maths.fast_inverse_sqrt
=======================

.. py:module:: maths.fast_inverse_sqrt

.. autoapi-nested-parse::

   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



Functions
---------

.. autoapisummary::

   maths.fast_inverse_sqrt.fast_inverse_sqrt


Module Contents
---------------

.. py:function:: 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