[v8,5/7] stdlib: Implement introsort for qsort (BZ 19305)
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Commit Message
This patch makes the quicksort implementation to acts as introsort, to
avoid worse-case performance (and thus making it O(nlog n)). It switch
to heapsort when the depth level reaches 2*log2(total elements). The
heapsort is a textbook implementation.
Checked on x86_64-linux-gnu and aarch64-linux-gnu.
---
stdlib/qsort.c | 89 ++++++++++++++++++++++++++++++++++++++++++++++----
1 file changed, 82 insertions(+), 7 deletions(-)
Comments
On Tue, Oct 3, 2023 at 7:23 AM Adhemerval Zanella
<adhemerval.zanella@linaro.org> wrote:
>
> This patch makes the quicksort implementation to acts as introsort, to
> avoid worse-case performance (and thus making it O(nlog n)). It switch
> to heapsort when the depth level reaches 2*log2(total elements). The
> heapsort is a textbook implementation.
>
> Checked on x86_64-linux-gnu and aarch64-linux-gnu.
> ---
> stdlib/qsort.c | 89 ++++++++++++++++++++++++++++++++++++++++++++++----
> 1 file changed, 82 insertions(+), 7 deletions(-)
>
> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
> index 80706b3357..d5f205affc 100644
> --- a/stdlib/qsort.c
> +++ b/stdlib/qsort.c
> @@ -98,6 +98,7 @@ typedef struct
> {
> char *lo;
> char *hi;
> + size_t depth;
> } stack_node;
>
> /* The stack needs log (total_elements) entries (we could even subtract
> @@ -107,22 +108,85 @@ 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;
> }
>
> +/* NB: N is inclusive bound for BASE. */
> +static inline void
> +siftdown (void *base, size_t size, size_t k, size_t n,
> + enum swap_type_t swap_type, __compar_d_fn_t cmp, void *arg)
> +{
> + while (k <= n / 2)
> + {
> + size_t j = 2 * k;
> + if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0)
> + j++;
> +
> + if (cmp (base + (k * size), base + (j * size), arg) >= 0)
> + break;
> +
> + do_swap (base + (size * j), base + (k * size), size, swap_type);
> + k = j;
> + }
> +}
> +
> +static inline void
> +heapify (void *base, size_t size, size_t n, enum swap_type_t swap_type,
> + __compar_d_fn_t cmp, void *arg)
> +{
> + size_t k = n / 2;
> + while (1)
> + {
> + siftdown (base, size, k, n, swap_type, cmp, arg);
> + if (k-- == 0)
> + break;
> + }
> +}
> +
> +/* A non-recursive heapsort, used on introsort implementation as a fallback
> + routine with worst-case performance of O(nlog n) and worst-case space
> + complexity of O(1). It sorts the array starting at BASE and ending at
> + END, with each element of SIZE bytes. The SWAP_TYPE is the callback
> + function used to swap elements, and CMP is the function used to compare
> + elements. */
> +static void
> +heapsort_r (void *base, void *end, size_t size, enum swap_type_t swap_type,
> + __compar_d_fn_t cmp, void *arg)
> +{
> + const size_t count = ((uintptr_t) end - (uintptr_t) base) / size;
> +
> + if (count < 2)
> + return;
> +
> + size_t n = count - 1;
> +
> + /* Build the binary heap, largest value at the base[0]. */
> + heapify (base, size, n, swap_type, cmp, arg);
> +
> + /* On each iteration base[0:n] is the binary heap, while base[n:count]
> + is sorted. */
> + while (n > 0)
> + {
> + do_swap (base, base + (n * size), size, swap_type);
> + n--;
> + siftdown (base, size, 0, n, swap_type, cmp, arg);
> + }
> +}
>
> static inline void
> insertion_sort_qsort_partitions (void *const pbase, size_t total_elems,
> @@ -208,7 +272,7 @@ _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;
>
> @@ -220,15 +284,26 @@ _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;
> char *hi = &lo[size * (total_elems - 1)];
> stack_node stack[STACK_SIZE];
> - stack_node *top = stack + 1;
> + stack_node *top = push (stack, NULL, NULL, depth);
>
> 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;
>
> @@ -292,7 +367,7 @@ _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;
> @@ -303,13 +378,13 @@ _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;
> }
> }
> --
> 2.34.1
>
LGTM
Reviewed-by: Noah Goldstein <goldstein.w.n@gmail.com>
@@ -98,6 +98,7 @@ typedef struct
{
char *lo;
char *hi;
+ size_t depth;
} stack_node;
/* The stack needs log (total_elements) entries (we could even subtract
@@ -107,22 +108,85 @@ 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;
}
+/* NB: N is inclusive bound for BASE. */
+static inline void
+siftdown (void *base, size_t size, size_t k, size_t n,
+ enum swap_type_t swap_type, __compar_d_fn_t cmp, void *arg)
+{
+ while (k <= n / 2)
+ {
+ size_t j = 2 * k;
+ if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0)
+ j++;
+
+ if (cmp (base + (k * size), base + (j * size), arg) >= 0)
+ break;
+
+ do_swap (base + (size * j), base + (k * size), size, swap_type);
+ k = j;
+ }
+}
+
+static inline void
+heapify (void *base, size_t size, size_t n, enum swap_type_t swap_type,
+ __compar_d_fn_t cmp, void *arg)
+{
+ size_t k = n / 2;
+ while (1)
+ {
+ siftdown (base, size, k, n, swap_type, cmp, arg);
+ if (k-- == 0)
+ break;
+ }
+}
+
+/* A non-recursive heapsort, used on introsort implementation as a fallback
+ routine with worst-case performance of O(nlog n) and worst-case space
+ complexity of O(1). It sorts the array starting at BASE and ending at
+ END, with each element of SIZE bytes. The SWAP_TYPE is the callback
+ function used to swap elements, and CMP is the function used to compare
+ elements. */
+static void
+heapsort_r (void *base, void *end, size_t size, enum swap_type_t swap_type,
+ __compar_d_fn_t cmp, void *arg)
+{
+ const size_t count = ((uintptr_t) end - (uintptr_t) base) / size;
+
+ if (count < 2)
+ return;
+
+ size_t n = count - 1;
+
+ /* Build the binary heap, largest value at the base[0]. */
+ heapify (base, size, n, swap_type, cmp, arg);
+
+ /* On each iteration base[0:n] is the binary heap, while base[n:count]
+ is sorted. */
+ while (n > 0)
+ {
+ do_swap (base, base + (n * size), size, swap_type);
+ n--;
+ siftdown (base, size, 0, n, swap_type, cmp, arg);
+ }
+}
static inline void
insertion_sort_qsort_partitions (void *const pbase, size_t total_elems,
@@ -208,7 +272,7 @@ _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;
@@ -220,15 +284,26 @@ _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;
char *hi = &lo[size * (total_elems - 1)];
stack_node stack[STACK_SIZE];
- stack_node *top = stack + 1;
+ stack_node *top = push (stack, NULL, NULL, depth);
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;
@@ -292,7 +367,7 @@ _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;
@@ -303,13 +378,13 @@ _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;
}
}