stdlib/qsort.c

   1 /* Copyright (C) 1991, 1992, 1996, 1997, 1999 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 /* If you consider tuning this algorithm, you should consult first:
  21    Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
  22    Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993.  */
  23
  24 #include <alloca.h>
  25 #include <limits.h>
  26 #include <stdlib.h>
  27 #include <string.h>
  28
  29 /* Byte-wise swap two items of size SIZE. */
  30 #define SWAP(a, b, size)                                                      \
  31   do                                                                          \
  32     {                                                                         \
  33       register size_t __size = (size);                                        \
  34       register char *__a = (a), *__b = (b);                                   \
  35       do                                                                      \
  36         {                                                                     \
  37           char __tmp = *__a;                                                  \
  38           *__a++ = *__b;                                                      \
  39           *__b++ = __tmp;                                                     \
  40         } while (--__size > 0);                                               \
  41     } while (0)
  42
  43 /* Discontinue quicksort algorithm when partition gets below this size.
  44    This particular magic number was chosen to work best on a Sun 4/260. */
  45 #define MAX_THRESH 4
  46
  47 /* Stack node declarations used to store unfulfilled partition obligations. */
  48 typedef struct
  49   {
  50     char *lo;
  51     char *hi;
  52   } stack_node;
  53
  54 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  55 /* The stack needs log (total_elements) entries (we could even subtract
  56    log(MAX_THRESH)).  Since total_elements has type size_t, we get as
  57    upper bound for log (total_elements):
  58    bits per byte (CHAR_BIT) * sizeof(size_t).  */
  59 #define STACK_SIZE      (CHAR_BIT * sizeof(size_t))
  60 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  61 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  62 #define STACK_NOT_EMPTY (stack < top)
  63
  64
  65 /* Order size using quicksort.  This implementation incorporates
  66    four optimizations discussed in Sedgewick:
  67
  68    1. Non-recursive, using an explicit stack of pointer that store the
  69       next array partition to sort.  To save time, this maximum amount
  70       of space required to store an array of SIZE_MAX is allocated on the
  71       stack.  Assuming a 32-bit (64 bit) integer for size_t, this needs
  72       only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
  73       Pretty cheap, actually.
  74
  75    2. Chose the pivot element using a median-of-three decision tree.
  76       This reduces the probability of selecting a bad pivot value and
  77       eliminates certain extraneous comparisons.
  78
  79    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  80       insertion sort to order the MAX_THRESH items within each partition.
  81       This is a big win, since insertion sort is faster for small, mostly
  82       sorted array segments.
  83
  84    4. The larger of the two sub-partitions is always pushed onto the
  85       stack first, with the algorithm then concentrating on the
  86       smaller partition.  This *guarantees* no more than log (total_elems)
  87       stack size is needed (actually O(1) in this case)!  */
  88
  89 void
  90 _quicksort (void *const pbase, size_t total_elems, size_t size,
  91             __compar_fn_t cmp)
  92 {
  93   register char *base_ptr = (char *) pbase;
  94
  95   /* Allocating SIZE bytes for a pivot buffer facilitates a better
  96      algorithm below since we can do comparisons directly on the pivot. */
  97   char *pivot_buffer = (char *) __alloca (size);
  98   const size_t max_thresh = MAX_THRESH * size;
  99
 100   if (total_elems == 0)
 101     /* Avoid lossage with unsigned arithmetic below.  */
 102     return;
 103
 104   if (total_elems > MAX_THRESH)
 105     {
 106       char *lo = base_ptr;
 107       char *hi = &lo[size * (total_elems - 1)];
 108       stack_node stack[STACK_SIZE];
 109       stack_node *top = stack + 1;
 110
 111       while (STACK_NOT_EMPTY)
 112         {
 113           char *left_ptr;
 114           char *right_ptr;
 115
 116           char *pivot = pivot_buffer;
 117
 118           /* Select median value from among LO, MID, and HI. Rearrange
 119              LO and HI so the three values are sorted. This lowers the
 120              probability of picking a pathological pivot value and
 121              skips a comparison for both the LEFT_PTR and RIGHT_PTR in
 122              the while loops. */
 123
 124           char *mid = lo + size * ((hi - lo) / size >> 1);
 125
 126           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 127             SWAP (mid, lo, size);
 128           if ((*cmp) ((void *) hi, (void *) mid) < 0)
 129             SWAP (mid, hi, size);
 130           else
 131             goto jump_over;
 132           if ((*cmp) ((void *) mid, (void *) lo) < 0)
 133             SWAP (mid, lo, size);
 134         jump_over:;
 135           memcpy (pivot, mid, size);
 136           pivot = pivot_buffer;
 137
 138           left_ptr  = lo + size;
 139           right_ptr = hi - size;
 140
 141           /* Here's the famous ``collapse the walls'' section of quicksort.
