}
}
-/* New quicksort implementation for arrays of object pointers.
- Thanks to discussions with Tim Peters. */
+/* Lots of code for an adaptive, stable, natural mergesort. There are many
+ * pieces to this algorithm; read listsort.txt for overviews and details.
+ */
/* Comparison function. Takes care of calling a user-supplied
- comparison function (any callable Python object). Calls the
- standard comparison function, PyObject_RichCompareBool(), if the user-
- supplied function is NULL.
- Returns <0 on error, >0 if x < y, 0 if x >= y. */
-
+ * comparison function (any callable Python object). Calls the
+ * standard comparison function, PyObject_RichCompareBool(), if the user-
+ * supplied function is NULL.
+ * Returns -1 on error, 1 if x < y, 0 if x >= y.
+ */
static int
islt(PyObject *x, PyObject *y, PyObject *compare)
{
return i < 0;
}
-/* MINSIZE is the smallest array that will get a full-blown samplesort
- treatment; smaller arrays are sorted using binary insertion. It must
- be at least 7 for the samplesort implementation to work. Binary
- insertion does fewer compares, but can suffer O(N**2) data movement.
- The more expensive compares, the larger MINSIZE should be. */
-#define MINSIZE 100
-
-/* MINPARTITIONSIZE is the smallest array slice samplesort will bother to
- partition; smaller slices are passed to binarysort. It must be at
- least 2, and no larger than MINSIZE. Setting it higher reduces the #
- of compares slowly, but increases the amount of data movement quickly.
- The value here was chosen assuming a compare costs ~25x more than
- swapping a pair of memory-resident pointers -- but under that assumption,
- changing the value by a few dozen more or less has aggregate effect
- under 1%. So the value is crucial, but not touchy <wink>. */
-#define MINPARTITIONSIZE 40
-
-/* MAXMERGE is the largest number of elements we'll always merge into
- a known-to-be sorted chunk via binary insertion, regardless of the
- size of that chunk. Given a chunk of N sorted elements, and a group
- of K unknowns, the largest K for which it's better to do insertion
- (than a full-blown sort) is a complicated function of N and K mostly
- involving the expected number of compares and data moves under each
- approach, and the relative cost of those operations on a specific
- architecure. The fixed value here is conservative, and should be a
- clear win regardless of architecture or N. */
-#define MAXMERGE 15
-
-/* STACKSIZE is the size of our work stack. A rough estimate is that
- this allows us to sort arrays of size N where
- N / ln(N) = MINPARTITIONSIZE * 2**STACKSIZE, so 60 is more than enough
- for arrays of size 2**64. Because we push the biggest partition
- first, the worst case occurs when all subarrays are always partitioned
- exactly in two. */
-#define STACKSIZE 60
-
/* Compare X to Y via islt(). Goto "fail" if the comparison raises an
error. Else "k" is set to true iff X<Y, and an "if (k)" block is
started. It makes more sense in context <wink>. X and Y are PyObject*s.
Even in case of error, the output slice will be some permutation of
the input (nothing is lost or duplicated).
*/
-
static int
binarysort(PyObject **lo, PyObject **hi, PyObject **start, PyObject *compare)
/* compare -- comparison function object, or NULL for default */
return -1;
}
-/* samplesortslice is the sorting workhorse.
- [lo, hi) is a contiguous slice of a list, to be sorted in place.
- On entry, must have lo <= hi,
- If islt() complains return -1, else 0.
- Even in case of error, the output slice will be some permutation of
- the input (nothing is lost or duplicated).
+/*
+Return the length of the run beginning at lo, in the slice [lo, hi). lo < hi
+is required on entry. "A run" is the longest ascending sequence, with
- samplesort is basically quicksort on steroids: a power of 2 close
- to n/ln(n) is computed, and that many elements (less 1) are picked at
- random from the array and sorted. These 2**k - 1 elements are then
- used as preselected pivots for an equal number of quicksort
- partitioning steps, partitioning the slice into 2**k chunks each of
- size about ln(n). These small final chunks are then usually handled
- by binarysort. Note that when k=1, this is roughly the same as an
- ordinary quicksort using a random pivot, and when k=2 this is roughly
- a median-of-3 quicksort. From that view, using k ~= lg(n/ln(n)) makes
- this a "median of n/ln(n)" quicksort. You can also view it as a kind
- of bucket sort, where 2**k-1 bucket boundaries are picked dynamically.
-
- The large number of samples makes a quadratic-time case almost
- impossible, and asymptotically drives the average-case number of
- compares from quicksort's 2 N ln N (or 12/7 N ln N for the median-of-
- 3 variant) down to N lg N.
-
- We also play lots of low-level tricks to cut the number of compares.
-
- Very obscure: To avoid using extra memory, the PPs are stored in the
- array and shuffled around as partitioning proceeds. At the start of a
- partitioning step, we'll have 2**m-1 (for some m) PPs in sorted order,
- adjacent (either on the left or the right!) to a chunk of X elements
- that are to be partitioned: P X or X P. In either case we need to
- shuffle things *in place* so that the 2**(m-1) smaller PPs are on the
- left, followed by the PP to be used for this step (that's the middle
- of the PPs), followed by X, followed by the 2**(m-1) larger PPs:
- P X or X P -> Psmall pivot X Plarge
- and the order of the PPs must not be altered. It can take a while
- to realize this isn't trivial! It can take even longer <wink> to
- understand why the simple code below works, using only 2**(m-1) swaps.
