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_PyLong_AsScaledDouble() writes the exponent in a int which have to be 
multiplied by PyLong_SHIFT to give the power of 2. I proposed to 
multiply the exponent by PyLong_SHIFT in _PyLong_AsScaledDouble() to 
directly get the power of 2. It avoids complex code to test integer 
overflow in code using _PyLong_AsScaledDouble() (the test is only done 
once, in _PyLong_AsScaledDouble).
I also propose to change exponent type from "int*" to "unsigned int*". 
Previous maximum exponent was INT_MAX//PyLong_SHIFT (eg. 143165576 for 
PyLong using base 2^15). The new maximum is now 
UINT_MAX//PyLong_SHIFT, the double ;-)
And since issue #4258 is commited (Use 30-bit digits instead of 15-bit 
digits for Python integers), PyLong_SHIFT value may be different 
depending on the compiler option. Using my patch, the long implement 
will be a little bit more hidden.
The function _PyLong_AsScaledDouble() should be private because the 
name starts with "_". But I see it in Include/longobject.h. In Python, 
it's used in longobject.c and mathmodule.c.

Thanks for this. I'll take a look.
How about making the exponent type size_t or Py_ssize_t, rather than 
[unsigned] int? It seems to me that that fits better with the usual size 
in digits.

Long double (80 bits) exponent is in range [-16382; 16383] and so would
fits in an int, unsigned int, size_t or Py_ssize_t. I don't know if a
signed or unsigned number is better. I know only one operation on
exponents: a-b in PyLong_AsDouble.

> Long double (80 bits) exponent is in range [-16382; 16383] and so 
would
> fits in an int, unsigned int, size_t or Py_ssize_t.
Sure, but I don't think that's relevant to the point I was attempting to 
make: PyLong_AsScaledDouble returns the number of bits in the given 
PyLong, and that number can be (theoretically) as large as 
PY_SSIZE_T_MAX * PyLong_SHIFT. So Py_ssize_t is a better fit than int 
to hold this number: otherwise you'll get unnecessary overflows on a 
64-bit system.
I'm working on refactoring PyLong_AsScaledDouble and PyLong_AsDouble to 
have them both use the same core code. This would make 
PyLong_AsScaledDouble correctly rounded, and hence independent of the 
implementation of a PyLong (in particular, independent of the decision 
to use 15-bit or 30-bit digits for PyLongs: this decision really 
shouldn't affect the result of a log function or any other functions 
using _PyLong_AsScaledDouble).

Here's a patch:
 - rename _PyLong_AsScaledDouble to _PyLong_Frexp (for the benefit of
 anyone foolish enough to be using an undocumented private API
 function)
 - make the exponent type Py_ssize_t instead of int
 - do the scaling by PyLong_SHIFT in _PyLong_Frexp instead of in the
 functions that call it (e.g., loghelper in the math module)
 - remove longintrepr.h include from math module, since it's no longer
 needed
 - change _PyLong_Frexp algorithm to do correct rounding
 - refactor PyLong_Double to use _PyLong_Frexp.

Applied in r77234 (trunk), r77237 (py3k).