Hi, On Tue, Dec 22, 2015 at 12:48 PM, Ganesh Ajjanagadde <gajja...@mit.edu> wrote:
> On Tue, Dec 22, 2015 at 8:04 AM, Ganesh Ajjanagadde <gajja...@mit.edu> > wrote: > > On Tue, Dec 22, 2015 at 3:35 AM, Michael Niedermayer > > <mich...@niedermayer.cc> wrote: > [...] > >> > >> IMHO a exp10 fallback should be implemented using exp2() if that is > faster > >> and available. > > > > I don't know whether the fallback should use exp or exp2, need to > > check which is faster. And if we fallback to exp or exp2, it will turn > > out that the fallback is significantly faster than the actual libm > > function (as demonstrated above, like erf), nothing wrong with that, > > just is somewhat strange. > > > >> > >> Code requiring absolute accuracy must be written using integers as C > >> does not gurantee accuracy for float and double. > >> A single libc or fallback providing more accuracy does not really help > >> as our code must function correctly in the absence of such accuracy > >> also the accuracy difference between exp2() and pow() should be > >> negligible > > > > A lot of our floating point code assumes IEEE-754, which has > > reasonably well defined semantics. Anyway, as a general statement, I > > agree. > > > > For a proper libm, exp2(x) and pow(2, x) should be identical. I guess > > what you are referring to is exp2(log2(10)*x) vs pow(10, x). In this > > case, I don't know how bad the difference is; I suspect it to be more > > than 1 ulp in some cases. > > Definitely way more than 1 ulp. Looks like exp2 fallback is the way to go: > 1. speed: it is approximately 25% faster on GNU libm, even faster on > BSD/Mac OS X and other libm's due to a table lookup approach. > 2. accuracy: it is marginally better. Measurement was via 3e8 points > spaced evenly from -310 to 310, maximum relative error is 1.7e-13 vs > 1.8e-13. For values in the 64 bit range (roughly 10^0 to 10^20), error > is around 7.5e-15. Basically errors are amplified at very small and > very large values which is intuitively clear. In fact, that is exactly > what GNU libm does: splits the exponent into a main term and a > correction term, computes exp twice, and then multiplies the two > together. > > Really, I guess the question is: > are people ok with this accuracy loss on non GNU/Linux? I think "yes". You'd use M_LOG2_10 instead of log2(10), right? Ronald _______________________________________________ ffmpeg-devel mailing list ffmpeg-devel@ffmpeg.org http://ffmpeg.org/mailman/listinfo/ffmpeg-devel
