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 extern void _quicksort __P ((void *const pbase, size_t total_elems,
  24                              size_t size, __compar_fn_t cmp));
  25
  26 /* Byte-wise swap two items of size SIZE. */
  27 #define SWAP(a, b, size)                                                      \
  28   do                                                                          \
  29     {                                                                         \
  30       register size_t __size = (size);                                        \
  31       register char *__a = (a), *__b = (b);                                   \
  32       do                                                                      \
  33         {                                                                     \
  34           char __tmp = *__a;                                                  \
  35           *__a++ = *__b;                                                      \
  36           *__b++ = __tmp;                                                     \
  37         } while (--__size > 0);                                               \
  38     } while (0)
  39
  40 /* Discontinue quicksort algorithm when partition gets below this size.
  41    This particular magic number was chosen to work best on a Sun 4/260. */
  42 #define MAX_THRESH 4
  43
  44 /* Stack node declarations used to store unfulfilled partition obligations. */
  45 typedef struct
  46   {
  47     char *lo;
  48     char *hi;
  49   } stack_node;
  50
  51 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  52 #define STACK_SIZE      (8 * sizeof(unsigned long int))
  53 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  54 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  55 #define STACK_NOT_EMPTY (stack < top)
  56
  57
  58 /* Order size using quicksort.  This implementation incorporates
  59    four optimizations discussed in Sedgewick:
  60
  61    1. Non-recursive, using an explicit stack of pointer that store the
  62       next array partition to sort.  To save time, this maximum amount
  63       of space required to store an array of MAX_INT is allocated on the
  64       stack.  Assuming a 32-bit integer, this needs only 32 *
  65       sizeof(stack_node) == 136 bits.  Pretty cheap, actually.
  66
  67    2. Chose the pivot element using a median-of-three decision tree.
  68       This reduces the probability of selecting a bad pivot value and
  69       eliminates certain extraneous comparisons.
  70
  71    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  72       insertion sort to order the MAX_THRESH items within each partition.
  73       This is a big win, since insertion sort is faster for small, mostly
  74       sorted array segments.
  75
  76    4. The larger of the two sub-partitions is always pushed onto the
  77       stack first, with the algorithm then concentrating on the
  78       smaller partition.  This *guarantees* no more than log (n)
  79       stack size is needed (actually O(1) in this case)!  */
  80
  81 void
  82 _quicksort (pbase, total_elems, size, cmp)
  83      void *const pbase;
  84      size_t total_elems;
  85      size_t size;
  86      __compar_fn_t cmp;
  87 {
  88   register char *base_ptr = (char *) pbase;
  89
  90   /* Allocating SIZE bytes for a pivot buffer facilitates a better
  91      algorithm below since we can do comparisons directly on the pivot. */
  92   char *pivot_buffer = (char *) __alloca (size);
  93   const size_t max_thresh = MAX_THRESH * size;
  94
  95   if (total_elems == 0)
  96     /* Avoid lossage with unsigned arithmetic below.  */
  97     return;
  98
  99   if (total_elems > MAX_THRESH)
 100     {
 101       char *lo = base_ptr;
 102       char *hi = &lo[size * (total_elems - 1)];
 103       /* Largest size needed for 32-bit int!!! */
 104       stack_node stack[STACK_SIZE];
 105       stack_node *top = stack + 1;
 106
 107       while (STACK_NOT_EMPTY)
 108         {
 109           char *left_ptr;
 110           char *right_ptr;
 111
 112           char *pivot = pivot_buffer;
 113
 114           /* Select median value from among LO, MID, and HI. Rearrange
 115              LO and HI so the three values are sorted. This lowers the
 116              probability of picking a pathological pivot value and
 117              skips a comparison for both the LEFT_PTR and RIGHT_PTR. */
 118
 119           char *mid = lo + size * ((hi - lo) / size >> 1);
 120
 121           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 122             SWAP (mid, lo, size);
 123           if ((*cmp) ((void *) hi, (void *) mid) < 0)
 124             SWAP (mid, hi, size);
 125           else
 126             goto jump_over;
 127           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 128             SWAP (mid, lo, size);
 129         jump_over:;
 130           memcpy (pivot, mid, size);
 131           pivot = pivot_buffer;
 132
 133           left_ptr  = lo + size;
 134           right_ptr = hi - size;
 135
 136           /* Here's the famous ``collapse the walls'' section of quicksort.
