common/qsort.h

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/* $Id: qsort.h,v 1.5 2008-01-28 18:16:49 mjt Exp $
 * Adopted from GNU glibc by Mjt.
 * See stdlib/qsort.c in glibc */

/* Copyright (C) 1991, 1992, 1996, 1997, 1999 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Written by Douglas C. Schmidt (schmidt@ics.uci.edu).

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

/* in-line qsort implementation.  Differs from traditional qsort() routine
 * in that it is a macro, not a function, and instead of passing an address
 * of a comparison routine to the function, it is possible to inline
 * comparison routine, thus speeding up sorting a lot.
 *
 * Usage:
 *  #include "iqsort.h"
 *  #define islt(a,b) (strcmp((*a),(*b))<0)
 *  char *arr[];
 *  int n;
 *  QSORT(char*, arr, n, islt);
 *
 * The "prototype" and 4 arguments are:
 *  QSORT(TYPE,BASE,NELT,ISLT)
 *  1) type of each element, TYPE,
 *  2) address of the beginning of the array, of type TYPE*,
 *  3) number of elements in the array, and
 *  4) comparision routine.
 * Array pointer and number of elements are referenced only once.
 * This is similar to a call
 *  qsort(BASE,NELT,sizeof(TYPE),ISLT)
 * with the difference in last parameter.
 * Note the islt macro/routine (it receives pointers to two elements):
 * the only condition of interest is whenever one element is less than
 * another, no other conditions (greather than, equal to etc) are tested.
 * So, for example, to define integer sort, use:
 *  #define islt(a,b) ((*a)<(*b))
 *  QSORT(int, arr, n, islt)
 *
 * The macro could be used to implement a sorting function (see examples
 * below), or to implement the sorting algorithm inline.  That is, either
 * create a sorting function and use it whenever you want to sort something,
 * or use QSORT() macro directly instead a call to such routine.  Note that
 * the macro expands to quite some code (compiled size of int qsort on x86
 * is about 700..800 bytes).
 *
 * Using this macro directly it isn't possible to implement traditional
 * qsort() routine, because the macro assumes sizeof(element) == sizeof(TYPE),
 * while qsort() allows element size to be different.
 *
 * Several ready-to-use examples:
 *
 * Sorting array of integers:
 * void int_qsort(int *arr, unsigned n) {
 * #define int_lt(a,b) ((*a)<(*b))
 *   QSORT(int, arr, n, int_lt);
 * }
 *
 * Sorting array of string pointers:
 * void str_qsort(char *arr[], unsigned n) {
 * #define str_lt(a,b) (strcmp((*a),(*b)) < 0)
 *   QSORT(char*, arr, n, str_lt);
 * }
 *
 * Sorting array of structures:
 *
 * struct elt {
 *   int key;
 *   ...
 * };
 * void elt_qsort(struct elt *arr, unsigned n) {
 * #define elt_lt(a,b) ((a)->key < (b)->key)
 *  QSORT(struct elt, arr, n, elt_lt);
 * }
 *
 * And so on.
 */

/* Swap two items pointed to by A and B using temporary buffer t. */
#define _QSORT_SWAP(a, b, t) ((void)((t = *a), (*a = *b), (*b = t)))

/* Discontinue quicksort algorithm when partition gets below this size.
   This particular magic number was chosen to work best on a Sun 4/260. */
#define _QSORT_MAX_THRESH 4

/* Stack node declarations used to store unfulfilled partition obligations
 * (inlined in QSORT).
typedef struct {
  QSORT_TYPE *_lo, *_hi;
} qsort_stack_node;
 */

/* The next 4 #defines implement a very fast in-line stack abstraction. */
/* The stack needs log (total_elements) entries (we could even subtract
   log(MAX_THRESH)).  Since total_elements has type unsigned, we get as
   upper bound for log (total_elements):
   bits per byte (CHAR_BIT) * sizeof(unsigned).  */
#define _QSORT_STACK_SIZE       (8 * sizeof(unsigned))
#define _QSORT_PUSH(top, low, high)     \
        (((top->_lo = (low)), (top->_hi = (high)), ++top))
#define _QSORT_POP(low, high, top)      \
        ((--top, (low = top->_lo), (high = top->_hi)))
#define _QSORT_STACK_NOT_EMPTY  (_stack < _top)


/* Order size using quicksort.  This implementation incorporates
   four optimizations discussed in Sedgewick:

   1. Non-recursive, using an explicit stack of pointer that store the
      next array partition to sort.  To save time, this maximum amount
      of space required to store an array of SIZE_MAX is allocated on the
      stack.  Assuming a 32-bit (64 bit) integer for size_t, this needs
      only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
      Pretty cheap, actually.

