Karim Belabas on Tue, 23 Sep 2014 14:23:25 +0200 |
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Re: Non-zero number plus zero is zero? |
* 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 your example, but contradicts mine. 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. N.B. If you want an equality operator with better properties, use '===' > which is also inconsistent with: > > gp> 0e1 < 1 > %13 = 1 > gp> 0e1 >= 1 > %17 = 0 problem with cmpir() in both cases, as explained above. > Do you consider this a bug? Yes, although possibly not the one you intended to report :-) Cheers, K.B. -- 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] `