective.sub(&zero).eql(a_projective)); try expect(b_projective.sub(&zero).eql(b_projective)); } } test "ProjectivePoint: fuzzing testing of arithmetic multiplication operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Convert affine points to projective points. var a_projective = ProjectivePoint.fromAffinePoint(&a); var b = Felt252.rand(random); var c = Felt252.rand(random); var zero = Felt252.zero(); var one = Felt252.one(); // Identity try expect(a_projective.mulByBitsBe(zero.toBitsBe()).eql(.{})); try expect(a_projective.mulByBitsBe(one.toBitsBe()).eql(a_projective)); try expect(a_projective.mulByScalar(&zero).eql(.{})); try expect(a_projective.mulByScalar(&one).eql(a_projective)); // Commutativity try expect(a_projective.mulByScalar(&b).mulByScalar(&c).eql( a_projective.mulByScalar(&c).mulByScalar(&b), )); // Inverses try expect(a_projective.mulByScalar(&b.inverse().?.mul(&b)).eql( a_projective, )); } }
0
repos/starknet-zig/src/math/curve
repos/starknet-zig/src/math/curve/short_weierstrass/projective_jacobian.zig
const std = @import("std"); const Felt252 = @import("../../fields/starknet.zig").Felt252; const CurveParams = @import("../curve_params.zig"); const EcPointError = @import("../errors.zig").EcPointError; const AffinePoint = @import("./affine.zig").AffinePoint; const TEST_ITERATIONS = @import("../../../main.zig").TEST_ITERATIONS; const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; /// Represents a point in projective space using Jacobian coordinates. /// /// Jacobian coordinates optimize operations in elliptic curve cryptography. /// They add a z-coordinate for representing points in projective space. /// In Jacobian coordinates, a point is represented as (X, Y, Z), where Z ≠ 0. /// The actual point is (X/Z^2, Y/Z^3). /// /// This struct holds x, y, and z coordinates along with an infinity flag. pub const ProjectivePointJacobian = struct { const Self = @This(); /// The x-coordinate of the projective point. x: Felt252 = Felt252.zero(), /// The y-coordinate of the projective point. y: Felt252 = Felt252.one(), /// The z-coordinate of the projective point. z: Felt252 = Felt252.zero(), /// Initializes a new projective point with the given coordinates without performing curve validation. /// /// This function creates a new projective point with the specified x, y, and z coordinates without /// performing any validation checks. It is the responsibility of the caller to ensure that the provided /// coordinates represent a valid point on the elliptic curve. /// /// # Arguments /// /// * `x` - The x-coordinate of the projective point. /// * `y` - The y-coordinate of the projective point. /// * `z` - The z-coordinate of the projective point. /// /// # Returns /// /// A new projective point initialized with the provided coordinates. /// /// # Example /// /// ```zig /// const point = ProjectivePointJacobian.initUnchecked(x_value, y_value, z_value); /// ``` /// /// This creates a new projective point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and the z-coordinate `z_value` without performing any validation checks. pub fn initUnchecked(x: Felt252, y: Felt252, z: Felt252) Self { return .{ .x = x, .y = y, .z = z }; } /// Initializes a new projective point with the given coordinates after performing curve validation. /// /// This function creates a new projective point with the specified x, y, and z coordinates and /// performs validation to ensure that the resulting point lies on the elliptic curve defined by /// the curve parameters. If the provided coordinates do not correspond to a point on the curve, /// it returns an error indicating that the point is not on the curve. /// /// # Arguments /// /// * `x` - The x-coordinate of the projective point. /// * `y` - The y-coordinate of the projective point. /// * `z` - The z-coordinate of the projective point. /// /// # Returns /// /// If the provided coordinates result in a point on the elliptic curve, it returns the newly /// initialized projective point. Otherwise, it returns an error indicating that the point is not /// on the curve. /// /// # Errors /// /// Returns an error of type `EcPointError` if the provided coordinates do not correspond to /// a point on the elliptic curve. /// /// # Example /// /// ```zig /// const point = try ProjectivePointJacobian.init(x_value, y_value, z_value); /// ``` /// /// This creates a new projective point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and the z-coordinate `z_value`. If the resulting point is not on the curve, it returns an error. pub fn init(x: Felt252, y: Felt252, z: Felt252) !Self { const p: Self = .{ .x = x, .y = y, .z = z }; if (!AffinePoint.fromProjectivePointJacobian(&p).isOnCurve()) return EcPointError.PointNotOnCurve; return p; } /// Constructs a projective point from an affine point. /// /// This function converts an affine point to a projective point, setting its coordinates /// accordingly and preserving the infinity flag. /// /// # Arguments /// /// * `p` - A pointer to the affine point. /// /// # Returns /// /// A projective point constructed from the given affine point. pub fn fromAffinePoint(p: *const AffinePoint) Self { return if (p.isIdentity()) .{} else .{ .x = p.x, .y = p.y, .z = Felt252.one() }; } /// Returns the identity element of the projective space. /// /// This function returns the identity element of the projective space, which is the zero point /// represented as the point at infinity. The identity element serves as the neutral element /// in projective space arithmetic. /// /// # Returns /// /// The identity element of the projective space, represented as the point at infinity. pub inline fn identity() Self { return .{}; } /// Checks whether two projective points are equal. /// /// This function determines whether two projective points are equal by comparing their coordinates. /// Two projective points are considered equal if they represent the same affine point on the elliptic curve. /// /// # Arguments /// /// * `self` - The first projective point. /// * `rhs` - The second projective point to compare. /// /// # Returns /// /// Returns true if the two projective points are equal, false otherwise. /// /// # Remarks /// /// Two projective points (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂) are considered equal if the following conditions hold: /// /// * X₁ * Z₂^2 = X₂ * Z₁^2 /// * Y₁ * Z₂^3 = Y₂ * Z₁^3 /// /// These conditions ensure that the two projective points represent the same affine point on the elliptic curve. /// If either point is the point at infinity, they are considered equal if and only if both points are the point at infinity. pub fn eql(self: Self, rhs: Self) bool { // Check if either point is the point at infinity. if (self.isIdentity()) return rhs.isIdentity(); if (rhs.isIdentity()) return false; // Compute Z₁^2 and Z₂^2. const z1z1 = self.z.square(); const z2z2 = rhs.z.square(); // Check if X₁ * Z₂^2 equals X₂ * Z₁^2. // Check if Y₁ * Z₂^3 equals Y₂ * Z₁^3. return self.x.mul(&z2z2).eql(rhs.x.mul(&z1z1)) and self.y.mul(&z2z2.mul(&rhs.z)).eql(rhs.y.mul(&z1z1.mul(&self.z))); } /// Checks if this projective point lies on the elliptic curve. /// /// This function determines whether the given projective point lies on the elliptic curve defined /// by the curve parameters. If the point is at infinity, it is considered to be on the curve. /// /// # Returns /// /// Returns `true` if the projective point lies on the elliptic curve, otherwise `false`. /// /// # Remarks /// /// If the point is at infinity, it is always considered to be on the curve. /// Otherwise, the function converts the projective point to an affine point and checks if it lies on the curve. pub fn isOnCurve(self: *const Self) bool { // Check if the point is at infinity. if (self.isIdentity()) return true; return AffinePoint.fromProjectivePointJacobian(self).isOnCurve(); } /// Checks if the projective point is the identity element. /// /// This function returns true if the provided projective point is the identity element of the /// projective space, which is represented as the point at infinity. Otherwise, it returns false. /// /// # Returns /// /// `true` if the projective point is the identity element (point at infinity), otherwise `false`. /// pub inline fn isIdentity(self: *const Self) bool { return self.z.isZero(); } /// Doubles the projective point. /// /// This function returns a new projective point that represents the result of /// doubling the given projective point, effectively performing point doubling /// in elliptic curve arithmetic. /// /// # Returns /// /// The resulting projective point after the doubling operation. /// /// # Remarks /// /// This function does not modify the original projective point, but instead /// returns a new point representing the result of the doubling operation. /// pub fn double(self: Self) Self { var a = self; a.doubleAssign(); return a; } /// Doubles the projective point in place. /// /// This function doubles the given projective point in place, effectively performing /// point doubling in elliptic curve arithmetic. /// /// # Remarks /// /// The point doubling operation doubles the given point in projective coordinates /// and stores the result back in the original point. /// /// Returns without performing any operation if the projective point is the identity element /// (point at infinity). /// /// # Cost /// /// The cost of this operation is calculated as follows: /// - 2 multiplications (2M) /// - 5 squarings (5S) /// - 6 additions (6add) /// - 3 multiplications by constants (3*2) /// - 1 multiplication by a curve parameter (1*3) /// - 1 constant-time multiplication by 8 (1*8) pub fn doubleAssign(self: *Self) void { // If the point is the point at infinity, no operation is needed. if (self.isIdentity()) return; // Calculate X1^2 const xx = self.x.square(); // Calculate Y1^2 const yy = self.y.square(); // Calculate YY^2 const yyyy = yy.square(); // Calculate Z1^2 const zz = self.z.square(); // Calculate 2*((X1+YY)^2-XX-YYYY) const s = self.x.add(&yy).square().sub(&xx).sub(&yyyy).double(); // Calculate 3*XX+a*ZZ^2 const m = xx.double().add(&xx).add(&CurveParams.ALPHA.mul(&zz.square())); // Calculate T = M^2-2*S // X3 = T self.x = m.square().sub(&s.double()); // Calculate Z3 = 2*Y1*Z1 // This is a faster way to compute (Y1+Z1)^2-YY-ZZ self.z = self.z.mul(&self.y).double(); // Calculate Y3 = M*(S-X3)-8*YYYY self.y = s.sub(&self.x).mul(&m).sub(&yyyy.double().double().double()); } /// Adds another projective point to this point and returns the result. /// /// This function adds the coordinates of the provided projective point (`rhs`) to the coordinates /// of this projective point (`self`), without modifying the original point. It returns a new /// projective point representing the result of the addition operation. /// /// # Arguments /// /// * `rhs` - A pointer to the projective point to be added to this point. /// /// # Returns /// /// A new projective point representing the result of the addition operation. pub fn add(self: Self, rhs: *const Self) Self { // Make a copy of the original point var a = self; // Perform point addition in place Self.addAssign(&a, rhs); // Return the resulting point return a; } /// Adds the coordinates of an affine point to this projective point. /// /// This function adds the coordinates of the provided affine point (`rhs`) to the coordinates /// of this projective point (`self`) and returns a new projective point representing the result /// of the addition operation. It does not modify the original point (`self`). /// /// # Arguments /// /// * `self` - The current projective point. /// * `rhs` - A pointer to the affine point to be added to `self`. /// /// # Returns /// /// A new projective point representing the result of the addition operation. /// /// # Remarks /// /// This function creates a copy of the original projective point (`self`), then performs the /// point addition operation in place by calling `addAffineAssign`. It returns a new projective /// point representing the result of the addition operation, leaving the original point unchanged. /// /// # Example /// /// ```zig /// const point = ProjectivePointJacobian.initUnchecked(x1, y1, z1); /// const affinePoint = AffinePoint.initUnchecked(x2, y2); /// const result = point.addAffine(&affinePoint); /// ``` /// /// This example adds the coordinates of `affinePoint` to the projective point `point` /// and stores the result in the `result` variable without modifying `point`. pub fn addAffine(self: Self, rhs: *const AffinePoint) Self { // Make a copy of the original point var a = self; // Perform point addition in place Self.addAffineAssign(&a, rhs); // Return the resulting point return a; } /// Negates this projective point. /// /// This function negates the coordinates of this projective point (`self`) and returns the result. /// Negation operation involves negating the y-coordinate while keeping the x and z-coordinates unchanged. /// /// # Returns /// /// The negated projective point. pub fn neg(self: Self) Self { return if (self.isIdentity()) .{} else .{ .x = self.x, .y = self.y.neg(), .z = self.z }; } /// Subtracts another projective point from this point and returns the result. /// /// This function subtracts the coordinates of the provided projective point (`rhs`) from the coordinates /// of this projective point (`self`), without modifying the original point. It returns a new /// projective point representing the result of the subtraction operation. /// /// # Arguments /// /// * `rhs` - A pointer to the projective point to be subtracted from this point. /// /// # Returns /// /// A new projective point representing the result of the subtraction operation. pub fn sub(self: Self, rhs: *const Self) Self { // Make a copy of the original point var a = self; // Add the negation of the rhs point to this point a.addAssign(&rhs.neg()); // Return the resulting point return a; } /// Subtracts the coordinates of an affine point from this projective point. /// /// This function subtracts the coordinates of the provided affine point (`rhs`) from the coordinates /// of this projective point (`self`) and returns a new projective point representing the result /// of the subtraction operation. It does not modify the original point (`self`). /// /// # Arguments /// /// * `self` - The current projective point. /// * `rhs` - A pointer to the affine point to be subtracted from `self`. /// /// # Returns /// /// A new projective point representing the result of the subtraction operation. /// /// # Remarks /// /// This function creates a copy of the original projective point (`self`), then subtracts the /// coordinates of the negated `rhs` point from `self` by calling `addAffineAssign`. It returns /// a new projective point representing the result of the subtraction operation, leaving the /// original point unchanged. /// /// # Example /// /// ```zig /// const point = ProjectivePointJacobian.initUnchecked(x1, y1, z1); /// const affinePoint = AffinePoint.initUnchecked(x2, y2); /// const result = point.subAffine(&affinePoint); /// ``` /// /// This example subtracts the coordinates of `affinePoint` from the projective point `point` /// and stores the result in the `result` variable without modifying `point`. pub fn subAffine(self: Self, rhs: *const AffinePoint) Self { // Make a copy of the original point var a = self; // Add the negation of the rhs point to this point a.addAffineAssign(&rhs.neg()); // Return the resulting point return a; } /// Adds the coordinates of an affine point to this projective point in place. /// /// This function adds the coordinates of the provided affine point (`rhs`) to the coordinates /// of this projective point (`self`), without modifying the original point. It returns void /// and updates the current point (`self`) to the result of the addition operation. /// /// # Arguments /// /// * `self` - A mutable reference to the current projective point. /// * `rhs` - A pointer to the affine point to be added to `self`. /// /// # Cost Analysis /// /// The function performs the point addition operation with the following costs: /// - 7M (multiplications) /// - 4S (squares) /// - 9add (additions) /// - 3*2 (doublings) /// - 1*4 (constants) pub fn addAffineAssign(self: *Self, rhs: *const AffinePoint) void { // If rhs is the identity point, no operation is needed. if (rhs.isIdentity()) return; // If self is the identity point, update self to rhs and return. if (self.isIdentity()) { self.* = Self.fromAffinePoint(rhs); return; } // https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-madd-2007-bl // Z1Z1 = Z1^2 const z1z1 = self.z.square(); // U2 = X2*Z1Z1 const u_2 = rhs.x.mul(&z1z1); // S2 = Y2*Z1*Z1Z1 const s2 = self.z.mul(&rhs.y).mul(&z1z1); if (self.x.eql(u_2)) { if (self.y.eql(s2)) { // Point doubling operation self.doubleAssign(); } else { // Point at infinity self.* = Self.identity(); } return; } // H = U2-X1 const h = u_2.sub(&self.x); // HH = H^2 const hh = h.square(); // I = 4*HH const i = hh.double().double(); // J = -H*I const j = h.neg().mul(&i); // r = 2*(S2-Y1) const r = s2.sub(&self.y).double(); // V = X1*I const v = self.x.mul(&i); // X3 = r^2 + J - 2*V self.x = r.square().add(&j).sub(&v.double()); // Y3 = r*(V-X3) + 2*Y1*J self.y = r.mul(&v.sub(&self.x)).add(&self.y.double().mul(&j)); // Z3 = 2 * Z1 * H; // Can alternatively be computed as (Z1+H)^2-Z1Z1-HH, but the latter is slower. self.z = self.z.mul(&h).double(); } /// Performs point addition in Jacobian projective coordinates. /// /// This function adds the point represented by `rhs` to the point represented by `self`. /// Points are represented in Jacobian projective coordinates, which optimize elliptic curve /// cryptography operations. The function returns void and updates the current point (`self`) /// to the result of the addition operation. /// /// # Arguments /// /// * `self` - A mutable reference to the current point. /// * `rhs` - A pointer to the point to be added to `self`. /// /// # Cost Analysis /// /// The function performs the point addition operation with the following costs: /// - 11M (multiplications) /// - 5S (squares) /// - 9add (additions) /// - 4*2 (doublings) pub fn addAssign(self: *Self, rhs: *const Self) void { // If rhs is the identity point, no operation is needed. if (rhs.isIdentity()) { return; } // If self is the identity point, update self to rhs and return. if (self.isIdentity()) { self.* = rhs.*; return; } // Precomputations for optimization based on the formulas from EFD. // See: https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl // Z1Z1 = Z1^2 const z1z1 = self.z.square(); // Z2Z2 = Z2^2 const z2z2 = rhs.z.square(); // U1 = X1*Z2Z2 const u_1 = self.x.mul(&z2z2); // U2 = X2*Z1Z1 const u_2 = rhs.x.mul(&z1z1); // S1 = Y1*Z2*Z2Z2 const s1 = self.y.mul(&rhs.z).mul(&z2z2); // S2 = Y2*Z1*Z1Z1 const s2 = rhs.y.mul(&self.z).mul(&z1z1); // Check if points are equal, leading to point doubling or point at infinity. if (u_1.eql(u_2)) { if (s1.eql(s2)) { // Point doubling operation self.doubleAssign(); } else { // Point at infinity self.* = Self.identity(); } return; } // If we're adding -a and a together, self.z becomes zero as H becomes zero. // H = U2-U1 const h = u_2.sub(&u_1); // I = (2*H)^2 const i = h.double().square(); // J = -H*I const j = h.neg().mul(&i); // r = 2*(S2-S1) const r = s2.sub(&s1).double(); // V = U1*I const v = u_1.mul(&i); // X3 = r^2 + J - 2*V self.x = r.square().add(&j).sub(&v.double()); // Y3 = r*(V - X3) + 2*S1*J self.y = r.mul(&v.sub(&self.x)).add(&s1.double().mul(&j)); // Z3 = ((Z1+Z2)^2 - Z1Z1 - Z2Z2)*H // This is equal to Z3 = 2 * Z1 * Z2 * H, and computing it this way is faster. self.z = self.z.mul(&rhs.z).double().mul(&h); } /// Multiplies the projective point by a scalar represented as a bit slice in big-endian format. /// /// This function performs scalar multiplication of the projective point by a scalar represented /// as a bit slice in big-endian format. /// /// # Arguments /// /// * `bits` - A bit slice representing the scalar value in big-endian format. /// /// # Returns /// /// The resulting projective point after scalar multiplication. /// /// # Errors /// /// Returns an error if any error occurs during the multiplication operation. pub fn mulByBitsBe(self: *const Self, bits: [@bitSizeOf(u256)]bool) Self { // Initialize the product as the identity element. var product = ProjectivePointJacobian.identity(); // Find the index of the first set bit in the scalar. const first_one = std.mem.indexOfScalar(bool, &bits, true) orelse @bitSizeOf(u256); // Iterate over the scalar bits starting from the first set bit. for (bits[first_one..]) |bit| { // Double the projective point. product.doubleAssign(); // Conditionally add the original point if the corresponding bit is set. if (bit) product.addAssign(self); } // Return the resulting product after scalar multiplication. return product; } /// Multiplies the projective point by a scalar represented as a field element. /// /// This function performs scalar multiplication of the projective point by a scalar represented /// as a field element. /// /// # Arguments /// /// * `rhs` - A pointer to the scalar value. /// /// # Returns /// /// The resulting projective point after scalar multiplication. /// /// # Errors /// /// Returns an error if any error occurs during the multiplication operation. pub fn mulByScalar(self: *const Self, rhs: *const Felt252) Self { return self.mulByBitsBe(rhs.toBitsBe()); } }; test "ProjectivePointJacobian: initUnchecked should return a projective point (even if not valid)" { try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 10), .y = Felt252.fromInt(u256, 20), .z = Felt252.one(), }, ProjectivePointJacobian.initUnchecked( Felt252.fromInt(u256, 10), Felt252.fromInt(u256, 20), Felt252.one(), ), ); try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, ProjectivePointJacobian.initUnchecked( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), Felt252.one(), ), ); } test "ProjectivePointJacobian: init should return a projective point and throw an error when not valid" { try expectError( EcPointError.PointNotOnCurve, ProjectivePointJacobian.init( Felt252.fromInt(u256, 10), Felt252.fromInt(u256, 20), Felt252.one(), ), ); try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, try ProjectivePointJacobian.init( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), Felt252.one(), ), ); } test "ProjectivePointJacobian: fromAffinePoint should return a projective point based on an affine point" { try expectEqual( ProjectivePointJacobian{}, ProjectivePointJacobian.fromAffinePoint(&.{}), ); try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }, ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }), ); } test "ProjectivePointJacobian: identity should return the point at infinity" { try expectEqual( ProjectivePointJacobian{}, ProjectivePointJacobian.identity(), ); } test "ProjectivePointJacobian: addAssign of P + 0 should return P" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }; var p = ProjectivePointJacobian.fromAffinePoint(&a); p.addAssign(&.{}); try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .z = Felt252.one(), }, p, ); } test "ProjectivePointJacobian: addAssign of 0 + P should return P" { var p: ProjectivePointJacobian = .{}; p.addAssign(&ProjectivePointJacobian.fromAffinePoint( &.{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }, )); try expectEqual( ProjectivePointJacobian{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .z = Felt252.one(), }, p, ); } test "ProjectivePointJacobian: addAssign P + (-P) should give 0" { var p = ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262).neg(), .infinity = false, })); try expectEqual(ProjectivePointJacobian{}, p); } test "ProjectivePointJacobian: addAssign P + P should give 2P" { var p = ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, })); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1007300233009797052089600572030536234678420387464749955693412487829103372971), .y = Felt252.fromInt(u256, 1628094014246951319213922206675864072767692386561452886899658728389307097247), .infinity = false, }, AffinePoint.fromProjectivePointJacobian(&p), ); } test "ProjectivePointJacobian: addAssign should give the proper point addition" { var p = ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); p.addAssign(&ProjectivePointJacobian.fromAffinePoint(&.{ .x = Felt252.fromInt(u256, 874739451), .y = Felt252.fromInt(u256, 78981980789517450823121602653688575320503877484645249556098070515590001476), .infinity = false, })); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1732660995762076585664239316986550513074833679175460014337184483203739567080), .y = Felt252.fromInt(u256, 2212051391075121985157657306991376790084194366385999148123095336409007912683), .infinity = false, }, AffinePoint.fromProjectivePointJacobian(&p), ); } test "ProjectivePointJacobian: isOnCurve should return true if the point is on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expect(ProjectivePointJacobian.fromAffinePoint(&a).isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }; try expect(ProjectivePointJacobian.fromAffinePoint(&b).isOnCurve()); } test "ProjectivePointJacobian: isOnCurve should return false if the point is not on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 10), .y = Felt252.fromInt(u256, 100), .infinity = false, }; try expect(!ProjectivePointJacobian.fromAffinePoint(&a).isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 5), .y = Felt252.fromInt(u256, 30), .infinity = false, }; try expect(!ProjectivePointJacobian.fromAffinePoint(&b).isOnCurve()); } test "ProjectivePointJacobian: fuzzing testing of arithmetic addition operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Generate a random affine point 'b'. var b = AffinePoint.rand(random); // Generate a random affine point 'c'. var c = AffinePoint.rand(random); // Convert affine points to Jacobian projective points. var a_projective = ProjectivePointJacobian.fromAffinePoint(&a); var b_projective = ProjectivePointJacobian.fromAffinePoint(&b); var c_projective = ProjectivePointJacobian.fromAffinePoint(&c); var zero: ProjectivePointJacobian = .{}; // Associativity try expect(a_projective.add(&b_projective).add(&c_projective).eql( a_projective.add(&b_projective.add(&c_projective)), )); // Identify try expect(a_projective.eql(zero.add(&a_projective))); try expect(b_projective.eql(zero.add(&b_projective))); try expect(c_projective.eql(zero.add(&c_projective))); try expect(a_projective.eql(a_projective.add(&zero))); try expect(b_projective.eql(b_projective.add(&zero))); try expect(c_projective.eql(c_projective.add(&zero))); // Negation try expect(zero.eql(a_projective.neg().add(&a_projective))); try expect(zero.eql(b_projective.neg().add(&b_projective))); try expect(zero.eql(c_projective.neg().add(&c_projective))); try expect(zero.eql(zero.neg())); // Commutativity try expect(a_projective.add(&b_projective).eql(b_projective.add(&a_projective))); // Associativity and commutativity simultaneously try expect(a_projective.add(&b_projective).add(&c_projective).eql( a_projective.add(&c_projective).add(&b_projective), )); try expect(a_projective.add(&c_projective).add(&b_projective).eql( b_projective.add(&c_projective).add(&a_projective), )); // Doubling try expect(a_projective.add(&a_projective).eql(a_projective.double())); try expect(b_projective.add(&b_projective).eql(b_projective.double())); try expect(c_projective.add(&c_projective).eql(c_projective.double())); try expect(zero.eql(zero.double())); try expect(zero.eql(zero.neg().double())); // Operation with an affine point try expect(a_projective.addAffine(&b).eql( a_projective.add(&b_projective), )); try expect(b_projective.addAffine(&c).eql( b_projective.add(&c_projective), )); try expect(a_projective.subAffine(&b).eql( a_projective.sub(&b_projective), )); try expect(b_projective.subAffine(&c).eql( b_projective.sub(&c_projective), )); try expect(zero.addAffine(&a).eql( a_projective, )); try expect(a_projective.addAffine(&b).addAffine(&c).eql( a_projective.add(&c_projective).add(&b_projective), )); try expect(a_projective.addAffine(&c).addAffine(&b).eql( b_projective.add(&c_projective).add(&a_projective), )); } } test "ProjectivePointJacobian: fuzzing testing of arithmetic subtraction operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Generate another random affine point 'b'. var b = AffinePoint.rand(random); // Convert affine points to projective points. var a_projective = ProjectivePointJacobian.fromAffinePoint(&a); var b_projective = ProjectivePointJacobian.fromAffinePoint(&b); var zero: ProjectivePointJacobian = .{}; // Anti-commutativity try expect(a_projective.sub(&b_projective).add( &b_projective.sub(&a_projective), ).isIdentity()); try expect(a_projective.subAffine(&b).add( &b_projective.subAffine(&a), ).isIdentity()); try expect(a_projective.subAffine(&b).addAffine( &try b.sub(&a), ).isIdentity()); // Identity try expect(zero.sub(&a_projective).eql(a_projective.neg())); try expect(zero.sub(&b_projective).eql(b_projective.neg())); try expect(a_projective.sub(&zero).eql(a_projective)); try expect(b_projective.sub(&zero).eql(b_projective)); } } test "ProjectivePointJacobian: fuzzing testing of arithmetic multiplication operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Convert affine points to projective points. var a_projective = ProjectivePointJacobian.fromAffinePoint(&a); var b = Felt252.rand(random); var c = Felt252.rand(random); var zero = Felt252.zero(); var one = Felt252.one(); // Identity try expect(a_projective.mulByBitsBe(zero.toBitsBe()).eql(.{})); try expect(a_projective.mulByBitsBe(one.toBitsBe()).eql(a_projective)); try expect(a_projective.mulByScalar(&zero).eql(.{})); try expect(a_projective.mulByScalar(&one).eql(a_projective)); // Associativity try expect(a_projective.mulByScalar(&b).mulByScalar(&c).eql( a_projective.mulByScalar(&c).mulByScalar(&b), )); // Inverses try expect(a_projective.mulByScalar(&b.inverse().?.mul(&b)).eql( a_projective, )); } }
0
repos/starknet-zig/src/math/curve
repos/starknet-zig/src/math/curve/short_weierstrass/affine.zig
