SvCOMPILED_on(sv);
}
-
-#ifdef TESTHARNESS
-#include <sys/types.h>
-typedef void SV;
-#define pTHXo_
-#define pTHX_
-#define STATIC
-#define New(ID,VAR,N,TYPE) VAR=(TYPE *)malloc((N)*sizeof(TYPE))
-#define Safefree(VAR) free(VAR)
-typedef int (*SVCOMPARE_t) (pTHXo_ SV*, SV*);
-#endif /* TESTHARNESS */
-
-typedef char * aptr; /* pointer for arithmetic on sizes */
-typedef SV * gptr; /* pointers in our lists */
-
-/*
- * The original author of the mergesort implementation included here
- * is Peter M. McIlroy <pmcilroy@lucent.com> (see: Optimistic Merge Sort
- * (SODA '92)), and the integrator of it to the Perl source code is
- * John P. Linderman <jpl@research.att.com>.
- *
- * Both Peter and John agree with the inclusion of their code in here
- * and with their code being distributed under the same terms as Perl.
- *
- * Much of this code is original source code from BSD4.4, and is
- * copyright (c) 1991 The Regents of the University of California.
+/*
+ * The rest of this file was derived from source code contributed
+ * by Tom Horsley.
*
- * 1. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- * 2. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
+ * NOTE: this code was derived from Tom Horsley's qsort replacement
+ * and should not be confused with the original code.
*/
-/* Binary merge internal sort, with a few special mods
-** for the special perl environment it now finds itself in.
-**
-** Things that were once options have been hotwired
-** to values suitable for this use. In particular, we'll always
-** initialize looking for natural runs, we'll always produce stable
-** output, and we'll always do Peter McIlroy's binary merge.
-*/
+/* Copyright (C) Tom Horsley, 1997. All rights reserved.
-/* Pointer types for arithmetic and storage and convenience casts */
+ Permission granted to distribute under the same terms as perl which are
+ (briefly):
-#define APTR(P) ((aptr)(P))
-#define GPTP(P) ((gptr *)(P))
-#define GPPP(P) ((gptr **)(P))
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of either:
+ a) the GNU General Public License as published by the Free
+ Software Foundation; either version 1, or (at your option) any
+ later version, or
-/* byte offset from pointer P to (larger) pointer Q */
-#define BYTEOFF(P, Q) (APTR(Q) - APTR(P))
+ b) the "Artistic License" which comes with this Kit.
-#define PSIZE sizeof(gptr)
+ Details on the perl license can be found in the perl source code which
+ may be located via the www.perl.com web page.
-/* If PSIZE is power of 2, make PSHIFT that power, if that helps */
+ This is the most wonderfulest possible qsort I can come up with (and
+ still be mostly portable) My (limited) tests indicate it consistently
+ does about 20% fewer calls to compare than does the qsort in the Visual
+ C++ library, other vendors may vary.
-#ifdef PSHIFT
-#define PNELEM(P, Q) (BYTEOFF(P,Q) >> (PSHIFT))
-#define PNBYTE(N) ((N) << (PSHIFT))
-#define PINDEX(P, N) (GPTP(APTR(P) + PNBYTE(N)))
-#else
-/* Leave optimization to compiler */
-#define PNELEM(P, Q) (GPTP(Q) - GPTP(P))
-#define PNBYTE(N) ((N) * (PSIZE))
-#define PINDEX(P, N) (GPTP(P) + (N))
-#endif
+ Some of the ideas in here can be found in "Algorithms" by Sedgewick,
+ others I invented myself (or more likely re-invented since they seemed
+ pretty obvious once I watched the algorithm operate for a while).
-/* Pointer into other corresponding to pointer into this */
-#define POTHER(P, THIS, OTHER) GPTP(APTR(OTHER) + BYTEOFF(THIS,P))
+ Most of this code was written while watching the Marlins sweep the Giants
+ in the 1997 National League Playoffs - no Braves fans allowed to use this
+ code (just kidding :-).
-#define FROMTOUPTO(src, dst, lim) do *dst++ = *src++; while(src<lim)
+ I realize that if I wanted to be true to the perl tradition, the only
+ comment in this file would be something like:
+ ...they shuffled back towards the rear of the line. 'No, not at the
+ rear!' the slave-driver shouted. 'Three files up. And stay there...
-/* Runs are identified by a pointer in the auxilliary list.
-** The pointer is at the start of the list,
-** and it points to the start of the next list.
-** NEXT is used as an lvalue, too.
+ However, I really needed to violate that tradition just so I could keep
+ track of what happens myself, not to mention some poor fool trying to
+ understand this years from now :-).
