This checkin is adapted from part 2 (of 3) of Trevor Perrin's patch set.
BACKWARD INCOMPATIBILITY: SHIFT must now be divisible by 5. AFAIK,
nobody will care. long_pow() could be complicated to worm around that,
if necessary.
long_pow():
- BUGFIX: This leaked the base and power when the power was negative
(and so the computation delegated to float pow).
- Instead of doing right-to-left exponentiation, do left-to-right. This
is more efficient for small bases, which is the common case.
- In addition, if the exponent is large (more than FIVEARY_CUTOFF
digits), precompute [a**i % c for i in range(32)], and go left to
right 5 bits at a time.
l_divmod():
- The signature changed so that callers who don't want the quotient,
or don't want the remainder, can pass NULL in the slot they don't
want. This saves them from having to declare a vrbl for unwanted
stuff, and remembering to decref it.
long_mod(), long_div(), long_classic_div():
- Adjust to new l_divmod() signature, and simplified as a result.
This checkin is adapted from part 1 (of 3) of Trevor Perrin's patch set.
x_mul()
- sped a little by optimizing the C
- sped a lot (~2X) if it's doing a square; note that long_pow() squares
often
k_mul()
- more cache-friendly now if it's doing a square
KARATSUBA_CUTOFF
- boosted; gradeschool mult is quicker now, and it may have been too low
for many platforms anyway
KARATSUBA_SQUARE_CUTOFF
- new
- since x_mul is a lot faster at squaring now, the point at which
Karatsuba pays for squaring is much higher than for general mult
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.
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.
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).
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 ...
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.
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.
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).
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.
The staticforward define was needed to support certain broken C
compilers (notably SCO ODT 3.0, perhaps early AIX as well) botched the
static keyword when it was used with a forward declaration of a static
initialized structure. Standard C allows the forward declaration with
static, and we've decided to stop catering to broken C compilers. (In
fact, we expect that the compilers are all fixed eight years later.)
I'm leaving staticforward and statichere defined in object.h as
static. This is only for backwards compatibility with C extensions
that might still use it.
XXX I haven't updated the documentation.
Martin v. Löwis
Tim Peters
Raymond Hettinger
Jeremy Hylton
Thomas Heller
Neal Norwitz
Guido van Rossum
Neil Schemenauer
Walter Dörwald
Skip Montanaro