The Zimmermann et al FFT takes us to about 65881 in the bench scores and 11419 overall.
That is totally untuned however. With correct tuning I am sure it makes a bigger difference. Bill. 2008/11/26 Bill Hart <[EMAIL PROTECTED]>: > Actually it wouldn't be a completely trivial merge. There is no tuning > code in the package. We'd have to write that. Not that this should be > hard. There is only prebuilt tuning files for K7 and Pentium 4 or > something like that. > > Bill. > > 2008/11/26 Bill Hart <[EMAIL PROTECTED]>: >> Cool! >> >> Paul Zimmermann, Pierrick Gaudry and Alexander Krupka (and possibly >> also Torbjorn Granlund) worked on a new FFT for GMP. It is comparable >> with the one in FLINT and uses Fermat numbers and Mersenne numbers I >> think. >> >> Also I think Torbjorn Granlund and Alexander Krupka worked on an FFT >> (perhaps a small prime FFT?) which is fast for very large operands. I >> have never seen the code or performance figures so I don't know all >> that much about this. I might just have this mixed up with the >> Zimmermann one. >> >> There is an improved fft patch on the gmp website which appears to be >> written by Paul Zimmermann, but it contains the following lines: >> >> "TODO: >> >> Implement some of the tricks published at ISSAC'2007 by Gaudry, Kruppa, and >> Zimmermann." >> >> The patch has also been relicensed GPL v3+ which is odd considering >> that wasn't around in 2007 and there is no indication of changes to >> the patch since then. >> >> There are plans to dramatically improve the FFT in eMPIRe. But we need >> to discuss the best strategy for that. Licensing is an issue. >> >> Looking at Paul Zimmermann's website there is an fft-mul patch which >> claims to be up to 2 times faster than the fft distributed with GMP. >> This appears to have been written by TG, PZ, AK and PG. >> >> We could just plug that straight in to eMPIRe. It is licensed LGPL >> v2.1+ and wouldn't need merging. I very much doubt Paul would change >> the license on that, but I've retrieved a version under LGPL v2.1+ >> anyhow. >> >> I know the FLINT one is faster again for small operands and >> occasionally for larger operands, but there is so much work to merge >> it, and it would be GPL only that I think we should avoid wasting our >> time for now. The original idea was for the Zimmermann et al FFT to >> end up in GMP and the FLINT one to end up in eMPIRe, but now I think >> we could save ourselves a lot of work by just using the Zimmermann et >> al one. >> >> Almost certainly we could improve the Zimmermann et al FFT using some >> of the tricks from FLINT. >> >> What does everyone think? >> >> Bill. >> >> 2008/11/26 <[EMAIL PROTECTED]>: >>> >>> On Wednesday 26 November 2008 18:12:15 Bill Hart wrote: >>>> 2008/11/26 <[EMAIL PROTECTED]>: >>>> > On Wednesday 26 November 2008 17:27:59 Bill Hart wrote: >>>> >> Brian and I have been having an interesting discussion off list about >>>> >> the preliminary GMP 4.3 figures posted here: >>>> >> >>>> >> http://gmplib.org/gmpbench.html >>>> >> >>>> >> Note that on a 2.6 GHz Opteron we would score about 11175 with about >>>> >> 60950 in the multiply bench. Note unbalanced operands are not relevant >>>> >> here (gmpbench multiply test only works with balanced operands). >>>> >> >>>> >> It will be interesting to see how much improvement we get from the new >>>> >> mul_1 and addmul_1. >>>> >> >>>> >> Any ideas about how we can further improve would be most welcome. >>>> > >>>> > from my gmpextra-1.0.1/changes >>>> > error mpn_newmul_n got thresholds backwards >>>> >>>> Are you saying the new code caused an error? If so, that is not >>>> surprising. It only works for n = 0 mod 4 and needs the prologue and >>>> epilogue changed to make it work in general. I modified the timing >>>> code you sent me to time it for n = 0 mod 4. >>>> >>>> > can give 3-20% on fft-sizes >>>> >>>> Or are you saying code of yours will improve fft multiplication. >>>> >>> >>> Yes , and no >>> I calculate x*y mod 2^k-1 , whereas GMP-fft uses x*y mod 2^k+1 >>> with k a high power of two , and my mod-1 is faster than gmp-mod+1 for a >>> reasonable range of sizes. The "error" was in the thresholds I calculated , >>> I >>> entered the decision logic backwards. >>> At the moment its faster at about 8k limbs to 100k limbs , although it's >>> very >>> uneven (and slower in places). >>> >>> >>>> In another one of my projects (FLINT) there exists FFT integer >>>> multiplication code written by David Harvey and myself which will give >>>> up to a factor of 2 improvement on FFT sizes. But it needs to be >>>> rewritten to merge with eMPIRe. Also it is GPL not LGPL and I can't >>>> (and probably don't want) to do anything about that. For now we don't >>>> have a GPL version of eMPIRe, and such code would probably not be >>>> helpful at this time. >>>> >>>> I've also been working with Gonzalo Tornaria on code which will >>>> multiply absolutely HUGE integers (well beyond what the current FFT's >>>> will do). But that won't get completed for another couple of months >>>> and will again need merging, which will be a non-trivial job. Again it >>>> relies on GPL'd code. >>>> >>>> Bill. >>>> >>>> >> Hmm, I wonder if they put new fft code in. That would certainly do the >>>> >> trick!! I think I see how they could have gotten this much improvement >>>> >> without improving the fft, but by my calculations it would be