*/
-#define NEXT(P) (*GPPP(P))
+/* ********************************************************** Configuration */
+#ifndef QSORT_ORDER_GUESS
+#define QSORT_ORDER_GUESS 2 /* Select doubling version of the netBSD trick */
+#endif
-/* PTHRESH is the minimum number of pairs with the same sense to justify
-** checking for a run and extending it. Note that PTHRESH counts PAIRS,
-** not just elements, so PTHRESH == 8 means a run of 16.
+/* QSORT_MAX_STACK is the largest number of partitions that can be stacked up for
+ future processing - a good max upper bound is log base 2 of memory size
+ (32 on 32 bit machines, 64 on 64 bit machines, etc). In reality can
+ safely be smaller than that since the program is taking up some space and
+ most operating systems only let you grab some subset of contiguous
+ memory (not to mention that you are normally sorting data larger than
+ 1 byte element size :-).
*/
+#ifndef QSORT_MAX_STACK
+#define QSORT_MAX_STACK 32
+#endif
-#define PTHRESH (8)
+/* QSORT_BREAK_EVEN is the size of the largest partition we should insertion sort.
+ Anything bigger and we use qsort. If you make this too small, the qsort
+ will probably break (or become less efficient), because it doesn't expect
+ the middle element of a partition to be the same as the right or left -
+ you have been warned).
+*/
+#ifndef QSORT_BREAK_EVEN
+#define QSORT_BREAK_EVEN 6
+#endif
-/* RTHRESH is the number of elements in a run that must compare low
-** to the low element from the opposing run before we justify
-** doing a binary rampup instead of single stepping.
-** In random input, N in a row low should only happen with
-** probability 2^(1-N), so we can risk that we are dealing
-** with orderly input without paying much when we aren't.
+/* ************************************************************* Data Types */
+
+/* hold left and right index values of a partition waiting to be sorted (the
+ partition includes both left and right - right is NOT one past the end or
+ anything like that).
*/
+struct partition_stack_entry {
+ int left;
+ int right;
+#ifdef QSORT_ORDER_GUESS
+ int qsort_break_even;
+#endif
+};
-#define RTHRESH (6)
+/* ******************************************************* Shorthand Macros */
+/* Note that these macros will be used from inside the qsort function where
+ we happen to know that the variable 'elt_size' contains the size of an
+ array element and the variable 'temp' points to enough space to hold a
+ temp element and the variable 'array' points to the array being sorted
+ and 'compare' is the pointer to the compare routine.
-/*
-** Overview of algorithm and variables.
-** The array of elements at list1 will be organized into runs of length 2,
-** or runs of length >= 2 * PTHRESH. We only try to form long runs when
-** PTHRESH adjacent pairs compare in the same way, suggesting overall order.
-**
-** Unless otherwise specified, pair pointers address the first of two elements.
-**
-** b and b+1 are a pair that compare with sense ``sense''.
-** b is the ``bottom'' of adjacent pairs that might form a longer run.
-**
-** p2 parallels b in the list2 array, where runs are defined by
-** a pointer chain.
-**
-** t represents the ``top'' of the adjacent pairs that might extend
-** the run beginning at b. Usually, t addresses a pair
-** that compares with opposite sense from (b,b+1).
-** However, it may also address a singleton element at the end of list1,
-** or it may be equal to ``last'', the first element beyond list1.
-**
-** r addresses the Nth pair following b. If this would be beyond t,
-** we back it off to t. Only when r is less than t do we consider the
-** run long enough to consider checking.
-**
-** q addresses a pair such that the pairs at b through q already form a run.
-** Often, q will equal b, indicating we only are sure of the pair itself.
-** However, a search on the previous cycle may have revealed a longer run,
-** so q may be greater than b.
-**
-** p is used to work back from a candidate r, trying to reach q,
-** which would mean b through r would be a run. If we discover such a run,
-** we start q at r and try to push it further towards t.
-** If b through r is NOT a run, we detect the wrong order at (p-1,p).
-** In any event, after the check (if any), we have two main cases.
-**
-** 1) Short run. b <= q < p <= r <= t.
-** b through q is a run (perhaps trivial)
-** q through p are uninteresting pairs
-** p through r is a run
-**
-** 2) Long run. b < r <= q < t.
-** b through q is a run (of length >= 2 * PTHRESH)
-**
-** Note that degenerate cases are not only possible, but likely.
-** For example, if the pair following b compares with opposite sense,
-** then b == q < p == r == t.
