Karim BELABAS on Tue, 3 Aug 1999 11:35:12 +0200 (MET DST)

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Re: Two bugs (2.0.16 on Linux/Alpha)

>> [Matias:]
>> ? allocatemem(256000000)
>> ? matrix(1000,5000,i,j,cos(0.5*i*j))
>>   ***   the PARI stack overflows !!!
>>   ***   Warning: doubling stack size; new stack = 512000000.
>> I repeated this with a stack of 800Mb and it gave me the same problem. 

>> It has improved since, for example, version 2.0.9, but still it's
>> far away from where it could eventually be.  It's not on the immediate
>> TODO list, but Karim will tell you whether it's planned for remote future.
> I would feel satisfied with this answer if I were actually DOING matrix
> operations, but I'm not. I use the matrix() command just to create a 2
> dimensinoal array with special entries, but after that I don't do anything
> other than extracting entries from it.


> So, in my opinion this problem would not mean that PARI does linear algebra
> poorly, but that it does memory management poorly.

No need for memory management in matrix(): The stack is clean after each
matrix entry is computed (i.e the stack only grows by the amount necessary to
fit the entry).

I don't understand why 800MB overflows, but 256MB definitely should. Your
machine is 64bit; using default precision (4 words), real numbers (2
codewords) need 6 words each. Multiplied by 5.10^6, it's about 230MB, and you
need a bit more to actually hold the entries. It fits, but barely.

Now it turns out that because of the way the computations were done, one
extra word of precision becomes available, hence most of the entries actually
need 7 words and not 6. That's enough to overflow.

1) experiment with sizebyte and check how much room this kind of matrices
needs on your architecture. Again it shouldn't overflow at 800MB, check
whether the size of your matrices is roughly equal to
  (number of entries) * (realprecision + 2 (or 3)) bytes

2) cut down the precision (\p19 for instance). Entries will now fit in 4
words at most.

Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
PARI/GP Home Page: http://hasse.mathematik.tu-muenchen.de/ntsw/pari/