Re: Radians Or Degrees?

MitchAlsup1 wrote:

Stefan Monnier wrote:

IIUC that was not the case before their work: it was "easy" to get the
correct result in 99% of the cases, but covering all 100% of the cases
used to be costly because those few cases needed a lot more
internal precision.

 Muller indicates one typically need 2×n+6 to 2×n+12 bits to get correct
roundings 100% of the time. FP128 only has 2×n+3 and is insufficient by
itself.

I agree with everything else you've written about this subject, but afair, fp128 is using 1:15:112 while double is of course 1:10:53.
On the one hand, 53*2+6 -> 112, on the other hand (if we include the hidden bits) we get 54*2+5 -> 113.
So significantly more than 2n+3 but not enough on its own to guarantee correct rounding.
As Michael S have mentioned, we want these algorithms to work for vector/SIMD calculations, and at that point both lookup tables and widening the size of the temporaries are very costly.
Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"