Karim BELABAS on Fri, 4 Oct 2002 22:11:56 +0200 (MEST)


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Re: bug in pari-gp precision? (fwd)


On Fri, 4 Oct 2002, Karim BELABAS wrote:
>  ? 1. + 10^-50 - 1.
>  %2 = -2.52435489 E-29
>
> What is happening here?

Short diagnostic: here's the computation chain

  1. + 10^-50 = (a + 1) / 10^50  \\ with a = 1. * 10^50
              = a / 10^50        \\ + 1 neglected, not significant at \p28

Culprit: a = 1. * 10^50 is computed "incorrectly", so that (a / 10^50) < 1

(15:44) gp > \p38
   realprecision = 38 significant digits
(15:44) gp > 1.*10^50;
(15:44) gp > \x
[...] a5880a69  fb6ac800

(15:42) gp > \p28
   realprecision = 28 significant digits
(15:43) gp > 1.*10^50;
(15:43) gp > \x
[...] a5880a69
            ^^ should be 6a (1 bit off).

    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/
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