text: /**********************************************************************
   * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell      *
   * Distributed under the MIT software license, see the accompanying   *
   * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   **********************************************************************/
  
  #if defined HAVE_CONFIG_H
  #include "libsecp256k1-config.h"
  #endif
  
  #include <stdio.h>
  #include <stdlib.h>
  
  #include <time.h>
  
  #include "secp256k1.c"
  #include "include/secp256k1.h"
  #include "testrand_impl.h"
  
  #ifdef ENABLE_OPENSSL_TESTS
  #include "openssl/bn.h"
  #include "openssl/ec.h"
  #include "openssl/ecdsa.h"
  #include "openssl/obj_mac.h"
  #endif
  
  #include "contrib/lax_der_parsing.c"
  #include "contrib/lax_der_privatekey_parsing.c"
  
  #if !defined(VG_CHECK)
  # if defined(VALGRIND)
  #  include <valgrind/memcheck.h>
  #  define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y))
  #  define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y))
  # else
  #  define VG_UNDEF(x,y)
  #  define VG_CHECK(x,y)
  # endif
  #endif
  
  static int count = 64;
  static secp256k1_context *ctx = NULL;
  
  static void counting_illegal_callback_fn(const char* str, void* data) {
      /* Dummy callback function that just counts. */
      int32_t *p;
      (void)str;
      p = data;
      (*p)++;
  }
  
  static void uncounting_illegal_callback_fn(const char* str, void* data) {
      /* Dummy callback function that just counts (backwards). */
      int32_t *p;
      (void)str;
      p = data;
      (*p)--;
  }
  
  void random_field_element_test(secp256k1_fe *fe) {
      do {
          unsigned char b32[32];
          secp256k1_rand256_test(b32);
          if (secp256k1_fe_set_b32(fe, b32)) {
              break;
          }
      } while(1);
  }
  
  void random_field_element_magnitude(secp256k1_fe *fe) {
      secp256k1_fe zero;
      int n = secp256k1_rand_int(9);
      secp256k1_fe_normalize(fe);
      if (n == 0) {
          return;
      }
      secp256k1_fe_clear(&zero);
      secp256k1_fe_negate(&zero, &zero, 0);
      secp256k1_fe_mul_int(&zero, n - 1);
      secp256k1_fe_add(fe, &zero);
      VERIFY_CHECK(fe->magnitude == n);
  }
  
  void random_group_element_test(secp256k1_ge *ge) {
      secp256k1_fe fe;
      do {
          random_field_element_test(&fe);
          if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) {
              secp256k1_fe_normalize(&ge->y);
              break;
          }
      } while(1);
  }
  
  void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) {
      secp256k1_fe z2, z3;
      do {
          random_field_element_test(&gej->z);
          if (!secp256k1_fe_is_zero(&gej->z)) {
              break;
          }
      } while(1);
      secp256k1_fe_sqr(&z2, &gej->z);
      secp256k1_fe_mul(&z3, &z2, &gej->z);
      secp256k1_fe_mul(&gej->x, &ge->x, &z2);
      secp256k1_fe_mul(&gej->y, &ge->y, &z3);
      gej->infinity = ge->infinity;
  }
  
  void random_scalar_order_test(secp256k1_scalar *num) {
      do {
          unsigned char b32[32];
          int overflow = 0;
          secp256k1_rand256_test(b32);
          secp256k1_scalar_set_b32(num, b32, &overflow);
          if (overflow || secp256k1_scalar_is_zero(num)) {
              continue;
          }
          break;
      } while(1);
  }
  
  void random_scalar_order(secp256k1_scalar *num) {
      do {
          unsigned char b32[32];
          int overflow = 0;
          secp256k1_rand256(b32);
          secp256k1_scalar_set_b32(num, b32, &overflow);
          if (overflow || secp256k1_scalar_is_zero(num)) {
              continue;
          }
          break;
      } while(1);
  }
  
  void run_context_tests(void) {
      secp256k1_pubkey pubkey;
      secp256k1_ecdsa_signature sig;
      unsigned char ctmp[32];
      int32_t ecount;
      int32_t ecount2;
      secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
      secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
      secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
      secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
  
      secp256k1_gej pubj;
      secp256k1_ge pub;
      secp256k1_scalar msg, key, nonce;
      secp256k1_scalar sigr, sigs;
  
      ecount = 0;
      ecount2 = 10;
      secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
      secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2);
      secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL);
      CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
  
      /*** clone and destroy all of them to make sure cloning was complete ***/
      {
          secp256k1_context *ctx_tmp;
  
          ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_destroy(ctx_tmp);
          ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_destroy(ctx_tmp);
          ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_destroy(ctx_tmp);
          ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_destroy(ctx_tmp);
      }
  
      /* Verify that the error callback makes it across the clone. */
      CHECK(vrfy->error_callback.fn != sign->error_callback.fn);
      /* And that it resets back to default. */
      secp256k1_context_set_error_callback(sign, NULL, NULL);
      CHECK(vrfy->error_callback.fn == sign->error_callback.fn);
  
      /*** attempt to use them ***/
      random_scalar_order_test(&msg);
      random_scalar_order_test(&key);
      secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key);
      secp256k1_ge_set_gej(&pub, &pubj);
  
      /* Verify context-type checking illegal-argument errors. */
      memset(ctmp, 1, 32);
      CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0);
      CHECK(ecount == 1);
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0);
      CHECK(ecount == 2);
      VG_UNDEF(&sig, sizeof(sig));
      CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1);
      VG_CHECK(&sig, sizeof(sig));
      CHECK(ecount2 == 10);
      CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0);
      CHECK(ecount2 == 11);
      CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1);
      CHECK(ecount == 2);
      CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0);
      CHECK(ecount2 == 12);
      CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1);
      CHECK(ecount == 2);
      CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0);
      CHECK(ecount2 == 13);
      CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1);
      CHECK(ecount == 2);
      CHECK(secp256k1_context_randomize(vrfy, ctmp) == 0);
      CHECK(ecount == 3);
      CHECK(secp256k1_context_randomize(sign, NULL) == 1);
      CHECK(ecount2 == 13);
      secp256k1_context_set_illegal_callback(vrfy, NULL, NULL);
      secp256k1_context_set_illegal_callback(sign, NULL, NULL);
  
      /* This shouldn't leak memory, due to already-set tests. */
      secp256k1_ecmult_gen_context_build(&sign->ecmult_gen_ctx, NULL);
      secp256k1_ecmult_context_build(&vrfy->ecmult_ctx, NULL);
  
      /* obtain a working nonce */
      do {
          random_scalar_order_test(&nonce);
      } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
  
      /* try signing */
      CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
      CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL));
  
      /* try verifying */
      CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg));
      CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg));
  
      /* cleanup */
      secp256k1_context_destroy(none);
      secp256k1_context_destroy(sign);
      secp256k1_context_destroy(vrfy);
      secp256k1_context_destroy(both);
      /* Defined as no-op. */
      secp256k1_context_destroy(NULL);
  }
  
  /***** HASH TESTS *****/
  
  void run_sha256_tests(void) {
      static const char *inputs[8] = {
          "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe",
          "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq",
          "For this sample, this 63-byte string will be used as input data",
          "This is exactly 64 bytes long, not counting the terminating byte"
      };
      static const unsigned char outputs[8][32] = {
          {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55},
          {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad},
          {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50},
          {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d},
          {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30},
          {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1},
          {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42},
          {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8}
      };
      int i;
      for (i = 0; i < 8; i++) {
          unsigned char out[32];
          secp256k1_sha256_t hasher;
          secp256k1_sha256_initialize(&hasher);
          secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
          secp256k1_sha256_finalize(&hasher, out);
          CHECK(memcmp(out, outputs[i], 32) == 0);
          if (strlen(inputs[i]) > 0) {
              int split = secp256k1_rand_int(strlen(inputs[i]));
              secp256k1_sha256_initialize(&hasher);
              secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
              secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
              secp256k1_sha256_finalize(&hasher, out);
              CHECK(memcmp(out, outputs[i], 32) == 0);
          }
      }
  }
  
  void run_hmac_sha256_tests(void) {
      static const char *keys[6] = {
          "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b",
          "\x4a\x65\x66\x65",
          "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
          "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19",
          "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa",
          "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
      };
      static const char *inputs[6] = {
          "\x48\x69\x20\x54\x68\x65\x72\x65",
          "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f",
          "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd",
          "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd",
          "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74",
          "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e"
      };
      static const unsigned char outputs[6][32] = {
          {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7},
          {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43},
          {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe},
          {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b},
          {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54},
          {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2}
      };
      int i;
      for (i = 0; i < 6; i++) {
          secp256k1_hmac_sha256_t hasher;
          unsigned char out[32];
          secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
          secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i]));
          secp256k1_hmac_sha256_finalize(&hasher, out);
          CHECK(memcmp(out, outputs[i], 32) == 0);
          if (strlen(inputs[i]) > 0) {
              int split = secp256k1_rand_int(strlen(inputs[i]));
              secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i]));
              secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split);
              secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split);
              secp256k1_hmac_sha256_finalize(&hasher, out);
              CHECK(memcmp(out, outputs[i], 32) == 0);
          }
      }
  }
  
  void run_rfc6979_hmac_sha256_tests(void) {
      static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0};
      static const unsigned char out1[3][32] = {
          {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb},
          {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a},
          {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e}
      };
  
      static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55};
      static const unsigned char out2[3][32] = {
          {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95},
          {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9},
          {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94}
      };
  
      secp256k1_rfc6979_hmac_sha256_t rng;
      unsigned char out[32];
      int i;
  
      secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64);
      for (i = 0; i < 3; i++) {
          secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
          CHECK(memcmp(out, out1[i], 32) == 0);
      }
      secp256k1_rfc6979_hmac_sha256_finalize(&rng);
  
      secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65);
      for (i = 0; i < 3; i++) {
          secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
          CHECK(memcmp(out, out1[i], 32) != 0);
      }
      secp256k1_rfc6979_hmac_sha256_finalize(&rng);
  
      secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64);
      for (i = 0; i < 3; i++) {
          secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32);
          CHECK(memcmp(out, out2[i], 32) == 0);
      }
      secp256k1_rfc6979_hmac_sha256_finalize(&rng);
  }
  
  /***** RANDOM TESTS *****/
  
  void test_rand_bits(int rand32, int bits) {
      /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to
       * get a false negative chance below once in a billion */
      static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316};
      /* We try multiplying the results with various odd numbers, which shouldn't
       * influence the uniform distribution modulo a power of 2. */
      static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011};
      /* We only select up to 6 bits from the output to analyse */
      unsigned int usebits = bits > 6 ? 6 : bits;
      unsigned int maxshift = bits - usebits;
      /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit
         number, track all observed outcomes, one per bit in a uint64_t. */
      uint64_t x[6][27] = {{0}};
      unsigned int i, shift, m;
      /* Multiply the output of all rand calls with the odd number m, which
         should not change the uniformity of its distribution. */
      for (i = 0; i < rounds[usebits]; i++) {
          uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits));
          CHECK((((uint64_t)r) >> bits) == 0);
          for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
              uint32_t rm = r * mults[m];
              for (shift = 0; shift <= maxshift; shift++) {
                  x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1)));
              }
          }
      }
      for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) {
          for (shift = 0; shift <= maxshift; shift++) {
              /* Test that the lower usebits bits of x[shift] are 1 */
              CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0);
          }
      }
  }
  
  /* Subrange must be a whole divisor of range, and at most 64 */
  void test_rand_int(uint32_t range, uint32_t subrange) {
      /* (1-1/subrange)^rounds < 1/10^9 */
      int rounds = (subrange * 2073) / 100;
      int i;
      uint64_t x = 0;
      CHECK((range % subrange) == 0);
      for (i = 0; i < rounds; i++) {
          uint32_t r = secp256k1_rand_int(range);
          CHECK(r < range);
          r = r % subrange;
          x |= (((uint64_t)1) << r);
      }
      /* Test that the lower subrange bits of x are 1. */
      CHECK(((~x) << (64 - subrange)) == 0);
  }
  
  void run_rand_bits(void) {
      size_t b;
      test_rand_bits(1, 32);
      for (b = 1; b <= 32; b++) {
          test_rand_bits(0, b);
      }
  }
  
  void run_rand_int(void) {
      static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432};
      static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64};
      unsigned int m, s;
      for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) {
          for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) {
              test_rand_int(ms[m] * ss[s], ss[s]);
          }
      }
  }
  
  /***** NUM TESTS *****/
  
  #ifndef USE_NUM_NONE
  void random_num_negate(secp256k1_num *num) {
      if (secp256k1_rand_bits(1)) {
          secp256k1_num_negate(num);
      }
  }
  
  void random_num_order_test(secp256k1_num *num) {
      secp256k1_scalar sc;
      random_scalar_order_test(&sc);
      secp256k1_scalar_get_num(num, &sc);
  }
  
  void random_num_order(secp256k1_num *num) {
      secp256k1_scalar sc;
      random_scalar_order(&sc);
      secp256k1_scalar_get_num(num, &sc);
  }
  
  void test_num_negate(void) {
      secp256k1_num n1;
      secp256k1_num n2;
      random_num_order_test(&n1); /* n1 = R */
      random_num_negate(&n1);
      secp256k1_num_copy(&n2, &n1); /* n2 = R */
      secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */
      CHECK(secp256k1_num_is_zero(&n1));
      secp256k1_num_copy(&n1, &n2); /* n1 = R */
      secp256k1_num_negate(&n1); /* n1 = -R */
      CHECK(!secp256k1_num_is_zero(&n1));
      secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */
      CHECK(secp256k1_num_is_zero(&n1));
      secp256k1_num_copy(&n1, &n2); /* n1 = R */
      secp256k1_num_negate(&n1); /* n1 = -R */
      CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2));
      secp256k1_num_negate(&n1); /* n1 = R */
      CHECK(secp256k1_num_eq(&n1, &n2));
  }
  
  void test_num_add_sub(void) {
      int i;
      secp256k1_scalar s;
      secp256k1_num n1;
      secp256k1_num n2;
      secp256k1_num n1p2, n2p1, n1m2, n2m1;
      random_num_order_test(&n1); /* n1 = R1 */
      if (secp256k1_rand_bits(1)) {
          random_num_negate(&n1);
      }
      random_num_order_test(&n2); /* n2 = R2 */
      if (secp256k1_rand_bits(1)) {
          random_num_negate(&n2);
      }
      secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */
      secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */
      secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */
      secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */
      CHECK(secp256k1_num_eq(&n1p2, &n2p1));
      CHECK(!secp256k1_num_eq(&n1p2, &n1m2));
      secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */
      CHECK(secp256k1_num_eq(&n2m1, &n1m2));
      CHECK(!secp256k1_num_eq(&n2m1, &n1));
      secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */
      CHECK(secp256k1_num_eq(&n2m1, &n1));
      CHECK(!secp256k1_num_eq(&n2p1, &n1));
      secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */
      CHECK(secp256k1_num_eq(&n2p1, &n1));
  
      /* check is_one */
      secp256k1_scalar_set_int(&s, 1);
      secp256k1_scalar_get_num(&n1, &s);
      CHECK(secp256k1_num_is_one(&n1));
      /* check that 2^n + 1 is never 1 */
      secp256k1_scalar_get_num(&n2, &s);
      for (i = 0; i < 250; ++i) {
          secp256k1_num_add(&n1, &n1, &n1);    /* n1 *= 2 */
          secp256k1_num_add(&n1p2, &n1, &n2);  /* n1p2 = n1 + 1 */
          CHECK(!secp256k1_num_is_one(&n1p2));
      }
  }
  
  void test_num_mod(void) {
      int i;
      secp256k1_scalar s;
      secp256k1_num order, n;
  
