Bill Allombert on Tue, 30 Apr 2002 10:51:24 +0200 |
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Re: GP: ffinit() bug |
On Mon, Apr 29, 2002 at 10:48:55PM -0400, Michael Somos wrote: > Pari Developers, > Using the up-to-the-minute CVS I find : > > ? \v > GP/PARI CALCULATOR Version 2.2.3 (development) > UltraSparc (MicroSparc kernel) 32-bit version > (readline v2.2 enabled, extended help not available) > ? ffinit(4,2) > ^C *** user interrupt after 23,010 ms. > > which appears to be an infinite loop. Shalom, Michael 4 is not a prime number, so the behaviour of ffinit is undefined in this case. Maybe the doc is misleading, it is written F_p, and F_4 make sense, but it is universally agreed that p is a prime else we wrote F_q, I think. Testing the primality of p is not a option, since the new ffinit is much faster than ispseudoprime or even BSW_psp() for large p. ? p=2^521-1; ? install(BSW_psp,lG); ? BSW_psp(p); %2 = 1 ? ## *** last result computed in 30 ms. ? ffinit(p,10); ? ## *** last result computed in 0 ms. Fixing the oo-loop is a little difficult. The algorithm looks for a odd prime number l so that 4 is not a square modulo l. Of course it will never find it, but that give no information on the fact that 4 is not a prime, unless we use Lagarias-Odlyzko bound but this is not really practical. Cheers, Bill. PS: there is a CVS branch for the stable version named 'release-2-1-patches'. You can also check it out if you are interested.