
"""simple docstring"""

import math
from timeit import timeit
def 		UpperCAmelCase					(		a_			):





		'''simple docstring'''


		lowerCamelCase     :			Optional[Any]		=    0
		lowerCamelCase     :			Dict		=    abs(a_			)
		while True:
				lowerCamelCase     :			str		=    n // 10
				digits += 1
				if n == 0:
						break
		return digits
def 		UpperCAmelCase					(		a_			):





		'''simple docstring'''


		return 1 if n == 0 else math.floor(math.log(abs(a_			),						10			) + 1			)
def 		UpperCAmelCase					(		a_			):





		'''simple docstring'''


		return len(str(abs(a_			)			)			)
def 		UpperCAmelCase					(		):





		'''simple docstring'''


		from collections.abc import Callable

		def benchmark_a_function(a_,						a_			) -> None:
				lowerCamelCase     :			Dict		=    F"""{func.__name__}({value})"""
				lowerCamelCase     :			str		=    timeit(F"""__main__.{call}""",						setup='import __main__'			)
				print(F"""{call}: {func(a_			)} -- {timing} seconds"""			)

		for value in (26_2144, 1125_8999_0684_2624, 126_7650_6002_2822_9401_4967_0320_5376):
				for func in (num_digits, num_digits_fast, num_digits_faster):
						benchmark_a_function(a_,						a_			)
				print()


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()








"""simple docstring"""

import numpy as np
def 		UpperCAmelCase					(		a_,						a_="utf-8",						a_="surrogatepass"			):





		'''simple docstring'''


		lowerCamelCase     :			str		=    bin(int.from_bytes(text.encode(a_,						a_			),						'big'			)			)[2:]
		return bits.zfill(8 * ((len(a_			) + 7) // 8)			)
def 		UpperCAmelCase					(		a_,						a_="utf-8",						a_="surrogatepass"			):





		'''simple docstring'''


		lowerCamelCase     :			List[Any]		=    int(a_,						2			)
		return n.to_bytes((n.bit_length() + 7) // 8,						'big'			).decode(a_,						a_			) or "\0"
def 		UpperCAmelCase					(		a_,						a_			):





		'''simple docstring'''


		if size_par + len(a_			) <= 2**size_par - (len(a_			) - 1):
				raise ValueError('size of parity don\'t match with size of data'			)

		lowerCamelCase     :			List[str]		=    []
		lowerCamelCase     :			str		=    []
		lowerCamelCase     :			Any		=    [bin(a_			)[2:] for x in range(1,						size_par + len(a_			) + 1			)]

		# sorted information data for the size of the output data
		lowerCamelCase     :			int		=    []
		# data position template + parity
		lowerCamelCase     :			Union[str, Any]		=    []
		# parity bit counter
		lowerCamelCase     :			Optional[int]		=    0
		# counter position of data bits
		lowerCamelCase     :			Any		=    0

		for x in range(1,						size_par + len(a_			) + 1			):
				# Performs a template of bit positions - who should be given,
				# and who should be parity
				if qtd_bp < size_par:
						if (np.log(a_			) / np.log(2			)).is_integer():
								data_out_gab.append('P'			)
								lowerCamelCase     :			List[Any]		=    qtd_bp + 1
						else:
								data_out_gab.append('D'			)
				else:
						data_out_gab.append('D'			)

				# Sorts the data to the new output size
				if data_out_gab[-1] == "D":
						data_ord.append(data[cont_data]			)
						cont_data += 1
				else:
						data_ord.append(a_			)

