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

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

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.
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Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
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