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Loss of Significance in Floating Point Subtraction and Addition

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2 Author(s)
Feldstein, A. ; Department of Mathematics, Arizona State University ; Goodman, R.

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.

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Computers, IEEE Transactions on  (Volume:C-31 ,  Issue: 4 )