another broken qsort

lib/stdlib/qsort.c

@@ -18,244 +18,139 @@
  * along with GNU Mes.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-/* Copyright (C) 1991, 1992 Free Software Foundation, Inc.
-This file is part of the GNU C Library.
-Written by Douglas C. Schmidt (schmidt@ics.uci.edu).
-
-The GNU C Library is free software; you can redistribute it and/or
-modify it under the terms of the GNU Library General Public License as
-published by the Free Software Foundation; either version 2 of the
-License, or (at your option) any later version.
-
-The GNU C Library is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-Library General Public License for more details.
-
-You should have received a copy of the GNU Library General Public
-License along with the GNU C Library; see the file COPYING.LIB.  If
-not, write to the Free Software Foundation, Inc., 675 Mass Ave,
-Cambridge, MA 02139, USA.  */
-
-#include <alloca.h>
 #include <stdlib.h>
 #include <string.h>
 
-/* Byte-wise swap two items of size SIZE. */
+#if 0
-#define SWAP(a, b, size)                        \
-  do                                            \
-    {                                           \
-      size_t __size = (size);                   \
-      char *__a = (a), *__b = (b);              \
-      do                                        \
-	{                                       \
-	  char __tmp = *__a;                    \
-	  *__a++ = *__b;                        \
-	  *__b++ = __tmp;                       \
-	} while (--__size > 0);                 \
-    } while (0)
-
-/* Discontinue quicksort algorithm when partition gets below this size.
-   This particular magic number was chosen to work best on a Sun 4/260. */
-#define MAX_THRESH 4
-
-/* Stack node declarations used to store unfulfilled partition obligations. */
-typedef struct
-  {
-    char *lo;
-    char *hi;
-  } stack_node;
-
-/* The next 4 #defines implement a very fast in-line stack abstraction. */
-#define STACK_SIZE	(8 * sizeof(unsigned long int))
-#define PUSH(low, high)	((void) ((top->lo = (low)), (top->hi = (high)), ++top))
-#define	POP(low, high)	((void) (--top, (low = top->lo), (high = top->hi)))
-#define	STACK_NOT_EMPTY	(stack < top)
-
-
-/* Order size using quicksort.  This implementation incorporates
-   four optimizations discussed in Sedgewick:
-
-   1. Non-recursive, using an explicit stack of pointer that store the
-      next array partition to sort.  To save time, this maximum amount
-      of space required to store an array of MAX_INT is allocated on the
-      stack.  Assuming a 32-bit integer, this needs only 32 *
-      sizeof(stack_node) == 136 bits.  Pretty cheap, actually.
-
-   2. Chose the pivot element using a median-of-three decision tree.
-      This reduces the probability of selecting a bad pivot value and
-      eliminates certain extraneous comparisons.
-
-   3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
-      insertion sort to order the MAX_THRESH items within each partition.
-      This is a big win, since insertion sort is faster for small, mostly
-      sorted array segements.
-
-   4. The larger of the two sub-partitions is always pushed onto the
-      stack first, with the algorithm then concentrating on the
-      smaller partition.  This *guarantees* no more than log (n)
-      stack size is needed (actually O(1) in this case)!  */
-
 void
-qsort (void* base, size_t total_elems, size_t size,
+qswap (void *a, void *b, size_t size)
-       int (*compare)(void const *, void const *))
 {
-  char *base_ptr = (char *) base;
+  char *pa = a;
-
+  char *pb = b;
-  /* Allocating SIZE bytes for a pivot buffer facilitates a better
-     algorithm below since we can do comparisons directly on the pivot. */
-  char *pivot_buffer = (char *) alloca (size);
-  const size_t max_thresh = MAX_THRESH * size;
-
-  if (total_elems == 0)
-    /* Avoid lossage with unsigned arithmetic below.  */
-    return;
-
-  if (total_elems > MAX_THRESH)
-    {
-      char *lo = base_ptr;
-      char *hi = &lo[size * (total_elems - 1)];
-      /* Largest size needed for 32-bit int!!! */
-      stack_node stack[STACK_SIZE];
-      stack_node *top = stack + 1;
-
-      while (STACK_NOT_EMPTY)
-        {
-          char *left_ptr;
-          char *right_ptr;
-
-	  char *pivot = pivot_buffer;
-
-	  /* Select median value from among LO, MID, and HI. Rearrange
-	     LO and HI so the three values are sorted. This lowers the
-	     probability of picking a pathological pivot value and
-	     skips a comparison for both the LEFT_PTR and RIGHT_PTR. */
-
-	  char *mid = lo + size * ((hi - lo) / size >> 1);
-
-	  if ((*compare)((void*) mid, (void*) lo) < 0)
-	    SWAP (mid, lo, size);
-	  if ((*compare)((void*) hi, (void*) mid) < 0)
-	    SWAP (mid, hi, size);
-	  else
-	    goto jump_over;
-	  if ((*compare)((void*) mid, (void*) lo) < 0)
-	    SWAP (mid, lo, size);
-	jump_over:;
-	  memcpy (pivot, mid, size);
-	  pivot = pivot_buffer;
-
-	  left_ptr  = lo + size;
-	  right_ptr = hi - size;
-
-	  /* Here's the famous ``collapse the walls'' section of quicksort.
-	     Gotta like those tight inner loops!  They are the main reason
-	     that this algorithm runs much faster than others. */
   do
     {
-	      while ((*compare)((void*) left_ptr, (void*) pivot) < 0)
+      char tmp = *pa;
-		left_ptr += size;
+      *pa++ = *pb;
-
+      *pb++ = tmp;
-	      while ((*compare)((void*) pivot, (void*) right_ptr) < 0)
+    } while (--size > 0);
-		right_ptr -= size;
+}
-
+#else
-	      if (left_ptr < right_ptr)
+void
+qswap (void *a, void *b, int size)
 {
-		  SWAP (left_ptr, right_ptr, size);
+  char buffer[size];
-		  left_ptr += size;
+  memcpy (buffer, a, size);
-		  right_ptr -= size;
+  memcpy (a, b, size);
+  memcpy (b, buffer, size);
 }
-	      else if (left_ptr == right_ptr)
+#endif
+
+
+/**
+ * Assuming precondition (P) that `end - begin >= 2`, this function reorders the elements
+ * of range [begin, end) and returns a pointer `ret` such that the following
+ * postconditions hold:
+ *   - (Q1): `ret > begin`
+ *   - (Q2): `ret < end`
+ * and, for some value `p` in [begin, end):
+ *   - (Q3): all values in [begin, ret) are lower than or equal to `p`
+ *   - (Q4): all values in [ret, end) are greater than or equal to `p`
+ */
+char *
+qpart (char *low, char *high, size_t size,
+       int (*compare) (void const *, void const *))
 {
-		  left_ptr += size;
+  char *pivot = (low + (high - low)/2);
-		  right_ptr -= size;
-		  break;
-		}
-	    }
-	  while (left_ptr <= right_ptr);
 
