Section: Software

SIPE: Small Integer Plus Exponent

Participant : Vincent Lefèvre.

SIPE (Small Integer Plus Exponent) is a mini-library in the form of a C header file, to perform computations in very low precisions with correct rounding to nearest in radix 2. The goal of such a tool is to do proofs of algorithms/properties or computations of tight error bounds in these precisions by exhaustive tests, in order to try to generalize them to higher precisions. The currently supported operations are the addition, subtraction, multiplication, FMA, minimum/maximum/comparison functions (of the signed numbers or in magnitude), and conversions.

A new macro SIPE_2MUL , returning the rounded result and the error of a multiplication, has been added.

A test program and scripts to perform timing comparisons with hardware IEEE-754 floating-point and with GNU MPFR are available, together with a discussion on the technical and algorithmic choices behind SIPE and timing results. [39]

• ACM: D.2.2 (Software libraries), G.4 (Mathematical software).

• AMS: 26-04 Real Numbers, Explicit machine computation and programs.

• License: LGPL version 2.1 or later.

• Type of human computer interaction: C header file.

• OS/Middleware: any OS.

• Required library or software: GCC compiler.

• Programming language: C.

• Documentation: Research report Inria RR-7832.

• URL: http://www.vinc17.net/software/sipe.h