Analysis of some known methods of improving the accuracy of floating-point sums

Some well-known methods for calculating the round-off error in floating-point addition are analyzed in this paper. The methods have been introduced by Møller [16], Kahan [11] and Knuth [12]. The necessary and sufficient conditions under which these methods produce the value of the round-off error, for rounding, truncating and parity arithmetic, are given. The computer-oriented parity arithmetic is not commonly known, but it has some desirable properties, as this paper will demonstrate. Some experimental results are also reported.

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