Re: [PATCH] stdlib: Optimize number of calls to comparison function

[Kuan-Wei Chiu <visitorckw@gmail.com>]

On Sun, Dec 03, 2023 at 05:48:39AM +0800, Kuan-Wei Chiu wrote:
> The current heapsort implementation in the siftdown function follows
> the standard textbook version, necessitating two comparisons at each
> level. Transitioning to the Bottom-up heapsort version allows us to
> decrease the required comparisons to just one per level. On average,
> this modification significantly reduces the comparison count from
> 2nlog2(n) - 3n + o(n) to nlog2(n) + 0.37*n + o(n).
> 
> Refs:
>   BOTTOM-UP-HEAPSORT, a new variant of HEAPSORT beating, on an average,
>   QUICKSORT (if n is not very small)
>   Ingo Wegener
>   Theoretical Computer Science, 118(1); Pages 81-98, 13 September 1993
>   https://doi.org/10.1016/0304-3975(93)90364-Y
> 
> Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
> ---
>  stdlib/qsort.c | 36 ++++++++++++++++++------------------
>  1 file changed, 18 insertions(+), 18 deletions(-)
> 
> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
> index be01fb5598..f5babef150 100644
> --- a/stdlib/qsort.c
> +++ b/stdlib/qsort.c
> @@ -132,26 +132,26 @@ 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)
>  {
> -  /* There can only be a heap condition violation if there are
> -     children.  */
> -  while (2 * k + 1 <= n)
> -    {
> -      /* Left child.  */
> -      size_t j = 2 * k + 1;
> -      /* If the right child is larger, use it.  */
> -      if (j < n && cmp (base + (j * size), base + ((j + 1) * size), arg) < 0)
> -	j++;
> -
> -      /* If k is already >= to its children, we are done.  */
> -      if (j == k || cmp (base + (k * size), base + (j * size), arg) >= 0)
> -	break;
> +  size_t i, j;
> +
> +  /* Find the sift-down path all the way to the leaves. */
> +  for (i = k; j = 2 * i + 1, j + 1 <= n;)
> +    i = cmp (base + j * size, base + (j + 1) * size, arg) >= 0 ? j : (j + 1);
>  
> -      /* Heal the violation.  */
> -      do_swap (base + (size * j), base + (k * size), size, swap_type);
> +  /* Special case for the last leaf with no sibling. */
> +  if (j == n)
> +    i = j;
>  
> -      /* Swapping with j may have introduced a violation at j.  Fix
> -	 it in the next loop iteration.  */
> -      k = j;
> +  /* Backtrack to the correct location. */
> +  while (i != k && cmp (base + k * size, base + i * size, arg) > 0)
> +    i = (i - 1) / 2;
> +
> +  /* Shift the element into its correct place. */
> +  j = i;
> +  while (i != k)
> +    {
> +      i = (i - 1) / 2;
> +      do_swap (base + i * size, base + j * size, size, swap_type);
>      }
>  }
>  
> -- 
> 2.25.1
>

Since we still retain heapsort as a fallback for mergesort, should we
reconsider applying this patch?

Thanks,
Kuan-Wei