Improved Trailing Digits Estimates Applied to Optimal Computer Arithmetic

Abstract

New results are given on the distribution of trailing digits for logarithmically distributed numbers and on error in floating-point multiplication Some of the results have application to computer design In particular, there are certain values of the base (indeed, β = 2, 4, 6, and sometimes 8, but NOT 16) which, when carefully balanced with other design parameters, minimize the mean multiphcative error For these special minimizing situations, it suffices to have only one guard flit provided that posmormahzatlon occurs after symmetric rounding. © 1979, ACM. All rights reserved.