-          /* Set up pointers for next iteration.  First determine whether
+  // Loop invariants, all trivially verified at the start of the loop:
-             left and right partitions are below the threshold size.  If so,
+  //   - (A): values strictly to the left of `low` are lower than or equal to `pivot`
-             ignore one or both.  Otherwise, push the larger partition's
+  //   - (B): there is at least one value at or to the right of `low` that is greater
-             bounds on the stack and continue sorting the smaller one. */
+  //     than or equal to `pivot`
-
+  //   - (C): values at or to the right of `high` are greater than or equal to `pivot`
-          if ((size_t) (right_ptr - lo) <= max_thresh)
+  //   - (D): there is at least one value strictly to the left of `high` that is lower
+  //     than or equal to `pivot`
+  //   - (E): `low <= high`
+  //
+  // The loop terminates because `high - low` decreases strictly at each execution of
+  // the body (obvious).
+  while (1)
     {
-              if ((size_t) (hi - left_ptr) <= max_thresh)
+      // This loop terminates because of (B).
-		/* Ignore both small partitions. */
+      int c = compare (low, pivot);
-                POP (lo, hi);
+      while (c < 0)
-              else
+        low += size;
-		/* Ignore small left partition. */
+
-                lo = left_ptr;
+      // Here, we have
-            }
+      //   - (1): `*low >= pivot`
-          else if ((size_t) (hi - left_ptr) <= max_thresh)
+      //   - (2): `low <= high` because of (E) and (C)
-	    /* Ignore small right partition. */
+      //   - properties (A) and (B) still hold because `low` has only moved
-            hi = right_ptr;
+      //     past values strictly less than `pivot`
-          else if ((right_ptr - lo) > (hi - left_ptr))
+
+      // This loop terminates because of (D).
+      do {
+        --high;
+        int c = compare (pivot, high);
+      } while (c < 0);
+
+      // Here, we have
+      //   - (3): `*high <= pivot`
+      //   - (4): by (C) which held before this loop, elements strictly to the
+      //     right of `high` are known to be greater than or equal to `pivot`
+      //     (but now (C) may not hold anymore)
+
+      if (low >= high)
         {
-	      /* Push larger left partition indices. */
+          // Due to (1), (A) and (4), (Q3) and (Q4) are established with `pivot`
-              PUSH( lo, right_ptr);
+          // as `p`.
-              lo = left_ptr;
+          // Clearly, (B) proves Q2.
+          // See the rest of the answer below for a proof of (Q1).
+          // This correctly finishes the qpart.
+          return low;
         }
-          else
+
+      // We have `low < high` and we swap...
+      qswap (low, high, size);
+
+      // ...and now,
+      //   - by (1) and (4), invariant (C) is re-established
+      //   - by (1), invariant (D) is re-established
+      //   - (5): by (3), `*low <= pivot`
+
+      ++low;
+      // (A) already held before this increment. Thus, because of (5), (A)
+      // still holds. Additionally, by (1), after the swap, (B) is
+      // re-established. Finally, (E) is obvious.
+    }
+}
+
+void
+_qsort (char *low, char *high, size_t size,
+       int (*compare) (void const *, void const *))
 {
-	      /* Push larger right partition indices. */
+  // Trivial base case...
-              PUSH (left_ptr, hi);
+  if (low - high < size)
-              hi = right_ptr;
+    return;
-            }
+
-        }
+  // ...therefore pre-condition (P) of `qpart` is satisfied.
+  char *p = qpart (low, high, size, compare);
+
+  // Thanks to postconditions (Q1) and (Q2) of `qpart`, the ranges
+  // [low, p) and [p, high) are non-empty, therefore the size of the ranges
+  // passed to the recursive calls below is strictly lower than the size of
+  // [low, high) in this call. Therefore the base case is eventually reached
+  // and the algorithm terminates.
+
+  // Thanks to postconditions (Q3) and (Q4) of `qpart`, and by induction
+  // on the size of [low, high), the recursive calls below sort their
+  // respective argument ranges and [low, high) is sorted as a result.
+  _qsort (low, p, size, compare);
+  _qsort (p, high, size, compare);
 }
 
