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

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

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.

Solution

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.