

"""simple docstring"""


from collections.abc import Callable






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     float:
		__lowerCAmelCase:	float   				=      a
		__lowerCAmelCase:	float   				=      b
		if function(__SCREAMING_SNAKE_CASE			) == 0:  # one of the a or b is a root for the function
				return a
		elif function(__SCREAMING_SNAKE_CASE			) == 0:
				return b
		elif (
		    function(__SCREAMING_SNAKE_CASE			) * function(__SCREAMING_SNAKE_CASE			) > 0
		):  # if none of these are root and they are both positive or negative,
				# then this algorithm can't find the root
				raise ValueError("could not find root in given interval."			)
		else:
				__lowerCAmelCase:	float   				=      start + (end - start) / 2.0
				while abs(start - mid			) > 1_0**-7:  # until precisely equals to 10^-7
						if function(__SCREAMING_SNAKE_CASE			) == 0:
								return mid
						elif function(__SCREAMING_SNAKE_CASE			) * function(__SCREAMING_SNAKE_CASE			) < 0:
								__lowerCAmelCase:	List[str]   				=      mid
						else:
								__lowerCAmelCase:	List[str]   				=      mid
						__lowerCAmelCase:	str   				=      start + (end - start) / 2.0
				return mid






def    a__   (   __SCREAMING_SNAKE_CASE			)     ->     float:
		return x**3 - 2 * x - 5


if __name__ == "__main__":
			print(bisection(f, 1, 1000))

			import doctest

			doctest.testmod()





"""simple docstring"""


from math import ceil






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     str:
		__lowerCAmelCase:	Tuple   				=      list(range(0 ,			__SCREAMING_SNAKE_CASE			)			)

		__lowerCAmelCase:	Optional[Any]   				=      [item for sublist in list(device_map.values()			) for item in sublist]

		# Duplicate check
		__lowerCAmelCase:	List[Any]   				=      []
		for i in device_map_blocks:
				if device_map_blocks.count(__SCREAMING_SNAKE_CASE			) > 1 and i not in duplicate_blocks:
						duplicate_blocks.append(__SCREAMING_SNAKE_CASE			)
    # Missing blocks
		__lowerCAmelCase:	Optional[Any]   				=      [i for i in blocks if i not in device_map_blocks]
		__lowerCAmelCase:	List[Any]   				=      [i for i in device_map_blocks if i not in blocks]

		if len(__SCREAMING_SNAKE_CASE			) != 0:
				raise ValueError(
				    "Duplicate attention blocks specified in device_map. Attention blocks must be specified to one device."
				    " These attention blocks were specified more than once: " + str(__SCREAMING_SNAKE_CASE			)			)
		if len(__SCREAMING_SNAKE_CASE			) != 0:
				raise ValueError(
				    "There are attention blocks for this model that are not specified in the device_map. Add these attention "
				    "blocks to a device on the device_map: " + str(__SCREAMING_SNAKE_CASE			)			)
		if len(__SCREAMING_SNAKE_CASE			) != 0:
				raise ValueError(
				    "The device_map contains more attention blocks than this model has. Remove these from the device_map:"
				    + str(__SCREAMING_SNAKE_CASE			)			)






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     str:
		__lowerCAmelCase:	List[Any]   				=      list(range(__SCREAMING_SNAKE_CASE			)			)
		__lowerCAmelCase:	Dict   				=      int(ceil(n_layers / len(__SCREAMING_SNAKE_CASE			)			)			)
		__lowerCAmelCase:	Union[str, Any]   				=      [layers[i : i + n_blocks] for i in range(0 ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)]

		return dict(zip(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)			)


