I should have mentioned that when I said that most people/codes don't care about super-accurate range reduction, I was speaking from my various previous lives as a radio astronomer, numerical hydrodynamicist (is that even a word?), and I think it's true for the weather and climate codes that I've worked with. I've never seen a benchmark for a bid fail its error-check due to inaccurate range reduction.
I suspect the typical scientific programmer has no idea that there's an issue, and, has never tripped up on it either. It's typical for compilers to stick in non-glibc trig routines at higher optimization levels, and these non-glibc trig routines use stuff like SSE with naive range reduction. On Sun, May 01, 2016 at 03:09:07AM +0800, C Bergström wrote: > I was hoping for feedback, from scientists, about what level of > accuracy their codes or fields of study typically require. Maybe the > weekend wasn't the best time to post.. hmm.. > > On Sun, May 1, 2016 at 1:31 AM, Peter St. John <peter.st.j...@gmail.com> > wrote: > > A bit off the wall, and not much help for what you are doing now, but sooner > > or later we won't be hand-crating ruthlessly optimal code; we'll be training > > neural nets. You could do this now if you wanted: the objective function is > > just accurate answers (which you get from sub-optimal but mathematically > > correct existing code) and the wall clock (faster is better), and you train > > with the target hardware. So in principle it's easy, and if you look at how > > fast Deep Mind trained AlphaGo it begins to sound feasible to train for fast > > fourier transforms or whatever. > > Peter > > > > On Fri, Apr 29, 2016 at 9:06 PM, William Johnson <meatheadmer...@gmail.com> > > wrote: > >> > >> Due to the finite nature of number representation on computers, > >> any answer will be an approximation to some degree. > >> To me, it looks to be a non-issue to some 15 significant digits. > >> I would say it depends how accurate you need. > >> You could do long-hand general calculations that track percent error, > >> and see how it gets compounded in a particular series of calculations. > >> > >> If you got right into the nuts and bolts of writing optimized functions, > >> there are many clever ways to calculate common functions > >> that you can find in certain math or algorithms & data structures texts. > >> You would also need intimate knowledge of the target chipset. > >> But it seems that would be way too much time in > >> research and development to reinvent the wheel. > >> > >> > >> On Fri, Apr 29, 2016 at 7:28 PM, Greg Lindahl <lind...@pbm.com> wrote: > >>> > >>> On Sat, Apr 30, 2016 at 02:23:31AM +0800, C Bergström wrote: > >>> > >>> > Surprisingly, glibc does a pretty respectable job in terms of > >>> > accuracy, but alas it's certainly not the fastest. > >>> > >>> If you go look in the source comments I believe it says which paper's > >>> algorithm it is using... doing range reduction for sin(6e5) is > >>> expensive to do accurately. Which is why the x86 sin() hardware > >>> instruction does it inaccurately but quickly, and most people/codes > >>> don't care. > >>> > >>> -- greg > >>> > >>> > >>> > >>> _______________________________________________ > >>> Beowulf mailing list, Beowulf@beowulf.org sponsored by Penguin Computing > >>> To change your subscription (digest mode or unsubscribe) visit > >>> http://www.beowulf.org/mailman/listinfo/beowulf > >> > >> > >> > >> _______________________________________________ > >> Beowulf mailing list, Beowulf@beowulf.org sponsored by Penguin Computing > >> To change your subscription (digest mode or unsubscribe) visit > >> http://www.beowulf.org/mailman/listinfo/beowulf > >> > > > > > > _______________________________________________ > > Beowulf mailing list, Beowulf@beowulf.org sponsored by Penguin Computing > > To change your subscription (digest mode or unsubscribe) visit > > http://www.beowulf.org/mailman/listinfo/beowulf > > > _______________________________________________ > Beowulf mailing list, Beowulf@beowulf.org sponsored by Penguin Computing > To change your subscription (digest mode or unsubscribe) visit > http://www.beowulf.org/mailman/listinfo/beowulf _______________________________________________ Beowulf mailing list, Beowulf@beowulf.org sponsored by Penguin Computing To change your subscription (digest mode or unsubscribe) visit http://www.beowulf.org/mailman/listinfo/beowulf
