Loop Tree and Induction Variables

• Published in: SSA-based Compiler Design pp. 123 - 133
• Main Authors: Pop, Sebastian, Cohen, Albert
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2022
• Subjects: Chain of recurrences; Compiler design; Induction variable recognition; Loop optimization; Phi-entry node; Phi-exit node; Reducible loop; Scalar evolution (SCEV); Static analysis; Static single assignment form (SSA form); Use-def chain
• ISBN: 303080514X; 9783030805142
• DOI: 10.1007/978-3-030-80515-9_10

Induction variables refer to a wide class of inductive definitions, where the sequence of values taken by a variable follows a regular pattern. The typical case is that of a loop counter. More generally, induction variables are associated with affine, geometric, or otherwise statically predictable progressions in loops. The purpose of the induction variable analysis is to provide a characterization of such sequences. There are numerous applications, from the detection of parallel loops to optimizations such as loop-invariant code motion, strength reduction, eliminating dependencies, and evaluating the number of iterations of a while loop. This chapter focuses particularly on the analysis and classification of induction variables in the presence of complex, low-level control flow (gotos, multiple loop exits, etc.). It describes the algorithm underlying the analysis of “scalar evolutions” in the GCC and LLVM compilers.