stdlib/qsort.c

   1 /* Copyright (C) 1991-2022 Free Software Foundation, Inc.
   2    This file is part of the GNU C Library.
   3
   4    The GNU C Library is free software; you can redistribute it and/or
   5    modify it under the terms of the GNU Lesser General Public
   6    License as published by the Free Software Foundation; either
   7    version 2.1 of the License, or (at your option) any later version.
   8
   9    The GNU C Library is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  12    Lesser General Public License for more details.
  13
  14    You should have received a copy of the GNU Lesser General Public
  15    License along with the GNU C Library; if not, see
  16    <https://www.gnu.org/licenses/>.  */
  17
  18 /* If you consider tuning this algorithm, you should consult first:
  19    Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
  20    Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993.  */
  21
  22 #include <alloca.h>
  23 #include <limits.h>
  24 #include <stdlib.h>
  25 #include <string.h>
  26
  27 /* Byte-wise swap two items of size SIZE. */
  28 #define SWAP(a, b, size)                                                      \
  29   do                                                                          \
  30     {                                                                         \
  31       size_t __size = (size);                                                 \
  32       char *__a = (a), *__b = (b);                                            \
  33       do                                                                      \
  34         {                                                                     \
  35           char __tmp = *__a;                                                  \
  36           *__a++ = *__b;                                                      \
  37           *__b++ = __tmp;                                                     \
  38         } while (--__size > 0);                                               \
  39     } while (0)
  40
  41 /* Discontinue quicksort algorithm when partition gets below this size.
  42    This particular magic number was chosen to work best on a Sun 4/260. */
  43 #define MAX_THRESH 4
  44
  45 /* Stack node declarations used to store unfulfilled partition obligations. */
  46 typedef struct
  47   {
  48     char *lo;
  49     char *hi;
  50   } stack_node;
  51
  52 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  53 /* The stack needs log (total_elements) entries (we could even subtract
  54    log(MAX_THRESH)).  Since total_elements has type size_t, we get as
  55    upper bound for log (total_elements):
  56    bits per byte (CHAR_BIT) * sizeof(size_t).  */
  57 #define STACK_SIZE      (CHAR_BIT * sizeof (size_t))
  58 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  59 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  60 #define STACK_NOT_EMPTY (stack < top)
  61
  62
  63 /* Order size using quicksort.  This implementation incorporates
  64    four optimizations discussed in Sedgewick:
  65
  66    1. Non-recursive, using an explicit stack of pointer that store the
  67       next array partition to sort.  To save time, this maximum amount
  68       of space required to store an array of SIZE_MAX is allocated on the
  69       stack.  Assuming a 32-bit (64 bit) integer for size_t, this needs
  70       only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
  71       Pretty cheap, actually.
  72
  73    2. Chose the pivot element using a median-of-three decision tree.
  74       This reduces the probability of selecting a bad pivot value and
  75       eliminates certain extraneous comparisons.
  76
  77    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  78       insertion sort to order the MAX_THRESH items within each partition.
  79       This is a big win, since insertion sort is faster for small, mostly
  80       sorted array segments.
  81
  82    4. The larger of the two sub-partitions is always pushed onto the
  83       stack first, with the algorithm then concentrating on the
  84       smaller partition.  This *guarantees* no more than log (total_elems)
  85       stack size is needed (actually O(1) in this case)!  */
  86
  87 void
  88 _quicksort (void *const pbase, size_t total_elems, size_t size,
  89             __compar_d_fn_t cmp, void *arg)
  90 {
  91   char *base_ptr = (char *) pbase;
  92
  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       stack_node stack[STACK_SIZE];
 104       stack_node *top = stack;
 105
 106       PUSH (NULL, NULL);
 107
 108       while (STACK_NOT_EMPTY)
 109         {
 110           char *left_ptr;
 111           char *right_ptr;
 112
 113           /* Select median value from among LO, MID, and HI. Rearrange
 114              LO and HI so the three values are sorted. This lowers the
 115              probability of picking a pathological pivot value and
 116              skips a comparison for both the LEFT_PTR and RIGHT_PTR in
 117              the while loops. */
 118
 119           char *mid = lo + size * ((hi - lo) / size >> 1);
 120
 121           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 122             SWAP (mid, lo, size);
 123           if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
 124             SWAP (mid, hi, size);
 125           else
 126             goto jump_over;
 127           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 128             SWAP (mid, lo, size);
 129         jump_over:;
 130
 131           left_ptr  = lo + size;
 132           right_ptr = hi - size;
 133
 134           /* Here's the famous ``collapse the walls'' section of quicksort.
