Open AccessJournal Article
Second order function approximation using a single multiplication on FPGAs
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TL;DR: In this article, a hardware evaluation of elementary functions, based on a piecewise second order minimax approximation, is presented. But this evaluation requires only one small rectangular multiplication, and the critical path is shorter than that of a plain first-order evaluation.
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Abstract: This paper presents a new scheme for the hardware evaluation of elementary functions, based on a piecewise second order minimax approximation The novelty is that this evaluation requires only one small rectangular multiplication Therefore the resulting architecture combines a small table size, thanks to second-order evaluation, with a short critical path: Consisting of one table lookup, the rectangular multiplication, and one addition, the critical path is shorter than that of a plain first-order evaluation Synthesis results for several functions show that this method outperforms all the previously published methods in both area and speed for precisions ranging from 12 to 24 bits and over
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Citations
Elementary Functions Hardware Implementation Using Constrained Piecewise-Polynomial Approximations
TL;DR: A novel technique for designing piecewise-polynomial interpolators for hardware implementation of elementary functions and it is found that the increase in the approximation error due to constraints between polynomial coefficients can easily be overcome by increasing the fractional bits of the coefficients.
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A Tool for Unbiased Comparison between Logarithmic and Floating-point Arithmetic
Jérémie Detrey,Florent de Dinechin +1 more
- 01 Oct 2007
TL;DR: Two concurrent libraries of parameterized arithmetic operators, targeting recent field-programmable gate arrays, are presented, and are unbiased in the sense that they strive to reflect the state-of-the-art for both number systems.
Programmable numerical function generators based on quadratic approximation: architecture and synthesis method
Shinobu Nagayama,Tsutomu Sasao,Jon T. Butler +2 more
- 24 Jan 2006
TL;DR: The architecture and a synthesis method for programmable numerical function generators (NFGs) for trigonometric, logarithmic, square root, and reciprocal functions are presented and it is shown that fast and compact NFGs for a wide range of functions are implemented.
Cotransformation Provides Area and Accuracy Improvement in an HDL Library for LNS Subtraction
Panagiotis D. Vouzis,Sylvain Collange,Mark G. Arnold +2 more
- 29 Aug 2007
TL;DR: This paper reviews the methods of interpolation, multipartite tables and cotransformation for LNS addition and subtraction, but special focus is given on a novel version of cotranformation, for which a new special case is identified.
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Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method*This paper is an extension of [15].
TL;DR: In this article, the authors present an architecture and a synthesis method for compact numerical function generators (NFGs) for trigonometric, logarithmic, square root, reciprocal, and combinations of these functions.
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References
•Book
Elementary Functions: Algorithms and Implementation
Jean-Michel Muller
- 15 Jul 1997
TL;DR: I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find.
676
Faithful bipartite ROM reciprocal tables
D. Das Sarma,David W. Matula +1 more
- 19 Jul 1995
TL;DR: B bipartite reciprocal tables are described that employ separate table lookup of the positive and negative portions of a borrow-save reciprocal value, and typically provide a round-to-nearest reciprocal for over 90% of input arguments.
188
The Symmetric Table Addition Method for Accurate Function Approximation
James E. Stine,Michael J. Schulte +1 more
- 01 Jun 1999
TL;DR: This method has a closed-form solution for the table entries and can be applied to any differentiable function and requires two to three orders of magnitude less memory than conventional table lookups.
141
Interleaved memory function interpolators with application to an accurate LNS arithmetic unit
TL;DR: A new method for polynomial interpolation in hardware, with advantages demonstrated by its application to an accurate logarithmic number system (LNS) arithmetic unit, using an interleaved memory function interpolator.
123
Function evaluation by table look-up and addition
H. Hassler,Naofumi Takagi +1 more
- 19 Jul 1995
TL;DR: A general approach decomposing a function into a sum of functions, each with a smaller input site than the original, which can be mapped with essentially the same precision using small ROM tables and adders.
119
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