1. Combined the base and length arrays into a single array of structs.
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.
diff --git a/Objects/listsort.txt b/Objects/listsort.txt
index 545ce51..c561288 100644
--- a/Objects/listsort.txt
+++ b/Objects/listsort.txt
@@ -95,31 +95,31 @@
below that, it's either astronomically lucky, or is finding exploitable
structure in the data.
- n lg(n!) *sort 3sort +sort %sort ~sort !sort
-------- ------- ------ -------- ------- ------ ------- --------
- 32768 444255 453096 453614 32908 452871 130491 469141 old
- 449235 33019 33016 51328 188720 65534 new
- 0.86% 1273.80% -0.33% 782.31% -30.85% 615.87% %ch from new
+ n lg(n!) *sort 3sort +sort %sort ~sort !sort
+------- ------- ------ ------- ------- ------ ------- --------
+ 32768 444255 453096 453614 32908 452871 130491 469141 old
+ 448885 33016 33007 50426 182083 65534 new
+ 0.94% 1273.92% -0.30% 798.09% -28.33% 615.87% %ch from new
65536 954037 972699 981940 65686 973104 260029 1004607
- 963714 65824 65809 103409 377634 131070
- 0.93% 1391.77% -0.19% 841.02% -31.14% 666.47%
+ 962991 65821 65808 101667 364341 131070
+ 1.01% 1391.83% -0.19% 857.15% -28.63% 666.47%
131072 2039137 2101881 2091491 131232 2092894 554790 2161379
- 2059092 131413 131362 209130 755476 262142
- 2.08% 1491.54% -0.10% 900.76% -26.56% 724.51%
+ 2057533 131410 131361 206193 728871 262142
+ 2.16% 1491.58% -0.10% 915.02% -23.88% 724.51%
262144 4340409 4464460 4403233 262314 4445884 1107842 4584560
- 4380687 262440 262460 421998 1511174 524286
- 1.91% 1577.81% -0.06% 953.53% -26.69% 774.44%
+ 4377402 262437 262459 416347 1457945 524286
+ 1.99% 1577.82% -0.06% 967.83% -24.01% 774.44%
524288 9205096 9453356 9408463 524468 9441930 2218577 9692015
- 9285709 524581 524634 848590 3022584 1048574
- 1.81% 1693.52% -0.03% 1012.66% -26.60% 824.30%
+ 9278734 524580 524633 837947 2916107 1048574
+ 1.88% 1693.52% -0.03% 1026.79% -23.92% 824.30%
1048576 19458756 19950272 19838588 1048766 19912134 4430649 20434212
- 19621118 1048960 1048942 1715806 6045418 2097150
- 1.68% 1791.26% -0.02% 1060.51% -26.71% 874.38%
+ 19606028 1048958 1048941 1694896 5832445 2097150
+ 1.76% 1791.27% -0.02% 1074.83% -24.03% 874.38%
Discussion of cases:
@@ -171,7 +171,6 @@
bytes each on this box) needed by each test, again with arguments
"15 20 1":
-
2**i *sort \sort /sort 3sort +sort %sort ~sort =sort !sort
32768 16384 0 0 6256 0 10821 12288 0 16383
65536 32766 0 0 21652 0 31276 24576 0 32767
@@ -430,6 +429,11 @@
less than MIN_GALLOP elements long, at which point we go back to one-pair-
at-a-time mode.
+A refinement: The MergeState struct contains the value of min_gallop that
+controls when we enter galloping mode, initialized to MIN_GALLOP.
+merge_lo() and merge_hi() adjust this higher when gallooping isn't paying
+off, and lower when it is.
+
Galloping
---------
@@ -536,13 +540,21 @@
We can't guess in advance when it's going to win, though, so we do one pair
at a time until the evidence seems strong that galloping may pay. MIN_GALLOP
-is 8 as I type this, and that's pretty strong evidence. However, if the data
-is random, it simply will trigger galloping mode purely by luck every now
-and again, and it's quite likely to hit one of the losing cases next. 8
-favors protecting against a slowdown on random data at the expense of giving
-up small wins on lightly clustered data, and tiny marginal wins on highly
-clustered data (they win huge anyway, and if you're getting a factor of
-10 speedup, another percent just isn't worth fighting for).
+is 7, and that's pretty strong evidence. However, if the data is random, it
+simply will trigger galloping mode purely by luck every now and again, and
+it's quite likely to hit one of the losing cases next. On the other hand,
+in cases like ~sort, galloping always pays, and MIN_GALLOP is larger than it
+"should be" then. So the MergeState struct keeps a min_gallop variable
+that merge_lo and merge_hi adjust: the longer we stay in galloping mode,
+the smaller min_gallop gets, making it easier to transition back to
+galloping mode (if we ever leave it in the current merge, and at the
+start of the next merge). But whenever the gallop loop doesn't pay,
+min_gallop is increased by one, making it harder to transition to back
+to galloping mode (and again both within a merge and across merges). For
+random data, this all but eliminates the gallop penalty: min_gallop grows
+large enough that we almost never get into galloping mode. And for cases
+like ~sort, min_gallop can fall to as low as 1. This seems to work well,
+but in all it's a minor improvement over using a fixed MIN_GALLOP value.
Galloping Complication
@@ -567,6 +579,9 @@
Comparing Average # of Compares on Random Arrays
------------------------------------------------
+[NOTE: This was done when the new algorithm used about 0.1% more compares
+ on random data than does its current incarnation.]
+
Here list.sort() is samplesort, and list.msort() this sort:
"""