stdlib/qsort.c

   1 /* Copyright (C) 1991 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
  17 not, write to the Free Software Foundation, Inc., 675 Mass Ave,
  18 Cambridge, MA 02139, USA.  */
  19
  20 #include <ansidecl.h>
  21 #include <stdlib.h>
  22 #include <string.h>
  23
  24 /* Byte-wise swap two items of size SIZE. */
  25 #define SWAP(a, b, size)                                                      \
  26   do                                                                          \
  27     {                                                                         \
  28       register size_t __size = (size);                                        \
  29       register char *__a = (a), *__b = (b);                                   \
  30       do                                                                      \
  31         {                                                                     \
  32           char __tmp = *__a;                                                  \
  33           *__a++ = *__b;                                                      \
  34           *__b++ = __tmp;                                                     \
  35         } while (--__size > 0);                                               \
  36     } while (0)
  37
  38 /* Discontinue quicksort algorithm when partition gets below this size.
  39    This particular magic number was chosen to work best on a Sun 4/260. */
  40 #define MAX_THRESH 4
  41
  42 /* Stack node declarations used to store unfulfilled partition obligations. */
  43 typedef struct
  44   {
  45     char *lo;
  46     char *hi;
  47   } stack_node;
  48
  49 /* The next 4 #defines implement a very fast in-line stack abstraction. */
  50 #define STACK_SIZE      (8 * sizeof(unsigned long int))
  51 #define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
  52 #define POP(low, high)  ((void) (--top, (low = top->lo), (high = top->hi)))
  53 #define STACK_NOT_EMPTY (stack < top)
  54
  55
  56 /* Order size using quicksort.  This implementation incorporates
  57    four optimizations discussed in Sedgewick:
  58
  59    1. Non-recursive, using an explicit stack of pointer that store the
  60       next array partition to sort.  To save time, this maximum amount
  61       of space required to store an array of MAX_INT is allocated on the
  62       stack.  Assuming a 32-bit integer, this needs only 32 *
  63       sizeof(stack_node) == 136 bits.  Pretty cheap, actually.
  64
  65    2. Chose the pivot element using a median-of-three decision tree.
  66       This reduces the probability of selecting a bad pivot value and
  67       eliminates certain extraneous comparisons.
  68
  69    3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
  70       insertion sort to order the MAX_THRESH items within each partition.
  71       This is a big win, since insertion sort is faster for small, mostly
  72       sorted array segements.
  73
  74    4. The larger of the two sub-partitions is always pushed onto the
  75       stack first, with the algorithm then concentrating on the
  76       smaller partition.  This *guarantees* no more than log (n)
  77       stack size is needed (actually O(1) in this case)!  */
  78
  79 void
  80 DEFUN(qsort, (pbase, total_elems, size, cmp),
  81       PTR CONST pbase AND size_t total_elems AND size_t size AND
  82       int EXFUN((*cmp), (CONST PTR, CONST PTR)))
  83 {
  84   register char *base_ptr = (char *) pbase;
  85
  86   /* Allocating SIZE bytes for a pivot buffer facilitates a better
  87      algorithm below since we can do comparisons directly on the pivot. */
  88   char *pivot_buffer = (char *) __alloca (size);
  89   CONST size_t max_thresh = MAX_THRESH * size;
  90
  91   if (total_elems > MAX_THRESH)
  92     {
  93       char *lo = base_ptr;
  94       char *hi = &lo[size * (total_elems - 1)];
  95       /* Largest size needed for 32-bit int!!! */
  96       stack_node stack[STACK_SIZE];
  97       stack_node *top = stack + 1;
  98
  99       while (STACK_NOT_EMPTY)
 100         {
 101           char *left_ptr;
 102           char *right_ptr;
 103
 104           char *pivot = pivot_buffer;
 105
 106           /* Select median value from among LO, MID, and HI. Rearrange
 107              LO and HI so the three values are sorted. This lowers the
 108              probability of picking a pathological pivot value and
 109              skips a comparison for both the LEFT_PTR and RIGHT_PTR. */
 110
 111           char *mid = lo + size * ((hi - lo) / size >> 1);
 112
 113           if ((*cmp)((PTR) mid, (PTR) lo) < 0)
 114             SWAP(mid, lo, size);
 115           if ((*cmp)((PTR) hi, (PTR) mid) < 0)
 116             SWAP(mid, hi, size);
 117           else
 118             goto jump_over;
 119           if ((*cmp)((PTR) mid, (PTR) lo) < 0)
 120             SWAP(mid, lo, size);
 121         jump_over:;
 122           memcpy(pivot, mid, size);
 123           pivot = pivot_buffer;
 124
 125           left_ptr  = lo + size;
 126           right_ptr = hi - size;
 127
 128           /* Here's the famous ``collapse the walls'' section of quicksort.
