[v6,4/6] stdlib: Implement introsort for qsort (BZ 19305)

  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.
---
 stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 79 insertions(+), 6 deletions(-)
  

On Tue, Jul 18, 2023 at 9:19 AM Adhemerval Zanella via Libc-alpha
<libc-alpha@sourceware.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.
> ---
>  stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
>  1 file changed, 79 insertions(+), 6 deletions(-)
>
> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
> index 640896a598..054c900b02 100644
> --- a/stdlib/qsort.c
> +++ b/stdlib/qsort.c
> @@ -119,6 +119,7 @@ typedef struct
>    {
>      char *lo;
>      char *hi;
> +    size_t depth;

You don't actually need to track depth in the "stack"
when you pop hi/lo you can take log2(hi - lo) to compute
what depth counter "should" be i.e

size_t loop_cnt = WORD_SIZE - clz(hi - lo);

then if --loop_cnt == 0 -> introsort that chunk.
>    } stack_node;
>
>  /* The stack needs log (total_elements) entries (we could even subtract
> @@ -128,22 +129,83 @@ 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 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;
> +    }
> +}
> +
> +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);
> +    }
> +}
>
>  /* Order size using quicksort.  This implementation incorporates
>     four optimizations discussed in Sedgewick:
> @@ -229,7 +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;
>
> @@ -241,6 +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;
> @@ -250,6 +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;
>
> @@ -313,7 +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;
> @@ -324,13 +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;
>              }
>          }
> --
> 2.34.1
>
  

On 18/07/23 14:37, Noah Goldstein wrote:
> On Tue, Jul 18, 2023 at 9:19 AM Adhemerval Zanella via Libc-alpha
> <libc-alpha@sourceware.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.
>> ---
>>  stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
>>  1 file changed, 79 insertions(+), 6 deletions(-)
>>
>> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
>> index 640896a598..054c900b02 100644
>> --- a/stdlib/qsort.c
>> +++ b/stdlib/qsort.c
>> @@ -119,6 +119,7 @@ typedef struct
>>    {
>>      char *lo;
>>      char *hi;
>> +    size_t depth;
> 
> You don't actually need to track depth in the "stack"
> when you pop hi/lo you can take log2(hi - lo) to compute
> what depth counter "should" be i.e

I don't think we can take the assumption quicksort will always iterate the
input array as a binary tree, so we can't really use log2(hi - lo) as the
depth.

However I found another issue, which a change to use 'stack_node *top = stack + 1'
removed the initial depth initialization.

> 
> size_t loop_cnt = WORD_SIZE - clz(hi - lo);
> 
> then if --loop_cnt == 0 -> introsort that chunk
  

On Tue, Jul 18, 2023 at 2:08 PM Adhemerval Zanella Netto
<adhemerval.zanella@linaro.org> wrote:
>
>
>
> On 18/07/23 14:37, Noah Goldstein wrote:
> > On Tue, Jul 18, 2023 at 9:19 AM Adhemerval Zanella via Libc-alpha
> > <libc-alpha@sourceware.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.
> >> ---
> >>  stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
> >>  1 file changed, 79 insertions(+), 6 deletions(-)
> >>
> >> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
> >> index 640896a598..054c900b02 100644
> >> --- a/stdlib/qsort.c
> >> +++ b/stdlib/qsort.c
> >> @@ -119,6 +119,7 @@ typedef struct
> >>    {
> >>      char *lo;
> >>      char *hi;
> >> +    size_t depth;
> >
> > You don't actually need to track depth in the "stack"
> > when you pop hi/lo you can take log2(hi - lo) to compute
> > what depth counter "should" be i.e
>
> I don't think we can take the assumption quicksort will always iterate the
> input array as a binary tree, so we can't really use log2(hi - lo) as the
> depth.
> However I found another issue, which a change to use 'stack_node *top = stack + 1'
> removed the initial depth initialization.
>

Bah, sorry missed your reply!

What i mean is not that you take `log2(hi - lo)` as the current depth,
but whenever
you pop a new set of bounds you set `max_depth = log2(hi - lo)`. Then
in the loop if
`--max_depth <= 0` we are in pessimistic state -> do introsort.

Think this works to avoid the O(N^2) state and saves a lot of state tracking.

