Re: [PATCH v8 5/7] stdlib: Implement introsort for qsort (BZ 19305)

[Noah Goldstein <goldstein.w.n@gmail.com>]

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>