On Sat, 10 Nov 2007, Daniel Fischer wrote:
Since you seem to know a lot about these things, out of curiosity, do you know how these functions are actually implemented? Do they use Taylor series or other techniques?
I think that for sin and cos the Taylor series are a good choice. For other functions like the square root, exponential, logarithm, inverse trigonometric functions the CORDIC algorithms are to be prefered. They are like a division, both in the idea and the speed. http://en.wikipedia.org/wiki/CORDIC E.g. exp(x1+x2+x3+...+xn) = exp(x1) * exp(x2) * ... * exp(xn) now you choose x1, x2, ..., xn such that exp(xi) is a number that allows a simple multiplication. x1 = ln(1.1 bin) x2 = ln(1.01 bin) x3 = ln(1.001 bin) Multiplying with xi is just a shift and a sum. You only need to precompute and store the xi.