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Thursday, March 3, 2011

M373 applied to computer games

The fact that computer games are computationally intensive forces game programmers to invent tricks to do their calculations in a minimal number of steps. A typical M373 optimization problem. It is much faster to calculate $\frac{1}{\sqrt{x}}$ using Newton approximation.

From the source code of Quake.
float InvSqrt(float x){
   float xhalf = 0.5f * x;
   int i = *(int*)&x; // store floating-point bits in integer
   i = 0x5f3759d5 - (i >> 1); // initial guess for Newton's method
   x = *(float*)&i; // convert new bits into float
   x = x*(1.5f - xhalf*x*x); // One round of Newton's method
   return x;

Link: Understanding Quake's fast inverse-square-root

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