      /* check that 0 mod anything is 0 */
      random_scalar_order_test(&s);
      secp256k1_scalar_get_num(&order, &s);
      secp256k1_scalar_set_int(&s, 0);
      secp256k1_scalar_get_num(&n, &s);
      secp256k1_num_mod(&n, &order);
      CHECK(secp256k1_num_is_zero(&n));
  
      /* check that anything mod 1 is 0 */
      secp256k1_scalar_set_int(&s, 1);
      secp256k1_scalar_get_num(&order, &s);
      secp256k1_scalar_get_num(&n, &s);
      secp256k1_num_mod(&n, &order);
      CHECK(secp256k1_num_is_zero(&n));
  
      /* check that increasing the number past 2^256 does not break this */
      random_scalar_order_test(&s);
      secp256k1_scalar_get_num(&n, &s);
      /* multiply by 2^8, which'll test this case with high probability */
      for (i = 0; i < 8; ++i) {
          secp256k1_num_add(&n, &n, &n);
      }
      secp256k1_num_mod(&n, &order);
      CHECK(secp256k1_num_is_zero(&n));
  }
  
  void test_num_jacobi(void) {
      secp256k1_scalar sqr;
      secp256k1_scalar small;
      secp256k1_scalar five;  /* five is not a quadratic residue */
      secp256k1_num order, n;
      int i;
      /* squares mod 5 are 1, 4 */
      const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 };
  
      /* check some small values with 5 as the order */
      secp256k1_scalar_set_int(&five, 5);
      secp256k1_scalar_get_num(&order, &five);
      for (i = 0; i < 10; ++i) {
          secp256k1_scalar_set_int(&small, i);
          secp256k1_scalar_get_num(&n, &small);
          CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]);
      }
  
      /** test large values with 5 as group order */
      secp256k1_scalar_get_num(&order, &five);
      /* we first need a scalar which is not a multiple of 5 */
      do {
          secp256k1_num fiven;
          random_scalar_order_test(&sqr);
          secp256k1_scalar_get_num(&fiven, &five);
          secp256k1_scalar_get_num(&n, &sqr);
          secp256k1_num_mod(&n, &fiven);
      } while (secp256k1_num_is_zero(&n));
      /* next force it to be a residue. 2 is a nonresidue mod 5 so we can
       * just multiply by two, i.e. add the number to itself */
      if (secp256k1_num_jacobi(&n, &order) == -1) {
          secp256k1_num_add(&n, &n, &n);
      }
  
      /* test residue */
      CHECK(secp256k1_num_jacobi(&n, &order) == 1);
      /* test nonresidue */
      secp256k1_num_add(&n, &n, &n);
      CHECK(secp256k1_num_jacobi(&n, &order) == -1);
  
      /** test with secp group order as order */
      secp256k1_scalar_order_get_num(&order);
      random_scalar_order_test(&sqr);
      secp256k1_scalar_sqr(&sqr, &sqr);
      /* test residue */
      secp256k1_scalar_get_num(&n, &sqr);
      CHECK(secp256k1_num_jacobi(&n, &order) == 1);
      /* test nonresidue */
      secp256k1_scalar_mul(&sqr, &sqr, &five);
      secp256k1_scalar_get_num(&n, &sqr);
      CHECK(secp256k1_num_jacobi(&n, &order) == -1);
      /* test multiple of the order*/
      CHECK(secp256k1_num_jacobi(&order, &order) == 0);
  
      /* check one less than the order */
      secp256k1_scalar_set_int(&small, 1);
      secp256k1_scalar_get_num(&n, &small);
      secp256k1_num_sub(&n, &order, &n);
      CHECK(secp256k1_num_jacobi(&n, &order) == 1);  /* sage confirms this is 1 */
  }
  
  void run_num_smalltests(void) {
      int i;
      for (i = 0; i < 100*count; i++) {
          test_num_negate();
          test_num_add_sub();
          test_num_mod();
          test_num_jacobi();
      }
  }
  #endif
  
  /***** SCALAR TESTS *****/
  
  void scalar_test(void) {
      secp256k1_scalar s;
      secp256k1_scalar s1;
      secp256k1_scalar s2;
  #ifndef USE_NUM_NONE
      secp256k1_num snum, s1num, s2num;
      secp256k1_num order, half_order;
  #endif
      unsigned char c[32];
  
      /* Set 's' to a random scalar, with value 'snum'. */
      random_scalar_order_test(&s);
  
      /* Set 's1' to a random scalar, with value 's1num'. */
      random_scalar_order_test(&s1);
  
      /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */
      random_scalar_order_test(&s2);
      secp256k1_scalar_get_b32(c, &s2);
  
  #ifndef USE_NUM_NONE
      secp256k1_scalar_get_num(&snum, &s);
      secp256k1_scalar_get_num(&s1num, &s1);
      secp256k1_scalar_get_num(&s2num, &s2);
  
      secp256k1_scalar_order_get_num(&order);
      half_order = order;
      secp256k1_num_shift(&half_order, 1);
  #endif
  
      {
          int i;
          /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */
          secp256k1_scalar n;
          secp256k1_scalar_set_int(&n, 0);
          for (i = 0; i < 256; i += 4) {
              secp256k1_scalar t;
              int j;
              secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4));
              for (j = 0; j < 4; j++) {
                  secp256k1_scalar_add(&n, &n, &n);
              }
              secp256k1_scalar_add(&n, &n, &t);
          }
          CHECK(secp256k1_scalar_eq(&n, &s));
      }
  
      {
          /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */
          secp256k1_scalar n;
          int i = 0;
          secp256k1_scalar_set_int(&n, 0);
          while (i < 256) {
              secp256k1_scalar t;
              int j;
              int now = secp256k1_rand_int(15) + 1;
              if (now + i > 256) {
                  now = 256 - i;
              }
              secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now));
              for (j = 0; j < now; j++) {
                  secp256k1_scalar_add(&n, &n, &n);
              }
              secp256k1_scalar_add(&n, &n, &t);
              i += now;
          }
          CHECK(secp256k1_scalar_eq(&n, &s));
      }
  
  #ifndef USE_NUM_NONE
      {
          /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */
          secp256k1_num rnum;
          secp256k1_num r2num;
          secp256k1_scalar r;
          secp256k1_num_add(&rnum, &snum, &s2num);
          secp256k1_num_mod(&rnum, &order);
          secp256k1_scalar_add(&r, &s, &s2);
          secp256k1_scalar_get_num(&r2num, &r);
          CHECK(secp256k1_num_eq(&rnum, &r2num));
      }
  
      {
          /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */
          secp256k1_scalar r;
          secp256k1_num r2num;
          secp256k1_num rnum;
          secp256k1_num_mul(&rnum, &snum, &s2num);
          secp256k1_num_mod(&rnum, &order);
          secp256k1_scalar_mul(&r, &s, &s2);
          secp256k1_scalar_get_num(&r2num, &r);
          CHECK(secp256k1_num_eq(&rnum, &r2num));
          /* The result can only be zero if at least one of the factors was zero. */
          CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2)));
          /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */
          CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2)));
          CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s)));
      }
  
      {
          secp256k1_scalar neg;
          secp256k1_num negnum;
          secp256k1_num negnum2;
          /* Check that comparison with zero matches comparison with zero on the number. */
          CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s));
          /* Check that comparison with the half order is equal to testing for high scalar. */
          CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0));
          secp256k1_scalar_negate(&neg, &s);
          secp256k1_num_sub(&negnum, &order, &snum);
          secp256k1_num_mod(&negnum, &order);
          /* Check that comparison with the half order is equal to testing for high scalar after negation. */
          CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0));
          /* Negating should change the high property, unless the value was already zero. */
          CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s));
          secp256k1_scalar_get_num(&negnum2, &neg);
          /* Negating a scalar should be equal to (order - n) mod order on the number. */
          CHECK(secp256k1_num_eq(&negnum, &negnum2));
          secp256k1_scalar_add(&neg, &neg, &s);
          /* Adding a number to its negation should result in zero. */
          CHECK(secp256k1_scalar_is_zero(&neg));
          secp256k1_scalar_negate(&neg, &neg);
          /* Negating zero should still result in zero. */
          CHECK(secp256k1_scalar_is_zero(&neg));
      }
  
      {
          /* Test secp256k1_scalar_mul_shift_var. */
          secp256k1_scalar r;
          secp256k1_num one;
          secp256k1_num rnum;
          secp256k1_num rnum2;
          unsigned char cone[1] = {0x01};
          unsigned int shift = 256 + secp256k1_rand_int(257);
          secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift);
          secp256k1_num_mul(&rnum, &s1num, &s2num);
          secp256k1_num_shift(&rnum, shift - 1);
          secp256k1_num_set_bin(&one, cone, 1);
          secp256k1_num_add(&rnum, &rnum, &one);
          secp256k1_num_shift(&rnum, 1);
          secp256k1_scalar_get_num(&rnum2, &r);
          CHECK(secp256k1_num_eq(&rnum, &rnum2));
      }
  
      {
          /* test secp256k1_scalar_shr_int */
          secp256k1_scalar r;
          int i;
          random_scalar_order_test(&r);
          for (i = 0; i < 100; ++i) {
              int low;
              int shift = 1 + secp256k1_rand_int(15);
              int expected = r.d[0] % (1 << shift);
              low = secp256k1_scalar_shr_int(&r, shift);
              CHECK(expected == low);
          }
      }
  #endif
  
      {
          /* Test that scalar inverses are equal to the inverse of their number modulo the order. */
          if (!secp256k1_scalar_is_zero(&s)) {
              secp256k1_scalar inv;
  #ifndef USE_NUM_NONE
              secp256k1_num invnum;
              secp256k1_num invnum2;
  #endif
              secp256k1_scalar_inverse(&inv, &s);
  #ifndef USE_NUM_NONE
              secp256k1_num_mod_inverse(&invnum, &snum, &order);
              secp256k1_scalar_get_num(&invnum2, &inv);
              CHECK(secp256k1_num_eq(&invnum, &invnum2));
  #endif
              secp256k1_scalar_mul(&inv, &inv, &s);
              /* Multiplying a scalar with its inverse must result in one. */
              CHECK(secp256k1_scalar_is_one(&inv));
              secp256k1_scalar_inverse(&inv, &inv);
              /* Inverting one must result in one. */
              CHECK(secp256k1_scalar_is_one(&inv));
  #ifndef USE_NUM_NONE
              secp256k1_scalar_get_num(&invnum, &inv);
              CHECK(secp256k1_num_is_one(&invnum));
  #endif
          }
      }
  
      {
          /* Test commutativity of add. */
          secp256k1_scalar r1, r2;
          secp256k1_scalar_add(&r1, &s1, &s2);
          secp256k1_scalar_add(&r2, &s2, &s1);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          secp256k1_scalar r1, r2;
          secp256k1_scalar b;
          int i;
          /* Test add_bit. */
          int bit = secp256k1_rand_bits(8);
          secp256k1_scalar_set_int(&b, 1);
          CHECK(secp256k1_scalar_is_one(&b));
          for (i = 0; i < bit; i++) {
              secp256k1_scalar_add(&b, &b, &b);
          }
          r1 = s1;
          r2 = s1;
          if (!secp256k1_scalar_add(&r1, &r1, &b)) {
              /* No overflow happened. */
              secp256k1_scalar_cadd_bit(&r2, bit, 1);
              CHECK(secp256k1_scalar_eq(&r1, &r2));
              /* cadd is a noop when flag is zero */
              secp256k1_scalar_cadd_bit(&r2, bit, 0);
              CHECK(secp256k1_scalar_eq(&r1, &r2));
          }
      }
  
      {
          /* Test commutativity of mul. */
          secp256k1_scalar r1, r2;
          secp256k1_scalar_mul(&r1, &s1, &s2);
          secp256k1_scalar_mul(&r2, &s2, &s1);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          /* Test associativity of add. */
          secp256k1_scalar r1, r2;
          secp256k1_scalar_add(&r1, &s1, &s2);
          secp256k1_scalar_add(&r1, &r1, &s);
          secp256k1_scalar_add(&r2, &s2, &s);
          secp256k1_scalar_add(&r2, &s1, &r2);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          /* Test associativity of mul. */
          secp256k1_scalar r1, r2;
          secp256k1_scalar_mul(&r1, &s1, &s2);
          secp256k1_scalar_mul(&r1, &r1, &s);
          secp256k1_scalar_mul(&r2, &s2, &s);
          secp256k1_scalar_mul(&r2, &s1, &r2);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          /* Test distributitivity of mul over add. */
          secp256k1_scalar r1, r2, t;
          secp256k1_scalar_add(&r1, &s1, &s2);
          secp256k1_scalar_mul(&r1, &r1, &s);
          secp256k1_scalar_mul(&r2, &s1, &s);
          secp256k1_scalar_mul(&t, &s2, &s);
          secp256k1_scalar_add(&r2, &r2, &t);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          /* Test square. */
          secp256k1_scalar r1, r2;
          secp256k1_scalar_sqr(&r1, &s1);
          secp256k1_scalar_mul(&r2, &s1, &s1);
          CHECK(secp256k1_scalar_eq(&r1, &r2));
      }
  
      {
          /* Test multiplicative identity. */
          secp256k1_scalar r1, v1;
          secp256k1_scalar_set_int(&v1,1);
          secp256k1_scalar_mul(&r1, &s1, &v1);
          CHECK(secp256k1_scalar_eq(&r1, &s1));
      }
  
      {
          /* Test additive identity. */
          secp256k1_scalar r1, v0;
          secp256k1_scalar_set_int(&v0,0);
          secp256k1_scalar_add(&r1, &s1, &v0);
          CHECK(secp256k1_scalar_eq(&r1, &s1));
      }
  
      {
          /* Test zero product property. */
          secp256k1_scalar r1, v0;
          secp256k1_scalar_set_int(&v0,0);
          secp256k1_scalar_mul(&r1, &s1, &v0);
          CHECK(secp256k1_scalar_eq(&r1, &v0));
      }
  
  }
  
  void run_scalar_tests(void) {
      int i;
      for (i = 0; i < 128 * count; i++) {
          scalar_test();
      }
  
      {
          /* (-1)+1 should be zero. */
          secp256k1_scalar s, o;
          secp256k1_scalar_set_int(&s, 1);
          CHECK(secp256k1_scalar_is_one(&s));
          secp256k1_scalar_negate(&o, &s);
          secp256k1_scalar_add(&o, &o, &s);
          CHECK(secp256k1_scalar_is_zero(&o));
          secp256k1_scalar_negate(&o, &o);
          CHECK(secp256k1_scalar_is_zero(&o));
      }
  
  #ifndef USE_NUM_NONE
      {
          /* A scalar with value of the curve order should be 0. */
          secp256k1_num order;
          secp256k1_scalar zero;
          unsigned char bin[32];
          int overflow = 0;
          secp256k1_scalar_order_get_num(&order);
          secp256k1_num_get_bin(bin, 32, &order);
          secp256k1_scalar_set_b32(&zero, bin, &overflow);
          CHECK(overflow == 1);
          CHECK(secp256k1_scalar_is_zero(&zero));
      }
  #endif
  
      {
          /* Does check_overflow check catch all ones? */
          static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST(
              0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
              0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL
          );
          CHECK(secp256k1_scalar_check_overflow(&overflowed));
      }
  