- The key is that the order of the X elements isn't necessarily
- preserved: X can end up as some cyclic permutation of its original
- order. That's OK, because X is unsorted anyway. If the order of X
- had to be preserved too, the simplest method I know of using O(1)
- scratch storage requires len(X) + 2**(m-1) swaps, spread over 2 passes.
- Since len(X) is typically several times larger than 2**(m-1), that
- would slow things down.
-*/
+ lo[0] <= lo[1] <= lo[2] <= ...
-struct SamplesortStackNode {
- /* Represents a slice of the array, from (& including) lo up
- to (but excluding) hi. "extra" additional & adjacent elements
- are pre-selected pivots (PPs), spanning [lo-extra, lo) if
- extra > 0, or [hi, hi-extra) if extra < 0. The PPs are
- already sorted, but nothing is known about the other elements
- in [lo, hi). |extra| is always one less than a power of 2.
- When extra is 0, we're out of PPs, and the slice must be
- sorted by some other means. */
- PyObject **lo;
- PyObject **hi;
- int extra;
-};
+or the longest descending sequence, with
-/* The number of PPs we want is 2**k - 1, where 2**k is as close to
- N / ln(N) as possible. So k ~= lg(N / ln(N)). Calling libm routines
- is undesirable, so cutoff values are canned in the "cutoff" table
- below: cutoff[i] is the smallest N such that k == CUTOFFBASE + i. */
-#define CUTOFFBASE 4
-static long cutoff[] = {
- 43, /* smallest N such that k == 4 */
- 106, /* etc */
- 250,
- 576,
- 1298,
- 2885,
- 6339,
- 13805,
- 29843,
- 64116,
- 137030,
- 291554,
- 617916,
- 1305130,
- 2748295,
- 5771662,
- 12091672,
- 25276798,
- 52734615,
- 109820537,
- 228324027,
- 473977813,
- 982548444, /* smallest N such that k == 26 */
- 2034159050 /* largest N that fits in signed 32-bit; k == 27 */
-};
+ lo[0] > lo[1] > lo[2] > ...
+Boolean *descending is set to 0 in the former case, or to 1 in the latter.
+For its intended use in a stable mergesort, the strictness of the defn of
+"descending" is needed so that the caller can safely reverse a descending
+sequence without violating stability (strict > ensures there are no equal
+elements to get out of order).
+
+Returns -1 in case of error.
+*/
static int
-samplesortslice(PyObject **lo, PyObject **hi, PyObject *compare)
- /* compare -- comparison function object, or NULL for default */
+count_run(PyObject **lo, PyObject **hi, PyObject *compare, int *descending)
{
- register PyObject **l, **r;
- register PyObject *tmp, *pivot;
- register int k;
- int n, extra, top, extraOnRight;
- struct SamplesortStackNode stack[STACKSIZE];
-
- assert(lo <= hi);
- n = hi - lo;
- if (n < MINSIZE)
- return binarysort(lo, hi, lo, compare);
-
- /* ----------------------------------------------------------
- * Normal case setup: a large array without obvious pattern.
- * --------------------------------------------------------*/
-
- /* extra := a power of 2 ~= n/ln(n), less 1.
- First find the smallest extra s.t. n < cutoff[extra] */
- for (extra = 0;
- extra < sizeof(cutoff) / sizeof(cutoff[0]);
- ++extra) {
- if (n < cutoff[extra])
- break;
- /* note that if we fall out of the loop, the value of
- extra still makes *sense*, but may be smaller than
- we would like (but the array has more than ~= 2**31
- elements in this case!) */
- }
- /* Now k == extra - 1 + CUTOFFBASE. The smallest value k can
- have is CUTOFFBASE-1, so
- assert MINSIZE >= 2**(CUTOFFBASE-1) - 1 */
- extra = (1 << (extra - 1 + CUTOFFBASE)) - 1;
- /* assert extra > 0 and n >= extra */
-
- /* Swap that many values to the start of the array. The
- selection of elements is pseudo-random, but the same on
- every run (this is intentional! timing algorithm changes is
- a pain if timing varies across runs). */
- {
- unsigned int seed = n / extra; /* arbitrary */
- unsigned int i;
- for (i = 0; i < (unsigned)extra; ++i) {
- /* j := random int in [i, n) */
- unsigned int j;
- seed = seed * 69069 + 7;
- j = i + seed % (n - i);
- tmp = lo[i]; lo[i] = lo[j]; lo[j] = tmp;
+ int k;
+ int n;
+
+ assert(lo < hi);
+ *descending = 0;
+ ++lo;
+ if (lo == hi)
+ return 1;
+
+ n = 2;
+ IFLT(*lo, *(lo-1)) {
+ *descending = 1;
+ for (lo = lo+1; lo < hi; ++lo, ++n) {
+ IFLT(*lo, *(lo-1))
+ ;
+ else
+ break;
+ }
+ }
+ else {
+ for (lo = lo+1; lo < hi; ++lo, ++n) {
+ IFLT(*lo, *(lo-1))
+ break;
}
}
- /* Recursively sort the preselected pivots. */
- if (samplesortslice(lo, lo + extra, compare) < 0)
- goto fail;
+ return n;
+fail:
+ return -1;
+}
- top = 0; /* index of available stack slot */
- lo += extra; /* point to first unknown */
- extraOnRight = 0; /* the PPs are at the left end */
+/*
+Locate the proper position of key in a sorted vector; if the vector contains
+an element equal to key, return the position immediately to the left of
+the leftmost equal element. [gallop_right() does the same except returns
+the position to the right of the rightmost equal element (if any).]
