gcd_ crashes for zero $-variables #191
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bug
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Output of Output of |
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I think Output: Should we not expect If the polynomial has only 1 term the result seems fine. Output: |
Actually Valgrind tells us something goes wrong at ratio.c:2063 in these cases, too: |
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OK, it is clear that the case that one of those arguments (or both) is zero is not
intercepted.
I guess there should be a runtime error, rather than a crash (or no crash but a nonsense
answer).
The gcd of 0 and any other number makes no sense.
I will put some if statements in the code.
Jos
… On 7 jun. 2017, at 01:01, Takahiro Ueda ***@***.***> wrote:
gcd_ also crashes occasionally on mac os x (though not on my linux machine) when a zero expression is in the first argument.
I think gcd_ also gives wrong results when called with a zero.
Actually Valgrind tells us something goes wrong at ratio.c:2063 <https://github.com/vermaseren/form/blob/76561be553a6215cf4ef70c6d1a5b848bda7e12d/sources/ratio.c#L2063> in these cases, too:
FORM 4.1 (Jun 6 2017, v4.1-20131025-347-g76561be) 64-bits Run: Wed Jun 7 00:49:52 2017
L p1 = 0;
L p2 = 1;
L gcd = gcd_(p1,p2);
.end
Time = 0.06 sec Generated terms = 0
p1 Terms in output = 0
Bytes used = 4
Time = 0.08 sec Generated terms = 1
p2 Terms in output = 1
Bytes used = 20
==23356== Invalid read of size 4
==23356== at 0x4BFDDD: GCDterms (ratio.c:2063)
==23356== by 0x4C1518: GCDfunction (ratio.c:1000)
==23356== by 0x4B7725: Generator (proces.c:3688)
==23356== by 0x4B7C7A: Generator (proces.c:3886)
==23356== by 0x4B93FA: Processor (proces.c:404)
==23356== by 0x437480: DoExecute (execute.c:812)
==23356== by 0x44D8FE: ExecModule (module.c:274)
==23356== by 0x4AF44B: PreProcessor (pre.c:962)
==23356== by 0x4E7A30: main (startup.c:1605)
==23356== Address 0x570977c is 4 bytes before a block of size 96 alloc'd
==23356== at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23356== by 0x4FE510: Malloc1 (tools.c:2236)
==23356== by 0x4E230B: EndSort (sort.c:741)
==23356== by 0x4BFD85: CreateExpression (ratio.c:2037)
==23356== by 0x4C141C: GCDfunction (ratio.c:977)
==23356== by 0x4B7725: Generator (proces.c:3688)
==23356== by 0x4B7C7A: Generator (proces.c:3886)
==23356== by 0x4B93FA: Processor (proces.c:404)
==23356== by 0x437480: DoExecute (execute.c:812)
==23356== by 0x44D8FE: ExecModule (module.c:274)
==23356== by 0x4AF44B: PreProcessor (pre.c:962)
==23356== by 0x4E7A30: main (startup.c:1605)
==23356==
==23356== Invalid read of size 4
==23356== at 0x4C0392: GCDterms (ratio.c:2224)
==23356== by 0x4C1518: GCDfunction (ratio.c:1000)
==23356== by 0x4B7725: Generator (proces.c:3688)
==23356== by 0x4B7C7A: Generator (proces.c:3886)
==23356== by 0x4B93FA: Processor (proces.c:404)
==23356== by 0x437480: DoExecute (execute.c:812)
==23356== by 0x44D8FE: ExecModule (module.c:274)
==23356== by 0x4AF44B: PreProcessor (pre.c:962)
==23356== by 0x4E7A30: main (startup.c:1605)
==23356== Address 0x570977c is 4 bytes before a block of size 96 alloc'd
==23356== at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23356== by 0x4FE510: Malloc1 (tools.c:2236)
==23356== by 0x4E230B: EndSort (sort.c:741)
==23356== by 0x4BFD85: CreateExpression (ratio.c:2037)
==23356== by 0x4C141C: GCDfunction (ratio.c:977)
==23356== by 0x4B7725: Generator (proces.c:3688)
==23356== by 0x4B7C7A: Generator (proces.c:3886)
==23356== by 0x4B93FA: Processor (proces.c:404)
==23356== by 0x437480: DoExecute (execute.c:812)
==23356== by 0x44D8FE: ExecModule (module.c:274)
==23356== by 0x4AF44B: PreProcessor (pre.c:962)
==23356== by 0x4E7A30: main (startup.c:1605)
==23356==
Time = 0.09 sec Generated terms = 1
gcd Terms in output = 1
Bytes used = 20
FORM 4.1 (Jun 6 2017, v4.1-20131025-347-g76561be) 64-bits Run: Wed Jun 7 00:51:07 2017
S x;
L p1 = 0;
L p2 = x+x^2;
L gcd = gcd_(p2,p1);
.end
Time = 0.06 sec Generated terms = 0
p1 Terms in output = 0
Bytes used = 4
Time = 0.08 sec Generated terms = 2
p2 Terms in output = 2
Bytes used = 60
==23416== Invalid read of size 4
==23416== at 0x4BFDDD: GCDterms (ratio.c:2063)
==23416== by 0x4C1518: GCDfunction (ratio.c:1000)
==23416== by 0x4B7725: Generator (proces.c:3688)
==23416== by 0x4B7C7A: Generator (proces.c:3886)
==23416== by 0x4B93FA: Processor (proces.c:404)
==23416== by 0x437480: DoExecute (execute.c:812)
==23416== by 0x44D8FE: ExecModule (module.c:274)
==23416== by 0x4AF44B: PreProcessor (pre.c:962)
==23416== by 0x4E7A30: main (startup.c:1605)
==23416== Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd
==23416== at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23416== by 0x4FE510: Malloc1 (tools.c:2236)
==23416== by 0x4E230B: EndSort (sort.c:741)
