On the Robustness of the 2Sum and Fast2Sum Algorithms
On the Robustness of the 2Sum and Fast2Sum Algorithms
复制标题
论2Sum和Fast2Sum算法的鲁棒性
DOI：
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发表时间：
2017
影响因子：
2.7
通讯作者：
J. Muller
中科院分区：
文献类型：
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作者：
S. Boldo;S. Graillat;J. Muller
2Sum和Fast2Sum算法是数值计算中的重要组成部分。它们被(隐式或显式地)用于许多补偿算法(例如补偿求和或补偿多项式求值)。它们还用于操作浮点扩展。我们证明了这些算法比通常认为的要健壮得多：即使在舍入函数不是舍入到最近的情况下，返回的结果也是有意义的，并且它们几乎不会溢出。
The 2Sum and Fast2Sum algorithms are important building blocks in numerical computing. They are used (implicitely or explicitely) in many compensated algorithms (such as compensated summation or compensated polynomial evaluation). They are also used for manipulating floating-point expansions. We show that these algorithms are much more robust than it is usually believed: The returned result makes sense even when the rounding function is not round-to-nearest, and they are almost immune to overflow.