On Wed, 26 Sep 2007, ok wrote:
[Concerning the fact that fmod(x,y) = -fmod(-x,y)] I wrote:
Interesting, perhaps. Surprising, no. fmod() is basically there for the sake of sin(), cos(), and tan() (or any other periodic and either symmetric or antisymmetric function).
On 25 Sep 2007, at 8:58 pm, Henning Thielemann wrote:
Why is this particular behaviour useful in connection with trigonometric functions?
Range reduction. sin(x) = sin(fmod(x, M_TWOPI)).
Whether that is the *best* way to handle range reduction is another matter.
This would work with any reasonable definition of fmod, not only with the one, where fmod(-1, M_TWOPI) = -1. I still think that this particular definition is disadvantageous. Say, you want to implement a periodic function and you want to implement the core computation only for the smallest necessary range (say because of fast convergence), then with fmod(x, M_TWOPI) you have to add another case splitting, or you must implement it for the range (-M_TWOPI, M_TWOPI). If fmod(x,y) would generate the same sign as y, you had 0 <= fmod(x, M_TWOPI) < M_TWOPI.