Efficient function approximation using truncated multipliers and squarers

E. George Walters, Michael J. Schulte

Research output: Contribution to conferencePaper

40 Citations (Scopus)

Abstract

This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev series approximation, and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24-bits (IEEE single precision). Designs for linear and quadratic interpolators that implement the reciprocal function, f(x) = 1/x, are presented and analyzed as an example. We show that a 24-bit truncated reciprocal quadratic interpolator with a design specification of ± 1 ulp error requires 24.1 % fewer partial products to implement than a comparable standard interpolator with the same error specification.

Original languageEnglish (US)
Pages232-239
Number of pages8
StatePublished - Dec 1 2005
Event17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005 - Cape Cod, MA, United States
Duration: Jun 27 2005Jun 29 2005

Other

Other17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005
CountryUnited States
CityCape Cod, MA
Period6/27/056/29/05

Fingerprint

Function Approximation
Multiplier
Specification
Chebyshev Series
Specifications
Minimise
Partial
Output
Coefficient
Approximation
Simulation
Design

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

Cite this

Walters, E. G., & Schulte, M. J. (2005). Efficient function approximation using truncated multipliers and squarers. 232-239. Paper presented at 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, Cape Cod, MA, United States.
Walters, E. George ; Schulte, Michael J. / Efficient function approximation using truncated multipliers and squarers. Paper presented at 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, Cape Cod, MA, United States.8 p.
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Walters, EG & Schulte, MJ 2005, 'Efficient function approximation using truncated multipliers and squarers', Paper presented at 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, Cape Cod, MA, United States, 6/27/05 - 6/29/05 pp. 232-239.

Efficient function approximation using truncated multipliers and squarers. / Walters, E. George; Schulte, Michael J.

2005. 232-239 Paper presented at 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, Cape Cod, MA, United States.

Research output: Contribution to conferencePaper

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Walters EG, Schulte MJ. Efficient function approximation using truncated multipliers and squarers. 2005. Paper presented at 17th IEEE Symposium on Computer Arithmetic, ARITH-17 2005, Cape Cod, MA, United States.