Programmable Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

Abstract

This paper presents an architecture and a synthesis method for programmable numerical function generators (NFGs) for trigonometric, logarithmic, square root, and reciprocal functions. Our NFG partitions a given domain of the function into non-uniform segments using an LUT cascade, and approximates the given function by a quadratic polynomial for each segment. Thus, we can implement fast and compact NFGs for a wide range of functions. Implementation results on an FPGA show that: (1) our NFGs require only 4% of the memory needed by NFGs based on the linear approximation with non-uniform segmentation; and (2) our NFGs require only 22% of the memory needed by NFGs based on the 5th-order approximation with uniform segmentation. Our automatic synthesis system generates such compact NFGs quickly.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA599939

Entities

People

  • Jon T. Butler
  • Shinobu Nagayama
  • Tsutomu Sasao

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Algorithms
  • Automatic
  • Chebyshev Approximations
  • Coefficients
  • Computations
  • Computer Graphics
  • Computer Vision
  • Digital Signal Processing
  • Errors
  • Exponential Functions
  • Generators
  • Logic
  • Logic Elements
  • Polynomials
  • Precision
  • Signal Processing
  • Square Roots

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Approximation Theory.
  • Computer Programming and Software Development.