Re: foursquares.gp

[hermann@stamm-wilbrandt.de]

On 2023-11-19 00:28, hermann@stamm-wilbrandt.de wrote:
> So quadratic in p runtime of foursquares() is cool.
>
>
> What I want is to determine sum of 4 squares for largest known
> (Mersenne) prime M_82589933 ;-)
>
> Unfortunately foursquares() projected runtime is 7.25 CPU years ...
Bill,

foursquares() does not only have a runtime problem for going direction 
of largest Mersenne prime.
It did use 10.5GB RAM short before end of 12:11h run:

top - 23:30:35 up 1 day, 10:06,  3 users,  load average: 1.01, 1.00, 
1.00
Tasks: 309 total,   2 running, 307 sleeping,   0 stopped,   0 zombie
%Cpu(s):  8.3 us,  0.0 sy,  0.0 ni, 91.4 id,  0.0 wa,  0.0 hi,  0.2 si,  
0.0 st
MiB Mem :  15092.2 total,   1162.3 free,  11517.8 used,   2412.1 
buff/cache
MiB Swap:   2048.0 total,   2048.0 free,      0.0 used.   3264.3 avail 
Mem

    PID USER      PR  NI    VIRT    RES    SHR S  %CPU  %MEM     TIME+ 
COMMAND
 291352 hermann   20   0   14.0g  10.5g   8960 R 100.0  71.2 727:30.86 
gp
 445876 hermann   20   0   13552   4480   3584 S   0.2   0.0   0:00.09 
top


Since when applying "foursquares()" to a Mersenne prime we know that the 
first "is_fact()" call is true ...

? isfact(2^756839-1)
1
? ##
  ***   last result computed in 1h, 12min, 11,683 ms.
?

... and takes quite some time, I did directly call foursquares_fact():


? sq=foursquares_fact(2^756839-1);
  ***   at top-level: sq=foursquares_fact(2^756839-1)
  ***                    ^----------------------------
  ***   in function foursquares_fact: abs(
  ***   qfsolve(matdiagonal([1,1,1,1,-n]))[1..4])~
  ***   ^------------------------------------------
  *** qfsolve: the PARI stack overflows !
  current stack size: 15000002560 (14305.117 Mbytes)
  [hint] you can increase 'parisizemax' using default()

  ***   Break loop: type 'break' to go back to GP prompt
break>


How can it be that computing "sq=foursquares(2^756839-1);" worked (which 
calls foursquares_fact()), and calling
it directly fails?
I have these settings with gp 2.15.4 on 16GB RAM 7600X CPU PC:

hermann@7600x:~$ grep ^parisize /etc/gprc
parisizemax = 15G
parisize = 15G
hermann@7600x:~$