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| -rw-r--r-- | Doc/tutorial/floatingpoint.rst | 26 |
1 files changed, 18 insertions, 8 deletions
diff --git a/Doc/tutorial/floatingpoint.rst b/Doc/tutorial/floatingpoint.rst index 78dc1d6..98e299d 100644 --- a/Doc/tutorial/floatingpoint.rst +++ b/Doc/tutorial/floatingpoint.rst @@ -109,14 +109,24 @@ It's important to realize that this is, in a real sense, an illusion: you're simply rounding the *display* of the true machine value. One illusion may beget another. For example, since 0.1 is not exactly 1/10, -summing ten values of 0.1 may not yield exactly 1.0, either:: - - >>> sum = 0.0 - >>> for i in range(10): - ... sum += 0.1 - ... - >>> sum - 0.9999999999999999 +summing three values of 0.1 may not yield exactly 0.3, either:: + + >>> .1 + .1 + .1 == .3 + False + +Also, since the 0.1 cannot get any closer to the exact value of 1/10 and +0.3 cannot get any closer to the exact value of 3/10, then pre-rounding with +:func:`round` function cannot help:: + + >>> round(.1, 1) + round(.1, 1) + round(.1, 1) == round(.3, 1) + False + +Though the numbers cannot be made closer to their intended exact values, +the :func:`round` function can be useful for post-rounding so that results +have inexact values that are comparable to one another:: + + >>> round(.1 + .1 + .1, 1) == round(.3, 1) + True Binary floating-point arithmetic holds many surprises like this. The problem with "0.1" is explained in precise detail below, in the "Representation Error" |