Correctly Rounded Functions For Vector Applications: A Performance Study
Cristina Anderson, Marius Cornea, Andrey Stepin, Mihai Tudor Panu
TL;DR
This paper presents the design and evaluation of SIMD algorithms for correctly rounded math functions, aiming to develop a cross-platform, correctly rounded vector math library for CPUs and GPUs by 2026.
Contribution
It introduces new SIMD algorithms for correctly rounded single and double precision functions and evaluates their performance on CPUs and GPUs.
Findings
Developed SIMD algorithms for correctly rounded functions
Integrated algorithms into a CPU math library for future release
Evaluated GPU implementations for cross-platform reproducibility
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.
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