#2384 Call stack overflow in evaluating a definite integral

[Nils Bruin]

Maxima 5.25.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.51-1.fc16
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) y: (x^2)*exp(x)/(1+exp(x))^2$
(%i2) integrate(y,x,-1000,1000);
[...]
Maxima encountered a Lisp error:

Control stack exhausted (no more space for function call frames).
[...]

This bug is reported to still be present in 5.26. Note that Maxima quite happily computes the indefinite integral:

(%i3) factor(diff(integrate(y,x),x)-y);
(%o3) 0

[Robert Dodier]

Hmm, I can't confirm this. Maxima 5.26.0 + SBCL 1.0.45 + Ubuntu 11.04.

I have seen problems caused by factoring terms like 1 + exp(n*x) where n is a large integer, but I'm not seeing a problem here.

(%i1) display2d : false;

(%o1) false
(%i2) y: (x^2)*exp(x)/(1+exp(x))^2$

(%i3) integrate(y,x,-1000,1000);

(%o3) -((2000*%e^1000+2000)*log(%e^-1000*(%e^1000+1))
+(-2*%e^1000-2)*li[2](-%e^-1000)+1000000)
/(%e^1000+1)
-((2000*%e^1000+2000)*log(%e^1000+1)+(2*%e^1000+2)*li[2](-%e^1000)
-1000000*%e^1000)
/(%e^1000+1)
(%i4) build_info ();

Maxima version: 5.26.0
Maxima build date: 9:15 3/27/2012
Host type: i686-pc-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.45.0.debian

[Nils Bruin]

Thanks, Robert!

Would you be able to check if bounds larger than 1000 are also good for you? For
both my 5.25/SBCL and my 5.26/ECL I'm finding the cutoff is between 745 and 746.
See below:

Maxima 5.25.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.51-1.fc16
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d : false;

(%o1) false
(%i2) y: (x^2)*exp(x)/(1+exp(x))^2$

(%i3) integrate(y,x,-745,745);

(%o3) -((1490*%e^745+1490)*log(%e^-745*(%e^745+1))
+(-2*%e^745-2)*li[2](-%e^-745)+555025)
/(%e^745+1)
-((1490*%e^745+1490)*log(%e^745+1)+(2*%e^745+2)*li[2](-%e^745)
-555025*%e^745)
/(%e^745+1)
(%i4) build_info ();

Maxima version: 5.25.0
Maxima build date: 18:46 8/22/2011
Host type: x86_64-redhat-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.51-1.fc16
-------------------------------------------------------------------------------
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 11.1.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d : false;

(%o1) false
(%i2) y: (x^2)*exp(x)/(1+exp(x))^2$

(%i3) integrate(y,x,-745,745);

(%o3) -((1490*%e^745+1490)*log(%e^-745*(%e^745+1))
+(-2*%e^745-2)*li[2](-%e^-745)+555025)
/(%e^745+1)
-((1490*%e^745+1490)*log(%e^745+1)+(2*%e^745+2)*li[2](-%e^745)-555025*%e^745)
/(%e^745+1)
(%i4) build_info ();

%% this is much slower than SBCL, though. Perhaps some tail call that SBCL
%% optimizes away and is left in place in ECL?
-------------------------------------------------------------------------------
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 11.1.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d : false;

(%o1) false
(%i2) y: (x^2)*exp(x)/(1+exp(x))^2$

(%i3) integrate(y,x,-746,746);

Condition of type: STACK-OVERFLOW
BINDING-STACK overflow at size 8448. Stack can probably be resized.

%% resizing the stack doesn't solve a problem and eventually runs out of
%% resources
-------------------------------------------------------------------------------
Maxima 5.25.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.51-1.fc16
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d : false;

(%o1) false
(%i2) y: (x^2)*exp(x)/(1+exp(x))^2$

(%i3) integrate(y,x,-746,746);
INFO: Control stack guard page unprotected
Control stack guard page temporarily disabled: proceed with caution

%% and then it hangs ...

[Michael Orlitzky]

Hmm, I'm still seeing this on 5.27/ECL:

(%i1) display2d: false;

(%o1) false
(%i2) f: (x^2)*%e^x/(1+%e^x)^2;

(%o2) x^2*%e^x/(%e^x+1)^2
(%i3) integrate(f, x, -1000, 1000);

Maxima encountered a Lisp error:

BINDING-STACK overflow at size 8448. Stack can probably be resized.

Automatically continuing.
To enable the Lisp debugger set *debugger-hook* to nil.
Maxima encountered a Lisp error:

Detected access to an invalid or protected memory address.

Automatically continuing.
To enable the Lisp debugger set *debugger-hook* to nil.
(%i4) build_info();

(%o4) ?%build_info("5.27.0","2012-04-14 12:45:56","x86_64-pc-linux-gnu","ECL",
"12.2.1")

[David Scherfgen]

In Maxima 5.50post (SBCL 2.6.7) this integral completes without any stack overflow, at the reporter's bounds -1000..1000 and at the -746..746 cutoff where the crash used to start. The result is also correct: at fpprec:40 it agrees with the exact value %pi^2/3 to 34 significant digits.

(%i2) fpprec:40$
(%i3) y : (x^2)*exp(x)/(1+exp(x))^2$
(%i4) r : integrate(y,x,-1000,1000)$
(%i5) bfloat(r);
(%o5) 3.289868133696452872944830333292050431491b0
(%i6) bfloat(%pi^2/3);
(%o6) 3.289868133696452872944830333292050378438b0

Verified by Claude.

[Nils Bruin]

I can confirm that on Maxima 5.47.0 on ECL 24.5.10 the integral is now also computed to a value that matches what @tomasriker observes for 5.50/SBCL2.6.7.