// code ported from starknet-curve: // https://github.com/xJonathanLEI/starknet-rs/blob/0857bd6cd3bd34cbb06708f0a185757044171d8d/starknet-curve/src/ec_point.rs const std = @import("std"); const Felt252 = @import("../../fields/starknet.zig").Felt252; const bigInt = @import("../../fields/biginteger.zig").bigInt; const CurveParams = @import("../curve_params.zig"); const EcPointError = @import("../errors.zig").EcPointError; const ProjectivePoint = @import("./projective.zig").ProjectivePoint; const ProjectivePointJacobian = @import("./projective_jacobian.zig").ProjectivePointJacobian; const TEST_ITERATIONS = @import("../../../main.zig").TEST_ITERATIONS; const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; /// This module defines a struct representing an affine point on an elliptic curve in the Short Weierstrass form. /// /// Affine points are pairs of field elements (x, y) that satisfy the Short Weierstrass cubic equation /// y^2 = x^3 + a * x + b, where a and b are constants defining the elliptic curve. /// Additionally, there is a distinguished symbol 'O', representing the point at infinity. /// /// The struct `AffinePoint` encapsulates an x-coordinate, a y-coordinate, and a boolean flag indicating /// whether the point is at infinity. pub const AffinePoint = struct { const Self = @This(); /// The x-coordinate of the affine point. x: Felt252 = Felt252.zero(), /// The y-coordinate of the affine point. y: Felt252 = Felt252.zero(), /// A boolean flag indicating whether the point is at infinity. infinity: bool = true, /// Initializes a new affine point with the given coordinates. /// /// This function creates a new affine point with the specified x-coordinate, y-coordinate, /// and infinity flag, and returns it. /// /// # Arguments /// /// * `x` - The x-coordinate of the affine point. /// * `y` - The y-coordinate of the affine point. /// * `infinity` - A boolean flag indicating whether the point is at infinity. /// /// # Returns /// /// A new affine point initialized with the provided coordinates. /// /// # Example /// /// ```zig /// const point = AffinePoint.initUnchecked(x_value, y_value, false); /// ``` /// /// This creates a new affine point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and sets the infinity flag to `false`. /// pub fn initUnchecked(x: Felt252, y: Felt252, infinity: bool) Self { return .{ .x = x, .y = y, .infinity = infinity }; } /// Initializes a new affine point with the given coordinates. /// /// This function creates a new affine point with the specified x-coordinate, y-coordinate, /// and infinity flag, and returns it. Additionally, it ensures that the generated point lies /// on the elliptic curve. /// /// # Arguments /// /// * `x` - The x-coordinate of the affine point. /// * `y` - The y-coordinate of the affine point. /// * `infinity` - A boolean flag indicating whether the point is at infinity. /// /// # Returns /// /// If the provided coordinates result in a point on the elliptic curve, it returns the newly /// initialized affine point. Otherwise, it returns an error indicating that the point is not /// on the curve. /// /// # Errors /// /// Returns an error of type `EcPointError` if the provided coordinates do not correspond to /// a point on the elliptic curve. /// /// # Example /// /// ```zig /// const point = try AffinePoint.init(x_value, y_value, false); /// ``` /// /// This creates a new affine point with the x-coordinate `x_value`, the y-coordinate `y_value`, /// and sets the infinity flag to `false`. If the resulting point is not on the curve, it returns /// an error. /// pub fn init(x: Felt252, y: Felt252, infinity: bool) EcPointError!Self { // Create the affine point using the provided coordinates. const point: Self = .{ .x = x, .y = y, .infinity = infinity, }; // Check if the point lies on the elliptic curve. if (!point.isOnCurve()) return EcPointError.PointNotOnCurve; // Return the initialized affine point. return point; } /// Returns the identity element of the elliptic curve. /// /// This function returns the identity element of the elliptic curve, which is the zero point /// represented as the point at infinity (denoted as `O`). The identity element serves as the /// neutral element in elliptic curve arithmetic. /// /// # Returns /// /// The identity element of the elliptic curve, represented as the zero point with the infinity flag set to true. /// /// # Remarks /// /// The identity element (`O`) behaves as the additive identity in elliptic curve arithmetic. Adding /// it to any rhs point (`O + P`) yields the rhs point `P`, and adding it to itself (`O + O`) /// results in the identity element `O`. /// pub inline fn identity() Self { return .{}; } /// Returns the generator point of the elliptic curve. /// /// This function retrieves and returns the pre-defined generator point G (base point). The generator point G is a constant point on the curve that, when multiplied by integers within a certain range, can generate any rhs point in its subgroup over the curve. /// /// # Returns /// /// The generator point G of the elliptic curve, which serves as the basis for generating all rhs points /// in its subgroup over the curve. pub inline fn generator() Self { return CurveParams.GENERATOR; } /// Checks if the affine point is the identity element. /// /// This function returns true if the provided affine point is the identity element of the /// elliptic curve, which is represented as the point at infinity (`O`). Otherwise, it returns false. /// /// # Returns /// /// `true` if the affine point is the identity element (`O`), otherwise `false`. /// pub inline fn isIdentity(self: *const Self) bool { return self.infinity; } /// Checks whether two affine points are equal. /// /// This function determines whether two affine points are equal by comparing their coordinates. /// Two affine points are considered equal if their x-coordinates and y-coordinates are equal. /// /// # Arguments /// /// * `self` - The first affine point. /// * `rhs` - The second affine point to compare. /// /// # Returns /// /// Returns true if the two affine points are equal, false otherwise. /// /// # Remarks /// /// Two affine points (x₁, y₁) and (x₂, y₂) are considered equal if and only if: /// /// * x₁ = x₂ /// * y₁ = y₂ /// pub fn eql(self: Self, rhs: Self) bool { // Check if either point is the point at infinity. if (self.isIdentity()) return rhs.isIdentity(); if (rhs.isIdentity()) return false; // Check if the x-coordinates, y-coordinates are equal. return self.x.eql(rhs.x) and self.y.eql(rhs.y); } /// Determines whether the affine point lies on the elliptic curve. /// /// This function checks if the given affine point lies on the elliptic curve defined by the Short Weierstrass equation: /// y^2 = x^3 + a * x + b, where (x, y) are the coordinates of the affine point and a, b are curve parameters. /// /// # Arguments /// /// * `self` - A pointer to the affine point to be checked. /// /// # Returns /// /// Returns true if the point lies on the elliptic curve, false otherwise. /// /// # Remarks /// /// The function handles the case of the point at infinity, which is always considered to be on the curve. /// For finite points, it evaluates whether the equation y^2 = x^3 + ax + b holds true. /// If the point lies on the curve, it returns true; otherwise, it returns false. /// pub fn isOnCurve(self: *const Self) bool { // Check if the point is at infinity. if (self.infinity) return true; // Calculate the right-hand side of the elliptic curve equation: x^3 + ax + b. const rhs = self.x.square().mul(&self.x).add( &CurveParams.ALPHA.mul(&self.x), ).add(&CurveParams.BETA); // Check if the calculated right-hand side is equal to the square of the y-coordinate. return rhs.eql(self.y.square()); } /// Computes the negation of the given affine point on the elliptic curve. /// /// This function calculates the negation of the given affine point on the elliptic curve, which is the point obtained by reflecting the original point across the x-axis. /// /// If the original point is at infinity, its negation remains the point at infinity. /// /// # Arguments /// /// * `self` - The affine point to be negated. /// /// # Returns /// /// The negation of the given affine point on the elliptic curve. /// /// # Remarks /// /// The negation operation is defined such that if the original point P has coordinates (x, y), its negation -P has coordinates (x, -y). /// The negation of the point at infinity remains the point at infinity, as it is the additive identity in elliptic curve arithmetic. pub fn neg(self: Self) Self { return .{ .x = self.x, .y = self.y.neg(), .infinity = self.infinity, }; } /// Adds another elliptic curve point to this point. /// /// Performs point addition between two elliptic curve points. /// /// # Arguments /// /// * `self` - The first elliptic curve point. /// * `rhs` - A pointer to the second elliptic curve point being added. /// /// # Returns /// /// The resulting elliptic curve point after the addition operation. /// /// # Errors /// /// Returns an error if any error occurs during the addition operation. pub fn add(self: Self, rhs: *const Self) !Self { // Make a copy of the original point var a = self; // Perform point addition in place try a.addAssign(rhs); // Return the resulting point return a; } /// Subtracts another affine point from this point in the context of elliptic curve arithmetic. /// /// This function performs point subtraction between two affine points on an elliptic curve in Short Weierstrass form. /// It calculates the difference between the two points and returns the result as a new affine point. /// /// # Arguments /// /// * `self` - The affine point from which the rhs point is subtracted. /// * `rhs` - A pointer to the affine point being subtracted. /// /// # Returns /// /// The result of subtracting the rhs point from this point, represented as a new affine point. /// /// # Errors /// /// Returns an error if an error occurs during the calculation, such as division by zero. /// pub fn sub(self: Self, rhs: *const Self) !Self { var a = self; try a.addAssign(&rhs.neg()); return a; } /// Subtracts another affine point from this point in place in the context of elliptic curve arithmetic. /// /// This function performs point subtraction between two affine points on an elliptic curve in Short Weierstrass form. /// It modifies the original point by subtracting the rhs point from it. /// /// # Arguments /// /// * `self` - A mutable reference to the affine point from which the rhs point is subtracted. /// * `rhs` - A pointer to the affine point being subtracted. /// /// # Errors /// /// Returns an error if an error occurs during the calculation, such as division by zero. /// pub fn subAssign(self: *Self, rhs: *const Self) !void { try self.addAssign(&rhs.neg()); } /// Adds another affine point to this point in the context of elliptic curve arithmetic. /// /// This function performs point addition between two affine points on an elliptic curve in Short Weierstrass form. /// /// # Arguments /// /// * `self` - A mutable reference to the affine point on which addition is performed. /// * `rhs` - A pointer to the affine point being added. /// /// # Errors /// /// Returns an error if division by zero occurs during the calculation of the slope. pub fn addAssign(self: *Self, rhs: *const AffinePoint) !void { // P + 0 = P // If the rhs point is the point at infinity, no operation is needed. if (rhs.infinity) return; // 0 + P = P // If this point is the point at infinity, the result is set to the rhs point. if (self.infinity) { self.* = rhs.*; return; } // If both points have the same x-coordinate. if (self.x.eql(rhs.x)) { // P + (-P) = I // If the y-coordinates are negations of each rhs, resulting in point at infinity. if (self.y.eql(rhs.y.neg())) { // Set this point to the point at infinity. self.* = .{}; } else { // Otherwise, the points are the same, perform point doubling. self.doubleAssign(); } return; } // Calculate the slope of the line passing through the two points. // l = (y2-y1)/(x2-x1) const lambda = try rhs.y.sub(&self.y).div(rhs.x.sub(&self.x)); // Compute x-coordinate of the resulting point: lambda^2 - x1 - x2 const result_x = lambda.square().sub(&self.x).sub(&rhs.x); // Compute y-coordinate of the resulting point: lambda * (x1 - x3) - y1 self.y = lambda.mul(&self.x.sub(&result_x)).sub(&self.y); // Update the x-coordinate of this point to the computed x-coordinate of the resulting point. self.x = result_x; } /// Doubles the given affine point on the elliptic curve. /// /// This function calculates the doubling of the given affine point on the elliptic curve, /// which involves finding the point that lies on the curve and is collinear with the tangent /// line at the original point, and then reflecting it across the x-axis. /// /// If the original point is at infinity, its doubling remains the point at infinity. /// /// # Arguments /// /// * `self` - The affine point to be doubled. /// /// # Returns /// /// The result of doubling the given affine point on the elliptic curve. pub fn double(self: Self) Self { var a = self; a.doubleAssign(); return a; } /// Performs point doubling on the given affine point in the context of elliptic curve arithmetic. /// /// This function doubles the given affine point on an elliptic curve in Short Weierstrass form. It calculates the new coordinates of the point after doubling based on the curve equation and the tangent line at the given point. /// /// # Arguments /// /// * `self` - A mutable reference to the affine point that will be doubled. pub fn doubleAssign(self: *Self) void { // If the point is the point at infinity, no operation is needed. if (self.infinity) return; // l = (3x^2+a)/2y with a=1 from stark curve const lambda = Felt252.three().mul( &self.x.mul(&self.x), ).add( &Felt252.one(), ).mul( &Felt252.two().mul(&self.y).inverse().?, ); // Compute the new x-coordinate of the point after doubling: lambda^2 - 2x const result_x = lambda.mul(&lambda).sub(&self.x).sub(&self.x); // Compute the new y-coordinate of the point after doubling: lambda * (x - result_x) - y self.y = lambda.mul(&self.x.sub(&result_x)).sub(&self.y); // Update the coordinates of the point with the new values self.x = result_x; } /// Constructs an elliptic curve point from the x-coordinate in the context of the STARK curve. /// /// This function constructs an elliptic curve point from the given x-coordinate on the STARK curve, /// satisfying the equation 𝑦^2 ≡ 𝑥^3 + 𝛼⋅𝑥 + 𝛽 (mod 𝑝). /// /// # Arguments /// /// * `x` - The x-coordinate of the point. /// /// # Errors /// /// Returns an error if the square root of the y-coordinate does not exist. /// /// # Remarks /// /// The point construction follows the equation of the STARK curve: /// /// * The x-coordinate is set to the provided value. /// * The y-coordinate is calculated as the square root of 𝑥^3 + 𝛼⋅𝑥 + 𝛽 (mod 𝑝). /// * If the square root of the y-coordinate does not exist, an error is returned. /// * The point is not set to the point at infinity. /// /// This code snippet constructs an elliptic curve point on the STARK curve from the given x-coordinate. pub fn fromX(x: Felt252) EcPointError!Self { return .{ .x = x, .y = x.mul(&x).mul(&x).add(&CurveParams.ALPHA.mul(&x)).add(&CurveParams.BETA).sqrt() orelse return EcPointError.SqrtNotExist, .infinity = false, }; } /// Generates a random affine point on the elliptic curve. /// /// This function generates a random affine point on the elliptic curve defined by the Short Weierstrass equation: 𝑦^2 = 𝑥^3 + 𝛼⋅𝑥 + 𝛽, where (𝑥, 𝑦) are the coordinates of the affine point and 𝛼, 𝛽 are curve parameters. /// /// # Arguments /// /// * `r` - An instance of the random number generator used to generate the x-coordinate of the point. /// /// # Returns /// /// A random affine point on the elliptic curve. /// /// # Remarks /// /// This function repeatedly generates random x-coordinates until it constructs a valid point on the elliptic curve. /// The resulting point is returned as an affine point with the x-coordinate generated randomly and the y-coordinate computed based on the curve equation. pub fn rand(r: std.Random) Self { // Continuously generate random x-coordinates until a valid point on the curve is constructed. while (true) { // Generate a random x-coordinate within the field. const random_x = Felt252.fromInt(u256, r.int(u256)); // Attempt to construct a point on the curve using the generated x-coordinate. if (Self.fromX(random_x) catch null) |p| return p; } } /// Converts a projective point to an affine point on the elliptic curve. /// /// This function converts a projective point representation to an affine point representation on the elliptic curve. /// Projective coordinates are used to represent points on elliptic curves efficiently. /// /// # Arguments /// /// * `p` - A pointer to the projective point to be converted. /// /// # Returns /// /// An affine point on the elliptic curve derived from the provided projective point. /// /// # Errors /// /// Returns an error if the inverse of the `z` coordinate of the projective point cannot be computed, such as when `z` is zero. pub fn fromProjectivePoint(p: *const ProjectivePoint) Self { // Point at infinity if (p.isIdentity()) return .{}; // Compute the inverse of the `z` coordinate of the projective point. // Note: `zinv` is always one, which is why we can unwrap the result. const zinv = p.z.inverse().?; // Create and return the resulting affine point. return .{ .x = p.x.mul(&zinv), .y = p.y.mul(&zinv), .infinity = false, }; } /// Converts a projective point in Jacobian coordinates to an affine point on the elliptic curve. /// /// This function converts a projective point representation in Jacobian coordinates to an affine point representation on the elliptic curve. /// Jacobian coordinates are an optimized representation for elliptic curve operations, offering improved efficiency compared to affine coordinates. /// /// # Arguments /// /// * `p` - A pointer to the projective point in Jacobian coordinates to be converted. /// /// # Returns /// /// An affine point on the elliptic curve derived from the provided projective point in Jacobian coordinates. /// /// # Remarks /// /// The `z` coordinate of the projective point is always assumed to be non-zero in Jacobian coordinates, ensuring that it has a valid inverse in the field. pub fn fromProjectivePointJacobian(p: *const ProjectivePointJacobian) Self { // Point at infinity if (p.isIdentity()) return .{}; // Compute the inverse of the `z` coordinate of the projective point. // Note: `z` is always non zero, so that it must have an inverse in the field. const zinv = p.z.inverse().?; const zinv_squared = zinv.square(); // Create and return the resulting affine point. return .{ .x = p.x.mul(&zinv_squared), .y = p.y.mul(&zinv_squared).mul(&zinv), .infinity = false, }; } /// Multiplies the affine point by a scalar represented as a bit slice in big-endian format. /// /// This function performs scalar multiplication of the affine point by a scalar represented /// as a bit slice in big-endian format. /// /// # Arguments /// /// * `bits` - A bit slice representing the scalar value in big-endian format. /// /// # Returns /// /// The resulting affine point after scalar multiplication. /// /// # Errors /// /// Returns an error if any error occurs during the multiplication operation. pub fn mulByBitsBe(self: *const Self, bits: [@bitSizeOf(u256)]bool) !Self { var product = AffinePoint.identity(); // Find the index of the first one bit in the bit slice. const first_one = std.mem.indexOfScalar(bool, &bits, true) orelse @bitSizeOf(u256); // Iterate over the bits in the scalar value. for (bits[first_one..]) |bit| { // Double the current product. product.doubleAssign(); // If the current bit is one, add the original affine point to the product. if (bit) try product.addAssign(self); } return product; } /// Multiplies the affine point by a scalar represented as a field element. /// /// This function performs scalar multiplication of the affine point by a scalar represented /// as a field element. /// /// # Arguments /// /// * `rhs` - A pointer to the scalar value. /// /// # Returns /// /// The resulting affine point after scalar multiplication. /// /// # Errors /// /// Returns an error if any error occurs during the multiplication operation. pub fn mulByScalar(self: *const Self, rhs: *const Felt252) !Self { // Convert the scalar value to a bit slice in big-endian format and perform scalar multiplication. return try self.mulByBitsBe(rhs.toBitsBe()); } /// Multiplies the affine point by a scalar represented as a field element in the projective space. /// /// This function performs scalar multiplication of the affine point by a scalar represented /// as a field element within the projective space. /// /// # Arguments /// /// * `self` - A pointer to the affine point. /// * `rhs` - A pointer to the scalar value. /// /// # Returns /// /// The resulting affine point after scalar multiplication in the projective space. /// /// Remarks: /// - This function converts the affine point to the projective point, performs scalar multiplication, /// and then converts the resulting projective point back to the affine point. pub inline fn mulByScalarProjective(self: *const Self, rhs: *const Felt252) Self { // Convert the affine point to the projective point, // perform scalar multiplication, and then convert back to the affine point. return Self.fromProjectivePoint( &ProjectivePoint .fromAffinePoint(self) .mulByScalar(rhs), ); } }; test "AffinePoint: default value should correspond to identity" { try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true }, AffinePoint{}, ); } test "AffinePoint: identity function should correspond to identity" { try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true }, AffinePoint.identity(), ); } test "AffinePoint: generator function should return the generator of the curve" { try expectEqual( AffinePoint{ .x = .{ .fe = bigInt(4).init( .{ 14484022957141291997, 5884444832209845738, 299981207024966779, 232005955912912577, }, ), }, .y = .{ .fe = bigInt(4).init( .{ 6241159653446987914, 664812301889158119, 18147424675297964973, 405578048423154473, }, ), }, .infinity = false, }, AffinePoint.generator(), ); } test "AffinePoint: isOnCurve should return true if the point is on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expect(a.isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }; try expect(b.isOnCurve()); } test "AffinePoint: isOnCurve should return false if the point is not on the curve" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 10), .y = Felt252.fromInt(u256, 100), .infinity = false, }; try expect(!a.isOnCurve()); const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 5), .y = Felt252.fromInt(u256, 30), .infinity = false, }; try expect(!b.isOnCurve()); } test "AffinePoint: isOnCurve should return true if the point is at infinity" { try expect(AffinePoint.identity().isOnCurve()); } test "AffinePoint: neg identity should return identity" { try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true }, AffinePoint.identity().neg(), ); } test "AffinePoint: neg a random point should return (x, -y)" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 3119986168776131983280236261251576523431128963685919687543048209950440350219), .infinity = false, }, a.neg(), ); } test "AffinePoint: initUnchecked should initialize an affine point with the provided coordinates" { try expectEqual( AffinePoint{ .x = Felt252.fromInt(u8, 10), .y = Felt252.fromInt(u8, 5), .infinity = false, }, AffinePoint.initUnchecked( Felt252.fromInt(u8, 10), Felt252.fromInt(u8, 5), false, ), ); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u8, 10), .y = Felt252.fromInt(u8, 5), .infinity = true, }, AffinePoint.initUnchecked( Felt252.fromInt(u8, 10), Felt252.fromInt(u8, 5), true, ), ); } test "AffinePoint: init should return an error is the provided point is not on the curve" { try expectError( EcPointError.PointNotOnCurve, AffinePoint.init( Felt252.fromInt(u8, 10), Felt252.fromInt(u8, 5), false, ), ); } test "AffinePoint: init should initialize a point if point is on the curve" { try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, try AffinePoint.init( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), false, ), ); } test "AffinePoint: addAssign P + 0 should give P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.addAssign(&.{}); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, a, ); } test "AffinePoint: addAssign 0 + P should give P" { var a: AffinePoint = .{}; try a.addAssign(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, a, ); } test "AffinePoint: addAssign P + (-P) should give 0" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.addAssign(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262).neg(), .infinity = false, }); try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true, }, a, ); } test "AffinePoint: addAssign P + P should give 2P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.addAssign(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1007300233009797052089600572030536234678420387464749955693412487829103372971), .y = Felt252.fromInt(u256, 1628094014246951319213922206675864072767692386561452886899658728389307097247), .infinity = false, }, a, ); } test "AffinePoint: addAssign should give the proper point addition" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.addAssign(&.{ .x = Felt252.fromInt(u256, 874739451), .y = Felt252.fromInt(u256, 78981980789517450823121602653688575320503877484645249556098070515590001476), .infinity = false, }); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1732660995762076585664239316986550513074833679175460014337184483203739567080), .y = Felt252.fromInt(u256, 2212051391075121985157657306991376790084194366385999148123095336409007912683), .infinity = false, }, a, ); } test "AffinePoint: doubleAssign should return the result of 2P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464987), .y = Felt252.fromInt(u256, 1706810360461260382053322601986439128304438960645702960907418619089749412278), .infinity = false, }; a.doubleAssign(); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 2351468578589314139010270743686619948996212672240729424672235643020198087569), .y = Felt252.fromInt(u256, 305861574354557676187499619608507066121174188916494330928491058389223641058), .infinity = false, }, a, ); } test "AffinePoint: double should return the result of 2P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464987), .y = Felt252.fromInt(u256, 1706810360461260382053322601986439128304438960645702960907418619089749412278), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 2351468578589314139010270743686619948996212672240729424672235643020198087569), .y = Felt252.fromInt(u256, 305861574354557676187499619608507066121174188916494330928491058389223641058), .infinity = false, }, a.double(), ); } test "AffinePoint: doubleAssign 2*0 should return 0" { var a: AffinePoint = .{}; a.doubleAssign(); try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true, }, a, ); } test "AffinePoint: fromX should return an affine point based on the provided x-coordinate" { try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464987), .y = Felt252.fromInt(u256, 1706810360461260382053322601986439128304438960645702960907418619089749412278), .infinity = false, }, try AffinePoint.fromX(Felt252.fromInt(u256, 874739451078007766457464987)), ); } test "AffinePoint: fromX should return an affine point based on the provided " { try expectError( EcPointError.SqrtNotExist, AffinePoint.fromX(Felt252.fromInt(u256, 87473945107800776645746498)), ); } test "AffinePoint: add P + 0 should give P" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, try a.add(&.{}), ); } test "AffinePoint: add 0 + P should give P" { var a: AffinePoint = .{}; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, try a.add(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }), ); } test "AffinePoint: add P + (-P) should give 0" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true, }, try a.add(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262).neg(), .infinity = false, }), ); } test "AffinePoint: add P + P should give 2P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1007300233009797052089600572030536234678420387464749955693412487829103372971), .y = Felt252.fromInt(u256, 1628094014246951319213922206675864072767692386561452886899658728389307097247), .infinity = false, }, try a.add(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }), ); } test "AffinePoint: add should give the proper point addition (P + Q)" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; const b: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451), .y = Felt252.fromInt(u256, 78981980789517450823121602653688575320503877484645249556098070515590001476), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 1732660995762076585664239316986550513074833679175460014337184483203739567080), .y = Felt252.fromInt(u256, 2212051391075121985157657306991376790084194366385999148123095336409007912683), .infinity = false, }, try a.add(&b), ); // Commutativity try expectEqual(try b.add(&a), try a.add(&b)); } test "AffinePoint: sub P - P should give 0" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true, }, try a.sub(&a), ); } test "AffinePoint: sub P - 0 should give P" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual(a, try a.sub(&.{})); } test "AffinePoint: sub 0 - P should give -P" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual(a.neg(), try AffinePoint.identity().sub(&a)); } test "AffinePoint: sub P1 - P2 should give P1 + (-P2)" { const a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 3170839098387265895893008062780951484244114197556826317838387523115006188371), .y = Felt252.fromInt(u256, 816850407800303493850322799005343907936137841827655002556778477319881342108), .infinity = false, }, try a.sub(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }), ); } test "AffinePoint: subAssign P - P should give 0" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.subAssign(&a); try expectEqual( AffinePoint{ .x = Felt252.zero(), .y = Felt252.zero(), .infinity = true, }, a, ); } test "AffinePoint: subAssign P - 0 should give P" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.subAssign(&.{}); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, a, ); } test "AffinePoint: subAssign 0 - P should give -P" { var a = AffinePoint.identity(); try a.subAssign(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }); try expectEqual( AffinePoint.initUnchecked( Felt252.fromInt(u256, 874739451078007766457464989), Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), false, ).neg(), a, ); } test "AffinePoint: subAssign P1 - P2 should give P1 + (-P2)" { var a: AffinePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }; try a.subAssign(&.{ .x = Felt252.fromInt(u256, 874739451078007766457464), .y = Felt252.fromInt(u256, 3202429691477156140440114086107030603959626074522568741397770080517060801394), .infinity = false, }); try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 3170839098387265895893008062780951484244114197556826317838387523115006188371), .y = Felt252.fromInt(u256, 816850407800303493850322799005343907936137841827655002556778477319881342108), .infinity = false, }, a, ); } test "AffinePoint: fromProjectivePoint should give an AffinePoint from a ProjectivePoint" { const a: ProjectivePoint = .{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .z = Felt252.one(), }; try expectEqual( AffinePoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989), .y = Felt252.fromInt(u256, 498516619889999230417086521843493582191978251645677012430043846185431670262), .infinity = false, }, AffinePoint.fromProjectivePoint(&a), ); } test "AffinePoint: fuzzing testing of arithmetic addition operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Generate another random affine point 'b'. var b = AffinePoint.rand(random); // Generate another random affine point 'c'. var c = AffinePoint.rand(random); const zero = AffinePoint.identity(); // Associativity try expect((try (try a.add(&b)).add(&c)).eql(try (try a.add(&b)).add(&c))); // Identify try expect(a.eql(try zero.add(&a))); try expect(b.eql(try zero.add(&b))); try expect(c.eql(try zero.add(&c))); try expect(a.eql(try a.add(&zero))); try expect(b.eql(try b.add(&zero))); try expect(c.eql(try c.add(&zero))); // Negation try expect(zero.eql(try a.neg().add(&a))); try expect(zero.eql(try b.neg().add(&b))); try expect(zero.eql(try c.neg().add(&c))); try expect(zero.eql(zero.neg())); // Commutativity try expect((try a.add(&b)).eql(try b.add(&a))); try expect((try a.add(&c)).eql(try c.add(&a))); try expect((try b.add(&c)).eql(try c.add(&b))); // Associativity and commutativity simultaneously try expect((try (try a.add(&b)).add(&c)).eql(try (try a.add(&c)).add(&b))); try expect((try (try a.add(&c)).add(&b)).eql(try (try b.add(&c)).add(&a))); // Doubling try expect((try a.add(&a)).eql(a.double())); try expect((try b.add(&b)).eql(b.double())); try expect((try c.add(&c)).eql(c.double())); try expect(zero.eql(zero.double())); try expect(zero.eql(zero.neg().double())); } } test "AffinePoint: fuzzing testing of arithmetic multiplication operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate a random affine point 'a'. var a = AffinePoint.rand(random); // Convert affine points to projective points. var b = Felt252.rand(random); var c = Felt252.rand(random); var zero = Felt252.zero(); var one = Felt252.one(); // Identity try expect((try a.mulByBitsBe(zero.toBitsBe())).eql(.{})); try expect((try a.mulByBitsBe(one.toBitsBe())).eql(a)); try expect((try a.mulByScalar(&zero)).eql(.{})); try expect((try a.mulByScalar(&one)).eql(a)); // Commutativity try expect((try (try a.mulByScalar(&b)).mulByScalar(&c)).eql( try (try a.mulByScalar(&c)).mulByScalar(&b), )); // Inverses try expect((try a.mulByScalar(&b.inverse().?.mul(&b))).eql( a, )); } }
