stdlib/qsort.c

   1 /* Copyright (C) 1991-2017 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, see
  17    <http://www.gnu.org/licenses/>.  */
  18
  19 /* If you consider tuning this algorithm, you should consult first:
  20    Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
  21    Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993.  */
  22
  23 #include <alloca.h>
  24 #include <limits.h>
  25 #include <stdlib.h>
  26 #include <string.h>
  27
  28 /* Byte-wise swap two items of size SIZE. */
  29 #define SWAP(a, b, size)                                                      \
  30   do                                                                          \
  31     {                                                                         \
  32       size_t __size = (size);                                                 \
  33       char *__a = (a), *__b = (b);                                            \
  34       do                                                                      \
  35         {                                                                     \
  36           char __tmp = *__a;                                                  \
  37           *__a++ = *__b;                                                      \
  38           *__b++ = __tmp;                                                     \
  39         } while (--__size > 0);                                               \
  40     } while (0)
  41
  42 /* Discontinue quicksort algorithm when partition gets below this size.
  43    This particular magic number was chosen to work best on a Sun 4/260. */
  44 #define MAX_THRESH 4
  45
  46 /* Stack node declarations used to store unfulfilled partition obligations. */
  47 typedef struct
  48   {
  49     char *lo;
  50     char *hi;
  51   } stack_node;
  52
  53 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  54 /* The stack needs log (total_elements) entries (we could even subtract
  55    log(MAX_THRESH)).  Since total_elements has type size_t, we get as
  56    upper bound for log (total_elements):
  57    bits per byte (CHAR_BIT) * sizeof(size_t).  */
  58 #define STACK_SIZE      (CHAR_BIT * sizeof(size_t))
  59 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  60 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  61 #define STACK_NOT_EMPTY (stack < top)
  62
  63
  64 /* Order size using quicksort.  This implementation incorporates
  65    four optimizations discussed in Sedgewick:
  66
  67    1. Non-recursive, using an explicit stack of pointer that store the
  68       next array partition to sort.  To save time, this maximum amount
  69       of space required to store an array of SIZE_MAX is allocated on the
  70       stack.  Assuming a 32-bit (64 bit) integer for size_t, this needs
  71       only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
  72       Pretty cheap, actually.
  73
  74    2. Chose the pivot element using a median-of-three decision tree.
  75       This reduces the probability of selecting a bad pivot value and
  76       eliminates certain extraneous comparisons.
  77
  78    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  79       insertion sort to order the MAX_THRESH items within each partition.
  80       This is a big win, since insertion sort is faster for small, mostly
  81       sorted array segments.
  82
  83    4. The larger of the two sub-partitions is always pushed onto the
  84       stack first, with the algorithm then concentrating on the
  85       smaller partition.  This *guarantees* no more than log (total_elems)
  86       stack size is needed (actually O(1) in this case)!  */
  87
  88 void
  89 _quicksort (void *const pbase, size_t total_elems, size_t size,
  90             __compar_d_fn_t cmp, void *arg)
  91 {
  92   char *base_ptr = (char *) pbase;
  93
  94   const size_t max_thresh = MAX_THRESH * size;
  95
  96   if (total_elems == 0)
  97     /* Avoid lossage with unsigned arithmetic below.  */
  98     return;
  99
 100   if (total_elems > MAX_THRESH)
 101     {
 102       char *lo = base_ptr;
 103       char *hi = &lo[size * (total_elems - 1)];
 104       stack_node stack[STACK_SIZE];
 105       stack_node *top = stack;
 106
 107       PUSH (NULL, NULL);
 108
 109       while (STACK_NOT_EMPTY)
 110         {
 111           char *left_ptr;
 112           char *right_ptr;
 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 in
 118              the while loops. */
 119
 120           char *mid = lo + size * ((hi - lo) / size >> 1);
 121
 122           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 123             SWAP (mid, lo, size);
 124           if ((*cmp) ((void *) hi, (void *) mid, arg) < 0)
 125             SWAP (mid, hi, size);
 126           else
 127             goto jump_over;
 128           if ((*cmp) ((void *) mid, (void *) lo, arg) < 0)
 129             SWAP (mid, lo, size);
 130         jump_over:;
 131
 132           left_ptr  = lo + size;
 133           right_ptr = hi - size;
 134
 135           /* Here's the famous ``collapse the walls'' section of quicksort.
