If operator< works properly for floating-point types, why can't we use it for equality testing?

Question

Properly testing two floating-point numbers for equality is something that a lot of people, including me, don\'t fully understand. Today, however, I thought about how some s

Answer 1

The following code (which I changed so it compiles: Specifically the call to floateq was changed to floatcmp) prints out float->double vs double: 1 0 , not 0 0 (as one would expect when comparing those two values as floats).

#include 

bool floatcmp(float a, float b) {
    //check NaN
    return !(a < b) && !(b < a);
}

int main()
{
    std::cout << "float->double vs double: "
              << floatcmp(static_cast(0.7f), 0.7) << " "
              << (static_cast(0.7f) == 0.7) << "\n";
}

However what matters for the standard library is that operator< defines a strict weak ordering, which it in fact does for floating point types.

The problem with equality is that two values may look the same when rounded to say 4 or 6 places but are in fact totally different and compare as not equal.