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/elliptic_curve.zig
const std = @import("std"); /// Enum representing possible errors for elliptic curve operations. pub const ECError = error{ /// Error indicating division by zero. DivisionByZero, /// Error indicating that x-coordinates are equal. XCoordinatesAreEqual, /// Error indicating that the y-coordinate is zero. YCoordinateIsZero, }; const Felt252 = @import("./starknet.zig").Felt252; /// Constant representing the alpha value in the elliptic curve. pub const ALPHA = Felt252.one(); /// Constant representing the beta value in the elliptic curve. pub const BETA = Felt252.fromInt(u256, 3141592653589793238462643383279502884197169399375105820974944592307816406665); /// A type that represents a point (x,y) on an elliptic curve. pub const ECPoint = struct { const Self = @This(); /// x-coordinate of the elliptic curve point. x: Felt252 = Felt252.zero(), /// y-coordinate of the elliptic curve point. y: Felt252 = Felt252.zero(), /// Initializes an `ECPoint` with the specified x and y coordinates. /// /// # Parameters /// - `x`: The x-coordinate of the point. /// - `y`: The y-coordinate of the point. /// /// # Returns /// An initialized `ECPoint` with the provided coordinates. pub fn init(x: Felt252, y: Felt252) Self { return .{ .x = x, .y = y }; } /// Adds two points on an elliptic curve. /// /// # Arguments /// - `self` - The original point. /// - `point` - The point that we are adding. /// /// # Returns /// The sum of the elliptic curve points. pub fn ecAdd(self: *Self, point: ECPoint) ECError!ECPoint { // The x coordinates of the two points must be different. if (self.x.sub(&point.x).eql(Felt252.zero())) { return ECError.XCoordinatesAreEqual; } const x_diff = self.x.sub(&point.x); const y_diff = self.y.sub(&point.y); const x_sum = self.x.add(&point.x); const m = try divMod(y_diff, x_diff); const x = m.powToBigInt(2).sub(&x_sum); const y = m.mul(&self.x.sub(&x)).sub(&self.y); return .{ .x = x, .y = y }; } /// Given a point (x, y) return (x, -y). /// /// # Arguments /// - `self` - The point. /// /// # Returns /// The new elliptic curve point. pub fn ecNeg(self: *Self) ECPoint { return .{ .x = self.x, .y = -self.y }; } /// Doubles a point on an elliptic curve with the equation y^2 = x^3 + alpha*x + beta. /// /// # Arguments /// - `self` - The point. /// - `alpha` - The alpha parameter of the elliptic curve. /// /// # Returns /// The doubled elliptic curve point. pub fn ecDouble(self: *Self, alpha: Felt252) ECError!ECPoint { // Assumes the point is given in affine form (x, y) and has y != 0. if (self.y.eql(Felt252.zero())) { return ECError.YCoordinateIsZero; } const m = try self.ecDoubleSlope(alpha); const x = m.powToBigInt(2).sub(&self.x.mul(&Felt252.two())); const y = m.mul(&self.x.sub(&x)).sub(&self.y); return .{ .x = x, .y = y }; } /// Computes the slope of an elliptic curve with the equation y^2 = x^3 + alpha*x + beta, at /// the given point. /// /// # Arguments /// - `self` - The point. /// - `alpha` - The alpha parameter of the elliptic curve. /// /// # Returns /// The slope. pub fn ecDoubleSlope(self: *Self, alpha: Felt252) ECError!Felt252 { return try divMod( self.x.powToBigInt(2).mul(&Felt252.three()).add(&alpha), self.y.mul(&Felt252.two()), ); } /// Returns True if the point (x, y) is on the elliptic curve defined as /// y^2 = x^3 + alpha * x + beta, or False otherwise. /// /// # Arguments /// - `self` - The point. /// - `alpha` - The alpha parameter of the elliptic curve. /// - `beta` - The beta parameter of the elliptic curve. /// /// # Returns boolean. pub fn pointOnCurve(self: *const Self, alpha: Felt252, beta: Felt252) bool { const lhs = self.y.powToBigInt(2); const rhs = self.x.powToBigInt(3).add(&self.x.mul(&alpha).add(&beta)); return lhs.eql(rhs); } }; /// Divides one field element by another. /// Finds a nonnegative integer 0 <= x < p such that (m * x) % p == n. /// /// # Arguments /// - `m` - The first felt. /// - `n` - The second felt. /// /// # Returns /// The result of the field modulo division. pub fn divMod(m: Felt252, n: Felt252) ECError!Felt252 { return try m.div(n); } /// Calculates the result of the elliptic curve operation P + m * Q, /// where P = const_partial_sum, and Q = const_doubled_point /// are points on the elliptic curve defined as: /// y^2 = x^3 + alpha * x + beta. /// /// # Arguments /// - `const_partial_sum` - The point P. /// - `const_doubled_point` - The point Q. /// /// # Returns /// The result of the EC operation P + m * Q. pub fn ecOpImpl(const_partial_sum: ECPoint, const_doubled_point: ECPoint, m: Felt252, alpha: Felt252, height: u32) ECError!ECPoint { var slope = m.toU256(); var partial_sum = const_partial_sum; var doubled_point = const_doubled_point; for (0..height) |_| { if (doubled_point.x.sub(&partial_sum.x).eql(Felt252.zero())) { return ECError.XCoordinatesAreEqual; } if (slope & 1 != 0) { partial_sum = try partial_sum.ecAdd(doubled_point); } doubled_point = try doubled_point.ecDouble(alpha); slope = slope >> 1; } return partial_sum; } /// ************************************************************ /// * TESTS * /// ************************************************************ const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectError = std.testing.expectError; test "Elliptic curve math: compute double slope for valid point A" { const x = Felt252.fromInt(u256, 3143372541908290873737380228370996772020829254218248561772745122290262847573); const y = Felt252.fromInt(u256, 1721586982687138486000069852568887984211460575851774005637537867145702861131); const alpha = Felt252.one(); var to_double = ECPoint{ .x = x, .y = y }; const actual_slope = try to_double.ecDoubleSlope(alpha); const expected_slope = Felt252.fromInt(u256, 3601388548860259779932034493250169083811722919049731683411013070523752439691); try expectEqual(expected_slope, actual_slope); } test "Elliptic curve math: compute double slope for valid point B" { const x = Felt252.fromInt(u256, 1937407885261715145522756206040455121546447384489085099828343908348117672673); const y = Felt252.fromInt(u256, 2010355627224183802477187221870580930152258042445852905639855522404179702985); const alpha = Felt252.one(); var to_double = ECPoint{ .x = x, .y = y }; const actual_slope = try to_double.ecDoubleSlope(alpha); const expected_slope = Felt252.fromInt(u256, 2904750555256547440469454488220756360634457312540595732507835416669695939476); try expectEqual(expected_slope, actual_slope); } test "Elliptic curve math: EC double for valid point A" { const x = Felt252.fromInt(u256, 1937407885261715145522756206040455121546447384489085099828343908348117672673); const y = Felt252.fromInt(u256, 2010355627224183802477187221870580930152258042445852905639855522404179702985); const alpha = Felt252.one(); var to_double = ECPoint{ .x = x, .y = y }; const actual_ec_point = try to_double.ecDouble(alpha); const expected_x = Felt252.fromInt(u256, 58460926014232092148191979591712815229424797874927791614218178721848875644); const expected_y = Felt252.fromInt(u256, 1065613861227134732854284722490492186040898336012372352512913425790457998694); const expected_ec_point = ECPoint{ .x = expected_x, .y = expected_y }; try expectEqual(expected_ec_point, actual_ec_point); } test "Elliptic curve math: EC double for valid point B" { const x = Felt252.fromInt(u256, 3143372541908290873737380228370996772020829254218248561772745122290262847573); const y = Felt252.fromInt(u256, 1721586982687138486000069852568887984211460575851774005637537867145702861131); const alpha = Felt252.one(); var to_double = ECPoint{ .x = x, .y = y }; const actual_ec_point = try to_double.ecDouble(alpha); const expected_x = Felt252.fromInt(u256, 1937407885261715145522756206040455121546447384489085099828343908348117672673); const expected_y = Felt252.fromInt(u256, 2010355627224183802477187221870580930152258042445852905639855522404179702985); const expected_ec_point = ECPoint{ .x = expected_x, .y = expected_y }; try expectEqual(expected_ec_point, actual_ec_point); } test "Elliptic curve math: EC double for valid point C" { const x = Felt252.fromInt(u256, 634630432210960355305430036410971013200846091773294855689580772209984122075); const y = Felt252.fromInt(u256, 904896178444785983993402854911777165629036333948799414977736331868834995209); const alpha = Felt252.one(); var to_double = ECPoint{ .x = x, .y = y }; const actual_ec_point = try to_double.ecDouble(alpha); const expected_x = Felt252.fromInt(u256, 3143372541908290873737380228370996772020829254218248561772745122290262847573); const expected_y = Felt252.fromInt(u256, 1721586982687138486000069852568887984211460575851774005637537867145702861131); const expected_ec_point = ECPoint{ .x = expected_x, .y = expected_y }; try expectEqual(expected_ec_point, actual_ec_point); } test "Elliptic curve math: EC add for valid pair of points A and B" { const x_a = Felt252.fromInt(u256, 1183418161532233795704555250127335895546712857142554564893196731153957537489); const y_a = Felt252.fromInt(u256, 1938007580204102038458825306058547644691739966277761828724036384003180924526); const x_b = Felt252.fromInt(u256, 1977703130303461992863803129734853218488251484396280000763960303272760326570); const y_b = Felt252.fromInt(u256, 2565191853811572867032277464238286011368568368717965689023024980325333517459); var point_a = ECPoint{ .x = x_a, .y = y_a }; const point_b = ECPoint{ .x = x_b, .y = y_b }; const actual_ec_point = try point_a.ecAdd(point_b); const expected_x = Felt252.fromInt(u256, 1977874238339000383330315148209250828062304908491266318460063803060754089297); const expected_y = Felt252.fromInt(u256, 2969386888251099938335087541720168257053975603483053253007176033556822156706); const expected_ec_point = ECPoint{ .x = expected_x, .y = expected_y }; try expectEqual(expected_ec_point, actual_ec_point); } test "Elliptic curve math: EC add for valid pair of points C and D" { const x_c = Felt252.fromInt(u256, 3139037544796708144595053687182055617920475701120786241351436619796497072089); const y_c = Felt252.fromInt(u256, 2119589567875935397690285099786081818522144748339117565577200220779667999801); const x_d = Felt252.fromInt(u256, 3324833730090626974525872402899302150520188025637965566623476530814354734325); const y_d = Felt252.fromInt(u256, 3147007486456030910661996439995670279305852583596209647900952752170983517249); var point_c = ECPoint{ .x = x_c, .y = y_c }; const point_d = ECPoint{ .x = x_d, .y = y_d }; const actual_ec_point = try point_c.ecAdd(point_d); const expected_x = Felt252.fromInt(u256, 1183418161532233795704555250127335895546712857142554564893196731153957537489); const expected_y = Felt252.fromInt(u256, 1938007580204102038458825306058547644691739966277761828724036384003180924526); const expected_ec_point = ECPoint{ .x = expected_x, .y = expected_y }; try expectEqual(expected_ec_point, actual_ec_point); } test "Elliptic curve math: point_is_on_curve_a" { const x = Felt252.fromInt(u256, 874739451078007766457464989774322083649278607533249481151382481072868806602); const y = Felt252.fromInt(u256, 152666792071518830868575557812948353041420400780739481342941381225525861407); var point = ECPoint{ .x = x, .y = y }; try expect(point.pointOnCurve(ALPHA, BETA)); } test "Elliptic curve math: point_is_on_curve_b" { const x = Felt252.fromInt(u256, 3139037544796708144595053687182055617920475701120786241351436619796497072089); const y = Felt252.fromInt(u256, 2119589567875935397690285099786081818522144748339117565577200220779667999801); var point = ECPoint{ .x = x, .y = y }; try expect(point.pointOnCurve(ALPHA, BETA)); } test "Elliptic curve math: point_is_not_on_curve_a" { const x = Felt252.fromInt(u256, 874739454078007766457464989774322083649278607533249481151382481072868806602); const y = Felt252.fromInt(u256, 152666792071518830868575557812948353041420400780739481342941381225525861407); var point = ECPoint{ .x = x, .y = y }; try expect(!point.pointOnCurve(ALPHA, BETA)); } test "Elliptic curve math: point_is_not_on_curve_b" { const x = Felt252.fromInt(u256, 3139037544756708144595053687182055617927475701120786241351436619796497072089); const y = Felt252.fromInt(u256, 2119589567875935397690885099786081818522144748339117565577200220779667999801); var point = ECPoint{ .x = x, .y = y }; try expect(!point.pointOnCurve(ALPHA, BETA)); } test "Elliptic curve math: compute_ec_op_impl_valid_a" { const partial_sum = ECPoint{ .x = Felt252.fromInt(u256, 3139037544796708144595053687182055617920475701120786241351436619796497072089), .y = Felt252.fromInt(u256, 2119589567875935397690285099786081818522144748339117565577200220779667999801), }; const doubled_point = ECPoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989774322083649278607533249481151382481072868806602), .y = Felt252.fromInt(u256, 152666792071518830868575557812948353041420400780739481342941381225525861407), }; const m = Felt252.fromInt(u8, 34); const height = 256; const actual_ec_point = try ecOpImpl(partial_sum, doubled_point, m, ALPHA, height); const expected_ec_point = ECPoint{ .x = Felt252.fromInt(u256, 1977874238339000383330315148209250828062304908491266318460063803060754089297), .y = Felt252.fromInt(u256, 2969386888251099938335087541720168257053975603483053253007176033556822156706), }; try expectEqual(actual_ec_point, expected_ec_point); } test "Elliptic curve math: compute_ec_op_impl_valid_b" { const partial_sum = ECPoint{ .x = Felt252.fromInt(u256, 2962412995502985605007699495352191122971573493113767820301112397466445942584), .y = Felt252.fromInt(u256, 214950771763870898744428659242275426967582168179217139798831865603966154129), }; const doubled_point = ECPoint{ .x = Felt252.fromInt(u256, 874739451078007766457464989774322083649278607533249481151382481072868806602), .y = Felt252.fromInt(u256, 152666792071518830868575557812948353041420400780739481342941381225525861407), }; const m = Felt252.fromInt(u8, 34); const height = 256; const actual_ec_point = try ecOpImpl(partial_sum, doubled_point, m, ALPHA, height); const expected_ec_point = ECPoint{ .x = Felt252.fromInt(u256, 2778063437308421278851140253538604815869848682781135193774472480292420096757), .y = Felt252.fromInt(u256, 3598390311618116577316045819420613574162151407434885460365915347732568210029), }; try expectEqual(actual_ec_point, expected_ec_point); } test "Elliptic curve math: compute_ec_op_invalid_same_x_coordinate" { const partial_sum = ECPoint{ .x = Felt252.one(), .y = Felt252.fromInt(u8, 9), }; const doubled_point = ECPoint{ .x = Felt252.one(), .y = Felt252.fromInt(u8, 12), }; const m = Felt252.fromInt(u8, 34); const height = 256; const actual_ec_point = ecOpImpl(partial_sum, doubled_point, m, ALPHA, height); try expectError(ECError.XCoordinatesAreEqual, actual_ec_point); }
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/fields.zig
const std = @import("std"); const arithmetic = @import("./arithmetic.zig"); const bigInt = @import("./biginteger.zig").bigInt; pub const FieldError = error{ DivisionByZero, }; /// Represents a finite field with a specified modulus. /// /// This finite field struct encapsulates operations and properties related to arithmetic operations modulo a given modulus. /// It provides methods for arithmetic operations on field elements within the finite field. /// /// # Parameters /// - `n_limbs`: The number of limbs used to represent a field element. /// - `modulo`: The modulus of the finite field. /// /// # Returns /// A finite field struct with the specified modulus. pub fn Field(comptime n_limbs: usize, comptime modulo: u256) type { return struct { const Self = @This(); /// Represents a big integer with a specified number of limbs. const big_int = bigInt(n_limbs); /// Represents the modular inverse of `modulus` modulo 2^64. /// /// This value is precomputed and represents the modular inverse of `modulus` modulo 2^64. It is used in Montgomery exponentiation. pub const Inv = computeInvMontgomery(); /// Represents the value of R^2 modulo the modulus. /// /// This value is precomputed and represents the square of R modulo the modulus. It is used for Montgomery operations. /// /// Explanation: /// Let `M` be the power of 2^64 nearest to `Self::MODULUS_BITS`. /// Then `R = M % Self::MODULUS`. pub const R2 = computeR2Montgomery(); /// Represents the value one less than the modulus. /// /// This value is calculated as the value of the modulus minus one and is used for certain arithmetic operations. pub const MaxField: Self = .{ .fe = big_int.fromInt(u256, modulo - 1) }; /// Represents the modulus in non-Montgomery format. /// /// This value is the modulus of the finite field represented in a non-Montgomery format. pub const Modulus = big_int.fromInt(u256, modulo); /// Represents the number of bytes required to store a field element. /// /// This value indicates the number of bytes required to store a single field element. pub const BytesSize = n_limbs * @sizeOf(u64); /// Represents half of the modulus value. /// /// This value is calculated as (modulo - 1) divided by 2 and is used in certain arithmetic computations. pub const QMinOneDiv2 = (modulo - 1) / 2; /// Represents the number of bits in each limb. /// /// This value indicates the number of bits in each limb used to represent a field element, typically 64 for u64. pub const Bits: usize = @bitSizeOf(u64); /// Represents the 2-adic valuation of the modulus. /// /// The 2-adic valuation of a number represents the highest power of 2 that divides that number. /// In the context of a modulus, it indicates how many times the modulus can be divided by 2 before reaching an odd number. /// This value is relevant for certain arithmetic computations and algorithms, such as Montgomery operations. pub const TwoAdicity = Modulus.twoAdicValuation(); /// Represents a field element in the finite field. /// /// This field element is a member of the finite field and is represented by a big integer with a specified number of limbs. fe: big_int = .{}, /// Creates a `Field` element from an integer value. /// /// This function constructs a `Field` element from an integer value of type `T`. The resulting field element is /// represented in Montgomery form, ensuring compatibility with the defined finite field (`Field`) and its modulo value. /// /// # Arguments: /// - `T`: The type of the integer value. /// - `num`: The integer value to create the `Field` element from. /// /// # Returns: /// A new `Field` element in Montgomery form representing the converted integer. /// /// Errors: /// If `num` is negative, an assertion failure occurs. /// If `T` represents an integer type with more than 128 bits, an error is raised due to unsupported integer sizes. pub fn fromInt(comptime T: type, num: T) Self { return toMontgomery(big_int.fromInt(T, num).rem(&Modulus)); } /// Generates a random field element within the finite field using a provided random number generator. /// /// This function generates a random field element within the specified finite field using a provided random number generator (`r`). /// The random field element is obtained by converting a randomly generated integer value to a field element within the finite field. /// /// # Arguments: /// - `r`: The random number generator used to generate the random integer value. /// /// # Returns: /// A random field element within the finite field. pub fn rand(r: std.Random) Self { return fromInt(u256, r.int(u256)); } /// Computes the value of -M^{-1} mod 2^64. /// /// This function calculates the modular inverse of `-MODULUS` modulo 2^64. /// The computation involves exponentiating by the multiplicative group order, which is Euler's totient function (φ(2^64)) - 1. /// /// # Returns: /// The modular inverse of `-MODULUS` modulo 2^64. /// /// Remarks: /// - This function is used in Montgomery exponentiation to compute the R value. /// - The computation involves exponentiating by the multiplicative group order, which is Euler's totient function (φ(2^64)) - 1. pub fn computeInvMontgomery() u64 { comptime { // Initialize the modular inverse. var inv: u64 = 1; // Iterate through 63 times. for (0..63) |_| { // Square the modular inverse. inv *%= inv; // Multiply the modular inverse by the least significant limb of the modulus. inv *%= Modulus.limbs[0]; } // Negate the computed modular inverse. return -%inv; } } /// Computes R^2 in Montgomery domain. /// /// Montgomery multiplication requires precomputing R^2 mod modulus, where R is a power of 2 /// such that R > modulus. R^2 is used to convert a product back to the Montgomery domain. /// /// Returns: /// A big integer representing R^2 in the Montgomery domain. pub fn computeR2Montgomery() big_int { comptime { @setEvalBranchQuota(50000); // Initialize the loop counter var l: u32 = 0; // Define `c` as the largest power of 2 smaller than `modulus` while (l < n_limbs * Bits) { // Check if modulus shifted right by `l` bits is not equal to zero if (Modulus.shr(l).ne(.{})) break; l += 1; } var c = big_int.one().shl(l); // Double `c` and reduce modulo `modulus` until getting // `2^{2 * number_limbs * word_size}` mod `modulus` var i: usize = 1; while (i <= 2 * n_limbs * Bits - l) { // Double `c` const double_c = c.addWithCarry(&c); // Update `c` using modular reduction c = if (Modulus.lte(&double_c[0]) or double_c[1]) double_c[0].subWithBorrow(&Modulus)[0] else double_c[0]; i += 1; } return c; } } /// Converts a `bigInt` value to Montgomery representation. /// /// This function converts a `bigInt` value to Montgomery representation, which is essential for arithmetic operations /// in finite fields. The resulting value is compatible with the defined finite field (`Field`) and its modulo value. /// /// If the input value is zero, it returns the Montgomery representation of zero. /// /// # Arguments: /// - `value`: The `bigInt` value to be converted to Montgomery representation. /// /// # Returns: /// A new `Field` element in Montgomery form representing the input value. pub fn toMontgomery(value: big_int) Self { // Initialize a field element with the given value var r: Self = .{ .fe = value }; // Check if the value is zero if (r.isZero()) { return r; } else { // If the value is non-zero, multiply it by R^2 in Montgomery form r.mulAssign(&.{ .fe = R2 }); return r; } } /// Converts a field element from Montgomery representation to a `bigInt` value. /// /// This function converts a field element from Montgomery representation to a `bigInt` value, allowing /// operations with non-Montgomery values or external usage. It reverses the Montgomery reduction /// process to obtain the original value represented by the field element. /// /// # Returns: /// A `bigInt` value representing the field element in non-Montgomery form. pub fn toBigInt(self: Self) big_int { // Initialize an array to store the limbs of the resulting value var r = self.fe.limbs; // Iterate over the limbs of the field element inline for (0..n_limbs) |i| { // Compute the Montgomery factor k const k: u64 = r[i] *% comptime Inv; var carry: u64 = 0; // Multiply the current limb with k and the modulus, adding the carry _ = arithmetic.macWithCarry(r[i], k, Modulus.limbs[0], &carry); // Iterate over the remaining limbs and perform multiplication with carry inline for (1..n_limbs) |j| r[(i + j) % n_limbs] = arithmetic.macWithCarry(r[(i + j) % n_limbs], k, Modulus.limbs[j], &carry); // Store the final carry r[i % n_limbs] = carry; } // Return the resulting `bigInt` value return .{ .limbs = r }; } /// This function returns a field element representing zero. /// /// Returns: /// - A field element with a value of zero. /// /// Notes: /// - This function is inline, ensuring efficient compilation and execution. /// - The returned field element has all limbs initialized to zero. pub inline fn zero() Self { comptime { return .{}; } } /// Get the field element representing one. /// /// Returns a field element with a value of one. pub inline fn one() Self { comptime { return toMontgomery(big_int.fromInt(u8, 1)); } } /// Get the field element representing two. /// /// Returns a field element with a value of two. pub inline fn two() Self { comptime { return toMontgomery(big_int.fromInt(u8, 2)); } } /// Get the field element representing three. /// /// Returns a field element with a value of three. pub inline fn three() Self { comptime { return toMontgomery(big_int.fromInt(u8, 3)); } } /// Converts a byte array into a field element in Montgomery representation. /// /// This function takes a byte array as input and converts it into a field element in Montgomery representation. /// The resulting field element is suitable for arithmetic operations within the defined finite field. /// /// # Arguments: /// - `bytes`: A byte array representing the field element. /// /// # Returns: /// A field element in Montgomery representation. pub fn fromBytesLe(bytes: [BytesSize]u8) Self { return toMontgomery(big_int.fromBytesLe(bytes)); } /// Converts a byte array into a field element in Montgomery representation. /// /// This function converts a byte array into a field element in Montgomery representation, allowing /// operations with Montgomery values or external usage. /// /// # Arguments: /// - `bytes`: A byte array representing the field element. /// /// # Returns: /// A field element in Montgomery representation. pub fn fromBytesBe(bytes: [BytesSize]u8) Self { return toMontgomery(big_int.fromBytesBe(bytes)); } /// Converts the field element to a little-endian bits array. /// /// This function converts the field element to a little-endian bits array, suitable for serialization purposes. /// /// # Returns: /// A little-endian bits array representing the field element. pub fn toBitsLe(self: Self) [@bitSizeOf(u256)]bool { return self.toBigInt().toBitsLe(); } /// Converts the field element to a big-endian bits array. /// /// This function converts the field element to a big-endian bits array, suitable for serialization purposes. /// /// # Returns: /// A big-endian bits array representing the field element. pub fn toBitsBe(self: Self) [@bitSizeOf(u256)]bool { return self.toBigInt().toBitsBe(); } /// Converts the field element to a little-endian byte array. /// /// This function converts the field element to a little-endian byte array, suitable for serialization purposes. /// /// # Returns: /// A little-endian byte array representing the field element. pub fn toBytesLe(self: Self) [BytesSize]u8 { return self.toBigInt().toBytesLe(); } /// Converts the field element to a big-endian byte array. /// /// This function converts the field element to a big-endian byte array, suitable for serialization purposes. /// /// # Returns: /// A big-endian byte array representing the field element. pub fn toBytesBe(self: Self) [BytesSize]u8 { return self.toBigInt().toBytesBe(); } /// Retrieves the minimum number of bits required to represent the field element. /// /// This function calculates and returns the minimum number of bits needed to represent the field element. /// It considers the current field element's value and returns the corresponding bit count. /// /// # Returns: /// The minimum number of bits needed to represent the field element. pub fn numBitsLe(self: Self) u64 { return self.toBigInt().numBitsLe(); } /// Check if the field element is lexicographically largest. /// /// Determines whether the field element is larger than half of the field's modulus. pub fn lexographicallyLargest(self: Self) bool { return self.toU256() > QMinOneDiv2; } /// Doubles a field element. /// /// This function doubles the value of the provided field element (`self`) and returns the result. /// It effectively performs the addition of a field element to itself. /// /// Parameters: /// - self: A pointer to the field element to be doubled. /// /// Returns: /// - The doubled field element. /// /// Notes: /// - This function does not modify the original field element; it returns a new field element representing the doubled value. pub fn double(self: *const Self) Self { // Dereference the pointer to obtain the actual field element var a = self.*; // Double the field element using the doubleAssign function a.doubleAssign(); // Return the doubled field element return a; } /// Doubles a field element in place. /// /// This function doubles the value of the provided field element (`self`) in place, modifying the original field element. /// It effectively performs the addition of a field element to itself. /// /// After doubling, if the result exceeds the modulus, it is reduced by subtracting the modulus to ensure it remains within the finite field. /// /// Parameters: /// - self: A pointer to the field element to be doubled. /// /// Returns: /// - void /// /// Notes: /// - This function modifies the original field element in place, doubling its value. /// - If the doubling result exceeds the modulus, it is reduced to remain within the finite field. pub fn doubleAssign(self: *Self) void { // Perform the doubling operation, effectively multiplying the field element by 2. const carry = self.fe.mul2Assign(); // Check if the result needs to be reduced modulo the modulus. // If the modulus has a spare bit (indicating it's not a power of two), reduction is necessary. if (comptime modulusHasSpareBit()) { // Reduce the result by subtracting the modulus to ensure it remains within the finite field. self.subModulusAssign(); } else { // If there was a carry during addition or the result exceeds the modulus, // reduce the result modulo the modulus to maintain field integrity. self.subModulusWithCarryAssign(carry); } } /// Calculating mod sqrt /// TODO: add precomution? pub fn sqrt(self: Self) ?Self { const v = arithmetic.tonelliShanks(self.toU256(), modulo); return if (v[2]) fromInt(u256, @intCast(v[0])) else null; } /// Determines whether the current modulus allows for a specific optimization in modular multiplication. /// /// This function checks if the highest bit of the modulus is zero and not all of the remaining bits are set, /// which is a condition required for a specific optimization in modular multiplication. /// /// The optimization aims to reduce the number of additions needed in CIOS Montgomery multiplication, /// resulting in a significant speed improvement for most moduli. /// /// # Returns: /// `true` if the optimization can be applied to the current modulus, `false` otherwise. pub fn canUseNoCarryMulOptimization() bool { comptime { // Check if all remaining bits are one var all_remaining_bits_are_one = Modulus.limbs[n_limbs - 1] == std.math.maxInt(u64) >> 1; for (1..n_limbs) |i| { all_remaining_bits_are_one = all_remaining_bits_are_one and (Modulus.limbs[n_limbs - i - 1] == std.math.maxInt(u64)); } // Return true if both conditions are met return modulusHasSpareBit() and !all_remaining_bits_are_one; } } /// Determines whether the modulus has a spare bit. /// /// This function checks if the highest bit of the modulus is zero, indicating that there is a spare bit available. /// The spare bit condition is crucial for certain optimizations in modular arithmetic operations. /// /// # Returns /// /// `true` if the highest bit of the modulus is zero, indicating the presence of a spare bit; otherwise, `false`. /// /// # Comptime /// /// This function is evaluated at compile time to determine the presence of a spare bit in the modulus. /// It ensures that the check is performed statically during compilation. pub fn modulusHasSpareBit() bool { comptime { // Check if the highest bit of the modulus is zero return Modulus.limbs[n_limbs - 1] >> 63 == 0; } } /// Performs multiplication of two field elements and returns the result. /// /// This function takes two pointers to field elements (`self` and `rhs`), /// multiplies them together, and returns the result as a new field element. /// /// # Arguments: /// - `self`: A pointer to the first field element. /// - `rhs`: A pointer to the second field element. /// /// # Returns: /// A new field element representing the result of the multiplication. pub fn mul(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual field element var a = self.