 137              Gotta like those tight inner loops!  They are the main reason
 138              that this algorithm runs much faster than others. */
 139           do
 140             {
 141               while ((*cmp) ((void *) left_ptr, (void *) pivot) < 0)
 142                 left_ptr += size;
 143
 144               while ((*cmp) ((void *) pivot, (void *) right_ptr) < 0)
 145                 right_ptr -= size;
 146
 147               if (left_ptr < right_ptr)
 148                 {
 149                   SWAP (left_ptr, right_ptr, size);
 150                   left_ptr += size;
 151                   right_ptr -= size;
 152                 }
 153               else if (left_ptr == right_ptr)
 154                 {
 155                   left_ptr += size;
 156                   right_ptr -= size;
 157                   break;
 158                 }
 159             }
 160           while (left_ptr <= right_ptr);
 161
 162           /* Set up pointers for next iteration.  First determine whether
 163              left and right partitions are below the threshold size.  If so,
 164              ignore one or both.  Otherwise, push the larger partition's
 165              bounds on the stack and continue sorting the smaller one. */
 166
 167           if ((size_t) (right_ptr - lo) <= max_thresh)
 168             {
 169               if ((size_t) (hi - left_ptr) <= max_thresh)
 170                 /* Ignore both small partitions. */
 171                 POP (lo, hi);
 172               else
 173                 /* Ignore small left partition. */
 174                 lo = left_ptr;
 175             }
 176           else if ((size_t) (hi - left_ptr) <= max_thresh)
 177             /* Ignore small right partition. */
 178             hi = right_ptr;
 179           else if ((right_ptr - lo) > (hi - left_ptr))
 180             {
 181               /* Push larger left partition indices. */
 182               PUSH (lo, right_ptr);
 183               lo = left_ptr;
 184             }
 185           else
 186             {
 187               /* Push larger right partition indices. */
 188               PUSH (left_ptr, hi);
 189               hi = right_ptr;
 190             }
 191         }
 192     }
 193
 194   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 195      is completely sorted using insertion sort, since this is efficient
 196      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 197      of the array to sort, and END_PTR points at the very last element in
 198      the array (*not* one beyond it!). */
 199
 200 #define min(x, y) ((x) < (y) ? (x) : (y))
 201
 202   {
 203     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 204     char *tmp_ptr = base_ptr;
 205     char *thresh = min(end_ptr, base_ptr + max_thresh);
 206     register char *run_ptr;
 207
 208     /* Find smallest element in first threshold and place it at the
 209        array's beginning.  This is the smallest array element,
 210        and the operation speeds up insertion sort's inner loop. */
 211
 212     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 213       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 214         tmp_ptr = run_ptr;
 215
 216     if (tmp_ptr != base_ptr)
 217       SWAP (tmp_ptr, base_ptr, size);
 218
 219     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 220
 221     run_ptr = base_ptr + size;
 222     while ((run_ptr += size) <= end_ptr)
 223       {
 224         tmp_ptr = run_ptr - size;
 225         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 226           tmp_ptr -= size;
 227
 228         tmp_ptr += size;
 229         if (tmp_ptr != run_ptr)
 230           {
 231             char *trav;
 232
 233             trav = run_ptr + size;
 234             while (--trav >= run_ptr)
 235               {
 236                 char c = *trav;
 237                 char *hi, *lo;
 238
 239                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 240                   *hi = *lo;
 241                 *hi = c;
 242               }
 243           }
 244       }
 245   }
 246 }