 135              Gotta like those tight inner loops!  They are the main reason
 136              that this algorithm runs much faster than others. */
 137           do
 138             {
 139               while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
 140                 left_ptr += size;
 141
 142               while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
 143                 right_ptr -= size;
 144
 145               if (left_ptr < right_ptr)
 146                 {
 147                   SWAP (left_ptr, right_ptr, size);
 148                   if (mid == left_ptr)
 149                     mid = right_ptr;
 150                   else if (mid == right_ptr)
 151                     mid = left_ptr;
 152                   left_ptr += size;
 153                   right_ptr -= size;
 154                 }
 155               else if (left_ptr == right_ptr)
 156                 {
 157                   left_ptr += size;
 158                   right_ptr -= size;
 159                   break;
 160                 }
 161             }
 162           while (left_ptr <= right_ptr);
 163
 164           /* Set up pointers for next iteration.  First determine whether
 165              left and right partitions are below the threshold size.  If so,
 166              ignore one or both.  Otherwise, push the larger partition's
 167              bounds on the stack and continue sorting the smaller one. */
 168
 169           if ((size_t) (right_ptr - lo) <= max_thresh)
 170             {
 171               if ((size_t) (hi - left_ptr) <= max_thresh)
 172                 /* Ignore both small partitions. */
 173                 POP (lo, hi);
 174               else
 175                 /* Ignore small left partition. */
 176                 lo = left_ptr;
 177             }
 178           else if ((size_t) (hi - left_ptr) <= max_thresh)
 179             /* Ignore small right partition. */
 180             hi = right_ptr;
 181           else if ((right_ptr - lo) > (hi - left_ptr))
 182             {
 183               /* Push larger left partition indices. */
 184               PUSH (lo, right_ptr);
 185               lo = left_ptr;
 186             }
 187           else
 188             {
 189               /* Push larger right partition indices. */
 190               PUSH (left_ptr, hi);
 191               hi = right_ptr;
 192             }
 193         }
 194     }
 195
 196   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 197      is completely sorted using insertion sort, since this is efficient
 198      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 199      of the array to sort, and END_PTR points at the very last element in
 200      the array (*not* one beyond it!). */
 201
 202 #define min(x, y) ((x) < (y) ? (x) : (y))
 203
 204   {
 205     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 206     char *tmp_ptr = base_ptr;
 207     char *thresh = min(end_ptr, base_ptr + max_thresh);
 208     char *run_ptr;
 209
 210     /* Find smallest element in first threshold and place it at the
 211        array's beginning.  This is the smallest array element,
 212        and the operation speeds up insertion sort's inner loop. */
 213
 214     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 215       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 216         tmp_ptr = run_ptr;
 217
 218     if (tmp_ptr != base_ptr)
 219       SWAP (tmp_ptr, base_ptr, size);
 220
 221     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 222
 223     run_ptr = base_ptr + size;
 224     while ((run_ptr += size) <= end_ptr)
 225       {
 226         tmp_ptr = run_ptr - size;
 227         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 228           tmp_ptr -= size;
 229
 230         tmp_ptr += size;
 231         if (tmp_ptr != run_ptr)
 232           {
 233             char *trav;
 234
 235             trav = run_ptr + size;
 236             while (--trav >= run_ptr)
 237               {
 238                 char c = *trav;
 239                 char *hi, *lo;
 240
 241                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 242                   *hi = *lo;
 243                 *hi = c;
 244               }
 245           }
 246       }
 247   }
 248 }