Karim BELABAS on Wed, 4 Sep 2002 23:31:35 +0200 (MEST) |
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Re: bug? |
On Wed, 28 Aug 2002, Paul van Wamelen wrote: > The following is strange but at least understandable: > > ? exp(10^-300) > %2 = 1.000000000000000000000000000 > ? %-1 > %3 = 1.000000000000000000000000000 E-300 > ? % - 10^-300 > %4 = 1.34971959 E-329 > > So exp of very small numbers are computed to large precision (I assume > because it is possible!) But then cos should work the same way, but it > doesn't: > > ? cos(10^-300) > %5 = 1.000000000000000000000000000 > ? %-1 > %6 = -4.999999999999999999708086868 E-601 > > well sort of, but that isn't .5 to relative precision 28. It looks worse > if you up the precision: > > ? default(realprecision,100) > realprecision = 105 significant digits (100 digits displayed) > ? cos(10^-300) - (1 - 10^-600/2) > %11 = > 2.91913131511413537189539175501010675755770891175910936852001807591773586414884430473814008517840 > E-620 > > Shouldn't this be about 10^-700? > > I'm using > GP/PARI CALCULATOR Version 2.1.1 (released) > UltraSparc (MicroSparc kernel) 32-bit version > (readline disabled, extended help available) > > but I believe this behaviour is VERY old. I have fixed this relatively recently [04/2002 says CVS. I had not yet decided to report as much as possible to pari-dev]: from CHANGES Done for version 2.2.3 (released 10/06/2002): 47- sin(1e-100) ---> 9.999999999999999999735998397 E-101 [ precision loss ] Since this involved changes to lots of functions, and the problem was not crucial [ nobody had complained for, say 15 years], I have not backported the patches to the stable version (and don't intend to). Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud Email: Karim.Belabas@math.u-psud.fr F-91405 Orsay (France) http://www.math.u-psud.fr/~belabas/ -- PARI/GP Home Page: http://www.parigp-home.de/