Title :
Loss of Significance in Floating Point Subtraction and Addition
Author :
Feldstein, Alan ; Goodman, Richard
Author_Institution :
Department of Mathematics, Arizona State University
fDate :
4/1/1982 12:00:00 AM
Abstract :
We study the loss of significant βits (Ξbase β digits) in floating point addition or subtraction. To do this, we calculate the conditional probability of a post-arithmetic normalization shift of m βits, given an exponent difference of k βits. The study is done for various bases β, under two different assumptions—that the operands are selected at random from the logarithmic distribution or from the uniform distribution.
Keywords :
Computer arithmetic; floating point addition and subtraction; floating point precision and significance; logarithmically distributed numbers; loss of significant digits; significant digits; uniformly distributed numbers; Floating-point arithmetic; Probability; Virtual manufacturing; Computer arithmetic; floating point addition and subtraction; floating point precision and significance; logarithmically distributed numbers; loss of significant digits; significant digits; uniformly distributed numbers;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.1982.1676002