      {
          /* Static test vectors.
           * These were reduced from ~10^12 random vectors based on comparison-decision
           *  and edge-case coverage on 32-bit and 64-bit implementations.
           * The responses were generated with Sage 5.9.
           */
          secp256k1_scalar x;
          secp256k1_scalar y;
          secp256k1_scalar z;
          secp256k1_scalar zz;
          secp256k1_scalar one;
          secp256k1_scalar r1;
          secp256k1_scalar r2;
  #if defined(USE_SCALAR_INV_NUM)
          secp256k1_scalar zzv;
  #endif
          int overflow;
          unsigned char chal[33][2][32] = {
              {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
                0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff,
                0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}},
              {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00,
                0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
               {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0,
                0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}},
              {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00,
                0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00,
                0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00},
               {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f,
                0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0,
                0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff,
                0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00,
                0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00,
                0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00,
                0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f,
                0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f,
                0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00,
                0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
               {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
                0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff,
                0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff,
                0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00,
                0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
                0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00,
                0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0},
               {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
              {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00,
                0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff,
                0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
              {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f},
               {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00,
                0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff,
                0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff,
                0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff},
               {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}},
              {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff,
                0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00,
                0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f,
                0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff,
                0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}},
              {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00},
               {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}},
              {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00,
                0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
               {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}},
              {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03,
                0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00,
                0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00},
               {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
                0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
               {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80,
                0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
                0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}},
              {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff,
                0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00,
                0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
                0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
               {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0,
                0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00,
                0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00,
                0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}},
              {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
                0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00,
                0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00,
                0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff},
               {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}},
              {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00,
                0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
                0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff,
                0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}},
              {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00},
               {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
                0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f,
                0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}},
              {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01,
                0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00},
               {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00,
                0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80,
                0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff,
                0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00,
                0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8,
                0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80},
               {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00,
                0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f,
                0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}},
              {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00,
                0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83,
                0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80,
                0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0},
               {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00,
                0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}},
              {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
                0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
                0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03},
               {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
                0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00,
                0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb,
                0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}}
          };
          unsigned char res[33][2][32] = {
              {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9,
                0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1,
                0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6,
                0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35},
               {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d,
                0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c,
                0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49,
                0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}},
              {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22,
                0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c,
                0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f,
                0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8},
               {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77,
                0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4,
                0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59,
                0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}},
              {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef,
                0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab,
                0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55,
                0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c},
               {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96,
                0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f,
                0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12,
                0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}},
              {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c,
                0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf,
                0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9,
                0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48},
               {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42,
                0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5,
                0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c,
                0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}},
              {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb,
                0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74,
                0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6,
                0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63},
               {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3,
                0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99,
                0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58,
                0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}},
              {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b,
                0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7,
                0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f,
                0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0},
               {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d,
                0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d,
                0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9,
                0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}},
              {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7,
                0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70,
                0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06,
                0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e},
               {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9,
                0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79,
                0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e,
                0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}},
              {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb,
                0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5,
                0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a,
                0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe},
               {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48,
                0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e,
                0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc,
                0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}},
              {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b,
                0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0,
                0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53,
                0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8},
               {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c,
                0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01,
                0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f,
                0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}},
              {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7,
                0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c,
                0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92,
                0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30},
               {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62,
                0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e,
                0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb,
                0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}},
              {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25,
                0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d,
                0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0,
                0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13},
               {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60,
                0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00,
                0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4,
                0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}},
              {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31,
                0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4,
                0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88,
                0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa},
               {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57,
                0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38,
                0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51,
                0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}},
              {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c,
                0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f,
                0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2,
                0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4},
               {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01,
                0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4,
                0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86,
                0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}},
              {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5,
                0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51,
                0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3,
                0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62},
               {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c,
                0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91,
                0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c,
                0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}},
              {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e,
                0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56,
                0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58,
                0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4},
               {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41,
                0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7,
                0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92,
                0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}},
              {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec,
                0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19,
                0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3,
                0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4},
               {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87,
                0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a,
                0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92,
                0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}},
              {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64,
                0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3,
                0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f,
                0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33},
               {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c,
                0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d,
                0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea,
                0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}},
              {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7,
                0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a,
                0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae,
                0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe},
               {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc,
                0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39,
                0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14,
                0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}},
              {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23,
                0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d,
                0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2,
                0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16},
               {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c,
                0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84,
                0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0,
                0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}},
              {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb,
                0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94,
                0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b,
                0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e},
               {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54,
                0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00,
                0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb,
                0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
              {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
                0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
                0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
                0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92},
               {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
                0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
                0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
                0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
              {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0,
                0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b,
                0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94,
                0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8},
               {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26,
                0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d,
                0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a,
                0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}},
              {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
                0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
                0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd},
               {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1,
                0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0,
                0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59,
                0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}},
              {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
                0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
                0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40},
               {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}},
              {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39,
                0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea,
                0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf,
                0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae},
               {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b,
                0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb,
                0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6,
                0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}},
              {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a,
                0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f,
                0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9,
                0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56},
               {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93,
                0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07,
                0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71,
                0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}},
              {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87,
                0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9,
                0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55,
                0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73},
               {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d,
                0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86,
                0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb,
                0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}},
              {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2,
                0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7,
                0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41,
                0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7},
               {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06,
                0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04,
                0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08,
                0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}},
              {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2,
                0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b,
                0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40,
                0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68},
               {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e,
                0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a,
                0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b,
                0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}},
              {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67,
                0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f,
                0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a,
                0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51},
               {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2,
                0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38,
                0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34,
                0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}},
              {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
                0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
                0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
                0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5},
               {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34,
                0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13,
                0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46,
                0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}}
          };
          secp256k1_scalar_set_int(&one, 1);
          for (i = 0; i < 33; i++) {
              secp256k1_scalar_set_b32(&x, chal[i][0], &overflow);
              CHECK(!overflow);
              secp256k1_scalar_set_b32(&y, chal[i][1], &overflow);
              CHECK(!overflow);
              secp256k1_scalar_set_b32(&r1, res[i][0], &overflow);
              CHECK(!overflow);
              secp256k1_scalar_set_b32(&r2, res[i][1], &overflow);
              CHECK(!overflow);
              secp256k1_scalar_mul(&z, &x, &y);
              CHECK(!secp256k1_scalar_check_overflow(&z));
              CHECK(secp256k1_scalar_eq(&r1, &z));
              if (!secp256k1_scalar_is_zero(&y)) {
                  secp256k1_scalar_inverse(&zz, &y);
                  CHECK(!secp256k1_scalar_check_overflow(&zz));
  #if defined(USE_SCALAR_INV_NUM)
                  secp256k1_scalar_inverse_var(&zzv, &y);
                  CHECK(secp256k1_scalar_eq(&zzv, &zz));
  #endif
                  secp256k1_scalar_mul(&z, &z, &zz);
                  CHECK(!secp256k1_scalar_check_overflow(&z));
                  CHECK(secp256k1_scalar_eq(&x, &z));
                  secp256k1_scalar_mul(&zz, &zz, &y);
                  CHECK(!secp256k1_scalar_check_overflow(&zz));
                  CHECK(secp256k1_scalar_eq(&one, &zz));
              }
              secp256k1_scalar_mul(&z, &x, &x);
              CHECK(!secp256k1_scalar_check_overflow(&z));
              secp256k1_scalar_sqr(&zz, &x);
              CHECK(!secp256k1_scalar_check_overflow(&zz));
              CHECK(secp256k1_scalar_eq(&zz, &z));
              CHECK(secp256k1_scalar_eq(&r2, &zz));
          }
      }
  }
  
  /***** FIELD TESTS *****/
  
  void random_fe(secp256k1_fe *x) {
      unsigned char bin[32];
      do {
          secp256k1_rand256(bin);
          if (secp256k1_fe_set_b32(x, bin)) {
              return;
          }
      } while(1);
  }
  
  void random_fe_test(secp256k1_fe *x) {
      unsigned char bin[32];
      do {
          secp256k1_rand256_test(bin);
          if (secp256k1_fe_set_b32(x, bin)) {
              return;
          }
      } while(1);
  }
  
  void random_fe_non_zero(secp256k1_fe *nz) {
      int tries = 10;
      while (--tries >= 0) {
          random_fe(nz);
          secp256k1_fe_normalize(nz);
          if (!secp256k1_fe_is_zero(nz)) {
              break;
          }
      }
      /* Infinitesimal probability of spurious failure here */
      CHECK(tries >= 0);
  }
  
  void random_fe_non_square(secp256k1_fe *ns) {
      secp256k1_fe r;
      random_fe_non_zero(ns);
      if (secp256k1_fe_sqrt(&r, ns)) {
          secp256k1_fe_negate(ns, ns, 1);
      }
  }
  
  int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
      secp256k1_fe an = *a;
      secp256k1_fe bn = *b;
      secp256k1_fe_normalize_weak(&an);
      secp256k1_fe_normalize_var(&bn);
      return secp256k1_fe_equal_var(&an, &bn);
  }
  
  int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) {
      secp256k1_fe x;
      secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
      secp256k1_fe_mul(&x, a, ai);
      return check_fe_equal(&x, &one);
  }
  
  void run_field_convert(void) {
      static const unsigned char b32[32] = {
          0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
          0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
          0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29,
          0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40
      };
      static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST(
          0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
          0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
      );
      static const secp256k1_fe fe = SECP256K1_FE_CONST(
          0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL,
          0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL
      );
      secp256k1_fe fe2;
      unsigned char b322[32];
      secp256k1_fe_storage fes2;
      /* Check conversions to fe. */
      CHECK(secp256k1_fe_set_b32(&fe2, b32));
      CHECK(secp256k1_fe_equal_var(&fe, &fe2));
      secp256k1_fe_from_storage(&fe2, &fes);
      CHECK(secp256k1_fe_equal_var(&fe, &fe2));
      /* Check conversion from fe. */
      secp256k1_fe_get_b32(b322, &fe);
      CHECK(memcmp(b322, b32, 32) == 0);
      secp256k1_fe_to_storage(&fes2, &fe);
      CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0);
  }
  
  int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) {
      secp256k1_fe t = *b;
  #ifdef VERIFY
      t.magnitude = a->magnitude;
      t.normalized = a->normalized;
  #endif
      return memcmp(a, &t, sizeof(secp256k1_fe));
  }
  
  void run_field_misc(void) {
      secp256k1_fe x;
      secp256k1_fe y;
      secp256k1_fe z;
      secp256k1_fe q;
      secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5);
      int i, j;
      for (i = 0; i < 5*count; i++) {
          secp256k1_fe_storage xs, ys, zs;
          random_fe(&x);
          random_fe_non_zero(&y);
          /* Test the fe equality and comparison operations. */
          CHECK(secp256k1_fe_cmp_var(&x, &x) == 0);
          CHECK(secp256k1_fe_equal_var(&x, &x));
          z = x;
          secp256k1_fe_add(&z,&y);
          /* Test fe conditional move; z is not normalized here. */
          q = x;
          secp256k1_fe_cmov(&x, &z, 0);
          VERIFY_CHECK(!x.normalized && x.magnitude == z.magnitude);
          secp256k1_fe_cmov(&x, &x, 1);
          CHECK(fe_memcmp(&x, &z) != 0);
          CHECK(fe_memcmp(&x, &q) == 0);
          secp256k1_fe_cmov(&q, &z, 1);
          VERIFY_CHECK(!q.normalized && q.magnitude == z.magnitude);
          CHECK(fe_memcmp(&q, &z) == 0);
          secp256k1_fe_normalize_var(&x);
          secp256k1_fe_normalize_var(&z);
          CHECK(!secp256k1_fe_equal_var(&x, &z));
          secp256k1_fe_normalize_var(&q);
          secp256k1_fe_cmov(&q, &z, (i&1));
          VERIFY_CHECK(q.normalized && q.magnitude == 1);
          for (j = 0; j < 6; j++) {
              secp256k1_fe_negate(&z, &z, j+1);
              secp256k1_fe_normalize_var(&q);
              secp256k1_fe_cmov(&q, &z, (j&1));
              VERIFY_CHECK(!q.normalized && q.magnitude == (j+2));
          }
          secp256k1_fe_normalize_var(&z);
          /* Test storage conversion and conditional moves. */
          secp256k1_fe_to_storage(&xs, &x);
          secp256k1_fe_to_storage(&ys, &y);
          secp256k1_fe_to_storage(&zs, &z);
          secp256k1_fe_storage_cmov(&zs, &xs, 0);
          secp256k1_fe_storage_cmov(&zs, &zs, 1);
          CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0);
          secp256k1_fe_storage_cmov(&ys, &xs, 1);
          CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0);
          secp256k1_fe_from_storage(&x, &xs);
          secp256k1_fe_from_storage(&y, &ys);
          secp256k1_fe_from_storage(&z, &zs);
          /* Test that mul_int, mul, and add agree. */
          secp256k1_fe_add(&y, &x);
          secp256k1_fe_add(&y, &x);
          z = x;
          secp256k1_fe_mul_int(&z, 3);
          CHECK(check_fe_equal(&y, &z));
          secp256k1_fe_add(&y, &x);
          secp256k1_fe_add(&z, &x);
          CHECK(check_fe_equal(&z, &y));
          z = x;
          secp256k1_fe_mul_int(&z, 5);
          secp256k1_fe_mul(&q, &x, &fe5);
          CHECK(check_fe_equal(&z, &q));
          secp256k1_fe_negate(&x, &x, 1);
          secp256k1_fe_add(&z, &x);
          secp256k1_fe_add(&q, &x);
          CHECK(check_fe_equal(&y, &z));
          CHECK(check_fe_equal(&q, &y));
      }
  }
  
  void run_field_inv(void) {
      secp256k1_fe x, xi, xii;
      int i;
      for (i = 0; i < 10*count; i++) {
          random_fe_non_zero(&x);
          secp256k1_fe_inv(&xi, &x);
          CHECK(check_fe_inverse(&x, &xi));
          secp256k1_fe_inv(&xii, &xi);
          CHECK(check_fe_equal(&x, &xii));
      }
  }
  
  void run_field_inv_var(void) {
      secp256k1_fe x, xi, xii;
      int i;
      for (i = 0; i < 10*count; i++) {
          random_fe_non_zero(&x);
          secp256k1_fe_inv_var(&xi, &x);
          CHECK(check_fe_inverse(&x, &xi));
          secp256k1_fe_inv_var(&xii, &xi);
          CHECK(check_fe_equal(&x, &xii));
      }
  }
  
  void run_field_inv_all_var(void) {
      secp256k1_fe x[16], xi[16], xii[16];
      int i;
      /* Check it's safe to call for 0 elements */
      secp256k1_fe_inv_all_var(xi, x, 0);
      for (i = 0; i < count; i++) {
          size_t j;
          size_t len = secp256k1_rand_int(15) + 1;
          for (j = 0; j < len; j++) {
              random_fe_non_zero(&x[j]);
          }
          secp256k1_fe_inv_all_var(xi, x, len);
          for (j = 0; j < len; j++) {
              CHECK(check_fe_inverse(&x[j], &xi[j]));
          }
          secp256k1_fe_inv_all_var(xii, xi, len);
          for (j = 0; j < len; j++) {
              CHECK(check_fe_equal(&x[j], &xii[j]));
          }
      }
  }
  
  void run_sqr(void) {
      secp256k1_fe x, s;
  
