Required scientific floating point arithmetic

Abstract

Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be attained using guard digits and careful algorithms on the floating point fractions. This paper combines that body of knowledge with proposed exponent forms that are closed with respect to inversion and detection and recovery of exponent under and over flow. In addition radix 2 is shown to be the only base radix meeting minimal variation of precision, a condition necessary for the safe use of floating point. An effort is made to establish objective criteria in answer to the question; "What is the best division of the computer word into exponent and fraction parts?". Combining the previous results allows a required scientific floating point arithmetic to be portrayed and compared with available arithmetics on current computers.