[issue3439] create a numbits() method for int and long types

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

About the footnote:

floor(log(n, 2)) is poor code.  This is not supposed to be a dramatic 
statement, just a statement of fact.  Its correctness is dependent on 
minute details of floating point.  It is poor code in exactly the same way 
that "while x < 1.0: x += 0.1" is poor code---behaviour in boundary cases 
is almost entirely unpredictable.

If 1 + floor(log(n, 2)) happens to give the correct result in the common 
corner case where x is a power of 2, then that's due to little more than 
sheer luck.  Correct rounding by itself is nowhere near enough to 
guarantee correct results.

In the case of IEEE 754 doubles, a large part of the luck is that the 
closest double to log(2) just happens to be *smaller* than log(2) itself, 
so that the implicit division by log(2) in log(x, 2) tends to give a 
larger result than the true one;  if things were the other way around, the 
formula above would likely fail for many (even small) n.

So I don't like seeing this poor code in the Python reference manual, for 
two reasons:  (1) it might get propagated to real world code, and (2) its 
presence in the docs reflects poorly on the numerical competence of the 
Python developers.

IMO, either: (1) the warning needs to be stronger, or (2) the formulation 
should be given purely mathematically, without any explicit code, or (3) 
the formula should be left out of the docs altogether.

Mark

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<http://bugs.python.org/issue3439>
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