- /* ----------------------------------------------------------
- * Partition [lo, hi), and repeat until out of work.
- * --------------------------------------------------------*/
- for (;;) {
- assert(lo <= hi);
- n = hi - lo;
+"a" is a sorted vector with n elements, starting at a[0]. n must be > 0.
- /* We may not want, or may not be able, to partition:
- If n is small, it's quicker to insert.
- If extra is 0, we're out of pivots, and *must* use
- another method.
- */
- if (n < MINPARTITIONSIZE || extra == 0) {
- if (n >= MINSIZE) {
- assert(extra == 0);
- /* This is rare, since the average size
- of a final block is only about
- ln(original n). */
- if (samplesortslice(lo, hi, compare) < 0)
- goto fail;
- }
- else {
- /* Binary insertion should be quicker,
- and we can take advantage of the PPs
- already being sorted. */
- if (extraOnRight && extra) {
- /* swap the PPs to the left end */
- k = extra;
- do {
- tmp = *lo;
- *lo = *hi;
- *hi = tmp;
- ++lo; ++hi;
- } while (--k);
- }
- if (binarysort(lo - extra, hi, lo,
- compare) < 0)
- goto fail;
- }
+"hint" is an index at which to begin the search, 0 <= hint < n. The closer
+hint is to the final result, the faster this runs.
+
+The return value is the int k in 0..n such that
+
+ a[k-1] < key <= a[k]
+
+pretending that *(a-1) is minus infinity and a[n] is plus infinity. IOW,
+key belongs at index k; or, IOW, the first k elements of a should precede
+key, and the last n-k should follow key.
+
+Returns -1 on error. See listsort.txt for info on the method.
+*/
+static int
+gallop_left(PyObject *key, PyObject **a, int n, int hint, PyObject *compare)
+{
+ int ofs;
+ int lastofs;
+ int k;
+
+ assert(key && a && n > 0 && hint >= 0 && hint < n);
- /* Find another slice to work on. */
- if (--top < 0)
- break; /* no more -- done! */
- lo = stack[top].lo;
- hi = stack[top].hi;
- extra = stack[top].extra;
- extraOnRight = 0;
- if (extra < 0) {
- extraOnRight = 1;
- extra = -extra;
+ a += hint;
+ lastofs = 0;
+ ofs = 1;
+ IFLT(*a, key) {
+ /* a[hint] < key -- gallop right, until
+ * a[hint + lastofs] < key <= a[hint + ofs]
+ */
+ const int maxofs = n - hint; /* &a[n-1] is highest */
+ while (ofs < maxofs) {
+ IFLT(a[ofs], key) {
+ lastofs = ofs;
+ ofs = (ofs << 1) + 1;
+ if (ofs <= 0) /* int overflow */
+ ofs = maxofs;
}
- continue;
+ else /* key <= a[hint + ofs] */
+ break;
}
+ if (ofs > maxofs)
+ ofs = maxofs;
+ /* Translate back to offsets relative to &a[0]. */
+ lastofs += hint;
+ ofs += hint;
+ }
+ else {
+ /* key <= a[hint] -- gallop left, until
+ * a[hint - ofs] < key <= a[hint - lastofs]
+ */
+ const int maxofs = hint + 1; /* &a[0] is lowest */
+ while (ofs < maxofs) {
+ IFLT(*(a-ofs), key)
+ break;
+ /* key <= a[hint - ofs] */
+ lastofs = ofs;
+ ofs = (ofs << 1) + 1;
+ if (ofs <= 0) /* int overflow */
+ ofs = maxofs;
+ }
+ if (ofs > maxofs)
+ ofs = maxofs;
+ /* Translate back to positive offsets relative to &a[0]. */
+ k = lastofs;
+ lastofs = hint - ofs;
+ ofs = hint - k;
+ }
+ a -= hint;
+
+ assert(-1 <= lastofs && lastofs < ofs && ofs <= n);
+ /* Now a[lastofs] < key <= a[ofs], so key belongs somewhere to the
+ * right of lastofs but no farther right than ofs. Do a binary
+ * search, with invariant a[lastofs-1] < key <= a[ofs].
+ */
+ ++lastofs;
+ while (lastofs < ofs) {
+ int m = lastofs + ((ofs - lastofs) >> 1);
+
+ IFLT(a[m], key)
+ lastofs = m+1; /* a[m] < key */
+ else
+ ofs = m; /* key <= a[m] */
+ }
+ assert(lastofs == ofs); /* so a[ofs-1] < key <= a[ofs] */
+ return ofs;
- /* Pretend the PPs are indexed 0, 1, ..., extra-1.
- Then our preselected pivot is at (extra-1)/2, and we
- want to move the PPs before that to the left end of
- the slice, and the PPs after that to the right end.
- The following section changes extra, lo, hi, and the
- slice such that:
- [lo-extra, lo) contains the smaller PPs.
- *lo == our PP.
- (lo, hi) contains the unknown elements.
- [hi, hi+extra) contains the larger PPs.
+fail:
+ return -1;
+}
+
+/*
+Exactly like gallop_left(), except that if key already exists in a[0:n],
+finds the position immediately to the right of the rightmost equal value.
