left-shifting an integer by more than 2**31 on a 64-bit machine.  Also
convert shift counts to a Py_ssize_t instead of a C long.

long long variant of PyLong_AsLongAndOverflow.  Patch by Case Van
Horsen.

(the latter renamed to _PyLong_Frexp) now use the same core code.  The
exponent produced by _PyLong_Frexp now has type Py_ssize_t instead of the
previously used int, and no longer needs scaling by PyLong_SHIFT.  This
frees the math module from having to know anything about the PyLong
implementation.  This closes issue #5576.

Thanks Case Van Horsen for the patch.

Initial patch by Gregory Smith;  some tweaks added.

  (high_bits << PyLong_SHIFT) + low_bits with
  (high_bits << PyLong_SHIFT) | low_bits
in Objects/longobject.c.  Motivation:
 - shouldn't unnecessarily mix bit ops with arithmetic ops (style)
 - this pattern should be spelt the same way thoughout (consistency)
 - it's very very very slightly faster: no need to worry about
   carries to the high digit (nano-optimization).

(up to 3.1 times faster in tests), by special-casing base 10 in
_PyLong_Format.  (Backport of r74851 from py3k.)

a couple of whitespace issues.

(Related to issue #5880).

correctly rounded, using round-half-to-even.  This ensures that the
value of float(n) doesn't depend on whether we're using 15-bit digits
or 30-bit digits for Python longs.

The basic algorithm remains the same; the most significant speedups
come from the following three changes:

  (1) normalize by shifting instead of multiplying and dividing
  (2) the old algorithm usually did an unnecessary extra iteration of
      the outer loop; remove this.  As a special case, this means that
      long divisions with a single-digit result run twice as fast as
      before.
  (3) make inner loop much tighter.

Various benchmarks show speedups of between 50% and 150% for long
integer divisions and modulo operations.

Backport of r70459.

on sizeof(digit) < sizeof(long)

and cleanups in Objects/longobject.c.  The most significant change is that
longs now use less memory:  average savings are 2 bytes per long on 32-bit
systems and 6 bytes per long on 64-bit systems.  (This memory saving already
exists in py3k.)

negative arguments.  Previously, it raised TypeError.

Thanks Lisandro Dalcin.

rewrap a line of length > 79, and update comments.

This change should silence a compiler warning on Windows.

 - fix some places where counters into ob_digit were declared as
   int instead of Py_ssize_t
 - add (twodigit) casts where necessary
 - fix code in _PyLong_AsByteArray that uses << on negative values

Thanks Fredrik Johansson and Victor Stinner for code,
Raymond Hettinger for review.

long raise ValueError instead of returning 0.  Also, change the error
message for conversion of an infinity to an integer, replacing 'long' by
'integer', so that it's appropriate for both long(float('inf')) and
int(float('inf')).

Issue3122.

Make bin() implementation parallel oct() and hex() so that int/long subclasses can override or so that other classes can support.

 http://mail.python.org/pipermail/python-dev/2008-June/079988.html

Python 2.6 should stick with PyString_* in its codebase.  The PyBytes_* names
in the spirit of 3.0 are available via a #define only.  See the email thread.