Bug in arb_div

[Jean Kieffer]

Hi,

I believe I found a bug in arb_div, causing it to return NaN when
dividing x/y where x = 0 +- something at high precision, for any y. (In
my case x was 0 on the nose.)

In src/arb/div.c, line 105, in arb_div_newton, the condition
arf_is_special(arb_midref(x)) will hold true when arb_midref(x) = 0,
triggering a NaN result. A probable fix would be to write

if (!arf_is_finite(arb_midref(x)) || arf_is_special(arb_midref(y)))

or possibly to edit the WANT_NEWTON macro.

Best,
Jean

--
Jean Kieffer
CNRS researcher at Loria (Nancy, France), CARAMBA team
https://members.loria.fr/JKieffer/

[Jean Kieffer]

Hi again,

Well it turns out this precise fix doesn't work (it leads to "error: ulp
error not defined for special value", at least for x=0), so I'm not sure
what the correct one would be !

Best,
Jean

[Jeffrey Sarnoff]

Would it make sense to define ulp(0) based on the working precision?

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[Fredrik Johansson]

Hi Jean,

Thanks for the bug report. arb_div was missing an early branch to deal specially with x = 0 or 0 +/- eps; it should not be entering the Newton code here.

Fixing this (hopefully) in https://github.com/flintlib/flint/pull/2322

Fredrik

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