Research Article

Parametric timing estimation with Newton–Gregory formulae

  1. Robert A. van Engelen*,
  2. Kyle A. Gallivan,
  3. Burt Walsh

Article first published online: 17 JAN 2006

DOI: 10.1002/cpe.1015

Issue

Concurrency and Computation: Practice and Experience

Concurrency and Computation: Practice and Experience

Special Issue: 10th International Workshop on Compilers for Parallel Computers (CPC 2003)

Volume 18, Issue 11, pages 1435–1463, September 2006

Additional Information

How to Cite

van Engelen, R. A., Gallivan, K. A. and Walsh, B. (2006), Parametric timing estimation with Newton–Gregory formulae. Concurrency Computat.: Pract. Exper., 18: 1435–1463. doi: 10.1002/cpe.1015

Author Information

  1. Department of Computer Science and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL 32306-4530, U.S.A.

*Department of Computer Science and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL 32306-4530, U.S.A.

Publication History

  1. Issue published online: 28 JUL 2006
  2. Article first published online: 17 JAN 2006
  3. Manuscript Accepted: 5 OCT 2004
  4. Manuscript Revised: 18 MAY 2004
  5. Manuscript Received: 16 MAY 2003

Funded by

  • NSF. Grant Numbers: CCR-0105422, CCR-0208892, EIA-0072043
  • DOE. Grant Number: DEFG02-02ER25543

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Keywords:

  • code analysis;
  • parametric estimation;
  • WCET;
  • interpolation

Abstract

This paper presents a novel method for parametric worst-case execution time (WCET) estimation of loops. The method determines a parametric bound on the iteration space size of loops with both affine and non-affine loop bounds in an efficient manner using a formulation based on Newton–Gregory interpolating polynomials. Parametric WCET formulae are used to support dynamic scheduling decisions at runtime, where the WCET of a scheduled task might not be known statically. To determine worst-case execution time estimates of scientific and multimedia codes, which spent most of the execution time on executing loop iterations, efficient and accurate symbolic loop WCET estimation methods must be capable of analyzing loops with symbolic bounds, non-rectangular loops, zero-trip loops, loops with multiple critical paths, and loops with non-unit strides. Copyright © 2006 John Wiley & Sons, Ltd.

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