 142              Gotta like those tight inner loops!  They are the main reason
 143              that this algorithm runs much faster than others. */
 144           do
 145             {
 146               while ((*cmp) ((void *) left_ptr, (void *) pivot) < 0)
 147                 left_ptr += size;
 148
 149               while ((*cmp) ((void *) pivot, (void *) right_ptr) < 0)
 150                 right_ptr -= size;
 151
 152               if (left_ptr < right_ptr)
 153                 {
 154                   SWAP (left_ptr, right_ptr, size);
 155                   left_ptr += size;
 156                   right_ptr -= size;
 157                 }
 158               else if (left_ptr == right_ptr)
 159                 {
 160                   left_ptr += size;
 161                   right_ptr -= size;
 162                   break;
 163                 }
 164             }
 165           while (left_ptr <= right_ptr);
 166
 167           /* Set up pointers for next iteration.  First determine whether
 168              left and right partitions are below the threshold size.  If so,
 169              ignore one or both.  Otherwise, push the larger partition's
 170              bounds on the stack and continue sorting the smaller one. */
 171
 172           if ((size_t) (right_ptr - lo) <= max_thresh)
 173             {
 174               if ((size_t) (hi - left_ptr) <= max_thresh)
 175                 /* Ignore both small partitions. */
 176                 POP (lo, hi);
 177               else
 178                 /* Ignore small left partition. */
 179                 lo = left_ptr;
 180             }
 181           else if ((size_t) (hi - left_ptr) <= max_thresh)
 182             /* Ignore small right partition. */
 183             hi = right_ptr;
 184           else if ((right_ptr - lo) > (hi - left_ptr))
 185             {
 186               /* Push larger left partition indices. */
 187               PUSH (lo, right_ptr);
 188               lo = left_ptr;
 189             }
 190           else
 191             {
 192               /* Push larger right partition indices. */
 193               PUSH (left_ptr, hi);
 194               hi = right_ptr;
 195             }
 196         }
 197     }
 198
 199   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 200      is completely sorted using insertion sort, since this is efficient
 201      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 202      of the array to sort, and END_PTR points at the very last element in
 203      the array (*not* one beyond it!). */
 204
 205 #define min(x, y) ((x) < (y) ? (x) : (y))
 206
 207   {
 208     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 209     char *tmp_ptr = base_ptr;
 210     char *thresh = min(end_ptr, base_ptr + max_thresh);
 211     register char *run_ptr;
 212
 213     /* Find smallest element in first threshold and place it at the
 214        array's beginning.  This is the smallest array element,
 215        and the operation speeds up insertion sort's inner loop. */
 216
 217     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 218       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 219         tmp_ptr = run_ptr;
 220
 221     if (tmp_ptr != base_ptr)
 222       SWAP (tmp_ptr, base_ptr, size);
 223
 224     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 225
 226     run_ptr = base_ptr + size;
 227     while ((run_ptr += size) <= end_ptr)
 228       {
 229         tmp_ptr = run_ptr - size;
 230         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr) < 0)
 231           tmp_ptr -= size;
 232
 233         tmp_ptr += size;
 234         if (tmp_ptr != run_ptr)
 235           {
 236             char *trav;
 237
 238             trav = run_ptr + size;
 239             while (--trav >= run_ptr)
 240               {
 241                 char c = *trav;
 242                 char *hi, *lo;
 243
 244                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 245                   *hi = *lo;
 246                 *hi = c;
 247               }
 248           }
 249       }
 250   }
 251 }