Icing: Supporting Fast-Math Style Optimizations in a Verified Compiler

Abstract

Verified compilers like CompCert and CakeML offer increasingly sophisticated optimizations. However, their deterministic source semantics and strict IEEE 754 compliance prevent the verification of "fast-math" style floating-point optimizations. Developers often selectively use these optimizations in mainstream compilers like GCC and LLVM to improve the performance of computations over noisy inputs or for heuristics by allowing the compiler to perform intuitive but IEEE 754-unsound rewrites. We designed, formalized, implemented, and verified a compiler for Icing, a new language which supports selectively applying fast-math style optimizations in a verified compiler. Icing's semantics provides the first formalization of fast-math in a verified compiler. We show how the Icing compiler can be connected to the existing verified CakeML compiler and verify the end-to-end translation by a sequence of refinement proofs from Icing to the translated CakeML. We evaluated Icing by incorporating several of GCC's fast-math rewrites. While Icing targets CakeML's source language, the techniques we developed are general and could also be incorporated in lower-level intermediate representations.

SMT-Based Translation Validation for Machine Learning Compiler

“…The concrete semantics of FP operations is hidden under the uninterpreted functions used for the abstract encoding. The semantics of unsafe FP arithmetic is often explained using nondeterministic execution [11] and encoding it in SMT requires universal quantification which is expensive.…”

“…Then, what is the semantics of x + y + z? One possible solution is that its evaluation nondeterministically yields either (x+y)+z or x+(y+z) [11]. However, encoding the semantics in SMT requires introducing quantified variables.…”

“…Compiler Verification. [11] relaxes FPA semantics since a compiler can ignore strict IEEE-754 behavior like fast-math optimizations in LLVM. They propose Icing which is a language allowing IEEE 754-unsafe FPA optimizations, and CakeML [28] which is a verified compiler with the optimizations.…”

Доверя́й, но проверя́й: SFI safety for native-compiled Wasm

“…For instance, Kroll et al [32] implement a verified SFI system on top of the Compcert verified compiler [40], and there is ongoing work to build a verified Wasm compiler [13]. More generally, CompCert and its variations [39], [79], [68] and CakeML [33] are examples of foundationally verified compilers, and there are many examples of verified optimizations for these compilers [48], [7].…”