Verified lifting of stencil computations

Abstract

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counterexample guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. Our experiments show that the lifted summaries allow domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1× and up to 24× as compared to the original implementation.

Automatic Matching of Legacy Code to Heterogeneous APIs

“…It relies on dynamic analysis and cannot easily be extended to other idioms. Another closely related paper is [27], which detects stencils in FORTRAN by the verified lifting of code segments to a representation that can be mapped to Halide DSL. It uses syntax guided synthesis to verify translation with added constrains to ensure that it can be mapped to Halide.…”

“…This requires large scale dynamic analysis of binary traces and replacing them with Halide calls. This is significantly extended in [27] which detects stencils in FORTRAN. In this work the focus is on inferring post invariants based on syntax guided synthesis in translation to Halide.…”

Towards Self-Verification in Finite Difference Code Generation

“…The automated verification of such transformations was previously demonstrated in [38] by proving the equivalence of the original and transformed codes. Other authors successfully attempted the verification of GPU parallelisation [6] and verified lifting to domain-specific languages [19] of stencil computations.…”

Leveraging Parallel Data Processing Frameworks with Verified Lifting

“…[19] is the most recent research that attempts to synthesize MapReduce solutions with user-provided input and output examples. QBS [7] and STNG [11] both use verified lifting and synthesis to convert low-level languages to specialized high-level DSLs for database applications and stencil computations respectively.…”

“…One way to improve the accessibility of these parallel data processing frameworks involves building compilers that automatically convert applications written in common general-purpose languages (such as Java or Python) to high-performance parallel processing frameworks, such as Hadoop or Spark. Such compilers let users write their applications in familiar general-purpose languages and let the compiler retarget portions of their code to high-performance DSLs [7,11,15]. The applications can then leverage the performance of these specialized frameworks without the overhead of learning how to program individual DSLs.…”