利用浮点运算计算乘积和的确切符号
计算几何
2021-09-20 v2
摘要
在计算几何中，凸包、Voronoi 图和 Delaunay 三角剖分等基本图元的构造需要计算行列式（即乘积和）的符号。线性规划问题与线性不等式组的精确求解同样需要这些符号。利用不精确浮点运算精确计算这些符号颇具挑战性，我们为此任务提出了又一种算法。我们的算法高效且仅使用浮点运算，比精确运算快得多。我们证明了该算法的正确性，并提供了高效且经过测试的 \texttt{C++} 代码。
引用
@article{arxiv.2109.07838,
title = {Computing the exact sign of sums of products with floating point arithmetic},
author = {Walter F. Mascarenhas},
journal= {arXiv preprint arXiv:2109.07838},
year = {2021}
}
备注
In this second version we fix some typos and provide a more precise description of the conditions under which our main algorithm is valid. We also rewrote the algorithm in order to make it more clear. We also make the C++ code mentioned in the article available as supplementary material on the arxiv