`select count(distinct ..)` query doesn't go to the specialized distinct accumulator

[jayzhan211]

Is your feature request related to a problem or challenge?

statement count 0
create table t(a int) as values (1), (2);

query I
select count(distinct a) from t; 
----
2

query TT
explain
select count(distinct a) from t; 
----
logical_plan
01)Projection: count(alias1) AS count(DISTINCT t.a)
02)--Aggregate: groupBy=[[]], aggr=[[count(alias1)]]
03)----Aggregate: groupBy=[[t.a AS alias1]], aggr=[[]]
04)------TableScan: t projection=[a]
physical_plan
01)ProjectionExec: expr=[count(alias1)@0 as count(DISTINCT t.a)]
02)--AggregateExec: mode=Final, gby=[], aggr=[count(alias1)]
03)----CoalescePartitionsExec
04)------AggregateExec: mode=Partial, gby=[], aggr=[count(alias1)]
05)--------AggregateExec: mode=FinalPartitioned, gby=[alias1@0 as alias1], aggr=[]
06)----------CoalesceBatchesExec: target_batch_size=8192
07)------------RepartitionExec: partitioning=Hash([alias1@0], 4), input_partitions=4
08)--------------RepartitionExec: partitioning=RoundRobinBatch(4), input_partitions=1
09)----------------AggregateExec: mode=Partial, gby=[a@0 as alias1], aggr=[]
10)------------------DataSourceExec: partitions=1, partition_sizes=[1]

I think we should execute with the specialized count distinct accumualator like PrimitiveDistinctCountAccumulator, BytesDistinctCountAccumulator, FloatDistinctCountAccumulator. Current execution path looks quite complex and probably not that optimized.

I expect specialized count distinct would be faster than two aggregate exec combined

Describe the solution you'd like

Investigate why distinct count accumulator is not called and whether switching to it improves the code.

ClickBench has query like count(distinct), so we could benchmark against it to see if the improvement works

Describe alternatives you've considered

No response

Additional context

No response

[chenkovsky]

take

[jayzhan211]

Another idea is that what if we alter this plan to count distinct specific

From

05)--------AggregateExec: mode=FinalPartitioned, gby=[alias1@0 as alias1], aggr=[]

To

05)--------AggregateExec: mode=Final, gby=[alias1@0 as alias1], aggr=[], count_distinct_specialized=true

And, we return the sum of group key number from each partition, it should be the same result as the output of 02)--AggregateExec: mode=Final, gby=[], aggr=[count(alias1)].

Ideal plan in my mind,

01)ProjectionExec: expr=[count(alias1)@0 as count(DISTINCT t.a)]
02)--------AggregateExec: mode=Final, gby=[alias1@0 as alias1], aggr=[], count_distinct_specialized=true
03)----------CoalesceBatchesExec: target_batch_size=8192
04)------------RepartitionExec: partitioning=Hash([alias1@0], 4), input_partitions=4
05)--------------RepartitionExec: partitioning=RoundRobinBatch(4), input_partitions=1
06)----------------AggregateExec: mode=Partial, gby=[a@0 as alias1], aggr=[]
07)------------------DataSourceExec: partitions=1, partition_sizes=[1]