#### Fast Inverse Sqrt

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A
R
```"""
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}")
```