 136              Gotta like those tight inner loops!  They are the main reason
 137              that this algorithm runs much faster than others. */
 138           do
 139             {
 140               while ((*cmp) ((void *) left_ptr, (void *) mid, arg) < 0)
 141                 left_ptr += size;
 142
 143               while ((*cmp) ((void *) mid, (void *) right_ptr, arg) < 0)
 144                 right_ptr -= size;
 145
 146               if (left_ptr < right_ptr)
 147                 {
 148                   SWAP (left_ptr, right_ptr, size);
 149                   if (mid == left_ptr)
 150                     mid = right_ptr;
 151                   else if (mid == right_ptr)
 152                     mid = left_ptr;
 153                   left_ptr += size;
 154                   right_ptr -= size;
 155                 }
 156               else if (left_ptr == right_ptr)
 157                 {
 158                   left_ptr += size;
 159                   right_ptr -= size;
 160                   break;
 161                 }
 162             }
 163           while (left_ptr <= right_ptr);
 164
 165           /* Set up pointers for next iteration.  First determine whether
 166              left and right partitions are below the threshold size.  If so,
 167              ignore one or both.  Otherwise, push the larger partition's
 168              bounds on the stack and continue sorting the smaller one. */
 169
 170           if ((size_t) (right_ptr - lo) <= max_thresh)
 171             {
 172               if ((size_t) (hi - left_ptr) <= max_thresh)
 173                 /* Ignore both small partitions. */
 174                 POP (lo, hi);
 175               else
 176                 /* Ignore small left partition. */
 177                 lo = left_ptr;
 178             }
 179           else if ((size_t) (hi - left_ptr) <= max_thresh)
 180             /* Ignore small right partition. */
 181             hi = right_ptr;
 182           else if ((right_ptr - lo) > (hi - left_ptr))
 183             {
 184               /* Push larger left partition indices. */
 185               PUSH (lo, right_ptr);
 186               lo = left_ptr;
 187             }
 188           else
 189             {
 190               /* Push larger right partition indices. */
 191               PUSH (left_ptr, hi);
 192               hi = right_ptr;
 193             }
 194         }
 195     }
 196
 197   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 198      is completely sorted using insertion sort, since this is efficient
 199      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 200      of the array to sort, and END_PTR points at the very last element in
 201      the array (*not* one beyond it!). */
 202
 203 #define min(x, y) ((x) < (y) ? (x) : (y))
 204
 205   {
 206     char *const end_ptr = &base_ptr[size * (total_elems - 1)];
 207     char *tmp_ptr = base_ptr;
 208     char *thresh = min(end_ptr, base_ptr + max_thresh);
 209     char *run_ptr;
 210
 211     /* Find smallest element in first threshold and place it at the
 212        array's beginning.  This is the smallest array element,
 213        and the operation speeds up insertion sort's inner loop. */
 214
 215     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 216       if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 217         tmp_ptr = run_ptr;
 218
 219     if (tmp_ptr != base_ptr)
 220       SWAP (tmp_ptr, base_ptr, size);
 221
 222     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 223
 224     run_ptr = base_ptr + size;
 225     while ((run_ptr += size) <= end_ptr)
 226       {
 227         tmp_ptr = run_ptr - size;
 228         while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, arg) < 0)
 229           tmp_ptr -= size;
 230
 231         tmp_ptr += size;
 232         if (tmp_ptr != run_ptr)
 233           {
 234             char *trav;
 235
 236             trav = run_ptr + size;
 237             while (--trav >= run_ptr)
 238               {
 239                 char c = *trav;
 240                 char *hi, *lo;
 241
 242                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 243                   *hi = *lo;
 244                 *hi = c;
 245               }
 246           }
 247       }
 248   }
 249 }