> >
> > size_t loop_cnt = WORD_SIZE - clz(hi - lo);
> >
> > then if --loop_cnt == 0 -> introsort that chunk
  

On 29/08/23 04:45, Noah Goldstein wrote:
> On Tue, Jul 18, 2023 at 2:08 PM Adhemerval Zanella Netto
> <adhemerval.zanella@linaro.org> wrote:
>>
>>
>>
>> On 18/07/23 14:37, Noah Goldstein wrote:
>>> On Tue, Jul 18, 2023 at 9:19 AM Adhemerval Zanella via Libc-alpha
>>> <libc-alpha@sourceware.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.
>>>> ---
>>>>  stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
>>>>  1 file changed, 79 insertions(+), 6 deletions(-)
>>>>
>>>> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
>>>> index 640896a598..054c900b02 100644
>>>> --- a/stdlib/qsort.c
>>>> +++ b/stdlib/qsort.c
>>>> @@ -119,6 +119,7 @@ typedef struct
>>>>    {
>>>>      char *lo;
>>>>      char *hi;
>>>> +    size_t depth;
>>>
>>> You don't actually need to track depth in the "stack"
>>> when you pop hi/lo you can take log2(hi - lo) to compute
>>> what depth counter "should" be i.e
>>
>> I don't think we can take the assumption quicksort will always iterate the
>> input array as a binary tree, so we can't really use log2(hi - lo) as the
>> depth.
>> However I found another issue, which a change to use 'stack_node *top = stack + 1'
>> removed the initial depth initialization.
>>
> 
> Bah, sorry missed your reply!
> 
> What i mean is not that you take `log2(hi - lo)` as the current depth,
> but whenever
> you pop a new set of bounds you set `max_depth = log2(hi - lo)`. Then
> in the loop if
> `--max_depth <= 0` we are in pessimistic state -> do introsort.
> 
> Think this works to avoid the O(N^2) state and saves a lot of state tracking.

The problem with this approach is not all architectures has a clz instruction,
so log2 will be a libgcc function call.  And due how partition are pushed on 
the stack, it is guarantee that no more than log (total_elems) state track is 
required (O(1)).  To track the state it is an extra of STACK_SIZE size_t state, 
so I am not sure if this will be a large improvement even archs with clz 
instructions.
  

On Thu, Aug 31, 2023 at 7:13 AM Adhemerval Zanella Netto
<adhemerval.zanella@linaro.org> wrote:
>
>
>
> On 29/08/23 04:45, Noah Goldstein wrote:
> > On Tue, Jul 18, 2023 at 2:08 PM Adhemerval Zanella Netto
> > <adhemerval.zanella@linaro.org> wrote:
> >>
> >>
> >>
> >> On 18/07/23 14:37, Noah Goldstein wrote:
> >>> On Tue, Jul 18, 2023 at 9:19 AM Adhemerval Zanella via Libc-alpha
> >>> <libc-alpha@sourceware.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.
> >>>> ---
> >>>>  stdlib/qsort.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++----
> >>>>  1 file changed, 79 insertions(+), 6 deletions(-)
> >>>>
> >>>> diff --git a/stdlib/qsort.c b/stdlib/qsort.c
> >>>> index 640896a598..054c900b02 100644
> >>>> --- a/stdlib/qsort.c
> >>>> +++ b/stdlib/qsort.c
> >>>> @@ -119,6 +119,7 @@ typedef struct
> >>>>    {
> >>>>      char *lo;
> >>>>      char *hi;
> >>>> +    size_t depth;
> >>>
> >>> You don't actually need to track depth in the "stack"
> >>> when you pop hi/lo you can take log2(hi - lo) to compute
> >>> what depth counter "should" be i.e
> >>
> >> I don't think we can take the assumption quicksort will always iterate the
> >> input array as a binary tree, so we can't really use log2(hi - lo) as the
> >> depth.
> >> However I found another issue, which a change to use 'stack_node *top = stack + 1'
> >> removed the initial depth initialization.
> >>
> >
> > Bah, sorry missed your reply!
> >
> > What i mean is not that you take `log2(hi - lo)` as the current depth,
> > but whenever
> > you pop a new set of bounds you set `max_depth = log2(hi - lo)`. Then
> > in the loop if
> > `--max_depth <= 0` we are in pessimistic state -> do introsort.
> >
> > Think this works to avoid the O(N^2) state and saves a lot of state tracking.
>
> The problem with this approach is not all architectures has a clz instruction,
> so log2 will be a libgcc function call.  And due how partition are pushed on
> the stack, it is guarantee that no more than log (total_elems) state track is
> required (O(1)).  To track the state it is an extra of STACK_SIZE size_t state,
> so I am not sure if this will be a large improvement even archs with clz
> instructions.

absolutely not necessary, just a thought.