Loss of Significance in Floating Point Subtraction and Addition

Authors:
A. Feldstein;R. Goodman
Affiliations:
Department of Mathematics, Arizona State University;-
Venue:
IEEE Transactions on Computers
Year:
1982

Citing 4
Cited 0

Convergence Estimates for the Distribution of Trailing Digits

Journal of the ACM (JACM)
On accurate floating-point summation

Communications of the ACM
Optimizing floating point arithmetic via post addition shift probabilities

AFIPS '69 (Spring) Proceedings of the May 14-16, 1969, spring joint computer conference
An analysis of floating-point addition

IBM Systems Journal

Quantified Score

Hi-index	14.98

Visualization

Abstract

We study the loss of significant βits (?base 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.