开平方与魔数0x5F3759DF：Quake III 开源代码

float Q_rsqrt( float number )
{
　　long i;
　　float x2, y;
　　const float threehalfs = 1.5F;

　　x2 = number * 0.5F;
　　y = number;
　　i = * ( long * ) &y; // evil floating point bit level hacking
　　i = 0x5f3759df - ( i >> 1 ); // what the fuck?
　　y = * ( float * ) &i;
　　y = y * ( threehalfs - ( x2 * y * y ) ); // 1st iteration
　　// y = y * ( threehalfs - ( x2 * y * y ) ); // 2nd iteration, this can be removed

　　#ifndef Q3_VM
　　#ifdef __linux__
　　assert( !isnan(y) ); // bk010122 - FPE?
　　#endif
　　#endif
　　return y;
}

 

float InvSqrt(float x)
{
    float xhalf = 0.5f*x;
    int i = *(int*)&x; // get bits for floating VALUE
    i = 0x5f375a86- (i>>1); // gives initial guess y0
    x = *(float*)&i; // convert bits BACK to float
    x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
    return x;
} 

参考：

http://www.matrix67.com/data/InvSqrt.pdf

http://www.guokr.com/post/90718/