Which is more efficient for sines and cosines? Sin and Cos or Sin and Sqrt?

Question

Unfortunately, the standard C++ library doesn't have a single call for sincos, which gives a place for this question.

First question:

If I want to calculate a sin and a cos, is it cheaper to calculate a sin and a cos, or calculate a sin then a sqrt(1-sin^2) to get the cos?

Second question:

The intel math kernel library provides very good functions for standard mathematical functions calculations, so a function vdSinCos() exists to solve the problem in a very optimized way, but the intel compiler isn't for free. Is there any open source library (C, C++, Fortran) available in linux distributions that would have those functions where I can simply link to them and have the optimum implementations?

Note: I wouldn't like to go into instruction calls, since they're not supported by all CPUs. I would like to link to a general library that would do the job for me on any CPU.

Thanks.

Answer 1

The GNU C library has a sincos() function, which will take advantage of the "FSINCOS" instruction which most modern instruction sets have. I'd say that's your best bet; it should be just as fast as the Intel library method.

If you don't do that, I'd go with the "sqrt(1-sin(x)^2)" route. In every processor architecture document I've looked at so far, the FSQRT instruction is significantly faster than the FSIN function.

Answer 2

The answer to almost every performance problem is "why don't you measure it in your code", because there are a large number of different factors that affect the performance of almost any calculation like this. For example, "Who produces the math functions". Square root is relatively simple to calculate, but I'm not convinced it's a huge difference between sqrt(1-sin*sin) and calculating cos again. What processor may also be a factor, and what other calculations are done "around" the sin/cos calculations.

I wouldn't be surprised if there is a library around somewhere that has this sort of function, but I haven't been looking.

Answer 3

If precision is not critical the fastest way to get sin or cos is to use tables. Hold some global const array with sin and cos values for all agles with a step you need. So your sin/cos function just need to cast angle to index and you get the result.