Search for the comment that begins "OK kiddies, time for the pros...." in http://stackoverflow.com/questions/2284860/how-does-c-compute-sin-and-other-math-functions
John On Saturday, October 17, 2015 at 9:00:35 AM UTC-4, John Gibson wrote: > > Why are you trying to roll your own sin(x) function? I think you will be > hard pressed to improve on the library sin(x) in either speed or accuracy. > > John > > On Saturday, October 17, 2015 at 3:38:17 AM UTC-4, Jeffrey Sarnoff wrote: >> >> I had tried to find a clean way to jump into the taylor series using the >> well approximated sin(x) or cos(x) and so additionally limit the terms used >> -- there may be / probably is a way in concert with an additional >> tabulation (which would be fine in this case). Taylor's theorem is not >> numerically crisp, so while I can identify the next term (using, perhaps >> eps(sin(x))/3) I don't know how to back out the delta between accumulation >> of the series to the prior term and the value sin(x::Float64). >> >> On Saturday, October 17, 2015 at 3:29:28 AM UTC-4, Jeffrey Sarnoff wrote: >>> >>> That has promise, Kristoffer. I did port something of that nature, >>> expecting it to work well -- but there was some numerical mush in more than >>> a couple of trailing bits in some cases. >>> Using more terms did not help. Thinking about it just now, it might be >>> more robustly stable if I expand in one direction only upfrom or downfrom >>> some pretabulated points. >>> >>> On Saturday, October 17, 2015 at 2:47:57 AM UTC-4, Kristoffer Carlsson >>> wrote: >>>> >>>> Use a truncated Taylor series around the point maybe? >>> >>>
