Re: Radians Or Degrees?

MitchAlsup1 wrote:

And thirdly::
 Let us postulate that the reduced argument r is indeed calculated with 0.5ULP
error.
 What makes you think you can calculate the polynomial without introducing
any more error ??

It should be obvious that any argument reduction step must return a value with significantly higher precision than the input(s), and that this higher precision value is then used in any polynomial evaluation.
With careful setup, it is very often possible to reduce the amount of extended-procision work needed to just one or two steps, i.e. for the classic Taylor sin(x) series, with x fairly small, the x^3 and higher terms can make do with double precision, so that the final step is to add the two parts of the leading x term: First the trailing part and then when adding the upper 53 bits of x you get a single rounding at this stage.
This is easier and better when done with 64-bit fixed-point values, augemented with a few 128-bit operations.
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"