numerical integral is wrong in pari master

[videlec]

Within pari master, the gp numerical integral gives

? intnum(x=0,13,sin(x)+sin(x^2) + x)
%1 = 84.181815392229652966739838357234264357

but should be 85.1885681951527 (as it was with previous pari release). Increasing the precision, it gets better but the relative error is incredibly huge

? \p 30
   realprecision = 38 significant digits (30 digits displayed)
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%2 = 84.1818153922296529667398383572
? \p 40
   realprecision = 57 significant digits (40 digits displayed)
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%3 = 85.18860335415782535357810701961378283432
? \p 50
? intnum(x=0,13,sin(x)+sin(x^2) + x)
%4 = 85.188603354157825353578107019613782834315433312524

Tested on PARI master at commit 17795-d04cdd3 with an amd64.

See also #18340

Upstream ticket: http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1694

Depends on #18340

Upstream: Reported upstream. Developers deny it's a bug.

Component: packages: standard

Issue created by migration from https://trac.sagemath.org/ticket/18342

[jdemeyer]

Changed upstream from Not yet reported upstream; Will do shortly. to Reported upstream. No feedback yet.

[jdemeyer]

Changed upstream from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

[jdemeyer]

comment:4

Upstream has answered essentially that we need to live with it. I think we should close this as wontfix.

[jdemeyer]

Changed upstream from Reported upstream. Developers acknowledge bug. to Reported upstream. Developers deny it's a bug.

[videlec]

comment:5

I just read the answer from Karim. We should document that this function is not adaptative and is likely to lead to wrong results with oscillating functions (though sin(x^2) at x=13 is not terribly oscillating compared to sin(1/x) at 0).

Vincent

[nexttime]

Dependencies: #18340

[jdemeyer]

comment:7

Replying to @videlec:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

[videlec]

comment:8

Replying to @jdemeyer:

Replying to @videlec:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

In the pari interface

sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x)")
85.1885681951527

[nexttime]

comment:9

Yep, e.g.

sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x)")
84.1818153922297
sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x,1)")
85.1885681951527
sage: pari("intnum(x=0,13,sin(x)+sin(x^2) + x,2)")
85.1885681951527

with an explanation in a comment.

[jdemeyer]

comment:10

Replying to @videlec:

Replying to @jdemeyer:

Replying to @videlec:

We should document

document where? intnum isn't available in the Sage interface for PARI (because it has a closure argument, see #18052 and #18038).

In the pari interface

The module docstring of pari_instance.pyx is not the place to document a specific function.