PWL SF 2017

19th August 2005

https://github.com/id-Software/Quake-III-Arena/blob/master/code/game/q_math.c#L552

Newton’s Method of Approximation

n = 2

1 / sqrt(n) = 0.70710678119

g = 1

n = 2

1 / sqrt(n) = 0.70710678119

g = 1

1st ng = g*(1.5 - (n/2)*g*g) 0.5 70.71067811831%

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%

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%

0x5f3759df

http://www.netlib.org/fdlibm/e_sqrt.c

May 2017

modern CPU - Intel Xeon E5-2667v3

the hack is actually ~x2 slower in 2017 used to be ~x4 times faster back in ~2003

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