A Model for Minimizing Numeric Function Generator Complexity and Delay

Abstract

Numeric Function Generators (NFGs) allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise linear (or quadratic) approximations that represent the value of the specified function for a given input value. The domain of the function is divided into enough segments so that the approximation is within the required error to the exact value. NFG hardware complexity and delay depend on the number of segments required, the arithmetic devices used to approximate the function, and the number of bits used to represent the numbers being calculated. This thesis develops an accurate method to quantify hardware complexity and delay for various NFG configurations implemented on a Field-Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods. It shows that quadratic NFGs perform better than linear NFGs when the precision is above a threshold. It also shows that the majority of the functions in our benchmark have lower complexity when uniform segmentation is implemented. A criterion for choosing a segmentation method is shown for specific cases.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2007
Accession Number
ADA475958

Entities

People

  • Timothy A> Knudstrup

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Application-Specific Integrated Circuits
  • Arithmetic
  • Chebyshev Polynomials
  • Circuits
  • Computations
  • Computer Programs
  • Computers
  • Engineering
  • Field Programmable Gate Arrays
  • Integrated Circuits
  • Logic
  • Logic Devices
  • Logic Gates
  • Precision
  • Statistics
  • Systems Engineering

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computer Vision.
  • Parallel and Distributed Computing.