Łukasz Jagiełło - Fast Inverse Square Root - Papers We Love SF 2017

Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5f3759df, is an algorithm that estimates 1/√x, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number x in IEEE 754 floating-point format.

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1. PWL SF 2017
5. 19th August 2005
7. https://github.com/id-Software/Quake-III-Arena/blob/master/ code/game/q_math.c#L552
12. Newton’s Method of Approximation
13. n = 2 1 / sqrt(n) = 0.70710678119 g = 1
14. n = 2 1 / sqrt(n) = 0.70710678119 g = 1 1st ng = g*(1.5 - (n/2)*g*g) 0.5 70.71067811831%
15. n = 2 1 / sqrt(n) = 0.70710678119 g = 1 1st ng = g*(1.5 - (n/2)*g*g) 0.5 70.71067811831% 2nd ng = g*(1.5 - (n/2)*g*g) 0.625 88.38834764789%
16. n = 2 1 / sqrt(n) = 0.70710678119 g = 1 1st ng = g*(1.5 - (n/2)*g*g) 0.5 70.71067811831% 2nd ng = g*(1.5 - (n/2)*g*g) 0.625 88.38834764789% 3rd ng = g*(1.5 - (n/2)*g*g) 0.693359375 98.05582317187% 4th ng = g*(1.5 - (n/2)*g*g) 0.7067084685 99.94367007917% 5th ng = g*(1.5 - (n/2)*g*g) 0.7071064447 99.99995241313%
18. 0x5f3759df
21. http://www.netlib.org/fdlibm/e_sqrt.c
23. May 2017
26. modern CPU - Intel Xeon E5-2667v3 the hack is actually ~x2 slower in 2017 used to be ~x4 times faster back in ~2003
27. ?