Why doesn't g++ -O3 change division to multiplication? - c++

Question

I thought g++ -O3 will change division to multiplication automatically. But accroding to this code:
#include <iostream>
#include <sys/time.h>
double compute0(int i) {
double d_2 = i * i;
double ret = 0;
for (int j = 0; j < 1000000; j++) {
ret += j;
}
return ret;
}
double compute1(int i) {
double d_2 = i * i;
double ret = 0;
for (int j = 0; j < 1000000; j++) {
ret += j / d_2;
}
return ret;
}
double compute2(int i) {
double d_2 = i * i;
double d_2_inv = 1.0 / d_2;
double ret = 0;
for (int j = 0; j < 1000000; j++) {
ret += j * d_2_inv;
}
return ret;
}
double tik() {
struct timeval tv;
gettimeofday(&tv, NULL);
return tv.tv_sec + tv.tv_usec * 1e-6;
}
int main() {
{
double begin = tik();
double ret = 0;
for(int i = 1; i < 100; i++)
ret += compute0(i);
double end = tik();
std::cout << "cost time: " << end - begin << " ret: " << ret << std::endl;
}
{
double begin = tik();
double ret = 0;
for(int i = 1; i < 100; i++)
ret += compute1(i);
double end = tik();
std::cout << "cost time: " << end - begin << " ret: " << ret << std::endl;
}
{
double begin = tik();
double ret = 0;
for(int i = 1; i < 100; i++)
ret += compute2(i);
double end = tik();
std::cout << "cost time: " << end - begin << " ret: " << ret << std::endl;
}
return 0;
}
the output is :
cost time: 0.105436 ret: 4.95e+13
cost time: 0.453676 ret: 8.17441e+11
cost time: 0.203873 ret: 8.17441e+11
WHY?

Answer 1

Compilers usually try to follow IEEE754. In this standard, division is defined exactly. It means, that for every a/b, there is a bit-exact answer. If one modifies this into a*(1/b), result may differ a little bit (you might see this effect, if you print your doubles with 16 significant digits)
Compilers usually have an option to relax this. GCC has -ffast-math, VC has /fp:fast.