用于32位浮点表示的高性能正确舍入数学库

Jay P. Lim, Santosh Nagarakatte
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引用次数: 13

摘要

本文提出了一套技术来为32位浮点数和浮点数类型开发正确的四舍五入数学库。它增强了我们的RLIBM方法,将在16位类型上下文中生成正确舍入库的问题作为线性规划问题框架,以扩展到32位类型。具体来说,本文提出了新的算法:(1)使用反例引导多项式生成生成多项式,为所有输入生成正确的四舍五入输出;(2)使用基于位模式的域分裂生成有效的分段多项式;(3)当涉及多个初等函数时,推导出可用于产生正确结果的自由度。生成的32位浮点类型的数学库比最先进的数学库更快,同时为所有输入生成正确的输出。我们还为32位的位置开发了一组正确舍入的初等函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
High performance correctly rounded math libraries for 32-bit floating point representations
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLIBM approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.
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