"Steven D'Aprano" <[EMAIL PROTECTED]> wrote: > Unfortunately, floating point maths is a bit of a black art. Try this > simple calculation: > > py> 4.0/3 - 5.0/6 > 0.49999999999999989 > > Should be 0.5 exactly. > > Many numbers which you can write exactly in decimal cannot be > stored exactly in floating point. Even something as simple as one tenth > 0.1 doesn't have an exact representation in binary: > > py> 1.0/10 > 0.10000000000000001
Given that 0.5 *can* be represented exactly in binary (try 0.3/0.6), your first example illustrates something worse about floating point arithmetic: not only many decimal numbers cannot be represented exactly as binary floating point, but that the kind and the order of operations in arithmetic expressions affects the accuracy of the result. *Even worse* than that, errors can be accumulated over a sequence of operations, so that even if each individual error is typically very small, the overall error might be non-trivial. There's a whole area studying the analysis and control of error in floating point arithmetic so it's not quite black art for everyone; e.g. see http://docs.sun.com/source/806-3568/ncg_goldberg.html, http://http.cs.berkeley.edu/~demmel/cs267/lecture21/lecture21.html for more. George -- http://mail.python.org/mailman/listinfo/python-list
