So I just discovered the very interesting Quake III inverse square root hack. After learning how it works and all, I decided to test it. I found that the hack only outperformed math.h 1/sqrt(X) when compiled with optimizations enabled.
The hack's implementation:
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;
}
To test how fast 1/sqrt(x) runs compared to q_sqrt(x):
//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);
}
On my system (Ryzen 3700X) I get:
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
My expectation was that q_sqrt(x) was going to work better than 1/sqrt(X) out of the box. After reading some more I now know that either libm is way better optimized or my CPU is equipped with a hardware solution for sqrt(X). After all, CPUs have changes by leaps and bounds since the development of the quick inverse root hack.
What I don't understand is what type of optimizations would the compiler be applying to make it so much faster. Of course maybe my benchmark is ill conceived?
Thanks for any help!!