      {
          int i;
          secp256k1_fe_set_int(&x, 1);
          secp256k1_fe_negate(&x, &x, 1);
  
          for (i = 1; i <= 512; ++i) {
              secp256k1_fe_mul_int(&x, 2);
              secp256k1_fe_normalize(&x);
              secp256k1_fe_sqr(&s, &x);
          }
      }
  }
  
  void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
      secp256k1_fe r1, r2;
      int v = secp256k1_fe_sqrt(&r1, a);
      CHECK((v == 0) == (k == NULL));
  
      if (k != NULL) {
          /* Check that the returned root is +/- the given known answer */
          secp256k1_fe_negate(&r2, &r1, 1);
          secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k);
          secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2);
          CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2));
      }
  }
  
  void run_sqrt(void) {
      secp256k1_fe ns, x, s, t;
      int i;
  
      /* Check sqrt(0) is 0 */
      secp256k1_fe_set_int(&x, 0);
      secp256k1_fe_sqr(&s, &x);
      test_sqrt(&s, &x);
  
      /* Check sqrt of small squares (and their negatives) */
      for (i = 1; i <= 100; i++) {
          secp256k1_fe_set_int(&x, i);
          secp256k1_fe_sqr(&s, &x);
          test_sqrt(&s, &x);
          secp256k1_fe_negate(&t, &s, 1);
          test_sqrt(&t, NULL);
      }
  
      /* Consistency checks for large random values */
      for (i = 0; i < 10; i++) {
          int j;
          random_fe_non_square(&ns);
          for (j = 0; j < count; j++) {
              random_fe(&x);
              secp256k1_fe_sqr(&s, &x);
              test_sqrt(&s, &x);
              secp256k1_fe_negate(&t, &s, 1);
              test_sqrt(&t, NULL);
              secp256k1_fe_mul(&t, &s, &ns);
              test_sqrt(&t, NULL);
          }
      }
  }
  
  /***** GROUP TESTS *****/
  
  void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) {
      CHECK(a->infinity == b->infinity);
      if (a->infinity) {
          return;
      }
      CHECK(secp256k1_fe_equal_var(&a->x, &b->x));
      CHECK(secp256k1_fe_equal_var(&a->y, &b->y));
  }
  
  /* This compares jacobian points including their Z, not just their geometric meaning. */
  int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) {
      secp256k1_gej a2;
      secp256k1_gej b2;
      int ret = 1;
      ret &= a->infinity == b->infinity;
      if (ret && !a->infinity) {
          a2 = *a;
          b2 = *b;
          secp256k1_fe_normalize(&a2.x);
          secp256k1_fe_normalize(&a2.y);
          secp256k1_fe_normalize(&a2.z);
          secp256k1_fe_normalize(&b2.x);
          secp256k1_fe_normalize(&b2.y);
          secp256k1_fe_normalize(&b2.z);
          ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0;
          ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0;
          ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0;
      }
      return ret;
  }
  
  void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) {
      secp256k1_fe z2s;
      secp256k1_fe u1, u2, s1, s2;
      CHECK(a->infinity == b->infinity);
      if (a->infinity) {
          return;
      }
      /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */
      secp256k1_fe_sqr(&z2s, &b->z);
      secp256k1_fe_mul(&u1, &a->x, &z2s);
      u2 = b->x; secp256k1_fe_normalize_weak(&u2);
      secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z);
      s2 = b->y; secp256k1_fe_normalize_weak(&s2);
      CHECK(secp256k1_fe_equal_var(&u1, &u2));
      CHECK(secp256k1_fe_equal_var(&s1, &s2));
  }
  
  void test_ge(void) {
      int i, i1;
  #ifdef USE_ENDOMORPHISM
      int runs = 6;
  #else
      int runs = 4;
  #endif
      /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4).
       * The second in each pair of identical points uses a random Z coordinate in the Jacobian form.
       * All magnitudes are randomized.
       * All 17*17 combinations of points are added to each other, using all applicable methods.
       *
       * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well.
       */
      secp256k1_ge *ge = (secp256k1_ge *)malloc(sizeof(secp256k1_ge) * (1 + 4 * runs));
      secp256k1_gej *gej = (secp256k1_gej *)malloc(sizeof(secp256k1_gej) * (1 + 4 * runs));
      secp256k1_fe *zinv = (secp256k1_fe *)malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
      secp256k1_fe zf;
      secp256k1_fe zfi2, zfi3;
  
      secp256k1_gej_set_infinity(&gej[0]);
      secp256k1_ge_clear(&ge[0]);
      secp256k1_ge_set_gej_var(&ge[0], &gej[0]);
      for (i = 0; i < runs; i++) {
          int j;
          secp256k1_ge g;
          random_group_element_test(&g);
  #ifdef USE_ENDOMORPHISM
          if (i >= runs - 2) {
              secp256k1_ge_mul_lambda(&g, &ge[1]);
          }
          if (i >= runs - 1) {
              secp256k1_ge_mul_lambda(&g, &g);
          }
  #endif
          ge[1 + 4 * i] = g;
          ge[2 + 4 * i] = g;
          secp256k1_ge_neg(&ge[3 + 4 * i], &g);
          secp256k1_ge_neg(&ge[4 + 4 * i], &g);
          secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]);
          random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]);
          secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
          random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
          for (j = 0; j < 4; j++) {
              random_field_element_magnitude(&ge[1 + j + 4 * i].x);
              random_field_element_magnitude(&ge[1 + j + 4 * i].y);
              random_field_element_magnitude(&gej[1 + j + 4 * i].x);
              random_field_element_magnitude(&gej[1 + j + 4 * i].y);
              random_field_element_magnitude(&gej[1 + j + 4 * i].z);
          }
      }
  
      /* Compute z inverses. */
      {
          secp256k1_fe *zs = malloc(sizeof(secp256k1_fe) * (1 + 4 * runs));
          for (i = 0; i < 4 * runs + 1; i++) {
              if (i == 0) {
                  /* The point at infinity does not have a meaningful z inverse. Any should do. */
                  do {
                      random_field_element_test(&zs[i]);
                  } while(secp256k1_fe_is_zero(&zs[i]));
              } else {
                  zs[i] = gej[i].z;
              }
          }
          secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1);
          free(zs);
      }
  
      /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */
      do {
          random_field_element_test(&zf);
      } while(secp256k1_fe_is_zero(&zf));
      random_field_element_magnitude(&zf);
      secp256k1_fe_inv_var(&zfi3, &zf);
      secp256k1_fe_sqr(&zfi2, &zfi3);
      secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
  
      for (i1 = 0; i1 < 1 + 4 * runs; i1++) {
          int i2;
          for (i2 = 0; i2 < 1 + 4 * runs; i2++) {
              /* Compute reference result using gej + gej (var). */
              secp256k1_gej refj, resj;
              secp256k1_ge ref;
              secp256k1_fe zr;
              secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
              /* Check Z ratio. */
              if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) {
                  secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
                  CHECK(secp256k1_fe_equal_var(&zrz, &refj.z));
              }
              secp256k1_ge_set_gej_var(&ref, &refj);
  
              /* Test gej + ge with Z ratio result (var). */
              secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr);
              ge_equals_gej(&ref, &resj);
              if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) {
                  secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z);
                  CHECK(secp256k1_fe_equal_var(&zrz, &resj.z));
              }
  
              /* Test gej + ge (var, with additional Z factor). */
              {
                  secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
                  secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
                  secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
                  random_field_element_magnitude(&ge2_zfi.x);
                  random_field_element_magnitude(&ge2_zfi.y);
                  secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
                  ge_equals_gej(&ref, &resj);
              }
  
              /* Test gej + ge (const). */
              if (i2 != 0) {
                  /* secp256k1_gej_add_ge does not support its second argument being infinity. */
                  secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]);
                  ge_equals_gej(&ref, &resj);
              }
  
              /* Test doubling (var). */
              if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) {
                  secp256k1_fe zr2;
                  /* Normal doubling with Z ratio result. */
                  secp256k1_gej_double_var(&resj, &gej[i1], &zr2);
                  ge_equals_gej(&ref, &resj);
                  /* Check Z ratio. */
                  secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z);
                  CHECK(secp256k1_fe_equal_var(&zr2, &resj.z));
                  /* Normal doubling. */
                  secp256k1_gej_double_var(&resj, &gej[i2], NULL);
                  ge_equals_gej(&ref, &resj);
              }
  
              /* Test adding opposites. */
              if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) {
                  CHECK(secp256k1_ge_is_infinity(&ref));
              }
  
              /* Test adding infinity. */
              if (i1 == 0) {
                  CHECK(secp256k1_ge_is_infinity(&ge[i1]));
                  CHECK(secp256k1_gej_is_infinity(&gej[i1]));
                  ge_equals_gej(&ref, &gej[i2]);
              }
              if (i2 == 0) {
                  CHECK(secp256k1_ge_is_infinity(&ge[i2]));
                  CHECK(secp256k1_gej_is_infinity(&gej[i2]));
                  ge_equals_gej(&ref, &gej[i1]);
              }
          }
      }
  
      /* Test adding all points together in random order equals infinity. */
      {
          secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY;
          secp256k1_gej *gej_shuffled = (secp256k1_gej *)malloc((4 * runs + 1) * sizeof(secp256k1_gej));
          for (i = 0; i < 4 * runs + 1; i++) {
              gej_shuffled[i] = gej[i];
          }
          for (i = 0; i < 4 * runs + 1; i++) {
              int swap = i + secp256k1_rand_int(4 * runs + 1 - i);
              if (swap != i) {
                  secp256k1_gej t = gej_shuffled[i];
                  gej_shuffled[i] = gej_shuffled[swap];
                  gej_shuffled[swap] = t;
              }
          }
          for (i = 0; i < 4 * runs + 1; i++) {
              secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL);
          }
          CHECK(secp256k1_gej_is_infinity(&sum));
          free(gej_shuffled);
      }
  
      /* Test batch gej -> ge conversion with and without known z ratios. */
      {
          secp256k1_fe *zr = (secp256k1_fe *)malloc((4 * runs + 1) * sizeof(secp256k1_fe));
          secp256k1_ge *ge_set_table = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
          secp256k1_ge *ge_set_all = (secp256k1_ge *)malloc((4 * runs + 1) * sizeof(secp256k1_ge));
          for (i = 0; i < 4 * runs + 1; i++) {
              /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */
              if (i < 4 * runs) {
                  secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z);
              }
          }
          secp256k1_ge_set_table_gej_var(ge_set_table, gej, zr, 4 * runs + 1);
          secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1, &ctx->error_callback);
          for (i = 0; i < 4 * runs + 1; i++) {
              secp256k1_fe s;
              random_fe_non_zero(&s);
              secp256k1_gej_rescale(&gej[i], &s);
              ge_equals_gej(&ge_set_table[i], &gej[i]);
              ge_equals_gej(&ge_set_all[i], &gej[i]);
          }
          free(ge_set_table);
          free(ge_set_all);
          free(zr);
      }
  
      free(ge);
      free(gej);
      free(zinv);
  }
  
  void test_add_neg_y_diff_x(void) {
      /* The point of this test is to check that we can add two points
       * whose y-coordinates are negatives of each other but whose x
       * coordinates differ. If the x-coordinates were the same, these
       * points would be negatives of each other and their sum is
       * infinity. This is cool because it "covers up" any degeneracy
       * in the addition algorithm that would cause the xy coordinates
       * of the sum to be wrong (since infinity has no xy coordinates).
       * HOWEVER, if the x-coordinates are different, infinity is the
       * wrong answer, and such degeneracies are exposed. This is the
       * root of https://github.com/bitcoin-core/secp256k1/issues/257
       * which this test is a regression test for.
       *
       * These points were generated in sage as
       * # secp256k1 params
       * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F)
       * C = EllipticCurve ([F (0), F (7)])
       * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
       * N = FiniteField(G.order())
       *
       * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F)
       * x = polygen(N)
       * lam  = (1 - x^3).roots()[1][0]
       *
       * # random "bad pair"
       * P = C.random_element()
       * Q = -int(lam) * P
       * print "    P: %x %x" % P.xy()
       * print "    Q: %x %x" % Q.xy()
       * print "P + Q: %x %x" % (P + Q).xy()
       */
      secp256k1_gej aj = SECP256K1_GEJ_CONST(
          0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30,
          0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb,
          0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8,
          0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d
      );
      secp256k1_gej bj = SECP256K1_GEJ_CONST(
          0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86,
          0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7,
          0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57,
          0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2
      );
      secp256k1_gej sumj = SECP256K1_GEJ_CONST(
          0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027,
          0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a,
          0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08,
          0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe
      );
      secp256k1_ge b;
      secp256k1_gej resj;
      secp256k1_ge res;
      secp256k1_ge_set_gej(&b, &bj);
  
      secp256k1_gej_add_var(&resj, &aj, &bj, NULL);
      secp256k1_ge_set_gej(&res, &resj);
      ge_equals_gej(&res, &sumj);
  
      secp256k1_gej_add_ge(&resj, &aj, &b);
      secp256k1_ge_set_gej(&res, &resj);
      ge_equals_gej(&res, &sumj);
  
      secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL);
      secp256k1_ge_set_gej(&res, &resj);
      ge_equals_gej(&res, &sumj);
  }
  
  void run_ge(void) {
      int i;
      for (i = 0; i < count * 32; i++) {
          test_ge();
      }
      test_add_neg_y_diff_x();
  }
  
  void test_ec_combine(void) {
      secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
      secp256k1_pubkey data[6];
      const secp256k1_pubkey* d[6];
      secp256k1_pubkey sd;
      secp256k1_pubkey sd2;
      secp256k1_gej Qj;
      secp256k1_ge Q;
      int i;
      for (i = 1; i <= 6; i++) {
          secp256k1_scalar s;
          random_scalar_order_test(&s);
          secp256k1_scalar_add(&sum, &sum, &s);
          secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s);
          secp256k1_ge_set_gej(&Q, &Qj);
          secp256k1_pubkey_save(&data[i - 1], &Q);
          d[i - 1] = &data[i - 1];
          secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum);
          secp256k1_ge_set_gej(&Q, &Qj);
          secp256k1_pubkey_save(&sd, &Q);
          CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1);
          CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0);
      }
  }
  
  void run_ec_combine(void) {
      int i;
      for (i = 0; i < count * 8; i++) {
           test_ec_combine();
      }
  }
  
  void test_group_decompress(const secp256k1_fe* x) {
      /* The input itself, normalized. */
      secp256k1_fe fex = *x;
      secp256k1_fe fez;
      /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */
      secp256k1_ge ge_quad, ge_even, ge_odd;
      secp256k1_gej gej_quad;
      /* Return values of the above calls. */
      int res_quad, res_even, res_odd;
  
      secp256k1_fe_normalize_var(&fex);
  
      res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
      res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
      res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);
  
      CHECK(res_quad == res_even);
      CHECK(res_quad == res_odd);
  
      if (res_quad) {
          secp256k1_fe_normalize_var(&ge_quad.x);
          secp256k1_fe_normalize_var(&ge_odd.x);
          secp256k1_fe_normalize_var(&ge_even.x);
          secp256k1_fe_normalize_var(&ge_quad.y);
          secp256k1_fe_normalize_var(&ge_odd.y);
          secp256k1_fe_normalize_var(&ge_even.y);
  
          /* No infinity allowed. */
          CHECK(!ge_quad.infinity);
          CHECK(!ge_even.infinity);
          CHECK(!ge_odd.infinity);
  
          /* Check that the x coordinates check out. */
          CHECK(secp256k1_fe_equal_var(&ge_quad.x, x));
          CHECK(secp256k1_fe_equal_var(&ge_even.x, x));
          CHECK(secp256k1_fe_equal_var(&ge_odd.x, x));
  
