Re: Abnormous memory use for gaussian gcd()?

[hermann@stamm-wilbrandt.de]

Thank you,

that made it work:

$ gp < 36401.gp
...
0322528922710200176909512750979384713015800665694494304[+++]
  ***   last result computed in 1min, 41,244 ms.
Goodbye!
$

I don't understand the difference yet, this is whole script 36401.gp 
without word wrapping:

assert(b, v, s) = { if(!(b), error(Str(v) Str(s))); }

R(n) = { (10^n - 1) \ 9; }

p = 34 * R(36400) - 42000040044444004000024 * 10^2264 * R(36400) \ 
R(4550) - 1

sqrtm1 = 
1185421332012243159428523992750322769458440239813025493580787813469305...

assert(Mod(sqrtm1^2, p) == Mod(p - 1, p), "sqrtm1", "not");
print("foobar");

g = gcd(p, sqrtm1 + I)
##
assert(real(g)^2 + imag(g)^2 == p, "g", "not sum of squares");



gp runtime is 7.9x slower than Python with gmpy2.

I eliminated gmpy2, but Python script keeps 7.9x faster than Pari/GP 
script.

$ diff 36401.py.orig 36401.py
11c11
< from gmpy2 import mpz  # pylint: disable=no-name-in-module
---
> mpz = lambda x: x
$ python3.9 36401.py
gcd(p, sqrtm1 + I): 12.798248767852783s
$


What can be the reason for that?
I ask because I read this (especially the part after "mainly due"):
https://oeis.org/wiki/PARI/GP#Comparison_to_other_CAS
In the domain of number theory, PARI/GP is a strong rival to
well established all-purpose CAS as Maple and Mathematica,
mainly due to its computational speed, where it typically outperforms
both of these well known commercial CAS, and its free availability.


Regards,

Hermann Stamm-Wilbrandt.

On 2023-06-05 18:18, Bill Allombert wrote:
> On Mon, Jun 05, 2023 at 05:51:37PM +0200, hermann@stamm-wilbrandt.de 
> wrote:
> > Transpiled GP code for 10000-digit number works fine:
> >
> > $ gp 10000.gp
> > ...
> > 39178247477405595462999004573259238447193580865522753006504996585341802644743745733315578184178833806642718982619192126965967031226198644279480298699929676[+++]
> >   ***   last result computed in 4,709 ms.
> > ?
> >
> > But even though I give 24G of my laptop's 32G to Pari, computation 
> > does not
> > complete.
> > What am I doing wrong?
> > Or is this a bug in Pari/GP?
> > Python 3.9, Pari/GP 2.15.3.
> >
> > $ grep ^parisize /etc/gprc
> > parisizemax = 24G
> > parisize = 24G
> > $ gp 36401.gp
> > Reading GPRC: /etc/gprc
> > GPRC Done.
> > ...
> > parisizemax = 24000000000, primelimit = 500000
> > foobar
> >   ***   The result history is empty.
>
> When doing 'gp 36401.gp' there is no "result history" (that is "%1 =
> blah") so referencing it fails.
> Probably 36401.gp is using ## (or %).
>
> I suggest you try
> ./gp < 36401.gp
>
> I do not see anything that suggest there is a memory error.
>
> Cheers,
> Bill.