PARI stack overflow crashes Sage

[jdemeyer]

The following crashes Sage hard:

sage: i = CDF.0
sage: fz=animate([line([zeta(s+i*t) for t in srange(0,50,0.01)]) for s in srange(0,0.9,0.01)],xmin=-1.5,ymin=-2,xmax=2.5,ymax=2)
  ***   the PARI stack overflows !
  current stack size: 16000000 (15.259 Mbytes)
  [hint] you can increase GP stack with allocatemem()

  ***   Error in the PARI system. End of program.

The problem is simple: instead of using the proper PARI interface in sage/libs/pari/gen.pyx, for some reason PARI is called directly in sage/rings/complex_double.pyx. This interface misses some features, such as cleaning up the PARI stack :-)

This code goes back to

changeset:   1292:28dfa54b6a23
parent:      1273:97f9271f8637
user:        William Stein <wstein@gmail.com>
date:        Sun Sep 24 23:13:32 2006 -0700
summary:     Finished the 2nd draft of the double precision complex numbers.

Solution: use the proper PARI interface instead.

Depends on #13618

Component: c_lib

Author: Jeroen Demeyer

Reviewer: David Roe

Merged: sage-5.8.beta3

Issue created by migration from https://trac.sagemath.org/ticket/14082

[jdemeyer]

Author: Jeroen Demeyer

[roed314]

Reviewer: David Roe

[roed314]

comment:7

This looks good, and the following change means that our eta function now agrees with Mathematica (and PARI as well)

-            sage: CDF(10^15,0.1).eta()     # slightly random-ish arch dependent output
-            -0.121339721991 - 0.19619461894*I   
+            sage: CDF(10^15, 0.1).eta()  # abs tol 1e-10
+            -0.115342592727 - 0.19977923088*I

[jdemeyer]

Dependencies: #13618

[jdemeyer]

comment:8

Attachment: 14082_pari_complex_double.patch.gz

Rebased.

[jdemeyer]

Merged: sage-5.8.beta3