Google Research

Seamless Compiler Integration of Variable Precision Floating Point Arithmetic

  • Albert Cohen
  • Christian Fabre
  • Frédéric Pétrot
  • Tiago Trevisan Jost
  • Yves Durand
CGO 2021, ACM

Abstract

Floating Point (FP) units in processors are generally limited to supporting a subset of formats defined by the IEEE 754 standard. As a result, high-efficiency languages and optimizing compilers for high-performance computing only support IEEE standard types and applications needing higher precision involve cumbersome memory management and calls to external libraries. Furthermore, numerical computations often involve iterative solvers where the residual error is a function of the input data, or where dynamically adaptive precision can accelerate convergence; numerical analysts have to resort to explicit conversions and multi-versioning, resulting in code bloat and making the intent of the program even less clear. We present an extension of the C type system that can represent generic FP operations and formats, supporting both static and dynamically variable precision. We design and implement a compilation flow bridging the abstraction gap between this type system and low-level FP instructions or software libraries. This flow enables classical optimizations as well as multi-precision-specific ones associated with memory management and target-specific implementation. The effectiveness of our solution is demonstrated through an LLVM-based implementation, leveraging aggressive optimizations in LLVM including the Polly loop nest optimizer, and leveraging two alternative backend code generators: one that targets the ISA of a variable precision FP arithmetic Co-processor, and one targeting the MPFR multi-precision floating point library. Both targets support the statically and dynamically adaptable precision and size of our language extension. On the PolyBench suite, our optimizing compilation flow targeting MPFR outperforms the Boost programming interface for the MPFR library by a factor of 1.84x.

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