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1: 27.17 Other Applications
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►Congruences are used in constructing perpetual calendars, splicing telephone cables, scheduling round-robin tournaments, devising systematic methods for storing computer files, and generating pseudorandom numbers.
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2: 3.1 Arithmetics and Error Measures
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Rounding
… ►Then rounding by chopping or rounding down of gives , with maximum relative error . Symmetric rounding or rounding to nearest of gives or , whichever is nearer to , with maximum relative error equal to the machine precision . ►Negative numbers are rounded in the same way as . … ►Interval arithmetic is intended for bounding the total effect of rounding errors of calculations with machine numbers. …3: 8.26 Tables
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Pearson (1965) tabulates the function () for , to 7D, where rounds off to 1 to 7D; also for , to 5D.
4: Bibliography Z
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Fast evaluation of elementary mathematical functions with correctly rounded last bit.
ACM Trans. Math. Software 17 (3), pp. 410–423.
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5: DLMF Project News
error generating summary6: Mathematical Introduction
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►Another numerical convention is that decimals followed by dots are unrounded; without the dots they are rounded.
…1416 (rounded).
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7: 12.11 Zeros
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►where the numerical coefficients have been rounded off.
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8: 2.11 Remainder Terms; Stokes Phenomenon
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►On rounding to 5D, we have , , .
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►Taking and rounding to 5D, we obtain
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►We now compute the forward differences , , of the moduli of the rounded values of the first 6 neglected terms:
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9: 3.2 Linear Algebra
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►Because of rounding errors, the residual vector
is nonzero as a rule.
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10: 3.6 Linear Difference Equations
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►Unless exact arithmetic is being used, however, each step of the calculation introduces rounding errors.
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