          /* Check that the Y coordinate result in ge_quad is a square. */
          CHECK(secp256k1_fe_is_quad_var(&ge_quad.y));
  
          /* Check odd/even Y in ge_odd, ge_even. */
          CHECK(secp256k1_fe_is_odd(&ge_odd.y));
          CHECK(!secp256k1_fe_is_odd(&ge_even.y));
  
          /* Check secp256k1_gej_has_quad_y_var. */
          secp256k1_gej_set_ge(&gej_quad, &ge_quad);
          CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
          do {
              random_fe_test(&fez);
          } while (secp256k1_fe_is_zero(&fez));
          secp256k1_gej_rescale(&gej_quad, &fez);
          CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
          secp256k1_gej_neg(&gej_quad, &gej_quad);
          CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
          do {
              random_fe_test(&fez);
          } while (secp256k1_fe_is_zero(&fez));
          secp256k1_gej_rescale(&gej_quad, &fez);
          CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad));
          secp256k1_gej_neg(&gej_quad, &gej_quad);
          CHECK(secp256k1_gej_has_quad_y_var(&gej_quad));
      }
  }
  
  void run_group_decompress(void) {
      int i;
      for (i = 0; i < count * 4; i++) {
          secp256k1_fe fe;
          random_fe_test(&fe);
          test_group_decompress(&fe);
      }
  }
  
  /***** ECMULT TESTS *****/
  
  void run_ecmult_chain(void) {
      /* random starting point A (on the curve) */
      secp256k1_gej a = SECP256K1_GEJ_CONST(
          0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3,
          0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004,
          0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f,
          0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f
      );
      /* two random initial factors xn and gn */
      secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
          0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c,
          0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407
      );
      secp256k1_scalar gn = SECP256K1_SCALAR_CONST(
          0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9,
          0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de
      );
      /* two small multipliers to be applied to xn and gn in every iteration: */
      static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337);
      static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113);
      /* accumulators with the resulting coefficients to A and G */
      secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
      secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
      /* actual points */
      secp256k1_gej x;
      secp256k1_gej x2;
      int i;
  
      /* the point being computed */
      x = a;
      for (i = 0; i < 200*count; i++) {
          /* in each iteration, compute X = xn*X + gn*G; */
          secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn);
          /* also compute ae and ge: the actual accumulated factors for A and G */
          /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */
          secp256k1_scalar_mul(&ae, &ae, &xn);
          secp256k1_scalar_mul(&ge, &ge, &xn);
          secp256k1_scalar_add(&ge, &ge, &gn);
          /* modify xn and gn */
          secp256k1_scalar_mul(&xn, &xn, &xf);
          secp256k1_scalar_mul(&gn, &gn, &gf);
  
          /* verify */
          if (i == 37772) {
              /* expected result after 37772 iterations */
              secp256k1_gej rp = SECP256K1_GEJ_CONST(
                  0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE,
                  0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830,
                  0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D,
                  0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88
              );
  
              secp256k1_gej_neg(&rp, &rp);
              secp256k1_gej_add_var(&rp, &rp, &x, NULL);
              CHECK(secp256k1_gej_is_infinity(&rp));
          }
      }
      /* redo the computation, but directly with the resulting ae and ge coefficients: */
      secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge);
      secp256k1_gej_neg(&x2, &x2);
      secp256k1_gej_add_var(&x2, &x2, &x, NULL);
      CHECK(secp256k1_gej_is_infinity(&x2));
  }
  
  void test_point_times_order(const secp256k1_gej *point) {
      /* X * (point + G) + (order-X) * (pointer + G) = 0 */
      secp256k1_scalar x;
      secp256k1_scalar nx;
      secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
      secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
      secp256k1_gej res1, res2;
      secp256k1_ge res3;
      unsigned char pub[65];
      size_t psize = 65;
      random_scalar_order_test(&x);
      secp256k1_scalar_negate(&nx, &x);
      secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */
      secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */
      secp256k1_gej_add_var(&res1, &res1, &res2, NULL);
      CHECK(secp256k1_gej_is_infinity(&res1));
      CHECK(secp256k1_gej_is_valid_var(&res1) == 0);
      secp256k1_ge_set_gej(&res3, &res1);
      CHECK(secp256k1_ge_is_infinity(&res3));
      CHECK(secp256k1_ge_is_valid_var(&res3) == 0);
      CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0);
      psize = 65;
      CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0);
      /* check zero/one edge cases */
      secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero);
      secp256k1_ge_set_gej(&res3, &res1);
      CHECK(secp256k1_ge_is_infinity(&res3));
      secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero);
      secp256k1_ge_set_gej(&res3, &res1);
      ge_equals_gej(&res3, point);
      secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one);
      secp256k1_ge_set_gej(&res3, &res1);
      ge_equals_ge(&res3, &secp256k1_ge_const_g);
  }
  
  void run_point_times_order(void) {
      int i;
      secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2);
      static const secp256k1_fe xr = SECP256K1_FE_CONST(
          0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C,
          0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45
      );
      for (i = 0; i < 500; i++) {
          secp256k1_ge p;
          if (secp256k1_ge_set_xo_var(&p, &x, 1)) {
              secp256k1_gej j;
              CHECK(secp256k1_ge_is_valid_var(&p));
              secp256k1_gej_set_ge(&j, &p);
              CHECK(secp256k1_gej_is_valid_var(&j));
              test_point_times_order(&j);
          }
          secp256k1_fe_sqr(&x, &x);
      }
      secp256k1_fe_normalize_var(&x);
      CHECK(secp256k1_fe_equal_var(&x, &xr));
  }
  
  void ecmult_const_random_mult(void) {
      /* random starting point A (on the curve) */
      secp256k1_ge a = SECP256K1_GE_CONST(
          0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b,
          0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a,
          0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c,
          0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d
      );
      /* random initial factor xn */
      secp256k1_scalar xn = SECP256K1_SCALAR_CONST(
          0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327,
          0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b
      );
      /* expected xn * A (from sage) */
      secp256k1_ge expected_b = SECP256K1_GE_CONST(
          0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd,
          0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786,
          0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f,
          0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
      );
      secp256k1_gej b;
      secp256k1_ecmult_const(&b, &a, &xn);
  
      CHECK(secp256k1_ge_is_valid_var(&a));
      ge_equals_gej(&expected_b, &b);
  }
  
  void ecmult_const_commutativity(void) {
      secp256k1_scalar a;
      secp256k1_scalar b;
      secp256k1_gej res1;
      secp256k1_gej res2;
      secp256k1_ge mid1;
      secp256k1_ge mid2;
      random_scalar_order_test(&a);
      random_scalar_order_test(&b);
  
      secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
      secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
      secp256k1_ge_set_gej(&mid1, &res1);
      secp256k1_ge_set_gej(&mid2, &res2);
      secp256k1_ecmult_const(&res1, &mid1, &b);
      secp256k1_ecmult_const(&res2, &mid2, &a);
      secp256k1_ge_set_gej(&mid1, &res1);
      secp256k1_ge_set_gej(&mid2, &res2);
      ge_equals_ge(&mid1, &mid2);
  }
  
  void ecmult_const_mult_zero_one(void) {
      secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0);
      secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1);
      secp256k1_scalar negone;
      secp256k1_gej res1;
      secp256k1_ge res2;
      secp256k1_ge point;
      secp256k1_scalar_negate(&negone, &one);
  
      random_group_element_test(&point);
      secp256k1_ecmult_const(&res1, &point, &zero);
      secp256k1_ge_set_gej(&res2, &res1);
      CHECK(secp256k1_ge_is_infinity(&res2));
      secp256k1_ecmult_const(&res1, &point, &one);
      secp256k1_ge_set_gej(&res2, &res1);
      ge_equals_ge(&res2, &point);
      secp256k1_ecmult_const(&res1, &point, &negone);
      secp256k1_gej_neg(&res1, &res1);
      secp256k1_ge_set_gej(&res2, &res1);
      ge_equals_ge(&res2, &point);
  }
  
  void ecmult_const_chain_multiply(void) {
      /* Check known result (randomly generated test problem from sage) */
      const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST(
          0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d,
          0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b
      );
      const secp256k1_gej expected_point = SECP256K1_GEJ_CONST(
          0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd,
          0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f,
          0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196,
          0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435
      );
      secp256k1_gej point;
      secp256k1_ge res;
      int i;
  
      secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g);
      for (i = 0; i < 100; ++i) {
          secp256k1_ge tmp;
          secp256k1_ge_set_gej(&tmp, &point);
          secp256k1_ecmult_const(&point, &tmp, &scalar);
      }
      secp256k1_ge_set_gej(&res, &point);
      ge_equals_gej(&res, &expected_point);
  }
  
  void run_ecmult_const_tests(void) {
      ecmult_const_mult_zero_one();
      ecmult_const_random_mult();
      ecmult_const_commutativity();
      ecmult_const_chain_multiply();
  }
  
  void test_wnaf(const secp256k1_scalar *number, int w) {
      secp256k1_scalar x, two, t;
      int wnaf[256];
      int zeroes = -1;
      int i;
      int bits;
      secp256k1_scalar_set_int(&x, 0);
      secp256k1_scalar_set_int(&two, 2);
      bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w);
      CHECK(bits <= 256);
      for (i = bits-1; i >= 0; i--) {
          int v = wnaf[i];
          secp256k1_scalar_mul(&x, &x, &two);
          if (v) {
              CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */
              zeroes=0;
              CHECK((v & 1) == 1); /* check non-zero elements are odd */
              CHECK(v <= (1 << (w-1)) - 1); /* check range below */
              CHECK(v >= -(1 << (w-1)) - 1); /* check range above */
          } else {
              CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */
              zeroes++;
          }
          if (v >= 0) {
              secp256k1_scalar_set_int(&t, v);
          } else {
              secp256k1_scalar_set_int(&t, -v);
              secp256k1_scalar_negate(&t, &t);
          }
          secp256k1_scalar_add(&x, &x, &t);
      }
      CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */
  }
  
  void test_constant_wnaf_negate(const secp256k1_scalar *number) {
      secp256k1_scalar neg1 = *number;
      secp256k1_scalar neg2 = *number;
      int sign1 = 1;
      int sign2 = 1;
  
      if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) {
          secp256k1_scalar_negate(&neg1, &neg1);
          sign1 = -1;
      }
      sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2));
      CHECK(sign1 == sign2);
      CHECK(secp256k1_scalar_eq(&neg1, &neg2));
  }
  
  void test_constant_wnaf(const secp256k1_scalar *number, int w) {
      secp256k1_scalar x, shift;
      int wnaf[256] = {0};
      int i;
      int skew;
      secp256k1_scalar num = *number;
  
      secp256k1_scalar_set_int(&x, 0);
      secp256k1_scalar_set_int(&shift, 1 << w);
      /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */
  #ifdef USE_ENDOMORPHISM
      for (i = 0; i < 16; ++i) {
          secp256k1_scalar_shr_int(&num, 8);
      }
  #endif
      skew = secp256k1_wnaf_const(wnaf, num, w);
  
      for (i = WNAF_SIZE(w); i >= 0; --i) {
          secp256k1_scalar t;
          int v = wnaf[i];
          CHECK(v != 0); /* check nonzero */
          CHECK(v & 1);  /* check parity */
          CHECK(v > -(1 << w)); /* check range above */
          CHECK(v < (1 << w));  /* check range below */
  
          secp256k1_scalar_mul(&x, &x, &shift);
          if (v >= 0) {
              secp256k1_scalar_set_int(&t, v);
          } else {
              secp256k1_scalar_set_int(&t, -v);
              secp256k1_scalar_negate(&t, &t);
          }
          secp256k1_scalar_add(&x, &x, &t);
      }
      /* Skew num because when encoding numbers as odd we use an offset */
      secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
      CHECK(secp256k1_scalar_eq(&x, &num));
  }
  
  void run_wnaf(void) {
      int i;
      secp256k1_scalar n = {{0}};
  
      /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
       *               have easier-to-diagnose failure modes  */
      n.d[0] = 1;
      test_constant_wnaf(&n, 4);
      n.d[0] = 2;
      test_constant_wnaf(&n, 4);
      /* Random tests */
      for (i = 0; i < count; i++) {
          random_scalar_order(&n);
          test_wnaf(&n, 4+(i%10));
          test_constant_wnaf_negate(&n);
          test_constant_wnaf(&n, 4 + (i % 10));
      }
      secp256k1_scalar_set_int(&n, 0);
      CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1);
      CHECK(secp256k1_scalar_is_zero(&n));
      CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1);
      CHECK(secp256k1_scalar_is_zero(&n));
  }
  
  void test_ecmult_constants(void) {
      /* Test ecmult_gen() for [0..36) and [order-36..0). */
      secp256k1_scalar x;
      secp256k1_gej r;
      secp256k1_ge ng;
      int i;
      int j;
      secp256k1_ge_neg(&ng, &secp256k1_ge_const_g);
      for (i = 0; i < 36; i++ ) {
          secp256k1_scalar_set_int(&x, i);
          secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
          for (j = 0; j < i; j++) {
              if (j == i - 1) {
                  ge_equals_gej(&secp256k1_ge_const_g, &r);
              }
              secp256k1_gej_add_ge(&r, &r, &ng);
          }
          CHECK(secp256k1_gej_is_infinity(&r));
      }
      for (i = 1; i <= 36; i++ ) {
          secp256k1_scalar_set_int(&x, i);
          secp256k1_scalar_negate(&x, &x);
          secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x);
          for (j = 0; j < i; j++) {
              if (j == i - 1) {
                  ge_equals_gej(&ng, &r);
              }
              secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g);
          }
          CHECK(secp256k1_gej_is_infinity(&r));
      }
  }
  
  void run_ecmult_constants(void) {
      test_ecmult_constants();
  }
  
  void test_ecmult_gen_blind(void) {
      /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */
      secp256k1_scalar key;
      secp256k1_scalar b;
      unsigned char seed32[32];
      secp256k1_gej pgej;
      secp256k1_gej pgej2;
      secp256k1_gej i;
      secp256k1_ge pge;
      random_scalar_order_test(&key);
      secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key);
      secp256k1_rand256(seed32);
      b = ctx->ecmult_gen_ctx.blind;
      i = ctx->ecmult_gen_ctx.initial;
      secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32);
      CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
      secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key);
      CHECK(!gej_xyz_equals_gej(&pgej, &pgej2));
      CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial));
      secp256k1_ge_set_gej(&pge, &pgej);
      ge_equals_gej(&pge, &pgej2);
  }
  
  void test_ecmult_gen_blind_reset(void) {
      /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */
      secp256k1_scalar b;
      secp256k1_gej initial;
      secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
      b = ctx->ecmult_gen_ctx.blind;
      initial = ctx->ecmult_gen_ctx.initial;
      secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0);
      CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind));
      CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial));
  }
  
  void run_ecmult_gen_blind(void) {
      int i;
      test_ecmult_gen_blind_reset();
      for (i = 0; i < 10; i++) {
          test_ecmult_gen_blind();
      }
  }
  
  #ifdef USE_ENDOMORPHISM
  /***** ENDOMORPHISH TESTS *****/
  void test_scalar_split(void) {
      secp256k1_scalar full;
      secp256k1_scalar s1, slam;
      const unsigned char zero[32] = {0};
      unsigned char tmp[32];
  
      random_scalar_order_test(&full);
      secp256k1_scalar_split_lambda(&s1, &slam, &full);
  