==23416== by 0x4BFD85: CreateExpression (ratio.c:2037)
==23416== by 0x4C141C: GCDfunction (ratio.c:977)
==23416== by 0x4B7725: Generator (proces.c:3688)
==23416== by 0x4B7C7A: Generator (proces.c:3886)
==23416== by 0x4B93FA: Processor (proces.c:404)
==23416== by 0x437480: DoExecute (execute.c:812)
==23416== by 0x44D8FE: ExecModule (module.c:274)
==23416== by 0x4AF44B: PreProcessor (pre.c:962)
==23416== by 0x4E7A30: main (startup.c:1605)
==23416==
==23416== Invalid read of size 4
==23416== at 0x4C0392: GCDterms (ratio.c:2224)
==23416== by 0x4C1518: GCDfunction (ratio.c:1000)
==23416== by 0x4B7725: Generator (proces.c:3688)
==23416== by 0x4B7C7A: Generator (proces.c:3886)
==23416== by 0x4B93FA: Processor (proces.c:404)
==23416== by 0x437480: DoExecute (execute.c:812)
==23416== by 0x44D8FE: ExecModule (module.c:274)
==23416== by 0x4AF44B: PreProcessor (pre.c:962)
==23416== by 0x4E7A30: main (startup.c:1605)
==23416== Address 0x1c9a566c is 4 bytes before a block of size 96 alloc'd
==23416== at 0x4A05A57: malloc (vg_replace_malloc.c:299)
==23416== by 0x4FE510: Malloc1 (tools.c:2236)
==23416== by 0x4E230B: EndSort (sort.c:741)
==23416== by 0x4BFD85: CreateExpression (ratio.c:2037)
==23416== by 0x4C141C: GCDfunction (ratio.c:977)
==23416== by 0x4B7725: Generator (proces.c:3688)
==23416== by 0x4B7C7A: Generator (proces.c:3886)
==23416== by 0x4B93FA: Processor (proces.c:404)
==23416== by 0x437480: DoExecute (execute.c:812)
==23416== by 0x44D8FE: ExecModule (module.c:274)
==23416== by 0x4AF44B: PreProcessor (pre.c:962)
==23416== by 0x4E7A30: main (startup.c:1605)
==23416==
Time = 0.10 sec Generated terms = 1
gcd Terms in output = 1
Bytes used = 20
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On Wed, 7 Jun 2017 at 8:11:12 -0700, Jos Vermaseren wrote:
The gcd of 0 and any other number makes no sense.
Unless I am misunderstanding I believe the proper definitions are
gcd(0,a) = a
gcd(0,0) = 0
See page 3 of the book http://williamstein.org/books/ent/ent.pdf
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It seems that mathematically it makes sense or at least there is some convention. Mathematica 11.0.1 Python 3.6.1 ginsh 1.7.2 gp/pari 2.9.2
If |
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If I look in the book, it is more like a definition or convention. Specially when both are 0.
If you have gcd(0,x) can you say that x divides zero?
At the least that is very shady.
I can make it like the ‘convention’ of course. It is not very elegant in my eyes, but if
it is what people want…..
Jos
… On 7 jun. 2017, at 17:28, Takahiro Ueda ***@***.***> wrote:
The gcd of 0 and any other number makes no sense.
It seems that mathematically it makes sense or at least there is some convention.
Mathematica 11.0.1
In[1]:= PolynomialGCD[0, 1+x]
Out[1] = 1 + x
In[2]:= PolynomialGCD[0, 0]
Out[2] = 0
Python 3.6.1
In [1]: import math
In [2]: math.gcd(0, 12)
Out[2]: 12
In [3]: math.gcd(0, 0)
Out[2]: 0
ginsh 1.7.2
> gcd(0, 1+x);
1+x
> gcd(0, 0);
0
gp/pari 2.9.2
? gcd(0, 1+x)
%1 = x + 1
? gcd(0, 0)
%2 = 0
GCD(0,0) = 0 would be true in mathematics, e.g., https://math.stackexchange.com/questions/495119/what-is-gcd0-0 <https://math.stackexchange.com/questions/495119/what-is-gcd0-0>, but in practice I'm happy with the fact that FORM gives the "wrong" answer for gcd_(0,0) -> 1 because usually what we want to do after taking a GCD is divisions by the GCD:
$gcd = gcd_($a,$b);
$a = div_($a,$gcd);
$b = div_($b,$gcd);
If gcd_(0,0) gives 0, I need to put more code to check if the GCD is 0 before the divisions.
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On Wed, 7 Jun 2017 at 9:21:38 -0700, Jos Vermaseren wrote:
If you have gcd(0,x) can you say that x divides zero?
Yes, for 0/x = 0 is well defined.
At the least that is very shady. I can make it like the ‘convention’ of
course. It is not very elegant in my eyes, but if it is what people
want…..
I don't think one can "define" gcd(0,x) any differently than 'x'
because one of the properties of the gcd() would be violated otherwise,
namely
gcd(a,b) = gcd(a,b-a).
The above lemma would be inconsistent with gcd(a,a) = a unless
gcd(a,0) = a.
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I believe @tueda and @crmafra are correct that That |
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After applying the patch 615cbcd, still broken... |
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I found cases that are still broken... |
tueda
added a commit
to tueda/form
that referenced
this issue
Jun 8, 2017
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Thanks a lot for quickly fixing this. With 541f847 on Mac everything runs as expected. |
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gcd_has a memory bug when the first argument is a zero $-variable.Valgrind output:
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