Gappa is a tool designed to formally verify the correctness of numerical software and
hardware. It uses interval arithmetic and forward error analysis to bound mathematical …

The crlibm project aims at develo** a portable, proven, correctly rounded, and efficient
mathematical library (libm) for double precision. Current libm implementation do not always …

There are several different libraries with code for mathematical functions such as exp, log,
sin, cos, etc. They provide only one implementation for each function. As there is a link …

ReLU is widely seen as the default choice for activation functions in neural networks.
However, there are cases where more complicated functions are required. In particular …

This article is a case study in the implementation of a portable, proven and efficient correctly
rounded elementary function in double-precision. We describe the methodology used to …

This article presents advances on the subject of correctly rounded elementary functions
since the publication of the libultim mathematical library developed by Ziv at IBM. This library …

We describe a new implementation of the elementary transcendental functions exp, sin, cos,
log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR …

The implementation of correctly rounded elementary functions needs high intermediate
accuracy before final rounding. This accuracy can be provided by (pseudo-) expansions of …

In the last decades embedded systems have been challenged with more and more
application variety, each time more constrained. This implies an ever growing need for …

1. は じめに精度保証付 き数値 計算 とは, 一 言で言 えば, 得られ た結果 が定量的 にどれ く
らい** しいか とい う情報 が付加 された数値 計算で ある. **年 の計算機の発 展に伴 って, 数 …