*; // Call the `mulAssign` method to perform the multiplication in place a.mulAssign(rhs); // Return the result return a; } /// Performs modular multiplication using Montgomery multiplication algorithm. /// /// Montgomery multiplication is a method used to compute modular products efficiently /// without expensive divisions, particularly beneficial for cryptographic protocols /// involving large moduli. The function takes two integers `a` and `b` and computes /// their modular product with respect to a given modulus `N`. The function assumes that /// the inputs `a`, `b`, and `N` are all in Montgomery form. /// /// The Montgomery form of an integer `a` with respect to a chosen radix `R` is `a * R mod N`. /// This representation allows for faster modular products, where `R` is carefully chosen /// such that `gcd(R, N) = 1`. /// /// The algorithm alternates between the multiplication and reduction steps involved in /// Montgomery modular multiplication, rather than carrying out full multiplication followed by /// reduction. /// /// Additional "no-carry optimization" is implemented, as outlined [here](https://hackmd.io/@gnark/modular_multiplication) /// as modulus has (a) a non-zero most significant bit, and (b) at least one /// zero bit in the rest of the modulus. /// /// For another reference implementation, see [arkworks-rs/algebra](https://github.com/arkworks-rs/algebra/blob/3a6156785e12eeb9083a7a402ac037de01f6c069/ff/src/fields/models/fp/montgomery_backend.rs#L151) pub inline fn mulAssign(self: *Self, rhs: *const Self) void { // TODO: add CIOS implementation in case no carry mul optimization cannot be used if (comptime canUseNoCarryMulOptimization()) { // Initialize the result array var r = [_]u64{0} ** n_limbs; // Iterate over the digits of the right-hand side operand inline for (0..n_limbs) |i| { // Perform the first multiplication and accumulation var carry1: u64 = 0; r[0] = arithmetic.mac(r[0], self.fe.limbs[0], rhs.fe.limbs[i], &carry1); // Compute the Montgomery factor k and perform the corresponding multiplication and reduction const k: u64 = r[0] *% comptime Inv; var carry2: u64 = 0; arithmetic.macDiscard(r[0], k, comptime Modulus.limbs[0], &carry2); // Iterate over the remaining digits and perform the multiplications and accumulations inline for (1..n_limbs) |j| { r[j] = arithmetic.macWithCarry(r[j], self.fe.limbs[j], rhs.fe.limbs[i], &carry1); r[j - 1] = arithmetic.macWithCarry(r[j], k, Modulus.limbs[j], &carry2); } // Add the final carries r[n_limbs - 1] = carry1 + carry2; } // Store the result back into the original object @memcpy(&self.fe.limbs, &r); // Perform modulus subtraction if needed self.subModulusAssign(); } } /// This function negates the provided field element and returns the result as a new field element. /// /// Parameters: /// - self: A pointer to the field element to be negated. /// /// Returns: /// - The negated field element. /// /// Notes: /// - The provided field element is dereferenced to obtain the actual field element. /// - The negation is performed in place using the `negAssign` method. /// - The negated field element is returned as the result. pub fn neg(self: *const Self) Self { // Dereference the pointer to obtain the actual field element var a = self.*; // Negate the field element using the negAssign function a.negAssign(); // Return the result return a; } /// This function negates the provided field element in place, modifying the original field element. /// /// Parameters: /// - self: A pointer to the field element to be negated. /// /// Returns: /// - void /// /// Notes: /// - If the provided field element is not zero, its negation is computed by subtracting it from the modulus. /// - The result is stored back into the original field element. pub fn negAssign(self: *Self) void { // Check if the field element is non-zero if (!self.isZero()) { // Create a temporary big integer representing the modulus var tmp = comptime Modulus; // Subtract the field element from the modulus with borrow and assign the result to tmp _ = tmp.subWithBorrowAssign(&self.fe); // Update the original field element with the negated value self.*.fe = tmp; } } /// This function checks if the provided field element is equal to zero. /// /// Parameters: /// - self: A pointer to the field element to be checked. /// /// Returns: /// - true if the field element is zero, false otherwise. /// /// Notes: /// - The function internally uses the `eql` method to compare the field element with zero. /// - Returns true if the field element is equal to zero, indicating it is zero. pub fn isZero(self: *const Self) bool { return self.eql(.{}); } /// Check if the field element is one. /// /// Determines if the current field element is equal to one. pub fn isOne(self: *const Self) bool { return self.eql(one()); } pub fn modInverse(operand: Self, modulus: Self) !Self { const ext = arithmetic.extendedGCD(@bitCast(operand.toU256()), @bitCast(modulus.toU256())); if (ext.gcd != 1) { @panic("GCD must be one"); } const result = if (ext.x < 0) ext.x + @as(i256, @bitCast(modulus.toU256())) else ext.x; return fromInt(u256, @bitCast(result)); } /// Computes the square of a finite field element. /// /// This function computes the square of the given finite field element using the `squareAssign` method /// and returns the result as a new field element. /// /// # Arguments /// /// - `self`: A pointer to the finite field element to be squared. /// /// # Returns /// /// A new finite field element representing the square of the input element. pub fn square(self: *const Self) Self { // Dereference the pointer to obtain the actual field element var a = self.*; // Call the `squareAssign` method to compute the square in place a.squareAssign(); // Return the result return a; } /// Computes the square of the current finite field element in place. /// /// This function calculates the square of the current finite field element and updates the value in place. /// /// It involves various steps including intermediate multiplication, carry propagation, squaring, and Montgomery reduction. /// The algorithm efficiently utilizes inline loops for performance optimization. /// Additionally, it supports modulus subtraction if the modulus has a spare bit. pub fn squareAssign(self: *Self) void { const MulBuffer = struct { const S = @This(); /// A tuple to store intermediate multiplication results. buf: std.meta.Tuple(&.{ [n_limbs]u64, [n_limbs]u64 }) = .{ [_]u64{0} ** n_limbs, [_]u64{0} ** n_limbs }, /// Retrieves a pointer to the buffer element at the specified index. fn getBuf(s: *S, index: usize) *u64 { return if (index < n_limbs) &s.buf[0][index] else &s.buf[1][index - n_limbs]; } }; var r: MulBuffer = .{}; var carry: u64 = 0; // Perform multiplication inline for (0..n_limbs - 1) |i| { inline for (i + 1..n_limbs) |j| { r.getBuf(i + j).* = arithmetic.macWithCarry(r.getBuf(i + j).*, self.fe.limbs[i], self.fe.limbs[j], &carry); } r.buf[1][i] = carry; carry = 0; } // Adjust carry for the last limb r.buf[1][n_limbs - 1] = r.buf[1][n_limbs - 2] >> 63; // Propagate carries inline for (2..2 * n_limbs - 1) |i| r.getBuf(2 * n_limbs - i).* = (r.getBuf(2 * n_limbs - i).* << 1) | (r.getBuf(2 * n_limbs - (i + 1)).* >> 63); r.buf[0][1] <<= 1; // Perform squaring inline for (0..n_limbs) |i| { r.getBuf(2 * i).* = arithmetic.macWithCarry(r.getBuf(2 * i).*, self.fe.limbs[i], self.fe.limbs[i], &carry); carry = arithmetic.adc(u64, r.getBuf(2 * i + 1), 0, carry); } // Montgomery reduction var carry2: u64 = 0; // Reduce and update buffer inline for (0..n_limbs) |i| { const k: u64 = r.buf[0][i] *% comptime Inv; carry = 0; arithmetic.macDiscard(r.buf[0][i], k, Modulus.limbs[0], &carry); inline for (1..n_limbs) |j| r.getBuf(j + i).* = arithmetic.macWithCarry(r.getBuf(j + i).*, k, Modulus.limbs[j], &carry); carry2 = arithmetic.adc(u64, &r.buf[1][i], carry, carry2); } // Copy result back to the field element @memcpy(&self.fe.limbs, &r.buf[1]); // Perform modulus subtraction if needed if (comptime modulusHasSpareBit()) self.subModulusAssign(); } /// Raise a field element to a general power. /// /// Computes the field element raised to a general power specified by the `exponent`. /// /// # Parameters /// - `exponent`: The exponent to raise the field element to. /// /// # Returns /// The result of raising the field element to the specified exponent. pub fn powToInt(self: Self, exponent: u256) Self { // Initialize result as the identity element var res = one(); // Copy the exponent for manipulation var exp = exponent; // Copy the base field element for manipulation var base = self; // Perform binary exponentiation algorithm while (exp > 0) : (exp /= 2) { // If current bit of exponent is 1, multiply result by base if (exp & 1 == 1) res.mulAssign(&base); // Square the base for the next iteration base.squareAssign(); } // Return the computed result return res; } /// Raise a field element to a power specified by a big integer. /// /// Computes the field element raised to a power specified by a big integer exponent. /// /// # Parameters /// - `exponent`: The big integer exponent to raise the field element to. /// /// # Returns /// The result of raising the field element to the specified big integer exponent. pub fn powToBigInt(self: *const Self, exponent: big_int) Self { // Copy the field element to a mutable variable var a = self.*; // Raise the field element to the specified big integer exponent a.powAssign(&exponent); // Return the result return a; } /// Raise a field element to a power specified by a big integer and assigns the result to the field element itself. /// /// Computes the field element raised to a power specified by a big integer exponent and assigns the result to the field element itself. /// /// # Parameters /// - `exponent`: The big integer exponent to raise the field element to. pub fn powAssign(self: *Self, exponent: *const big_int) void { // If the exponent is zero, assign 1 to the field element and return if (exponent.isZero()) { self.* = comptime one(); return; } // If the exponent is 1, no computation needed, return if (exponent.eql(comptime big_int.one())) return; // Copy the exponent for manipulation var exp = exponent.*; // Perform binary exponentiation algorithm while (exp.bitAnd(&comptime big_int.one()).eql(comptime .{})) { // Square the field element for each bit of exponent self.squareAssign(); // Divide the exponent by 2 for the next iteration exp.shrAssign(1); } // If exponent is zero then return, end of the calculation if (exp.isZero()) return; // Copy the base field element for manipulation var base = self.*; // Divide the exponent by 2 for the first iteration exp.shrAssign(1); // While exponent not equal to zero while (exp.ne(comptime .{})) { // Square the base base.squareAssign(); // If current bit of exponent is 1, multiply field element by base if (exp.bitAnd(&comptime big_int.one()).eql(comptime big_int.one())) { self.mulAssign(&base); } // Divide the exponent by 2 for the next iteration exp.shrAssign(1); } } /// Batch inversion of multiple field elements. /// /// Performs batch inversion of a slice of field elements in place. pub fn batchinverse(out: []Self, in: []const Self) !void { std.debug.assert(out.len == in.len); var acc = one(); for (0..in.len) |i| { out[i] = acc; acc = acc.mul(&in[i]); } acc = acc.inverse() orelse return error.CantInvertZeroElement; for (0..in.len) |i| { out[in.len - i - 1] = out[in.len - i - 1].mul(&acc); acc = acc.mul(&in[in.len - i - 1]); } } /// Checks if the field element is greater than or equal to the modulus. /// /// This function compares the field element `self` with the modulus of the finite field. /// It returns true if `self` is greater than or equal to the modulus, and false otherwise. /// /// Parameters: /// - self: A pointer to the field element to be checked. /// /// Returns: /// - true if the field element is greater than or equal to the modulus, false otherwise. pub fn isGeModulus(self: *const Self) bool { return self.fe.gte(&Modulus); } /// Subtracts the modulus from the field element in place. /// /// This function subtracts the modulus from the field element `self` if `self` is greater than or equal to the modulus. /// It performs the subtraction operation in place and modifies `self`. /// /// Parameters: /// - self: A pointer to the field element from which the modulus will be subtracted. /// /// Returns: /// - void /// /// Notes: /// - This function modifies the field element in place. pub fn subModulusAssign(self: *Self) void { if (self.isGeModulus()) _ = self.fe.subWithBorrowAssign(&Modulus); } /// Subtracts the modulus from the field element with carry in place. /// /// This function subtracts the modulus from the field element `self` with an optional carry bit. /// If the `carry` parameter is true or if `self` is greater than or equal to the modulus, the subtraction is performed. /// It performs the subtraction operation in place and modifies `self`. /// /// Parameters: /// - self: A pointer to the field element from which the modulus will be subtracted. /// - carry: A boolean flag indicating whether there was a carry from a previous operation. /// /// Returns: /// - void /// /// Notes: /// - This function modifies the field element in place. pub fn subModulusWithCarryAssign(self: *Self, carry: bool) void { if (carry or self.isGeModulus()) _ = self.fe.subWithBorrowAssign(&Modulus); } /// Adds a field element to another field element and returns the result. /// /// This function takes a pointer to the first field element (`self`) and adds another field element (`rhs`) to it. /// It then returns the result of the addition operation as a new field element. /// /// Parameters: /// - self: A pointer to the first field element. /// - rhs: The second field element to be added to the first. /// /// Returns: /// - The result of the addition operation as a new field element. pub fn add(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual field element. var a = self.*; // Perform the addition operation by calling the `addAssign` method. a.addAssign(rhs); // Return the result of the addition operation. return a; } /// Adds a field element to the current field element and assigns the result. /// /// This function takes a pointer to the current field element (`self`) and adds another field element (`rhs`) to it. /// It performs the addition operation in place, modifying the current field element. /// /// After the addition, if the result exceeds the modulus, it is reduced by subtracting the modulus to ensure it remains within the finite field. /// /// Parameters: /// - self: A pointer to the current field element to which the addition result will be assigned. /// - rhs: A pointer to the field element to be added. /// /// Returns: /// - void /// /// Notes: /// - This function modifies the current field element in place. /// - If the addition result exceeds the modulus, it is reduced to remain within the finite field. pub fn addAssign(self: *Self, rhs: *const Self) void { // Perform the addition operation, ensuring it does not exceed the backing capacity. const carry = self.fe.addWithCarryAssign(&rhs.fe); // Check if the result needs to be reduced modulo the modulus. // If the modulus has a spare bit (indicating it's not a power of two), reduction is necessary. if (comptime modulusHasSpareBit()) { // Reduce the result by subtracting the modulus to ensure it remains within the finite field. self.subModulusAssign(); } else { // If there was a carry during addition or the result exceeds the modulus, // reduce the result modulo the modulus to maintain field integrity. self.subModulusWithCarryAssign(carry); } } /// Subtracts a field element from another field element. /// /// This function subtracts a field element `rhs` from another field element `self`. /// It dereferences the pointers `self` and `rhs` to obtain the actual field elements, /// performs the subtraction operation using the `subAssign` function, and returns the result. /// /// Parameters: /// - self: A pointer to the first field element from which the second field element will be subtracted. /// - rhs: A pointer to the second field element that will be subtracted from the first field element. /// /// Returns: /// - The result of the subtraction operation as a new field element. /// /// Notes: /// - This function does not modify the original field elements; it only performs the subtraction operation. /// - The subtraction operation is performed using the `subAssign` function, which modifies the first field element in place. pub fn sub(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual field element var a = self.*; // Perform the subtraction operation in place a.subAssign(rhs); // Return the result return a; } /// Subtracts a bigint from another bigint and assigns the result to the first bigint. /// /// This function subtracts a bigint `b` from another bigint `a` and assigns the result to `a`. /// If `b` is greater than `a`, it adds the modulus to `a` first to ensure correct subtraction in a finite field. /// /// Parameters: /// - a: A pointer to the bigint from which `b` will be subtracted, and the result will be assigned. /// - b: A pointer to the bigint that will be subtracted from `a`. /// /// Returns: /// - void /// /// Notes: /// - If `b` is greater than `a`, the modulus of the finite field is added to `a` before subtraction to ensure correct arithmetic in a finite field context. /// - The subtraction operation is performed in place, and the result is assigned to `a`. pub fn subAssign(self: *Self, rhs: *const Self) void { // If b > a, add the modulus to `a` first. if (rhs.fe.cmp(&self.fe) == .gt) _ = self.fe.addWithCarryAssign(&Modulus); // Perform the subtraction operation _ = self.fe.subWithBorrowAssign(&rhs.fe); } /// Computes the multiplicative inverse of a given element in a finite field using the binary Extended Euclidean Algorithm (BEA). /// /// Reference: Efficient Software-Implementation of Finite Fields with Applications to Cryptography /// DOI: DOI: 10.1007/s10440-006-9046-1 /// /// This function implements the binary Extended Euclidean Algorithm (BEA) to compute the multiplicative inverse of a given element in a finite field. /// It follows the steps outlined in the BEA, including successive division and modular arithmetic operations, to determine the inverse. /// /// BEA does not require integer divisions but only simple operations such as shifts and additions /// /// Parameters: /// - self: A pointer to the element for which the inverse is to be computed. /// /// Returns: /// - On success: A structure containing the computed inverse. /// - On failure (if the input is zero): `null`. /// /// Notes: /// - The binary Extended Euclidean Algorithm (BEA) is a general and efficient method for computing multiplicative inverses in finite fields. /// - Montgomery parameters are used to optimize the computation, improving performance on digital computers. /// - Overflow handling is performed to ensure correct arithmetic operations during the inversion process. pub fn inverse(self: *const Self) ?Self { // Check if the input is zero if (self.isZero()) return null; // Constant representing the value 1 in the field const o = comptime big_int.one(); var u = self.fe; var v = Modulus; var b: Self = .{ .fe = R2 }; var c = zero(); // Iterate while both u and v are not one while (!u.eql(o) and !v.eql(o)) { // Perform operations while u is even while (u.isEven()) { u.div2Assign(); if (b.fe.isEven()) { b.fe.div2Assign(); } else { const carry = b.fe.addWithCarryAssign(&Modulus); b.fe.div2Assign(); // Handle overflow if necessary if (comptime !modulusHasSpareBit() and carry) { b.fe.limbs[n_limbs - 1] |= 1 << 63; } } } // Perform operations while v is even while (v.isEven()) { v.div2Assign(); if (c.fe.isEven()) { c.fe.div2Assign(); } else { const carry = c.fe.addWithCarryAssign(&Modulus); c.fe.div2Assign(); // Handle overflow if necessary if (comptime !modulusHasSpareBit() and carry) { c.fe.limbs[n_limbs - 1] |= 1 << 63; } } } // Update based on u vs v values if (v.cmp(&u) == .lt) { _ = u.subWithBorrowAssign(&v); b.subAssign(&c); } else { _ = v.subWithBorrowAssign(&u); c.subAssign(&b); } } // Return the inverse based on the final values of u and v return if (u.eql(o)) b else c; } /// Divides one field element by another field element. /// /// This function divides the current field element (`self`) by another field element (`den`). /// If the denominator (`den`) is zero, it returns an error indicating a division by zero. /// /// # Arguments: /// - `den`: The field element by which to divide the current field element. /// /// # Returns: /// - Result of the division operation as a new field element. /// /// Errors: /// - If the denominator is zero, a division by zero error is returned. pub fn div(self: Self, den: Self) FieldError!Self { return self.mul(&(den.inverse() orelse return FieldError.DivisionByZero)); } /// Check if two field elements are equal. /// /// Determines whether the current field element is equal to another field element. /// /// Parameters: /// - self: The first field element to compare. /// - rhs: The second field element to compare. /// /// Returns: /// - true if the field elements are equal, false otherwise. pub fn eql(self: Self, rhs: Self) bool { return self.fe.eql(rhs.fe); } /// Convert the field element to a u256 integer. /// /// Converts the field element to a u256 integer. /// /// Parameters: /// - self: The field element to convert. /// /// Returns: /// - A u256 integer representing the field element. pub fn toU256(self: Self) u256 { return std.mem.readInt( u256, &self.toBigInt().toBytesLe(), .little, ); } /// Try to convert the field element to a u64 if its value is small enough. /// /// Attempts to convert the field element to a u64 if its value is within the representable range. /// /// Parameters: /// - self: The field element to convert. /// - T: The target type for conversion (must be u64 or smaller). /// /// Returns: /// - A u64 representation of the field element if conversion succeeds. /// - Error(ValueTooLarge) if the value exceeds the representable range of the target type. pub fn toInt(self: Self, comptime T: type) !T { const asU256 = self.toU256(); // Check if the value is small enough to fit into a type T integer if (asU256 > std.math.maxInt(T)) return error.ValueTooLarge; // Otherwise, it's safe to cast return @intCast(asU256); } /// Calculate the Legendre symbol of a field element. /// /// Computes the Legendre symbol of the field element using Euler's criterion. /// The Legendre symbol is a mathematical function commonly used in number theory /// to determine whether a given integer is a quadratic residue modulo a prime number. /// /// # Arguments: /// - `a`: The field element for which the Legendre symbol is calculated. /// /// # Returns: /// - `1` if `a` has a square root modulo the modulus (`p`), /// - `-1` if `a` does not have a square root modulo `p`, /// - `0` if `a` is zero modulo `p`. pub fn legendre(a: Self) i2 { // Compute the Legendre symbol a|p using // Euler's criterion. p is a prime, a is // relatively prime to p (if p divides // a, then a|p = 0) // Returns 1 if a has a square root modulo // p, -1 otherwise. // Calculate a^(p-1)/2 modulo p const ls = a.powToBigInt(comptime big_int.fromInt(u256, QMinOneDiv2)); // Check if a^(p-1)/2 is equivalent to -1 modulo p if (ls.toU256() == comptime modulo - 1) return -1; // Check if a^(p-1)/2 is equivalent to 0 modulo p if (ls.isZero()) return 0; // Otherwise, a^(p-1)/2 is equivalent to 1 modulo p return 1; } /// Compare two field elements and return the ordering result. /// /// # Parameters /// - `self` - The first field element to compare. /// - `rhs` - The second field element to compare. /// /// # Returns /// A `std.math.Order` enum indicating the ordering relationship. pub fn cmp(self: *const Self, rhs: *const Self) std.math.Order { return self.toBigInt().cmp(&rhs.toBigInt()); } /// Check if this field element is less than the rhs. /// /// # Parameters /// - `self` - The field element to check. /// - `rhs` - The field element to compare against. /// /// # Returns /// `true` if `self` is less than `rhs`, `false` otherwise. pub fn lt(self: *const Self, rhs: *const Self) bool { return self.cmp(rhs) == .lt; } /// Check if this field element is less than or equal to the rhs. /// /// # Parameters /// - `self` - The field element to check. /// - `rhs` - The field element to compare against. /// /// # Returns /// `true` if `self` is less than or equal to `rhs`, `false` otherwise. pub fn lte(self: *const Self, rhs: *const Self) bool { return self.cmp(rhs).compare(.lte); } /// Check if this field element is greater than the rhs. /// /// # Parameters /// - `self` - The field element to check. /// - `rhs` - The field element to compare against. /// /// # Returns /// `true` if `self` is greater than `rhs`, `false` otherwise. pub fn gt(self: *const Self, rhs: *const Self) bool { return self.cmp(rhs) == .gt; } /// Check if this field element is greater than or equal to the rhs. /// /// # Parameters /// - `self` - The field element to check. /// - `rhs` - The field element to compare against. /// /// # Returns /// `true` if `self` is greater than or equal to `rhs`, `false` otherwise. pub fn gte(self: *const Self, rhs: *const Self) bool { return self.cmp(rhs).compare(.gte); } }; }
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repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/constants.zig
pub const STARKNET_PRIME = 0x800000000000011000000000000000000000000000000000000000000000001; pub const FELT_BYTE_SIZE = 32;
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repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/const_choice.zig
const std = @import("std"); const expectEqual = std.testing.expectEqual; const expect = std.testing.expect; /// Provides functionality for working with constant-time boolean choices. pub const ConstChoice = struct { const Self = @This(); /// The underlying word value. word: u64 = 0, /// The truthy value. pub const TRUE: Self = .{ .word = std.math.maxInt(u64) }; /// The falsy value. pub const FALSE: Self = .{}; /// Retrieves the mask value associated with the ConstChoice. /// Returns the mask value as type `T`. pub fn asMask(self: *const Self, comptime T: type) T { return switch (@typeInfo(T).Int.bits) { 64 => self.word, else => |b| if (b < 64) @as(T, @truncate(self.word)) else @intCast(self.word), }; } /// Initializes a ConstChoice instance from a Word mask value. /// `value`: The Word mask value. /// Returns the initialized ConstChoice instance. pub fn initFromWordMask(value: u64) Self { std.debug.assert(value == TRUE.word or value == FALSE.word); return .{ .word = value }; } /// Initializes a ConstChoice instance from a Word least significant bit (LSB) value. /// `value`: The Word LSB value. /// Returns the initialized ConstChoice instance. pub fn initFromWordLsb(comptime T: type, value: T) Self { std.debug.assert(value == 0 or value == 1); return .{ .word = switch (@typeInfo(T).Int.bits) { 64 => -%value, else => -%@as(u64, @intCast(value)), }, }; } /// Initializes a ConstChoice instance from a boolean value. /// `flag`: The boolean value. /// Returns the truthy value if `flag` is true, and the falsy value if `flag` is false. pub fn initFromBool(flag: bool) Self { return if (flag) TRUE else FALSE; } /// Initializes a ConstChoice instance from a non-zero word value. /// `T`: The type of the value. /// `value`: The word value. /// Returns the truthy value if `value != 0`, and the falsy value otherwise. pub fn initFromWordNonZero(comptime T: type, value: T) Self { return Self.initFromBool(value != 0); } /// Initializes a ConstChoice instance from the equality comparison of two values. /// `T`: The type of the values. /// `x`: The first value for comparison. /// `y`: The second value for comparison. /// Returns the truthy value if `x == y`, and the falsy value otherwise. pub fn initFromWordEq(comptime T: type, x: T, y: T) Self { return Self.initFromBool(x == y); } /// Initializes a ConstChoice instance from the comparison of two values where the first value is less than the second. /// `T`: The type of the values. /// `x`: The first value for comparison. /// `y`: The second value for comparison. /// Returns the truthy value if `x < y`, and the falsy value otherwise. pub fn initFromWordLt(comptime T: type, x: T, y: T) Self { return Self.initFromBool(x < y); } /// Initializes a ConstChoice instance from the comparison of two values where the first value is less than or equal to the second. /// `T`: The type of the values. /// `x`: The first value for comparison. /// `y`: The second value for comparison. /// Returns the truthy value if `x <= y`, and the falsy value otherwise. pub fn initFromWordLe(comptime T: type, x: T, y: T) Self { return Self.initFromBool(x <= y); } /// Initializes a ConstChoice instance from the comparison of two values where the first value is greater than the second. /// `T`: The type of the values. /// `x`: The first value for comparison. /// `y`: The second value for comparison. /// Returns the truthy value if `x > y`, and the falsy value otherwise. pub fn initFromWordGt(comptime T: type, x: T, y: T) Self { return Self.initFromWordLt(T, y, x); } /// Initializes a ConstChoice instance from the comparison of two values where the first value is greater than or equal to the second. /// `T`: The type of the values. /// `x`: The first value for comparison. /// `y`: The second value for comparison. /// Returns the truthy value if `x >= y`, and the falsy value otherwise. pub fn initFromWordGe(comptime T: type, x: T, y: T) Self { return Self.initFromBool(x >= y); } /// Performs logical negation on a ConstChoice instance. /// `self`: The ConstChoice instance to negate. /// Returns the negated ConstChoice instance. pub fn not(self: *const Self) Self { return .{ .word = ~self.word }; } /// Performs a bitwise OR operation between two ConstChoice instances. /// `self`: The first ConstChoice operand. /// `rhs`: The second ConstChoice operand. /// Returns the result of the bitwise OR operation. pub fn orWord(self: *const Self, rhs: *const Self) Self { return .{ .word = self.word | rhs.word }; } /// Performs a bitwise AND operation between two ConstChoice instances. /// `self`: The first ConstChoice operand. /// `rhs`: The second ConstChoice operand. /// Returns the result of the bitwise AND operation. pub fn andWord(self: *const Self, rhs: *const Self) Self { return .{ .word = self.word & rhs.word }; } /// Returns either `a` or `b` based on the truthiness of `self`. /// `self`: The ConstChoice instance determining the selection. /// `T`: The type of values `a` and `b`. /// `a`: The value to return if `self` is falsy. /// `b`: The value to return if `self` is truthy. /// Returns `a` if `self` is falsy, otherwise returns `b`. pub fn selectWord(self: *const Self, comptime T: type, a: T, b: T) T { return if (self.eql(&TRUE)) b else a; } /// Returns `a` if `self` is truthy, otherwise returns 0. /// `self`: The ConstChoice instance determining the selection. /// `T`: The type of the value `a`. /// `a`: The value to return if `self` is truthy. /// Returns `a` if `self` is truthy, otherwise returns 0. pub fn ifTrue(self: *const Self, comptime T: type, a: T) T { return if (self.eql(&TRUE)) a else 0; } /// Checks if two ConstChoice instances are equal. /// `self`: The first ConstChoice instance. /// `rhs`: The second ConstChoice instance to compare with `self`. /// Returns `true` if the two instances are equal, otherwise `false`. pub fn eql(self: *const Self, rhs: *const Self) bool { return self.word == rhs.word; } }; test "ConstChoice: initFromWordMask" { try expect(ConstChoice.initFromWordMask(0).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordMask(std.math.maxInt(u64)).eql(&ConstChoice.TRUE)); } test "ConstChoice: initFromWordLsb" { // u64 try expect(ConstChoice.initFromWordLsb(u64, 0).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordLsb(u64, 1).eql(&ConstChoice.TRUE)); // u8 try expect(ConstChoice.initFromWordLsb(u8, 0).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordLsb(u8, 1).eql(&ConstChoice.TRUE)); } test "ConstChoice: initFromBool" { try expect(ConstChoice.initFromBool(true).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromBool(false).eql(&ConstChoice.FALSE)); } test "ConstChoice: initFromWordNonZero" { // u64 try expect(ConstChoice.initFromWordNonZero(u64, 555).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordNonZero(u64, 0).eql(&ConstChoice.FALSE)); // u32 try expect(ConstChoice.initFromWordNonZero(u32, 32).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordNonZero(u32, 0).eql(&ConstChoice.FALSE)); } test "ConstChoice: asMask" { // To u64 try expectEqual(@as(u64, 0), ConstChoice.initFromWordMask(0).asMask(u64)); try expectEqual( @as(u64, std.math.maxInt(u64)), ConstChoice.initFromWordMask(std.math.maxInt(u64)).asMask(u64), ); // To smaller unsigned integer type u8 try expectEqual(@as(u8, 0), ConstChoice.initFromWordMask(0).asMask(u8)); try expectEqual( @as(u8, std.math.maxInt(u8)), ConstChoice.initFromWordMask(std.math.maxInt(u64)).asMask(u8), ); // To larger unsigned integer type u128 try expectEqual(@as(u128, 0), ConstChoice.initFromWordMask(0).asMask(u128)); try expectEqual( @as(u128, std.math.maxInt(u64)), ConstChoice.initFromWordMask(std.math.maxInt(u64)).asMask(u128), ); } test "ConstChoice: initFromWordEq" { try expect(ConstChoice.initFromWordEq(u64, 4, 5).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordEq(u64, 5, 5).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordEq(u64, 6, 5).eql(&ConstChoice.FALSE)); } test "ConstChoice: initFromWordLt" { try expect(ConstChoice.initFromWordLt(u64, 4, 5).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordLt(u64, 5, 5).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordLt(u64, 6, 5).eql(&ConstChoice.FALSE)); } test "ConstChoice: initFromWordLe" { try expect(ConstChoice.initFromWordLe(u64, 4, 5).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordLe(u64, 5, 5).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordLe(u64, 6, 5).eql(&ConstChoice.FALSE)); } test "ConstChoice: initFromWordGt" { try expect(ConstChoice.initFromWordGt(u64, 4, 5).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordGt(u64, 5, 5).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordGt(u64, 6, 5).eql(&ConstChoice.TRUE)); } test "ConstChoice: initFromWordGe" { try expect(ConstChoice.initFromWordGe(u64, 4, 5).eql(&ConstChoice.FALSE)); try expect(ConstChoice.initFromWordGe(u64, 5, 5).eql(&ConstChoice.TRUE)); try expect(ConstChoice.initFromWordGe(u64, 6, 5).eql(&ConstChoice.TRUE)); } test "ConstChoice: not" { try expect(ConstChoice.TRUE.not().eql(&ConstChoice.FALSE)); try expect(ConstChoice.FALSE.not().eql(&ConstChoice.TRUE)); } test "ConstChoice: orWord" { try expect(ConstChoice.TRUE.orWord(&ConstChoice.TRUE).eql(&ConstChoice.TRUE)); try expect(ConstChoice.FALSE.orWord(&ConstChoice.TRUE).eql(&ConstChoice.TRUE)); try expect(ConstChoice.FALSE.orWord(&ConstChoice.FALSE).eql(&ConstChoice.FALSE)); } test "ConstChoice: andWord" { try expect(ConstChoice.TRUE.andWord(&ConstChoice.TRUE).eql(&ConstChoice.TRUE)); try expect(ConstChoice.FALSE.andWord(&ConstChoice.TRUE).eql(&ConstChoice.FALSE)); try expect(ConstChoice.FALSE.andWord(&ConstChoice.FALSE).eql(&ConstChoice.FALSE)); } test "ConstChoice: selectWord" { const a: u64 = 1; const b: u64 = 2; try expect(ConstChoice.TRUE.selectWord(u64, a, b) == b); try expect(ConstChoice.FALSE.selectWord(u64, a, b) == a); } test "ConstChoice: ifTrue" { // u64 try expectEqual(@as(u64, 10), ConstChoice.TRUE.ifTrue(u64, 10)); try expectEqual(@as(u64, 0), ConstChoice.FALSE.ifTrue(u64, 10)); // u32 try expectEqual(@as(u32, 10), ConstChoice.TRUE.ifTrue(u32, 10)); try expectEqual(@as(u32, 0), ConstChoice.FALSE.ifTrue(u32, 10)); }
