


'''simple docstring'''



from __future__ import annotations

from math import gcd







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ = 2 ,      UpperCamelCase__ = 1 ,      UpperCamelCase__ = 3 ,      ):
			# A value less than 2 can cause an infinite loop in the algorithm.
			if num < 2:
						raise ValueError("""The input value cannot be less than 2"""					)

			# Because of the relationship between ``f(f(x))`` and ``f(x)``, this
			# algorithm struggles to find factors that are divisible by two.
			# As a workaround, we specifically check for two and even inputs.
			#   See: https://math.stackexchange.com/a/2856214/165820
			if num > 2 and num % 2 == 0:
						return 2

			# Pollard's Rho algorithm requires a function that returns pseudorandom
			# values between 0 <= X < ``num``.  It doesn't need to be random in the
			# sense that the output value is cryptographically secure or difficult
			# to calculate, it only needs to be random in the sense that all output
			# values should be equally likely to appear.
			# For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
			# However, the success of Pollard's algorithm isn't guaranteed and is
			# determined in part by the initial seed and the chosen random function.
			# To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
			# where ``C`` is a value that we can modify between each attempt.
			def rand_fn(UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					) -> int:
						return (pow(UpperCamelCase__ ,      2					) + step) % modulus

			for _ in range(UpperCamelCase__					):
						# These track the position within the cycle detection logic.
						UpperCAmelCase__  :					Any        =     seed
						UpperCAmelCase__  :					Union[str, Any]        =     seed

						while True:
									# At each iteration, the tortoise moves one step and the hare moves two.
									UpperCAmelCase__  :					str        =     rand_fn(UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)
									UpperCAmelCase__  :					int        =     rand_fn(UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)
									UpperCAmelCase__  :					List[Any]        =     rand_fn(UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)

									# At some point both the tortoise and the hare will enter a cycle whose
									# length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
									# the tortoise and hare will end up on the same value modulo ``p``.
									# We can detect when this happens because the position difference between
									# the tortoise and the hare will share a common divisor with ``num``.
									UpperCAmelCase__  :					Any        =     gcd(hare - tortoise ,      UpperCamelCase__					)

									if divisor == 1:
												# No common divisor yet, just keep searching.
												continue
									else:
												# We found a common divisor!
												if divisor == num:
															# Unfortunately, the divisor is ``num`` itself and is useless.
															break
												else:
															# The divisor is a nontrivial factor of ``num``!
															return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
						UpperCAmelCase__  :					Optional[Any]        =     hare

						# The new step value for the random function can just be incremented.
						# At first the results will be similar to what the old function would
						# have produced, but the value will quickly diverge after a bit.
						step += 1

			# We haven't found a divisor within the requested number of attempts.
			# We were unlucky or ``num`` itself is actually prime.
			return None


if __name__ == "__main__":
		import argparse

		__A	=argparse.ArgumentParser()
		parser.add_argument(
		    'num',
		    type=int,
		    help='The value to find a divisor of',
		)
		parser.add_argument(
		    '--attempts',
		    type=int,
		    default=3,
		    help='The number of attempts before giving up',
		)
		__A	=parser.parse_args()

		__A	=pollard_rho(args.num, attempts=args.attempts)
		if divisor is None:
				print(f"""{args.num} is probably prime""")
		else:
				__A	=args.num // divisor
				print(f"""{args.num} = {divisor} * {quotient}""")



'''simple docstring'''



import re

import jax.numpy as jnp
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.random import PRNGKey

from ..utils import logging


__A	=logging.get_logger(__name__)







def     _UpperCamelCase      (		UpperCamelCase__					):
			UpperCAmelCase__  :					List[str]        =     R"""\w+[.]\d+"""
			UpperCAmelCase__  :					List[Any]        =     re.findall(UpperCamelCase__ ,      UpperCamelCase__					)
			for pat in pats:
						UpperCAmelCase__  :					str        =     key.replace(UpperCamelCase__ ,      """_""".join(pat.split("""."""					)					)					)
			return key







