Karim Belabas on Tue, 23 Sep 2014 16:34:13 +0200

 Re: Non-zero number plus zero is zero?

```* Karim Belabas [2014-09-23 14:23]:
> * Jeroen Demeyer [2014-09-23 12:48]:
> > The following is probably consistent with PARI's floating point
> > model, but it was certainly surprising to me: a non-zero number plus
> > 0 can be 0:
> >
> > gp> 1 + 0e1
> > %1 = 0.E1
>
> See section 1.4, "The PARI philosophy", in the user's manual. We spend a
> few lines studying an analogous example.
>
> Thus not a bug.
>
> > An easy proof of 1 == 0 in PARI/GP:
> >
> > gp> 0e1 == 1
> > %5 = 1
>
> The above is expected, but we indeed have an inconsistency here:
>
>   ? 0e1 == 1.0
>   %1 = 0
>
> The problem is that 'x==y' is "defined" as equal0(x-y), which explains
>
> The reason is that the comparison is done as per the definition whenever
> x and y have different types only, and via a specialized type-specific
> routine otherwise.
>
> Unfortunately, the equalrr() function is not consistent with the
> definition and starts by comparing signs: two t_REAL of different signs
> are different. cmprr() and cmpir() have analogous problems: when one of
> the t_REAL inputs has sign 0 (of comparatively large exponent), they do
> not agree with the definition.
>
> I will fix that.

Done in 'master'. Thanks !

K.B.

P.S. Now

gp > 0e1 < 1
%1 = 0
gp > 0e1 <= 1
%2 = 1
gp > 0e1 > 1
%3 = 0
gp > 0e1 >= 1
%4 = 1
gp > 0e1 == 1
%5 = 1
gp > 0e1 === 1
%6 = 0

(same with 1 replaced by 1.0).

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
`

```