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.
(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.
currently return inconsistent results for ints and longs; in
particular: hex/oct/%u/%o/%x/%X of negative short ints, and x<<n that
either loses bits or changes sign. (No warnings for repr() of a long,
though that will also change to lose the trailing 'L' eventually.)
This introduces some warnings in the test suite; I'll take care of
those later.
This is friendlier for caches.
2. Cut MIN_GALLOP to 7, but added a per-sort min_gallop vrbl that adapts
the "get into galloping mode" threshold higher when galloping isn't
paying, and lower when it is. There's no known case where this hurts.
It's (of course) neutral for /sort, \sort and =sort. It also happens
to be neutral for !sort. It cuts a tiny # of compares in 3sort and +sort.
For *sort, it reduces the # of compares to better than what this used to
do when MIN_GALLOP was hardcoded to 10 (it did about 0.1% more *sort
compares before, but given how close we are to the limit, this is "a
lot"!). %sort used to do about 1.5% more compares, and ~sort about
3.6% more. Here are exact counts:
i *sort 3sort +sort %sort ~sort !sort
15 449235 33019 33016 51328 188720 65534 before
448885 33016 33007 50426 182083 65534 after
0.08% 0.01% 0.03% 1.79% 3.65% 0.00% %ch from after
16 963714 65824 65809 103409 377634 131070
962991 65821 65808 101667 364341 131070
0.08% 0.00% 0.00% 1.71% 3.65% 0.00%
17 2059092 131413 131362 209130 755476 262142
2057533 131410 131361 206193 728871 262142
0.08% 0.00% 0.00% 1.42% 3.65% 0.00%
18 4380687 262440 262460 421998 1511174 524286
4377402 262437 262459 416347 1457945 524286
0.08% 0.00% 0.00% 1.36% 3.65% 0.00%
19 9285709 524581 524634 848590 3022584 1048574
9278734 524580 524633 837947 2916107 1048574
0.08% 0.00% 0.00% 1.27% 3.65% 0.00%
20 19621118 1048960 1048942 1715806 6045418 2097150
19606028 1048958 1048941 1694896 5832445 2097150
0.08% 0.00% 0.00% 1.23% 3.65% 0.00%
3. Added some key asserts I overlooked before.
4. Updated the doc file.
before %sort was introduced. Redid them (the numbers change, but the
conclusions don't). Also did the samplesort counts with the released
2.2.1, as they're slightly different under the last CVS 2.3 samplesort
(some higher, some lower -- CVS had been changed to stop doing the
special-case business on recursive samplesort calls).
directories clean where the packages are unpacked. Each package now
contains a single directory, Python-Docs-<version>/, which contains the
files for that version of the documentation.
Closes SF feature request #567576.
Tim Peters
Guido van Rossum
Mark Hammond
Marc-André Lemburg
Neal Norwitz
Ka-Ping Yee
Martin v. Löwis
Fred Drake