[Beowulf] Optimized math routines/transcendentals

[Peter St. John]

I'm betting the answer to that will be "any" (i.e. "it depends").

In cryptography, we used to think of 128 bits for a PGP key as a lot, but
some folks have started using 4096 bits. Of course in exact arithmetic it's
much easier to deal with arbitrary precision than in quantitative analysis
of measurements with error intervals.

Peter

On Sat, Apr 30, 2016 at 3:09 PM, C Bergström <cbergstrom at pathscale.com>
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.john at 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 <
> meatheadmerlin at 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 <lindahl at 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
> >>>
> >>>
> >>>
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> >>
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