On the relative error of computing complex square roots in floating-point arithmetic

Claude-Pierre Jeannerod 1 Jean-Michel Muller 2, 1
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We study the accuracy of a classical approach to computing complex square-roots in floating-point arithmetic. Our analyses are done in binary floating-point arithmetic in precision p, and we assume that the (real) arithmetic operations +, −, ×, ÷, √ are rounded to nearest, so the unit roundoff is u = 2^−p. We show that in the absence of underflow and overflow, the componentwise and normwise relative errors of this approach are at most 7 / 2 u and u √ 37/2, respectively, and this without having to neglect terms of higher order in u. We then provide some input examples showing that these bounds are reasonably sharp for the three basic binary interchange formats (binary32, binary64, and binary128) of the IEEE 754 standard for floating-point arithmetic.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [5 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01780265
Contributor : Jean-Michel Muller <>
Submitted on : Friday, April 27, 2018 - 1:17:28 PM
Last modification on : Tuesday, July 17, 2018 - 4:18:42 PM
Document(s) archivé(s) le : Thursday, September 20, 2018 - 3:04:03 AM

File

asilomar17.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Claude-Pierre Jeannerod, Jean-Michel Muller. On the relative error of computing complex square roots in floating-point arithmetic. ACSSC 2017 - 51st Asilomar Conference on Signals, Systems, and Computers, Oct 2017, Pacific Grove, United States. pp.1-4, ⟨10.1109/ACSSC.2017.8335442⟩. ⟨ensl-01780265⟩

Share

Metrics

Record views

151

Files downloads

46