Math::Prime::Util 0.41 was released, with new functions (valuation, invmod, vecsum, binomial, forpart), and the usual crop of performance improvements. In particular, primality testing on x86_64 got another big speedup.
I decided to add a binomial(n,k) function to Math::Prime::Util, and found some interesting things while doing it. Overflow detection and mitigation in C and Perl were the first thing. Next was looking at negative arguments, which led to finding some differences in various solutions as well as filing a bug report for Math::BigInt.
Math::Prime::Util, and the optional Math::Prime::Util::GMP back end, are a set of modules for number theory in Perl, with a large overlap of functionality with PARI/GP. This is an update on some of the things that were new in the April release (0.40 of MPU, 0.19 of MPU::GMP).
The usual speed improvements in various areas, some approximation improvements, and new functions. Primality testing benchmarks also show Perl has state of the art solutions.
Recently I've been working on factoring and primality proofs (with certificates) for Math::Prime::Util. I thought I'd give a brief summary and comparison of the modules I know of for factoring integers from Perl.
Crypt::RSA is a module that's been around since 2001, when Vipul Ved Prakash put it on CPAN. It's had only very minor updates since then, and gets used by a few other modules. However, it's had one big problem: it uses Math::Pari for all its calculations, and two of its dependencies (Crypt::Primes and Crypt::Random) also use Pari. Debian in particular has been pining for a…