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/arithmetic.zig
const std = @import("std"); const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; /// Calculates the result of a + b * c: /// - returning the lower 64 bits of the result /// - setting `carry` to the upper 64 bits. pub inline fn mac(a: u64, b: u64, c: u64, carry: *u64) u64 { const tmp = @as(u128, a) + @as(u128, b) * @as(u128, c); carry.* = @intCast(tmp >> 64); return @truncate(tmp); } /// Calculates the result of a + b * c: /// - returning the lower 64 bits of the result /// - setting `carry` to the upper 64 bits. /// /// This function performs the same calculation as the `mac` function but discards the result, /// making it suitable for cases where only the carry value is needed. pub inline fn macDiscard(a: u64, b: u64, c: u64, carry: *u64) void { const tmp = @as(u128, a) + @as(u128, b) * @as(u128, c); carry.* = @intCast(tmp >> 64); } /// Calculates the result of a + b * c + carry: /// - returning the lower 64 bits of the result /// - setting `carry` to the upper 64 bits. pub inline fn macWithCarry(a: u64, b: u64, c: u64, carry: *u64) u64 { const tmp = @as(u128, a) + @as(u128, b) * @as(u128, c) + @as(u128, carry.*); carry.* = @intCast(tmp >> 64); return @truncate(tmp); } /// Calculates the result of a - b - borrow for 64-bit integers: /// - returning the result of the subtraction as the lower 64 bits /// - setting `borrow` to 1 if there is a borrow, and 0 otherwise. /// /// This function subtracts the values `b` and `borrow` from the value at the memory address `a`. /// /// It returns the result of the subtraction as the lower 64 bits, and sets `borrow` to 1 if there /// was a borrow during the subtraction (i.e., if the result would have been negative), and 0 otherwise. pub inline fn sbb(comptime T: type, a: *u64, b: u64, borrow: T) T { const tmp = (@as(u128, 1) << 64) + @as(u128, a.*) - @as(u128, b) - @as(u128, @intCast(borrow)); a.* = @truncate(tmp); return @intCast(@intFromBool(tmp >> 64 == 0)); } /// Sets a = a + b + carry, and returns the new carry. /// /// This function performs the addition of two 64-bit integers `a` and `b` along with a carry `carry`. /// It updates the value at the memory address `a` to the sum of `a`, `b`, and `carry`, and returns /// the new carry resulting from the addition. pub inline fn adc(comptime T: type, a: *u64, b: u64, carry: T) T { const tmp = @as(u128, a.*) + @as(u128, b) + @as(u128, carry); a.* = @truncate(tmp); return @intCast(tmp >> 64); } pub fn powModulus(b: u512, e: u512, modulus: u512) u512 { var base: u512 = b; var exponent: u512 = e; if (modulus == 1) return 0; base = base % modulus; var result: u512 = 1; while (exponent > 0) { if ((exponent & 1) == 1) { result = @rem(result * base, modulus); } base = @rem(base * base, modulus); exponent = exponent >> 1; } return result; } pub fn legendre(a: u512, p: u512) u512 { return powModulus(a, (p - 1) / 2, p); } pub fn tonelliShanks(n: u512, p: u512) struct { u512, u512, bool } { if (legendre(n, p) != 1) { return .{ 0, 0, false }; } // Factor out powers of 2 from p - 1 var q: u512 = p - 1; var s: u512 = 0; while (q % 2 == 0) { q = q / 2; s = s + 1; } if (s == 1) { const result: u512 = powModulus(n, (p + 1) / 4, p); return .{ result, p - result, true }; } // Find a non-square z such as ( z | p ) = -1 var z: u512 = 2; while (legendre(z, p) != p - 1) { z = z + 1; } var c: u512 = powModulus(z, q, p); var t: u512 = powModulus(n, q, p); var m: u512 = s; var result: u512 = powModulus(n, (q + 1) >> 1, p); while (t != 1) { var i: u512 = 1; z = @rem(t * t, p); while (z != 1 and i < m - 1) { i = i + 1; z = @rem(z * z, p); } const b: u512 = powModulus(c, @as(u512, 1) << @intCast(m - i - 1), p); c = @rem(b * b, p); t = @rem(t * c, p); m = i; result = @rem(result * b, p); } return .{ result, p - result, true }; } pub fn extendedGCD(self: i256, rhs: i256) struct { gcd: i256, x: i256, y: i256 } { var s = [_]i256{ 0, 1 }; var t = [_]i256{ 1, 0 }; var r = [_]i256{ rhs, self }; while (r[0] != 0) { const q = @divFloor(r[1], r[0]); std.mem.swap(i256, &r[0], &r[1]); std.mem.swap(i256, &s[0], &s[1]); std.mem.swap(i256, &t[0], &t[1]); r[0] = r[0] - q * r[1]; s[0] = s[0] - q * s[1]; t[0] = t[0] - q * t[1]; } if (r[1] >= 0) { return .{ .gcd = r[1], .x = s[1], .y = t[1] }; } else { return .{ .gcd = -r[1], .x = -s[1], .y = -t[1] }; } } test "Multiply accumulate basic test" { var carry: u64 = 0; try expectEqual(@as(u64, 25), mac(5, 10, 2, &carry)); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate with overflow" { var carry: u64 = 0; try expectEqual(9, mac(std.math.maxInt(u64) - 10, 10, 2, &carry)); try expectEqual(@as(u64, 1), carry); } test "Multiply accumulate with overflow in carry" { var carry: u64 = 0; try expectEqual(0, mac(std.math.maxInt(u64), std.math.maxInt(u64), std.math.maxInt(u64), &carry)); try expectEqual(@as(u64, std.math.maxInt(u64)), carry); } test "Multiply accumulate with 0 as input" { var carry: u64 = 0; try expectEqual(200, mac(0, 10, 20, &carry)); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate discard basic test" { var carry: u64 = 0; macDiscard(5, 10, 2, &carry); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate discard with overflow" { var carry: u64 = 0; macDiscard(std.math.maxInt(u64) - 10, 10, 2, &carry); try expectEqual(@as(u64, 1), carry); } test "Multiply accumulate discard with overflow in carry" { var carry: u64 = 0; macDiscard(std.math.maxInt(u64), std.math.maxInt(u64), std.math.maxInt(u64), &carry); try expectEqual(@as(u64, std.math.maxInt(u64)), carry); } test "Multiply accumulate discard with 0 as input" { var carry: u64 = 0; macDiscard(0, 10, 20, &carry); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate with carry discard with 0 as input and initial carry" { var carry: u64 = 123; try expectEqual(@as(u64, 123), macWithCarry(0, 0, 0, &carry)); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate with carry discard with carry at the end" { var carry: u64 = 123; try expectEqual(@as(u64, 132), macWithCarry(std.math.maxInt(u64) - 10, 10, 2, &carry)); try expectEqual(@as(u64, 1), carry); } test "Multiply accumulate with carry discard with no at the end" { var carry: u64 = 0; try expectEqual(@as(u64, std.math.maxInt(u64)), macWithCarry(std.math.maxInt(u64), 0, 0, &carry)); try expectEqual(@as(u64, 0), carry); } test "Multiply accumulate with carry discard - some edge cases" { var carry: u64 = 123; try expectEqual(@as(u64, 123), macWithCarry(std.math.maxInt(u64), 1, 1, &carry)); try expectEqual(@as(u64, 1), carry); carry = 123; try expectEqual(@as(u64, 122), macWithCarry(std.math.maxInt(u64), 0, 1, &carry)); try expectEqual(@as(u64, 1), carry); carry = 123; try expectEqual(@as(u64, 122), macWithCarry(std.math.maxInt(u64), 1, 0, &carry)); try expectEqual(@as(u64, 1), carry); } test "Subtraction with borrow basic operation" { var a: u64 = 10; try expectEqual(@as(u64, 0), sbb(u64, &a, 5, 0)); try expectEqual(@as(u64, 5), a); a = 10; try expectEqual(@as(u8, 0), sbb(u64, &a, 5, 0)); try expectEqual(@as(u8, 5), a); } test "Subtraction with borrow negative result" { var a: u64 = 5; try expectEqual(@as(u64, 1), sbb(u64, &a, 10, 0)); try expectEqual(@as(u64, std.math.maxInt(u64) - 4), a); } test "Subtraction with borrow non zero borrow" { var a: u64 = 10; try expectEqual(@as(u64, 0), sbb(u64, &a, 5, 1)); try expectEqual(@as(u64, 4), a); } test "Subtraction with all zero" { var a: u64 = 0; try expectEqual(@as(u64, 0), sbb(u64, &a, 0, 0)); try expectEqual(@as(u64, 0), a); } test "Add with carry with no carry" { var a: u64 = 100; try expectEqual(@as(u64, 0), adc(u64, &a, 50, 0)); try expectEqual(@as(u64, 150), a); } test "Add with carry with carry" { var a: u64 = std.math.maxInt(u64); try expectEqual(@as(u64, 1), adc(u64, &a, 1, 1)); try expectEqual(@as(u64, 1), a); } test "Add with carry with large numbers" { var a: u64 = std.math.maxInt(u64); try expectEqual(@as(u64, 1), adc(u64, &a, std.math.maxInt(u64), 1)); try expectEqual(@as(u64, std.math.maxInt(u64)), a); } test "Add with carry with maximum value and no carry" { var a: u64 = std.math.maxInt(u64); try expectEqual(@as(u64, 0), adc(u64, &a, 0, 0)); try expectEqual(@as(u64, std.math.maxInt(u64)), a); }
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/biginteger.zig
const std = @import("std"); const arithmetic = @import("./arithmetic.zig"); const Field = @import("./fields.zig").Field; const ConstChoice = @import("./const_choice.zig").ConstChoice; const TEST_ITERATIONS = @import("../../main.zig").TEST_ITERATIONS; const expectEqual = std.testing.expectEqual; const expect = std.testing.expect; /// This function generates a new type representing an arbitrary-precision integer with a fixed number of limbs. /// Each limb is a 64-bit unsigned integer, allowing the representation of integers larger than the native machine word size. /// /// Parameters: /// - N: The number of limbs for the big integer. /// /// Returns: /// - A struct representing a big integer with the specified number of limbs. pub fn bigInt(comptime N: usize) type { return struct { const Self = @This(); /// The `limbs` field is an array of u64 integers that store the individual limbs of the big integer. /// /// Each limb contributes to the overall magnitude of the integer, allowing representation of large numbers. limbs: [N]u64 = [_]u64{0} ** N, /// Initializes a big integer with the specified limbs. /// /// This function initializes a big integer with the given array of limbs. /// It creates a new instance of the `bigInt` struct and assigns the provided limbs to the `limbs` field. /// /// Parameters: /// - limbs: An array of u64 integers representing the limbs of the big integer. /// /// Returns: /// - A new instance of the `bigInt` struct with the specified limbs. pub fn init(limbs: [N]u64) Self { return .{ .limbs = limbs }; } /// Converts an integer value to a big integer. /// /// This function converts an integer value to a big integer representation. The big integer type has a fixed number of limbs, each being a 64-bit unsigned integer. The function handles conversion for various sizes of integer values. /// /// Parameters: /// - T: The type of the integer to convert. /// - num: The integer value to convert. /// /// Returns: /// - A big integer representation of the provided integer value. /// /// Remarks: /// - The function assumes that the provided integer value is non-negative. /// - For integers up to 63 bits, the function directly initializes the field element. /// - For 64-bit integers, the function initializes the field element directly. /// - For integers from 65 to 128 bits, the function performs truncation and division to fit into the limbs of the big integer. /// - For larger integers, the function converts the integer to bytes and then initializes the field element. pub fn fromInt(comptime T: type, num: T) Self { std.debug.assert(num >= 0); // Switch based on the size of the integer value return switch (@typeInfo(T).Int.bits) { // For integers up to 63 bits, directly initialize the field element 0...63 => .{ .limbs = .{ @intCast(num), 0, 0, 0 } }, // For 64-bit integers, initialize the field element directly 64 => .{ .limbs = .{ num, 0, 0, 0 } }, // For integers from 65 to 128 bits, perform truncation and division 65...128 => .{ .limbs = .{ @truncate(@mod(num, @as(u128, @intCast(std.math.maxInt(u64))) + 1)), @truncate(@divTrunc(num, @as(u128, @intCast(std.math.maxInt(u64))) + 1)), 0, 0, }, }, // For larger integers, convert to bytes and then initialize the field element else => blk: { var lbe = [_]u8{0} ** (N * @sizeOf(u64)); std.mem.writeInt(T, &lbe, num, .little); break :blk Self.fromBytesLe(lbe); }, }; } /// Convert the field element to a u256 integer. /// /// Converts the field element to a u256 integer. /// /// Parameters: /// - self: The field element to convert. /// /// Returns: /// - A u256 integer representing the field element. pub fn toU256(self: Self) u256 { return std.mem.readInt( u256, &self.toBytesLe(), .little, ); } /// Try to convert the field element to a u64 if its value is small enough. /// /// Attempts to convert the field element to a u64 if its value is within the representable range. /// /// Parameters: /// - self: The field element to convert. /// - T: The target type for conversion (must be u64 or smaller). /// /// Returns: /// - A u64 representation of the field element if conversion succeeds. /// - Error(ValueTooLarge) if the value exceeds the representable range of the target type. pub fn toInt(self: Self, comptime T: type) !T { const asU256 = self.toU256(); // Check if the value is small enough to fit into a type T integer if (asU256 > std.math.maxInt(T)) return error.ValueTooLarge; // Otherwise, it's safe to cast return @intCast(asU256); } /// Returns a big integer representing the value one. /// /// This function generates a big integer with a value of one. It creates a new instance of the `bigInt` struct /// where all limbs are initialized to zero, except for the first limb which is set to one, representing the value one. /// /// Returns: /// - A new instance of the `bigInt` struct representing the value one. pub fn one() Self { // Compile-time computation to generate a big integer with a value of one comptime { // Initialize an array of limbs with all zeros var o = [_]u64{0} ** N; // Set the first limb to one o[0] = 1; // Return a new instance of the `bigInt` struct with the generated limbs return .{ .limbs = o }; } } /// Checks if a big integer is zero. /// /// This function iterates through each limb of the big integer to determine if it is zero. /// If any limb is non-zero, the function returns false, indicating that the big integer is not zero. /// If all limbs are zero, the function returns true, indicating that the big integer is zero. /// /// Parameters: /// - self: A pointer to the big integer to be checked. /// /// Returns: /// - true if the big integer is zero, false otherwise. pub inline fn isZero(self: *const Self) bool { // Iterate through each limb of the big integer for (0..N) |i| { // Check if the current limb is non-zero if (self.limbs[i] != 0) return false; } // If all limbs are zero, return true return true; } /// Generates a random big integer with the specified limbs. /// /// This function generates a random big integer with the specified number of limbs using a provided random number generator. /// It creates a new instance of the `bigInt` struct and assigns randomly generated values to each limb within the specified range. /// /// Parameters: /// - r: An instance of the `std.Random` random number generator used to generate random limb values. /// /// Returns: /// - A new instance of the `bigInt` struct representing a randomly generated big integer. pub fn rand(r: std.Random) Self { // Create a new instance of the `bigInt` struct var big_int: Self = .{}; // Iterate over each limb for (0..N) |i| // Generate a random u64 value and assign it to the current limb big_int.limbs[i] = r.int(u64); // Return the randomly generated big integer return big_int; } /// Checks if two big integers are equal. /// /// This function compares two big integers for equality by performing a byte-wise memory comparison of their limbs. /// It returns true if the big integers have identical limb values, indicating equality, and false otherwise. /// /// Parameters: /// - self: The first big integer to compare. /// - rhs: The second big integer to compare. /// /// Returns: /// - true if the big integers are equal, false otherwise. pub fn eql(self: Self, rhs: Self) bool { return std.mem.eql(u64, &self.limbs, &rhs.limbs); } /// Checks if two big integers are not equal. /// /// This function compares two big integers for inequality by iterating over their limbs and checking if any corresponding pair of limbs is not equal. /// /// Parameters: /// - self: The first big integer to compare. /// - rhs: The second big integer to compare. /// /// Returns: /// - true if the big integers are not equal, false otherwise. pub fn ne(self: Self, rhs: Self) bool { // Iterate over each limb pair of the big integers inline for (self.limbs, rhs.limbs) |ll, rl| { // Check if the corresponding limbs are not equal if (ll != rl) return true; } // If all corresponding limbs are equal, return false return false; } /// Checks if a big integer is odd. /// /// This function determines whether a given big integer is odd by examining the least significant bit of its first limb. /// It returns true if the integer is odd (i.e., the LSB is set), and false otherwise. /// /// Parameters: /// - self: A pointer to the big integer to be checked. /// /// Returns: /// - true if the big integer is odd, false otherwise. pub fn isOdd(self: *const Self) bool { return self.limbs[0] & 1 == 1; } /// Checks if a big integer is even. /// /// This function determines whether a given big integer is even by negating the result of the `isOdd` function. /// It returns true if the integer is even (i.e., not odd), and false otherwise. /// /// Parameters: /// - self: A pointer to the big integer to be checked. /// /// Returns: /// - true if the big integer is even, false otherwise. pub fn isEven(self: *const Self) bool { return !self.isOdd(); } /// Divides a big integer by two. /// /// This function divides the value of the provided big integer (`self`) by two and returns the result. /// It effectively performs a right shift operation on each limb of the big integer. /// /// Parameters: /// - self: A pointer to the big integer to be divided by two. /// /// Returns: /// - The big integer resulting from the division by two. /// /// Notes: /// - This function does not modify the original big integer; it returns a new big integer representing the result of the division. /// - The division is performed in place, and the result is updated in the original big integer. /// - Inline loops are used for performance optimization. /// - The operation effectively performs a right shift of each limb by one bit, equivalent to division by two. pub inline fn div2(self: *const Self) Self { // Dereference the pointer to obtain the actual big integer var a = self.*; // Divide the big integer by two using the div2Assign function a.div2Assign(); // Return the result of the division return a; } /// Divides a big integer by two in place. /// /// This function divides a big integer by two in place, effectively performing a right shift operation on each limb. /// It iterates through each limb of the big integer, starting from the most significant limb, and performs the division operation. /// During the iteration, it propagates the carry bit from the higher-order bits to the lower-order bits to maintain precision. /// /// Parameters: /// - self: A pointer to the big integer to be divided by two. /// /// Returns: /// - void /// /// Notes: /// - This function modifies the big integer in place, effectively dividing it by two. /// - The carry bit from the higher-order bits is propagated to the lower-order bits to maintain precision during the division operation. /// - Inline loops are used for performance optimization. /// - The operation effectively performs a right shift of each limb by one bit, equivalent to division by two. /// - The division is performed in place, and the result is updated in the original big integer. pub inline fn div2Assign(self: *Self) void { // Initialize a variable to hold the carry var t: u64 = 0; // Compile-time variable to iterate through limbs comptime var i = N; // Iterate through limbs starting from the most significant inline while (i > 0) { // Decrement the iterator i -= 1; // Get a pointer to the current limb const a = &self.limbs[i]; // Shift the carry bit to the left const t2 = a.* << 63; // Divide the limb by 2 (right shift) a.* >>= 1; // Add the carry bit to the current limb a.* |= t; // Update the carry with the previous carry bit t = t2; } } /// Multiplies a big integer by two. /// /// This function multiplies the value of the provided big integer (`self`) by two and returns the result along with the carry bit. /// It effectively performs a left shift operation on each limb of the big integer. /// /// Parameters: /// - self: A pointer to the big integer to be multiplied by two. /// /// Returns: /// - A tuple containing the result of the multiplication and a boolean indicating whether there was a carry. /// /// Notes: /// - This function does not modify the original big integer; it returns a new big integer representing the result of the multiplication. /// - The multiplication is performed in place, and the result is updated in the original big integer. /// - Inline loops are used for performance optimization. /// - The operation effectively performs a left shift of each limb by one bit, equivalent to multiplication by two. pub inline fn mul2(self: *const Self) std.meta.Tuple(&.{ Self, bool }) { // Dereference the pointer to obtain the actual big integer var a = self.*; // Multiply the big integer by two using the mul2Assign function const c = a.mul2Assign(); // Return the result of the multiplication along with the carry bit return .{ a, c }; } /// Multiplies a big integer by two in place. /// /// This function multiplies the value of the provided big integer (`self`) by two in place, modifying the original big integer. /// It iterates through each limb of the big integer, starting from the least significant limb, and performs the multiplication operation. /// During the iteration, it propagates the carry bit from the lower-order bits to the higher-order bits to maintain precision. /// /// Parameters: /// - self: A pointer to the big integer to be multiplied by two. /// /// Returns: /// - A boolean indicating whether there was a carry during the multiplication. /// /// Notes: /// - This function modifies the big integer in place, effectively multiplying it by two. /// - The carry bit from the lower-order bits is propagated to the higher-order bits to maintain precision during the multiplication operation. /// - Inline loops are used for performance optimization. /// - The operation effectively performs a left shift of each limb by one bit, equivalent to multiplication by two. /// - The multiplication is performed in place, and the result is updated in the original big integer. pub inline fn mul2Assign(self: *Self) bool { // Initialize a variable to hold the carry var last: u64 = 0; // Iterate through limbs starting from the least significant inline for (0..N) |i| { // Get a pointer to the current limb const a = &self.limbs[i]; // Extract the least significant bit const tmp = a.* >> 63; // Left shift the limb by one bit a.* <<= 1; // Add the carry bit to the current limb a.* |= last; // Update the carry with the previous least significant bit last = tmp; } // Return true if there was a carry during the multiplication, false otherwise return last != 0; } /// Adds a big integer to another big integer with carry and returns the result along with a carry flag. /// /// This function adds a big integer `rhs` to another big integer `self` with carry and returns the result along with a carry flag. /// It dereferences the pointers to obtain the actual big integers, performs the addition operation using the `addWithCarryAssign` function, /// and then returns a tuple containing the result of the addition operation (`a`) and a boolean flag indicating whether there was a carry. /// /// Parameters: /// - self: A pointer to the first big integer to which the second big integer will be added. /// - rhs: A pointer to the second big integer that will be added to the first big integer. /// /// Returns: /// - A tuple containing the result of the addition operation and a boolean flag indicating whether there was a carry. /// /// Notes: /// - This function does not modify the original big integers; it only performs the addition operation. /// - Addition with carry is performed using the `addWithCarryAssign` function. /// - The result of the addition operation and the carry flag are returned as a tuple. /// - The carry flag can be used to detect overflow during addition operations. pub fn addWithCarry(self: *const Self, rhs: *const Self) std.meta.Tuple(&.{ Self, bool }) { // Dereference the pointer to obtain the actual big integer var a = self.*; // Perform addition with carry and obtain the carry flag const carry = a.addWithCarryAssign(rhs); // Return a tuple containing the result of the addition operation and the carry flag return .{ a, carry }; } /// Adds a big integer to another big integer with carry and assigns the result to the first big integer. /// /// This function performs addition with carry between two big integers and assigns the result to the first big integer. /// It iterates through each limb of the big integers, adding the corresponding limbs along with the carry bit. /// At the end of the addition operation, it returns a flag indicating whether there was a carry during the addition process. /// /// Parameters: /// - self: A pointer to the first big integer to which the addition result will be assigned. /// - rhs: A pointer to the second big integer that will be added to the first big integer. /// /// Returns: /// - A boolean flag indicating whether there was a carry during the addition operation. /// /// Notes: /// - This function modifies the first big integer in place, assigning the result of the addition operation to it. /// - Addition with carry is performed for each corresponding limb of the big integers, starting from the least significant limb. /// - The carry bit from each addition operation is propagated to the next higher-order limb to ensure correct arithmetic. /// - Inline loops are used for performance optimization. /// - At the end of the addition operation, the function returns true if there was a carry, and false otherwise. /// - The carry flag can be used to detect overflow during addition operations. /// pub fn addWithCarryAssign(self: *Self, rhs: *const Self) bool { // Initialize a variable to hold the carry var carry: u8 = 0; // Iterate through each limb and perform addition with carry inline for (0..N) |i| // Perform addition with carry for the current limb carry = arithmetic.adc(u8, &self.limbs[i], rhs.limbs[i], carry); // Return a flag indicating whether there was a carry during addition return carry != 0; } /// Subtracts a big integer from another big integer with borrow and returns the result along with a borrow flag. /// /// This function subtracts a big integer `rhs` from another big integer `self` with borrow and returns the result along with a borrow flag. /// It dereferences the pointers to obtain the actual big integers, performs the subtraction operation using the `subWithBorrowAssign` function, /// and then returns a tuple containing the result of the subtraction operation (`a`) and a boolean flag indicating whether there was a borrow. /// /// Parameters: /// - self: A pointer to the first big integer from which the second big integer will be subtracted. /// - rhs: A pointer to the second big integer that will be subtracted from the first big integer. /// /// Returns: /// - A tuple containing the result of the subtraction operation and a boolean flag indicating whether there was a borrow. /// /// Notes: /// - This function does not modify the original big integers; it only performs the subtraction operation. /// - Subtraction with borrow is performed using the `subWithBorrowAssign` function. /// - The result of the subtraction operation and the borrow flag are returned as a tuple. /// - The borrow flag can be used to detect underflow during subtraction operations. pub fn subWithBorrow(self: *const Self, rhs: *const Self) std.meta.Tuple(&.{ Self, bool }) { // Dereference the pointer to obtain the actual big integer var a = self.*; // Perform subtraction with borrow and obtain the borrow flag const borrow = a.subWithBorrowAssign(rhs); // Return a tuple containing the result of the subtraction operation and the borrow flag return .