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.