      /* check that both are <= 128 bits in size */
      if (secp256k1_scalar_is_high(&s1)) {
          secp256k1_scalar_negate(&s1, &s1);
      }
      if (secp256k1_scalar_is_high(&slam)) {
          secp256k1_scalar_negate(&slam, &slam);
      }
  
      secp256k1_scalar_get_b32(tmp, &s1);
      CHECK(memcmp(zero, tmp, 16) == 0);
      secp256k1_scalar_get_b32(tmp, &slam);
      CHECK(memcmp(zero, tmp, 16) == 0);
  }
  
  void run_endomorphism_tests(void) {
      test_scalar_split();
  }
  #endif
  
  void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) {
      unsigned char pubkeyc[65];
      secp256k1_pubkey pubkey;
      secp256k1_ge ge;
      size_t pubkeyclen;
      int32_t ecount;
      ecount = 0;
      secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
      for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) {
          /* Smaller sizes are tested exhaustively elsewhere. */
          int32_t i;
          memcpy(&pubkeyc[1], input, 64);
          VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen);
          for (i = 0; i < 256; i++) {
              /* Try all type bytes. */
              int xpass;
              int ypass;
              int ysign;
              pubkeyc[0] = i;
              /* What sign does this point have? */
              ysign = (input[63] & 1) + 2;
              /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */
              xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2);
              /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */
              ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) &&
                  ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65));
              if (xpass || ypass) {
                  /* These cases must parse. */
                  unsigned char pubkeyo[65];
                  size_t outl;
                  memset(&pubkey, 0, sizeof(pubkey));
                  VG_UNDEF(&pubkey, sizeof(pubkey));
                  ecount = 0;
                  CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
                  VG_CHECK(&pubkey, sizeof(pubkey));
                  outl = 65;
                  VG_UNDEF(pubkeyo, 65);
                  CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
                  VG_CHECK(pubkeyo, outl);
                  CHECK(outl == 33);
                  CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0);
                  CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0]));
                  if (ypass) {
                      /* This test isn't always done because we decode with alternative signs, so the y won't match. */
                      CHECK(pubkeyo[0] == ysign);
                      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
                      memset(&pubkey, 0, sizeof(pubkey));
                      VG_UNDEF(&pubkey, sizeof(pubkey));
                      secp256k1_pubkey_save(&pubkey, &ge);
                      VG_CHECK(&pubkey, sizeof(pubkey));
                      outl = 65;
                      VG_UNDEF(pubkeyo, 65);
                      CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
                      VG_CHECK(pubkeyo, outl);
                      CHECK(outl == 65);
                      CHECK(pubkeyo[0] == 4);
                      CHECK(memcmp(&pubkeyo[1], input, 64) == 0);
                  }
                  CHECK(ecount == 0);
              } else {
                  /* These cases must fail to parse. */
                  memset(&pubkey, 0xfe, sizeof(pubkey));
                  ecount = 0;
                  VG_UNDEF(&pubkey, sizeof(pubkey));
                  CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0);
                  VG_CHECK(&pubkey, sizeof(pubkey));
                  CHECK(ecount == 0);
                  CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
                  CHECK(ecount == 1);
              }
          }
      }
      secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
  }
  
  void run_ec_pubkey_parse_test(void) {
  #define SECP256K1_EC_PARSE_TEST_NVALID (12)
      const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = {
          {
              /* Point with leading and trailing zeros in x and y serialization. */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83,
              0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00
          },
          {
              /* Point with x equal to a 3rd root of unity.*/
              0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9,
              0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee,
              0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
              0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
          },
          {
              /* Point with largest x. (1/2) */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
              0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e,
              0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d,
          },
          {
              /* Point with largest x. (2/2) */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c,
              0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1,
              0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2,
          },
          {
              /* Point with smallest x. (1/2) */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
              0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
              0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
          },
          {
              /* Point with smallest x. (2/2) */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
              0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
              0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
          },
          {
              /* Point with largest y. (1/3) */
              0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
              0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
          },
          {
              /* Point with largest y. (2/3) */
              0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
              0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
          },
          {
              /* Point with largest y. (3/3) */
              0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
              0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
          },
          {
              /* Point with smallest y. (1/3) */
              0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
              0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
          },
          {
              /* Point with smallest y. (2/3) */
              0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
              0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
          },
          {
              /* Point with smallest y. (3/3) */
              0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
              0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
          }
      };
  #define SECP256K1_EC_PARSE_TEST_NXVALID (4)
      const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = {
          {
              /* Valid if y overflow ignored (y = 1 mod p). (1/3) */
              0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6,
              0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
          },
          {
              /* Valid if y overflow ignored (y = 1 mod p). (2/3) */
              0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c,
              0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
          },
          {
              /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/
              0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc,
              0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
          },
          {
              /* x on curve, y is from y^2 = x^3 + 8. */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03
          }
      };
  #define SECP256K1_EC_PARSE_TEST_NINVALID (7)
      const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = {
          {
              /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */
              0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c,
              0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
          },
          {
              /* Valid if x overflow ignored (x = 1 mod p). */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
              0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14,
              0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee,
          },
          {
              /* Valid if x overflow ignored (x = 1 mod p). */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30,
              0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb,
              0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41,
          },
          {
              /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
              0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f,
              0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28,
          },
          {
              /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e,
              0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0,
              0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07,
          },
          {
              /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d,
              0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc,
          },
          {
              /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2,
              0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53
          }
      };
      const unsigned char pubkeyc[66] = {
          /* Serialization of G. */
          0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
          0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
          0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08,
          0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4,
          0xB8, 0x00
      };
      unsigned char sout[65];
      unsigned char shortkey[2];
      secp256k1_ge ge;
      secp256k1_pubkey pubkey;
      size_t len;
      int32_t i;
      int32_t ecount;
      int32_t ecount2;
      ecount = 0;
      /* Nothing should be reading this far into pubkeyc. */
      VG_UNDEF(&pubkeyc[65], 1);
      secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
      /* Zero length claimed, fail, zeroize, no illegal arg error. */
      memset(&pubkey, 0xfe, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(shortkey, 2);
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 0);
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
      CHECK(ecount == 1);
      /* Length one claimed, fail, zeroize, no illegal arg error. */
      for (i = 0; i < 256 ; i++) {
          memset(&pubkey, 0xfe, sizeof(pubkey));
          ecount = 0;
          shortkey[0] = i;
          VG_UNDEF(&shortkey[1], 1);
          VG_UNDEF(&pubkey, sizeof(pubkey));
          CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0);
          VG_CHECK(&pubkey, sizeof(pubkey));
          CHECK(ecount == 0);
          CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
          CHECK(ecount == 1);
      }
      /* Length two claimed, fail, zeroize, no illegal arg error. */
      for (i = 0; i < 65536 ; i++) {
          memset(&pubkey, 0xfe, sizeof(pubkey));
          ecount = 0;
          shortkey[0] = i & 255;
          shortkey[1] = i >> 8;
          VG_UNDEF(&pubkey, sizeof(pubkey));
          CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0);
          VG_CHECK(&pubkey, sizeof(pubkey));
          CHECK(ecount == 0);
          CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
          CHECK(ecount == 1);
      }
      memset(&pubkey, 0xfe, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(&pubkey, sizeof(pubkey));
      /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 0);
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
      CHECK(ecount == 1);
      /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */
      CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0);
      CHECK(ecount == 2);
      /* NULL input string. Illegal arg and zeroize output. */
      memset(&pubkey, 0xfe, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 1);
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
      CHECK(ecount == 2);
      /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */
      memset(&pubkey, 0xfe, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 0);
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
      CHECK(ecount == 1);
      /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */
      memset(&pubkey, 0xfe, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 0);
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0);
      CHECK(ecount == 1);
      /* Valid parse. */
      memset(&pubkey, 0, sizeof(pubkey));
      ecount = 0;
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(ecount == 0);
      VG_UNDEF(&ge, sizeof(ge));
      CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1);
      VG_CHECK(&ge.x, sizeof(ge.x));
      VG_CHECK(&ge.y, sizeof(ge.y));
      VG_CHECK(&ge.infinity, sizeof(ge.infinity));
      ge_equals_ge(&secp256k1_ge_const_g, &ge);
      CHECK(ecount == 0);
      /* secp256k1_ec_pubkey_serialize illegal args. */
      ecount = 0;
      len = 65;
      CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
      CHECK(ecount == 1);
      CHECK(len == 0);
      CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0);
      CHECK(ecount == 2);
      len = 65;
      VG_UNDEF(sout, 65);
      CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0);
      VG_CHECK(sout, 65);
      CHECK(ecount == 3);
      CHECK(len == 0);
      len = 65;
      CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0);
      CHECK(ecount == 4);
      CHECK(len == 0);
      len = 65;
      VG_UNDEF(sout, 65);
      CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1);
      VG_CHECK(sout, 65);
      CHECK(ecount == 4);
      CHECK(len == 65);
      /* Multiple illegal args. Should still set arg error only once. */
      ecount = 0;
      ecount2 = 11;
      CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
      CHECK(ecount == 1);
      /* Does the illegal arg callback actually change the behavior? */
      secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2);
      CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0);
      CHECK(ecount == 1);
      CHECK(ecount2 == 10);
      secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
      /* Try a bunch of prefabbed points with all possible encodings. */
      for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) {
          ec_pubkey_parse_pointtest(valid[i], 1, 1);
      }
      for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) {
          ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0);
      }
      for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) {
          ec_pubkey_parse_pointtest(invalid[i], 0, 0);
      }
  }
  
  void run_eckey_edge_case_test(void) {
      const unsigned char orderc[32] = {
          0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
          0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
          0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
          0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41
      };
      const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00};
      unsigned char ctmp[33];
      unsigned char ctmp2[33];
      secp256k1_pubkey pubkey;
      secp256k1_pubkey pubkey2;
      secp256k1_pubkey pubkey_one;
      secp256k1_pubkey pubkey_negone;
      const secp256k1_pubkey *pubkeys[3];
      size_t len;
      int32_t ecount;
      /* Group order is too large, reject. */
      CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0);
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      /* Maximum value is too large, reject. */
      memset(ctmp, 255, 32);
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
      memset(&pubkey, 1, sizeof(pubkey));
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      /* Zero is too small, reject. */
      memset(ctmp, 0, 32);
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
      memset(&pubkey, 1, sizeof(pubkey));
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      /* One must be accepted. */
      ctmp[31] = 0x01;
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
      memset(&pubkey, 0, sizeof(pubkey));
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
      pubkey_one = pubkey;
      /* Group order + 1 is too large, reject. */
      memcpy(ctmp, orderc, 32);
      ctmp[31] = 0x42;
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0);
      memset(&pubkey, 1, sizeof(pubkey));
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      /* -1 must be accepted. */
      ctmp[31] = 0x40;
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
      memset(&pubkey, 0, sizeof(pubkey));
      VG_UNDEF(&pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1);
      VG_CHECK(&pubkey, sizeof(pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
      pubkey_negone = pubkey;
      /* Tweak of zero leaves the value changed. */
      memset(ctmp2, 0, 32);
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, ctmp2) == 1);
      CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40);
      memcpy(&pubkey2, &pubkey, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
      CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
      /* Multiply tweak of zero zeroizes the output. */
      CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, ctmp2) == 0);
      CHECK(memcmp(zeros, ctmp, 32) == 0);
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0);
      CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
      memcpy(&pubkey, &pubkey2, sizeof(pubkey));
      /* Overflowing key tweak zeroizes. */
      memcpy(ctmp, orderc, 32);
      ctmp[31] = 0x40;
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, orderc) == 0);
      CHECK(memcmp(zeros, ctmp, 32) == 0);
      memcpy(ctmp, orderc, 32);
      ctmp[31] = 0x40;
      CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, orderc) == 0);
      CHECK(memcmp(zeros, ctmp, 32) == 0);
      memcpy(ctmp, orderc, 32);
      ctmp[31] = 0x40;
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0);
      CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
      memcpy(&pubkey, &pubkey2, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0);
      CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
      memcpy(&pubkey, &pubkey2, sizeof(pubkey));
      /* Private key tweaks results in a key of zero. */
      ctmp2[31] = 1;
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 0);
      CHECK(memcmp(zeros, ctmp2, 32) == 0);
      ctmp2[31] = 1;
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
      CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
      memcpy(&pubkey, &pubkey2, sizeof(pubkey));
      /* Tweak computation wraps and results in a key of 1. */
      ctmp2[31] = 2;
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp2, ctmp) == 1);
      CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1);
      ctmp2[31] = 2;
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
      ctmp2[31] = 1;
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1);
      CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
      /* Tweak mul * 2 = 1+1. */
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1);
      ctmp2[31] = 2;
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1);
      CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
      /* Test argument errors. */
      ecount = 0;
      secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
      CHECK(ecount == 0);
      /* Zeroize pubkey on parse error. */
      memset(&pubkey, 0, 32);
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0);
      CHECK(ecount == 1);
      CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0);
      memcpy(&pubkey, &pubkey2, sizeof(pubkey));
      memset(&pubkey2, 0, 32);
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0);
      CHECK(ecount == 2);
      CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0);
      /* Plain argument errors. */
      ecount = 0;
      CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1);
      CHECK(ecount == 0);
      CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0);
      CHECK(ecount == 1);
      ecount = 0;
      memset(ctmp2, 0, 32);
      ctmp2[31] = 4;
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0);
      CHECK(ecount == 1);
      CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0);
      CHECK(ecount == 2);
      ecount = 0;
      memset(ctmp2, 0, 32);
      ctmp2[31] = 4;
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0);
      CHECK(ecount == 1);
      CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0);
      CHECK(ecount == 2);
      ecount = 0;
      memset(ctmp2, 0, 32);
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, NULL, ctmp2) == 0);
      CHECK(ecount == 1);
      CHECK(secp256k1_ec_privkey_tweak_add(ctx, ctmp, NULL) == 0);
      CHECK(ecount == 2);
      ecount = 0;
      memset(ctmp2, 0, 32);
      ctmp2[31] = 1;
      CHECK(secp256k1_ec_privkey_tweak_mul(ctx, NULL, ctmp2) == 0);
      CHECK(ecount == 1);
      CHECK(secp256k1_ec_privkey_tweak_mul(ctx, ctmp, NULL) == 0);
      CHECK(ecount == 2);
      ecount = 0;
      CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0);
      CHECK(ecount == 1);
      memset(&pubkey, 1, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
      CHECK(ecount == 2);
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      /* secp256k1_ec_pubkey_combine tests. */
      ecount = 0;
      pubkeys[0] = &pubkey_one;
      VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *));
      VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *));
      VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *));
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      CHECK(ecount == 1);
      CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0);
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      CHECK(ecount == 2);
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      CHECK(ecount == 3);
      pubkeys[0] = &pubkey_negone;
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
      CHECK(ecount == 3);
      len = 33;
      CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
      CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1);
      CHECK(memcmp(ctmp, ctmp2, 33) == 0);
      /* Result is infinity. */
      pubkeys[0] = &pubkey_one;
      pubkeys[1] = &pubkey_negone;
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0);
      CHECK(ecount == 3);
      /* Passes through infinity but comes out one. */
      pubkeys[2] = &pubkey_one;
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
      CHECK(ecount == 3);
      len = 33;
      CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1);
      CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1);
      CHECK(memcmp(ctmp, ctmp2, 33) == 0);
      /* Adds to two. */
      pubkeys[1] = &pubkey_one;
      memset(&pubkey, 255, sizeof(secp256k1_pubkey));
      VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1);
      VG_CHECK(&pubkey, sizeof(secp256k1_pubkey));
      CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0);
      CHECK(ecount == 3);
      secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
  }
  
  void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) {
      secp256k1_scalar nonce;
      do {
          random_scalar_order_test(&nonce);
      } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid));
  }
  
  void test_ecdsa_sign_verify(void) {
      secp256k1_gej pubj;
      secp256k1_ge pub;
      secp256k1_scalar one;
      secp256k1_scalar msg, key;
      secp256k1_scalar sigr, sigs;
      int recid;
      int getrec;
      random_scalar_order_test(&msg);
      random_scalar_order_test(&key);
      secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key);
      secp256k1_ge_set_gej(&pub, &pubj);
      getrec = secp256k1_rand_bits(1);
      random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL);
      if (getrec) {
          CHECK(recid >= 0 && recid < 4);
      }
      CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
      secp256k1_scalar_set_int(&one, 1);
      secp256k1_scalar_add(&msg, &msg, &one);
      CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg));
  }
  
  void run_ecdsa_sign_verify(void) {
      int i;
      for (i = 0; i < 10*count; i++) {
          test_ecdsa_sign_verify();
      }
  }
  
