Issue No. 04 - April (1982 vol. 31)
A. Feldstein , Department of Mathematics, Arizona State University
We study the loss of significant ?its (?base ? digits) in floating point addition or subtraction. To do this, we calculate the conditional probability of a post-arithmetic normalization shift of m ?its, given an exponent difference of k ?its. The study is done for various bases ?, under two different assumptions?that the operands are selected at random from the logarithmic distribution or from the uniform distribution.
uniformly distributed numbers, Computer arithmetic, floating point addition and subtraction, floating point precision and significance, logarithmically distributed numbers, loss of significant digits, significant digits
R. Goodman, A. Feldstein, "Loss of Significance in Floating Point Subtraction and Addition", IEEE Transactions on Computers, vol. 31, no. , pp. 328-335, April 1982, doi:10.1109/TC.1982.1676002