Karim BELABAS on Mon, 6 Oct 2003 19:15:33 +0200 (MEST) |
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zetak |
I've just noticed that zetak gives bogus results in moderately high accuracy: (19:04) gp > \p300 (19:04) gp > precision( zetak(zetakinit(x^2-2),2.5), 28 ) %1 = 7.291915302409519060840727684 E182 (19:05) gp > \p28 (19:05) gp > zetak(zetakinit(x^2-2),2.5) %2 = 1.243482357570925192192537147 I don't see anything obvious like a stack corruption. It looks like a problem with the algorithm (coeff explosion + instability). Should be rewritten from scratch I'm afraid... The routine is already quite unable to handle inputs very close to integers, for obvious reasons this time (using the functional equation and trying to compute gamma values, with much less accurate output than apparently expected) (19:05) gp > \p28 (19:05) gp > zetak(zetakinit(x^2-2), 2 - 1e-80) *** division by zero in gdiv, gdivgs or ginv 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://www.parigp-home.de/ [PARI/GP]