🤖 AI Summary
This work addresses the widespread lack of correctly rounded results in high-performance vector math libraries, which undermines bit-level reproducibility across platforms. The authors propose a unified framework that integrates SIMD parallelism with correctly rounded algorithms to efficiently implement multiple single-precision, single-input mathematical functions on CPUs and, for the first time, extend this approach to GPUs. They also provide a prototype implementation for double-precision functions. This research lays the foundation for the first cross-platform vector math library supporting correct rounding, with a planned public release by mid-2026, significantly advancing reproducibility and precision guarantees in numerical computing.
📝 Abstract
Following recent interest in correctly rounded math library functions (as currently recommended by the IEEE 754 standard), we have designed several SIMD algorithms for one-input single precision functions and integrated them into our CPU math library; these will form the core of the first correctly rounded vector math library, to be available to users in mid-2026. To take advantage of the cross-platform bitwise reproducibility afforded by correct rounding, we adapted and evaluated a few SIMD implementations on graphics processing units (GPU). In addition, we designed and evaluated proof-of-concept SIMD implementations of two correctly rounded double precision functions.