stdlib/qsort.c

   1 /* Copyright (C) 1991,1992,1996,1997,1999,2004 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 Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the 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    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, write to the Free
  17    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  18    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_d_fn_t cmp, void *arg)
  92 {
  93   register char *base_ptr = (char *) pbase;
  94
  95   const size_t max_thresh = MAX_THRESH * size;
  96
  97   if (total_elems == 0)
  98     /* Avoid lossage with unsigned arithmetic below.  */
  99     return;
 100
 101   if (total_elems > MAX_THRESH)
 102     {
 103       char *lo = base_ptr;
 104       char *hi = &lo[size * (total_elems - 1)];
 105       stack_node stack[STACK_SIZE];
 106       stack_node *top = stack;
 107
 108       PUSH (NULL, NULL);
 109
 110       while (STACK_NOT_EMPTY)
 111         {
 112           char *left_ptr;
 113           char *right_ptr;
 114
 115           /* Select median value from among LO, MID, and HI. Rearrange
 116              LO and HI so the three values are sorted. This lowers the
 117              probability of picking a pathological pivot value and
 118              skips a comparison for both the LEFT_PTR and RIGHT_PTR in
 119              the while loops. */
 120
 121           char *mid = lo + size * ((hi - lo) / size >> 1);
 122
 123           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 124             SWAP (mid, lo, size);
 125           if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
 126             SWAP (mid, hi, size);
 127           else
 128             goto jump_over;
 129           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 130             SWAP (mid, lo, size);
 131         jump_over:;
 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 *) mid, arg) < 0)
 142                 left_ptr += size;
 143
 144               while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
 145                 right_ptr -= size;
 146
 147               if (left_ptr < right_ptr)
 148                 {
 149                   SWAP (left_ptr, right_ptr, size);
 150                   if (mid == left_ptr)
 151                     mid = right_ptr;
 152                   else if (mid == right_ptr)
 153                     mid = left_ptr;
 154                   left_ptr += size;
 155                   right_ptr -= size;
 156                 }
 157               else if (left_ptr == right_ptr)
 158                 {
 159                   left_ptr += size;
 160                   right_ptr -= size;
 161                   break;
 162                 }
 163             }
 164           while (left_ptr <= right_ptr);
 165
 166           /* Set up pointers for next iteration.  First determine whether
 167              left and right partitions are below the threshold size.  If so,
 168              ignore one or both.  Otherwise, push the larger partition's
 169              bounds on the stack and continue sorting the smaller one. */
 170
 171           if ((size_t) (right_ptr - lo) <= max_thresh)
 172             {
 173               if ((size_t) (hi - left_ptr) <= max_thresh)
 174                 /* Ignore both small partitions. */
 175                 POP (lo, hi);
 176               else
 177                 /* Ignore small left partition. */
 178                 lo = left_ptr;
 179             }
 180           else if ((size_t) (hi - left_ptr) <= max_thresh)
 181             /* Ignore small right partition. */
 182             hi = right_ptr;
 183           else if ((right_ptr - lo) > (hi - left_ptr))
 184             {
 185               /* Push larger left partition indices. */
 186               PUSH (lo, right_ptr);
 187               lo = left_ptr;
 188             }
 189           else
 190             {
 191               /* Push larger right partition indices. */
 192               PUSH (left_ptr, hi);
 193               hi = right_ptr;
 194             }
 195         }
 196     }
 197
 198   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 199      is completely sorted using insertion sort, since this is efficient
 200      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 201      of the array to sort, and END_PTR points at the very last element in
 202      the array (*not* one beyond it!). */
 203
 204 #define min(x, y) ((x) < (y) ? (x) : (y))
 205
 206   {
 207     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 208     char *tmp_ptr = base_ptr;
 209     char *thresh = min(end_ptr, base_ptr + max_thresh);
 210     register char *run_ptr;
 211
 212     /* Find smallest element in first threshold and place it at the
 213        array's beginning.  This is the smallest array element,
 214        and the operation speeds up insertion sort's inner loop. */
 215
 216     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 217       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 218         tmp_ptr = run_ptr;
 219
 220     if (tmp_ptr != base_ptr)
 221       SWAP (tmp_ptr, base_ptr, size);
 222
 223     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 224
 225     run_ptr = base_ptr + size;
 226     while ((run_ptr += size) <= end_ptr)
 227       {
 228         tmp_ptr = run_ptr - size;
 229         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 230           tmp_ptr -= size;
 231
 232         tmp_ptr += size;
 233         if (tmp_ptr != run_ptr)
 234           {
 235             char *trav;
 236
 237             trav = run_ptr + size;
 238             while (--trav >= run_ptr)
 239               {
 240                 char c = *trav;
 241                 char *hi, *lo;
 242
 243                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 244                   *hi = *lo;
 245                 *hi = c;
 246               }
 247           }
 248       }
 249   }
 250 }