Comparing floating point numbers in C

Also, one often overlooked features of floating point number are the denormalized numbers. That's numbers which have the minimal exponent, yet don't fit in the 0.5-1 range.

Those numbers are lower than FLT_MIN for float, and DBL_MIN for double.

A common mistake with using a threshold is to compare two values, or use FLT_MIN/DBL_MIN as limit.

For example, this would lead unlogical result (if you don't know about denormals):

bool areDifferent(float a, float b) {
    if (a == b) return false;  // Or also: if ((a - b) == FLT_MIN) 
    return true;
}


// What is the output of areDifferent(val, val + FLT_MIN * 0.5f) ?
// true, not false, even if adding half the "minimum value".

Denormals also usually implies a performance loss in computation. Yet, you can not disable them, else such code could still produce a DIVIDE BY ZERO floating point exception (if enabled):

float getInverse(float a, float b) {
    if (a != b)
        return 1.0f / (a-b); // With denormals disabled, a != b can be true, but (a - b) can still be denormals, it'll rounded to 0 and throw the exception
    return FLT_MAX;
}