perf: Optimize approx count distinct using bitmaps instead of HLL for smaller int datatypes (#21453)

## Which issue does this PR close?

<!--
We generally require a GitHub issue to be filed for all bug fixes and
enhancements and this helps us generate change logs for our releases.
You can link an issue to this PR using the GitHub syntax. For example
`Closes #123` indicates that this PR will close issue #123.
-->

- Closes #1109 

## Rationale for this change

<!--
Why are you proposing this change? If this is already explained clearly
in the issue then this section is not needed.
Explaining clearly why changes are proposed helps reviewers understand
your changes and offer better suggestions for fixes.
-->

## What changes are included in this PR?

<!--
There is no need to duplicate the description in the issue here but it
is sometimes worth providing a summary of the individual changes in this
PR.
-->

## Are these changes tested?

<!--
We typically require tests for all PRs in order to:
1. Prevent the code from being accidentally broken by subsequent changes
2. Serve as another way to document the expected behavior of the code

If tests are not included in your PR, please explain why (for example,
are they covered by existing tests)?
-->

## Are there any user-facing changes?

<!--
If there are user-facing changes then we may require documentation to be
updated before approving the PR.
-->

<!--
If there are any breaking changes to public APIs, please add the `api
change` label.
-->

Author: coderfender

datafusion/functions-aggregate/src/approx_distinct.rs

@@ -23,11 +23,10 @@ use arrow::array::{
     GenericBinaryArray, GenericStringArray, OffsetSizeTrait, PrimitiveArray,
 };
 use arrow::datatypes::{
-    ArrowPrimitiveType, Date32Type, Date64Type, FieldRef, Int8Type, Int16Type, Int32Type,
-    Int64Type, Time32MillisecondType, Time32SecondType, Time64MicrosecondType,
-    Time64NanosecondType, TimeUnit, TimestampMicrosecondType, TimestampMillisecondType,
-    TimestampNanosecondType, TimestampSecondType, UInt8Type, UInt16Type, UInt32Type,
-    UInt64Type,
+    ArrowPrimitiveType, Date32Type, Date64Type, FieldRef, Int32Type, Int64Type,
+    Time32MillisecondType, Time32SecondType, Time64MicrosecondType, Time64NanosecondType,
+    TimeUnit, TimestampMicrosecondType, TimestampMillisecondType,
+    TimestampNanosecondType, TimestampSecondType, UInt32Type, UInt64Type,
 };
 use arrow::{array::ArrayRef, datatypes::DataType, datatypes::Field};
 use datafusion_common::ScalarValue;
@@ -40,6 +39,10 @@ use datafusion_expr::utils::format_state_name;
 use datafusion_expr::{
     Accumulator, AggregateUDFImpl, Documentation, Signature, Volatility,
 };
+use datafusion_functions_aggregate_common::aggregate::count_distinct::{
+    Bitmap65536DistinctCountAccumulator, Bitmap65536DistinctCountAccumulatorI16,
+    BoolArray256DistinctCountAccumulator, BoolArray256DistinctCountAccumulatorI8,
+};
 use datafusion_functions_aggregate_common::noop_accumulator::NoopAccumulator;
 use datafusion_macros::user_doc;
 use std::fmt::{Debug, Formatter};
@@ -84,6 +87,36 @@ impl<T: Hash + ?Sized> TryFrom<&ScalarValue> for HyperLogLog<T> {
     }
 }
 
+#[derive(Debug)]
+struct ApproxDistinctBitmapWrapper<A: Accumulator> {
+    inner: A,
+}
+
+impl<A: Accumulator> Accumulator for ApproxDistinctBitmapWrapper<A> {
+    fn update_batch(&mut self, values: &[ArrayRef]) -> Result<()> {
+        self.inner.update_batch(values)
+    }
+
+    fn evaluate(&mut self) -> Result<ScalarValue> {
+        match self.inner.evaluate()? {
+            ScalarValue::Int64(Some(v)) => Ok(ScalarValue::UInt64(Some(v as u64))),
+            other => internal_err!("unexpected: {other}"),
+        }
+    }
+
+    fn size(&self) -> usize {
+        self.inner.size()
+    }
+
+    fn state(&mut self) -> Result<Vec<ScalarValue>> {
+        self.inner.state()
+    }
+
+    fn merge_batch(&mut self, states: &[ArrayRef]) -> Result<()> {
+        self.inner.merge_batch(states)
+    }
+}
+
 #[derive(Debug)]
 struct NumericHLLAccumulator<T>
 where
@@ -302,6 +335,39 @@ impl ApproxDistinct {
     }
 }
 
