






from math import cos, sin

def 			__lowerCamelCase     (						snake_case__						)				->    list[list[float]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    float(snake_case__						)
						return [[scaling_factor * int(x == y						) for x in range(2						)] for y in range(2						)]

def 			__lowerCamelCase     (						snake_case__						)				->    list[list[float]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    cos(snake_case__						), sin(snake_case__						)
						return [[c, -s], [s, c]]

def 			__lowerCamelCase     (						snake_case__						)				->    list[list[float]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    cos(snake_case__						), sin(snake_case__						)
						_SCREAMING_SNAKE_CASE       =    c * s
						return [[c * c, cs], [cs, s * s]]

def 			__lowerCamelCase     (						snake_case__						)				->    list[list[float]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE       =    cos(snake_case__						), sin(snake_case__						)
						_SCREAMING_SNAKE_CASE       =    c * s
						return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f"    {scaling(5) = }")
print(f"  {rotation(45) = }")
print(f"{projection(45) = }")




print(f"{reflection(45) = }")









import math
from timeit import timeit

def 			__lowerCamelCase     (						snake_case__						)				->    int:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE       =    0
						_SCREAMING_SNAKE_CASE       =    abs(snake_case__						)
						while True:
												_SCREAMING_SNAKE_CASE       =    n // 10
												digits += 1
												if n == 0:
																		break
						return digits

def 			__lowerCamelCase     (						snake_case__						)				->    int:






						"""simple docstring"""





						return 1 if n == 0 else math.floor(math.log(abs(snake_case__						)			,10						) + 1						)

def 			__lowerCamelCase     (						snake_case__						)				->    int:






						"""simple docstring"""





						return len(str(abs(snake_case__						)						)						)

def 			__lowerCamelCase     (						)				->    None:






						"""simple docstring"""





						from collections.abc import Callable

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

						for value in (26_21_44, 11_25_89_99_06_84_26_24, 1_26_76_50_60_02_28_22_94_01_49_67_03_20_53_76):
												for func in (num_digits, num_digits_fast, num_digits_faster):
																		benchmark_a_function(snake_case__			,snake_case__						)
												print()


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		benchmark()