   2. Chose the pivot element using a median-of-three decision tree.
      This reduces the probability of selecting a bad pivot value and
      eliminates certain extraneous comparisons.

   3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
      insertion sort to order the MAX_THRESH items within each partition.
      This is a big win, since insertion sort is faster for small, mostly
      sorted array segments.

   4. The larger of the two sub-partitions is always pushed onto the
      stack first, with the algorithm then concentrating on the
      smaller partition.  This *guarantees* no more than log (total_elems)
      stack size is needed (actually O(1) in this case)!  */

/* The main code starts here... */
#define QSORT(QSORT_TYPE,QSORT_BASE,QSORT_NELT,QSORT_LT)                \
{                                                                       \
  QSORT_TYPE *const _base = (QSORT_BASE);                               \
  const unsigned _elems = (QSORT_NELT);                                 \
  QSORT_TYPE _hold;                                                     \
                                                                        \
  /* Don't declare two variables of type QSORT_TYPE in a single         \
   * statement: eg `TYPE a, b;', in case if TYPE is a pointer,          \
   * expands to `type* a, b;' wich isn't what we want.                  \
   */                                                                   \
                                                                        \
  if (_elems > _QSORT_MAX_THRESH) {                                     \
    QSORT_TYPE *_lo = _base;                                            \
    QSORT_TYPE *_hi = _lo + _elems - 1;                                 \
    struct {                                                            \
      QSORT_TYPE *_hi; QSORT_TYPE *_lo;                                 \
    } _stack[_QSORT_STACK_SIZE], *_top = _stack + 1;                    \
                                                                        \
    while (_QSORT_STACK_NOT_EMPTY) {                                    \
      QSORT_TYPE *_left_ptr; QSORT_TYPE *_right_ptr;                    \
                                                                        \
      /* Select median value from among LO, MID, and HI. Rearrange      \
         LO and HI so the three values are sorted. This lowers the      \
         probability of picking a pathological pivot value and          \
         skips a comparison for both the LEFT_PTR and RIGHT_PTR in      \
         the while loops. */                                            \
                                                                        \
      QSORT_TYPE *_mid = _lo + ((_hi - _lo) >> 1);                      \
                                                                        \
      if (QSORT_LT (_mid, _lo))                                         \
        _QSORT_SWAP (_mid, _lo, _hold);                                 \
      if (QSORT_LT (_hi, _mid)) {                                       \
        _QSORT_SWAP (_mid, _hi, _hold);                                 \
        if (QSORT_LT (_mid, _lo))                                       \
          _QSORT_SWAP (_mid, _lo, _hold);                               \
      }                                                                 \
                                                                        \
      _left_ptr  = _lo + 1;                                             \
      _right_ptr = _hi - 1;                                             \
                                                                        \
      /* Here's the famous ``collapse the walls'' section of quicksort. \
         Gotta like those tight inner loops!  They are the main reason  \
         that this algorithm runs much faster than others. */           \
      do {                                                              \
        while (QSORT_LT (_left_ptr, _mid))                              \
         ++_left_ptr;                                                   \
                                                                        \
        while (QSORT_LT (_mid, _right_ptr))                             \
          --_right_ptr;                                                 \
                                                                        \
        if (_left_ptr < _right_ptr) {                                   \
          _QSORT_SWAP (_left_ptr, _right_ptr, _hold);                   \
          if (_mid == _left_ptr)                                        \
            _mid = _right_ptr;                                          \
          else if (_mid == _right_ptr)                                  \
            _mid = _left_ptr;                                           \
          ++_left_ptr;                                                  \
          --_right_ptr;                                                 \
        }                                                               \
        else if (_left_ptr == _right_ptr) {                             \
          ++_left_ptr;                                                  \
          --_right_ptr;                                                 \
          break;                                                        \
        }                                                               \
      } while (_left_ptr <= _right_ptr);                                \
                                                                        \
     /* Set up pointers for next iteration.  First determine whether    \
        left and right partitions are below the threshold size.  If so, \
