@@ -112,6 +112,7 @@ typedef struct
{
char *lo;
char *hi;
+ size_t depth;
} stack_node;
/* The stack needs log (total_elements) entries (we could even subtract
@@ -121,22 +122,90 @@ typedef struct
enum { STACK_SIZE = CHAR_BIT * sizeof (size_t) };
static inline stack_node *
-push (stack_node *top, char *lo, char *hi)
+push (stack_node *top, char *lo, char *hi, size_t depth)
{
top->lo = lo;
top->hi = hi;
+ top->depth = depth;
return ++top;
}
static inline stack_node *
-pop (stack_node *top, char **lo, char **hi)
+pop (stack_node *top, char **lo, char **hi, size_t *depth)
{
--top;
*lo = top->lo;
*hi = top->hi;
+ *depth = top->depth;
return top;
}
+/* A fast, small, non-recursive O(nlog n) heapsort, adapted from Linux
+ lib/sort.c. Used on introsort implementation as a fallback routine with
+ worst-case performance of O(nlog n) and worst-case space complexity of
+ O(1). */
+
+static inline size_t
+parent (size_t i, unsigned int lsbit, size_t size)
+{
+ i -= size;
+ i -= size & -(i & lsbit); /* i.e., 'if (i & lsbit) i -= size;' */
+ return i / 2;
+}
+
+static void
+heapsort_r (void *base, void *end, size_t size, enum swap_type_t swap_type,
+ __compar_d_fn_t cmp, void *arg)
+{
+ size_t num = ((uintptr_t) end - (uintptr_t) base) / size;
+ size_t n = num * size, a = (num/2) * size;
+ /* Used to find parent */
+ const size_t lsbit = size & -size;
+
+ /* num < 2 || size == 0. */
+ if (a == 0)
+ return;
+
+ for (;;)
+ {
+ size_t b, c, d;
+
+ if (a != 0)
+ /* Building heap: sift down --a */
+ a -= size;
+ else if (n -= size)
+ /* Sorting: Extract root to --n */
+ do_swap (base, base + n, size, swap_type);
+ else
+ break;
+
+ /* Sift element at "a" down into heap. This is the "bottom-up" variant,
+ which significantly reduces calls to cmp_func(): we find the
+ sift-down path all the way to the leaves (one compare per level),
+ then backtrack to find where to insert the target element.
+
+ Because elements tend to sift down close to the leaves, this uses
+ fewer compares than doing two per level on the way down. (A bit more
+ than half as many on average, 3/4 worst-case.). */
+ for (b = a; c = 2 * b + size, (d = c + size) < n;)
+ b = cmp (base + c, base + d, arg) >= 0 ? c : d;
+ if (d == n)
+ /* Special case last leaf with no sibling. */
+ b = c;
+
+ /* Now backtrack from "b" to the correct location for "a". */
+ while (b != a && cmp (base + a, base + b, arg) >= 0)
+ b = parent (b, lsbit, size);
+ /* Where "a" belongs. */
+ c = b;
+ while (b != a)
+ {
+ /* Shift it into place. */
+ b = parent (b, lsbit, size);
+ do_swap (base + b, base + c, size, swap_type);
+ }
+ }
+}
/* Order size using quicksort. This implementation incorporates
four optimizations discussed in Sedgewick:
@@ -222,7 +291,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
const size_t max_thresh = MAX_THRESH * size;
- if (total_elems == 0)
+ if (total_elems <= 1)
/* Avoid lossage with unsigned arithmetic below. */
return;
@@ -234,6 +303,10 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
else
swap_type = SWAP_BYTES;
+ /* Maximum depth before quicksort switches to heapsort. */
+ size_t depth = 2 * (sizeof (size_t) * CHAR_BIT - 1
+ - __builtin_clzl (total_elems));
+
if (total_elems > MAX_THRESH)
{
char *lo = base_ptr;
@@ -243,6 +316,13 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
while (stack < top)
{
+ if (depth == 0)
+ {
+ heapsort_r (lo, hi, size, swap_type, cmp, arg);
+ top = pop (top, &lo, &hi, &depth);
+ continue;
+ }
+
char *left_ptr;
char *right_ptr;
@@ -306,7 +386,7 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
{
if ((size_t) (hi - left_ptr) <= max_thresh)
/* Ignore both small partitions. */
- top = pop (top, &lo, &hi);
+ top = pop (top, &lo, &hi, &depth);
else
/* Ignore small left partition. */
lo = left_ptr;
@@ -317,13 +397,13 @@ _quicksort (void *const pbase, size_t total_elems, size_t size,
else if ((right_ptr - lo) > (hi - left_ptr))
{
/* Push larger left partition indices. */
- top = push (top, lo, right_ptr);
+ top = push (top, lo, right_ptr, depth - 1);
lo = left_ptr;
}
else
{
/* Push larger right partition indices. */
- top = push (top, left_ptr, hi);
+ top = push (top, left_ptr, hi, depth - 1);
hi = right_ptr;
}
}