I was a member of the IEEE-754 committee, I’ll try to help clarify things a bit. First off, floating-point numbers are not real numbers, and floating-point arithmetic does not satisfy the axioms of real arithmetic. Trichotomy is not the only property of real arithmetic that does not hold for floats, nor even the most important. … Read more
There are basically two major pitfalls people stumble in with floating-point numbers. The problem of scale. Each FP number has an exponent which determines the overall “scale” of the number so you can represent either really small values or really larges ones, though the number of digits you can devote for that is limited. Adding … Read more
Because floats and doubles cannot accurately represent the base 10 multiples that we use for money. This issue isn’t just for Java, it’s for any programming language that uses base 2 floating-point types. In base 10, you can write 10.25 as 1025 * 10-2 (an integer times a power of 10). IEEE-754 floating-point numbers are … Read more
In most programming languages, floating point numbers are represented a lot like scientific notation: with an exponent and a mantissa (also called the significand). A very simple number, say 9.2, is actually this fraction: 5179139571476070 * 2 -49 Where the exponent is -49 and the mantissa is 5179139571476070. The reason it is impossible to represent … Read more