{ a, borrow }; } /// Subtracts a big integer from another big integer with borrow and assigns the result to the first big integer. /// /// This function performs subtraction with borrow between two big integers and assigns the result to the first big integer. /// It iterates through each limb of the big integers, subtracting the corresponding limbs along with the borrow bit. /// At the end of the subtraction operation, it returns a flag indicating whether there was a borrow during the subtraction process. /// /// Parameters: /// - self: A pointer to the first big integer from which the second big integer will be subtracted, and the result will be assigned. /// - rhs: A pointer to the second big integer that will be subtracted from the first big integer. /// /// Returns: /// - A boolean flag indicating whether there was a borrow during the subtraction operation. /// /// Notes: /// - This function modifies the first big integer in place, assigning the result of the subtraction operation to it. /// - Subtraction with borrow is performed for each corresponding limb of the big integers, starting from the least significant limb. /// - The borrow bit from each subtraction operation is propagated to the next higher-order limb to ensure correct arithmetic. /// - Inline loops are used for performance optimization. /// - At the end of the subtraction operation, the function returns true if there was a borrow, and false otherwise. /// - The borrow flag can be used to detect underflow during subtraction operations. pub fn subWithBorrowAssign(self: *Self, rhs: *const Self) bool { // Initialize a variable to hold the borrow var borrow: u8 = 0; // Iterate through each limb and perform subtraction with borrow inline for (0..N) |i| // Perform subtraction with borrow for the current limb borrow = arithmetic.sbb(u8, &self.limbs[i], rhs.limbs[i], borrow); // Return a flag indicating whether there was a borrow during subtraction return borrow != 0; } /// This function performs a multiplication operation between two big integers. /// It multiplies the big integer pointed to by `self` with the big integer pointed to by `rhs`. /// The result of the multiplication is stored in the big integer pointed to by `self`. /// /// Parameters: /// - self: A pointer to the first big integer operand. /// - rhs: A pointer to the second big integer operand. /// /// Returns: /// - A tuple containing the updated value of the big integer pointed to by `self` and the result of the multiplication. pub fn mul(self: *const Self, rhs: *const Self) std.meta.Tuple(&.{ Self, Self }) { // Dereference the pointer to obtain the actual big integer var a = self.*; // Call the `mulAssign` method to perform the multiplication return a.mulAssign(rhs); } /// This function performs a high multiplication operation between two big integers. /// It multiplies the big integer pointed to by `self` with the big integer pointed to by `rhs`, /// and returns the high part of the result. /// /// Parameters: /// - self: A pointer to the first big integer operand. /// - rhs: A pointer to the second big integer operand. /// /// Returns: /// - The high part of the result of the multiplication. pub fn mulHigh(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual big integer var a = self.*; // Call the `mulAssign` method to perform the multiplication and return the high part return a.mulAssign(rhs)[1]; } /// This function performs an in-place multiplication operation between two big integers. /// It multiplies the big integer pointed to by `self` with the big integer pointed to by `rhs`, /// and stores the result in the big integer pointed to by `self`. /// /// Parameters: /// - self: A pointer to the first big integer operand. /// - rhs: A pointer to the second big integer operand. /// /// Returns: /// - A tuple containing the updated value of the big integer pointed to by `self` and the result of the multiplication. pub fn mulAssign(self: *Self, rhs: *const Self) std.meta.Tuple(&.{ Self, Self }) { // Check if either operand is zero if (self.isZero() or rhs.isZero()) { // If either operand is zero, set the result to zero and return self.* = .{}; return .{ .{}, .{} }; } // Define a buffer to store intermediate multiplication results const MulBuffer = struct { const S = @This(); // A tuple to store intermediate multiplication results buf: std.meta.Tuple(&.{ [N]u64, [N]u64 }) = .{ [_]u64{0} ** N, [_]u64{0} ** N }, // Retrieves a pointer to the buffer element at the specified index fn getBuf(s: *S, index: usize) *u64 { return if (index < N) &s.buf[0][index] else &s.buf[1][index - N]; } }; // Initialize variables for intermediate results and carry var r: MulBuffer = .{}; var carry: u64 = 0; // Perform the multiplication using schoolbook multiplication algorithm for (0..N) |i| { for (0..N - i) |j| // Perform multiplication with carry and update the buffer r.getBuf(i + j).* = arithmetic.macWithCarry(r.getBuf(i + j).*, self.limbs[i], rhs.limbs[j], &carry); // Store the carry in the high buffer r.buf[1][i] = carry; // Reset the carry for the next iteration carry = 0; } // Copy the result from the buffer to the big integer pointed to by `self` @memcpy(&self.limbs, &r.buf[0]); // Return a tuple containing the updated value of `self` and the result of the multiplication return .{ Self.init(r.buf[0]), Self.init(r.buf[1]) }; } /// This function performs a low multiplication operation between two big integers. /// It multiplies the big integer pointed to by `self` with the big integer pointed to by `rhs`, /// and returns the low part of the result. /// /// Parameters: /// - self: A pointer to the first big integer operand. /// - rhs: A pointer to the second big integer operand. /// /// Returns: /// - The low part of the result of the multiplication. pub fn mulLow(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual big integer var a = self.*; // Call the `mulLowAssign` method to perform the low multiplication and return the result a.mulLowAssign(rhs); return a; } /// This function performs an in-place low multiplication operation between two big integers. /// It multiplies the big integer pointed to by `self` with the big integer pointed to by `rhs`, /// and stores the low part of the result in the big integer pointed to by `self`. /// /// Parameters: /// - self: A pointer to the first big integer operand. /// - rhs: A pointer to the second big integer operand. /// /// Returns: /// - void pub fn mulLowAssign(self: *Self, rhs: *const Self) void { // Check if either operand is zero if (self.isZero() or rhs.isZero()) // If either operand is zero, set the result to zero and return self.* = .{}; // Initialize a variable to store the result var r: Self = .{}; // Initialize a variable to hold the carry var carry: u64 = 0; // Perform the low multiplication using schoolbook multiplication algorithm for (0..N) |i| { for (0..N - i) |j| // Perform multiplication with carry and update the result r.limbs[i + j] = arithmetic.macWithCarry(r.limbs[i + j], self.limbs[i], rhs.limbs[j], &carry); // Reset the carry for the next iteration carry = 0; } // Copy the result to the big integer pointed to by `self` @memcpy(&self.limbs, &r.limbs); } /// Compares two big integers and returns their relative order. /// /// This function compares two big integers `self` and `rhs` and returns their relative order. /// It first reverses the order of limbs from little-endian to big-endian to ensure correct comparison. /// Then, it compares the big integers using byte-wise comparison to determine their relative order. /// /// Parameters: /// - self: A pointer to the first big integer to be compared. /// - rhs: A pointer to the second big integer to be compared. /// /// Returns: /// - An enum value representing the relative order of the two big integers: /// - `std.math.Order.lt` if `self` is less than `rhs`. /// - `std.math.Order.eq` if `self` is equal to `rhs`. /// - `std.math.Order.gt` if `self` is greater than `rhs`. /// /// Notes: /// - This function does not modify the original big integers; it only performs the comparison operation. /// - The big integers are compared in a byte-wise manner after converting their limbs to big-endian order. /// - The comparison result is returned as an enum value indicating the relative order. /// - This function can be used to determine the relative order of big integers for sorting or comparison purposes. pub fn cmp(self: *const Self, rhs: *const Self) std.math.Order { // Obtain pointers to the limbs of the big integers var a = self.limbs; var b = rhs.limbs; // Reverse the order of limbs from little-endian to big-endian _ = std.mem.reverse(u64, a[0..]); _ = std.mem.reverse(u64, b[0..]); // Compare the big integers using byte-wise comparison return std.mem.order(u64, &a, &b); } /// Checks if a big integer is less than another big integer. /// /// This function compares the current big integer (`self`) with another big integer (`rhs`) and returns true if `self` is less than `rhs`, and false otherwise. /// /// Parameters: /// - self: A pointer to the current big integer. /// - rhs: A pointer to the big integer to compare against. /// /// Returns: /// - `true` if `self` is less than `rhs`, otherwise `false`. pub fn lt(self: *const Self, rhs: *const Self) bool { // Compare the big integers and return true if self is less than rhs return self.cmp(rhs) == .lt; } /// Checks if a big integer is less than or equal to another big integer. /// /// This function compares the current big integer (`self`) with another big integer (`rhs`) and returns true if `self` is less than or equal to `rhs`, and false otherwise. /// /// Parameters: /// - self: A pointer to the current big integer. /// - rhs: A pointer to the big integer to compare against. /// /// Returns: /// - `true` if `self` is less than or equal to `rhs`, otherwise `false`. pub fn lte(self: *const Self, rhs: *const Self) bool { // Compare the big integers and return true if self is less than or equal to rhs return self.cmp(rhs).compare(.lte); } /// Checks if a big integer is greater than another big integer. /// /// This function compares the current big integer (`self`) with another big integer (`rhs`) and returns true if `self` is greater than `rhs`, and false otherwise. /// /// Parameters: /// - self: A pointer to the current big integer. /// - rhs: A pointer to the big integer to compare against. /// /// Returns: /// - `true` if `self` is greater than `rhs`, otherwise `false`. pub fn gt(self: *const Self, rhs: *const Self) bool { // Compare the big integers and return true if self is greater than rhs return self.cmp(rhs) == .gt; } /// Checks if a big integer is greater than or equal to another big integer. /// /// This function compares the current big integer (`self`) with another big integer (`rhs`) and returns true if `self` is greater than or equal to `rhs`, and false otherwise. /// /// Parameters: /// - self: A pointer to the current big integer. /// - rhs: A pointer to the big integer to compare against. /// /// Returns: /// - `true` if `self` is greater than or equal to `rhs`, otherwise `false`. pub fn gte(self: *const Self, rhs: *const Self) bool { // Compare the big integers and return true if self is greater than or equal to rhs return self.cmp(rhs).compare(.gte); } /// Converts a big integer to a little-endian bit representation. /// /// This function converts a big integer to its little-endian bit representation. /// It iterates through each limb of the big integer, starting from the least significant limb, /// and generates a bit representation where each bit corresponds to a single limb. /// /// Parameters: /// - self: A pointer to the big integer to be converted to a little-endian bit representation. /// /// Returns: /// - An array of boolean values representing the little-endian bit representation of the big integer. /// /// Notes: /// - The function generates a bit representation where the least significant bit of the big integer corresponds to the first bit of the array. /// - Each limb of the big integer contributes 64 bits to the overall bit representation. /// - The resulting bit representation is little-endian, with the least significant bits appearing first. /// - Inline loops are used for performance optimization. /// - The function returns an array of boolean values representing the bit representation of the big integer. pub fn toBitsLe(self: *const Self) [N * 64]bool { // Initialize an array to hold the bit representation var bits = [_]bool{false} ** (N * 64); // Iterate through each limb of the big integer inline for (0..N) |idx_limb| { // Calculate the starting index for the current limb const i = idx_limb * 64; // Iterate through each bit of the current limb inline for (0..64) |ind_bit| // Extract the bit value and assign it to the corresponding position in the bit representation array bits[i + ind_bit] = (self.limbs[idx_limb] >> ind_bit) & 1 == 1; } // Return the little-endian bit representation of the big integer return bits; } /// Converts a big integer to a big-endian bit representation. /// /// This function converts a big integer to its big-endian bit representation. /// It iterates through each limb of the big integer, starting from the most significant limb, /// and generates a bit representation where each bit corresponds to a single limb. /// /// Parameters: /// - self: A pointer to the big integer to be converted to a big-endian bit representation. /// /// Returns: /// - An array of boolean values representing the big-endian bit representation of the big integer. /// /// Notes: /// - The function generates a bit representation where the most significant bit of the big integer corresponds to the first bit of the array. /// - Each limb of the big integer contributes 64 bits to the overall bit representation. /// - The resulting bit representation is big-endian, with the most significant bits appearing first. /// - Inline loops are used for performance optimization. /// - The function returns an array of boolean values representing the bit representation of the big integer. pub fn toBitsBe(self: *const Self) [N * 64]bool { // Initialize an array to hold the bit representation var bits = [_]bool{false} ** (N * 64); // Iterate through each limb of the big integer inline for (0..N) |idx_limb| { // Calculate the starting index for the current limb in the big-endian bit representation const pre_index = (N - idx_limb - 1) * 64 + 63; // Iterate through each bit of the current limb inline for (0..64) |ind_bit| // Calculate the index in the bit representation array and extract the bit value bits[pre_index - ind_bit] = (self.limbs[idx_limb] >> ind_bit) & 1 == 1; } // Return the big-endian bit representation of the big integer return bits; } /// Converts a big integer to a little-endian byte representation. /// /// This function converts a big integer to its little-endian byte representation. /// It iterates through each limb of the big integer, starting from the least significant limb, /// and generates a byte representation where each byte corresponds to a single limb. /// /// Parameters: /// - self: A pointer to the big integer to be converted to a little-endian byte representation. /// /// Returns: /// - An array of bytes representing the little-endian byte representation of the big integer. /// /// Notes: /// - The function generates a byte representation where the least significant byte of the big integer corresponds to the first byte of the array. /// - Each limb of the big integer contributes 8 bytes to the overall byte representation. /// - The resulting byte representation is little-endian, with the least significant bytes appearing first. /// - Inline loops are used for performance optimization. /// - The function returns an array of bytes representing the byte representation of the big integer. pub fn toBytesLe(self: *const Self) [@sizeOf(u256)]u8 { // Initialize an array to hold the byte representation var buf: [@sizeOf(u256)]u8 = undefined; // Iterate through each limb of the big integer inline for (0..N) |i| { // Calculate the starting index for the current limb in the little-endian byte representation const idx_bytes = i * 8; // Write the current limb to the byte representation array using little-endian byte order std.mem.writeInt( u64, buf[idx_bytes .. idx_bytes + 8], self.limbs[i], .little, ); } // Return the little-endian byte representation of the big integer return buf; } /// Converts a big integer to a big-endian byte representation. /// /// This function converts a big integer to its big-endian byte representation. /// It iterates through each limb of the big integer, starting from the most significant limb, /// and generates a byte representation where each byte corresponds to a single limb. /// /// Parameters: /// - self: The big integer to be converted to a big-endian byte representation. /// /// Returns: /// - An array of bytes representing the big-endian byte representation of the big integer. /// /// Notes: /// - The function generates a byte representation where the most significant byte of the big integer corresponds to the first byte of the array. /// - Each limb of the big integer contributes 8 bytes to the overall byte representation. /// - The resulting byte representation is big-endian, with the most significant bytes appearing first. /// - Inline loops are used for performance optimization. /// - The function returns an array of bytes representing the byte representation of the big integer. pub fn toBytesBe(self: Self) [@sizeOf(u256)]u8 { // Initialize an array to hold the byte representation var buf: [@sizeOf(u256)]u8 = undefined; // Iterate through each limb of the big integer inline for (0..N) |i| { // Calculate the starting index for the current limb in the big-endian byte representation const idx_bytes = i * 8; // Write the current limb to the byte representation array using big-endian byte order std.mem.writeInt( u64, buf[idx_bytes .. idx_bytes + 8], self.limbs[N - 1 - i], .big, ); } // Return the big-endian byte representation of the big integer return buf; } /// Creates a big integer from a byte array in little-endian order. /// /// This function constructs a big integer from a byte array by converting each set of 8 bytes /// (corresponding to one limb) into a u64 integer and storing it in the big integer's limbs array. /// The byte array is assumed to represent the limbs of the big integer in little-endian order. /// /// Parameters: /// - bytes: A byte array representing the limbs of the big integer in little-endian order. /// /// Returns: /// - A big integer constructed from the provided byte array. pub fn fromBytesLe(bytes: [N * @sizeOf(u64)]u8) Self { // Initialize a new big integer with all limbs set to zero. var r: Self = .{}; // Iterate through each limb and populate it with data from the byte array. inline for (0..N) |i| { // Calculate the index of the first byte of the current limb. const idx_byte = i * 8; // Read 8 bytes from the byte array and convert them to a u64 integer in little-endian order. // Store the resulting u64 integer in the current limb of the big integer. r.limbs[i] = std.mem.readInt(u64, bytes[idx_byte .. idx_byte + 8], .little); } // Return the constructed big integer. return r; } /// Creates a big integer from a byte array in big-endian order. /// /// This function constructs a big integer from a byte array by converting each set of 8 bytes /// (corresponding to one limb) into a u64 integer and storing it in the big integer's limbs array. /// The byte array is assumed to represent the limbs of the big integer in big-endian order. /// /// Parameters: /// - bytes: A byte array representing the limbs of the big integer in big-endian order. /// /// Returns: /// - A big integer constructed from the provided byte array. pub fn fromBytesBe(bytes: [@sizeOf(u256)]u8) Self { // Initialize a new big integer with all limbs set to zero. var r: Self = .{}; // Iterate through each limb and populate it with data from the byte array. inline for (0..N) |i| { // Calculate the index of the first byte of the current limb. const idx_byte = i * 8; // Read 8 bytes from the byte array and convert them to a u64 integer in big-endian order. // Store the resulting u64 integer in the current limb of the big integer. r.limbs[N - 1 - i] = std.mem.readInt(u64, bytes[idx_byte .. idx_byte + 8], .big); } // Return the constructed big integer. return r; } /// Creates a big integer from a little-endian bit representation. /// /// This function constructs a big integer from a little-endian bit representation stored in a boolean array. /// /// Parameters: /// - bits: A boolean array representing the little-endian bit representation of the big integer. /// /// Returns: /// - A new instance of the big integer constructed from the little-endian bit representation. pub fn fromBitsLe(bits: [@bitSizeOf(u256)]bool) Self { // Initialize the result big integer var res: Self = .{}; // Iterate over each limb of the big integer inline for (&res.limbs, 0..) |*res_limb, i| { // Calculate the starting index for the current limb in the bit array const limb_start_index = i * 64; // Iterate over each bit within the current limb inline for (0..@bitSizeOf(u64)) |j| { // Convert the boolean value to an integer (0 or 1) and shift it to its position within the limb // Then, bitwise OR it with the current limb of the result big integer res_limb.* |= @as(u64, @intCast(@intFromBool(bits[limb_start_index + j]))) << j; } } // Return the constructed big integer return res; } /// Constructs a big integer from a big-endian array of bits. /// /// This function constructs a big integer from a big-endian array of bits and returns the result. /// /// # Parameters /// - `bits`: A big-endian array of bits representing the big integer. /// /// # Returns /// The big integer constructed from the big-endian array of bits. pub fn fromBitsBe(bits: [@bitSizeOf(u256)]bool) Self { // Create a copy of the input bits array to work with little-endian representation. var bits_le: [@bitSizeOf(u256)]bool = bits; // Reverse the bits array to convert it to little-endian representation. std.mem.reverse(bool, &bits_le); // Construct the big integer from the little-endian bits representation. return Self.fromBitsLe(bits_le); } /// Retrieves the value of the bit at the specified index in the big integer. /// /// This function checks if the bit at the specified index is set (1) or unset (0) in the big integer. /// /// Parameters: /// - self: A pointer to the big integer from which the bit value will be retrieved. /// - i: The index of the bit to retrieve. Indices start from 0 for the least significant bit. /// /// Returns: /// - `true` if the bit at the specified index is set (1), `false` otherwise. /// /// Notes: /// - If the specified index is greater than or equal to the total number of bits in the big integer, the function returns `false`. /// - The function calculates the index of the limb and the position within the limb corresponding to the specified bit index. /// - It then checks if the bit at the calculated position within the corresponding limb is set. pub fn getBit(self: *const Self, i: usize) bool { // Check if the specified index exceeds the total number of bits in the big integer. if (i >= comptime 64 * N) return false; // Calculate the index of the limb containing the specified bit. const limb: usize = i / 64; // Calculate the position within the limb corresponding to the specified bit index. // Check if the bit at the calculated position within the limb is set. return (self.limbs[limb] & (@as(usize, 1) << @intCast(i - (64 * limb)))) != 0; } /// Performs a bitwise left shift operation on a big integer. /// /// This function shifts the bits of the big integer to the left by the specified number of positions. /// The shift is performed in place, and the result is returned as a new instance of the `BigInt` struct. /// /// Parameters: /// - self: A pointer to the big integer to be shifted. /// - rhs: The number of positions to shift the bits to the left. /// /// Returns: /// - A new instance of the `BigInt` struct representing the result of the bitwise left shift operation. pub fn shl(self: *const Self, rhs: u32) Self { // Dereference the pointer to obtain the actual big integer. var a = self.*; // Call the shlAssign function to perform the bitwise left shift operation in place. a.shlAssign(rhs); // Return the resulting big integer after the shift operation. return a; } /// Performs a bitwise left shift operation on a big integer in place. /// /// This function shifts the bits of the big integer to the left by the specified number of positions. /// The shift is performed in place, modifying the original big integer. /// /// The operation does not return an overflow if the number of bit shifted is greater than N * 64. /// Result will be saturated to zero in this scenario. /// /// Parameters: /// - self: A pointer to the big integer to be shifted. /// - rhs: The number of positions to shift the bits to the left. /// /// Returns: /// - void /// /// Notes: /// - If the number of positions to shift is greater than or equal to `64 * N`, where `N` is the number of limbs of the big integer, /// the big integer is set to zero and the function returns early. /// - The shift is performed by shifting each limb for one position to the left. If a shift of more than 64 positions is required, /// multiple iterations are performed until the remaining shift is less than 64. pub fn shlAssign(self: *Self, rhs: u32) void { // Check for overflow. // If the number of positions to shift is greater than or equal to the total bit width of the big integer, // set the big integer to zero and return early. if (rhs >= comptime 64 * N) { self.* = .{}; return; } // Initialize the remaining shift count. var shift = rhs; // Perform the shift operation in blocks of 64 bits until the remaining shift count is less than 64. while (shift >= 64) { // Temporary variable to hold the shifted out bits. var t: u64 = 0; // Shift each limb for one position to the left within the block of 64 bits. inline for (0..N) |i| { std.mem.swap(u64, &t, &self.limbs[i]); } // Update the remaining shift count. shift -= 64; } // If there are remaining shifts to perform. if (shift > 0) { // Temporary variable to hold the shifted out bits. var t: u64 = 0; // Iterate through each limb and perform the remaining shifts. inline for (0..N) |i| { // Dereference the pointer to the current limb. const a = &self.limbs[i]; // Perform a logical right shift on the current limb to get the bits shifted out. const t2 = a.* >> @intCast(64 - shift); // Perform the left shift operation on the current limb. a.* <<= @intCast(shift); // Combine the shifted out bits with the current limb using bitwise OR. a.* |= t; // Update the temporary variable with the shifted out bits for the next iteration. t = t2; } } } /// Performs a bitwise right shift operation on a big integer. /// /// This function shifts the bits of the big integer to the right by the specified number of positions. /// The shift is performed in place, and the result is returned as a new instance of the `BigInt` struct. /// /// Parameters: /// - self: A pointer to the big integer to be shifted. /// - rhs: The number of positions to shift the bits to the right. /// /// Returns: /// - A new instance of the `BigInt` struct representing the result of the bitwise right shift operation. pub fn shr(self: *const Self, rhs: u32) Self { // Dereference the pointer to obtain the actual big integer. var a = self.*; // Call the shrAssign function to perform the bitwise right shift operation in place. a.shrAssign(rhs); // Return the resulting big integer after the shift operation. return a; } /// Performs a bitwise right shift operation on a big integer in place. /// /// This function shifts the bits of the big integer to the right by the specified number of positions. /// The shift is performed in place, modifying the original big integer. /// /// The operation does not return an overflow if the number of bit shifted is greater than N * 64. /// Result will be saturated to zero in this scenario. /// /// Parameters: /// - self: A pointer to the big integer to be shifted. /// - rhs: The number of positions to shift the bits to the right. /// /// Returns: /// - void /// /// Notes: /// - If the number of positions to shift is greater than or equal to `64 * N`, where `N` is the number of limbs of the big integer, /// the big integer is set to zero and the function returns early. /// - The shift is performed by shifting each limb for one position to the right. If a shift of more than 64 positions is required, /// multiple iterations are performed until the remaining shift is less than 64. pub fn shrAssign(self: *Self, rhs: u32) void { // Check for overflow. // If the number of positions to shift is greater than or equal to the total bit width of the big integer, // set the big integer to zero and return early. if (rhs >= comptime 64 * N) { self.* = .{}; return; } // Initialize the remaining shift count. var shift = rhs; // Perform the shift operation in blocks of 64 bits until the remaining shift count is less than 64. while (shift >= 64) { // Temporary variable to hold the shifted out bits. var t: u64 = 0; // Start from the most significant limb and shift each limb for one position to the right. var limb = N; while (limb > 0) { limb -= 1; std.mem.swap(u64, &t, &self.limbs[limb]); } // Update the remaining shift count. shift -= 64; } // If there are remaining shifts to perform. if (shift > 0) { // Temporary variable to hold the shifted out bits. var t: u64 = 0; // Start from the most significant limb and perform the remaining shifts. var limb = N; while (limb > 0) { limb -= 1; // Dereference the pointer to the current limb. const a = &self.limbs[limb]; // Perform a logical left shift on the current limb to get the bits shifted out. const t2 = a.* << @intCast(64 - shift); // Perform the right shift operation on the current limb. a.* >>= @intCast(shift); // Combine the shifted out bits with the current limb using bitwise OR. a.* |= t; // Update the temporary variable with the shifted out bits for the next iteration. t = t2; } } } /// Generates a new instance of `Self` with all limbs set to the maximum value of `u64`. /// /// This function creates and returns a new instance of `Self` with each limb initialized to the maximum value of `u64`. /// /// Returns: /// - A new instance of `Self` with all limbs set to the maximum value of `u64`. pub fn max() Self { // Creates a new instance of `Self` with all limbs set to the maximum value of `u64`. return .{ .limbs = .{ std.math.maxInt(u64), std.math.maxInt(u64), std.math.maxInt(u64), std.math.maxInt(u64), }, }; } /// Returns the number of bits needed to represent the number as little endian. /// /// This function calculates and returns the number of bits needed to represent the number as little endian format. /// /// # Parameters /// - `self`: A pointer to the struct instance. /// /// # Returns /// The number of bits needed to represent the number as little endian. pub fn numBitsLe(self: *const Self) usize { // Initialize the variable `l` to the number of limbs. var l: usize = N; // Iterate over each limb in reverse order. while (l > 0) { // Decrement `l`. l -= 1; // Check if the current limb is non-zero. if (self.limbs[l] != 0) { // Calculate the number of bits needed to represent the non-zero limb. return @bitSizeOf(u64) * (l + 1) - @clz(self.limbs[l]); } } // Return 0 if all limbs are zero. return 0; } /// Performs a bitwise OR operation between two big integers. /// /// This function calculates the bitwise OR between two big integers and returns the result. /// /// # Parameters /// - `self`: A pointer to the first big integer. /// - `rhs`: A pointer to the second big integer. /// /// # Returns /// The result of the bitwise OR operation between the two big integers. pub fn bitOr(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual big integer. var a = self.