Ralf Stephan on Thu, 5 Dec 2002 15:29:32 +0100

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unrestricted partition function

there is installable code for the unrestricted partition function at


for inclusion into your GP programs.

The code was stress-tested up to an arg of 10^6 and the maximum arg
is 10^15 due to space restrictions --- you would need days already 
at 10^10, though. Error conditions are caught etc. I would ask the
maintainers to mail if I should add documentation to pari directly.

NOTE: install worked only with gp-2.1, with gp-2.2 the function was
not found. To get the DLL I used -fPIC when compiling and ld -shared
for linking.

Algorithms / speed issues
I used the Hardy-Ramanujan-Rademacher form; computation of Dedekind
sums is done in longs, so the main bottleneck remains gcos (=mulrr)
at higher precision, although that was tightly calculated. Guesswork
is that the implementation would benefit from real Karatsuba (above
my head, sorry).