<div dir="ltr">If by 128b floats, you mean IEEE754 quad precision implemented in SW, then the associated dot product will run ~50x slower on conventional hardware (that is, hardware that does not support QP).<div><br></div><div>It should be possible to implement DDP or some form of compensated summation more efficiently.<br><div><br></div><div>Jeff<br><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Jul 31, 2015 at 4:18 PM, Brian Van Straalen <span dir="ltr"><<a href="mailto:bvstraalen@lbl.gov" target="_blank">bvstraalen@lbl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word"><div><br></div><div>I would think that we could probably implement a reproducible dot product in the krylov code since it only happens on the coarse grid which should be small enough.</div><div><br></div><div>HPGMG uses max norms, so we should be ok for that part.</div><span class="HOEnZb"><font color="#888888"><div><br></div><div>Brian</div></font></span><div><div class="h5"><div><br></div><br><div><blockquote type="cite"><div>On Jul 31, 2015, at 3:27 PM, Hoemmen, Mark <<a href="mailto:mhoemme@sandia.gov" target="_blank">mhoemme@sandia.gov</a>> wrote:</div><br><div><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">On 7/31/15, 3:45 PM, "Jed Brown" <</span><a href="mailto:jed@jedbrown.org" style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px" target="_blank">jed@jedbrown.org</a><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">> wrote:</span><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><blockquote type="cite" style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">Brian Van Straalen <<a href="mailto:bvstraalen@lbl.gov" target="_blank">bvstraalen@lbl.gov</a>> writes:<br><blockquote type="cite">The concern is not trivial.  I¹ve spent some time re-reading<br>Precimonious paper (<a href="http://eecs.berkeley.edu/~rubio/includes/sc13.pdf" target="_blank">eecs.berkeley.edu/~rubio/includes/sc13.pdf</a><br><<a href="http://eecs.berkeley.edu/~rubio/includes/sc13.pdf" target="_blank">http://eecs.berkeley.edu/~rubio/includes/sc13.pdf</a>>) and I realize<br>that it would not be hard to make a faster version of FMG using mixed<br>precision.  <br></blockquote><br>Just a quick comment now.  I think there's not as much fat to trim as<br>you think.  In general, the precision needs to be as accurate as the<br>discretization.  Most flops occur on fine grids where the discretization<br>is more accurate than single precision.  I challenge you to speed up<br>HPGMG by more than, say, 15%, while maintaining order of accuracy on<br>fine grids.<br><br><blockquote type="cite">There have been papers over the last few years using 4-byte AMG as a<br>preconditioner<span> </span><br></blockquote><br>So much fat already.  Then you have a Krylov method and full-accuracy<br>residuals, but HPGMG solves in the cost of a few residual evaluations.<br>Also, these low-accuracy preconditioners are usually used for problems<br>that are only modestly ill-conditioned.  Try it with an operator with<br>condition number 10^{12} like you see in solid mechanics or geodynamics<br>and it doesn't look so hot any more.<br></blockquote><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">It could be fun to use such a tool to find out the best places to put</span><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">128-bit floating-point arithmetic.  That could help with some really hard</span><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">problems, or at least avoid some reproducibility issues.</span><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><br style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span style="font-family:Helvetica;font-size:14px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">mfh</span></div></blockquote></div><br></div></div><span class=""><div>
<span style="border-collapse:separate;color:rgb(0,0,0);font-family:Helvetica;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:auto;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><div><div><font face="'Courier New'">Brian Van Straalen         Lawrence Berkeley Lab</font></div><div><font face="'Courier New'"><a href="mailto:BVStraalen@lbl.gov" target="_blank">BVStraalen@lbl.gov</a>         Computational Research</font></div><div><font face="'Courier New'">(510) 486-4976             Division (<a href="http://crd.lbl.gov" target="_blank">crd.lbl.gov</a>)</font></div></div><div><br></div><div><br></div></span><br>
</div>
<br></span></div><br>_______________________________________________<br>
HPGMG-Forum mailing list<br>
<a href="mailto:HPGMG-Forum@hpgmg.org">HPGMG-Forum@hpgmg.org</a><br>
<a href="https://hpgmg.org/lists/listinfo/hpgmg-forum" rel="noreferrer" target="_blank">https://hpgmg.org/lists/listinfo/hpgmg-forum</a><br>
<br></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature">Jeff Hammond<br><a href="mailto:jeff.science@gmail.com" target="_blank">jeff.science@gmail.com</a><br><a href="http://jeffhammond.github.io/" target="_blank">http://jeffhammond.github.io/</a></div>
</div></div></div></div>