+
+The return value is the int k in 0..n such that
+
+ a[k-1] <= key < a[k]
+
+or -1 if error.
+
+The code duplication is massive, but this is enough different given that
+we're sticking to "<" comparisons that it's much harder to follow if
+written as one routine with yet another "left or right?" flag.
+*/
+static int
+gallop_right(PyObject *key, PyObject **a, int n, int hint, PyObject *compare)
+{
+ int ofs;
+ int lastofs;
+ int k;
+
+ assert(key && a && n > 0 && hint >= 0 && hint < n);
+
+ a += hint;
+ lastofs = 0;
+ ofs = 1;
+ IFLT(key, *a) {
+ /* key < a[hint] -- gallop left, until
+ * a[hint - ofs] <= key < a[hint - lastofs]
+ */
+ const int maxofs = hint + 1; /* &a[0] is lowest */
+ while (ofs < maxofs) {
+ IFLT(key, *(a-ofs)) {
+ lastofs = ofs;
+ ofs = (ofs << 1) + 1;
+ if (ofs <= 0) /* int overflow */
+ ofs = maxofs;
+ }
+ else /* a[hint - ofs] <= key */
+ break;
+ }
+ if (ofs > maxofs)
+ ofs = maxofs;
+ /* Translate back to positive offsets relative to &a[0]. */
+ k = lastofs;
+ lastofs = hint - ofs;
+ ofs = hint - k;
+ }
+ else {
+ /* a[hint] <= key -- gallop right, until
+ * a[hint + lastofs] <= key < a[hint + ofs]
*/
- k = extra >>= 1; /* num PPs to move */
- if (extraOnRight) {
- /* Swap the smaller PPs to the left end.
- Note that this loop actually moves k+1 items:
- the last is our PP */
- do {
- tmp = *lo; *lo = *hi; *hi = tmp;
- ++lo; ++hi;
- } while (k--);
+ const int maxofs = n - hint; /* &a[n-1] is highest */
+ while (ofs < maxofs) {
+ IFLT(key, a[ofs])
+ break;
+ /* a[hint + ofs] <= key */
+ lastofs = ofs;
+ ofs = (ofs << 1) + 1;
+ if (ofs <= 0) /* int overflow */
+ ofs = maxofs;
}
- else {
- /* Swap the larger PPs to the right end. */
- while (k--) {
- --lo; --hi;
- tmp = *lo; *lo = *hi; *hi = tmp;
+ if (ofs > maxofs)
+ ofs = maxofs;
+ /* Translate back to offsets relative to &a[0]. */
+ lastofs += hint;
+ ofs += hint;
+ }
+ a -= hint;
+
+ assert(-1 <= lastofs && lastofs < ofs && ofs <= n);
+ /* Now a[lastofs] <= key < a[ofs], so key belongs somewhere to the
+ * right of lastofs but no farther right than ofs. Do a binary
+ * search, with invariant a[lastofs-1] <= key < a[ofs].
+ */
+ ++lastofs;
+ while (lastofs < ofs) {
+ int m = lastofs + ((ofs - lastofs) >> 1);
+
+ IFLT(key, a[m])
+ ofs = m; /* key < a[m] */
+ else
+ lastofs = m+1; /* a[m] <= key */
+ }
+ assert(lastofs == ofs); /* so a[ofs-1] <= key < a[ofs] */
+ return ofs;
+
+fail:
+ return -1;
+}
+
+/* The maximum number of entries in a MergeState's pending-runs stack.
+ * This is enough to sort arrays of size up to about
+ * 32 * phi ** MAX_MERGE_PENDING
+ * where phi ~= 1.618. 85 is ridiculouslylarge enough, good for an array
+ * with 2**64 elements.
+ */
+#define MAX_MERGE_PENDING 85
+
+/* If a run wins MIN_GALLOP times in a row, we switch to galloping mode,
+ * and stay there until both runs win less often than MIN_GALLOP
+ * consecutive times. See listsort.txt for more info.
+ */
+#define MIN_GALLOP 8
+
+/* Avoid malloc for small temp arrays. */
+#define MERGESTATE_TEMP_SIZE 256
+
+/* One MergeState exists on the stack per invocation of mergesort. It's just
+ * a convenient way to pass state around among the helper functions.
+ */
+typedef struct s_MergeState {
+ /* The user-supplied comparison function. or NULL if none given. */
+ PyObject *compare;
+
+ /* 'a' is temp storage to help with merges. It contains room for
+ * alloced entries.
+ */
+ PyObject **a; /* may point to temparray below */
+ int alloced;
+
+ /* A stack of n pending runs yet to be merged. Run #i starts at
+ * address base[i] and extends for len[i] elements. It's always
+ * true (so long as the indices are in bounds) that
+ *
+ * base[i] + len[i] == base[i+1]
+ *
+ * so we could cut the storage for this, but it's a minor amount,
+ * and keeping all the info explicit simplifies the code.
