Supervision : Jean-Claude BAJARD

Co-supervision : LAUTER Christoph

Toward a Modern Floating-Point Environment

This work investigates two ways of enlarging the current floating-point environment:

1. support of several implementation versions for each mathematical function (elementary such as exp or log and special such as erf or ?);
2. provide IEEE754 operations that mix the inputs and the output of different radices.

As the number of various implementations for each mathematical function is large, this work is focused on code generation. We support black-box functions, so user-specified parametrized functions. This work contains a novel algorithm for domain splitting and an approach to replace branching on reconstruction by a polynomial. Since the revision of the IEEE754 Standard in 2008 it is possible to mix numbers of different precisions in one operation. However, there is no mechanism that allows users to mix numbers of different radices in one operation. This research starts an examination of mixed-radix arithmetic with the worst cases search for FMA. A novel algorithm to convert a decimal character sequence of arbitrary length to a binary floating-point number is presented. It is independent of currently-set rounding mode and produces correctly-rounded results.

2012-2015 Publications

• 2015
  • O. Kupriianova : “Vers l’environnement Flottant Moderne”, thesis, phd defence 12/11/2015, supervision Bajard, Jean-Claude, co-supervision : Lauter, Christoph (2015)
  • N. Brunie, F. De Dinechin, O. Kupriianova, Ch. Lauter : “Code generators for mathematical functions”, 22d IEEE Symposium on Computer Arithmetic, Lyon, France (2015)
• 2014
  • O. Kupriianova, Ch. Lauter : “A Domain Splitting Algorithm for the Mathematical Functions Code Generator”, ACSSC 2014 - 48^th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, pp. 1271-1275, (IEEE) (2014)
  • O. Kupriianova, Ch. Lauter : “Metalibm: A Mathematical Functions Code Generator”, Mathematical Software – ICMS 2014. 4^th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings, vol. 8592, Lecture Notes in Computer Science, Seoul, Korea, Republic of, pp. 713-717, (Springer) (2014)
• 2013
  • O. Kupriianova, Ch. Lauter, J.‑M. Muller : “Radix conversion for IEEE754-2008 mixed radix floating-point arithmetic”, 2013 Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, pp. 1134-1138 (2013)
• 2012
  • Ch. Lauter, Olga A. Kupriianova : “The libieee754 compliance library for the IEEE 754-2008 standard”, Proceedings of the 15’th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations, 2012, Novosibirsk, Russian Federation (2012)