On the Rounding Rules for Logarithmic and Exponential Operations

Wei-Da Chen ； Wei Lee ； Christopher L. Mulliss

《Chinese Journal of Physics》 43卷6期 (2005/12) Pp. 1017-1034

並列摘要

This work is a detailed investigation of the rounding rules for logarithmic and exponential operations, including mathematical derivations and statistical analyses via Monte-Carlo simulations. H. Lawrence Clever suggested rounding rules for logarithmic and exponential operations in 1979. We have found Clever's rules for logarithmic operations to be quite good, especially for natural logarithms, and found that they never lead to a loss of information. We propose a refinement to Clever's rounding rule for common (i.e. base 10) logarithmic operations that significantly increases its accuracy. Clever's rules for exponential operations were found to be extremely poor, almost never predicting the correct number of significant figures in the result. We suggest two alternate rules for exponential operations, both of which are demonstrated to be far more accurate and completely safe for data (i.e. never leading to a loss of information).