+ */
+ int n;
+ PyObject **base[MAX_MERGE_PENDING];
+ int len[MAX_MERGE_PENDING];
+
+ /* 'a' points to this when possible, rather than muck with malloc. */
+ PyObject *temparray[MERGESTATE_TEMP_SIZE];
+} MergeState;
+
+/* Conceptually a MergeState's constructor. */
+static void
+merge_init(MergeState *ms, PyObject *compare)
+{
+ assert(ms != NULL);
+ ms->compare = compare;
+ ms->a = ms->temparray;
+ ms->alloced = MERGESTATE_TEMP_SIZE;
+ ms->n = 0;
+}
+
+/* Free all the temp memory owned by the MergeState. This must be called
+ * when you're done with a MergeState, and may be called before then if
+ * you want to free the temp memory early.
+ */
+static void
+merge_freemem(MergeState *ms)
+{
+ assert(ms != NULL);
+ if (ms->a != ms->temparray)
+ PyMem_Free(ms->a);
+ ms->a = ms->temparray;
+ ms->alloced = MERGESTATE_TEMP_SIZE;
+}
+
+/* Ensure enough temp memory for 'need' array slots is available.
+ * Returns 0 on success and -1 if the memory can't be gotten.
+ */
+static int
+merge_getmem(MergeState *ms, int need)
+{
+ assert(ms != NULL);
+ if (need <= ms->alloced)
+ return 0;
+ /* Don't realloc! That can cost cycles to copy the old data, but
+ * we don't care what's in the block.
+ */
+ merge_freemem(ms);
+ ms->a = (PyObject **)PyMem_Malloc(need * sizeof(PyObject*));
+ if (ms->a) {
+ ms->alloced = need;
+ return 0;
+ }
+ PyErr_NoMemory();
+ merge_freemem(ms); /* reset to sane state */
+ return -1;
+}
+#define MERGE_GETMEM(MS, NEED) ((NEED) <= (MS)->alloced ? 0 : \
+ merge_getmem(MS, NEED))
+
+/* Merge the na elements starting at pa with the nb elements starting at pb
+ * in a stable way, in-place. na and nb must be > 0, and pa + na == pb.
+ * Must also have that *pb < *pa, that pa[na-1] belongs at the end of the
+ * merge, and should have na <= nb. See listsort.txt for more info.
+ * Return 0 if successful, -1 if error.
+ */
+static int
+merge_lo(MergeState *ms, PyObject **pa, int na, PyObject **pb, int nb)
+{
+ int k;
+ PyObject *compare;
+ PyObject **dest;
+ int result = -1; /* guilty until proved innocent */
+
+ assert(ms && pa && pb && na > 0 && nb > 0 && pa + na == pb);
+ if (MERGE_GETMEM(ms, na) < 0)
+ return -1;
+ memcpy(ms->a, pa, na * sizeof(PyObject*));
+ dest = pa;
+ pa = ms->a;
+
+ *dest++ = *pb++;
+ --nb;
+ if (nb == 0)
+ goto Succeed;
+ if (na == 1)
+ goto CopyB;
+
+ compare = ms->compare;
+ for (;;) {
+ int acount = 0; /* # of times A won in a row */
+ int bcount = 0; /* # of times B won in a row */
+
+ /* Do the straightforward thing until (if ever) one run
+ * appears to win consistently.
+ */
+ for (;;) {
+ k = islt(*pb, *pa, compare);
+ if (k) {
+ if (k < 0)
+ goto Fail;
+ *dest++ = *pb++;
+ ++bcount;
+ acount = 0;
+ --nb;
+ if (nb == 0)
+ goto Succeed;
+ if (bcount >= MIN_GALLOP)
+ break;
}
- }
- --lo; /* *lo is now our PP */
- pivot = *lo;
-
- /* Now an almost-ordinary quicksort partition step.
- Note that most of the time is spent here!
- Only odd thing is that we partition into < and >=,
- instead of the usual <= and >=. This helps when
- there are lots of duplicates of different values,
- because it eventually tends to make subfiles
- "pure" (all duplicates), and we special-case for
- duplicates later. */
- l = lo + 1;
- r = hi - 1;
- assert(lo < l && l < r && r < hi);
+ else {
+ *dest++ = *pa++;
+ ++acount;
+ bcount = 0;
+ --na;
+ if (na == 1)
+ goto CopyB;
+ if (acount >= MIN_GALLOP)
+ break;
+ }
+ }
+ /* One run is winning so consistently that galloping may
+ * be a huge win. So try that, and continue galloping until
+ * (if ever) neither run appears to be winning consistently
+ * anymore.
+ */
do {
- /* slide l right, looking for key >= pivot */
- do {
- IFLT(*l, pivot)
- ++l;
- else
+ k = gallop_right(*pb, pa, na, 0, compare);
+ acount = k;
+ if (k) {
+ if (k < 0)
+ goto Fail;
+ memcpy(dest, pa, k * sizeof(PyObject *));
+ dest += k;
+ pa += k;
+ na -= k;
+ if (na == 1)
+ goto CopyB;
+ /* na==0 is impossible now if the comparison
+ * function is consistent, but we can't assume
+ * that it is.