tight. >>>> >> >>>> >> Bill. >>>> >> >>>> >> 2008/11/26 Bill Hart <[EMAIL PROTECTED]>: >>>> >> > I should also add the following. >>>> >> > >>>> >> > In the case of addmul_1, I don't think the oOo hardware is relevant. >>>> >> > The Opteron has three sets of 8 reservation stations and essentially >>>> >> > it just executes what it can. That's pretty simple oOo logic. >>>> >> > >>>> >> > It can happen that an entire 8 reservation stations become full with >>>> >> > dependent instructions. But that is not an issue with mul_1 or >>>> >> > addmul_1. There are only 30 macro-ops in the whole loop, so nearly the >>>> >> > whole loop is in reservation stations at any one time. >>>> >> > >>>> >> > Instead the issue is that all the muls need to be executed by ALU0 >>>> >> > (there is only 64 bit multiply hardware attached to ALU0). The problem >>>> >> > then is that too much might be put in the 8 reservation stations for >>>> >> > ALU0. The hardware which chooses which of the three "pipelines" or >>>> >> > sets of 8 reservation stations that a macro-op goes into is called the >>>> >> > pick hardware. I have thus far been unable to find a description of >>>> >> > how it chooses which pipe to stick macro-ops into. >>>> >> > >>>> >> > One big drawback of the K8 is that once in a pipe, other pipes cannot >>>> >> > steal work from that pipe, even if they are doing nothing and there >>>> >> > are independent instructions to be executed queueing in another pipe. >>>> >> > >>>> >> > So the only relevant piece of hardware here is the pick hardware. >>>> >> > >>>> >> > As I say, ptlsim would give us a definitive answer, if it could be >>>> >> > make to work. >>>> >> > >>>> >> > Bill. >>>> >> > >>>> >> > 2008/11/26 Bill Hart <[EMAIL PROTECTED]>: >>>> >> >> Ah, this probably won't make that much difference to pverall >>>> >> >> performance. Here is why: >>>> >> >> >>>> >> >> In rearranging the instructions in this way we have had to mix up the >>>> >> >> instructions in an unrolled loop. That means that one can't just jump >>>> >> >> into the loop at the required spot as before. The wind up and wind >>>> >> >> down code needs to be made more complex. This is fine, but it >>>> >> >> possibly adds a few cycles for small sizes. >>>> >> >> >>>> >> >> Large mul_1's and addmul_1's are never used by GMP for mul_n. Recall >>>> >> >> that mul_basecase switches over to Karatsuba after about 30 limbs on >>>> >> >> the Opteron. >>>> >> >> >>>> >> >> But it also probably takes a number of iterations of the loop before >>>> >> >> the hardware settles into a pattern. The data cache hardware needs to >>>> >> >> prime, the branch prediction needs to prime, the instruction cache >>>> >> >> needs to prime and the actual picking of instructions in the correct >>>> >> >> order does not necessarily happen on the first iteration of the loop. >>>> >> >> >>>> >> >> I might be overstating the case a little. Perhaps by about 8 limbs >>>> >> >> you win, I don't know. >>>> >> >> >>>> >> >> Anyhow, I believe jason (not Martin) is working on getting fully >>>> >> >> working mul_1 and addmul_1 ready for inclusion into eMPIRe. Since he >>>> >> >> has actually done all the really hard work here with the initial >>>> >> >> scheduling to get down to 2.75 c/l, I'll let him post any performance >>>> >> >> figures once he is done with the code. He deserves the credit! >>>> >> >> >>>> >> >> Bill. >>>> >> >> >>>> >> >> 2008/11/26 mabshoff <[EMAIL PROTECTED]>: >>>> >> >>> On Nov 26, 6:18 am, Bill Hart <[EMAIL PROTECTED]> wrote: >>>> >> >>>> Some other things I forgot to mention: >>>> >> >>>> >>>> >> >>>> 1) It probably wouldn't have been possible for me to get 2.5c/l >>>> >> >>>> without jason's code, in both the mul_1 and addmul_1 cases. >>>> >> >>>> >>>> >> >>> :) >>>> >> >>>> >>>> >> >>>> 2) You can often insert nops with lone or pair instructions which >>>> >> >>>> are not 3 macro ops together, further proving that the above >>>> >> >>>> analysis is correct. >>>> >> >>>> >>>> >> >>>> 3) The addmul_1 code I get is very close to the code obtained by >>>> >> >>>> someone else through independent means, so I won't post it here. >>>> >> >>>> Once the above tricks have been validated on other code, I'll >>>> >> >>>> commit the addmul_1 code I have to the repo. Or perhaps someone >>>> >> >>>> else will rediscover it from what I have written above. >>>> >> >>>> >>>> >> >>>> In fact I was only able to find about 16 different versions of >>>> >> >>>> addmul_1 that run in 2.5c/l all of which look very much like the >>>> >> >>>> solution obtained independently. The order and location of most >>>> >> >>>> instructions is fixed by the dual requirements of having triplets >>>> >> >>>> of macro-ops and having almost nothing run in ALU0 other than muls. >>>> >> >>>> There are very few degrees of freedom. >>>> >> >>>> >>>> >> >>>> Bill. >>>> >> >>> >>>> >> >>> This is very, very cool and I am happy that this is discussed in >>>> >> >>> public. Any chance to see some performance numbers before and after >>>> >> >>> the checkin? >>>> >> >>> >>>> >> >>> <SNIP> >>>> >> >>> >>>> >> >>> Cheers, >>>> >> >>> >>>> >> >>> Michael >>>> >>>> >>> >>> >>> >>> >>> >> > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "mpir-devel" group. To post to this group, send email to mpir-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/mpir-devel?hl=en -~----------~----~----~----~------~----~------~--~---
