Alan G Isaac wrote:
I am a user, not a numerics type, so this is undoubtedly a naive question.
Might the sin function be written to give greater accuracy for large real numbers? It seems that significant digits are in some sense being discarded needlessly.
Not really. The floating point representation of pi is not exact. The problem only gets worse when you multiply it with something. The method you showed of using % (2*pi) is only accurate when the values are created by multiplying the same pi by another value. Otherwise, it just introduces another source of error, I think.
This is one of the few places where a version of trig functions that directly operate on degrees are preferred. 360.0*n is exactly representable by floating point arithmetic until n~=12509998964918 (give or take a power of two). Doing % 360 can be done exactly.