Paul Koning wrote: > Scott> Yes, but within the defined mathematical ranges for sine and > Scott> cosine -- [0, 2 * PI) -- the processor intrinsics are quite > Scott> accurate. > > Huh? Sine and consine are mathematically defined for all finite > inputs.
Defined, yes. However, I'm speaking as a mathematician in this case, not a programmer. Pick up an trig book, and it will have a statement similar to this one, taken from a text (Trigonometry Demystified, Gibilisco, McGraw-Hill, 2003) randomly grabbed from the shelf next to me: "These trigonometric identities apply to angles in the *standard range* of 0 rad <= theta < 2 * PI rad. Angles outside the standard range are converted to values within the standard range by adding or subtracting the appropriate multiple of 2 * PI rad. You might hear of an angle with negative measurement or with a measure more than 2 * PI rad, but this can always be converted..." I can assure you that other texts (of which I have several) make similar statements. > Yes, normally the first step is to reduce the arguments to a small > range around zero and then do the series expansion after that, because > the series expansion convergest fastest near zero. But sin(100) is > certainly a valid call, even if not a common one. I *said* that such statements are outside the standard range of trigonometric identities. Writing sin(100) is not a matter of necessity, nor should people using "regular" math be penalized in speed or accuracy for extreme cases. ..Scott
