[Beowulf] Optimized math routines/transcendentals

[C Bergström]

I assume, possibly incorrectly, that scientists know what level of
tolerance/accuracy they need. While we can all dream about the futures
or past - the present day needs are useful to know. In general a
certain field may need A and another field will tolerate B...

I guess this is a NaN... if(signal/noise>0)


On Sun, May 1, 2016 at 3:29 AM, Peter St. John <peter.st.john at gmail.com> wrote:
> 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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