Approximate equality: Difference between revisions

This solution compares the normalized (i.e. between 0.5 and 1 on implementations which use binary floating point) significands of the floating point numbers, correcting each significand by half the difference in the exponents so that the corrected numbers used for comparison have the same difference in order of magnitude as the original numbers and are stable when the order of the arguments is changed. Unlike the metric of comparing the difference to some fraction of the numbers' size, this approach only requires a single floating point operation (the subtraction at the end), and more directly maps to the fundamental issue which leads to the need for floating-point comparisons, i.e. the limited precision of the significand.