Karim BELABAS on Wed, 16 Apr 2003 18:35:52 +0200 (MEST) |
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Re: Euler constant |
On Fri, 11 Apr 2003, Klaus Brockhaus wrote: > I am using PARI/GP 2.0.17 for Windows. > > For realprecision = 32000 or higher, Euler leads to the message > " *** division by zero in R/S". > > For several reasons I became sceptical as to the reliability of the Euler value for higher realprecision, so I compared the digits produced by Pari for realprecision 25000 and the digits given by J. > Borwein, 170000 digits of Euler or > gamma constant: > < > http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap35.html > > > and found that from digit 19292 onward there is disagreement. Digits 19281 to 19300: > > 05228370342108957865 on the web page, > 05228370342566205373 by PARI. > > Can someone confirm this observation? Is it a known bug? There was an integer overflow in mpeuler. The problem is fixed in the CVS version [ agrees with chap35.html to 33000 decimals ]. It is still unacceptably slow for these operands size though. I'll try a trivial implementation of binary splitting for e.g Pi, and see whether the ratio improvement/effort is worth the trouble. It probably is... 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]