一句话：提出舍入不变输出与舍入不变输入界两种方法，使 RLibm 数学库无需频繁切换舍入模式，性能提升超过 2 倍。
RLibm 此前能为至多 32 位表示、多种舍入模式生成单一正确舍入初等函数实现，其多项式逼近基于 round-to-odd 与额外两位表示以避免双重舍入；但实现依赖 round-to-nearest，应用使用其他舍入模式时需保存、切换并恢复系统舍入模式，频繁切换带来性能开销。本文提出舍入不变输出与舍入不变输入界两种方法：前者用 round-to-zero 实现多项式逼近，并用快速无误差变换在不改变舍入模式的情况下从任意标准舍入模式模拟 round-to-zero；后者在 RLibm 流程中用区间界吸收不同舍入模式导致的误差。两种方法各有取舍，均使生成库性能提升 2 倍以上。
Our RLibm project has recently proposed methods to generate a single implementation for an elementary function that produces correctly rounded results for multiple rounding modes and representations with up to 32-bits. They are appealing for developing fast reference libraries without double rounding issues. The key insight is to build polynomial approximations that produce the correctly rounded result for a representation with two additional bits when compared to the largest target representation and with the “non-standard” round-to-odd rounding mode, which makes double rounding the RLibm math library result to any smaller target representation innocuous. The resulting approximations generated by the RLibm approach are implemented with machine supported foating-point operations with the round-to-nearest rounding mode. When an application uses a rounding mode other than the round-to-nearest mode, the RLibm math library saves the application’s rounding mode, changes the system’s rounding mode to round-to-nearest, computes the correctly rounded result, and restores the application’s rounding mode. This frequent change of rounding modes has a performance cost. This paper proposes two new methods, which we call rounding-invariant outputs and rounding-invariant input bounds, to avoid the frequent changes to the rounding mode and the dependence on the round-to-nearest mode. First, our new rounding-invariant outputs method proposes using the round-to-zero rounding mode to implement RLibm ’s polynomial approximations. We propose fast, error-free transformations to emulate a round-to-zero result from any standard rounding mode without changing the rounding mode. Second, our rounding-invariant input bounds method factors any rounding error due to different rounding modes using interval bounds in the RLibm pipeline. Both methods make a different set of trade-offs and improve the performance of resulting libraries by more than 2×.
@article{paperbot3093,
title = {Correctly Rounded Math Libraries without Worrying about the Application’s Rounding Mode},
author = {Sehyeok Park and Justin Kim and Santosh Nagarakatte},
journal = {Proceedings of the ACM on Programming Languages},
volume = {9},
number = {PLDI},
year = {2025},
doi = {10.1145/3729332}
}