 129              Gotta like those tight inner loops!  They are the main reason
 130              that this algorithm runs much faster than others. */
 131           do
 132             {
 133               while ((*cmp)((PTR) left_ptr, (PTR) pivot) < 0)
 134                 left_ptr += size;
 135
 136               while ((*cmp)((PTR) pivot, (PTR) right_ptr) < 0)
 137                 right_ptr -= size;
 138
 139               if (left_ptr < right_ptr)
 140                 {
 141                   SWAP(left_ptr, right_ptr, size);
 142                   left_ptr += size;
 143                   right_ptr -= size;
 144                 }
 145               else if (left_ptr == right_ptr)
 146                 {
 147                   left_ptr += size;
 148                   right_ptr -= size;
 149                   break;
 150                 }
 151             }
 152           while (left_ptr <= right_ptr);
 153
 154           /* Set up pointers for next iteration.  First determine whether
 155              left and right partitions are below the threshold size.  If so,
 156              ignore one or both.  Otherwise, push the larger partition's
 157              bounds on the stack and continue sorting the smaller one. */
 158
 159           if ((size_t) (right_ptr - lo) <= max_thresh)
 160             {
 161               if ((size_t) (hi - left_ptr) <= max_thresh)
 162                 /* Ignore both small partitions. */
 163                 POP(lo, hi);
 164               else
 165                 /* Ignore small left partition. */
 166                 lo = left_ptr;
 167             }
 168           else if ((size_t) (hi - left_ptr) <= max_thresh)
 169             /* Ignore small right partition. */
 170             hi = right_ptr;
 171           else if ((right_ptr - lo) > (hi - left_ptr))
 172             {
 173               /* Push larger left partition indices. */
 174               PUSH(lo, right_ptr);
 175               lo = left_ptr;
 176             }
 177           else
 178             {
 179               /* Push larger right partition indices. */
 180               PUSH(left_ptr, hi);
 181               hi = right_ptr;
 182             }
 183         }
 184     }
 185
 186   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 187      is completely sorted using insertion sort, since this is efficient
 188      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 189      of the array to sort, and END_PTR points at the very last element in
 190      the array (*not* one beyond it!). */
 191
 192 #define min(x, y) ((x) < (y) ? (x) : (y))
 193
 194   {
 195     char *CONST end_ptr = &base_ptr[size * (total_elems - 1)];
 196     char *tmp_ptr = base_ptr;
 197     char *thresh = min(end_ptr, base_ptr + max_thresh);
 198     register char *run_ptr;
 199
 200     /* Find smallest element in first threshold and place it at the
 201        array's beginning.  This is the smallest array element,
 202        and the operation speeds up insertion sort's inner loop. */
 203
 204     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 205       if ((*cmp)((PTR) run_ptr, (PTR) tmp_ptr) < 0)
 206         tmp_ptr = run_ptr;
 207
 208     if (tmp_ptr != base_ptr)
 209       SWAP(tmp_ptr, base_ptr, size);
 210
 211     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 212
 213     run_ptr = base_ptr + size;
 214     while ((run_ptr += size) <= end_ptr)
 215       {
 216         tmp_ptr = run_ptr - size;
 217         while ((*cmp)((PTR) run_ptr, (PTR) tmp_ptr) < 0)
 218           tmp_ptr -= size;
 219
 220         tmp_ptr += size;
 221         if (tmp_ptr != run_ptr)
 222           {
 223             char *trav;
 224
 225             trav = run_ptr + size;
 226             while (--trav >= run_ptr)
 227               {
 228                 char c = *trav;
 229                 char *hi, *lo;
 230
 231                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 232                   *hi = *lo;
 233                 *hi = c;
 234               }
 235           }
 236       }
 237   }
 238 }
 239