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Communications of the ACM

Communications of the ACM

Precision averaging for real-time analysis

An analysis of the computation of the arithmetic mean using only single-precision fixed-point arithmetic is presented. This is done to ease the timing constraints common to many on-line applications. Others have introduced several averaging algorithms in floating-point arithmetic for use in inferential statistics. In this paper, these algorithms are evaluated with respect to their feasibility as fixed-point methods in the context of real-time analysis. Modifications of these algorithms are presented, and previously unpublished ones are introduced in the interest of avoiding overflow (necessary) and minimizing truncation errors (highly desirable). All algorithms presented are tested for speed and accuracy on several sets of data, including their own “worst case.” The applicability of each algorithm is discussed with respect to some of the basic functions that real-time programs must perform.

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