John Carmack的sqrt函数为什么计算结果与系统库sqrt的结果不一致

xf331785508 · 发表于 2015-1-23 16:02:42

本帖最后由 xf331785508 于 2015-1-23 16:05 编辑

如题，网上找的Carmack的神奇函数，函数体如下：

static float Q_rsqrt( float x )
{
long i;
float x2, y;
const float threehalfs = 1.5F;
printf("Q_rsqrt start: x=%-6.7f\n", x);
x2 = x * 0.5F;
y = x;
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
#ifndef Q3_VM
#ifdef __linux__
assert( !isnan(y) ); // bk010122 - FPE?
#endif
#endif
printf("Q_rsqrt end: y=%-6.5f\n", y);
return y;
}

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最简化的函数体如下：

static float CarmackSqrt (float x)
{
float xhalf = 0.5f*x;
int i = *(int*)&x; // get bits for floating VALUE
printf("x=%-6.7f\n", x);
i = 0x5f3759df- (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
printf("x=%-6.3f\n", x);
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
printf("x=%-6.3f\n", x);
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
printf("x=%-6.3f\n", x);
return x;

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我用EXCEL的计算结果与用库函数sqrtf计算的结果一致，但利用上述函数就错的很大，怎么回事呢。
------------------------------------------
测试算法平台： CPU i3-2120 VC++ 6.0 控制台工程，输出结果到文本文件。截图即文本文件结果。

xf331785508 · 发表于 2015-1-23 16:34:28

void TestSqrt(void)
{
unsigned char i = 0;
float measureValue[] = {
2.132f, 5.043f, 4.563f, 0.503f, 7.223f,
2.181f, 5.247f, 3.799f, 0.536f, 7.163f,
2.152f, 5.201f, 3.912f, 0.528f, 7.189f,
2.142f, 5.178f, 3.582f, 0.528f, 7.165f,
2.181f, 5.316f, 3.453f, 0.547f, 7.143f,
2.171f, 5.340f, 3.378f, 0.547f, 7.169f};
printf("==============测试Carmack函数=====================\n");
for( i = 0; i < COUNTOF(measureValue); i++ )
{
printf("Source data is %-6.6f,\nCarmack's result is: %-6.6f,\nSystem's result is: %-6.6f\n",
measureValue[i], CarmackSqrt(measureValue[i]), sqrtf(measureValue[i]));
printf("\n");
}
printf("==============测试Carmack函数结束=================\n");
}
==============测试Carmack函数=====================
Source data is 2.132000,
Carmack's result is: 0.684867,
System's result is: 1.460137
Source data is 5.043000,
Carmack's result is: 0.445303,
System's result is: 2.245663
Source data is 4.563000,
Carmack's result is: 0.468139,
System's result is: 2.136118
Source data is 0.503000,
Carmack's result is: 1.409990,
System's result is: 0.709225
Source data is 7.223000,
Carmack's result is: 0.372084,
System's result is: 2.687564
Source data is 2.181000,
Carmack's result is: 0.677130,
System's result is: 1.476821
Source data is 5.247000,
Carmack's result is: 0.436561,
System's result is: 2.290633
Source data is 3.799000,
Carmack's result is: 0.513057,
System's result is: 1.949102
Source data is 0.536000,
Carmack's result is: 1.365896,
System's result is: 0.732120
Source data is 7.163000,
Carmack's result is: 0.373639,
System's result is: 2.676378
Source data is 2.152000,
Carmack's result is: 0.681677,
System's result is: 1.466970
Source data is 5.201000,
Carmack's result is: 0.438487,
System's result is: 2.280570
Source data is 3.912000,
Carmack's result is: 0.505592,
System's result is: 1.977878
Source data is 0.528000,
Carmack's result is: 1.376205,
System's result is: 0.726636
Source data is 7.189000,
Carmack's result is: 0.372963,
System's result is: 2.681231
Source data is 2.142000,
Carmack's result is: 0.683267,
System's result is: 1.463557
Source data is 5.178000,
Carmack's result is: 0.439460,
System's result is: 2.275522
Source data is 3.582000,
Carmack's result is: 0.528369,
System's result is: 1.892617
Source data is 0.528000,
Carmack's result is: 1.376205,
System's result is: 0.726636
Source data is 7.165000,
Carmack's result is: 0.373587,
System's result is: 2.676752
Source data is 2.181000,
Carmack's result is: 0.677130,
System's result is: 1.476821
Source data is 5.316000,
Carmack's result is: 0.433718,
System's result is: 2.305645
Source data is 3.453000,
Carmack's result is: 0.538148,
System's result is: 1.858225
Source data is 0.547000,
Carmack's result is: 1.352092,
System's result is: 0.739594
Source data is 7.143000,
Carmack's result is: 0.374162,
System's result is: 2.672639
Source data is 2.171000,
Carmack's result is: 0.678688,
System's result is: 1.473431
Source data is 5.340000,
Carmack's result is: 0.432742,
System's result is: 2.310844
Source data is 3.378000,
Carmack's result is: 0.544089,
System's result is: 1.837934
Source data is 0.547000,
Carmack's result is: 1.352092,
System's result is: 0.739594
Source data is 7.169000,
Carmack's result is: 0.373483,
System's result is: 2.677499
==============测试Carmack函数结束=================

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xf331785508 · 发表于 2015-1-23 16:44:41

呵呵，个人低级错误，返回值取倒就OK 了。

ecut · 发表于 2015-1-24 04:20:18

这是求isqrt not sqrt

John Carmack的sqrt函数为什么计算结果与系统库sqrt的结果不一致

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