Distribution of roundoff noise in binary floating-point addition

Author

Kalliojarvi, K. ; Neuvo, Yrjöo

Author_Institution

Signal Process. Lab., Tampere Univ. of Technol., Finland

Volume

4

fYear

1992

fDate

3-6 May 1992

Firstpage

1796

Abstract

A method for deriving the distribution of relative round off error in addition of two binary floating-point numbers is introduced. The distribution is needed in the calculation of variance of the relative roundoff error in floating-point addition. The resulting distribution depends on the statistics of the addends and the rounding strategy chosen. As an example, the distribution is derived for the addition of two uncorrelated numbers from Gaussian distribution. The result was verified by simulation

Keywords

digital arithmetic; digital simulation; roundoff errors; signal processing; Gaussian distribution; addends; binary floating-point addition; calculation of variance; distribution of relative round off error; relative roundoff error; rounding strategy; roundoff noise; simulation; two uncorrelated numbers; Distribution functions; Floating-point arithmetic; Gaussian distribution; Laboratories; Laplace equations; Probability density function; Random variables; Roundoff errors; Signal processing; Statistical distributions;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1992. ISCAS '92. Proceedings., 1992 IEEE International Symposium on

Conference_Location

San Diego, CA

Print_ISBN

0-7803-0593-0

Type

conf

DOI

10.1109/ISCAS.1992.230406

Filename

230406