Interesting , although I notice that this was before GMP 4.3.1 , which is where the asembler code for x64 got added , so the difference will be less now.
Noting future directions on how cpu's are going , it seems that their floating point units are going to get faster than their int units (consider the new AVX) , so even if the integer scheme is inherently more efficient , it may pay to use a floating point FFT Jason On Saturday 07 August 2010 23:02:34 Bill Hart wrote: > Ouch, this is going to prompt an "I told you so" from Richard Fateman. > > Gambit Scheme apparently multiplies large integers using a floating > point FFT based on proven error bounds from Colin Percival's paper. > The amazing thing is, this was/is implemented in Scheme, not in C and > assembly. (There are some interesting observations about this > approach, recorded for posterity from those in the integer FFT camp. > > :-) ) > > For those who don't know what my first sentence above is about, > Richard Fateman and I have had a *very* long off-list exchange about > multiplying large polynomials using the FFT, including the potential > use of the floating point FFT. I insisted that only in very special > situations could a floating point FFT be competitive with a modern > integer FFT (mainly on intel hardware for "medium sized" large > inputs). I'm now less certain of that. > > At least I did make the comment that a certain type of number > theoretic transform should be just as competitive, and I think I still > stand by that. An implementation will follow in due course. > > Bill. > > On 6 August 2010 13:18, Bill Hart <[email protected]> wrote: > > Wow, I just discovered something incredible. The Gambit Scheme > > compiler used to have *faster* bignum capabilities than GMP. > > > > And yes, I'm talking about actual bignums of millions of digits and by > > "used to", I mean recently, as in just before GMP 4.3.1 was released > > last year!! > > > > Now, I don't know whether they just mis-timed it or something. But > > they used to have a reproof of the "fastest bignnum library on the > > planet" on their website, until GMP beat them again. However I assume > > these guys know what they are talking about, as they mention a talk of > > Paul Zimmermann! > > > > And yes, it is now open source. > > > > So, until last year. Lisp was actually better than C for mathematics. > > > > Bill. > > > > On 6 August 2010 12:01, Harald Schilly <[email protected]> wrote: > >> On Aug 6, 6:17 am, Nils Bruin <[email protected]> wrote: > >>> Python has an > >>> extension module for (labelled!) gotos ... > >> > >> wow, interesting. but it makes perfect sense ... python defers the > >> parsing and execution of each line to the last possible moment > >> (calling undefined functions in dead code does not hurt) and since > >> while and for loops are the civilized version of gotos, why not ;) > >> > >> h > >> > >> -- > >> You received this message because you are subscribed to the Google > >> Groups "sage-flame" group. To post to this group, send email to > >> [email protected]. To unsubscribe from this group, send email > >> to [email protected]. For more options, visit > >> this group at http://groups.google.com/group/sage-flame?hl=en. -- You received this message because you are subscribed to the Google Groups "mpir-devel" group. To post to this group, send email to [email protected]. 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.
