Automated optimization of look-up table implementation for function evaluation on FPGAs

L. Deng, Chaitali Chakrabarti, N. Pitsianis, X. Sun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations


This paper presents a systematic approach for automatic generation of look-up-table (LUT) for function evaluations and minimization in hardware resource on field programmable gate arrays (FPGAs). The class of functions supported by this approach includes sine, cosine, exponentials, Gaussians, the central B-splines, and certain cylinder functions that are frequently used in applications for signal and image processing and data processing. In order to meet customer requirements in accuracy and speed as well as constraints on the use of area and on-chip memory, the function evaluation is based on numerical approximation with Taylor polynomials. Customized data precisions are supported in both fixed point and floating point representations. The optimization procedure involves a search in three-dimensional design space of data precision, sampling density and approximation degree. It utilizes both model-based estimates and gradient-based information gathered during the search. The approach was tested with actual synthesis results on the Xilinx Virtex-2Pro FPGA platform.

Original languageEnglish (US)
Title of host publicationMathematics for Signal and Information Processing
EditorsMark S. Schmalz
StatePublished - 2009
EventMathematics for Signal and Information Processing - San Diego, CA, United States
Duration: Aug 2 2009Aug 5 2009

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherMathematics for Signal and Information Processing
Country/TerritoryUnited States
CitySan Diego, CA


  • Automatic generation
  • FPGAs
  • Function evaluation
  • Look-up table
  • Resource minimization

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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