在game/code/q_math.c裡發現了這樣一段代碼。它的作用是將一個數開平方並取倒,經測試這段代碼比(float)(1.0/sqrt(x))快4倍:
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
參考:<IEEE Standard 754 for Binary Floating-Point Arithmetic><FAST INVERSE SQUARE ROOT>
最後,給出最精簡的1/sqrt()函數:
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;
}
大家可以嘗試在PC機、51、AVR、430、ARM、上面編譯並實驗,驚訝一下它的工作效率。