+#[cold]
+fn get_small_int_approx_accumulator(
+    data_type: &DataType,
+) -> Result<Box<dyn Accumulator>> {
+    match data_type {
+        DataType::UInt8 => Ok(Box::new(ApproxDistinctBitmapWrapper {
+            inner: BoolArray256DistinctCountAccumulator::new(),
+        })),
+        DataType::Int8 => Ok(Box::new(ApproxDistinctBitmapWrapper {
+            inner: BoolArray256DistinctCountAccumulatorI8::new(),
+        })),
+        DataType::UInt16 => Ok(Box::new(ApproxDistinctBitmapWrapper {
+            inner: Bitmap65536DistinctCountAccumulator::new(),
+        })),
+        DataType::Int16 => Ok(Box::new(ApproxDistinctBitmapWrapper {
+            inner: Bitmap65536DistinctCountAccumulatorI16::new(),
+        })),
+        _ => internal_err!("unsupported small int type: {}", data_type),
+    }
+}
+
+#[cold]
+fn get_small_int_state_field(name: &str, data_type: &DataType) -> Result<Vec<FieldRef>> {
+    Ok(vec![
+        Field::new_list(
+            format_state_name(name, "approx_distinct"),
+            Field::new_list_field(data_type.clone(), true),
+            false,
+        )
+        .into(),
+    ])
+}
+
 impl AggregateUDFImpl for ApproxDistinct {
     fn name(&self) -> &str {
         "approx_distinct"
@@ -316,40 +382,39 @@ impl AggregateUDFImpl for ApproxDistinct {
     }
 
     fn state_fields(&self, args: StateFieldsArgs) -> Result<Vec<FieldRef>> {
-        if args.input_fields[0].data_type().is_null() {
-            Ok(vec![
+        let data_type = args.input_fields[0].data_type();
+        match data_type {
+            DataType::Null => Ok(vec![
                 Field::new(
                     format_state_name(args.name, self.name()),
                     DataType::Null,
                     true,
                 )
                 .into(),
-            ])
-        } else {
-            Ok(vec![
+            ]),
+            DataType::UInt8 | DataType::Int8 | DataType::UInt16 | DataType::Int16 => {
+                get_small_int_state_field(args.name, data_type)
+            }
+            _ => Ok(vec![
                 Field::new(
                     format_state_name(args.name, "hll_registers"),
                     DataType::Binary,
                     false,
                 )
                 .into(),
-            ])
+            ]),
         }
     }
 
     fn accumulator(&self, acc_args: AccumulatorArgs) -> Result<Box<dyn Accumulator>> {
         let data_type = acc_args.expr_fields[0].data_type();
 
         let accumulator: Box<dyn Accumulator> = match data_type {
-            // TODO u8, i8, u16, i16 shall really be done using bitmap, not HLL
-            // TODO support for boolean (trivial case)
-            // https://github.com/apache/datafusion/issues/1109
-            DataType::UInt8 => Box::new(NumericHLLAccumulator::<UInt8Type>::new()),
-            DataType::UInt16 => Box::new(NumericHLLAccumulator::<UInt16Type>::new()),
+            DataType::UInt8 | DataType::Int8 | DataType::UInt16 | DataType::Int16 => {
+                return get_small_int_approx_accumulator(data_type);
+            }
             DataType::UInt32 => Box::new(NumericHLLAccumulator::<UInt32Type>::new()),
             DataType::UInt64 => Box::new(NumericHLLAccumulator::<UInt64Type>::new()),
-            DataType::Int8 => Box::new(NumericHLLAccumulator::<Int8Type>::new()),
-            DataType::Int16 => Box::new(NumericHLLAccumulator::<Int16Type>::new()),
             DataType::Int32 => Box::new(NumericHLLAccumulator::<Int32Type>::new()),
             DataType::Int64 => Box::new(NumericHLLAccumulator::<Int64Type>::new()),
             DataType::Date32 => Box::new(NumericHLLAccumulator::<Date32Type>::new()),