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alt qsort

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Jan (janneke) Nieuwenhuizen 2022-10-25 08:51:32 +02:00
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lib/stdlib/qsort.c
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@ -1,242 +1,97 @@
/* Copyright (C) 1991, 1992 Free Software Foundation, Inc. /* -*-comment-start: "//";comment-end:""-*-
This file is part of the GNU C Library. * GNU Mes --- Maxwell Equations of Software
Written by Douglas C. Schmidt (schmidt@ics.uci.edu). * Copyright © 2017,2018 Jan (janneke) Nieuwenhuizen <janneke@gnu.org>
*
* This file is part of GNU Mes.
*
* GNU Mes is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* GNU Mes 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Mes. If not, see <http://www.gnu.org/licenses/>.
*/
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If
not, write to the Free Software Foundation, Inc., 675 Mass Ave,
Cambridge, MA 02139, USA. */
#include <alloca.h>
#include <stdlib.h> #include <stdlib.h>
#include <string.h>
/* Byte-wise swap two items of size SIZE. */
#define SWAP(a, b, size) \
do \
{ \
size_t __size = (size); \
char *__a = (a), *__b = (b); \
do \
{ \
char __tmp = *__a; \
*__a++ = *__b; \
*__b++ = __tmp; \
} while (--__size > 0); \
} while (0)
/* Discontinue quicksort algorithm when partition gets below this size.
This particular magic number was chosen to work best on a Sun 4/260. */
#define MAX_THRESH 4
/* Stack node declarations used to store unfulfilled partition obligations. */
typedef struct
{
char *lo;
char *hi;
} stack_node;
/* The next 4 #defines implement a very fast in-line stack abstraction. */
#define STACK_SIZE (8 * sizeof(unsigned long int))
#define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
#define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
#define 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 MAX_INT is allocated on the
stack. Assuming a 32-bit integer, this needs only 32 *
sizeof(stack_node) == 136 bits. 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 segements.
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 (n)
stack size is needed (actually O(1) in this case)! */
void void
qsort (void* base, size_t total_elems, size_t size, qswap (void *a, void *b, size_t size)
int (*compare)(void const *, void const *))
{ {
char *base_ptr = (char *) base; char *pa = a;
char *pb = b;
/* Allocating SIZE bytes for a pivot buffer facilitates a better
algorithm below since we can do comparisons directly on the pivot. */
char *pivot_buffer = (char *) alloca (size);
const size_t max_thresh = MAX_THRESH * size;
if (total_elems == 0)
/* Avoid lossage with unsigned arithmetic below. */
return;
if (total_elems > MAX_THRESH)
{
char *lo = base_ptr;
char *hi = &lo[size * (total_elems - 1)];
/* Largest size needed for 32-bit int!!! */
stack_node stack[STACK_SIZE];
stack_node *top = stack + 1;
while (STACK_NOT_EMPTY)
{
char *left_ptr;
char *right_ptr;
char *pivot = pivot_buffer;
/* 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. */
char *mid = lo + size * ((hi - lo) / size >> 1);
if ((*compare)((void*) mid, (void*) lo) < 0)
SWAP(mid, lo, size);
if ((*compare)((void*) hi, (void*) mid) < 0)
SWAP(mid, hi, size);
else
goto jump_over;
if ((*compare)((void*) mid, (void*) lo) < 0)
SWAP(mid, lo, size);
jump_over:;
memcpy(pivot, mid, size);
pivot = pivot_buffer;
left_ptr = lo + size;
right_ptr = hi - size;
/* 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 do
{ {
while ((*compare)((void*) left_ptr, (void*) pivot) < 0) char tmp = *pa;
left_ptr += size; *pa++ = *pb;
*pb++ = tmp;
} while (--size > 0);
}
