diff --git a/lib/stdlib/qsort.c b/lib/stdlib/qsort.c
index 723395cc..21eceb2b 100644
--- a/lib/stdlib/qsort.c
+++ b/lib/stdlib/qsort.c
@@ -18,244 +18,139 @@
* along with GNU Mes. If not, see .
*/
-/* 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
#include
#include
-/* 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)
+#if 0
+void
+qswap (void *a, void *b, size_t size)
+{
+ char *pa = a;
+ char *pb = b;
+ do
+ {
+ char tmp = *pa;
+ *pa++ = *pb;
+ *pb++ = tmp;
+ } while (--size > 0);
+}
+#else
+void
+qswap (void *a, void *b, int size)
+{
+ char buffer[size];
+ memcpy (buffer, a, size);
+ memcpy (a, b, size);
+ memcpy (b, buffer, size);
+}
+#endif
-/* 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
- 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.
+ // Loop invariants, all trivially verified at the start of the loop:
+ // - (A): values strictly to the left of `low` are lower than or equal to `pivot`
+ // - (B): there is at least one value at or to the right of `low` that is greater
+ // than or equal to `pivot`
+ // - (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.
- This reduces the probability of selecting a bad pivot value and
- eliminates certain extraneous comparisons.
+ // Here, we have
+ // - (1): `*low >= pivot`
+ // - (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
- 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.
+ // This loop terminates because of (D).
+ do {
+ --high;
+ int c = compare (pivot, high);
+ } while (c < 0);
- 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)! */
+ // Here, we have
+ // - (3): `*high <= pivot`
+ // - (4): by (C) which held before this loop, elements strictly to the
+ // 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
-qsort (void* base, size_t total_elems, size_t size,
- int (*compare)(void const *, void const *))
+_qsort (char *low, char *high, size_t size,
+ int (*compare) (void const *, void const *))
{
- char *base_ptr = (char *) base;
-
- /* 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. */
+ // Trivial base case...
+ if (low - high < size)
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;
+ // ...therefore pre-condition (P) of `qpart` is satisfied.
+ char *p = qpart (low, high, size, compare);
- while (STACK_NOT_EMPTY)
- {
- char *left_ptr;
- char *right_ptr;
+ // Thanks to postconditions (Q1) and (Q2) of `qpart`, the ranges
+ // [low, p) and [p, high) are non-empty, therefore the size of the ranges
+ // passed to the recursive calls below is strictly lower than the size of
+ // [low, high) in this call. Therefore the base case is eventually reached
+ // and the algorithm terminates.
- 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
- {
- 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;
- }
- }
- }
- }
+ // Thanks to postconditions (Q3) and (Q4) of `qpart`, and by induction
+ // on the size of [low, high), the recursive calls below sort their
+ // respective argument ranges and [low, high) is sorted as a result.
+ _qsort (low, p, size, compare);
+ _qsort (p, high, size, compare);
+}
+
+void
+qsort (void *base, size_t count, size_t size,
+ int (*compare) (void const *, void const *))
+{
+ char *high = base + count * size;
+ _qsort (base, high, size, compare);
}