Submitted By: Christopher A. Craig

Fillin some missing decrefs.

Some version of gcc in the "RTEMS port running on the Coldfire (m5200)
processor" generates bad code for a loop in long_from_binary_base(),
comparing the wrong half of an int to a short.  The patch changes the
decl of the short temp to be an int temp instead.  This "simplifies"
the code enough that gcc no longer blows it.

New functions:
  unsigned long PyInt_AsUnsignedLongMask(PyObject *);
  unsigned PY_LONG_LONG) PyInt_AsUnsignedLongLongMask(PyObject *);
  unsigned long PyLong_AsUnsignedLongMask(PyObject *);
  unsigned PY_LONG_LONG) PyLong_AsUnsignedLongLongMask(PyObject *);

New and changed format codes:

b unsigned char 0..UCHAR_MAX
B unsigned char none **
h unsigned short 0..USHRT_MAX
H unsigned short none **
i int INT_MIN..INT_MAX
I * unsigned int 0..UINT_MAX
l long LONG_MIN..LONG_MAX
k * unsigned long none
L long long LLONG_MIN..LLONG_MAX
K * unsigned long long none

Notes:

* New format codes.

** Changed from previous "range-and-a-half" to "none"; the
range-and-a-half checking wasn't particularly useful.

New test test_getargs2.py, to verify all this.

On a 64-bit machine, a dictionary could contain duplicate int/long keys
if the value was > 2**32.

wasn't used outside the assert (and hence caused a compiler warning
about an unused variable in NDEBUG mode).  The assert wasn't very
useful any more.

_PyLong_NumBits(): moved the calculation of ndigits after asserting
that v != NULL.

needed outside the first loop.

power of 2.  Enabled the tail end of test_long() in pickletester.py
because it no longer takes forever when run from test_pickle.py.

Assorted code cleanups; e.g., sizeof(char) is 1 by definition, so there's
no need to do things like multiply by sizeof(char) in hairy malloc
arguments.  Fixed an undetected-overflow bug in readline_file().

longobject.c:  Fixed a really stupid bug in the new _PyLong_NumBits.

pickle.py:  Fixed stupid bug in save_long():  When proto is 2, it
wrote LONG1 or LONG4, but forgot to return then -- it went on to
append the proto 1 LONG opcode too.
Fixed equally stupid cancelling bugs in load_long1() and
load_long4():  they *returned* the unpickled long instead of pushing
it on the stack.  The return values were ignored.  Tests passed
before only because save_long() pickled the long twice.

Fixed bugs in encode_long().

Noted that decode_long() is quadratic-time despite our hopes,
because long(string, 16) is still quadratic-time in len(string).
It's hex() that's linear-time.  I don't know a way to make decode_long()
linear-time in Python, short of maybe transforming the 256's-complement
bytes into marshal's funky internal format, and letting marshal decode
that.  It would be more valuable to make long(string, 16) linear time.

pickletester.py:  Added a global "protocols" vector so tests can try
all the protocols in a sane way.  Changed test_ints() and test_unicode()
to do so.  Added a new test_long(), but the tail end of it is disabled
because it "takes forever" under pickle.py (but runs very quickly under
cPickle:  cPickle proto 2 for longs is linear-time).

needs of pickling longs.  Backed off to a definition that's much easier
to understand.  The pickler will have to work a little harder, but other
uses are more likely to be correct <0.5 wink>.

_PyLong_Sign():  New teensy function to characterize a long, as to <0, ==0,
or >0.

types.  The special handling for these can now be removed from save_newobj().
Add some testing for this.

Also add support for setting the 'fast' flag on the Python Pickler class,
which suppresses use of the memo.

start for the C implemention of new pickle LONG1 and LONG4 opcodes (the
linear-time way to pickle a long is to call _PyLong_AsByteArray, but
the caller has no idea how big an array to allocate, and correct
calculation is a bit subtle).

integers checked for integer overflow but longs did not.

that is outside the integer range no longer raises OverflowError, but
returns a long object instead.

This fixes SF bug http://www.python.org/sf/635115

Also remove the 512 character limitation for int(u"...") and long(u"...").

This closes SF bug #629989.

globals, _Py_Ticker and _Py_CheckInterval.  This also implements Jeremy's
shortcut in Py_AddPendingCall that zeroes out _Py_Ticker.  This allows the
test in the main loop to only test a single value.

The gory details are at

    http://python.org/sf/602191

SHIFT and MASK, and widen digit.  One problem is that code of the form

    digit << small_integer

implicitly assumes that the result fits in an int or unsigned int
(platform-dependent, but "int sized" in any case), since digit is
promoted "just" to int or unsigned via the usual integer promotions.
But if digit is typedef'ed as unsigned int, this loses information.
The cure for this is just to cast digit to twodigits first.

rigorous instead of hoping for testing not to turn up counterexamples.
Call me heretical, but despite that I'm wholly confident in the proof,
and have done it two different ways now, I still put more faith in
testing ...

normalized result, so no point to normalizing it again.  The number
of test+branches was also excessive.

al*bl "always fit":  it's actually trivial given what came before.

ah*bh and al*bl.  This is much easier than explaining why that's true
for (ah+al)*(bh+bl), and follows directly from the simple part of the
(ah+al)*(bh+bl) explanation.

space is no longer needed, so removed the code.  It was only possible when
a degenerate (ah->ob_size == 0) split happened, but after that fix went
in I added k_lopsided_mul(), which saves the body of k_mul() from seeing
a degenerate split.  So this removes code, and adds a honking long comment
block explaining why spilling out of bounds isn't possible anymore.  Note:
ff we end up spilling out of bounds anyway <wink>, an assert in v_iadd()
is certain to trigger.

is an *unsigned* long.

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.

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.

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.

(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).

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).