A Statistical Study of the Accuracy of Floating Point Number Systems

This paper presents the statistical results
of tests of the accuracy of certain arithmetic 
systems in evaluating sums, products and inner products,
and analytic error estimates for some of the 
computations.  The arithmetic systems studied are 6-digit
hexadecimal and 22-digit binary floating point 
number representations combined with the usual chop
and round modes of arithmetic with various numbers 
of guard digits, and with a modified round mode with guard
digits.  In a certain sense, arithmetic systems 
differing only in their use of binary or hexadecimal number
representations are shown to be approximately 
statistically equivalent inaccuracy.  Further, the
usual round mode with guard digits is shown to be 
statistically superior in accuracy to the usual chop
mode in all cases save one.  The modified round 
mode is found to be superior to the chop mode in all cases.

CACM April, 1973

Kuki, H.
Cody, W. J.

error analysis, floating point arithmetic,
rounding, guard digits, number representation

5.11 5.5 6.32

CA730403 JB January 24, 1978  10:04 AM

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