Yesterday I wrote a post describing how I managed to convince Sage to use MPIR instead of GMP on my desktop. Today I deleted that post, to write this post instead.

Probably everybody except me knows that MPIR is slower than GMP under Linux, and nobody except me cares to publish a benchmark result proving this. Due to my lack of knowledge on the matter, I asked naive questions on the forum.

Benchmarks with fat matrice (that is, when matrice with big entries is used as input) shows that double-determinant HNF algorithm runs significantly faster when using GMP 6.0.0a, than MPIR 2.7.0.

n=1000 bits=196 Sage time=3612.14 (MPIR) n=1000 bits=196 Sage time=2545.51 (GMP)

41%.

This only happens with fat matrices (for 8-bit matrices little or no difference).

GMP is significantly faster in integer arithmetic, documented interface nearly the same.

Links: script that does benchmarks, MPIR results, GMP results. "untuned" within filename means that the benchmark is for quickly-installed GMP (without proper tuning).

If you use Linux, and need to operate on big integers, you do not ever need MPIR.

Use latest recommended GMP version, do not forget to tune it. Under Gentoo, USE='doc pgo' emerge =gmp-X.Y.Z. Under other Linux, check build log for something like ./tune/tuneup; if such line is not present, then your GMP installation is slow.

linux

MPIR is for Windoz, GMP is for Linux