<div dir="ltr"><div><div class="gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div>On Wed, Aug 1, 2018, 16:12 Mark Abraham <mark.j.abraham at <a href="http://gmail.com">gmail.com</a>> wrote:</div><div><br></div><div>> It does sound like a generic hope, rather than one based on extensive</div><div>> understanding of how high performance MD codes work. :-) I don't mean to be</div><div>> negative, but MD codes are probably not the low hanging fruit for</div><div>> demonstrating the benefits of this approach.</div><div><br></div><div>It doesn't need to be low hanging fruit. We are building a custom supercomputer for this, </div><div>so we are interested how to speed up this workload.</div><div><br></div><div>In broad strokes, posits improve on IEEE float in reduced complexity, higher accuracy, </div><div>and adherence to associative and distributive laws of arithmetic. The latter is where</div><div>the reproducibility comes from.</div><div><br></div><div>The basic mechanism to produce reproducibility is by explicit management of rounding</div><div>events. In a posit system, we can accumulate the unrounded output of the adders</div><div>and multipliers and if you say, 1/sqrt(x) is important we can accumulate that unrounded too,</div><div>although we all know that is not quite a true statement when div is involved. </div><div><br></div><div>Our initial thought was that this mechanism to accumulate large number of arbitrary small</div><div>and large values without error could be used advantageously for the force field calculation.</div><div><br></div><div>Secondly, for forward/inverse transform calculations, this mechanism yields a pure identity</div><div>matrix, and our FFT/iFFT take advantage of this and suddenly 16-bit posits can compete</div><div>with 64-bit doubles.</div><div><br></div><div>If we need some education on how best to apply this to MM-style MDs, we are eager</div><div>to learn how best to apply this from GROMACS SMEs.</div><div><br><br></div></div></div></div></div></div></div></div></div></div></div>
</div>