Just one physical oceanographer might need very different precision for a 3-day forecast of currents than for a one-day forecast. I suspect that precision needs will vary even within a lab, much less within a field much less between fields. In the cryptography example, precision is proportional to security needs, and that always depends on specific applications. I don't want to waste bandwidth using HTTPS to connect to Facebook, myself, but I might have to use 4096-bit PGP to administer my secret Cayman Islands money-laundering account that the IRS doesn't know about. Oops. Peter
On Sat, Apr 30, 2016 at 3:37 PM, C Bergström <cbergst...@pathscale.com> wrote: > 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.j...@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 <cbergst...@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.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 > >> > > > > > >
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