High-speed function approximation using a minimax quadratic interpolator

A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), o...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:IEEE transactions on computers Ročník 54; číslo 3; s. 304 - 318
Hlavní autori: Pineiro, J.-A., Oberman, S.F., Muller, J.-M., Bruguera, J.D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.03.2005
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Predmet:
Algorithms
Approximation
computer arithmetic
Computer Science
elementary functions
Floating point arithmetic
High speed
Index Terms- Table-based methods
Interpolation
Mathematical analysis
Mathematical models
Minimax methods
minimax polynomial approximation
Minimax technique
Other
reciprocal
Roots
single-precision computations
square root
Studies
Table lookup
elementary functions
minimax polynomial approximation
computer arithmetic
table-based methods
reciprocal
single-precision computations
square root
ISSN:0018-9340, 1557-9956
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:A table-based method for high-speed function approximation in single-precision floating-point format is presented in this paper. Our focus is the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithms, trigonometric functions, powering (with a fixed exponent p), or special functions. The algorithm presented here combines table look-up, an enhanced minimax quadratic approximation, and an efficient evaluation of the second-degree polynomial (using a specialized squaring unit, redundant arithmetic, and multioperand addition). The execution times and area costs of an architecture implementing our method are estimated, showing the achievement of the fast execution times of linear approximation methods and the reduced area requirements of other second-degree interpolation algorithms. Moreover, the use of an enhanced minimax approximation which, through an iterative process, takes into account the effect of rounding the polynomial coefficients to a finite size allows for a further reduction in the size of the look-up tables to be used, making our method very suitable for the implementation of an elementary function generator in state-of-the-art DSPs or graphics processing units (GPUs).
Bibliografia:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
content type line 23
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2005.52