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* Feat: Added Fast inverse square root * Fix: Added typehint * Fix: Added doctests that break the code, changed var name * updating DIRECTORY.md * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix: fixed length of docstring * Update fast_inverse_sqrt.py --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
55 lines
1.7 KiB
Python
55 lines
1.7 KiB
Python
"""
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Fast inverse square root (1/sqrt(x)) using the Quake III algorithm.
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Reference: https://en.wikipedia.org/wiki/Fast_inverse_square_root
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Accuracy: https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy
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"""
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import struct
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def fast_inverse_sqrt(number: float) -> float:
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"""
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Compute the fast inverse square root of a floating-point number using the famous
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Quake III algorithm.
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:param float number: Input number for which to calculate the inverse square root.
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:return float: The fast inverse square root of the input number.
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Example:
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>>> fast_inverse_sqrt(10)
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0.3156857923527257
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>>> fast_inverse_sqrt(4)
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0.49915357479239103
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>>> fast_inverse_sqrt(4.1)
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0.4932849504615651
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>>> fast_inverse_sqrt(0)
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Traceback (most recent call last):
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...
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ValueError: Input must be a positive number.
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>>> fast_inverse_sqrt(-1)
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Traceback (most recent call last):
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...
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ValueError: Input must be a positive number.
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>>> from math import isclose, sqrt
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>>> all(isclose(fast_inverse_sqrt(i), 1 / sqrt(i), rel_tol=0.00132)
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... for i in range(50, 60))
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True
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"""
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if number <= 0:
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raise ValueError("Input must be a positive number.")
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i = struct.unpack(">i", struct.pack(">f", number))[0]
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i = 0x5F3759DF - (i >> 1)
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y = struct.unpack(">f", struct.pack(">i", i))[0]
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return y * (1.5 - 0.5 * number * y * y)
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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# https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy
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from math import sqrt
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for i in range(5, 101, 5):
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print(f"{i:>3}: {(1 / sqrt(i)) - fast_inverse_sqrt(i):.5f}")
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