-  /* Once the BASE_void* array is partially sorted by quicksort the rest
+void
-     is completely sorted using insertion sort, since this is efficient
+qsort (void *base, size_t count, size_t size,
-     for partitions below MAX_THRESH size. BASE_void* points to the beginning
+       int (*compare) (void const *, void const *))
-     of the array to sort, and END_void* points at the very last element in
-     the array (*not* one beyond it!). */
-
-#define min(x, y) ((x) < (y) ? (x) : (y))
-
 {
-    char *const end_ptr = &base_ptr[size * (total_elems - 1)];
+  char *high = base + count * size;
-    char *tmp_ptr = base_ptr;
+  _qsort (base, high, size, compare);
-    char *thresh = min(end_ptr, base_ptr + max_thresh);
-    char *run_ptr;
-
-    /* Find smallest element in first threshold and place it at the
-       array's beginning.  This is the smallest array element,
-       and the operation speeds up insertion sort's inner loop. */
-
-    for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
-      if ((*compare)((void*) run_ptr, (void*) tmp_ptr) < 0)
-        tmp_ptr = run_ptr;
-
-    if (tmp_ptr != base_ptr)
-      SWAP (tmp_ptr, base_ptr, size);
-
-    /* Insertion sort, running from left-hand-side up to right-hand-side.  */
-
-    run_ptr = base_ptr + size;
-    while ((run_ptr += size) <= end_ptr)
-      {
-	tmp_ptr = run_ptr - size;
-	while ((*compare)((void*) run_ptr, (void*) tmp_ptr) < 0)
-	  tmp_ptr -= size;
-
-	tmp_ptr += size;
-        if (tmp_ptr != run_ptr)
-          {
-            char *trav;
-
-	    trav = run_ptr + size;
-	    while (--trav >= run_ptr)
-              {
-                char c = *trav;
-                char *hi, *lo;
-
-                for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
-                  *hi = *lo;
-                *hi = c;
-              }
-          }
-      }
-  }
 }