+ */
+ if (na == 0)
+ goto Succeed;
+ }
+ *dest++ = *pb++;
+ --nb;
+ if (nb == 0)
+ goto Succeed;
+
+ k = gallop_left(*pa, pb, nb, 0, compare);
+ bcount = k;
+ if (k) {
+ if (k < 0)
+ goto Fail;
+ memmove(dest, pb, k * sizeof(PyObject *));
+ dest += k;
+ pb += k;
+ nb -= k;
+ if (nb == 0)
+ goto Succeed;
+ }
+ *dest++ = *pa++;
+ --na;
+ if (na == 1)
+ goto CopyB;
+ } while (acount >= MIN_GALLOP || bcount >= MIN_GALLOP);
+ }
+Succeed:
+ result = 0;
+Fail:
+ if (na)
+ memcpy(dest, pa, na * sizeof(PyObject*));
+ return result;
+CopyB:
+ assert(na == 1 && nb > 0);
+ /* The last element of pa belongs at the end of the merge. */
+ memmove(dest, pb, nb * sizeof(PyObject *));
+ dest[nb] = *pa;
+ return 0;
+}
+
+/* Merge the na elements starting at pa with the nb elements starting at pb
+ * in a stable way, in-place. na and nb must be > 0, and pa + na == pb.
+ * Must also have that *pb < *pa, that pa[na-1] belongs at the end of the
+ * merge, and should have na >= nb. See listsort.txt for more info.
+ * Return 0 if successful, -1 if error.
+ */
+static int
+merge_hi(MergeState *ms, PyObject **pa, int na, PyObject **pb, int nb)
+{
+ int k;
+ PyObject *compare;
+ PyObject **dest;
+ int result = -1; /* guilty until proved innocent */
+ PyObject **basea;
+ PyObject **baseb;
+
+ assert(ms && pa && pb && na > 0 && nb > 0 && pa + na == pb);
+ if (MERGE_GETMEM(ms, nb) < 0)
+ return -1;
+ dest = pb + nb - 1;
+ memcpy(ms->a, pb, nb * sizeof(PyObject*));
+ basea = pa;
+ baseb = ms->a;
+ pb = ms->a + nb - 1;
+ pa += na - 1;
+
+ *dest-- = *pa--;
+ --na;
+ if (na == 0)
+ goto Succeed;
+ if (nb == 1)
+ goto CopyA;
+
+ compare = ms->compare;
+ for (;;) {
+ int acount = 0; /* # of times A won in a row */
+ int bcount = 0; /* # of times B won in a row */
+
+ /* Do the straightforward thing until (if ever) one run
+ * appears to win consistently.
+ */
+ for (;;) {
+ k = islt(*pb, *pa, compare);
+ if (k) {
+ if (k < 0)
+ goto Fail;
+ *dest-- = *pa--;
+ ++acount;
+ bcount = 0;
+ --na;
+ if (na == 0)
+ goto Succeed;
+ if (acount >= MIN_GALLOP)
break;
- } while (l < r);
-
- /* slide r left, looking for key < pivot */
- while (l < r) {
- register PyObject *rval = *r--;
- IFLT(rval, pivot) {
- /* swap and advance */
- r[1] = *l;
- *l++ = rval;
+ }
+ else {
+ *dest-- = *pb--;
+ ++bcount;
+ acount = 0;
+ --nb;
+ if (nb == 1)
+ goto CopyA;
+ if (bcount >= MIN_GALLOP)
break;
- }
}
+ }
- } while (l < r);
+ /* One run is winning so consistently that galloping may
+ * be a huge win. So try that, and continue galloping until
+ * (if ever) neither run appears to be winning consistently
+ * anymore.
+ */
+ do {
+ k = gallop_right(*pb, basea, na, na-1, compare);
+ if (k < 0)
+ goto Fail;
+ k = na - k;
+ acount = k;
+ if (k) {
+ dest -= k;
+ pa -= k;
+ memmove(dest+1, pa+1, k * sizeof(PyObject *));
+ na -= k;
+ if (na == 0)
+ goto Succeed;
+ }
+ *dest-- = *pb--;
+ --nb;
+ if (nb == 1)
+ goto CopyA;
+
+ k = gallop_left(*pa, baseb, nb, nb-1, compare);
+ if (k < 0)
+ goto Fail;
+ k = nb - k;
+ bcount = k;
+ if (k) {
+ dest -= k;
+ pb -= k;
+ memcpy(dest+1, pb+1, k * sizeof(PyObject *));
+ nb -= k;
+ if (nb == 1)
+ goto CopyA;
+ /* nb==0 is impossible now if the comparison
+ * function is consistent, but we can't assume
+ * that it is.
+ */
+ if (nb == 0)
+ goto Succeed;
+ }
+ *dest-- = *pa--;
+ --na;
+ if (na == 0)
+ goto Succeed;
+ } while (acount >= MIN_GALLOP || bcount >= MIN_GALLOP);
+ }
+Succeed:
+ result = 0;
+Fail:
+ if (nb)
+ memcpy(dest-(nb-1), baseb, nb * sizeof(PyObject*));
+ return result;
+CopyA:
+ assert(nb == 1 && na > 0);
+ /* The first element of pb belongs at the front of the merge. */
+ dest -= na;
+ pa -= na;
+ memmove(dest+1, pa+1, na * sizeof(PyObject *));
+ *dest = *pb;
+ return 0;
+}
- assert(lo < r && r <= l && l < hi);
- /* everything to the left of l is < pivot, and
- everything to the right of r is >= pivot */
+/* Merge the two runs at stack indices i and i+1.
+ * Returns 0 on success, -1 on error.
