A unified framework for nonlinear dependence testing and symbolic analysis

  • Authors:

  • Robert A. van Engelen;J. Birch;Y. Shou;B. Walsh;Kyle A. Gallivan

  • Affiliations:

  • Florida State University, Tallahassee, FL;Florida State University, Tallahassee, FL;Florida State University, Tallahassee, FL;Florida State University, Tallahassee, FL;Florida State University, Tallahassee, FL

  • Venue:
  • Proceedings of the 18th annual international conference on Supercomputing
  • Year:
  • 2004

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Abstract

This paper presents a unified approach for generalized induction variable recognition and substitution, pointer analysis, analysis of conditionally updated variables, value range analysis, array region analysis, and nonlinear dependence testing. The analysis techniques share a well-defined uniform approach based on the chains of recurrences algebra. The uniform algebraic approach provides a powerful unified framework for developing analysis algorithms for restructuring compilers. The paper introduces a new set of analysis algorithms that accurately handle conditional control flow, pointer arithmetic, and nonlinear symbolic expressions in loops, which are known to be problematic for conventional restructuring compilers.