I'm trying to plot a function involving the gamma function. It's this one:
-(gamma(1/2*k, 1/2*R*k) - gamma(1/2*k))/gamma(1/2*k)
If I try to plot the function with a k value any greater than 40, I get a
segfault:
sum(
plot(
integrated(k=k),
(x, 0, 2.5),
ymax=1.6,
color=color,
legend_label='k=%i' % k,
figsize=6,
aspect_ratio=1.0,
)
for k, color in zip(
[21, 22, 23, 26, 31, 41],
['blue', 'brown', 'red', 'green', 'black', 'yellow', 'orange'],
)
)
/Users/buck/trees/mine/sage/sage: line 134: 12283 Segmentation fault: 11
"$SAGE_ROOT/src/bin/sage" "$@"
[I 12:15:10.735 NotebookApp] KernelRestarter: restarting kernel (1/5)
This is extremely similar to the behavior I was getting with the pre-built
6.5 sage, so I think it's an old bug rather than a problem with my build.
In 6.5 there was no output (I suspect the Segmentation Fault message was
gobbled somehow), so I never tried to enable / debug a core dump in 6.5.
Inspecting the 6.6 core dump, I see that it used 27528, mostly calling back
and forth between two functions.
Smells like stack overflow to me.
(lldb) bt
[27503/47384]
* thread #1: tid = 0x0000, 0x0000000103588007
libpython2.7.dylib`vgetargskeywords + 23, stop reason = signal SIGSTOP
* frame #0: 0x0000000103588007 libpython2.7.dylib`vgetargskeywords + 23
frame #1: 0x000000010358890e
libpython2.7.dylib`PyArg_ParseTupleAndKeywords + 174
frame #2: 0x000000010356c40e libpython2.7.dylib`builtin___import__ + 94
frame #3: 0x00000001034a377f
libpython2.7.dylib`PyObject_CallFunctionObjArgs + 367
frame #4: 0x000000010774c1c4 coerce.so`__Pyx_Import(name=<unavailable>,
from_list=0x0000000117da7560, level=<unavailable>) + 180 at coerce.c:
20339
frame #5: 0x000000010774d08e
coerce.so`__pyx_f_4sage_9structure_6coerce_py_scalar_parent(__pyx_v_py_type=<unavailable>,
__pyx_skip_dispatch=<
unavailable>) + 510 at coerce.c:2938
frame #6: 0x0000000107760318
coerce.so`__pyx_f_4sage_9structure_6coerce_24CoercionModel_cache_maps_canonical_coercion(__pyx_v_self=0x00000001
07648d50, __pyx_v_x=0x00007f8fbfc37238, __pyx_v_y=0x0000000118c5f390,
__pyx_skip_dispatch=<unavailable>) + 3128 at coerce.c:9585
frame #7: 0x0000000107763cfe
coerce.so`__pyx_pw_4sage_9structure_6coerce_24CoercionModel_cache_maps_25canonical_coercion
+ 13 at coerce.c:105
64
frame #8: 0x0000000107763cf1
coerce.so`__pyx_pw_4sage_9structure_6coerce_24CoercionModel_cache_maps_25canonical_coercion(__pyx_v_self=0x00000
00107648d50, __pyx_args=0x0000000117e5f248, __pyx_kwds=0x0000000000000000)
+ 65
frame #9: 0x0000000103574f10 libpython2.7.dylib`PyEval_EvalFrameEx +
26208
frame #10: 0x0000000103575fb0 libpython2.7.dylib`PyEval_EvalCodeEx +
2144
frame #11: 0x00000001034dae0c libpython2.7.dylib`function_call + 124
frame #12: 0x000000010d680381
pynac.so`__Pyx_PyObject_Call(func=0x0000000108f0c410, arg=<unavailable>,
kw=PyObject * at scalar) + 65 at pynac
.cpp:26785
frame #13: 0x000000010d6a76e9
pynac.so`py_gcd(__pyx_v_n=0x00007f8fbfc37238, __pyx_v_k=0x0000000118c5f390)
+ 521 at pynac.cpp:8416
frame #14: 0x000000010d7d0f28
libpynac.1.dylib`GiNaC::gcd(GiNaC::numeric const&, GiNaC::numeric const&) +
56
frame #15: 0x000000010d7ad100
libpynac.1.dylib`GiNaC::add::integer_content() const + 496
frame #16: 0x000000010d7acef0
libpynac.1.dylib`GiNaC::ex::integer_content() const + 16
frame #17: 0x000000010d79fe01 libpynac.1.dylib`GiNaC::mul::eval(int)
const + 1377
frame #18: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #19: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #20: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #21: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #22: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #23: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #24: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #25: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #26: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #28: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #29: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
...
frame #27502: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27503: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27504: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27505: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27506: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27507: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27508: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27509: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27510: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27511: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27512: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27513: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27514: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27515: 0x000000010d7a026b libpynac.1.dylib`GiNaC::mul::eval(int)
const + 2507
frame #27516: 0x000000010d71ba91
libpynac.1.dylib`GiNaC::ex::construct_from_basic(GiNaC::basic const&) + 113
frame #27517: 0x000000010d7d1ccd
libpynac.1.dylib`GiNaC::operator*(GiNaC::ex const&, GiNaC::ex const&) + 77
frame #27518: 0x000000010da76768
expression.so`__pyx_f_4sage_8symbolic_10expression_10Expression__mul_(__pyx_v_left=0x0000000117db6cb0,
__pyx_v_right=0x0000000117db6ea8, __pyx_skip_dispatch=<unavailable>) + 2504
at expression.cpp:18109
frame #27519: 0x00000001075bed30
element.so`__pyx_pw_4sage_9structure_7element_11RingElement_11__mul__ + 64
at element.c:17301
frame #27520: 0x00000001075becf0
element.so`__pyx_pw_4sage_9structure_7element_11RingElement_11__mul__(__pyx_v_left=0x0000000117db6cb0,
__pyx_v_right=0x0000000117db6ea8) + 14
frame #27521: 0x000000010349ff8b libpython2.7.dylib`PyNumber_Multiply +
187
frame #27522: 0x0000000117bceb47
wrapper_py.so`interp_py(args=0x0000000117dbeda8,
constants=0x00007f8fbd980f30, stack=<unavailable>, code=0x00007f8fbd9a8eac)
+ 519 at interp_py.c:110
frame #27523: 0x0000000117bc1cca
wrapper_py.so`__pyx_pw_4sage_3ext_12interpreters_10wrapper_py_10Wrapper_py_5__call__(__pyx_v_self=0x00000001181db380,
__pyx_args=0x0000000117dbed90, __pyx_kwds=0x0000000000000000) + 138 at
wrapper_py.c:1478
frame #27524: 0x00000001034a2bd3 libpython2.7.dylib`PyObject_Call + 67
frame #27525: 0x00000001035727bd libpython2.7.dylib`PyEval_EvalFrameEx
+ 16141
frame #27526: 0x0000000103575fb0 libpython2.7.dylib`PyEval_EvalCodeEx +
2144
frame #27527: 0x000000010357513d libpython2.7.dylib`PyEval_EvalFrameEx
+ 26765
frame #27528: 0x000000010e399354
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