A unified framework for nonlinear dependence testing and symbolic analysis

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.