*; // Perform the bitwise OR operation and assign the result to `a`. a.bitOrAssign(rhs); // Return the result of the operation. return a; } /// Performs a bitwise OR operation in place on a big integer. /// /// This function calculates the bitwise OR between two big integers and assigns the result to the first big integer. /// /// # Parameters /// - `self`: A pointer to the big integer to be modified. /// - `rhs`: A pointer to the big integer used for the OR operation. pub fn bitOrAssign(self: *Self, rhs: *const Self) void { // Perform a bitwise OR operation on each limb of the big integers. inline for (0..N) |i| self.limbs[i] |= rhs.limbs[i]; } /// Performs a bitwise AND operation between two big integers. /// /// This function calculates the bitwise AND between two big integers and returns the result. /// /// # Parameters /// - `self`: A pointer to the first big integer. /// - `rhs`: A pointer to the second big integer. /// /// # Returns /// The result of the bitwise AND operation between the two big integers. pub fn bitAnd(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual big integer. var a = self.*; // Perform the bitwise AND operation and assign the result to `a`. a.bitAndAssign(rhs); // Return the result of the operation. return a; } /// Performs a bitwise AND operation in place on a big integer. /// /// This function calculates the bitwise AND between two big integers and assigns the result to the first big integer. /// /// # Parameters /// - `self`: A pointer to the big integer to be modified. /// - `rhs`: A pointer to the big integer used for the AND operation. pub fn bitAndAssign(self: *Self, rhs: *const Self) void { // Perform a bitwise AND operation on each limb of the big integers. inline for (0..N) |i| self.limbs[i] &= rhs.limbs[i]; } /// Performs a bitwise XOR operation between two big integers. /// /// This function performs a bitwise XOR operation between two big integers and returns the result. /// /// # Parameters /// - `self`: A pointer to the first big integer operand. /// - `rhs`: A pointer to the second big integer operand. /// /// # Returns /// The result of the bitwise XOR operation. pub fn bitXor(self: *const Self, rhs: *const Self) Self { // Dereference the pointer to obtain the actual big integer. var a = self.*; // Perform a bitwise XOR operation between the two big integers. a.bitXorAssign(rhs); // Return the result of the operation. return a; } /// Performs an in-place bitwise XOR operation with another big integer. /// /// This function performs an in-place bitwise XOR operation with another big integer. /// /// # Parameters /// - `self`: A pointer to the big integer to be modified. /// - `rhs`: A pointer to the second big integer operand. pub fn bitXorAssign(self: *Self, rhs: *const Self) void { // Iterate over the limbs of the big integers and perform the bitwise XOR operation. inline for (0..N) |i| self.limbs[i] ^= rhs.limbs[i]; } /// Selects between two big integers based on a constant choice. /// /// This function selects between two big integers based on a constant choice provided as an argument. If the constant choice is `TRUE`, the function returns the second big integer (`rhs`), otherwise, it returns the first big integer (`self`). /// /// Parameters: /// - self: A pointer to the first big integer. /// - rhs: A pointer to the second big integer. /// - c: A constant choice indicating which big integer to select. /// /// Returns: /// - The selected big integer. pub fn select(self: *const Self, rhs: *const Self, c: ConstChoice) Self { return if (c.eql(&ConstChoice.TRUE)) rhs.* else self.*; } /// Computes division with remainder for two big integers. /// /// This function computes division with remainder for two big integers using a variant of long division algorithm. It returns a tuple containing the quotient and the remainder. /// /// Parameters: /// - self: A pointer to the dividend big integer. /// - rhs: A pointer to the divisor big integer. /// /// Returns: /// - A tuple containing the quotient and the remainder. /// /// Remarks: /// - The function assumes that the divisor big integer is non-zero. /// - The division algorithm used is a variant of long division. pub fn divRem(self: *const Self, rhs: *const Self) std.meta.Tuple(&.{ Self, Self }) { // Ensure that the divisor is not zero std.debug.assert(!rhs.isZero()); // Calculate the number of bits in the divisor const mb = rhs.numBitsLe(); // Initialize the remainder as the dividend var rm = self.*; // Initialize the quotient as zero var qt: Self = .{}; // Calculate the number of bits to shift the divisor var bd: u32 = @intCast(N * @bitSizeOf(u64) - mb); // Shift the divisor to align with the most significant bit of the remainder var c = rhs.shl(bd); // Perform long division algorithm while (true) { // Compute the difference between the remainder and the shifted divisor const rb = rm.subWithBorrow(&c); // Determine whether to subtract or not based on the borrow const choice = ConstChoice.initFromBool(rb[1]); // Update the remainder based on the choice rm = rb[0].select(&rm, choice); // Update the quotient based on the choice qt = qt.bitOr(&comptime Self.one()).select(&qt, choice); // Check if the division process is complete if (bd == 0) break; // Update the shift count and the shifted divisor bd -= 1; c.shrAssign(1); qt.shlAssign(1); } // Return the computed quotient and remainder as a tuple return .{ qt, rm }; } /// Computes the remainder of dividing `self` by `rhs`, returning the remainder in variable-time with respect to `rhs`. /// /// When used with a fixed `rhs`, this function is constant-time with respect to `self`. /// /// Parameters: /// - self: A pointer to the dividend big integer. /// - rhs: A pointer to the divisor big integer. /// /// Returns: /// - The remainder of dividing `self` by `rhs`. /// /// Remarks: /// - This function is equivalent to obtaining the second element of the tuple returned by `divRem`. pub fn rem(self: *const Self, rhs: *const Self) Self { // Ensure that the divisor is not zero std.debug.assert(!rhs.isZero()); // Calculate the number of bits in the divisor const mb = rhs.numBitsLe(); // Initialize the remainder as the dividend var rm = self.*; // Calculate the number of bits to shift the divisor var bd: u32 = @intCast(N * @bitSizeOf(u64) - mb); // Shift the divisor to align with the most significant bit of the remainder var c = rhs.shl(bd); // Perform long division algorithm while (true) { // Compute the difference between the remainder and the shifted divisor const rb = rm.subWithBorrow(&c); // Update the remainder based on the choice rm = rb[0].select(&rm, ConstChoice.initFromBool(rb[1])); // Check if the division process is complete if (bd == 0) break; // Update the shift count and the shifted divisor bd -= 1; c.shrAssign(1); } // Return the computed remainder return rm; } /// Performs the modular multiplication operation of two big integers within the Montgomery field modulo `p`. /// /// This function computes the product of `self` and `rhs` modulo `p` using the Montgomery reduction technique. /// It ensures that the modulus `p` is odd, as even moduli are currently unsupported and will panic. /// /// Parameters: /// - self: A pointer to the multiplicand big integer. /// - rhs: A pointer to the multiplier big integer. /// - p: A pointer to the modulus big integer. /// /// Returns: /// - The result of the modular multiplication operation (`self * rhs % p`) within the Montgomery field. /// /// Remarks: /// - This function leverages the Montgomery reduction technique for efficient modular multiplication. /// - It requires `p` to be an odd modulus; otherwise, it will panic. /// - Montgomery multiplication is efficient for repeated modular multiplications with the same modulus. pub fn mulMod(self: *const Self, rhs: *const Self, comptime p: *const Self) Self { // Ensure that the modulus is odd if (p.isOdd()) { // Initialize the Montgomery field with modulus `p` const field = Field(N, comptime p.toU256()); // Perform Montgomery multiplication return field.toBigInt(field.fromBytesLe(self.toBytesLe()) .mul(&field.fromBytesLe(rhs.toBytesLe()))); } // Panics if the modulus is even (unsupported) // TODO: support for even `p`? @panic("even moduli are currently unsupported"); } /// Computes the 2-adic valuation of a big integer. /// /// This function computes the 2-adic valuation of a big integer, which represents the largest power of 2 that divides the big integer. /// /// # Parameters /// - `self`: A pointer to the big integer for which the 2-adic valuation is to be computed. /// /// # Returns /// The 2-adic valuation of the big integer. /// /// Remarks /// - The function assumes that the big integer is odd. pub fn twoAdicValuation(self: *const Self) u32 { // Assert that the big integer is odd std.debug.assert(self.isOdd()); // Dereference the pointer to obtain the actual big integer var a = self.*; // Initialize the 2-adic valuation var twoAdicity: u32 = 0; // Since `self` is odd, we can always subtract one without a borrow a.limbs[0] -= 1; // Compute the 2-adic valuation while (a.isEven()) { a.shrAssign(1); twoAdicity += 1; } // Return the 2-adic valuation return twoAdicity; } }; } test "bigInt: div2 function should divide by 2" { // Test case: Divide a big integer by 2 // Initialize a big integer with a value var a = bigInt(4).init(.{ 8446744, 0, 0, 0 }); // Perform division by 2 in place a.div2Assign(); // Assert that the result matches the expected value try expectEqual([_]u64{ 4223372, 0, 0, 0 }, a.limbs); // Test case: Divide zero by 2 // Initialize a big integer with zero value var b = bigInt(4).init(.{ 0, 0, 0, 0 }); // Perform division by 2 in place b.div2Assign(); // Assert that the result is still zero try expectEqual([_]u64{ 0, 0, 0, 0 }, b.limbs); } test "bigInt: constants" { // Test case: Verify initialization of zero constant // Assert that the zero constant matches the expected value try expectEqual(bigInt(4).init(.{ 0, 0, 0, 0 }), comptime bigInt(4){}); // Test case: Verify initialization of one constant // Assert that the one constant matches the expected value try expectEqual(bigInt(4).init(.{ 1, 0, 0, 0 }), comptime bigInt(4).one()); } test "bigInt: fuzzing test for comparison" { // Test case: Fuzzing test for equality // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Test case: Verify equality of randomly generated big integers // Generate random unsigned integers of different sizes. var a = bigInt(4).rand(random); var b = bigInt(4).rand(random); var c = bigInt(4).rand(random); // Obtain constant big integers for comparison var one = comptime bigInt(4).one(); var zero = comptime bigInt(4){}; // Assert that each big integer is equal to itself try expect(a.eql(a)); try expect(b.eql(b)); try expect(c.eql(c)); // Assert that each big integer is equal to itself try expect(!a.ne(a)); try expect(!b.ne(b)); try expect(!c.ne(c)); // Assert non equality if (!a.eql(b)) try expect(a.ne(b)); if (!a.eql(c)) try expect(a.ne(c)); if (!b.eql(c)) try expect(b.ne(c)); // Assert isZero method for each big integer try expect(!a.isZero()); try expect(!b.isZero()); try expect(!c.isZero()); try expect(!one.isZero()); try expect(zero.isZero()); // Assert that each big integer is equal to itself using the cmp function try expect(a.cmp(&a) == .eq); try expect(b.cmp(&b) == .eq); try expect(c.cmp(&c) == .eq); // Assert that each big integer is less than or equal to itself try expect(a.lte(&a)); try expect(b.lte(&b)); try expect(c.lte(&c)); // Assert that each big integer is not less than itself try expect(!a.lt(&a)); try expect(!b.lt(&b)); try expect(!c.lt(&c)); // Assert that each big integer is not greater than itself try expect(!a.gt(&a)); try expect(!b.gt(&b)); try expect(!c.gt(&c)); // Assert that each big integer is greater than or equal to itself try expect(a.gte(&a)); try expect(b.gte(&b)); try expect(c.gte(&c)); // Assert that constant big integers are equal to themselves try expect(one.eql(one)); try expect(zero.eql(zero)); // Assert that one is greater than zero and greater than or equal to zero try expect(one.gt(&zero)); try expect(one.gte(&zero)); // Assert that one is not less than zero and not less than or equal to zero try expect(!one.lt(&zero)); try expect(!one.lte(&zero)); // Assert that zero is not greater than one and not greater than or equal to one try expect(!zero.gt(&one)); try expect(!zero.gte(&one)); // Assert that zero is less than one and less than or equal to one try expect(zero.lt(&one)); try expect(zero.lte(&one)); } } test "bigInt: fuzzing test for add and sub operations" { // Test case: Fuzzing test for addition and subtraction operations // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Test case: Verify addition and subtraction operations with random big integers // Generate random unsigned integers of different sizes. const a = bigInt(4).rand(random); const b = bigInt(4).rand(random); const c = bigInt(4).rand(random); // Constant zero big integer const zero = comptime bigInt(4){}; // Test addition with zero // Assert that adding zero to a big integer results in the same big integer try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ a, false }), a.addWithCarry(&zero), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ b, false }), b.addWithCarry(&zero), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ c, false }), c.addWithCarry(&zero), ); // Test subtraction with zero // Assert that subtracting zero from a big integer results in the same big integer try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ a, false }), a.subWithBorrow(&zero), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ b, false }), b.subWithBorrow(&zero), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ c, false }), c.subWithBorrow(&zero), ); // Test subtraction resulting in zero // Assert that subtracting a big integer from itself results in zero try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ zero, false }), a.subWithBorrow(&a), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ zero, false }), b.subWithBorrow(&b), ); try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bool }), .{ zero, false }), c.subWithBorrow(&c), ); } } test "bigInt: fuzzing test for mul and div operations" { // Test case: Fuzzing test for multiplication and division operations // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Test case: Verify multiplication and division operations with random big integers // Generate random unsigned integers of different sizes. const a = bigInt(4).rand(random); const b = bigInt(4).rand(random); const c = bigInt(4).rand(random); // Constant zero big integer const zero = comptime bigInt(4){}; // Constant one big integer const one = comptime bigInt(4).one(); // Test addition with carry operation // Verify that adding a big integer with carry yields the same result as multiplying by two try expectEqual(zero.addWithCarry(&zero), zero.mul2()); try expectEqual(one.addWithCarry(&one), one.mul2()); try expectEqual(a.addWithCarry(&a), a.mul2()); try expectEqual(b.addWithCarry(&b), b.mul2()); try expectEqual(c.addWithCarry(&c), c.mul2()); // Multiplication by zero try expect(a.mul(&zero)[0].eql(zero)); try expect(zero.mul(&a)[0].eql(zero)); try expect(zero.mul(&zero)[0].eql(zero)); try expect(a.mulLow(&zero).eql(zero)); try expect(zero.mulLow(&a).eql(zero)); try expect(zero.mulLow(&zero).eql(zero)); try expect(a.mulHigh(&zero).eql(zero)); try expect(zero.mulHigh(&a).eql(zero)); try expect(zero.mulHigh(&zero).eql(zero)); // Associativity try expect(a.mul(&b)[0].mul(&c)[0].eql( a.mul(&b.mul(&c)[0])[0], )); try expect(a.mul(&b)[0].mul(&c)[0].eql( a.mulLow(&b.mulLow(&c)), )); // Commutativity try expect(a.mul(&b)[0].eql(b.mul(&a)[0])); try expect(a.mul(&c)[0].eql(c.mul(&a)[0])); try expect(b.mul(&c)[0].eql(c.mul(&b)[0])); try expect(b.mulLow(&a).eql(a.mulLow(&b))); try expect(c.mulLow(&a).eql(a.mulLow(&c))); try expect(c.mulLow(&b).eql(b.mulLow(&c))); // Associativity and commutativity simultaneously try expect(a.mul(&b)[0].mul(&c)[0].eql(a.mul(&c)[0].mul(&b)[0])); try expect(a.mul(&c)[0].mul(&b)[0].eql(b.mul(&c)[0].mul(&a)[0])); try expect(a.mulLow(&b).mulLow(&c).eql(a.mulLow(&c).mulLow(&b))); try expect(a.mulLow(&c).mulLow(&b).eql(b.mulLow(&c).mulLow(&a))); } } test "bigInt: division with remainder" { // Test case: Fuzzing test for division operations // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Test case: Verify multiplication and division operations with random big integers // Generate random unsigned integers of different sizes. const a = bigInt(4).rand(random); const b = bigInt(4).rand(random); // Verify that the division with remainder operation works correctly. try expectEqual( @as( std.meta.Tuple(&.{ bigInt(4), bigInt(4) }), .{ a.shr(128), .{} }, ), a.shr(128).mulLow(&b.shr(128)).divRem(&b.shr(128)), ); } // Iterate over predefined test cases. for ( [_]std.meta.Tuple(&.{ u256, u256, u256, u256 }){ .{ 200, 2, 100, 0 }, .{ 100, 25, 4, 0 }, .{ 100, 10, 10, 0 }, .{ 1024, 8, 128, 0 }, .{ 27, 13, 2, 1 }, .{ 26, 13, 2, 0 }, .{ 14, 13, 1, 1 }, .{ 13, 13, 1, 0 }, .{ 12, 13, 0, 12 }, .{ 1, 13, 0, 1 }, .{ 10, 1, 10, 0 }, .{ 8, 3, 2, 2 }, .{ 500721, 5, 100144, 1 }, .{ 4758402376589578934275873583589345, 43950384634609, 108267593472721187331, 12368508650766 }, }, ) |r| { // Create big integers from the test case values. const a = bigInt(4).fromInt(u256, r[0]); const b = bigInt(4).fromInt(u256, r[1]); const c = bigInt(4).fromInt(u256, r[2]); const d = bigInt(4).fromInt(u256, r[3]); // Verify that the division with remainder operation works correctly for predefined test cases. try expectEqual( @as(std.meta.Tuple(&.{ bigInt(4), bigInt(4) }), .{ c, d }), a.divRem(&b), ); // Verify the remainder. try expectEqual(d, a.rem(&b)); } // Test case: Verify division with remainder operation for large integers. const a = bigInt(4).fromInt(u256, 12678920202929299999999999282828); const b = bigInt(4).fromInt(u256, 9000000000000); // Verify that the division with remainder operation works correctly for large integers. try expectEqual( @as( std.meta.Tuple(&.{ bigInt(4), bigInt(4) }), .{ a, .{} }, ), a.mulLow(&b).divRem(&b), ); } test "bigInt: fuzzing test for shift operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Define a constant zero big integer. const zero = comptime bigInt(4){}; // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate random big integers of different sizes. const a = bigInt(4).rand(random); const b = bigInt(4).rand(random); const c = bigInt(4).rand(random); // Initialize variables to hold the expected results after shifting. var a_mul_expected = a; var b_mul_expected = b; var c_mul_expected = c; var a_div_expected = a; var b_div_expected = b; var c_div_expected = c; // Perform multiple left shifts and right shifts on each big integer to compute the expected results. inline for (0..5) |_| { _ = a_mul_expected.mul2Assign(); _ = b_mul_expected.mul2Assign(); _ = c_mul_expected.mul2Assign(); _ = a_div_expected.div2Assign(); _ = b_div_expected.div2Assign(); _ = c_div_expected.div2Assign(); } // Assert that the result of shifting each big integer by 5 bits to the left is equal to the expected result after multiple left shifts. try expect(a.shl(5).eql(a_mul_expected)); try expect(b.shl(5).eql(b_mul_expected)); try expect(c.shl(5).eql(c_mul_expected)); // Assert that shifting a big integer by an excessive number of bits results in zero. try expect(a.shl(6 * 64).eql(zero)); // Assert that the result of shifting each big integer by 5 bits to the right is equal to the expected result after multiple right shifts. try expect(a.shr(5).eql(a_div_expected)); try expect(b.shr(5).eql(b_div_expected)); try expect(c.shr(5).eql(c_div_expected)); // Assert that shifting a big integer by an excessive number of bits results in zero. try expect(c.shr(6 * 64).eql(zero)); } } test "bigInt: fuzzing test for bits operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate random big integers of different sizes. const a = bigInt(4).rand(random); // Compute a new big integer by performing a logical right shift operation on `a` by 3 bits and assign it to `b`. const b = a.shr(3); // Test null bits of `b` to ensure the correctness of the logical right shift operation. try expect(!b.getBit(4 * 64 - 1)); try expect(!b.getBit(4 * 64 - 2)); try expect(!b.getBit(4 * 64 - 3)); // Bitwise OR operation try expect(a.bitOr(&a).eql(a)); try expect(a.bitOr(&b).bitOr(&b).eql(a.bitOr(&b))); // Bitwise XOR operation const xor = a.bitXor(&b); inline for (0..4) |i| try expect(xor.limbs[i] == a.limbs[i] ^ b.limbs[i]); // Bitwise AND operation try expect(a.bitAnd(&a).eql(a)); try expect(a.bitAnd(&b).bitAnd(&b).eql(a.bitAnd(&b))); // From/to bits operations try expect(bigInt(4).fromBitsLe(a.toBitsLe()).eql(a)); try expect(bigInt(4).fromBitsBe(a.toBitsBe()).eql(a)); } // Define a constant `one` representing a big integer with the value 1. const one = comptime bigInt(4).one(); // Test the bits of `one` to verify the bit representation of the value 1. // - The 0th bit of BigInteger representing 1 is 1 try expect(one.getBit(0)); // - The 1st bit of BigInteger representing 1 is not 1 try expect(!one.getBit(1)); // Define a constant `thirty_two` representing a big integer with the value 32, obtained by shifting `one` by 5 bits to the left. const thirty_two = one.shl(5); // Test the bits of `thirty_two` to verify the bit representation of the value 32. // - The 0th bit of BigInteger representing 32 is not 1 try expect(!thirty_two.getBit(0)); // - The 1st bit of BigInteger representing 32 is not 1 try expect(!thirty_two.getBit(1)); // - The 2nd bit of BigInteger representing 32 is not 1 try expect(!thirty_two.getBit(2)); // - The 3rd bit of BigInteger representing 32 is not 1 try expect(!thirty_two.getBit(3)); // - The 4th bit of BigInteger representing 32 is not 1 try expect(!thirty_two.getBit(4)); // - The 5th bit of BigInteger representing 32 is 1 try expect(thirty_two.getBit(5)); // Define a constant `zero` representing a big integer with the value 0. const zero = comptime bigInt(4){}; // Test the number of bits needed to represent some big integers try expectEqual(@as(usize, 0), zero.numBitsLe()); try expectEqual(@as(usize, 65), bigInt(4).init(.{ 0b0, 0b1, 0, 0 }).numBitsLe()); try expectEqual(@as(usize, 64 + 3), bigInt(4).init(.{ 0b0, 0b111, 0, 0 }).numBitsLe()); try expectEqual( @as(usize, 128), bigInt(4).init(.{ std.math.maxInt(u64), std.math.maxInt(u64), 0, 0 }).numBitsLe(), ); try expectEqual(@bitSizeOf(u256), bigInt(4).max().numBitsLe()); // Test to obtain big integer from bit array in little endian order var bits_array_one_le = [_]bool{false} ** (@bitSizeOf(u256)); bits_array_one_le[0] = true; try expect(bigInt(4).fromBitsLe(bits_array_one_le).eql(one)); try expect(bigInt(4).fromBitsLe([_]bool{true} ** (@bitSizeOf(u256))).eql(bigInt(4).max())); try expect(bigInt(4).fromBitsLe([_]bool{false} ** (@bitSizeOf(u256))).eql(zero)); // Test to obtain big integer from bit array in big endian order var bits_array_one_be = [_]bool{false} ** (@bitSizeOf(u256)); bits_array_one_be[@bitSizeOf(u256) - 1] = true; try expect(bigInt(4).fromBitsBe(bits_array_one_be).eql(one)); var bits_array_max = [_]bool{false} ** (@bitSizeOf(u256)); bits_array_max[0] = true; try expect(bigInt(4).fromBitsBe(bits_array_max).mul2()[0].eql(zero)); try expect(bigInt(4).fromBitsBe([_]bool{true} ** (@bitSizeOf(u256))).eql(bigInt(4).max())); try expect(bigInt(4).fromBitsBe([_]bool{false} ** (@bitSizeOf(u256))).eql(zero)); } test "bigInt: mulMod operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); const p: u256 = 0x61daf9a1ad4fd3345c3816c1d45c7eb10556c81331ad3d612bdd8fb9d8d8dd79; const p_big_int = comptime bigInt(4).fromInt(u256, p); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { const a = random.int(u256); const b = random.int(u256); const a_big_int = bigInt(4).fromInt(u256, a); const b_big_int = bigInt(4).fromInt(u256, b); try expectEqual( @mod(@as(u512, a) * @as(u512, b), p), a_big_int.mulMod(&b_big_int, &p_big_int).toU256(), ); } } test "bigInt: two adic valuation" { try expectEqual( @as(u32, 2), bigInt(4).fromInt(u256, 29).twoAdicValuation(), ); try expectEqual( @as(u32, 3), bigInt(4).fromInt(u256, 25).twoAdicValuation(), ); try expectEqual( @as(u32, 1), bigInt(4).fromInt(u256, 0x6C5E69E06D144792DC5CCDA014D108233D3A98E77387B26A4EE4487785644E5F).twoAdicValuation(), ); try expectEqual( @as(u32, 2), bigInt(4).fromInt(u256, 0xB49E79F09077C47B76690D8104622E5A1EC4805B646D157DBA58BE6B2E2EC6F5).twoAdicValuation(), ); try expectEqual( @as(u32, 46), bigInt(6).fromInt(u384, 0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001).twoAdicValuation(), ); }
0
repos/starknet-zig/src/math
repos/starknet-zig/src/math/fields/starknet.zig
const std = @import("std"); const fields = @import("fields.zig"); const bigInt = @import("biginteger.zig").bigInt; const STARKNET_PRIME = @import("./constants.zig").STARKNET_PRIME; const FELT_BYTE_SIZE = @import("./constants.zig").FELT_BYTE_SIZE; const TEST_ITERATIONS = @import("../../main.zig").TEST_ITERATIONS; const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const expectEqualSlices = std.testing.expectEqualSlices; // Base field for the Stark curve. // The prime is 0x800000000000011000000000000000000000000000000000000000000000001. pub const Felt252 = fields.Field(4, STARKNET_PRIME); test "Felt252: fromU8 should return a field element from a u8" { try expectEqual( @as(u256, std.math.maxInt(u8)), Felt252.fromInt(u8, std.math.maxInt(u8)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u8) / 3 * 2), Felt252.fromInt(u8, std.math.maxInt(u8) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u8) / 3), Felt252.fromInt(u8, std.math.maxInt(u8) / 3).toU256(), ); } test "Felt252: fromU16 should return a field element from a u16" { try expectEqual( @as(u256, std.math.maxInt(u16)), Felt252.fromInt(u16, std.math.maxInt(u16)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u16) / 3 * 2), Felt252.fromInt(u16, std.math.maxInt(u16) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u16) / 3), Felt252.fromInt(u16, std.math.maxInt(u16) / 3).toU256(), ); } test "Felt252: fromU32 should return a field element from a u32" { try expectEqual( @as(u256, std.math.maxInt(u32)), Felt252.fromInt(u32, std.math.maxInt(u32)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u32) / 3 * 2), Felt252.fromInt(u32, std.math.maxInt(u32) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u32) / 3), Felt252.fromInt(u32, std.math.maxInt(u32) / 3).toU256(), ); } test "Felt252: fromU64 should return a field element from a u64" { try expectEqual( @as(u256, std.math.maxInt(u64)), Felt252.fromInt(u64, std.math.maxInt(u64)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u64) / 3 * 2), Felt252.fromInt(u64, std.math.maxInt(u64) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u64) / 3), Felt252.fromInt(u64, std.math.maxInt(u64) / 3).toU256(), ); } test "Felt252: fromUsize should return a field element from a usize" { try expectEqual( @as(u256, std.math.maxInt(usize)), Felt252.fromInt(usize, std.math.maxInt(usize)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(usize) / 3 * 2), Felt252.fromInt(usize, std.math.maxInt(usize) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(usize) / 3), Felt252.fromInt(usize, std.math.maxInt(usize) / 3).toU256(), ); } test "Felt252: fromU128 should return a field element from a u128" { try expectEqual( @as(u256, std.math.maxInt(u128)), Felt252.fromInt(u128, std.math.maxInt(u128)).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u128) / 3 * 2), Felt252.fromInt(u128, std.math.maxInt(u128) / 3 * 2).toU256(), ); try expectEqual( @as(u256, std.math.maxInt(u128) / 3), Felt252.fromInt(u128, std.math.maxInt(u128) / 3).toU256(), ); } test "Felt252 testing for field numBitsLe()" { try expectEqual(@as(u64, 1), Felt252.fromInt(u8, 1).numBitsLe()); try expectEqual(@as(u64, 4), Felt252.fromInt(u8, 10).numBitsLe()); try expectEqual(@as(u64, 252), Felt252.fromInt(u8, 1).neg().numBitsLe()); try expectEqual(@as(u64, 0), Felt252.fromInt(u8, 0).numBitsLe()); } test "Felt252 fromInteger" { try expectEqual( Felt252{ .fe = bigInt(4).init( .{ 0xfffffffffffffec1, 0xffffffffffffffff, 0xffffffffffffffff, 0x7ffffffffffead0, }, ), }, Felt252.fromInt(u8, 10), ); try expectEqual( Felt252{ .fe = bigInt(4).init( .{ 0xfffffd737e000421, 0x1330fffff, 0xffffffffff6f8000, 0x7ffd4ab5e008a30, }, ), }, Felt252.fromInt(u256, std.math.maxInt(u256)), ); } test "Felt252 toU256" { try expectEqual( @as(u256, 10), Felt252.fromInt(u8, 10).toU256(), ); try expectEqual( @as( u256, 0x7fffffffffffdf0ffffffffffffffffffffffffffffffffffffffffffffffe0, ), Felt252.fromInt(u256, std.math.maxInt(u256)).toU256(), ); } test "Felt252 one" { try expectEqual( Felt252{ .fe = bigInt(4).init( .{ 0xffffffffffffffe1, 0xffffffffffffffff, 0xffffffffffffffff, 0x7fffffffffffdf0, }, ), }, Felt252.one(), ); } test "Felt252 zero" { try expectEqual( Felt252{ .fe = bigInt(4).init( .{ 0, 0, 0, 0, }, ), }, Felt252.zero(), ); } test "Felt252 equal" { try expect(Felt252.zero().eql(Felt252.zero())); try expect(Felt252.fromInt(u8, 10).eql(Felt252.fromInt(u8, 10))); try expect(!Felt252.fromInt(u8, 100).eql(Felt252.fromInt(u8, 10))); } test "Felt252 isZero" { try expect(Felt252.zero().isZero()); try expect(!Felt252.one().isZero()); try expect(!Felt252.fromInt(u8, 10).isZero()); } test "Felt252 isOne" { try expect(Felt252.one().isOne()); try expect(!Felt252.zero().isOne()); try expect(!Felt252.fromInt(u8, 10).isOne()); } test "Felt252 fromBytesLe" { const a: [FELT_BYTE_SIZE]u8 = .{ 0x4E, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x19, 0x67, 0x2F, 0xDF, 0x76, 0xCE, 0x51, 0xBA, 0x69, 0xC6, 0x07, 0x6A, 0x0F, 0x77, 0xEA, 0xBC, 0xB2, 0xA9, 0x3B, 0xE6, 0xF8, 0x96, 0x00, }; try expectEqual( @as( u256, 0x96f8e63ba9b2bcea770f6a07c669ba51ce76df2f67195f5f5f5f5f5f5f5f4e, ), Felt252.fromBytesLe(a).toU256(), ); try expectEqual( Felt252.fromInt(u256, 0x96f8e63ba9b2bcea770f6a07c669ba51ce76df2f67195f5f5f5f5f5f5f5f4e), Felt252.fromBytesLe(a), ); } test "Felt252 toBytesLe" { const expected = [_]u8{ 0x4E, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x5F, 0x19, 0x67, 0x2F, 0xDF, 0x76, 0xCE, 0x51, 0xBA, 0x69, 0xC6, 0x07, 0x6A, 0x0F, 0x77, 0xEA, 0xBC, 0xB2, 0xA9, 0x3B, 0xE6, 0xF8, 0x96, 0x00, }; try expectEqual( expected, Felt252.fromInt(u256, 0x96f8e63ba9b2bcea770f6a07c669ba51ce76df2f67195f5f5f5f5f5f5f5f4e).toBytesLe(), ); } test "Felt252 toU64" { try expectEqual( @as(u64, 10), try Felt252.fromInt(u8, 10).toInt(u64), ); try expectEqual( @as(u64, std.math.maxInt(u64)), try Felt252.fromInt(u64, std.math.maxInt(u64)).toInt(u64), ); try std.testing.expectError( error.ValueTooLarge, Felt252.fromInt(u128, std.math.maxInt(u64) + 1).toInt(u64), ); } test "Felt252 arithmetic operations" { const a = Felt252.one(); const b = Felt252.two(); const c = a.add(&b); try expect(c.eql(Felt252.three())); } test "Felt252 add" { try expectEqual( @as(u256, 0xf), Felt252.fromInt(u8, 10).add(&Felt252.fromInt(u8, 5)).toU256(), ); try expect(Felt252.one().add(&Felt252.zero()).isOne()); try expect(Felt252.zero().add(&Felt252.zero()).isZero()); try expectEqual( @as( u256, 0x7fffffffffffbd0ffffffffffffffffffffffffffffffffffffffffffffffbf, ), Felt252.fromInt(u256, std.math.maxInt(u256)).add(&Felt252.fromInt(u256, std.math.maxInt(u256))).toU256(), ); } test "Felt252 sub" { try expectEqual( @as(u256, 0x5), Felt252.fromInt(u8, 10).sub(&Felt252.fromInt(u8, 5)).toU256(), ); try expect(Felt252.fromInt(u256, std.math.maxInt(u256)).sub(&Felt252.fromInt(u256, std.math.maxInt(u256))).isZero()); try expect(Felt252.zero().sub(&Felt252.zero()).isZero()); } test "Felt252 mul" { try expect(Felt252.zero().mul(&Felt252.zero()).isZero()); try expect(Felt252.one().mul(&Felt252.one()).isOne()); try expectEqual( @as(u256, 0x32), Felt252.fromInt(u8, 10).mul(&Felt252.fromInt(u8, 5)).toU256(), ); try expectEqual( @as( u256, 0x7fffffffffffbd0ffffffffffffffffffffffffffffffffffffffffffffffbf, ), Felt252.fromInt(u256, std.math.maxInt(u256)).mul(&Felt252.two()).toU256(), ); } test "Felt252 neg" { try expectEqual( @as( u256, 0x800000000000010fffffffffffffffffffffffffffffffffffffffffffffff7, ), Felt252.fromInt(u8, 10).neg().toU256(), ); try expectEqual( @as( u256, 0x220000000000000000000000000000000000000000000000021, ), Felt252.fromInt(u256, std.math.maxInt(u256)).neg().toU256(), ); } test "Felt252 square" { try expectEqual( @as(u256, 0x64), Felt252.fromInt(u8, 10).square().toU256(), ); try expectEqual( @as( u256, 0x7ffd4ab5e008c50ffffffffff6f800000000001330ffffffffffd737e000442, ), Felt252.fromInt(u256, std.math.maxInt(u256)).square().toU256(), ); } test "Felt252 pow" { try expectEqual( @as(u256, 0x2540be400), Felt252.fromInt(u8, 10).powToBigInt(bigInt(4).fromInt(u8, 10)).toU256(), ); try expectEqual( @as( u256, 0x48ea9fffffffffffffff5ffffffffffffffe5000000000000449f, ), Felt252.fromInt(u64, std.math.maxInt(u64)).powToBigInt(bigInt(4).fromInt(u64, 5)).toU256(), ); } test "Felt252 inv" { try expectEqual( @as( u256, 0x733333333333342800000000000000000000000000000000000000000000001, ), Felt252.fromInt(u8, 10).inverse().?.toU256(), ); try expectEqual( @as( u256, 0x538bf4edb6bf78474ef0f1979a0db0bdd364ce7aeda9f3c6c04bea822682ba, ), Felt252.fromInt(u256, std.math.maxInt(u256)).inverse().?.toU256(), ); try expectEqual( @as(?Felt252, null), Felt252.zero().inverse(), ); } test "Felt252 batchInv" { var out: [2]Felt252 = undefined; const in: [2]Felt252 = .