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Goodman, Richard H.; Feldstein, Alan; Bustoz, J.

Relative error in floating-point multiplication. (English) Zbl 0564.65030

Computing 35, 127-139 (1985).
A model of the relative error in floating point multiplication is developed and is analyzed stochastically for various choices of computer design parameters. These parameters include the base, the type of rounding rule, the number of guard digits, and whether the post- arithmetic normalization shift (if needed) is done before or after rounding. Under the assumption of logarithmic distribution for the fraction (mantissa), the major stochastic conclusions are:
1. The average relative error in multiplication increases as the base increases. 2. This error is minimized by selecting the machine based to be binary (better yet, binary with a hidden bit) and is rather large for machines with base 16. 3. The classical relative error bounds are pessimistic. The average overestimation by those bounds increases as the base increases.

Cited in 2 Documents

MSC:

65G50 Roundoff error

Keywords:

relative error; computer arithmetic; floating point multiplication; normalization options; guard digits; floating point numbers; floating point precision and significance; round-off error; fraction error; mean and standard deviation of errors; logarithmically distributed numbers
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References:

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