A Compiler for Sound Floating-Point Computations using Affine Arithmetic

Abstract

Floating-point arithmetic is extensively used in scientific and engineering applications to approximate real arithmetic. Unfortunately, floating-point arithmetic is not a sound implementation of real arithmetic, i.e., it may produce different results, does not provide error guarantees, and the errors can become arbitrarily large. In this paper, we introduce SafeGen, a source-to-source compiler that rewrites a given C program using floating-point arithmetic to an efficient C program performing the same computation soundly, i.e., it returns an error bound that is guaranteed to contain the correct result of the program if it had been executed in real arithmetic. Equivalently, it gives a precision certificate on the number of correct bits in the result. SafeGen uses affine arithmetic (AA) that keeps accuracy high compared to interval arithmetic by preserving linear correlations between variables. To mitigate its high cost, SafeGen combines a novel form of static analysis to identify these correlations with a flexible policy-based approach for their selection. SafeGen supports SIMD intrinsics in the input and can output SIMDoptimized code. Our results show that SafeGen-generated code is 30–70 times faster than manually rewritten code using AA libraries. Equivalently, SafeGen can offer many more bits of certified accuracy within a reduced time budget.