Re: Euler constant

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

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]