期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 26, 期 6, 页码 1955-1988出版社
SIAM PUBLICATIONS
DOI: 10.1137/030601818
关键词
accurate summation; accurate dot product; fast algorithms; verified error bounds; high precision
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.
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