Twofold exp and log

TL;DR

This paper introduces twofold arithmetic algorithms and code for standard exponential and logarithm functions in C/C++, achieving nearly double precision and significantly faster performance for accuracy assessment.

Contribution

It presents novel twofold variants of exp, log, expm1, and log1p functions, with algorithms and experimental implementation for improved precision and performance.

Findings

Twofold functions are nearly 2x more precise than standard functions.

Twofold texp() over double is approximately 10x faster than GNU quadmath's expq().

The approach enables on-the-fly accuracy assessment.

Abstract

This article is about twofold arithmetic. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function $y_0+y_1 \approx f(x_0+x_1)$ is nearly 2x-precise so can assess accuracy of standard one. Performance allows assessing on-fly: twofold texp() over double is ~10x times faster than expq() by GNU quadmath.