An Interval Compiler for Sound Floating-Point Computations

Floating-point arithmetic is widely used by software developers but is unsound, i.e., there is no guarantee on the accuracy obtained, which can be imperative in safety-critical applications. We present IGen, a source-to-source compiler that translates a given C function using floating-point into an equivalent sound C function that uses interval arithmetic. IGen supports Intel SIMD intrinsics in the input function using a specially designed code generator and can produce SIMD-optimized output. To mitigate a possible loss of accuracy due to the increase of interval sizes, IGen can compile to double-double precision, again SIMD-optimized. Finally, IGen implements an accuracy optimization for the common reduction pattern. We benchmark our compiler on high-performance code in the domain of linear algebra and signal processing. The results show that the generated code delivers sound double precision results at high performance. In particular, we observe speed-ups of up to 9.8 when compared to commonly used interval libraries using double precision. When compiling to double-double, our compiler delivers intervals that keep error accumulation small enough to compute results with at most one bit of error in double precision, i.e., certified double precision results.

I. Introduction

Floating-point data types are a natural choice for software developers when implementing numerical computations. They are widely used in computer science and engineering, including in cyber-physical systems that interact with the physical world. Even relatively small embedded processors nowadays provide floating-point units. For example, the recent Helium Vector Extension [1] by ARM targets low-power microcontrollers and supports vectorized single and half precision floating-point operations.