stdlib/qsort.c

   1 /* Copyright (C) 1991, 1992 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(_quicksort, (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 == 0)
  92     /* Avoid lossage with unsigned arithmetic below.  */
  93     return;
  94
  95   if (total_elems > MAX_THRESH)
  96     {
  97       char *lo = base_ptr;
  98       char *hi = &lo[size * (total_elems - 1)];
  99       /* Largest size needed for 32-bit int!!! */
 100       stack_node stack[STACK_SIZE];
 101       stack_node *top = stack + 1;
 102
 103       while (STACK_NOT_EMPTY)
 104         {
 105           char *left_ptr;
 106           char *right_ptr;
 107
 108           char *pivot = pivot_buffer;
 109
 110           /* Select median value from among LO, MID, and HI. Rearrange
 111              LO and HI so the three values are sorted. This lowers the
 112              probability of picking a pathological pivot value and
 113              skips a comparison for both the LEFT_PTR and RIGHT_PTR. */
 114
 115           char *mid = lo + size * ((hi - lo) / size >> 1);
 116
 117           if ((*cmp)((PTR) mid, (PTR) lo) < 0)
 118             SWAP(mid, lo, size);
 119           if ((*cmp)((PTR) hi, (PTR) mid) < 0)
 120             SWAP(mid, hi, size);
 121           else
 122             goto jump_over;
 123           if ((*cmp)((PTR) mid, (PTR) lo) < 0)
 124             SWAP(mid, lo, size);
 125         jump_over:;
 126           memcpy(pivot, mid, size);
 127           pivot = pivot_buffer;
 128
 129           left_ptr  = lo + size;
 130           right_ptr = hi - size;
 131
 132           /* Here's the famous ``collapse the walls'' section of quicksort.
 133              Gotta like those tight inner loops!  They are the main reason
 134              that this algorithm runs much faster than others. */
 135           do
 136             {
 137               while ((*cmp)((PTR) left_ptr, (PTR) pivot) < 0)
 138                 left_ptr += size;
 139
 140               while ((*cmp)((PTR) pivot, (PTR) right_ptr) < 0)
 141                 right_ptr -= size;
 142
 143               if (left_ptr < right_ptr)
 144                 {
 145                   SWAP(left_ptr, right_ptr, size);
 146                   left_ptr += size;
 147                   right_ptr -= size;
 148                 }
 149               else if (left_ptr == right_ptr)
 150                 {
 151                   left_ptr += size;
 152                   right_ptr -= size;
 153                   break;
 154                 }
 155             }
 156           while (left_ptr <= right_ptr);
 157
 158           /* Set up pointers for next iteration.  First determine whether
 159              left and right partitions are below the threshold size.  If so,
 160              ignore one or both.  Otherwise, push the larger partition's
 161              bounds on the stack and continue sorting the smaller one. */
 162
 163           if ((size_t) (right_ptr - lo) <= max_thresh)
 164             {
 165               if ((size_t) (hi - left_ptr) <= max_thresh)
 166                 /* Ignore both small partitions. */
 167                 POP(lo, hi);
 168               else
 169                 /* Ignore small left partition. */
 170                 lo = left_ptr;
 171             }
 172           else if ((size_t) (hi - left_ptr) <= max_thresh)
 173             /* Ignore small right partition. */
 174             hi = right_ptr;
 175           else if ((right_ptr - lo) > (hi - left_ptr))
 176             {
 177               /* Push larger left partition indices. */
 178               PUSH(lo, right_ptr);
 179               lo = left_ptr;
 180             }
 181           else
 182             {
 183               /* Push larger right partition indices. */
 184               PUSH(left_ptr, hi);
 185               hi = right_ptr;
 186             }
 187         }
 188     }
 189
 190   /* Once the BASE_PTR array is partially sorted by quicksort the rest
 191      is completely sorted using insertion sort, since this is efficient
 192      for partitions below MAX_THRESH size. BASE_PTR points to the beginning
 193      of the array to sort, and END_PTR points at the very last element in
 194      the array (*not* one beyond it!). */
 195
 196 #define min(x, y) ((x) < (y) ? (x) : (y))
 197
 198   {
 199     char *CONST end_ptr = &base_ptr[size * (total_elems - 1)];
 200     char *tmp_ptr = base_ptr;
 201     char *thresh = min(end_ptr, base_ptr + max_thresh);
 202     register char *run_ptr;
 203
 204     /* Find smallest element in first threshold and place it at the
 205        array's beginning.  This is the smallest array element,
 206        and the operation speeds up insertion sort's inner loop. */
 207
 208     for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
 209       if ((*cmp)((PTR) run_ptr, (PTR) tmp_ptr) < 0)
 210         tmp_ptr = run_ptr;
 211
 212     if (tmp_ptr != base_ptr)
 213       SWAP(tmp_ptr, base_ptr, size);
 214
 215     /* Insertion sort, running from left-hand-side up to right-hand-side.  */
 216
 217     run_ptr = base_ptr + size;
 218     while ((run_ptr += size) <= end_ptr)
 219       {
 220         tmp_ptr = run_ptr - size;
 221         while ((*cmp)((PTR) run_ptr, (PTR) tmp_ptr) < 0)
 222           tmp_ptr -= size;
 223
 224         tmp_ptr += size;
 225         if (tmp_ptr != run_ptr)
 226           {
 227             char *trav;
 228
 229             trav = run_ptr + size;
 230             while (--trav >= run_ptr)
 231               {
 232                 char c = *trav;
 233                 char *hi, *lo;
 234
 235                 for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
 236                   *hi = *lo;
 237                 *hi = c;
 238               }
 239           }
 240       }
 241   }
 242 }
 243