Logical inference techniques for loop parallelization

Abstract

This paper presents a fully automatic approach to loop parallelization that integrates the use of static and run-time analysis and thus overcomes many known difficulties such as nonlinear and indirect array indexing and complex control flow. Our hybrid analysis framework validates the parallelization transformation by verifying the independence of the loop's memory references. To this end it represents array references using the USR (uniform set representation) language and expresses the independence condition as an equation, S =0, where S is a set expression representing array indexes. Using a language instead of an array-abstraction representation for S results in a smaller number of conservative approximations but exhibits a potentially-high runtime cost. To alleviate this cost we introduce a language translation F from the USR set-expression language to an equally rich language of predicates ( F ( S ) ==> S = 0). Loop parallelization is then validated using a novel logic inference algorithm that factorizes the obtained complex predicates (F( S )) into a sequence of sufficient independence conditions that are evaluated first statically and, when needed, dynamically, in increasing order of their estimated complexities. We evaluate our automated solution on 26 benchmarks from PERFECT-Club and SPEC suites and show that our approach is effective in parallelizing large, complex loops and obtains much better full program speedups than the Intel and IBM Fortran compilers.