+ Also note that there are very many highly architecture specific ways
+ these might be sped up, but this is simply the most generally portable
+ code I could think of.
+*/
+
+/* Return < 0 == 0 or > 0 as the value of elt1 is < elt2, == elt2, > elt2
*/
+#define qsort_cmp(elt1, elt2) \
+ ((*compare)(aTHXo_ array[elt1], array[elt2]))
+#ifdef QSORT_ORDER_GUESS
+#define QSORT_NOTICE_SWAP swapped++;
+#else
+#define QSORT_NOTICE_SWAP
+#endif
+
+/* swaps contents of array elements elt1, elt2.
+*/
+#define qsort_swap(elt1, elt2) \
+ STMT_START { \
+ QSORT_NOTICE_SWAP \
+ temp = array[elt1]; \
+ array[elt1] = array[elt2]; \
+ array[elt2] = temp; \
+ } STMT_END
+
+/* rotate contents of elt1, elt2, elt3 such that elt1 gets elt2, elt2 gets
+ elt3 and elt3 gets elt1.
+*/
+#define qsort_rotate(elt1, elt2, elt3) \
+ STMT_START { \
+ QSORT_NOTICE_SWAP \
+ temp = array[elt1]; \
+ array[elt1] = array[elt2]; \
+ array[elt2] = array[elt3]; \
+ array[elt3] = temp; \
+ } STMT_END
+
+/* ************************************************************ Debug stuff */
+
+#ifdef QSORT_DEBUG
static void
-dynprep(pTHX_ gptr *list1, gptr *list2, size_t nmemb, SVCOMPARE_t cmp)
+break_here()
{
- int sense;
- register gptr *b, *p, *q, *t, *p2;
- register gptr c, *last, *r;
- gptr *savep;
-
- b = list1;
- last = PINDEX(b, nmemb);
- sense = (cmp(aTHX_ *b, *(b+1)) > 0);
- for (p2 = list2; b < last; ) {
- /* We just started, or just reversed sense.
- ** Set t at end of pairs with the prevailing sense.
- */
- for (p = b+2, t = p; ++p < last; t = ++p) {
- if ((cmp(aTHX_ *t, *p) > 0) != sense) break;
- }
- q = b;
- /* Having laid out the playing field, look for long runs */
- do {
- p = r = b + (2 * PTHRESH);
- if (r >= t) p = r = t; /* too short to care about */
- else {
- while (((cmp(aTHX_ *(p-1), *p) > 0) == sense) &&
- ((p -= 2) > q));
- if (p <= q) {
- /* b through r is a (long) run.
- ** Extend it as far as possible.
- */
- p = q = r;
- while (((p += 2) < t) &&
- ((cmp(aTHX_ *(p-1), *p) > 0) == sense)) q = p;
- r = p = q + 2; /* no simple pairs, no after-run */
- }
- }
- if (q > b) { /* run of greater than 2 at b */
- savep = p;
- p = q += 2;
- /* pick up singleton, if possible */
- if ((p == t) &&
- ((t + 1) == last) &&
- ((cmp(aTHX_ *(p-1), *p) > 0) == sense))
- savep = r = p = q = last;
- p2 = NEXT(p2) = p2 + (p - b);
- if (sense) while (b < --p) {
- c = *b;
- *b++ = *p;
- *p = c;
- }
- p = savep;
- }
- while (q < p) { /* simple pairs */
- p2 = NEXT(p2) = p2 + 2;
- if (sense) {
- c = *q++;
- *(q-1) = *q;
- *q++ = c;
- } else q += 2;
- }
- if (((b = p) == t) && ((t+1) == last)) {
- NEXT(p2) = p2 + 1;
- b++;
- }
- q = r;
- } while (b < t);
- sense = !sense;
- }
- return;
+ return; /* good place to set a breakpoint */
}
+#define qsort_assert(t) (void)( (t) || (break_here(), 0) )
-/* Overview of bmerge variables:
-**
-** list1 and list2 address the main and auxiliary arrays.
-** They swap identities after each merge pass.
-** Base points to the original list1, so we can tell if
-** the pointers ended up where they belonged (or must be copied).
-**
-** When we are merging two lists, f1 and f2 are the next elements
-** on the respective lists. l1 and l2 mark the end of the lists.
-** tp2 is the current location in the merged list.
-**
-** p1 records where f1 started.
-** After the merge, a new descriptor is built there.
-**
-** p2 is a ``parallel'' pointer in (what starts as) descriptor space.
-** It is used to identify and delimit the runs.
-**
-** In the heat of determining where q, the greater of the f1/f2 elements,
-** belongs in the other list, b, t and p, represent bottom, top and probe
-** locations, respectively, in the other list.
