Accurate sum and dot product
Accurate sum and dot product
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DOI：
10.1137/030601818
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发表时间：
2005-01-01
影响因子：
3.1
通讯作者：
Oishi, S
中科院分区：
文献类型：
--
作者：
Ogita, T;Rump, SM;Oishi, S
提出了浮点数的求和和点积的算法，这些算法在测量计算时间方面是快速的。我们表明，计算结果是准确的，如果计算的两倍或K倍的工作精度，K >= 3。对于两倍的工作精度，我们的求和和点积算法比相应的XBLAS例程快约40%，同时共享类似的误差估计。我们的算法是广泛适用的，因为它们只需要在相同的工作精度作为给定的数据的浮点数的加法，减法和乘法。不需要更高的精度，算法是没有分支的直接循环，并且不需要访问尾数或指数。
Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or K-fold working precision, K >= 3. For twice the working precision our algorithms for summation and dot product are some 40% faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.