Some models of relative error in products (Q908659)

For various choices of computer design parameters the stochastical model and analysis of magnitude relative error in floating point multiplication is given. The parameters include the base, the type of rounding rule, the number of guard digit and the fact whether the normalization shift is done before or after rounding. If a logarithmic distribution of the mantissa is assumed, the following stochastical conclusions are obtained: 1. The average magnitude relative error in multiplication increases as the base increases. 2. The average error is minimized by selecting the machine base to be binary with a hidden bit, and is larger for base 16. Other models of relative error are also developed and analyzed.