How reliable are floating-point comparisons?

Floating-point numbers are the “black art” of computer programming. One reason why this is so is that there is no optimal way to represent an arbitrary number. The Institute of Electrical and Electronic Engineers (IEEE) has developed a standard for the representation of floating-point numbers, but you cannot guarantee that every machine you use will conform to the standard.

Even if your machine does conform to the standard, there are deeper issues. It can be shown mathematically that there are an infinite number of “real” numbers between any two numbers. For the computer to distinguish between two numbers, the bits that