(rev. 2.86).  The other type is only disqualified from sq_repeat when
it has the CHECKTYPES flag.  This means that for extension types that
only support "old-style" numeric ops, such as Zope 2's ExtensionClass,
sq_repeat still trumps nb_multiply.

"lopsided Karatsuba" driver also gets some exercise.

test was written.  So boosted the number of "digits" this generates, and
also beefed up the "* / divmod" test to tickle numbers big enough to
trigger the Karatsuba algorithm.  It takes about 2 seconds now on my box.

is an *unsigned* long.

updated when checkins are made, but I can get that updated when needed.

k_mul() when inputs have vastly different sizes, and a little more
efficient when they're close to a factor of 2 out of whack.

I consider this done now, although I'll set up some more correctness
tests to run overnight.

that file itself (because it's the parser that reports them).

correct filename and line number are reported.

alive in the memo.  This fixes SF bug 592567.

multiply via Ctrl+C could cause a NULL-pointer dereference due to
the assert.

the good one <wink>.  Also checked in a test-aid by mistake.

cases, overflow the allocated result object by 1 bit.  In such cases,
it would have been brought back into range if we subtracted al*bl and
ah*bh from it first, but I don't want to do that because it hurts cache
behavior.  Instead we just ignore the excess bit when it appears -- in
effect, this is forcing unsigned mod BASE**(asize + bsize) arithmetic
in a case where that doesn't happen all by itself.

1. You can now have __dict__ and/or __weakref__ in your __slots__
   (before only __weakref__ was supported).  This is treated
   differently than before: it merely sets a flag that the object
   should support the corresponding magic.

2. Dynamic types now always have descriptors __dict__ and __weakref__
   thrust upon them.  If the type in fact does not support one or the
   other, that descriptor's __get__ method will raise AttributeError.

3. (This is the reason for all this; it fixes SF bug 575229, reported
   by Cesar Douady.)  Given this code:
      class A(object): __slots__ = []
      class B(object): pass
      class C(A, B): __slots__ = []
   the class object for C was broken; its size was less than that of
   B, and some descriptors on B could cause a segfault.  C now
   correctly inherits __weakrefs__ and __dict__ from B, even though A
   is the "primary" base (C.__base__ is A).

4. Some code cleanup, and a few comments added.

algorithm.  MSVC 6 wasn't impressed <wink>.

Something odd:  the x_mul algorithm appears to get substantially worse
than quadratic time as the inputs grow larger:

bits in each input   x_mul time   k_mul time
------------------   ----------   ----------
             15360         0.01         0.00
             30720         0.04         0.01
             61440         0.16         0.04
            122880         0.64         0.14
            245760         2.56         0.40
            491520        10.76         1.23
            983040        71.28         3.69
           1966080       459.31        11.07

That is, x_mul is perfectly quadratic-time until a little burp at
2.56->10.76, and after that goes to hell in a hurry.  Under Karatsuba,
doubling the input size "should take" 3 times longer instead of 4, and
that remains the case throughout this range.  I conclude that my "be nice
to the cache" reworkings of k_mul() are paying.

correct now, so added some final comments, did some cleanup, and enabled
it for all long-int multiplies.  The KARAT envar no longer matters,
although I left some #if 0'ed code in there for my own use (temporary).
k_mul() is still much slower than x_mul() if the inputs have very
differenent sizes, and that still needs to be addressed.

CRCs.

(it's possible, but should be harmless -- this requires more thought,
and allocating enough space in advance to prevent it requires exactly
as much thought, to know exactly how much that is -- the end result
certainly fits in the allocated space -- hmm, but that's really all
the thought it needs!  borrows/carries out of the high digits really
are harmless).

to use new extern macro.

Thanks to Skip Montanaro and Kalle Svensson for the patches.

k_mul():  This didn't allocate enough result space when one input had
more than twice as many bits as the other.  This was partly hidden by
that x_mul() didn't normalize its result.

The Karatsuba recurrence is pretty much hosed if the inputs aren't
roughly the same size.  If one has at least twice as many bits as the
other, we get a degenerate case where the "high half" of the smaller
input is 0.  Added a special case for that, for speed, but despite that
it helped, this can still be much slower than the "grade school" method.
It seems to take a really wild imbalance to trigger that; e.g., a
2**22-bit input times a 1000-bit input on my box runs about twice as slow
under k_mul than under x_mul.  This still needs to be addressed.

I'm also not sure that allocating a->ob_size + b->ob_size digits is
enough, given that this is computing k = (ah+al)*(bh+bl) instead of
k = (ah-al)*(bl-bh); i.e., it's certainly enough for the final result,
but it's vaguely possible that adding in the "artificially" large k may
overflow that temporarily.  If so, an assert will trigger in the debug
build, but we'll probably compute the right result anyway(!).

addition and subtraction.  Reworked the tail end of k_mul() to use them.
This saves oodles of one-shot longobject allocations (this is a triply-
recursive routine, so saving one allocation in the body saves 3**n
allocations at depth n; we actually save 2 allocations in the body).

new-style object creation/deallocation.

Moved all news about type/class unification and new-stype classes to a
separate section at the top.

SF 560379:  Karatsuba multiplication.
Lots of things were changed from that.  This needs a lot more testing,
for correctness and speed, the latter especially when bit lengths are
unbalanced.  For now, the Karatsuba code gets invoked if and only if
envar KARAT exists.

Add resolve() to handle looking up objects and names (fix SF bug 586931).
Add a nicer error message when given a filename that doesn't exist.

a lot of work, including I/O (e.g. to import warnings.py), which might
affect errno.