  /** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */
  static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
      (void)msg32;
      (void)key32;
      (void)algo16;
      memcpy(nonce32, data, 32);
      return (counter == 0);
  }
  
  static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
     /* Dummy nonce generator that has a fatal error on the first counter value. */
     if (counter == 0) {
         return 0;
     }
     return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1);
  }
  
  static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
     /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */
     if (counter < 3) {
         memset(nonce32, counter==0 ? 0 : 255, 32);
         if (counter == 2) {
             nonce32[31]--;
         }
         return 1;
     }
     if (counter < 5) {
         static const unsigned char order[] = {
             0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
             0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
             0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
             0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
         };
         memcpy(nonce32, order, 32);
         if (counter == 4) {
             nonce32[31]++;
         }
         return 1;
     }
     /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */
     /* If someone does fine a case where it retries for secp256k1, we'd like to know. */
     if (counter > 5) {
         return 0;
     }
     return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5);
  }
  
  int is_empty_signature(const secp256k1_ecdsa_signature *sig) {
      static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0};
      return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0;
  }
  
  void test_ecdsa_end_to_end(void) {
      unsigned char extra[32] = {0x00};
      unsigned char privkey[32];
      unsigned char message[32];
      unsigned char privkey2[32];
      secp256k1_ecdsa_signature signature[6];
      secp256k1_scalar r, s;
      unsigned char sig[74];
      size_t siglen = 74;
      unsigned char pubkeyc[65];
      size_t pubkeyclen = 65;
      secp256k1_pubkey pubkey;
      unsigned char seckey[300];
      size_t seckeylen = 300;
  
      /* Generate a random key and message. */
      {
          secp256k1_scalar msg, key;
          random_scalar_order_test(&msg);
          random_scalar_order_test(&key);
          secp256k1_scalar_get_b32(privkey, &key);
          secp256k1_scalar_get_b32(message, &msg);
      }
  
      /* Construct and verify corresponding public key. */
      CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1);
      CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1);
  
      /* Verify exporting and importing public key. */
      CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED));
      memset(&pubkey, 0, sizeof(pubkey));
      CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1);
  
      /* Verify private key import and export. */
      CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1));
      CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1);
      CHECK(memcmp(privkey, privkey2, 32) == 0);
  
      /* Optionally tweak the keys using addition. */
      if (secp256k1_rand_int(3) == 0) {
          int ret1;
          int ret2;
          unsigned char rnd[32];
          secp256k1_pubkey pubkey2;
          secp256k1_rand256_test(rnd);
          ret1 = secp256k1_ec_privkey_tweak_add(ctx, privkey, rnd);
          ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd);
          CHECK(ret1 == ret2);
          if (ret1 == 0) {
              return;
          }
          CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
          CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
      }
  
      /* Optionally tweak the keys using multiplication. */
      if (secp256k1_rand_int(3) == 0) {
          int ret1;
          int ret2;
          unsigned char rnd[32];
          secp256k1_pubkey pubkey2;
          secp256k1_rand256_test(rnd);
          ret1 = secp256k1_ec_privkey_tweak_mul(ctx, privkey, rnd);
          ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd);
          CHECK(ret1 == ret2);
          if (ret1 == 0) {
              return;
          }
          CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1);
          CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0);
      }
  
      /* Sign. */
      CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1);
      CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1);
      CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1);
      extra[31] = 1;
      CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1);
      extra[31] = 0;
      extra[0] = 1;
      CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1);
      CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0);
      CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0);
      CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0);
      CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0);
      CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0);
      CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0);
      CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0);
      /* Verify. */
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1);
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1);
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1);
      /* Test lower-S form, malleate, verify and fail, test again, malleate again */
      CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0]));
      secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]);
      secp256k1_scalar_negate(&s, &s);
      secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0);
      CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
      CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
      CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
      CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5]));
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
      secp256k1_scalar_negate(&s, &s);
      secp256k1_ecdsa_signature_save(&signature[5], &r, &s);
      CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5]));
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1);
      CHECK(memcmp(&signature[5], &signature[0], 64) == 0);
  
      /* Serialize/parse DER and verify again */
      CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
      memset(&signature[0], 0, sizeof(signature[0]));
      CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1);
      CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1);
      /* Serialize/destroy/parse DER and verify again. */
      siglen = 74;
      CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1);
      sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255);
      CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 ||
            secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0);
  }
  
  void test_random_pubkeys(void) {
      secp256k1_ge elem;
      secp256k1_ge elem2;
      unsigned char in[65];
      /* Generate some randomly sized pubkeys. */
      size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33;
      if (secp256k1_rand_bits(2) == 0) {
          len = secp256k1_rand_bits(6);
      }
      if (len == 65) {
        in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7);
      } else {
        in[0] = secp256k1_rand_bits(1) ? 2 : 3;
      }
      if (secp256k1_rand_bits(3) == 0) {
          in[0] = secp256k1_rand_bits(8);
      }
      if (len > 1) {
          secp256k1_rand256(&in[1]);
      }
      if (len > 33) {
          secp256k1_rand256(&in[33]);
      }
      if (secp256k1_eckey_pubkey_parse(&elem, in, len)) {
          unsigned char out[65];
          unsigned char firstb;
          int res;
          size_t size = len;
          firstb = in[0];
          /* If the pubkey can be parsed, it should round-trip... */
          CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33));
          CHECK(size == len);
          CHECK(memcmp(&in[1], &out[1], len-1) == 0);
          /* ... except for the type of hybrid inputs. */
          if ((in[0] != 6) && (in[0] != 7)) {
              CHECK(in[0] == out[0]);
          }
          size = 65;
          CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0));
          CHECK(size == 65);
          CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size));
          ge_equals_ge(&elem,&elem2);
          /* Check that the X9.62 hybrid type is checked. */
          in[0] = secp256k1_rand_bits(1) ? 6 : 7;
          res = secp256k1_eckey_pubkey_parse(&elem2, in, size);
          if (firstb == 2 || firstb == 3) {
              if (in[0] == firstb + 4) {
                CHECK(res);
              } else {
                CHECK(!res);
              }
          }
          if (res) {
              ge_equals_ge(&elem,&elem2);
              CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0));
              CHECK(memcmp(&in[1], &out[1], 64) == 0);
          }
      }
  }
  
  void run_random_pubkeys(void) {
      int i;
      for (i = 0; i < 10*count; i++) {
          test_random_pubkeys();
      }
  }
  
  void run_ecdsa_end_to_end(void) {
      int i;
      for (i = 0; i < 64*count; i++) {
          test_ecdsa_end_to_end();
      }
  }
  
  int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) {
      static const unsigned char zeroes[32] = {0};
  #ifdef ENABLE_OPENSSL_TESTS
      static const unsigned char max_scalar[32] = {
          0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
          0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
          0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
          0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40
      };
  #endif
  
      int ret = 0;
  
      secp256k1_ecdsa_signature sig_der;
      unsigned char roundtrip_der[2048];
      unsigned char compact_der[64];
      size_t len_der = 2048;
      int parsed_der = 0, valid_der = 0, roundtrips_der = 0;
  
      secp256k1_ecdsa_signature sig_der_lax;
      unsigned char roundtrip_der_lax[2048];
      unsigned char compact_der_lax[64];
      size_t len_der_lax = 2048;
      int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0;
  
  #ifdef ENABLE_OPENSSL_TESTS
      ECDSA_SIG *sig_openssl;
      const unsigned char *sigptr;
      unsigned char roundtrip_openssl[2048];
      int len_openssl = 2048;
      int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0;
  #endif
  
      parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen);
      if (parsed_der) {
          ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0;
          valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0);
      }
      if (valid_der) {
          ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1;
          roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0;
      }
  
      parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen);
      if (parsed_der_lax) {
          ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10;
          valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0);
      }
      if (valid_der_lax) {
          ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11;
          roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0;
      }
  
      if (certainly_der) {
          ret |= (!parsed_der) << 2;
      }
      if (certainly_not_der) {
          ret |= (parsed_der) << 17;
      }
      if (valid_der) {
          ret |= (!roundtrips_der) << 3;
      }
  
      if (valid_der) {
          ret |= (!roundtrips_der_lax) << 12;
          ret |= (len_der != len_der_lax) << 13;
          ret |= (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0) << 14;
      }
      ret |= (roundtrips_der != roundtrips_der_lax) << 15;
      if (parsed_der) {
          ret |= (!parsed_der_lax) << 16;
      }
  
  #ifdef ENABLE_OPENSSL_TESTS
      sig_openssl = ECDSA_SIG_new();
      sigptr = sig;
      parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL);
      if (parsed_openssl) {
          valid_openssl = !BN_is_negative(sig_openssl->r) && !BN_is_negative(sig_openssl->s) && BN_num_bits(sig_openssl->r) > 0 && BN_num_bits(sig_openssl->r) <= 256 && BN_num_bits(sig_openssl->s) > 0 && BN_num_bits(sig_openssl->s) <= 256;
          if (valid_openssl) {
              unsigned char tmp[32] = {0};
              BN_bn2bin(sig_openssl->r, tmp + 32 - BN_num_bytes(sig_openssl->r));
              valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
          }
          if (valid_openssl) {
              unsigned char tmp[32] = {0};
              BN_bn2bin(sig_openssl->s, tmp + 32 - BN_num_bytes(sig_openssl->s));
              valid_openssl = memcmp(tmp, max_scalar, 32) < 0;
          }
      }
      len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL);
      if (len_openssl <= 2048) {
          unsigned char *ptr = roundtrip_openssl;
          CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl);
          roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0);
      } else {
          len_openssl = 0;
      }
      ECDSA_SIG_free(sig_openssl);
  
      ret |= (parsed_der && !parsed_openssl) << 4;
      ret |= (valid_der && !valid_openssl) << 5;
      ret |= (roundtrips_openssl && !parsed_der) << 6;
      ret |= (roundtrips_der != roundtrips_openssl) << 7;
      if (roundtrips_openssl) {
          ret |= (len_der != (size_t)len_openssl) << 8;
          ret |= (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0) << 9;
      }
  #endif
      return ret;
  }
  
  static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) {
      size_t i;
      for (i = 0; i < ptrlen; i++) {
          int shift = ptrlen - 1 - i;
          if (shift >= 4) {
              ptr[i] = 0;
          } else {
              ptr[i] = (val >> shift) & 0xFF;
          }
      }
  }
  
  static void damage_array(unsigned char *sig, size_t *len) {
      int pos;
      int action = secp256k1_rand_bits(3);
      if (action < 1 && *len > 3) {
          /* Delete a byte. */
          pos = secp256k1_rand_int(*len);
          memmove(sig + pos, sig + pos + 1, *len - pos - 1);
          (*len)--;
          return;
      } else if (action < 2 && *len < 2048) {
          /* Insert a byte. */
          pos = secp256k1_rand_int(1 + *len);
          memmove(sig + pos + 1, sig + pos, *len - pos);
          sig[pos] = secp256k1_rand_bits(8);
          (*len)++;
          return;
      } else if (action < 4) {
          /* Modify a byte. */
          sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255);
          return;
      } else { /* action < 8 */
          /* Modify a bit. */
          sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3);
          return;
      }
  }
  
  static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) {
      int der;
      int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2];
      size_t tlen, elen, glen;
      int indet;
      int n;
  
      *len = 0;
      der = secp256k1_rand_bits(2) == 0;
      *certainly_der = der;
      *certainly_not_der = 0;
      indet = der ? 0 : secp256k1_rand_int(10) == 0;
  
      for (n = 0; n < 2; n++) {
          /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */
          nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0);
          /* The length of the number in bytes (the first byte of which will always be nonzero) */
          nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8;
          CHECK(nlen[n] <= 232);
          /* The top bit of the number. */
          nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1));
          /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */
          nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127));
          /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */
          nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8);
          if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) {
              *certainly_not_der = 1;
          }
          CHECK(nlen[n] + nzlen[n] <= 300);
          /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */
          nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2);
          if (!der) {
              /* nlenlen[n] max 127 bytes */
              int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
              nlenlen[n] += add;
              if (add != 0) {
                  *certainly_not_der = 1;
              }
          }
          CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427);
      }
  
      /* The total length of the data to go, so far */
      tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1];
      CHECK(tlen <= 856);
  
      /* The length of the garbage inside the tuple. */
      elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8;
      if (elen != 0) {
          *certainly_not_der = 1;
      }
      tlen += elen;
      CHECK(tlen <= 980);
  
      /* The length of the garbage after the end of the tuple. */
      glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8;
      if (glen != 0) {
          *certainly_not_der = 1;
      }
      CHECK(tlen + glen <= 990);
  
      /* Write the tuple header. */
      sig[(*len)++] = 0x30;
      if (indet) {
          /* Indeterminate length */
          sig[(*len)++] = 0x80;
          *certainly_not_der = 1;
      } else {
          int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2);
          if (!der) {
              int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256;
              tlenlen += add;
              if (add != 0) {
                  *certainly_not_der = 1;
              }
          }
          if (tlenlen == 0) {
              /* Short length notation */
              sig[(*len)++] = tlen;
          } else {
              /* Long length notation */
              sig[(*len)++] = 128 + tlenlen;
              assign_big_endian(sig + *len, tlenlen, tlen);
              *len += tlenlen;
          }
          tlen += tlenlen;
      }
      tlen += 2;
      CHECK(tlen + glen <= 1119);
  
      for (n = 0; n < 2; n++) {
          /* Write the integer header. */
          sig[(*len)++] = 0x02;
          if (nlenlen[n] == 0) {
              /* Short length notation */
              sig[(*len)++] = nlen[n] + nzlen[n];
          } else {
              /* Long length notation. */
              sig[(*len)++] = 128 + nlenlen[n];
              assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]);
              *len += nlenlen[n];
          }
          /* Write zero padding */
          while (nzlen[n] > 0) {
              sig[(*len)++] = 0x00;
              nzlen[n]--;
          }
          if (nlen[n] == 32 && !nlow[n]) {
              /* Special extra 16 0xFF bytes in "high" 32-byte numbers */
              int i;
              for (i = 0; i < 16; i++) {
                  sig[(*len)++] = 0xFF;
              }
              nlen[n] -= 16;
          }
          /* Write first byte of number */
          if (nlen[n] > 0) {
              sig[(*len)++] = nhbyte[n];
              nlen[n]--;
          }
          /* Generate remaining random bytes of number */
          secp256k1_rand_bytes_test(sig + *len, nlen[n]);
          *len += nlen[n];
          nlen[n] = 0;
      }
  
      /* Generate random garbage inside tuple. */
      secp256k1_rand_bytes_test(sig + *len, elen);
      *len += elen;
  