+ */
+static int
+merge_at(MergeState *ms, int i)
+{
+ PyObject **pa, **pb;
+ int na, nb;
+ int k;
+ PyObject *compare;
+
+ assert(ms != NULL);
+ assert(ms->n >= 2);
+ assert(i >= 0);
+ assert(i == ms->n - 2 || i == ms->n - 3);
+
+ pa = ms->base[i];
+ pb = ms->base[i+1];
+ na = ms->len[i];
+ nb = ms->len[i+1];
+ assert(na > 0 && nb > 0);
+ assert(pa + na == pb);
+
+ /* Record the length of the combined runs; if i is the 3rd-last
+ * run now, also slide over the last run (which isn't involved
+ * in this merge). The current run i+1 goes away in any case.
+ */
+ if (i == ms->n - 3) {
+ ms->len[i+1] = ms->len[i+2];
+ ms->base[i+1] = ms->base[i+2];
+ }
+ ms->len[i] = na + nb;
+ --ms->n;
- if (l == r) {
- IFLT(*r, pivot)
- ++l;
- else
- --r;
- }
- assert(lo <= r && r+1 == l && l <= hi);
- /* assert r == lo or a[r] < pivot */
- assert(*lo == pivot);
- /* assert l == hi or a[l] >= pivot */
- /* Swap the pivot into "the middle", so we can henceforth
- ignore it. */
- *lo = *r;
- *r = pivot;
-
- /* The following is true now, & will be preserved:
- All in [lo,r) are < pivot
- All in [r,l) == pivot (& so can be ignored)
- All in [l,hi) are >= pivot */
-
- /* Check for duplicates of the pivot. One compare is
- wasted if there are no duplicates, but can win big
- when there are.
- Tricky: we're sticking to "<" compares, so deduce
- equality indirectly. We know pivot <= *l, so they're
- equal iff not pivot < *l.
- */
- while (l < hi) {
- /* pivot <= *l known */
- IFLT(pivot, *l)
- break;
- else
- /* <= and not < implies == */
- ++l;
- }
+ /* Where does b start in a? Elements in a before that can be
+ * ignored (already in place).
+ */
+ compare = ms->compare;
+ k = gallop_right(*pb, pa, na, 0, compare);
+ if (k < 0)
+ return -1;
+ pa += k;
+ na -= k;
+ if (na == 0)
+ return 0;
+
+ /* Where does a end in b? Elements in b after that can be
+ * ignored (already in place).
+ */
+ nb = gallop_left(pa[na-1], pb, nb, nb-1, compare);
+ if (nb <= 0)
+ return nb;
- assert(lo <= r && r < l && l <= hi);
- /* Partitions are [lo, r) and [l, hi)
- :ush fattest first; remember we still have extra PPs
- to the left of the left chunk and to the right of
- the right chunk! */
- assert(top < STACKSIZE);
- if (r - lo <= hi - l) {
- /* second is bigger */
- stack[top].lo = l;
- stack[top].hi = hi;
- stack[top].extra = -extra;
- hi = r;
- extraOnRight = 0;
+ /* Merge what remains of the runs, using a temp array with
+ * min(na, nb) elements.
+ */
+ if (na <= nb)
+ return merge_lo(ms, pa, na, pb, nb);
+ else
+ return merge_hi(ms, pa, na, pb, nb);
+}
+
+/* Examine the stack of runs waiting to be merged, merging adjacent runs
+ * until the stack invariants are re-established:
+ *
+ * 1. len[-3] > len[-2] + len[-1]
+ * 2. len[-2] > len[-1]
+ *
+ * See listsort.txt for more info.
+ *
+ * Returns 0 on success, -1 on error.
+ */
+static int
+merge_collapse(MergeState *ms)
+{
+ int *len = ms->len;
+
+ assert(ms);
+ while (ms->n > 1) {
+ int n = ms->n - 2;
+ if (n > 0 && len[n-1] <= len[n] + len[n+1]) {
+ if (len[n-1] < len[n+1])
+ --n;
+ if (merge_at(ms, n) < 0)
+ return -1;
}
- else {
- /* first is bigger */
- stack[top].lo = lo;
- stack[top].hi = r;
- stack[top].extra = extra;
- lo = l;
- extraOnRight = 1;
+ else if (len[n] <= len[n+1]) {
+ if (merge_at(ms, n) < 0)
+ return -1;
}
- ++top;
-
- } /* end of partitioning loop */
+ else
+ break;
+ }
+ return 0;
+}
+/* Regardless of invariants, merge all runs on the stack until only one
+ * remains. This is used at the end of the mergesort.
+ *
+ * Returns 0 on success, -1 on error.
+ */
+static int
+merge_force_collapse(MergeState *ms)
+{
+ int *len = ms->len;
+
+ assert(ms);
+ while (ms->n > 1) {
+ int n = ms->n - 2;
+ if (n > 0 && len[n-1] < len[n+1])
+ --n;
+ if (merge_at(ms, n) < 0)
+ return -1;
+ }
return 0;
+}
- fail:
- return -1;
+/* Compute a good value for the minimum run length; natural runs shorter
+ * than this are boosted artificially via binary insertion.
+ *
+ * If n < 64, return n (it's too small to bother with fancy stuff).
+ * Else if n is an exact power of 2, return 32.
+ * Else return an int k, 32 <= k <= 64, such that n/k is close to, but
+ * strictly less than, an exact power of 2.
+ *
+ * See listsort.txt for more info.
+ */
+static int
+merge_compute_minrun(int n)
+{
+ int r = 0; /* becomes 1 if any 1 bits are shifted off */
+
+ assert(n >= 0);
+ while (n >= 64) {
+ r |= n & 1;
+ n >>= 1;
+ }
+ return n + r;
}
static PyTypeObject immutable_list_type;
+/* An adaptive, stable, natural mergesort. See listsort.txt.
