Comment #39 on issue 3809 by dana.jac...@gmail.com: isprime can be faster
http://code.google.com/p/sympy/issues/detail?id=3809
I can check the gmpy2 functions -- the underlying code should be solid
since it was written for a PRIMO validator that has been used a lot in the
last two years, but it wouldn't hurt to run a few more tests on the code
that's present. The issue I had with is_strong_bpsw_prp looks like some
sort of wrapping issue where the second internal call is getting the wrong
number of arguments.
Perl modules, (note links to the github pages for the development versions):
https://metacpan.org/release/Math-Prime-Util
https://metacpan.org/release/Math-Prime-Util-GMP
License is the Perl artistic license (which is either GPL or Artistic
License), and a LICENSE file is included. The GMP module uses a derivative
of SIMPQS which is GPL v2+, though that is only used for certain factoring
tasks.
There are versions in pure Perl, C, and for many things (including the
primality tests) C+GMP in the Math::Prime::Util::GMP module. The timing
above all went to C+GMP for the real work. The pure Perl code really is
two parts:
1) a lot of wrapping and tasks where performance isn't critical
2) backup for all other functionality, or for big number use when
MPU::GMP isn't installed
The performance of pure Perl for big number operations leaves a lot to be
desired, especially with the default bigint backend, but at least it works.
If you'd like, I can write something to start, for instance:
- use deterministic bases for numbers < 2^64 which should simplify the
code and make it a little faster
- put try / except for HAS_GMPY == 2 and use the tests it has to do a
BPSW test.
and tests.
Implementing the strong Lucas test in pure Python should be possible -- it
isn't that much code. I'll give it a shot and we'll see what the
performance looks like.
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