while ((*compare)((void*) pivot, (void*) right_ptr) < 0) size_t
right_ptr -= size; partition (void *base, size_t low, size_t high, size_t size,
int (*compare) (void const *, void const *))
{
// select the rightmost element as pivot
void *pivot = base + high * size;
if (left_ptr < right_ptr) // pointer for greater element
size_t i = (low - 1);
// traverse each element of the array
// compare them with the pivot
for (int j = low; j < high; j++)
{ {
SWAP(left_ptr, right_ptr, size); int c = compare (base + j * size, pivot);
left_ptr += size; if (c < 0)
right_ptr -= size;
}
else if (left_ptr == right_ptr)
{ {
left_ptr += size; // swap element at i with element at j
right_ptr -= size; void *p1 = base + i * size;
break; void *p2 = base + j * size;
qswap (p1, p2, size);
// if element smaller than pivot is found
// swap it with the greater element pointed by i
i++;
} }
} }
while (left_ptr <= right_ptr);
/* Set up pointers for next iteration. First determine whether // swap the pivot element with the greater element at i
left and right partitions are below the threshold size. If so, void *p1 = base + (i + 1) * size;
ignore one or both. Otherwise, push the larger partition's void *p2 = base + high * size;
bounds on the stack and continue sorting the smaller one. */ qswap (p1, p2, size);
if ((size_t) (right_ptr - lo) <= max_thresh) // return the partition point
return (i + 1);
}
void
_qsort (void *base, size_t low, size_t high, size_t size,
int (*compare) (void const *, void const *))
{
if (low < high)
{ {
if ((size_t) (hi - left_ptr) <= max_thresh) // find the pivot element such that
/* Ignore both small partitions. */ // elements smaller than pivot are on left of pivot
POP(lo, hi); // elements greater than pivot are on right of pivot
else int pi = partition (base, low, high, size, compare);
/* Ignore small left partition. */
lo = left_ptr;
}
else if ((size_t) (hi - left_ptr) <= max_thresh)
/* Ignore small right partition. */
hi = right_ptr;
else if ((right_ptr - lo) > (hi - left_ptr))
{
/* Push larger left partition indices. */
PUSH(lo, right_ptr);
lo = left_ptr;
}
else
{
/* Push larger right partition indices. */
PUSH(left_ptr, hi);
hi = right_ptr;
}
}
}
/* Once the BASE_void* array is partially sorted by quicksort the rest // recursive call on the left of pivot
is completely sorted using insertion sort, since this is efficient _qsort (base, low, pi - 1, size, compare);
for partitions below MAX_THRESH size. BASE_void* points to the beginning
of the array to sort, and END_void* points at the very last element in
the array (*not* one beyond it!). */
#define min(x, y) ((x) < (y) ? (x) : (y)) // recursive call on the right of pivot
_qsort (base, pi + 1, high, size, compare);
{
char *const end_ptr = &base_ptr[size * (total_elems - 1)];
char *tmp_ptr = base_ptr;
char *thresh = min(end_ptr, base_ptr + max_thresh);
char *run_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 + size; run_ptr <= thresh; run_ptr += size)
if ((*compare)((void*) run_ptr, (void*) tmp_ptr) < 0)
tmp_ptr = run_ptr;
if (tmp_ptr != base_ptr)
SWAP(tmp_ptr, base_ptr, size);
/* Insertion sort, running from left-hand-side up to right-hand-side. */
run_ptr = base_ptr + size;
while ((run_ptr += size) <= end_ptr)
{
tmp_ptr = run_ptr - size;
while ((*compare)((void*) run_ptr, (void*) tmp_ptr) < 0)
tmp_ptr -= size;
tmp_ptr += size;
if (tmp_ptr != run_ptr)
{
char *trav;
trav = run_ptr + size;
while (--trav >= run_ptr)
{
char c = *trav;
char *hi, *lo;
for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
*hi = *lo;
*hi = c;
}
}
}
} }
} }
void
qsort (void *base, size_t count, size_t size,
int (*compare) (void const *, void const *))
{
_qsort (base, 0, count, size, compare);
}