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					):
			UpperCAmelCase__  :					str        =     pt_tuple_key[:-1] + ("""scale""",)
			if (
			    any("""norm""" in str_ for str_ in pt_tuple_key					)
			    and (pt_tuple_key[-1] == "bias")
			    and (pt_tuple_key[:-1] + ("bias",) not in random_flax_state_dict)
			    and (pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict)
			):
						UpperCAmelCase__  :					Union[str, Any]        =     pt_tuple_key[:-1] + ("""scale""",)
						return renamed_pt_tuple_key, pt_tensor
			elif pt_tuple_key[-1] in ["weight", "gamma"] and pt_tuple_key[:-1] + ("scale",) in random_flax_state_dict:
						UpperCAmelCase__  :					str        =     pt_tuple_key[:-1] + ("""scale""",)
						return renamed_pt_tuple_key, pt_tensor

			# embedding
			if pt_tuple_key[-1] == "weight" and pt_tuple_key[:-1] + ("embedding",) in random_flax_state_dict:
						UpperCAmelCase__  :					Union[str, Any]        =     pt_tuple_key[:-1] + ("""embedding""",)
						return renamed_pt_tuple_key, pt_tensor

			# conv layer
			UpperCAmelCase__  :					Any        =     pt_tuple_key[:-1] + ("""kernel""",)
			if pt_tuple_key[-1] == "weight" and pt_tensor.ndim == 4:
						UpperCAmelCase__  :					Any        =     pt_tensor.transpose(2 ,      3 ,      1 ,      0					)
						return renamed_pt_tuple_key, pt_tensor

			# linear layer
			UpperCAmelCase__  :					Optional[int]        =     pt_tuple_key[:-1] + ("""kernel""",)
			if pt_tuple_key[-1] == "weight":
						UpperCAmelCase__  :					Any        =     pt_tensor.T
						return renamed_pt_tuple_key, pt_tensor

			# old PyTorch layer norm weight
			UpperCAmelCase__  :					Optional[Any]        =     pt_tuple_key[:-1] + ("""weight""",)
			if pt_tuple_key[-1] == "gamma":
						return renamed_pt_tuple_key, pt_tensor

			# old PyTorch layer norm bias
			UpperCAmelCase__  :					Dict        =     pt_tuple_key[:-1] + ("""bias""",)
			if pt_tuple_key[-1] == "beta":
						return renamed_pt_tuple_key, pt_tensor

			return pt_tuple_key, pt_tensor







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__=4_2					):
			# Step 1: Convert pytorch tensor to numpy
			UpperCAmelCase__  :					str        =     {k: v.numpy() for k, v in pt_state_dict.items()}

			# Step 2: Since the model is stateless, get random Flax params
			UpperCAmelCase__  :					str        =     flax_model.init_weights(PRNGKey(UpperCamelCase__					)					)

			UpperCAmelCase__  :					Union[str, Any]        =     flatten_dict(UpperCamelCase__					)
			UpperCAmelCase__  :					int        =     {}

			# Need to change some parameters name to match Flax names
			for pt_key, pt_tensor in pt_state_dict.items():
						UpperCAmelCase__  :					str        =     rename_key(UpperCamelCase__					)
						UpperCAmelCase__  :					Optional[Any]        =     tuple(renamed_pt_key.split("""."""					)					)

						# Correctly rename weight parameters
						UpperCAmelCase__   ,       UpperCAmelCase__  :					Tuple        =     rename_key_and_reshape_tensor(UpperCamelCase__ ,      UpperCamelCase__ ,      UpperCamelCase__					)

						if flax_key in random_flax_state_dict:
									if flax_tensor.shape != random_flax_state_dict[flax_key].shape:
												raise ValueError(
												    f'''PyTorch checkpoint seems to be incorrect. Weight {pt_key} was expected to be of shape '''
												    f'''{random_flax_state_dict[flax_key].shape}, but is {flax_tensor.shape}.'''					)

        # also add unexpected weight so that warning is thrown
						UpperCAmelCase__  :					str        =     jnp.asarray(UpperCamelCase__					)

			return unflatten_dict(UpperCamelCase__					)