      /* Generate end-of-contents bytes. */
      if (indet) {
          sig[(*len)++] = 0;
          sig[(*len)++] = 0;
          tlen += 2;
      }
      CHECK(tlen + glen <= 1121);
  
      /* Generate random garbage outside tuple. */
      secp256k1_rand_bytes_test(sig + *len, glen);
      *len += glen;
      tlen += glen;
      CHECK(tlen <= 1121);
      CHECK(tlen == *len);
  }
  
  void run_ecdsa_der_parse(void) {
      int i,j;
      for (i = 0; i < 200 * count; i++) {
          unsigned char buffer[2048];
          size_t buflen = 0;
          int certainly_der = 0;
          int certainly_not_der = 0;
          random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der);
          CHECK(buflen <= 2048);
          for (j = 0; j < 16; j++) {
              int ret = 0;
              if (j > 0) {
                  damage_array(buffer, &buflen);
                  /* We don't know anything anymore about the DERness of the result */
                  certainly_der = 0;
                  certainly_not_der = 0;
              }
              ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der);
              if (ret != 0) {
                  size_t k;
                  fprintf(stderr, "Failure %x on ", ret);
                  for (k = 0; k < buflen; k++) {
                      fprintf(stderr, "%02x ", buffer[k]);
                  }
                  fprintf(stderr, "\n");
              }
              CHECK(ret == 0);
          }
      }
  }
  
  /* Tests several edge cases. */
  void test_ecdsa_edge_cases(void) {
      int t;
      secp256k1_ecdsa_signature sig;
  
      /* Test the case where ECDSA recomputes a point that is infinity. */
      {
          secp256k1_gej keyj;
          secp256k1_ge key;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 1);
          secp256k1_scalar_negate(&ss, &ss);
          secp256k1_scalar_inverse(&ss, &ss);
          secp256k1_scalar_set_int(&sr, 1);
          secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr);
          secp256k1_ge_set_gej(&key, &keyj);
          msg = ss;
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
      }
  
      /* Verify signature with r of zero fails. */
      {
          const unsigned char pubkey_mods_zero[33] = {
              0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
              0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
              0x41
          };
          secp256k1_ge key;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 1);
          secp256k1_scalar_set_int(&msg, 0);
          secp256k1_scalar_set_int(&sr, 0);
          CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33));
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
      }
  
      /* Verify signature with s of zero fails. */
      {
          const unsigned char pubkey[33] = {
              0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x01
          };
          secp256k1_ge key;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 0);
          secp256k1_scalar_set_int(&msg, 0);
          secp256k1_scalar_set_int(&sr, 1);
          CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
      }
  
      /* Verify signature with message 0 passes. */
      {
          const unsigned char pubkey[33] = {
              0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x02
          };
          const unsigned char pubkey2[33] = {
              0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0,
              0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41,
              0x43
          };
          secp256k1_ge key;
          secp256k1_ge key2;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 2);
          secp256k1_scalar_set_int(&msg, 0);
          secp256k1_scalar_set_int(&sr, 2);
          CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
          CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
          secp256k1_scalar_negate(&ss, &ss);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
          secp256k1_scalar_set_int(&ss, 1);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
      }
  
      /* Verify signature with message 1 passes. */
      {
          const unsigned char pubkey[33] = {
              0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22,
              0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05,
              0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c,
              0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76,
              0x25
          };
          const unsigned char pubkey2[33] = {
              0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40,
              0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae,
              0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f,
              0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10,
              0x62
          };
          const unsigned char csr[32] = {
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
              0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
              0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb
          };
          secp256k1_ge key;
          secp256k1_ge key2;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 1);
          secp256k1_scalar_set_int(&msg, 1);
          secp256k1_scalar_set_b32(&sr, csr, NULL);
          CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
          CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33));
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
          secp256k1_scalar_negate(&ss, &ss);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1);
          secp256k1_scalar_set_int(&ss, 2);
          secp256k1_scalar_inverse_var(&ss, &ss);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0);
      }
  
      /* Verify signature with message -1 passes. */
      {
          const unsigned char pubkey[33] = {
              0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0,
              0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52,
              0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27,
              0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20,
              0xf1
          };
          const unsigned char csr[32] = {
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
              0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4,
              0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee
          };
          secp256k1_ge key;
          secp256k1_scalar msg;
          secp256k1_scalar sr, ss;
          secp256k1_scalar_set_int(&ss, 1);
          secp256k1_scalar_set_int(&msg, 1);
          secp256k1_scalar_negate(&msg, &msg);
          secp256k1_scalar_set_b32(&sr, csr, NULL);
          CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33));
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          secp256k1_scalar_negate(&ss, &ss);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1);
          secp256k1_scalar_set_int(&ss, 3);
          secp256k1_scalar_inverse_var(&ss, &ss);
          CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0);
      }
  
      /* Signature where s would be zero. */
      {
          secp256k1_pubkey pubkey;
          size_t siglen;
          int32_t ecount;
          unsigned char signature[72];
          static const unsigned char nonce[32] = {
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
          };
          static const unsigned char nonce2[32] = {
              0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
              0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
              0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
              0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
          };
          const unsigned char key[32] = {
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
              0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
          };
          unsigned char msg[32] = {
              0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53,
              0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7,
              0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62,
              0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9,
          };
          ecount = 0;
          secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0);
          msg[31] = 0xaa;
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1);
          CHECK(ecount == 0);
          CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0);
          CHECK(ecount == 1);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0);
          CHECK(ecount == 2);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0);
          CHECK(ecount == 3);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1);
          CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1);
          CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0);
          CHECK(ecount == 4);
          CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0);
          CHECK(ecount == 5);
          CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0);
          CHECK(ecount == 6);
          CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1);
          CHECK(ecount == 6);
          CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0);
          CHECK(ecount == 7);
          /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */
          CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0);
          CHECK(ecount == 8);
          siglen = 72;
          CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0);
          CHECK(ecount == 9);
          CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0);
          CHECK(ecount == 10);
          CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0);
          CHECK(ecount == 11);
          CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1);
          CHECK(ecount == 11);
          CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0);
          CHECK(ecount == 12);
          CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0);
          CHECK(ecount == 13);
          CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1);
          CHECK(ecount == 13);
          siglen = 10;
          /* Too little room for a signature does not fail via ARGCHECK. */
          CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0);
          CHECK(ecount == 13);
          ecount = 0;
          CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0);
          CHECK(ecount == 1);
          CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0);
          CHECK(ecount == 2);
          CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0);
          CHECK(ecount == 3);
          CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1);
          CHECK(ecount == 3);
          CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0);
          CHECK(ecount == 4);
          CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0);
          CHECK(ecount == 5);
          CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1);
          CHECK(ecount == 5);
          memset(signature, 255, 64);
          CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0);
          CHECK(ecount == 5);
          secp256k1_context_set_illegal_callback(ctx, NULL, NULL);
      }
  
      /* Nonce function corner cases. */
      for (t = 0; t < 2; t++) {
          static const unsigned char zero[32] = {0x00};
          int i;
          unsigned char key[32];
          unsigned char msg[32];
          secp256k1_ecdsa_signature sig2;
          secp256k1_scalar sr[512], ss;
          const unsigned char *extra;
          extra = t == 0 ? NULL : zero;
          memset(msg, 0, 32);
          msg[31] = 1;
          /* High key results in signature failure. */
          memset(key, 0xFF, 32);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
          CHECK(is_empty_signature(&sig));
          /* Zero key results in signature failure. */
          memset(key, 0, 32);
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0);
          CHECK(is_empty_signature(&sig));
          /* Nonce function failure results in signature failure. */
          key[31] = 1;
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0);
          CHECK(is_empty_signature(&sig));
          /* The retry loop successfully makes its way to the first good value. */
          CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1);
          CHECK(!is_empty_signature(&sig));
          CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1);
          CHECK(!is_empty_signature(&sig2));
          CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
          /* The default nonce function is deterministic. */
          CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
          CHECK(!is_empty_signature(&sig2));
          CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0);
          /* The default nonce function changes output with different messages. */
          for(i = 0; i < 256; i++) {
              int j;
              msg[0] = i;
              CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
              CHECK(!is_empty_signature(&sig2));
              secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
              for (j = 0; j < i; j++) {
                  CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
              }
          }
          msg[0] = 0;
          msg[31] = 2;
          /* The default nonce function changes output with different keys. */
          for(i = 256; i < 512; i++) {
              int j;
              key[0] = i - 256;
              CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1);
              CHECK(!is_empty_signature(&sig2));
              secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2);
              for (j = 0; j < i; j++) {
                  CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j]));
              }
          }
          key[0] = 0;
      }
  
      {
          /* Check that optional nonce arguments do not have equivalent effect. */
          const unsigned char zeros[32] = {0};
          unsigned char nonce[32];
          unsigned char nonce2[32];
          unsigned char nonce3[32];
          unsigned char nonce4[32];
          VG_UNDEF(nonce,32);
          VG_UNDEF(nonce2,32);
          VG_UNDEF(nonce3,32);
          VG_UNDEF(nonce4,32);
          CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1);
          VG_CHECK(nonce,32);
          CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1);
          VG_CHECK(nonce2,32);
          CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1);
          VG_CHECK(nonce3,32);
          CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1);
          VG_CHECK(nonce4,32);
          CHECK(memcmp(nonce, nonce2, 32) != 0);
          CHECK(memcmp(nonce, nonce3, 32) != 0);
          CHECK(memcmp(nonce, nonce4, 32) != 0);
          CHECK(memcmp(nonce2, nonce3, 32) != 0);
          CHECK(memcmp(nonce2, nonce4, 32) != 0);
          CHECK(memcmp(nonce3, nonce4, 32) != 0);
      }
  
  
      /* Privkey export where pubkey is the point at infinity. */
      {
          unsigned char privkey[300];
          unsigned char seckey[32] = {
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
              0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe,
              0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b,
              0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41,
          };
          size_t outlen = 300;
          CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0));
          outlen = 300;
          CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1));
      }
  }
  
  void run_ecdsa_edge_cases(void) {
      test_ecdsa_edge_cases();
  }
  
  #ifdef ENABLE_OPENSSL_TESTS
  EC_KEY *get_openssl_key(const unsigned char *key32) {
      unsigned char privkey[300];
      size_t privkeylen;
      const unsigned char* pbegin = privkey;
      int compr = secp256k1_rand_bits(1);
      EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1);
      CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr));
      CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen));
      CHECK(EC_KEY_check_key(ec_key));
      return ec_key;
  }
  
  void test_ecdsa_openssl(void) {
      secp256k1_gej qj;
      secp256k1_ge q;
      secp256k1_scalar sigr, sigs;
      secp256k1_scalar one;
      secp256k1_scalar msg2;
      secp256k1_scalar key, msg;
      EC_KEY *ec_key;
      unsigned int sigsize = 80;
      size_t secp_sigsize = 80;
      unsigned char message[32];
      unsigned char signature[80];
      unsigned char key32[32];
      secp256k1_rand256_test(message);
      secp256k1_scalar_set_b32(&msg, message, NULL);
      random_scalar_order_test(&key);
      secp256k1_scalar_get_b32(key32, &key);
      secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key);
      secp256k1_ge_set_gej(&q, &qj);
      ec_key = get_openssl_key(key32);
      CHECK(ec_key != NULL);
      CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key));
      CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize));
      CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg));
      secp256k1_scalar_set_int(&one, 1);
      secp256k1_scalar_add(&msg2, &msg, &one);
      CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2));
  
      random_sign(&sigr, &sigs, &key, &msg, NULL);
      CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs));
      CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1);
  
      EC_KEY_free(ec_key);
  }
  
  void run_ecdsa_openssl(void) {
      int i;
      for (i = 0; i < 10*count; i++) {
          test_ecdsa_openssl();
      }
  }
  #endif
  
  #ifdef ENABLE_MODULE_ECDH
  # include "modules/ecdh/tests_impl.h"
  #endif
  
  #ifdef ENABLE_MODULE_SCHNORR
  # include "modules/schnorr/tests_impl.h"
  #endif
  
  #ifdef ENABLE_MODULE_RECOVERY
  # include "modules/recovery/tests_impl.h"
  #endif
  
  int main(int argc, char **argv) {
      unsigned char seed16[16] = {0};
      unsigned char run32[32] = {0};
      /* find iteration count */
      if (argc > 1) {
          count = strtol(argv[1], NULL, 0);
      }
  
      /* find random seed */
      if (argc > 2) {
          int pos = 0;
          const char* ch = argv[2];
          while (pos < 16 && ch[0] != 0 && ch[1] != 0) {
              unsigned short sh;
              if (sscanf(ch, "%2hx", &sh)) {
                  seed16[pos] = sh;
              } else {
                  break;
              }
              ch += 2;
              pos++;
          }
      } else {
          FILE *frand = fopen("/dev/urandom", "r");
          if ((frand == NULL) || !fread(&seed16, sizeof(seed16), 1, frand)) {
              uint64_t t = time(NULL) * (uint64_t)1337;
              seed16[0] ^= t;
              seed16[1] ^= t >> 8;
              seed16[2] ^= t >> 16;
              seed16[3] ^= t >> 24;
              seed16[4] ^= t >> 32;
              seed16[5] ^= t >> 40;
              seed16[6] ^= t >> 48;
              seed16[7] ^= t >> 56;
          }
          fclose(frand);
      }
      secp256k1_rand_seed(seed16);
  
      printf("test count = %i\n", count);
      printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]);
  
      /* initialize */
      run_context_tests();
      ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
      if (secp256k1_rand_bits(1)) {
          secp256k1_rand256(run32);
          CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL));
      }
  
      run_rand_bits();
      run_rand_int();
  
      run_sha256_tests();
      run_hmac_sha256_tests();
      run_rfc6979_hmac_sha256_tests();
  
  #ifndef USE_NUM_NONE
      /* num tests */
      run_num_smalltests();
  #endif
  
      /* scalar tests */
      run_scalar_tests();
  
      /* field tests */
      run_field_inv();
      run_field_inv_var();
      run_field_inv_all_var();
      run_field_misc();
      run_field_convert();
      run_sqr();
      run_sqrt();
  
      /* group tests */
      run_ge();
      run_group_decompress();
  
      /* ecmult tests */
      run_wnaf();
      run_point_times_order();
      run_ecmult_chain();
      run_ecmult_constants();
      run_ecmult_gen_blind();
      run_ecmult_const_tests();
      run_ec_combine();
  
      /* endomorphism tests */
  #ifdef USE_ENDOMORPHISM
      run_endomorphism_tests();
  #endif
  
      /* EC point parser test */
      run_ec_pubkey_parse_test();
  
      /* EC key edge cases */
      run_eckey_edge_case_test();
  
  #ifdef ENABLE_MODULE_ECDH
      /* ecdh tests */
      run_ecdh_tests();
  #endif
  
      /* ecdsa tests */
      run_random_pubkeys();
      run_ecdsa_der_parse();
      run_ecdsa_sign_verify();
      run_ecdsa_end_to_end();
      run_ecdsa_edge_cases();
  #ifdef ENABLE_OPENSSL_TESTS
      run_ecdsa_openssl();
  #endif
  
  #ifdef ENABLE_MODULE_SCHNORR
      /* Schnorr tests */
      run_schnorr_tests();
  #endif
  
  #ifdef ENABLE_MODULE_RECOVERY
      /* ECDSA pubkey recovery tests */
      run_recovery_tests();
  #endif
  
      secp256k1_rand256(run32);
      printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]);
  
      /* shutdown */
      secp256k1_context_destroy(ctx);
  
      printf("no problems found\n");
      return 0;
  }
  