Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction

In this paper it is shown that, under the assumption of thelogarithmic distribution of numbers, floating-point additionand subtraction can result in overflow or underflow with alarmingfrequency—a frequency that increases rapidly with machinespeed unless the range of the exponent is also increased. Ifnumbers are assumed to be distributed in accordance with Sweeney's(1965) experiments, then severe loss of significance occurswith large probability in floating point subtraction. Theseresults have implications for computer design and lead to thesuggestion of a long word format which will reduce the risksto acceptable levels.