Retract the mergesort code, way too incompatible licensing

and copyrights.

p4raw-id: //depot/perl@6963

2 files changed, 633 insertions, 338 deletions

diff --git a/pod/perldelta.pod b/pod/perldelta.pod
index 961ded3c86..d739204571 100644
--- a/pod/perldelta.pod
+++ b/pod/perldelta.pod
@@ -290,17 +290,6 @@ distribution.
 
 map() that changes the size of the list should now work faster.
 
-=item *
-
-sort() has been changed to use mergesort internally as opposed to the
-earlier quicksort.  For very small lists this may result in slightly
-slower sorting times, but in general the speedup should be at least 20%.
-Additional bonuses are that the worst case behaviour of sort() is now
-better (in computer science terms it now runs in time O(N log N), as
-opposed to quicksorts Theta(N**2) worst-case run time behaviour), and
-that sort() is now stable (meaning that elements with identical keys
-will stay ordered as they were before the sort).
-
 =back
 
 =head1 Installation and Configuration Improvements
diff --git a/pp_ctl.c b/pp_ctl.c
index ac09d42422..45f9a7e2a3 100644
--- a/pp_ctl.c
+++ b/pp_ctl.c
@@ -3672,377 +3672,683 @@ S_doparseform(pTHX_ SV *sv)
     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! */
 }