{ Felt252.fromInt(u8, 10), Felt252.fromInt(u8, 5) }; try Felt252.batchinverse(&out, &in); try expectEqual( @as( u256, 0x733333333333342800000000000000000000000000000000000000000000001, ), out[0].toU256(), ); try expectEqual( @as( u256, 0x666666666666674000000000000000000000000000000000000000000000001, ), out[1].toU256(), ); } test "Felt252 batchInv with zero" { var out: [3]Felt252 = undefined; try std.testing.expectError( error.CantInvertZeroElement, Felt252.batchinverse(&out, &.{ Felt252.fromInt(u8, 10), Felt252.fromInt(u8, 5), Felt252.zero() }), ); } test "Felt252 div" { const div_10_by_10 = try Felt252.fromInt(u8, 10).div(Felt252.fromInt(u8, 10)); try expect( div_10_by_10.isOne(), ); try std.testing.expectError( error.DivisionByZero, Felt252.fromInt(u8, 10).div(Felt252.zero()), ); } test "Felt252 legendre" { try expectEqual( @as(i2, 0), Felt252.fromInt(u256, 0x1000000000000022000000000000000000000000000000000000000000000002).legendre(), ); try expectEqual( @as(i2, 1), Felt252.fromInt(u8, 10).legendre(), ); try expectEqual( @as(i2, -1), Felt252.fromInt(u8, 135).legendre(), ); } test "Felt252 cmp" { try expect(Felt252.fromInt(u8, 10).cmp(&Felt252.fromInt(u64, 343535)) == .lt); try expect(Felt252.fromInt(u64, 433).cmp(&Felt252.fromInt(u64, 343535)) == .lt); try expect(Felt252.fromInt(u64, 543636535).cmp(&Felt252.fromInt(u64, 434)) == .gt); try expect(Felt252.fromInt(u256, std.math.maxInt(u256)).cmp(&Felt252.fromInt(u64, 21313)) == .gt); try expect(Felt252.fromInt(u8, 10).cmp(&Felt252.fromInt(u8, 10)) == .eq); try expect(Felt252.one().cmp(&Felt252.one()) == .eq); try expect(Felt252.zero().cmp(&Felt252.zero()) == .eq); try expect(Felt252.fromInt(u8, 10).cmp(&Felt252.fromInt(u256, 10 + STARKNET_PRIME)) == .eq); } test "Felt252 lt" { try expect(Felt252.fromInt(u8, 10).lt(&Felt252.fromInt(u64, 343535))); try expect(Felt252.fromInt(u64, 433).lt(&Felt252.fromInt(u64, 343535))); try expect(!Felt252.fromInt(u64, 543636535).lt(&Felt252.fromInt(u64, 434))); try expect(!Felt252.fromInt(u256, std.math.maxInt(u256)).lt(&Felt252.fromInt(u64, 21313))); try expect(!Felt252.fromInt(u8, 10).lt(&Felt252.fromInt(u8, 10))); try expect(!Felt252.one().lt(&Felt252.one())); try expect(!Felt252.zero().lt(&Felt252.zero())); try expect(!Felt252.fromInt(u8, 10).lt( &Felt252.fromInt(u256, 10 + STARKNET_PRIME), )); } test "Felt252 lte" { try expect(Felt252.fromInt(u8, 10).lte(&Felt252.fromInt(u64, 343535))); try expect(Felt252.fromInt(u64, 433).lte(&Felt252.fromInt(u64, 343535))); try expect(!Felt252.fromInt(u64, 543636535).lte(&Felt252.fromInt(u64, 434))); try expect(!Felt252.fromInt(u256, std.math.maxInt(u256)).lte(&Felt252.fromInt(u64, 21313))); try expect(Felt252.fromInt(u8, 10).lte(&Felt252.fromInt(u8, 10))); try expect(Felt252.one().lte(&Felt252.one())); try expect(Felt252.zero().lte(&Felt252.zero())); try expect(Felt252.fromInt(u8, 10).lte( &Felt252.fromInt(u256, 10 + STARKNET_PRIME), )); } test "Felt252 gt" { try expect(!Felt252.fromInt(u8, 10).gt(&Felt252.fromInt(u64, 343535))); try expect(!Felt252.fromInt(u64, 433).gt(&Felt252.fromInt(u64, 343535))); try expect(Felt252.fromInt(u64, 543636535).gt(&Felt252.fromInt(u64, 434))); try expect(Felt252.fromInt(u256, std.math.maxInt(u256)).gt(&Felt252.fromInt(u64, 21313))); try expect(!Felt252.fromInt(u8, 10).gt(&Felt252.fromInt(u8, 10))); try expect(!Felt252.one().gt(&Felt252.one())); try expect(!Felt252.zero().gt(&Felt252.zero())); try expect(!Felt252.fromInt(u8, 10).gt( &Felt252.fromInt(u256, 10 + STARKNET_PRIME), )); } test "Felt252 gte" { try expect(!Felt252.fromInt(u8, 10).gte(&Felt252.fromInt(u64, 343535))); try expect(!Felt252.fromInt(u64, 433).gte(&Felt252.fromInt(u64, 343535))); try expect(Felt252.fromInt(u64, 543636535).gte(&Felt252.fromInt(u64, 434))); try expect(Felt252.fromInt(u256, std.math.maxInt(u256)).gte(&Felt252.fromInt(u64, 21313))); try expect(Felt252.fromInt(u8, 10).gte(&Felt252.fromInt(u8, 10))); try expect(Felt252.one().gte(&Felt252.one())); try expect(Felt252.zero().gte(&Felt252.zero())); try expect(Felt252.fromInt(u8, 10).gte( &Felt252.fromInt(u256, 10 + STARKNET_PRIME), )); } test "Felt252 lexographicallyLargest" { try expect(!Felt252.zero().lexographicallyLargest()); try expect(!Felt252.fromInt( u256, 0x400000000000008800000000000000000000000000000000000000000000000, ).lexographicallyLargest()); try expect(!Felt252.fromInt( u256, 0x4000000000000087fffffffffffffffffffffffffffffffffffffffffffffff, ).lexographicallyLargest()); try expect(Felt252.fromInt( u256, 0x400000000000008800000000000000000000000000000000000000000000001, ).lexographicallyLargest()); try expect(Felt252.fromInt(u256, std.math.maxInt(u256)).lexographicallyLargest()); } test "Felt252: toBitsLe" { const one = Felt252.one(); var bits_one = [_]bool{false} ** @bitSizeOf(u256); bits_one[0] = true; try expectEqualSlices(bool, &bits_one, &one.toBitsLe()); const max_u64 = Felt252.fromInt(u64, std.math.maxInt(u64)); var bits_max_u64 = [_]bool{false} ** @bitSizeOf(u256); for (0..64) |i| bits_max_u64[i] = true; try expectEqualSlices(bool, &bits_max_u64, &max_u64.toBitsLe()); } test "Felt252: toBitsBe" { const one = Felt252.one(); var bits_one = [_]bool{false} ** @bitSizeOf(u256); bits_one[255] = true; try expectEqualSlices(bool, &bits_one, &one.toBitsBe()); const max_u64 = Felt252.fromInt(u64, std.math.maxInt(u64)); var bits_max_u64 = [_]bool{false} ** @bitSizeOf(u256); for (3 * 64..256) |i| bits_max_u64[i] = true; try expectEqualSlices(bool, &bits_max_u64, &max_u64.toBitsBe()); } test "Felt252: arithmetic addition operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { const a = Felt252.rand(random); const b = Felt252.rand(random); const c = Felt252.rand(random); const zero = Felt252.zero(); // Associativity try expect(a.add(&b).add(&c).eql(a.add(&c.add(&b)))); // Identify try expect(a.eql(zero.add(&a))); try expect(b.eql(zero.add(&b))); try expect(c.eql(zero.add(&c))); try expect(a.eql(a.add(&zero))); try expect(b.eql(b.add(&zero))); try expect(c.eql(c.add(&zero))); // Negation try expect(zero.eql(a.neg().add(&a))); try expect(zero.eql(b.neg().add(&b))); try expect(zero.eql(c.neg().add(&c))); try expect(zero.eql(zero.neg().add(&zero))); // Commutativity try expect(a.add(&b).eql(b.add(&a))); // Associativity and commutativity simultaneously try expect(a.add(&b).add(&c).eql(a.add(&c).add(&b))); try expect(a.add(&c).add(&b).eql(b.add(&c).add(&a))); // Doubling try expect(a.add(&a).eql(a.double())); try expect(b.add(&b).eql(b.double())); try expect(c.add(&c).eql(c.double())); try expect(zero.eql(zero.double())); try expect(zero.eql(zero.neg().double())); } } test "Felt252: arithmetic subtraction operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { const a = Felt252.rand(random); const b = Felt252.rand(random); const zero = Felt252.zero(); // Associativity try expect(a.sub(&b).add(&b.sub(&a)).isZero()); // Identity try expect(zero.sub(&a).eql(a.neg())); try expect(zero.sub(&b).eql(b.neg())); try expect(a.sub(&zero).eql(a)); try expect(b.sub(&zero).eql(b)); } } test "Felt252: arithmetic multiplication operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { const a = Felt252.rand(random); const b = Felt252.rand(random); const c = Felt252.rand(random); const zero = Felt252.zero(); const one = Felt252.one(); const rnd_u8 = random.int(u8); const bigint_rnd_u8 = bigInt(4).fromInt(u256, rnd_u8); // Associativity try expect(a.mul(&b).mul(&c).eql(a.mul(&c.mul(&b)))); // Commutativity try expect(a.mul(&b).eql(b.mul(&a))); // Identity try expect(one.mul(&a).eql(a)); try expect(one.mul(&b).eql(b)); try expect(one.mul(&c).eql(c)); try expect(zero.mul(&a).eql(zero)); try expect(zero.mul(&b).eql(zero)); try expect(zero.mul(&c).eql(zero)); // Inverses try expect(a.mul(&a.inverse().?).eql(one)); try expect(b.mul(&b.inverse().?).eql(one)); try expect(c.mul(&c.inverse().?).eql(one)); try expectEqual(null, zero.inverse()); try expect(one.inverse().?.eql(one)); // Associativity and commutativity simultaneously try expect(a.mul(&b).mul(&c).eql(a.mul(&c).mul(&b))); try expect(a.mul(&c).mul(&b).eql(b.mul(&c).mul(&(a)))); // Squaring try expect(a.mul(&a).eql(a.square())); try expect(b.mul(&b).eql(b.square())); try expect(c.mul(&c).eql(c.square())); // Distributivity try expect(a.mul(&b.add(&c)).eql(a.mul(&b).add(&a.mul(&c)))); try expect(b.mul(&a.add(&c)).eql(b.mul(&a).add(&b.mul(&c)))); try expect(c.mul(&a.add(&b)).eql(c.mul(&a).add(&c.mul(&b)))); try expect(a.add(&b).square().eql( a.square().add(&b.square()).add(&a.mul(&b).double()), )); try expect(b.add(&c).square().eql( b.square().add(&c.square()).add(&b.mul(&c).double()), )); try expect(c.add(&a).square().eql( c.square().add(&a.square()).add(&c.mul(&a).double()), )); // Power var a_100 = one; var b_100 = one; var c_100 = one; for (0..rnd_u8) |_| { a_100 = a_100.mul(&a); b_100 = b_100.mul(&b); c_100 = c_100.mul(&c); } try expect(a.powToBigInt(bigint_rnd_u8).eql(a_100)); try expect(b.powToBigInt(bigint_rnd_u8).eql(b_100)); try expect(c.powToBigInt(bigint_rnd_u8).eql(c_100)); try expect(a.powToInt(rnd_u8).eql(a_100)); try expect(b.powToInt(rnd_u8).eql(b_100)); try expect(c.powToInt(rnd_u8).eql(c_100)); } } test "Felt252: fromInt operations" { // Initialize a pseudo-random number generator (PRNG) with a seed of 0. var prng = std.Random.DefaultPrng.init(0); // Generate a random number using the PRNG. const random = prng.random(); // Iterate over the test iterations. for (0..TEST_ITERATIONS) |_| { // Generate random unsigned integers of different sizes. const u_8 = random.int(u8); const u_16: u16 = u_8; const u_32: u32 = u_8; const u_64: u64 = u_8; const u_128: u128 = u_8; const u_256: u256 = u_8; // Test the equality of `Felt252` instances created from different-sized integers. try expect(Felt252.fromInt(u8, u_8).eql(Felt252.fromInt(u16, u_16))); try expect(Felt252.fromInt(u8, u_8).eql(Felt252.fromInt(u32, u_32))); try expect(Felt252.fromInt(u8, u_8).eql(Felt252.fromInt(u64, u_64))); try expect(Felt252.fromInt(u8, u_8).eql(Felt252.fromInt(u128, u_128))); try expect(Felt252.fromInt(u8, u_8).eql(Felt252.fromInt(u256, u_256))); } } test "Felt252: modulus properties checks" { try expect(comptime Felt252.canUseNoCarryMulOptimization()); try expect(comptime Felt252.modulusHasSpareBit()); }
0
repos/starknet-zig/src
repos/starknet-zig/src/utils/time.zig
// Source: https://github.com/nektro/zig-time/commit/ca9c0e6b644d74c1d549cc2c1ee22113aa021bd8 // // MIT License // // Copyright (c) 2021 Meghan Denny // // Permission is hereby granted, free of charge, to any person obtaining a copy of // this software and associated documentation files (the "Software"), to deal in // the Software without restriction, including without limitation the rights to // use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of // the Software, and to permit persons to whom the Software is furnished to do so, // subject to the following conditions: // // The above copyright notice and this permission notice shall be included in all // copies or substantial portions of the Software. // // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS // FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR // COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER // IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN // CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. const std = @import("std"); const string = []const u8; const time = @This(); pub const DateTime = struct { ms: u16, seconds: u16, minutes: u16, hours: u16, days: u16, months: u16, years: u16, timezone: TimeZone, weekday: WeekDay, era: Era, const Self = @This(); pub fn initUnixMs(unix: u64) Self { return epoch_unix.addMs(unix); } pub fn initUnix(unix: u64) Self { return epoch_unix.addSecs(unix); } /// Caller asserts that this is > epoch pub fn init(year: u16, month: u16, day: u16, hr: u16, min: u16, sec: u16) Self { return epoch_unix .addYears(year - epoch_unix.years) .addMonths(month) .addDays(day) .addHours(hr) .addMins(min) .addSecs(sec); } pub fn now() Self { return initUnixMs(@as(u64, @intCast(std.time.milliTimestamp()))); } pub const epoch_unix = Self{ .ms = 0, .seconds = 0, .minutes = 0, .hours = 0, .days = 0, .months = 0, .years = 1970, .timezone = .UTC, .weekday = .Thu, .era = .AD, }; pub fn eql(self: Self, rhs: Self) bool { return self.ms == rhs.ms and self.seconds == rhs.seconds and self.minutes == rhs.minutes and self.hours == rhs.hours and self.days == rhs.days and self.months == rhs.months and self.years == rhs.years and self.timezone == rhs.timezone and self.weekday == rhs.weekday; } pub fn addMs(self: Self, count: u64) Self { if (count == 0) return self; var result = self; result.ms += @as(u16, @intCast(count % 1000)); return result.addSecs(count / 1000); } pub fn addSecs(self: Self, count: u64) Self { if (count == 0) return self; var result = self; result.seconds += @as(u16, @intCast(count % 60)); return result.addMins(count / 60); } pub fn addMins(self: Self, count: u64) Self { if (count == 0) return self; var result = self; result.minutes += @as(u16, @intCast(count % 60)); return result.addHours(count / 60); } pub fn addHours(self: Self, count: u64) Self { if (count == 0) return self; var result = self; result.hours += @as(u16, @intCast(count % 24)); return result.addDays(count / 24); } pub fn addDays(self: Self, count: u64) Self { if (count == 0) return self; var result = self; var input = count; while (true) { const year_len = result.daysThisYear(); if (input >= year_len) { result.years += 1; input -= year_len; result.incrementWeekday(year_len); continue; } break; } while (true) { const month_len = result.daysThisMonth(); if (input >= month_len) { result.months += 1; input -= month_len; result.incrementWeekday(month_len); if (result.months == 12) { result.years += 1; result.months = 0; } continue; } break; } { const month_len = result.daysThisMonth(); if (result.days + input > month_len) { const left = month_len - result.days; input -= left; result.months += 1; result.days = 0; result.incrementWeekday(left); } result.days += @as(u16, @intCast(input)); result.incrementWeekday(input); if (result.months == 12) { result.years += 1; result.months = 0; } } return result; } pub fn addMonths(self: Self, count: u64) Self { if (count == 0) return self; var result = self; var input = count; while (input > 0) { const new = result.addDays(result.daysThisMonth()); result = new; input -= 1; } return result; } pub fn addYears(self: Self, count: u64) Self { if (count == 0) return self; return self.addMonths(count * 12); } pub fn isLeapYear(self: Self) bool { return time.isLeapYear(self.years); } pub fn daysThisYear(self: Self) u16 { return time.daysInYear(self.years); } pub fn daysThisMonth(self: Self) u16 { return self.daysInMonth(self.months); } fn daysInMonth(self: Self, month: u16) u16 { return time.daysInMonth(self.years, month); } fn incrementWeekday(self: *Self, count: u64) void { var i = count % 7; while (i > 0) : (i -= 1) { self.weekday = self.weekday.next(); } } pub fn dayOfThisYear(self: Self) u16 { var ret: u16 = 0; for (0..self.months) |item| { ret += self.daysInMonth(@as(u16, @intCast(item))); } ret += self.days; return ret; } pub fn toUnix(self: Self) u64 { const x = self.toUnixMilli(); return x / 1000; } pub fn toUnixMilli(self: Self) u64 { var res: u64 = 0; res += self.ms; res += @as(u64, self.seconds) * std.time.ms_per_s; res += @as(u64, self.minutes) * std.time.ms_per_min; res += @as(u64, self.hours) * std.time.ms_per_hour; res += self.daysSinceEpoch() * std.time.ms_per_day; return res; } fn daysSinceEpoch(self: Self) u64 { var res: u64 = 0; res += self.days; for (0..self.years - epoch_unix.years) |i| res += time.daysInYear(@as(u16, @intCast(i))); for (0..self.months) |i| res += self.daysInMonth(@as(u16, @intCast(i))); return res; } /// fmt is based on https://momentjs.com/docs/#/displaying/format/ pub fn format(self: Self, comptime fmt: string, options: std.fmt.FormatOptions, writer: anytype) !void { _ = options; if (fmt.len == 0) @compileError("DateTime: format string can't be empty"); @setEvalBranchQuota(100000); comptime var s = 0; comptime var e = 0; comptime var next: ?FormatSeq = null; inline for (fmt, 0..) |c, i| { e = i + 1; if (comptime std.meta.stringToEnum(FormatSeq, fmt[s..e])) |tag| { next = tag; if (i < fmt.len - 1) continue; } if (next) |tag| { switch (tag) { .MM => try writer.print("{:0>2}", .{self.months + 1}), .M => try writer.print("{}", .{self.months + 1}), .Mo => try printOrdinal(writer, self.months + 1), .MMM => try printLongName(writer, self.months, &[_]string{ "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec" }), .MMMM => try printLongName(writer, self.months, &[_]string{ "January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December" }), .Q => try writer.print("{}", .{self.months / 3 + 1}), .Qo => try printOrdinal(writer, self.months / 3 + 1), .D => try writer.print("{}", .{self.days + 1}), .Do => try printOrdinal(writer, self.days + 1), .DD => try writer.print("{:0>2}", .{self.days + 1}), .DDD => try writer.print("{}", .{self.dayOfThisYear() + 1}), .DDDo => try printOrdinal(writer, self.dayOfThisYear() + 1), .DDDD => try writer.print("{:0>3}", .{self.dayOfThisYear() + 1}), .d => try writer.print("{}", .{@intFromEnum(self.weekday)}), .do => try printOrdinal(writer, @intFromEnum(self.weekday)), .dd => try writer.writeAll(@tagName(self.weekday)[0..2]), .ddd => try writer.writeAll(@tagName(self.weekday)), .dddd => try printLongName(writer, @intFromEnum(self.weekday), &[_]string{ "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday" }), .e => try writer.print("{}", .{@intFromEnum(self.weekday)}), .E => try writer.print("{}", .{@intFromEnum(self.weekday) + 1}), .w => try writer.print("{}", .{self.dayOfThisYear() / 7 + 1}), .wo => try printOrdinal(writer, self.dayOfThisYear() / 7 + 1), .ww => try writer.print("{:0>2}", .{self.dayOfThisYear() / 7 + 1}), .Y => try writer.print("{}", .{self.years + 10000}), .YY => try writer.print("{:0>2}", .{self.years % 100}), .YYY => try writer.print("{}", .{self.years}), .YYYY => try writer.print("{:0>4}", .{self.years}), .N => try writer.writeAll(@tagName(self.era)), .NN => try writer.writeAll("Anno Domini"), .A => try printLongName(writer, self.hours / 12, &[_]string{ "AM", "PM" }), .a => try printLongName(writer, self.hours / 12, &[_]string{ "am", "pm" }), .H => try writer.print("{}", .{self.hours}), .HH => try writer.print("{:0>2}", .{self.hours}), .h => try writer.print("{}", .{wrap(self.hours, 12)}), .hh => try writer.print("{:0>2}", .{wrap(self.hours, 12)}), .k => try writer.print("{}", .{wrap(self.hours, 24)}), .kk => try writer.print("{:0>2}", .{wrap(self.hours, 24)}), .m => try writer.print("{}", .{self.minutes}), .mm => try writer.print("{:0>2}", .{self.minutes}), .s => try writer.print("{}", .{self.seconds}), .ss => try writer.print("{:0>2}", .{self.seconds}), .S => try writer.print("{}", .{self.ms / 100}), .SS => try writer.print("{:0>2}", .{self.ms / 10}), .SSS => try writer.print("{:0>3}", .{self.ms}), .z => try writer.writeAll(@tagName(self.timezone)), .Z => try writer.writeAll("+00:00"), .ZZ => try writer.writeAll("+0000"), .x => try writer.print("{}", .{self.toUnixMilli()}), .X => try writer.print("{}", .{self.toUnix()}), } next = null; s = i; } switch (c) { ',', ' ', ':', '-', '.', 'T', 'W', => { try writer.writeAll(&.{c}); s = i + 1; continue; }, else => {}, } } } pub fn formatAlloc(self: Self, alloc: std.mem.Allocator, comptime fmt: string) !string { var list = std.ArrayList(u8).init(alloc); defer list.deinit(); try self.format(fmt, .{}, list.writer()); return list.toOwnedSlice(); } const FormatSeq = enum { M, // 1 2 ... 11 12 Mo, // 1st 2nd ... 11th 12th MM, // 01 02 ... 11 12 MMM, // Jan Feb ... Nov Dec MMMM, // January February ... November December Q, // 1 2 3 4 Qo, // 1st 2nd 3rd 4th D, // 1 2 ... 30 31 Do, // 1st 2nd ... 30th 31st DD, // 01 02 ... 30 31 DDD, // 1 2 ... 364 365 DDDo, // 1st 2nd ... 364th 365th DDDD, // 001 002 ... 364 365 d, // 0 1 ... 5 6 do, // 0th 1st ... 5th 6th dd, // Su Mo ... Fr Sa ddd, // Sun Mon ... Fri Sat dddd, // Sunday Monday ... Friday Saturday e, // 0 1 ... 5 6 (locale) E, // 1 2 ... 6 7 (ISO) w, // 1 2 ... 52 53 wo, // 1st 2nd ... 52nd 53rd ww, // 01 02 ... 52 53 Y, // 11970 11971 ... 19999 20000 20001 (Holocene calendar) YY, // 70 71 ... 29 30 YYY, // 1 2 ... 1970 1971 ... 2029 2030 YYYY, // 0001 0002 ... 1970 1971 ... 2029 2030 N, // BC AD NN, // Before Christ ... Anno Domini A, // AM PM a, // am pm H, // 0 1 ... 22 23 HH, // 00 01 ... 22 23 h, // 1 2 ... 11 12 hh, // 01 02 ... 11 12 k, // 1 2 ... 23 24 kk, // 01 02 ... 23 24 m, // 0 1 ... 58 59 mm, // 00 01 ... 58 59 s, // 0 1 ... 58 59 ss, // 00 01 ... 58 59 S, // 0 1 ... 8 9 (second fraction) SS, // 00 01 ... 98 99 SSS, // 000 001 ... 998 999 z, // EST CST ... MST PST Z, // -07:00 -06:00 ... +06:00 +07:00 ZZ, // -0700 -0600 ... +0600 +0700 x, // unix milli X, // unix }; pub fn since(self: Self, other_in_the_past: Self) Duration { return Duration{ .ms = self.toUnixMilli() - other_in_the_past.toUnixMilli(), }; } }; pub const format = struct { pub const LT = ""; pub const LTS = ""; pub const L = ""; pub const l = ""; pub const LL = ""; pub const ll = ""; pub const LLL = ""; pub const lll = ""; pub const LLLL = ""; pub const llll = ""; }; pub const TimeZone = enum { UTC, }; pub const WeekDay = enum { Sun, Mon, Tue, Wed, Thu, Fri, Sat, pub fn next(self: WeekDay) WeekDay { return switch (self) { .Sun => .Mon, .Mon => .Tue, .Tue => .Wed, .Wed => .Thu, .Thu => .Fri, .Fri => .Sat, .Sat => .Sun, }; } }; pub const Era = enum { // BC, AD, }; pub fn isLeapYear(year: u16) bool { var ret = false; if (year % 4 == 0) ret = true; if (year % 100 == 0) ret = false; if (year % 400 == 0) ret = true; return ret; } pub fn daysInYear(year: u16) u16 { return if (isLeapYear(year)) 366 else 365; } fn daysInMonth(year: u16, month: u16) u16 { const norm = [12]u16{ 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }; const leap = [12]u16{ 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }; const month_days = if (!isLeapYear(year)) norm else leap; return month_days[month]; } fn printOrdinal(writer: anytype, num: u16) !void { try writer.print("{}", .{num}); try writer.writeAll(switch (num) { 1 => "st", 2 => "nd", 3 => "rd", else => "th", }); } fn printLongName(writer: anytype, index: u16, names: []const string) !void { try writer.writeAll(names[index]); } fn wrap(val: u16, at: u16) u16 { const tmp = val % at; return if (tmp == 0) at else tmp; } pub const Duration = struct { ms: u64, }; // ************************************************************ // * TESTS * // ************************************************************ const expect = std.testing.expect; test "time format" { // Initialize an allocator. // TODO: Consider using a testing allocator. const allocator = std.heap.page_allocator; const utc_format = "YYYY-MM-DDTHH:mm:ss"; const dt = DateTime.initUnix(1697696484); const formatted_dt = try dt.formatAlloc(allocator, utc_format); const expected_formatted_dt = "2023-10-19T06:21:24"; try expect(std.mem.eql(u8, formatted_dt, expected_formatted_dt)); }
0
repos/starknet-zig/src
repos/starknet-zig/src/utils/log.zig
// ***************************************************************************** // * CUSTOM LOGGING * // ***************************************************************************** // Core imports. const std = @import("std"); // Local imports. const DateTime = @import("time.zig").DateTime; // Define a memory allocator. // TODO: Make this configurable. const allocator = std.heap.page_allocator; /// Custom log function. /// This function is used to log messages with a custom format. /// The format is as follows: /// time={time} level={level} ({scope}) msg={message} /// Where: /// - {time} is the current time in ISO 8601 format. /// - {level} is the log level. /// - {scope} is the scope of the log message. /// - {message} is the message to log. /// # Arguments /// - `level` is the log level. /// - `scope` is the scope of the log message. /// - `format` is the format string. /// - `args` are the arguments to the format string. pub fn logFn( comptime level: std.log.Level, comptime scope: @TypeOf(.EnumLiteral), comptime format: []const u8, args: anytype, ) void { // Capture the current time in UTC format. const utc_format = "YYYY-MM-DDTHH:mm:ss"; const time_str = DateTime.now().formatAlloc(allocator, utc_format) catch unreachable; // Convert the log level and scope to string using @tagName. const level_str = @tagName(level); const scope_str = @tagName(scope); const stderr = std.io.getStdErr().writer(); // Log the header _ = stderr.print("time={s} level={s} ({s}) msg=", .{ time_str, level_str, scope_str }) catch unreachable; // Log the main message nosuspend stderr.print(format, args) catch return; // Write a newline for better readability. nosuspend stderr.writeAll("\n") catch return; }
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repos/starknet-zig/src
repos/starknet-zig/src/bench/bench_field.zig
const benchmark = @import("bench.zig").benchmark; const bigInt = @import("../math/fields/biginteger.zig").bigInt; const Felt252 = @import("../math/fields/starknet.zig").Felt252; const field = @import("../math/fields/fields.zig"); const std = @import("std"); test "benchmark field multiplication" { try benchmark(struct { // How many iterations to run each benchmark. // If not present then a default will be used. pub const iterations = 100000; var a = Felt252.fromInt( u256, 0x6606d7dccf23a0f61182da8d1149497f01b909036384bedb3e4c3284e2f2c1e1, ); const b = Felt252.fromInt( u256, 0x4cd366c0feadabcd6c61a395f6d9f91484ac4e51c3f8aede6c0ab49e2a55446a, ); pub fn bench_mul() void { _ = std.mem.doNotOptimizeAway(a.mul(&b)); } }); }
0
repos/starknet-zig/src
repos/starknet-zig/src/bench/bench.zig
const std = @import("std"); const Decl = std.builtin.Type.Declaration; // Inspired by the following work: https://github.com/Hejsil/zig-bench pub fn benchmark(comptime B: type) !void { const args = if (@hasDecl(B, "args")) B.args else [_]void{{}}; const arg_names = if (@hasDecl(B, "arg_names")) B.arg_names else [_]u8{}; const iterations = if (@hasDecl(B, "iterations")) B.iterations else 100000; const functions = comptime blk: { var res: []const Decl = &[_]Decl{}; for (std.meta.declarations(B)) |decl| { if (@typeInfo(@TypeOf(@field(B, decl.name))) == .Fn) res = res ++ [_]Decl{decl}; } break :blk res; }; if (functions.len == 0) @compileError("No benchmarks to run."); const min_width = blk: { const writer = std.io.null_writer; var res = [_]u64{ 0, 0, 0, 0, 0, 0 }; res = try printBenchmark( writer, res, "Benchmark", formatter("{s}", ""), formatter("{s}", "Iterations"), formatter("{s}", "Min(ns)"), formatter("{s}", "Max(ns)"), formatter("{s}", "Variance"), formatter("{s}", "Mean(ns)"), ); inline for (functions) |f| { var i: usize = 0; while (i < args.len) : (i += 1) { res = if (i < arg_names.len) try printBenchmark( writer, res, f.name, formatter("{s}", arg_names[i]), std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), ) else try printBenchmark( writer, res, f.name, i, std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), std.math.maxInt(u32), ); } } break :blk res; }; var _stderr = std.io.bufferedWriter(std.io.getStdErr().writer()); const stderr = _stderr.writer(); try stderr.writeAll("\n"); _ = try printBenchmark( stderr, min_width, "Benchmark", formatter("{s}", ""), formatter("{s}", "Iterations"), formatter("{s}", "Min(ns)"), formatter("{s}", "Max(ns)"), formatter("{s}", "Variance"), formatter("{s}", "Mean(ns)"), ); try stderr.writeAll("\n"); for (min_width) |w| try stderr.writeByteNTimes('-', w); try stderr.writeByteNTimes('-', min_width.len - 1); try stderr.writeAll("\n"); try stderr.context.flush(); var timer = try std.time.Timer.start(); inline for (functions) |def| { inline for (args, 0..) |arg, index| { timer.reset(); for (0..iterations) |_| { _ = switch (@TypeOf(arg)) { void => @field(B, def.name)(), else => @field(B, def.name)(arg), }; } const runtime_mean: f64 = @as(f64, @floatFromInt(timer.read())) / @as(f64, @floatFromInt(iterations)); const variance = 0; if (index < arg_names.len) { const arg_name = formatter("{s}", arg_names[index]); _ = try printBenchmark(stderr, min_width, def.name, arg_name, iterations, 0, 0, variance, runtime_mean); } else { _ = try printBenchmark(stderr, min_width, def.name, index, iterations, 0, 0, variance, runtime_mean); } try stderr.writeAll("\n"); try stderr.context.flush(); } } } fn printBenchmark( writer: anytype, min_widths: [6]u64, func_name: []const u8, arg_name: anytype, iterations: anytype, min_runtime: anytype, max_runtime: anytype, variance: anytype, mean_runtime: anytype, ) ![6]u64 { const arg_len = std.fmt.count("{}", .{arg_name}); const name_len = try alignedPrint( writer, .left, min_widths[0], "{s}{s}{}{s}", .{ func_name, "("[0..@intFromBool(arg_len != 0)], arg_name, ")"[0..@intFromBool(arg_len != 0)], }, ); try writer.writeAll(" "); const it_len = try alignedPrint(writer, .right, min_widths[1], "{}", .{iterations}); try writer.writeAll(" "); const min_runtime_len = try alignedPrint(writer, .right, min_widths[2], "{}", .{min_runtime}); try writer.writeAll(" "); const max_runtime_len = try alignedPrint(writer, .right, min_widths[3], "{}", .{max_runtime}); try writer.writeAll(" "); const variance_len = try alignedPrint(writer, .right, min_widths[4], "{}", .{variance}); try writer.writeAll(" "); const mean_runtime_len = try alignedPrint(writer, .right, min_widths[5], "{}", .{mean_runtime}); return [_]u64{ name_len, it_len, min_runtime_len, max_runtime_len, variance_len, mean_runtime_len, }; } fn formatter(comptime fmt_str: []const u8, value: anytype) Formatter(fmt_str, @TypeOf(value)) { return .{ .value = value }; } fn Formatter(comptime fmt_str: []const u8, comptime T: type) type { return struct { value: T, pub fn format( self: @This(), comptime fmt: []const u8, options: std.fmt.FormatOptions, writer: anytype, ) !void { _ = fmt; _ = options; try std.fmt.format(writer, fmt_str, .{self.value}); } }; } fn alignedPrint(writer: anytype, dir: enum { left, right }, width: u64, comptime fmt: []const u8, args: anytype) !u64 { const value_len = std.fmt.count(fmt, args); var cow = std.io.countingWriter(writer); if (dir == .right) try cow.writer().writeByteNTimes(' ', std.math.sub(u64, width, value_len) catch 0); try cow.writer().print(fmt, args); if (dir == .left) try cow.writer().writeByteNTimes(' ', std.math.sub(u64, width, value_len) catch 0); return cow.bytes_written; }
0
repos
repos/asdf-zig/renovate.json
{ "$schema": "https://docs.renovatebot.com/renovate-schema.json", "extends": [ "config:base" ] }