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Loss of Significance in Floating Point Subtraction and Addition
April 1982 (vol. 31 no. 4)
pp. 328-335
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.
Index Terms:
uniformly distributed numbers, Computer arithmetic, floating point addition and subtraction, floating point precision and significance, logarithmically distributed numbers, loss of significant digits, significant digits
Citation:
A. Feldstein, R. Goodman, "Loss of Significance in Floating Point Subtraction and Addition," IEEE Transactions on Computers, vol. 31, no. 4, pp. 328-335, April 1982, doi:10.1109/TC.1982.1676002
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