快速求根算法

//---Algorithm float(IEEE754)用------
inline float t_sqrtF( const float& x )
{
float xHalf = 0.5f * x;
int   tmp   = 0x5F3759DF - ( *(int*)&x >> 1 ); //initial guess
float xRes  = *(float*)&tmp;

xRes *= ( 1.5f - ( xHalf * xRes * xRes ) );
//xRes *= ( 1.5f - ( xHalf * xRes * xRes ) );//二次牛顿迭代，可提高精度
return xRes * x;   //所得xRes为平方根倒数值
}

 

//---Algorithm double(IEEE754)用------
inline double t_sqrtD( const double &x)
{
double         xHalf = 0.5 * x;
long long int  tmp   = 0x5FE6EB50C7B537AAl - ( *(long long int*)&x >> 1);//initial guess
double         xRes  = * (double*)&tmp;

xRes *= ( 1.5 - ( xHalf * xRes * xRes ) );
//xRes *= ( 1.5 - ( xHalf * xRes * xRes ) );//二次牛顿迭代，可提高精度
return xRes * x;  //所得xRes为平方根倒数值
}

 

原文链接：http://takashiijiri.com/study/miscs/fastsqrt.html

原文参考文献：

[1] David Eberly, Fast Inverse Square Root (Revisited), http://www.geometrictools.com/Documentation/ FastInverseSqrt.pdf, 1/2002-.

该算法详细分析：https://blog.youkuaiyun.com/xtlisk/article/details/51249371