        ignore one or both.  Otherwise, push the larger partition's     \
        bounds on the stack and continue sorting the smaller one. */    \
                                                                        \
      if (_right_ptr - _lo <= _QSORT_MAX_THRESH) {                      \
        if (_hi - _left_ptr <= _QSORT_MAX_THRESH)                       \
          /* Ignore both small partitions. */                           \
          _QSORT_POP (_lo, _hi, _top);                                  \
        else                                                            \
          /* Ignore small left partition. */                            \
          _lo = _left_ptr;                                              \
      }                                                                 \
      else if (_hi - _left_ptr <= _QSORT_MAX_THRESH)                    \
        /* Ignore small right partition. */                             \
        _hi = _right_ptr;                                               \
      else if (_right_ptr - _lo > _hi - _left_ptr) {                    \
        /* Push larger left partition indices. */                       \
        _QSORT_PUSH (_top, _lo, _right_ptr);                            \
        _lo = _left_ptr;                                                \
      }                                                                 \
      else {                                                            \
        /* Push larger right partition indices. */                      \
        _QSORT_PUSH (_top, _left_ptr, _hi);                             \
        _hi = _right_ptr;                                               \
      }                                                                 \
    }                                                                   \
  }                                                                     \
                                                                        \
  /* Once the BASE array is partially sorted by quicksort the rest      \
     is completely sorted using insertion sort, since this is efficient \
     for partitions below MAX_THRESH size. BASE points to the           \
     beginning of the array to sort, and END_PTR points at the very     \
     last element in the array (*not* one beyond it!). */               \
                                                                        \
  {                                                                     \
    QSORT_TYPE *const _end_ptr = _base + _elems - 1;                    \
    QSORT_TYPE *_tmp_ptr = _base;                                       \
    register QSORT_TYPE *_run_ptr;                                      \
    QSORT_TYPE *_thresh;                                                \
                                                                        \
    _thresh = _base + _QSORT_MAX_THRESH;                                \
    if (_thresh > _end_ptr)                                             \
      _thresh = _end_ptr;                                               \
                                                                        \
    /* Find smallest element in first threshold and place it at the     \
       array's beginning.  This is the smallest array element,          \
       and the operation speeds up insertion sort's inner loop. */      \
                                                                        \
    for (_run_ptr = _tmp_ptr + 1; _run_ptr <= _thresh; ++_run_ptr)      \
      if (QSORT_LT (_run_ptr, _tmp_ptr))                                \
        _tmp_ptr = _run_ptr;                                            \
                                                                        \
    if (_tmp_ptr != _base)                                              \
      _QSORT_SWAP (_tmp_ptr, _base, _hold);                             \
                                                                        \
    /* Insertion sort, running from left-hand-side                      \
     * up to right-hand-side.  */                                       \
                                                                        \
    _run_ptr = _base + 1;                                               \
    while (++_run_ptr <= _end_ptr) {                                    \
      _tmp_ptr = _run_ptr - 1;                                          \
      while (QSORT_LT (_run_ptr, _tmp_ptr))                             \
        --_tmp_ptr;                                                     \
                                                                        \
      ++_tmp_ptr;                                                       \
      if (_tmp_ptr != _run_ptr) {                                       \
        QSORT_TYPE *_trav = _run_ptr + 1;                               \
        while (--_trav >= _run_ptr) {                                   \
          QSORT_TYPE *_hi; QSORT_TYPE *_lo;                             \
          _hold = *_trav;                                               \
                                                                        \
          for (_hi = _lo = _trav; --_lo >= _tmp_ptr; _hi = _lo)         \
            *_hi = *_lo;                                                \
          *_hi = _hold;                                                 \
        }                                                               \
      }                                                                 \
    }                                                                   \
  }                                                                     \
                                                                        \
}