changed from zeta(CDF(1)) go boom! + zeta of 1 return value be consistent in different rings

[williamstein]

wstein@bsd:~/build/sage-3.4.1.rc1$ uname -a
Darwin bsd.local 9.6.0 Darwin Kernel Version 9.6.0: Mon Nov 24 17:37:00 PST 2008; root:xnu-1228.9.59~1/RELEASE_I386 i386

wstein@bsd:~/build/sage-3.4.1.rc1$ sage
----------------------------------------------------------------------
| Sage Version 3.4.1.rc1, Release Date: 2009-04-05                   |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: zeta(CDF(1))


------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occured in SAGE.
This probably occured because a *compiled* component
of SAGE has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run SAGE under gdb with 'sage -gdb' to debug this.
SAGE will now terminate (sorry).
------------------------------------------------------------

CC: @robertwb @sagetrac-fredrik

Component: number theory

Author: Mike Hansen, Robert Bradshaw

Reviewer: Karl-Dieter Crisman, Robert Bradshaw, David Loeffler

Merged: sage-4.6.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/5739

[williamstein]

comment:1

I think Robert Bradshaw massively optimized CDF special functions, and that's where this comes from. Changing the code for zeta in complex_double.pyx to:

        cdef pari_sp sp
        sp = avma
        _sig_on
        x = self._new_from_gen_c(  gzeta(self._gen(), PREC),   sp)
        _sig_off
        return x

somewhat fixes the problem, though doing

sage: zeta(CDF(0))

then raises a RuntimeError. Unfortunately, doing this doesn't work because the _sig_on/_sig_off stuff doesn't play well with Cython exceptions:

        cdef pari_sp sp
        sp = avma
        try:
           _sig_on
           x = self._new_from_gen_c(  gzeta(self._gen(), PREC),   sp)
           _sig_off
        except:
           raise ValueError
        return x

So I'm not sure how to fix this in general in a nice way with the right exception, but definitely adding _sig_on/_sig_off's around all the calls to pari is a very very good idea.

[mwhansen]

comment:2

We should be able to replace the calls to pari with calls to mpmath.

[mwhansen]

Author: Mike Hansen

[kcrisman]

comment:5

Attachment: trac_5739.patch.gz

The patch looks fine, but results in zeta of a CDF being approximately fifty times slower. This seems problematic, and perhaps also something that would happen a lot if we start switching things to mpmath? Mpmath looks like a great package, but if it has the same issue as NetworkX versus C graphs, we might not want to move default behavior there quite yet.

Marking as needs_info since there does not seem to be a Sage-wide policy on mpmath at this point, and I am reluctant to give positive review to such a marked slowdown.

[robertwb]

Attachment: 5739-CDF-zeta.patch.gz