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? If yes, then will post with an exp2 based fallback, if not, will post with a pow based fallback. Summary: Current patch 1. Accuracy: identical to old behavior on all platforms. 2. Speed: improve slightly (~30%) on GNU/Linux, identical to before on all other platforms. Thus a Pareto improvement. exp2 fallback 1. Accuracy: identical on GNU/Linux, regression on all other platforms (assuming their pow is correct), to the tune of relative error of 1e-13. 2. Speed: improve slightly (~30%) on GNU/Linux, improve drastically on platforms with exp2 (2-3x). Trades off significant speed gains for slight reduction in accuracy on most platforms. I favor the exp2 fallback, but decision left to others here. [...] _______________________________________________ ffmpeg-devel mailing list ffmpeg-devel@ffmpeg.org http://ffmpeg.org/mailman/listinfo/ffmpeg-devel