-** They make convenient temporary pointers in other places.
-*/
-
-STATIC void
-S_qsortsv(pTHX_ gptr *list1, size_t nmemb, SVCOMPARE_t cmp)
+static void
+doqsort_all_asserts(
+ void * array,
+ size_t num_elts,
+ size_t elt_size,
+ int (*compare)(const void * elt1, const void * elt2),
+ int pc_left, int pc_right, int u_left, int u_right)
{
- int i, run;
- int sense;
- register gptr *f1, *f2, *t, *b, *p, *tp2, *l1, *l2, *q;
- gptr *aux, *list2, *p2, *last;
- gptr *base = list1;
- gptr *p1;
-
- if (nmemb <= 1) return; /* sorted trivially */
- New(799,list2,nmemb,gptr); /* allocate auxilliary array */
- aux = list2;
- dynprep(aTHX_ list1, list2, nmemb, cmp);
- last = PINDEX(list2, nmemb);
- while (NEXT(list2) != last) {
- /* More than one run remains. Do some merging to reduce runs. */
- l2 = p1 = list1;
- for (tp2 = p2 = list2; p2 != last;) {
- /* The new first run begins where the old second list ended.
- ** Use the p2 ``parallel'' pointer to identify the end of the run.
- */
- f1 = l2;
- t = NEXT(p2);
- f2 = l1 = POTHER(t, list2, list1);
- if (t != last) t = NEXT(t);
- l2 = POTHER(t, list2, list1);
- p2 = t;
- while (f1 < l1 && f2 < l2) {
- /* If head 1 is larger than head 2, find ALL the elements
- ** in list 2 strictly less than head1, write them all,
- ** then head 1. Then compare the new heads, and repeat,
- ** until one or both lists are exhausted.
- **
- ** In all comparisons (after establishing
- ** which head to merge) the item to merge
- ** (at pointer q) is the first operand of
- ** the comparison. When we want to know
- ** if ``q is strictly less than the other'',
- ** we can't just do
- ** cmp(q, other) < 0
- ** because stability demands that we treat equality
- ** as high when q comes from l2, and as low when
- ** q was from l1. So we ask the question by doing
- ** cmp(q, other) <= sense
- ** and make sense == 0 when equality should look low,
- ** and -1 when equality should look high.
- */
-
-
- if (cmp(aTHX_ *f1, *f2) <= 0) {
- q = f2; b = f1; t = l1;
- sense = -1;
- } else {
- q = f1; b = f2; t = l2;
- sense = 0;
- }
+ int i;
+
+ qsort_assert(pc_left <= pc_right);
+ qsort_assert(u_right < pc_left);
+ qsort_assert(pc_right < u_left);
+ for (i = u_right + 1; i < pc_left; ++i) {
+ qsort_assert(qsort_cmp(i, pc_left) < 0);
+ }
+ for (i = pc_left; i < pc_right; ++i) {
+ qsort_assert(qsort_cmp(i, pc_right) == 0);
+ }
+ for (i = pc_right + 1; i < u_left; ++i) {
+ qsort_assert(qsort_cmp(pc_right, i) < 0);
+ }
+}
+#define qsort_all_asserts(PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT) \
+ doqsort_all_asserts(array, num_elts, elt_size, compare, \
+ PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT)
- /* ramp up
- **
- ** Leave t at something strictly
- ** greater than q (or at the end of the list),
- ** and b at something strictly less than q.
- */
- for (i = 1, run = 0 ;;) {
- if ((p = PINDEX(b, i)) >= t) {
- /* off the end */
- if (((p = PINDEX(t, -1)) > b) &&
- (cmp(aTHX_ *q, *p) <= sense))
- t = p;
- else b = p;
- break;
- } else if (cmp(aTHX_ *q, *p) <= sense) {
- t = p;
- break;
- } else b = p;
- if (++run >= RTHRESH) i += i;
- }
+#else
+#define qsort_assert(t) ((void)0)
- /* q is known to follow b and must be inserted before t.
- ** Increment b, so the range of possibilities is [b,t).
- ** Round binary split down, to favor early appearance.
- ** Adjust b and t until q belongs just before t.
