Relative error in floating-point multiplication
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.
floating point precision and significance
scientific article; zbMATH DE number 3900053