


from __future__ import annotations

import math
from collections.abc import Callable






def 						a__			(				A__,      A__,      A__,      A__ = 1_0_0,      ):
			SCREAMING_SNAKE_CASE_		:     Tuple					=					x_start
			SCREAMING_SNAKE_CASE_		:     Dict					=					fnc(A__				)
			SCREAMING_SNAKE_CASE_		:     Tuple					=					0.0

			for _ in range(A__				):
						# Approximates curve as a sequence of linear lines and sums their length
						SCREAMING_SNAKE_CASE_		:     int					=					(x_end - x_start) / steps + xa
						SCREAMING_SNAKE_CASE_		:     Any					=					fnc(A__				)
						length += math.hypot(xa - xa,      fxa - fxa				)

						# Increment step
						SCREAMING_SNAKE_CASE_		:     int					=					xa
						SCREAMING_SNAKE_CASE_		:     Optional[int]					=					fxa

			return length


if __name__ == "__main__":






				def 						a__			(				A__				):
							return math.sin(1_0 * x				)

				print('f(x) = sin(10 * x)')
				print('The length of the curve from x = -10 to x = 10 is:')
				lowerCAmelCase__			:      Union[str, Any]								=10
				while i <= 10_00_00:
								print(F"""With {i} steps: {line_length(f, -10, 10, i)}""")
								i *= 10











'''simple docstring'''





import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
UpperCamelCase_		:     Optional[int]          =		object()

# For specifying empty leaf dict `{}`
UpperCamelCase_		:     Optional[int]          =		object()





def       __a      (  _UpperCamelCase:       Union[str, Any]   ,		_UpperCamelCase:       Optional[Any]       )		->					Optional[Any]:

     """simple docstring"""




     _snake_case				= tuple((re.compile(x + "$"       ) for x in qs)       )
     for i in range(len(_UpperCamelCase       ) - len(_UpperCamelCase       ) + 1       ):
          _snake_case				= [x.match(_UpperCamelCase       ) for x, y in zip(_UpperCamelCase   ,		ks[i:]       )]
          if matches and all(_UpperCamelCase       ):
               return True
     return False





def       __a      (  _UpperCamelCase:       Optional[Any]       )		->					Union[str, Any]:

     """simple docstring"""




     def replace(_UpperCamelCase:       Tuple   ,		_UpperCamelCase:       List[str]       ):
          for rule, replacement in rules:
               if _match(_UpperCamelCase   ,		_UpperCamelCase       ):
                    return replacement
          return val

     return replace





def       __a      (  )		->					Any:

     """simple docstring"""




     return [
         # embeddings
         (("transformer", "wpe", "embedding"), P("mp"   ,		_UpperCamelCase       )),
         (("transformer", "wte", "embedding"), P("mp"   ,		_UpperCamelCase       )),
         # atention
         (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(_UpperCamelCase   ,		"mp"       )),
         (("attention", "out_proj", "kernel"), P("mp"   ,		_UpperCamelCase       )),
         (("attention", "out_proj", "bias"), None),
         # mlp
         (("mlp", "c_fc", "kernel"), P(_UpperCamelCase   ,		"mp"       )),
         (("mlp", "c_fc", "bias"), P("mp"       )),
         (("mlp", "c_proj", "kernel"), P("mp"   ,		_UpperCamelCase       )),
         (("mlp", "c_proj", "bias"), None),
         # layer norms
         ((r"ln_\d+", "bias"), None),
         ((r"\d+", r"ln_\d+", "scale"), None),
         (("ln_f", "bias"), None),
         (("ln_f", "scale"), None),
     ]





def       __a      (  _UpperCamelCase:       Union[str, Any]       )		->					Any:

     """simple docstring"""




     _snake_case				= _get_partition_rules()
     _snake_case				= _replacement_rules(_UpperCamelCase       )
     _snake_case				= {k: _unmatched for k in flatten_dict(_UpperCamelCase       )}
     _snake_case				= {k: replace(_UpperCamelCase   ,		_UpperCamelCase       ) for k, v in initd.items()}
     assert _unmatched not in result.values(), "Incomplete partition spec."
     return freeze(unflatten_dict(_UpperCamelCase       )       )


