Dan Bron wrote: >>while it's relatively simple to make integers arbitrarily large, >>floating point is a much more difficult proposition: > > I know, rationally, that this is true. But intuitively it's always struck > a sour note. A floating point number is just an integer with a dot in the > middle. Why is it such a different beast? >
To mention a few differences: - Computer integers exactly represent mathematical integers, within limits: floating-point numbers represent almost no real numbers exactly. - Integer arithmetic is exact, floating-point arithmetic is not. - Figuring out how to calculate mathematical functions accurate to 1 ulp is not easy: for example. no-one knows how many guard digits are needed to calculate x^y over the full range of floating-point numbers. - Neglecting overflow, integer addition and multiplication mirror their mathematical counterparts. Floating-point addition is not commutative and associative. - It is nontrivial to devise algorithms that give acceptably accurate results reasonably quickly while working to a fixed maximum precision. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
