Numerical methods for scientists and engineers (2nd ed.)
Numerical methods for scientists and engineers (2nd ed.)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On Local Roundoff Errors in Floating-Point Arithmetic
Journal of the ACM (JACM)
Tests of probabilistic models for propagation of roundoff errors
Communications of the ACM
Test of probabilistic models for the propagation of roundoff errors
Communications of the ACM
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
A Survey of Some Recent Contributions to Computer Arithmetic
IEEE Transactions on Computers
Static and Dynamic Numerical Characteristics of Floating-Point Arithmetic
IEEE Transactions on Computers
On the Precision Attainable with Various Floating-Point Number Systems
IEEE Transactions on Computers
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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 in accuracy. 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.