Performance and memory use are two areas of concern for many libraries.
Last December I made a number of changes in my Math::Prime::Util module
to reduce memory use, and bulk88 helped really tweak some of the XS.
I thought I'd pick a simple task and look at the speed and memory use
of a number of solutions.

`isprime` from 1 to 10 million
Memory | Time | Solution |

2096k | 72.6s | Perl trial division mod 6 |

2100k | 124.8s | Perl trial division |

3652k | 36.2s | Math::GMP |

3940k | 14.8s | Math::GMPz |

4040k | 1.9s | Math::Prime::Util (no GMP backend) |

4388k | 1.9s | Math::Prime::Util (with GMP backend) |

4568k | 1.4s | Math::Prime::Util (GMP + precalc) |

4888k | 4.4s | Math::Prime::XS |

5316k | 245.1s | Math::Primality |

5492k | 29.8s | Math::Pari |

6260k | 1.5s | Math::Prime::FastSieve |

~16MB | >1 year | regex |

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.