- */
+#define qsort_all_asserts(PC_LEFT, PC_RIGHT, U_LEFT, U_RIGHT) ((void)0)
- b++;
- while (b < t) {
- p = PINDEX(b, (PNELEM(b, t) - 1) / 2);
- if (cmp(aTHX_ *q, *p) <= sense) {
- t = p;
- } else b = p + 1;
- }
+#endif
+/* ****************************************************************** qsort */
- /* Copy all the strictly low elements */
+STATIC void
+S_qsortsv(pTHX_ SV ** array, size_t num_elts, SVCOMPARE_t compare)
+{
+ register SV * temp;
- if (q == f1) {
- FROMTOUPTO(f2, tp2, t);
- *tp2++ = *f1++;
- } else {
- FROMTOUPTO(f1, tp2, t);
- *tp2++ = *f2++;
- }
- }
+ struct partition_stack_entry partition_stack[QSORT_MAX_STACK];
+ int next_stack_entry = 0;
+ int part_left;
+ int part_right;
+#ifdef QSORT_ORDER_GUESS
+ int qsort_break_even;
+ int swapped;
+#endif
- /* Run out remaining list */
- if (f1 == l1) {
- if (f2 < l2) FROMTOUPTO(f2, tp2, l2);
- } else FROMTOUPTO(f1, tp2, l1);
- p1 = NEXT(p1) = POTHER(tp2, list2, list1);
- }
- t = list1;
- list1 = list2;
- list2 = t;
- last = PINDEX(list2, nmemb);
- }
- if (base == list2) {
- last = PINDEX(list1, nmemb);
- FROMTOUPTO(list1, list2, last);
- }
- Safefree(aux);
- return;
+ /* Make sure we actually have work to do.
+ */
+ if (num_elts <= 1) {
+ return;
+ }
+
+ /* Setup the initial partition definition and fall into the sorting loop
+ */
+ part_left = 0;
+ part_right = (int)(num_elts - 1);
+#ifdef QSORT_ORDER_GUESS
+ qsort_break_even = QSORT_BREAK_EVEN;
+#else
+#define qsort_break_even QSORT_BREAK_EVEN
+#endif
+ for ( ; ; ) {
+ if ((part_right - part_left) >= qsort_break_even) {
+ /* OK, this is gonna get hairy, so lets try to document all the
+ concepts and abbreviations and variables and what they keep
+ track of:
+
+ pc: pivot chunk - the set of array elements we accumulate in the
+ middle of the partition, all equal in value to the original
+ pivot element selected. The pc is defined by:
+
+ pc_left - the leftmost array index of the pc
+ pc_right - the rightmost array index of the pc
+
+ we start with pc_left == pc_right and only one element
+ in the pivot chunk (but it can grow during the scan).
+
+ u: uncompared elements - the set of elements in the partition
+ we have not yet compared to the pivot value. There are two
+ uncompared sets during the scan - one to the left of the pc
+ and one to the right.
+
+ u_right - the rightmost index of the left side's uncompared set
+ u_left - the leftmost index of the right side's uncompared set
+
+ The leftmost index of the left sides's uncompared set
+ doesn't need its own variable because it is always defined
+ by the leftmost edge of the whole partition (part_left). The
+ same goes for the rightmost edge of the right partition
+ (part_right).
+
+ We know there are no uncompared elements on the left once we
+ get u_right < part_left and no uncompared elements on the
+ right once u_left > part_right. When both these conditions
+ are met, we have completed the scan of the partition.
+
+ Any elements which are between the pivot chunk and the
+ uncompared elements should be less than the pivot value on
+ the left side and greater than the pivot value on the right
+ side (in fact, the goal of the whole algorithm is to arrange
+ for that to be true and make the groups of less-than and
+ greater-then elements into new partitions to sort again).
+
+ As you marvel at the complexity of the code and wonder why it
+ has to be so confusing. Consider some of the things this level
+ of confusion brings:
+
+ Once I do a compare, I squeeze every ounce of juice out of it. I
+ never do compare calls I don't have to do, and I certainly never
+ do redundant calls.
+
+ I also never swap any elements unless I can prove there is a
+ good reason. Many sort algorithms will swap a known value with
+ an uncompared value just to get things in the right place (or
+ avoid complexity :-), but that uncompared value, once it gets
+ compared, may then have to be swapped again. A lot of the
+ complexity of this code is due to the fact that it never swaps
+ anything except compared values, and it only swaps them when the
+ compare shows they are out of position.
+ */
+ int pc_left, pc_right;
+ int u_right, u_left;
+
+ int s;
+
+ pc_left = ((part_left + part_right) / 2);
+ pc_right = pc_left;
+ u_right = pc_left - 1;
+ u_left = pc_right + 1;
+
+ /* Qsort works best when the pivot value is also the median value
+ in the partition (unfortunately you can't find the median value
+ without first sorting :-), so to give the algorithm a helping
+ hand, we pick 3 elements and sort them and use the median value
+ of that tiny set as the pivot value.
