andrius
/
mes
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

another broken qsort

This commit is contained in:
Jan (janneke) Nieuwenhuizen 2022-10-25 09:26:27 +02:00
parent d5cb2ae8cb
commit 386341092e
No known key found for this signature in database
GPG Key ID: F3C1A0D9C1D65273
1 changed files with 119 additions and 224 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

343
lib/stdlib/qsort.c
View File

@ -18,244 +18,139 @@
* along with GNU Mes. If not, see <http://www.gnu.org/licenses/>. * along with GNU Mes. If not, see <http://www.gnu.org/licenses/>.
*/ */
/* Copyright (C) 1991, 1992 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 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> #include <string.h>
/* Byte-wise swap two items of size SIZE. */ #if 0
#define SWAP(a, b, size) \ void
do \ qswap (void *a, void *b, size_t size)
{ \ {
size_t __size = (size); \ char *pa = a;
char *__a = (a), *__b = (b); \ char *pb = b;
do \ do
{ \ {
char __tmp = *__a; \ char tmp = *pa;
*__a++ = *__b; \ *pa++ = *pb;
*__b++ = __tmp; \ *pb++ = tmp;
} while (--__size > 0); \ } while (--size > 0);
} while (0) }
#else
/* Discontinue quicksort algorithm when partition gets below this size. void
This particular magic number was chosen to work best on a Sun 4/260. */ qswap (void *a, void *b, int size)
#define MAX_THRESH 4 {
char buffer[size];
/* Stack node declarations used to store unfulfilled partition obligations. */ memcpy (buffer, a, size);
typedef struct memcpy (a, b, size);
{ memcpy (b, buffer, size);
char *lo; }
char *hi; #endif
} 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: * Assuming precondition (P) that `end - begin >= 2`, this function reorders the elements
* of range [begin, end) and returns a pointer `ret` such that the following
* postconditions hold:
* - (Q1): `ret > begin`
* - (Q2): `ret < end`
* and, for some value `p` in [begin, end):
* - (Q3): all values in [begin, ret) are lower than or equal to `p`
* - (Q4): all values in [ret, end) are greater than or equal to `p`
*/
char *
qpart (char *low, char *high, size_t size,
int (*compare) (void const *, void const *))
{
char *pivot = (low + (high - low)/2);
1. Non-recursive, using an explicit stack of pointer that store the // Loop invariants, all trivially verified at the start of the loop:
next array partition to sort. To save time, this maximum amount // - (A): values strictly to the left of `low` are lower than or equal to `pivot`
of space required to store an array of MAX_INT is allocated on the // - (B): there is at least one value at or to the right of `low` that is greater
stack. Assuming a 32-bit integer, this needs only 32 * // than or equal to `pivot`
sizeof(stack_node) == 136 bits. Pretty cheap, actually. // - (C): values at or to the right of `high` are greater than or equal to `pivot`
// - (D): there is at least one value strictly to the left of `high` that is lower
// than or equal to `pivot`
// - (E): `low <= high`
//
// The loop terminates because `high - low` decreases strictly at each execution of
// the body (obvious).
while (1)
{
// This loop terminates because of (B).
int c = compare (low, pivot);
while (c < 0)
low += size;
2. Chose the pivot element using a median-of-three decision tree. // Here, we have
This reduces the probability of selecting a bad pivot value and // - (1): `*low >= pivot`
eliminates certain extraneous comparisons. // - (2): `low <= high` because of (E) and (C)
// - properties (A) and (B) still hold because `low` has only moved
// past values strictly less than `pivot`
3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving // This loop terminates because of (D).
insertion sort to order the MAX_THRESH items within each partition. do {
This is a big win, since insertion sort is faster for small, mostly --high;
sorted array segements. int c = compare (pivot, high);
} while (c < 0);
4. The larger of the two sub-partitions is always pushed onto the // Here, we have
stack first, with the algorithm then concentrating on the // - (3): `*high <= pivot`
smaller partition. This *guarantees* no more than log (n) // - (4): by (C) which held before this loop, elements strictly to the
stack size is needed (actually O(1) in this case)! */ // right of `high` are known to be greater than or equal to `pivot`
// (but now (C) may not hold anymore)
if (low >= high)
{
// Due to (1), (A) and (4), (Q3) and (Q4) are established with `pivot`
// as `p`.
// Clearly, (B) proves Q2.
// See the rest of the answer below for a proof of (Q1).
// This correctly finishes the qpart.
return low;
}
// We have `low < high` and we swap...
qswap (low, high, size);
// ...and now,
// - by (1) and (4), invariant (C) is re-established
// - by (1), invariant (D) is re-established
// - (5): by (3), `*low <= pivot`
++low;
// (A) already held before this increment. Thus, because of (5), (A)
// still holds. Additionally, by (1), after the swap, (B) is
// re-established. Finally, (E) is obvious.
}
}
void void
qsort (void* base, size_t total_elems, size_t size, _qsort (char *low, char *high, size_t size,
int (*compare)(void const *, void const *)) int (*compare) (void const *, void const *))
{ {
char *base_ptr = (char *) base; // Trivial base case...
if (low - high < size)
/* 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; return;
if (total_elems > MAX_THRESH) // ...therefore pre-condition (P) of `qpart` is satisfied.
{ char *p = qpart (low, high, size, compare);
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) // Thanks to postconditions (Q1) and (Q2) of `qpart`, the ranges
{ // [low, p) and [p, high) are non-empty, therefore the size of the ranges
char *left_ptr; // passed to the recursive calls below is strictly lower than the size of
char *right_ptr; // [low, high) in this call. Therefore the base case is eventually reached
// and the algorithm terminates.
char *pivot = pivot_buffer; // Thanks to postconditions (Q3) and (Q4) of `qpart`, and by induction
// on the size of [low, high), the recursive calls below sort their
/* Select median value from among LO, MID, and HI. Rearrange // respective argument ranges and [low, high) is sorted as a result.
LO and HI so the three values are sorted. This lowers the _qsort (low, p, size, compare);
probability of picking a pathological pivot value and _qsort (p, high, size, compare);
skips a comparison for both the LEFT_PTR and RIGHT_PTR. */ }
char *mid = lo + size * ((hi - lo) / size >> 1); void
qsort (void *base, size_t count, size_t size,
if ((*compare)((void*) mid, (void*) lo) < 0) int (*compare) (void const *, void const *))
SWAP (mid, lo, size); {
if ((*compare)((void*) hi, (void*) mid) < 0) char *high = base + count * size;
SWAP (mid, hi, size); _qsort (base, high, size, compare);
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
{
while ((*compare)((void*) left_ptr, (void*) pivot) < 0)
left_ptr += size;
while ((*compare)((void*) pivot, (void*) right_ptr) < 0)
right_ptr -= size;
if (left_ptr < right_ptr)
{
SWAP (left_ptr, right_ptr, size);
left_ptr += size;
right_ptr -= size;
}
else if (left_ptr == right_ptr)
{
left_ptr += size;
right_ptr -= size;
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 ((size_t) (right_ptr - lo) <= max_thresh)
{
if ((size_t) (hi - left_ptr) <= max_thresh)
/* Ignore both small partitions. */
POP (lo, hi);
else
/* 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
is completely sorted using insertion sort, since this is efficient
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))
{
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;
}
}
}
}
} }