Fast and correctly rounded logarithms in double-precision
Florent de Dinechin; Christoph Lauter; Jean-Michel Muller
RAIRO - Theoretical Informatics and Applications (2007)
- Volume: 41, Issue: 1, page 85-102
- ISSN: 0988-3754
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topde Dinechin, Florent, Lauter, Christoph, and Muller, Jean-Michel. "Fast and correctly rounded logarithms in double-precision." RAIRO - Theoretical Informatics and Applications 41.1 (2007): 85-102. <http://eudml.org/doc/250078>.
@article{deDinechin2007,
abstract = {
This article is a case study in the implementation of a portable,
proven and efficient correctly rounded elementary function in
double-precision. We describe the methodology used to achieve these
goals in the crlibm library. There are two novel aspects to
this approach. The first is the proof framework, and in general the
techniques used to balance performance and provability. The second
is the introduction of processor-specific optimization to get
performance equivalent to the best current mathematical libraries,
while trying to minimize the proof work. The implementation of the
natural logarithm is detailed to illustrate these questions.
},
author = {de Dinechin, Florent, Lauter, Christoph, Muller, Jean-Michel},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Floating-point; elementary functions; logarithm; correct rounding.},
language = {eng},
month = {4},
number = {1},
pages = {85-102},
publisher = {EDP Sciences},
title = {Fast and correctly rounded logarithms in double-precision},
url = {http://eudml.org/doc/250078},
volume = {41},
year = {2007},
}
TY - JOUR
AU - de Dinechin, Florent
AU - Lauter, Christoph
AU - Muller, Jean-Michel
TI - Fast and correctly rounded logarithms in double-precision
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 85
EP - 102
AB -
This article is a case study in the implementation of a portable,
proven and efficient correctly rounded elementary function in
double-precision. We describe the methodology used to achieve these
goals in the crlibm library. There are two novel aspects to
this approach. The first is the proof framework, and in general the
techniques used to balance performance and provability. The second
is the introduction of processor-specific optimization to get
performance equivalent to the best current mathematical libraries,
while trying to minimize the proof work. The implementation of the
natural logarithm is detailed to illustrate these questions.
LA - eng
KW - Floating-point; elementary functions; logarithm; correct rounding.
UR - http://eudml.org/doc/250078
ER -
References
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