stdlib/qsort.c

   1 /* Copyright (C) 1991, 1992, 1996, 1997 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3    Written by Douglas C. Schmidt (schmidt@ics.uci.edu).
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Library General Public License as
   7    published by the Free Software Foundation; either version 2 of the
   8    License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Library General Public License for more details.
  14
  15    You should have received a copy of the GNU Library General Public
  16    License along with the GNU C Library; see the file COPYING.LIB.  If not,
  17    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  18    Boston, MA 02111-1307, USA.  */
  19
  20 #include <stdlib.h>
  21 #include <string.h>
  22
  23 /* Byte-wise swap two items of size SIZE. */
  24 #define SWAP(a, b, size)                                                      \
  25   do                                                                          \
  26     {                                                                         \
  27       register size_t __size = (size);                                        \
  28       register char *__a = (a), *__b = (b);                                   \
  29       do                                                                      \
  30         {                                                                     \
  31           char __tmp = *__a;                                                  \
  32           *__a++ = *__b;                                                      \
  33           *__b++ = __tmp;                                                     \
  34         } while (--__size > 0);                                               \
  35     } while (0)
  36
  37 /* Discontinue quicksort algorithm when partition gets below this size.
  38    This particular magic number was chosen to work best on a Sun 4/260. */
  39 #define MAX_THRESH 4
  40
  41 /* Stack node declarations used to store unfulfilled partition obligations. */
  42 typedef struct
  43   {
  44     char *lo;
  45     char *hi;
  46   } stack_node;
  47
  48 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  49 #define STACK_SIZE      (8 * sizeof(unsigned long int))
  50 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  51 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  52 #define STACK_NOT_EMPTY (stack < top)
  53
  54
  55 /* Order size using quicksort.  This implementation incorporates
  56    four optimizations discussed in Sedgewick:
  57
  58    1. Non-recursive, using an explicit stack of pointer that store the
  59       next array partition to sort.  To save time, this maximum amount
  60       of space required to store an array of MAX_INT is allocated on the
  61       stack.  Assuming a 32-bit integer, this needs only 32 *
  62       sizeof(stack_node) == 136 bits.  Pretty cheap, actually.
  63
  64    2. Chose the pivot element using a median-of-three decision tree.
  65       This reduces the probability of selecting a bad pivot value and
  66       eliminates certain extraneous comparisons.
  67
  68    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  69       insertion sort to order the MAX_THRESH items within each partition.
  70       This is a big win, since insertion sort is faster for small, mostly
  71       sorted array segments.
  72
  73    4. The larger of the two sub-partitions is always pushed onto the
  74       stack first, with the algorithm then concentrating on the
  75       smaller partition.  This *guarantees* no more than log (n)
  76       stack size is needed (actually O(1) in this case)!  */
  77
  78 void
  79 _quicksort (pbase, total_elems, size, cmp)
  80      void *const pbase;
  81      size_t total_elems;
  82      size_t size;
  83      int (*cmp) __P ((const void *, const void *));
  84 {
  85   register char *base_ptr = (char *) pbase;
  86
  87   /* Allocating SIZE bytes for a pivot buffer facilitates a better
  88      algorithm below since we can do comparisons directly on the pivot. */
  89   char *pivot_buffer = (char *) __alloca (size);
  90   const size_t max_thresh = MAX_THRESH * size;
  91
  92   if (total_elems == 0)
  93     /* Avoid lossage with unsigned arithmetic below.  */
  94     return;
  95
  96   if (total_elems > MAX_THRESH)
  97     {
  98       char *lo = base_ptr;
  99       char *hi = &lo[size * (total_elems - 1)];
 100       /* Largest size needed for 32-bit int!!! */
 101       stack_node stack[STACK_SIZE];
 102       stack_node *top = stack + 1;
 103
 104       while (STACK_NOT_EMPTY)
 105         {
 106           char *left_ptr;
 107           char *right_ptr;
 108
 109           char *pivot = pivot_buffer;
 110
 111           /* Select median value from among LO, MID, and HI. Rearrange
 112              LO and HI so the three values are sorted. This lowers the
 113              probability of picking a pathological pivot value and
 114              skips a comparison for both the LEFT_PTR and RIGHT_PTR. */
 115
 116           char *mid = lo + size * ((hi - lo) / size >> 1);
 117
 118           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 119             SWAP (mid, lo, size);
 120           if ((*cmp) ((void *) hi, (void *) mid) < 0)
 121             SWAP (mid, hi, size);
 122           else
 123             goto jump_over;
 124           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 125             SWAP (mid, lo, size);
 126         jump_over:;
 127           memcpy (pivot, mid, size);
 128           pivot = pivot_buffer;
 129
 130           left_ptr  = lo + size;
 131           right_ptr = hi - size;
 132
 133           /* Here's the famous ``collapse the walls'' section of quicksort.