+ * Returns Py_None on success, NULL on error. Even in case of error, the
+ * list will be some permutation of its input state (nothing is lost or
+ * duplicated).
+ */
static PyObject *
listsort(PyListObject *self, PyObject *args)
{
- int k;
- PyObject *compare = NULL;
- PyObject **hi, **p;
+ MergeState ms;
+ PyObject **lo, **hi;
+ int nremaining;
+ int minrun;
PyTypeObject *savetype;
+ PyObject *compare = NULL;
+ PyObject *result = NULL; /* guilty until proved innocent */
+ assert(self != NULL);
if (args != NULL) {
- if (!PyArg_ParseTuple(args, "|O:sort", &compare))
+ if (!PyArg_ParseTuple(args, "|O:msort", &compare))
return NULL;
}
+ merge_init(&ms, compare);
savetype = self->ob_type;
- if (self->ob_size < 2) {
- k = 0;
- goto done;
- }
-
self->ob_type = &immutable_list_type;
- hi = self->ob_item + self->ob_size;
-
- /* Set p to the largest value such that [lo, p) is sorted.
- This catches the already-sorted case, the all-the-same
- case, and the appended-a-few-elements-to-a-sorted-list case.
- If the array is unsorted, we're very likely to get out of
- the loop fast, so the test is cheap if it doesn't pay off.
- */
- for (p = self->ob_item + 1; p < hi; ++p) {
- IFLT(*p, *(p-1))
- break;
- }
- /* [lo, p) is sorted, [p, hi) unknown. Get out cheap if there are
- few unknowns, or few elements in total. */
- if (hi - p <= MAXMERGE || self->ob_size < MINSIZE) {
- k = binarysort(self->ob_item, hi, p, compare);
- goto done;
- }
- /* Check for the array already being reverse-sorted, or that with
- a few elements tacked on to the end. */
- for (p = self->ob_item + 1; p < hi; ++p) {
- IFLT(*(p-1), *p)
- break;
- }
- /* [lo, p) is reverse-sorted, [p, hi) unknown. */
- if (hi - p <= MAXMERGE) {
- /* Reverse the reversed prefix, then insert the tail */
- reverse_slice(self->ob_item, p);
- k = binarysort(self->ob_item, hi, p, compare);
- goto done;
- }
+ nremaining = self->ob_size;
+ if (nremaining < 2)
+ goto succeed;
+
+ /* March over the array once, left to right, finding natural runs,
+ * and extending short natural runs to minrun elements.
+ */
+ lo = self->ob_item;
+ hi = lo + nremaining;
+ minrun = merge_compute_minrun(nremaining);
+ do {
+ int descending;
+ int n;
- /* A large array without obvious pattern. */
- k = samplesortslice(self->ob_item, hi, compare);
+ /* Identify next run. */
+ n = count_run(lo, hi, compare, &descending);
+ if (n < 0)
+ goto fail;
+ if (descending)
+ reverse_slice(lo, lo + n);
+ /* If short, extend to min(minrun, nremaining). */
+ if (n < minrun) {
+ const int force = nremaining <= minrun ?
+ nremaining : minrun;
+ if (binarysort(lo, lo + force, lo + n, compare) < 0)
+ goto fail;
+ n = force;
+ }
+ /* Push run onto pending-runs stack, and maybe merge. */
+ assert(ms.n < MAX_MERGE_PENDING);
+ ms.base[ms.n] = lo;
+ ms.len[ms.n] = n;
+ ++ms.n;
+ if (merge_collapse(&ms) < 0)
+ goto fail;
+ /* Advance to find next run. */
+ lo += n;
+ nremaining -= n;
+ } while (nremaining);
+ assert(lo == hi);
+
+ if (merge_force_collapse(&ms) < 0)
+ goto fail;
+ assert(ms.n == 1);
+ assert(ms.base[0] == self->ob_item);
+ assert(ms.len[0] == self->ob_size);
-done: /* The IFLT macro requires a label named "fail". */;
+succeed:
+ result = Py_None;
fail:
self->ob_type = savetype;
- if (k >= 0) {
- Py_INCREF(Py_None);
- return Py_None;
- }
- else
- return NULL;
+ merge_freemem(&ms);
+ Py_XINCREF(result);
+ return result;
}
-
#undef IFLT
int
PyDoc_STRVAR(reverse_doc,
"L.reverse() -- reverse *IN PLACE*");
PyDoc_STRVAR(sort_doc,
-"L.sort([cmpfunc]) -- sort *IN PLACE*; if given, cmpfunc(x, y) -> -1, 0, 1");
+"L.sort([cmpfunc]) -- stable sort *IN PLACE*; cmpfunc(x, y) -> -1, 0, 1");
static PyMethodDef list_methods[] = {
{"append", (PyCFunction)listappend, METH_O, append_doc},
{"count", (PyCFunction)listcount, METH_O, count_doc},
{"reverse", (PyCFunction)listreverse, METH_NOARGS, reverse_doc},
{"sort", (PyCFunction)listsort, METH_VARARGS, sort_doc},
- {NULL, NULL} /* sentinel */
+ {NULL, NULL} /* sentinel */
};
static PySequenceMethods list_as_sequence = {
projects / python / commitdiff