lrsarith: a small fixed/hybrid arithmetic C library

TL;DR

lrsarith is a compact C library providing fixed and hybrid precision arithmetic for integers and rationals, enhancing polyhedral computations with overflow control and minimal code modifications.

Contribution

It introduces a flexible, small C library supporting fixed and hybrid arithmetic modes for integers and rationals, integrated into lrslib for polyhedral computations.

Findings

Hybrid mode effectively manages overflow in computations.

Performance varies with fixed, GMP, and hybrid arithmetic modes.

Minimal code changes needed for integration into existing software.

Abstract

We describe lrsarith which is a small fixed precision and hybrid arithmetic C library for integers and rationals that we developed for use in the lrslib library for polyhedral computation. Using a generic set of operations, a program can be compiled with either 64-bit or 128-bit (if available) fixed precision, with an extended precision library such as GMP or the built-in MP routines. A simple scheme checks for overflow and either terminates the program or, in hybrid mode, changes to a higher precision arithmetic. Implementing these arithmetics in lrslib resulted in only minimal changes to the original code. We give computational results using lrs and mplrs, vertex/facet enumeration codes in lrslib, using 64 and 128 bit fixed integer arithmetic with and without overflow checking, GMP arithmetic, lrsarith hybrid arithmetic with both GMP and MP, and FLINT hybrid arithmetic. We give a small self-contained example C program using the lrsarith package in both fixed precision and hybrid mode.