 134              Gotta like those tight inner loops!  They are the main reason
 135              that this algorithm runs much faster than others. */
 136           do
 137             {
 138               while ((*cmp) ((void *) left_ptr, (void *) pivot) < 0)
 139                 left_ptr += size;
 140
 141               while ((*cmp) ((void *) pivot, (void *) right_ptr) < 0)
 142                 right_ptr -= size;
 143
 144               if (left_ptr < right_ptr)
 145                 {
 146                   SWAP (left_ptr, right_ptr, size);
 147                   left_ptr += size;
 148                   right_ptr -= size;
 149                 }
 150               else if (left_ptr == right_ptr)
 151                 {
 152                   left_ptr += size;
 153                   right_ptr -= size;
 154                   break;
 155                 }
 156             }
 157           while (left_ptr <= right_ptr);
 158
 159           /* Set up pointers for next iteration.  First determine whether
 160              left and right partitions are below the threshold size.  If so,
 161              ignore one or both.  Otherwise, push the larger partition's
 162              bounds on the stack and continue sorting the smaller one. */
 163
 164           if ((size_t) (right_ptr - lo) <= max_thresh)
 165             {
 166               if ((size_t) (hi - left_ptr) <= max_thresh)
 167                 /* Ignore both small partitions. */
 168                 POP (lo, hi);
 169               else
 170                 /* Ignore small left partition. */
 171                 lo = left_ptr;
 172             }
 173           else if ((size_t) (hi - left_ptr) <= max_thresh)
 174             /* Ignore small right partition. */
 175             hi = right_ptr;
 176           else if ((right_ptr - lo) > (hi - left_ptr))
 177             {
 178               /* Push larger left partition indices. */
 179               PUSH (lo, right_ptr);
 180               lo = left_ptr;
 181             }
 182           else
 183             {
 184               /* Push larger right partition indices. */
 185               PUSH (left_ptr, hi);
 186               hi = right_ptr;
 187             }
 188         }
 189     }
 190
 191   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 192      is completely sorted using insertion sort, since this is efficient
 193      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 194      of the array to sort, and END_PTR points at the very last element in
 195      the array (*not* one beyond it!). */
 196
 197 #define min(x, y) ((x) < (y) ? (x) : (y))
 198
 199   {
 200     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 201     char *tmp_ptr = base_ptr;
 202     char *thresh = min(end_ptr, base_ptr + max_thresh);
 203     register char *run_ptr;
 204
 205     /* Find smallest element in first threshold and place it at the
 206        array's beginning.  This is the smallest array element,
 207        and the operation speeds up insertion sort's inner loop. */
 208
 209     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 210       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 211         tmp_ptr = run_ptr;
 212
 213     if (tmp_ptr != base_ptr)
 214       SWAP (tmp_ptr, base_ptr, size);
 215
 216     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 217
 218     run_ptr = base_ptr + size;
 219     while ((run_ptr += size) <= end_ptr)
 220       {
 221         tmp_ptr = run_ptr - size;
 222         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 223           tmp_ptr -= size;
 224
 225         tmp_ptr += size;
 226         if (tmp_ptr != run_ptr)
 227           {
 228             char *trav;
 229
 230             trav = run_ptr + size;
 231             while (--trav >= run_ptr)
 232               {
 233                 char c = *trav;
 234                 char *hi, *lo;
 235
 236                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 237                   *hi = *lo;
 238                 *hi = c;
 239               }
 240           }
 241       }
 242   }
 243 }