Treffer: Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic

Title:
Computing Correctly Rounded Integer Powers in Floating-Point Arithmetic
Authors:
Kornerup, Peter, Lauter, Christoph, Lefèvre, Vincent, Louvet, Nicolas, Muller, Jean-Michel
Contributors:
Department of Mathematics and Computer Science [Odense] (IMADA), University of Southern Denmark (SDU), Computer arithmetic (ARENAIRE), Centre Inria de l'Université Grenoble Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ANR-06-BLAN-0257,EVA-Flo,Evaluation et Validation Automatique pour le calcul Flottant(2006)
Source:
ACM Transactions on Mathematical Software. 37(1):4-4
Publisher Information:
CCSD; Association for Computing Machinery, 2010.
Publication Year:
2010
Collection:
collection:ENS-LYON
collection:CNRS
collection:INRIA
collection:UNIV-LYON1
collection:INRIA-RHA
collection:PRUNEL
collection:LIP
collection:INRIA_TEST
collection:TESTALAIN1
collection:INRIA2
collection:INRIA-RENGRE
collection:UDL
collection:UNIV-LYON
collection:ANR
Subject Terms:
correct rounding, floating-point arithmetic, integer power function, ACM: G.: Mathematics of Computing, G.1: NUMERICAL ANALYSIS, G.1.0: General, G.1.0.0: Computer arithmetic, G.4: MATHEMATICAL SOFTWARE, G.4.0: Algorithm design and analysis, [INFO.INFO-AO]Computer Science [cs], Computer Arithmetic
Original Identifier:
HAL:
Document Type:
Zeitschrift article<br />Journal articles
Language:
English
ISSN:
0098-3500
Relation:
info:eu-repo/semantics/altIdentifier/doi/10.1145/1644001.1644005
DOI:
10.1145/1644001.1644005
Availability:
https://inria.hal.science/inria-00388501
Accession Number:
edshal.inria.00388501v1
Database:
HAL

Weitere Informationen

We introduce several algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. For bounded, yet very large values of the exponent, we aim at obtaining correctly-rounded results in round-to-nearest mode, that is, our algorithms return the floating-point number that is nearest the exact value.