所以我刚刚发现了非常有趣的 Quake III 逆平方根 hack。在了解了它的工作原理之后，我决定对其进行测试。我发现只有在启用优化的情况下编译时，hack 才优于 math.h 1/sqrt(X)。
hack的实现：
float q_sqrt(float x) {
float x2 = x * 0.5F;
int i = *( int* )&x; // evil floating point bit hack
i = 0x5f3759df - (i >> 1); // what the fuck?
x = *( float* )&i;
x = x * ( 1.5F - ( (x2 * x * x) ) ); //1st iteration
//y = y * ( 1.5F - ( (x2 * y * y) ) ); //2nd iteration, can be removed
return x;
}
测试 1/sqrt(x) 与 q_sqrt(x) 相比的运行速度：
//qtest.c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
/*
Implementation of 1/sqrt(x) used in tue quake III game
*/
float q_sqrt(float x) {
float x2 = x * 0.5F;
int i = *( int* )&x; // evil floating point bit hack
i = 0x5f3759df - (i >> 1); // what the fuck?
x = *( float* )&i;
x = x * ( 1.5F - ( (x2 * x * x) ) ); //1st iteration
//y = y * ( 1.5F - ( (x2 * y * y) ) ); //2nd iteration, can be removed
return x;
}
int main(int argc, char *argv[]) {
struct timespec start, stop;
//Will work on floats in the range [0,100]
float maxn = 100;
//Work on 10000 random floats or as many as user provides
size_t num = 10000;
//Bogus
float ans = 0;
//Measure nanoseconds
size_t ns = 0;
if (argc > 1)
num = atoll(argv[1]);
if (num <= 0) return -1;
//Compute "num" random floats
float *vecs = malloc(num * sizeof(float));
if (!vecs) return -1;
for (int i = 0; i < num; i++)
vecs[i] = maxn * ( (float)rand() / (float)RAND_MAX );
fprintf(stderr, "Measuring 1/sqrt(x)\n");
clock_gettime( CLOCK_REALTIME, &start);
for (size_t i = 0; i < num; i++)
ans += 1 / sqrt(vecs[i]);
clock_gettime( CLOCK_REALTIME, &stop);
ns = ( stop.tv_sec - start.tv_sec ) * 1E9 + ( stop.tv_nsec - start.tv_nsec );
fprintf(stderr, "1/sqrt(x) took %.6f nanosecods\n", (double)ns/num );
fprintf(stderr, "Measuring q_sqrt(x)\n");
clock_gettime( CLOCK_REALTIME, &start);
for (size_t i = 0; i < num; i++)
ans += q_sqrt(vecs[i]);
clock_gettime( CLOCK_REALTIME, &stop);
ns = ( stop.tv_sec - start.tv_sec ) * 1E9 + ( stop.tv_nsec - start.tv_nsec );
fprintf(stderr, "q_sqrt(x) took %.6f nanosecods\n", (double)ns/num );
//Side by side
//for (size_t i = 0; i < num; i++)
// fprintf(stdout, "%.6f\t%.6f\n", 1/sqrt(vecs[i]),q_sqrt(vecs[i]));
free(vecs);
}
在我的系统（Ryzen 3700X）上，我得到：
gcc -Wall -pedantic -o qtest qtest.c -lm
./qtest
Measuring 1/sqrt(x)
1/sqrt(x) took 4.470000 nanosecods
Measuring q_sqrt(x)
q_sqrt(x) took 4.859000 nanosecods
gcc -Wall -pedantic -O1 -o qtest qtest.c -lm
./qtest
Measuring 1/sqrt(x)
1/sqrt(x) took 0.378000 nanosecods
Measuring q_sqrt(x)
q_sqrt(x) took 0.497000 nanosecods
gcc -Wall -pedantic -O2 -o qtest qtest.c -lm
qtest.c: In function ‘q_sqrt’:
qtest.c:11:14: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
11 | int i = *( int* )&x; // evil floating point bit hack
|
qtest.c:13:10: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
13 | x = *( float* )&i;
|
./qtest
Measuring 1/sqrt(x)
1/sqrt(x) took 0.500000 nanosecods
Measuring q_sqrt(x)
q_sqrt(x) took 0.002000 nanosecods
我的期望是 q_sqrt(x) 会比开箱即用的 1/sqrt(X) 更好。在阅读了更多内容之后，我现在知道要么 libm 得到了更好的优化，要么我的 CPU 配备了 sqrt(X) 的硬件解决方案。毕竟，自从快速逆根破解的发展以来，CPU 发生了突飞猛进的变化。
我不明白的是编译器会应用什么类型的优化来使它更快。当然，也许我的基准是错误的？
谢谢你的帮助！！