Comparation of sum of square roots

Question

I have MinGW GCC 4.8.1 and the following code:

#include <iostream>
#include <cmath>

double eval(int a, int b){
    return std::sqrt(a) + std::sqrt(b);
}

int main(){
    double first = eval(545, 331);
    double second = eval(545, 331);

    if(first < second)
        std::cout << "first <  second" << std::endl;
    if(first == second)
        std::cout << "first == second" << std::endl;
    if(first > second)
        std::cout << "first >  second" << std::endl;
}

If compiled with -O0, the program prints the expected result:

first == second

However, if compiled with -O1, -O2 or -O3, the program prints: (the result on ideone)

first <  second
first == second

Why? How to fix it?

Answer 1

In x86 Architectures the precision of floating point is 80-bit but a double has only 64-bit. And with GCC Optimization evaluating an expression resulting a floating number and storing it on a double can result different values since the optimization changes how the floating number get adjusted to less precision.

To get the same result with different GCC Otimizations use -ffloat-store option.