+
+ Some versions of qsort like to use the left middle and right as
+ the 3 elements to sort so they can insure the ends of the
+ partition will contain values which will stop the scan in the
+ compare loop, but when you have to call an arbitrarily complex
+ routine to do a compare, its really better to just keep track of
+ array index values to know when you hit the edge of the
+ partition and avoid the extra compare. An even better reason to
+ avoid using a compare call is the fact that you can drop off the
+ edge of the array if someone foolishly provides you with an
+ unstable compare function that doesn't always provide consistent
+ results.
+
+ So, since it is simpler for us to compare the three adjacent
+ elements in the middle of the partition, those are the ones we
+ pick here (conveniently pointed at by u_right, pc_left, and
+ u_left). The values of the left, center, and right elements
+ are refered to as l c and r in the following comments.
+ */
+
+#ifdef QSORT_ORDER_GUESS
+ swapped = 0;
+#endif
+ s = qsort_cmp(u_right, pc_left);
+ if (s < 0) {
+ /* l < c */
+ s = qsort_cmp(pc_left, u_left);
+ /* if l < c, c < r - already in order - nothing to do */
+ if (s == 0) {
+ /* l < c, c == r - already in order, pc grows */
+ ++pc_right;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else if (s > 0) {
+ /* l < c, c > r - need to know more */
+ s = qsort_cmp(u_right, u_left);
+ if (s < 0) {
+ /* l < c, c > r, l < r - swap c & r to get ordered */
+ qsort_swap(pc_left, u_left);
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else if (s == 0) {
+ /* l < c, c > r, l == r - swap c&r, grow pc */
+ qsort_swap(pc_left, u_left);
+ --pc_left;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else {
+ /* l < c, c > r, l > r - make lcr into rlc to get ordered */
+ qsort_rotate(pc_left, u_right, u_left);
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ }
+ }
+ } else if (s == 0) {
+ /* l == c */
+ s = qsort_cmp(pc_left, u_left);
+ if (s < 0) {
+ /* l == c, c < r - already in order, grow pc */
+ --pc_left;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else if (s == 0) {
+ /* l == c, c == r - already in order, grow pc both ways */
+ --pc_left;
+ ++pc_right;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else {
+ /* l == c, c > r - swap l & r, grow pc */
+ qsort_swap(u_right, u_left);
+ ++pc_right;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ }
+ } else {
+ /* l > c */
+ s = qsort_cmp(pc_left, u_left);
+ if (s < 0) {
+ /* l > c, c < r - need to know more */
+ s = qsort_cmp(u_right, u_left);
+ if (s < 0) {
+ /* l > c, c < r, l < r - swap l & c to get ordered */
+ qsort_swap(u_right, pc_left);
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else if (s == 0) {
+ /* l > c, c < r, l == r - swap l & c, grow pc */
+ qsort_swap(u_right, pc_left);
+ ++pc_right;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else {
+ /* l > c, c < r, l > r - rotate lcr into crl to order */
+ qsort_rotate(u_right, pc_left, u_left);
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ }
+ } else if (s == 0) {
+ /* l > c, c == r - swap ends, grow pc */
+ qsort_swap(u_right, u_left);
+ --pc_left;
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ } else {
+ /* l > c, c > r - swap ends to get in order */
+ qsort_swap(u_right, u_left);
+ qsort_all_asserts(pc_left, pc_right, u_left + 1, u_right - 1);
+ }
+ }
+ /* We now know the 3 middle elements have been compared and
+ arranged in the desired order, so we can shrink the uncompared
+ sets on both sides
+ */
+ --u_right;
+ ++u_left;
+ qsort_all_asserts(pc_left, pc_right, u_left, u_right);
+
+ /* The above massive nested if was the simple part :-). We now have
+ the middle 3 elements ordered and we need to scan through the
+ uncompared sets on either side, swapping elements that are on
+ the wrong side or simply shuffling equal elements around to get
+ all equal elements into the pivot chunk.
+ */
+
+ for ( ; ; ) {
+ int still_work_on_left;
+ int still_work_on_right;
+
+ /* Scan the uncompared values on the left. If I find a value
+ equal to the pivot value, move it over so it is adjacent to
+ the pivot chunk and expand the pivot chunk. If I find a value
+ less than the pivot value, then just leave it - its already
+ on the correct side of the partition. If I find a greater
+ value, then stop the scan.
