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maths/fast_inverse_sqrt.py
54 строки
2 KB
Aryansh B
Added Fast Inverse Square Root (#11054)
29 окт 2023, 23:57
Не верифицирован
29 окт 2023, 23:57
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""" Fast inverse square root (1/sqrt(x)) using the Quake III algorithm. Reference: https://en.wikipedia.org/wiki/Fast_inverse_square_root Accuracy: https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy """ import struct def fast_inverse_sqrt(number: float) -> float: """ Compute the fast inverse square root of a floating-point number using the famous Quake III algorithm. :param float number: Input number for which to calculate the inverse square root. :return float: The fast inverse square root of the input number. Example: >>> fast_inverse_sqrt(10) 0.3156857923527257 >>> fast_inverse_sqrt(4) 0.49915357479239103 >>> fast_inverse_sqrt(4.1) 0.4932849504615651 >>> fast_inverse_sqrt(0) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> fast_inverse_sqrt(-1) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> from math import isclose, sqrt >>> all(isclose(fast_inverse_sqrt(i), 1 / sqrt(i), rel_tol=0.00132) ... for i in range(50, 60)) True """ if number <= 0: raise ValueError("Input must be a positive number.") i = struct.unpack(">i", struct.pack(">f", number))[0] i = 0x5F3759DF - (i >> 1) y = struct.unpack(">f", struct.pack(">i", i))[0] return y * (1.5 - 0.5 * number * y * y) if __name__ == "__main__": from doctest import testmod testmod() # https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy from math import sqrt for i in range(5, 101, 5): print(f"{i:>3}: {(1 / sqrt(i)) - fast_inverse_sqrt(i):.5f}")