Karim BELABAS on Thu, 06 Nov 2003 20:46:50 +0100 |
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Re: Experimenting with the Alpha build. |
On Thu, 6 Nov 2003, Phil Carmody wrote: > I was wondering if -ffast-math would do to Pari/GP/GMP on the alpha. > The speed-ups weren't significant on the whole (I should have tried > -mno-ieee too perhaps) This is expected: there's almost no floating point code in PARI (everything is emulated using 'unsigned long' arithmetic). Might be considered a shortcoming. There are lots of variables of type 'double', but they are used in parts of the code which is negligible timewise. And never where stability / accuracy is important. I.e --fast-math should be a no-op with respect to performances or results. > and did cause just one test to fail: This component of the result is quite useless [ debugging output which has stuck here for the past 10 years or so... ]. It is actually computed from sqrt(disc) / PI, where PI is #define'd to 3.141592653589 which is probably computed "incorrectly" with --fast-math, e.g 1./ PI is presumably precomputed. Note: this value is converted to a t_REAL D, say, used in a trivial computation h / (L * D) where h is the class number and L is a very rough approximation of L(1, chi) (obtained through ulong arithmetic). This component should be relatively close to 1 ( certainly in [0.5, 1.5] ), and this is all we care about. Note that GP will never output a result where this parameter has a dubious value: it will restart the main relation loop instead, or recompute things properly to higher accuracy. Hence outputing it serves no purpose. I have just dumped this part of the result in CVS. Same goes for bnfinit, and a few other diagnostics which have cluttered outputs for no good reason ( bnfisprincipal / bnrisprincipal ). The minor backward incompatibility should not pose a problem, since I do not see any situation where this component would need to be accessed. Cheers, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathématiques, Bât. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]