Translation and Run-Time Validation of Loop Transformations

Abstract

This paper presents new approaches to the validation of loop optimizations that compilers use to obtain the highest performance from modern architectures. Rather than verify the compiler, the approach of translation validation performs a validation check after every run of the compiler, producing a formal proof that the produced target code is a correct implementation of the source code.As part of an active and ongoing research project on translation validation, we have previously described approaches for validating optimizations that preserve the loop structure of the code and have presented a simulationbased general technique for validating such optimizations. In this paper, for more aggressive optimizations that alter the loop structure of the code-such as distribution, fusion, tiling, and interchange-we present a set of permutation rules which establish that the transformed code satisfies all the implied data dependencies necessary for the validity of the considered transformation. We describe the extensions to our tool VOC-64which are required to validate these structure-modifying optimizations.This paper also discusses preliminary work on run-time validation of speculative loop optimizations. This involves using run-time tests to ensure the correctness of loop optimizations whose correctness cannot be guaranteed at compile time. Unlike compiler validation, run-time validation must not only determine when an optimization has generated incorrect code, but also recover from the optimization without aborting the program or producing an incorrect result. This technique has been applied to several loop optimizations, including loop interchange and loop tiling, and appears to be quite promising.

Automatic Equivalence Checking of UF+IA Programs

“…The second part is a set of optimizations that PEC can prove correct without the help of heuristics. The third part is a set of optimizations that PEC can only prove correct by using the permute heuristic [14,48], since otherwise it could not find a bisimulation relation automatically. The fourth and last part of the table contains a set of optimizations that PEC cannot prove correct, since it cannot find a bisimulation automatically, even with the permute heuristic.…”

“…It works by automatically finding a bisimulation relation [38] between the original and the optimized template programs. For structurally different loops, PEC relies on a set of heuristics inspired in [14,48].…”

“…Proving the equivalence of programs has several important applications, including, but not limited to, algorithm recognition [2], regression checking [11,13,25], compiler optimization verification [18,24] and validation [31,33,41,44,47,48], and information flow proofs [5,43].…”

Abstract Semantic Differencing for Numerical Programs

“…In previous work regarding translation validation [23,20,30], in order to establish equivalence for a (looping) code fragment being translated or optimized by a compiler, a simulation relation between the basic blocks of the translated code is found. This method is limited in the context of semantic differencing as, for instance, a simulation relation for examples such as Fig.…”

Translation Validation of High-Level Synthesis

“…Our work is related to translation validation [19], [33], [42], [46], [47], [53], [54], relational approaches to reasoning about programs [5], [7], [15], [28], [35], CSP refinement checking [13], [27], [39], [51], and HLS verification [2], [14], [31], [34], [41]. We now discuss each area in more detail.…”