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A new error-free floating-point summation algorithm

✍ Scribed by V.Y. Pan; B. Murphy; G. Qian; R.E. Rosholt

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
368 KB
Volume
57
Category
Article
ISSN
0898-1221

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✦ Synopsis

Summation is a basic operation in scientific computing; furthermore division-free arithmetic computations can be boiled down to summation. We propose a new summation algorithm, which consists of double-precision floating-point operations and outputs the error-free sums. The computational time is proportional to the condition number of the problem, is low according to both our estimates and extensive experiments, and further decreases for producing faithful rounding of the sum, rather than its error-free value.

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## Abstract This paper proposes an algorithm to accurately compute the sum of floating‐point numbers on parallel computers. This algorithm is an extension of the well‐known recursive doubling technique which computes the sum of __n__ floating‐point number in log~2~__n__ parallel steps. The time com