Comparison between Binary64 and Decimal64 Floating-Point Numbers

Author

Brisebarre, N. ; Mezzarobba, M. ; Muller, J.-M. ; Lauter, C.

Author_Institution

Lab. LIP, Univ. Claude Bernard Lyon 1, Lyon, France

fYear

2013

fDate

7-10 April 2013

Firstpage

145

Lastpage

152

Abstract

We introduce a software-oriented algorithm that allows one to quickly compare a binary64 floating-point (FP) number and a decimal64 FP number, assuming the "binary encoding" of the decimal formats specified by the IEEE 754-2008 standard for FP arithmetic is used. It is a two-step algorithm: a first pass, based on the exponents only, makes it possible to quickly eliminate most cases, then when the first pass does not suffice, a more accurate second pass is required. We provide an implementation of several variants of our algorithm, and compare them.

Keywords

IEEE standards; encoding; floating point arithmetic; Binary64 floating-point numbers; Decimal64 floating-point numbers; FP arithmetic; IEEE 754-2008 standard; binary encoding; binary64 FP number; decimal64 FP number; first pass; second pass; software-oriented algorithm; two-step algorithm; Accuracy; Approximation methods; Digital arithmetic; Encoding; Hardware; Standards; Testing; Decimal Floating-Point; Floating-Point Arithmetic; Floating-Point Comparisons;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic (ARITH), 2013 21st IEEE Symposium on

Conference_Location

Austin, TX

ISSN

1063-6889

Print_ISBN

978-1-4673-5644-2

Type

conf

DOI

10.1109/ARITH.2013.23

Filename

6545902