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.