+ */
+ while ((still_work_on_left = (u_right >= part_left))) {
+ s = qsort_cmp(u_right, pc_left);
+ if (s < 0) {
+ --u_right;
+ } else if (s == 0) {
+ --pc_left;
+ if (pc_left != u_right) {
+ qsort_swap(u_right, pc_left);
+ }
+ --u_right;
+ } else {
+ break;
+ }
+ qsort_assert(u_right < pc_left);
+ qsort_assert(pc_left <= pc_right);
+ qsort_assert(qsort_cmp(u_right + 1, pc_left) <= 0);
+ qsort_assert(qsort_cmp(pc_left, pc_right) == 0);
+ }
+
+ /* Do a mirror image scan of uncompared values on the right
+ */
+ while ((still_work_on_right = (u_left <= part_right))) {
+ s = qsort_cmp(pc_right, u_left);
+ if (s < 0) {
+ ++u_left;
+ } else if (s == 0) {
+ ++pc_right;
+ if (pc_right != u_left) {
+ qsort_swap(pc_right, u_left);
+ }
+ ++u_left;
+ } else {
+ break;
+ }
+ qsort_assert(u_left > pc_right);
+ qsort_assert(pc_left <= pc_right);
+ qsort_assert(qsort_cmp(pc_right, u_left - 1) <= 0);
+ qsort_assert(qsort_cmp(pc_left, pc_right) == 0);
+ }
+
+ if (still_work_on_left) {
+ /* I know I have a value on the left side which needs to be
+ on the right side, but I need to know more to decide
+ exactly the best thing to do with it.
+ */
+ if (still_work_on_right) {
+ /* I know I have values on both side which are out of
+ position. This is a big win because I kill two birds
+ with one swap (so to speak). I can advance the
+ uncompared pointers on both sides after swapping both
+ of them into the right place.
+ */
+ qsort_swap(u_right, u_left);
+ --u_right;
+ ++u_left;
+ qsort_all_asserts(pc_left, pc_right, u_left, u_right);
+ } else {
+ /* I have an out of position value on the left, but the
+ right is fully scanned, so I "slide" the pivot chunk
+ and any less-than values left one to make room for the
+ greater value over on the right. If the out of position
+ value is immediately adjacent to the pivot chunk (there
+ are no less-than values), I can do that with a swap,
+ otherwise, I have to rotate one of the less than values
+ into the former position of the out of position value
+ and the right end of the pivot chunk into the left end
+ (got all that?).
+ */
+ --pc_left;
+ if (pc_left == u_right) {
+ qsort_swap(u_right, pc_right);
+ qsort_all_asserts(pc_left, pc_right-1, u_left, u_right-1);
+ } else {
+ qsort_rotate(u_right, pc_left, pc_right);
+ qsort_all_asserts(pc_left, pc_right-1, u_left, u_right-1);
+ }
+ --pc_right;
+ --u_right;
+ }
+ } else if (still_work_on_right) {
+ /* Mirror image of complex case above: I have an out of
+ position value on the right, but the left is fully
+ scanned, so I need to shuffle things around to make room
+ for the right value on the left.
+ */
+ ++pc_right;
+ if (pc_right == u_left) {
+ qsort_swap(u_left, pc_left);
+ qsort_all_asserts(pc_left+1, pc_right, u_left+1, u_right);
+ } else {
+ qsort_rotate(pc_right, pc_left, u_left);
+ qsort_all_asserts(pc_left+1, pc_right, u_left+1, u_right);
+ }
+ ++pc_left;
+ ++u_left;
+ } else {
+ /* No more scanning required on either side of partition,
+ break out of loop and figure out next set of partitions
+ */
+ break;
+ }
+ }
+
+ /* The elements in the pivot chunk are now in the right place. They
+ will never move or be compared again. All I have to do is decide
+ what to do with the stuff to the left and right of the pivot
+ chunk.
+
+ Notes on the QSORT_ORDER_GUESS ifdef code:
+
+ 1. If I just built these partitions without swapping any (or
+ very many) elements, there is a chance that the elements are
+ already ordered properly (being properly ordered will
+ certainly result in no swapping, but the converse can't be
+ proved :-).
+
+ 2. A (properly written) insertion sort will run faster on
+ already ordered data than qsort will.
+
+ 3. Perhaps there is some way to make a good guess about
+ switching to an insertion sort earlier than partition size 6
+ (for instance - we could save the partition size on the stack
+ and increase the size each time we find we didn't swap, thus
+ switching to insertion sort earlier for partitions with a
+ history of not swapping).
+
+ 4. Naturally, if I just switch right away, it will make
+ artificial benchmarks with pure ascending (or descending)
+ data look really good, but is that a good reason in general?
