Dear All
The following might help you to understand what is going on.
It comes from a colleague Dr Maurice Cox:
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This interesting example can be "explained" using the IEEE model of floating point arithmetic.
The exact result of dividing a by b is X = a/b.
Based on the IEEE model of fp arithmetic, the calculated result is x = (a/b)(1 + e), where |e| <= u, the unit roundoff.
u = 2^{-52} = 2.2e-16 for Intel, Motorola, ...
The error E in x is x - X = (a/b)e.
Thus, |E| <= |a/b|u.
For the example, a = 1926, b = 100, giving |E| <= (19.26)(2.2e-16) = 4.2e-15.
The observed error using CIAO is 2.9e-15 and using C is 1.6e-15, both of which are consistent with the bound.
This concept of fp error analysis is widely applicable to explain results and analyse and compare algorithms.
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Best Wishes Graeme I Parkin Centre Mathematics and Scientific Computing National Physical Laboratory Queens Road Teddington, Middlesex TW11 0LW Tel: +44 20 8943 7104 Fax: +44 20 8977 7091
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