    # Calculates parity
		lowerCamelCase     :			Optional[Any]		=    0  # parity bit counter
		for bp in range(1,						size_par + 1			):
				# Bit counter one for a given parity
				lowerCamelCase     :			Union[str, Any]		=    0
				# counter to control the loop reading
				lowerCamelCase     :			Optional[int]		=    0
				for x in data_ord:
						if x is not None:
								try:
										lowerCamelCase     :			Union[str, Any]		=    (bin_pos[cont_loop])[-1 * (bp)]
								except IndexError:
										lowerCamelCase     :			str		=    '0'
								if aux == "1" and x == "1":
										cont_bo += 1
						cont_loop += 1
				parity.append(cont_bo % 2			)

				qtd_bp += 1

		# Mount the message
		lowerCamelCase     :			Tuple		=    0  # parity bit counter
		for x in range(0,						size_par + len(a_			)			):
				if data_ord[x] is None:
						data_out.append(str(parity[cont_bp]			)			)
						cont_bp += 1
				else:
						data_out.append(data_ord[x]			)

		return data_out
def 		UpperCAmelCase					(		a_,						a_			):





		'''simple docstring'''


		lowerCamelCase     :			str		=    []
		# Parity bit counter
		lowerCamelCase     :			Dict		=    0
		# Counter p data bit reading
		lowerCamelCase     :			int		=    0
		# list of parity received
		lowerCamelCase     :			Optional[int]		=    []
		lowerCamelCase     :			Any		=    []

		for x in range(1,						len(a_			) + 1			):
				# Performs a template of bit positions - who should be given,
				#  and who should be parity
				if qtd_bp < size_par and (np.log(a_			) / np.log(2			)).is_integer():
						data_out_gab.append('P'			)
						lowerCamelCase     :			List[Any]		=    qtd_bp + 1
				else:
						data_out_gab.append('D'			)

				# Sorts the data to the new output size
				if data_out_gab[-1] == "D":
						data_output.append(data[cont_data]			)
				else:
						parity_received.append(data[cont_data]			)
				cont_data += 1

		# -----------calculates the parity with the data
		lowerCamelCase     :			Dict		=    []
		lowerCamelCase     :			Optional[Any]		=    []
		lowerCamelCase     :			Dict		=    [bin(a_			)[2:] for x in range(1,						size_par + len(a_			) + 1			)]

		#  sorted information data for the size of the output data
		lowerCamelCase     :			Any		=    []
		# Data position feedback + parity
		lowerCamelCase     :			List[str]		=    []
		# Parity bit counter
		lowerCamelCase     :			List[str]		=    0
		# Counter p data bit reading
		lowerCamelCase     :			int		=    0

		for x in range(1,						size_par + len(a_			) + 1			):
				# Performs a template position of bits - who should be given,
				# and who should be parity
				if qtd_bp < size_par and (np.log(a_			) / np.log(2			)).is_integer():
						data_out_gab.append('P'			)
						lowerCamelCase     :			Tuple		=    qtd_bp + 1
				else:
						data_out_gab.append('D'			)

				# Sorts the data to the new output size
				if data_out_gab[-1] == "D":
						data_ord.append(data_output[cont_data]			)
						cont_data += 1
				else:
						data_ord.append(a_			)

    # Calculates parity
		lowerCamelCase     :			List[str]		=    0  # parity bit counter
		for bp in range(1,						size_par + 1			):
				# Bit counter one for a certain parity
				lowerCamelCase     :			List[Any]		=    0
				# Counter to control loop reading
				lowerCamelCase     :			List[Any]		=    0
				for x in data_ord:
						if x is not None:
								try:
										lowerCamelCase     :			Dict		=    (bin_pos[cont_loop])[-1 * (bp)]
								except IndexError:
										lowerCamelCase     :			List[Any]		=    '0'
								if aux == "1" and x == "1":
										cont_bo += 1
						cont_loop += 1
				parity.append(str(cont_bo % 2			)			)

				qtd_bp += 1

		# Mount the message
		lowerCamelCase     :			Tuple		=    0  # Parity bit counter
		for x in range(0,						size_par + len(a_			)			):
				if data_ord[x] is None:
						data_out.append(str(parity[cont_bp]			)			)
						cont_bp += 1
				else:
						data_out.append(data_ord[x]			)

		lowerCamelCase     :			Union[str, Any]		=    parity_received == parity
		return data_output, ack