+ Hard to say...
+ */
+
+#ifdef QSORT_ORDER_GUESS
+ if (swapped < 3) {
+#if QSORT_ORDER_GUESS == 1
+ qsort_break_even = (part_right - part_left) + 1;
+#endif
+#if QSORT_ORDER_GUESS == 2
+ qsort_break_even *= 2;
+#endif
+#if QSORT_ORDER_GUESS == 3
+ int prev_break = qsort_break_even;
+ qsort_break_even *= qsort_break_even;
+ if (qsort_break_even < prev_break) {
+ qsort_break_even = (part_right - part_left) + 1;
+ }
+#endif
+ } else {
+ qsort_break_even = QSORT_BREAK_EVEN;
+ }
+#endif
+
+ if (part_left < pc_left) {
+ /* There are elements on the left which need more processing.
+ Check the right as well before deciding what to do.
+ */
+ if (pc_right < part_right) {
+ /* We have two partitions to be sorted. Stack the biggest one
+ and process the smallest one on the next iteration. This
+ minimizes the stack height by insuring that any additional
+ stack entries must come from the smallest partition which
+ (because it is smallest) will have the fewest
+ opportunities to generate additional stack entries.
+ */
+ if ((part_right - pc_right) > (pc_left - part_left)) {
+ /* stack the right partition, process the left */
+ partition_stack[next_stack_entry].left = pc_right + 1;
+ partition_stack[next_stack_entry].right = part_right;
+#ifdef QSORT_ORDER_GUESS
+ partition_stack[next_stack_entry].qsort_break_even = qsort_break_even;
+#endif
+ part_right = pc_left - 1;
+ } else {
+ /* stack the left partition, process the right */
+ partition_stack[next_stack_entry].left = part_left;
+ partition_stack[next_stack_entry].right = pc_left - 1;
+#ifdef QSORT_ORDER_GUESS
+ partition_stack[next_stack_entry].qsort_break_even = qsort_break_even;
+#endif
+ part_left = pc_right + 1;
+ }
+ qsort_assert(next_stack_entry < QSORT_MAX_STACK);
+ ++next_stack_entry;
+ } else {
+ /* The elements on the left are the only remaining elements
+ that need sorting, arrange for them to be processed as the
+ next partition.
+ */
+ part_right = pc_left - 1;
+ }
+ } else if (pc_right < part_right) {
+ /* There is only one chunk on the right to be sorted, make it
+ the new partition and loop back around.
+ */
+ part_left = pc_right + 1;
+ } else {
+ /* This whole partition wound up in the pivot chunk, so
+ we need to get a new partition off the stack.
+ */
+ if (next_stack_entry == 0) {
+ /* the stack is empty - we are done */
+ break;
+ }
+ --next_stack_entry;
+ part_left = partition_stack[next_stack_entry].left;
+ part_right = partition_stack[next_stack_entry].right;
+#ifdef QSORT_ORDER_GUESS
+ qsort_break_even = partition_stack[next_stack_entry].qsort_break_even;
+#endif
+ }
+ } else {
+ /* This partition is too small to fool with qsort complexity, just
+ do an ordinary insertion sort to minimize overhead.
+ */
+ int i;
+ /* Assume 1st element is in right place already, and start checking
+ at 2nd element to see where it should be inserted.
+ */
+ for (i = part_left + 1; i <= part_right; ++i) {
+ int j;
+ /* Scan (backwards - just in case 'i' is already in right place)
+ through the elements already sorted to see if the ith element
+ belongs ahead of one of them.
+ */
+ for (j = i - 1; j >= part_left; --j) {
+ if (qsort_cmp(i, j) >= 0) {
+ /* i belongs right after j
+ */
+ break;
+ }
+ }
+ ++j;
+ if (j != i) {
+ /* Looks like we really need to move some things
+ */
+ int k;
+ temp = array[i];
+ for (k = i - 1; k >= j; --k)
+ array[k + 1] = array[k];
+ array[j] = temp;
+ }
+ }
+
+ /* That partition is now sorted, grab the next one, or get out
+ of the loop if there aren't any more.
+ */
+
+ if (next_stack_entry == 0) {
+ /* the stack is empty - we are done */
+ break;
+ }
+ --next_stack_entry;
+ part_left = partition_stack[next_stack_entry].left;
+ part_right = partition_stack[next_stack_entry].right;
+#ifdef QSORT_ORDER_GUESS
+ qsort_break_even = partition_stack[next_stack_entry].qsort_break_even;
+#endif
+ }
+ }
+
+ /* Believe it or not, the array is sorted at this point! */
}
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