[Document] Adding UDF by impl ScalarUDFImpl (apache#9172)

* doc: update scalar udf

* Update docs/source/library-user-guide/adding-udfs.md

Co-authored-by: Andrew Lamb <[email protected]>

* Update docs/source/library-user-guide/adding-udfs.md

Co-authored-by: Andrew Lamb <[email protected]>

* apply suggestions and format

---------

Co-authored-by: Andrew Lamb <[email protected]>

docs/source/library-user-guide/adding-udfs.md

@@ -34,7 +34,87 @@ First we'll talk about adding an Scalar UDF end-to-end, then we'll talk about th
 
 ## Adding a Scalar UDF
 
-A Scalar UDF is a function that takes a row of data and returns a single value. For example, this function takes a single i64 and returns a single i64 with 1 added to it:
+A Scalar UDF is a function that takes a row of data and returns a single value. In order for good performance
+such functions are "vectorized" in DataFusion, meaning they get one or more Arrow Arrays as input and produce
+an Arrow Array with the same number of rows as output.
+
+To create a Scalar UDF, you
+
+1.  Implement the `ScalarUDFImpl` trait to tell DataFusion about your function such as what types of arguments it takes and how to calculate the results.
+2.  Create a `ScalarUDF` and register it with `SessionContext::register_udf` so it can be invoked by name.
+
+In the following example, we will add a function takes a single i64 and returns a single i64 with 1 added to it:
+
+For brevity, we'll skipped some error handling, but e.g. you may want to check that `args.len()` is the expected number of arguments.
+
+### Adding by `impl ScalarUDFImpl`
+
+This a lower level API with more functionality but is more complex, also documented in [`advanced_udf.rs`].
+
+```rust
+use std::any::Any;
+use arrow::datatypes::DataType;
+use datafusion_common::{DataFusionError, plan_err, Result};
+use datafusion_expr::{col, ColumnarValue, Signature, Volatility};
+use datafusion_expr::{ScalarUDFImpl, ScalarUDF};
+
+#[derive(Debug)]
+struct AddOne {
+    signature: Signature
+};
+
+impl AddOne {
+    fn new() -> Self {
+        Self {
+            signature: Signature::uniform(1, vec![DataType::Int32], Volatility::Immutable)
+        }
+    }
+}
+
+/// Implement the ScalarUDFImpl trait for AddOne
+impl ScalarUDFImpl for AddOne {
+    fn as_any(&self) -> &dyn Any { self }
+    fn name(&self) -> &str { "add_one" }
+    fn signature(&self) -> &Signature { &self.signature }
+    fn return_type(&self, args: &[DataType]) -> Result<DataType> {
+      if !matches!(args.get(0), Some(&DataType::Int32)) {
+        return plan_err!("add_one only accepts Int32 arguments");
+      }
+      Ok(DataType::Int32)
+    }
+    // The actual implementation would add one to the argument
+    fn invoke(&self, args: &[ColumnarValue]) -> Result<ColumnarValue> {
+        let args = columnar_values_to_array(args)?;
+        let i64s = as_int64_array(&args[0])?;
+
+        let new_array = i64s
+        .iter()
+        .map(|array_elem| array_elem.map(|value| value + 1))
+        .collect::<Int64Array>();
+        Ok(Arc::new(new_array))
+    }
+}
+```
+
+We now need to register the function with DataFusion so that it can be used in the context of a query.
+
+```rust
+// Create a new ScalarUDF from the implementation
+let add_one = ScalarUDF::from(AddOne::new());
+
+// register the UDF with the context so it can be invoked by name and from SQL
+let mut ctx = SessionContext::new();
+ctx.register_udf(add_one.clone());
+
+// Call the function `add_one(col)`
+let expr = add_one.call(vec![col("a")]);
+```
+
+### Adding a Scalar UDF by [`create_udf`]
+
+There is a an older, more concise, but also more limited API [`create_udf`] available as well
+
+#### Adding a Scalar UDF
 
 ```rust
 use std::sync::Arc;
@@ -58,8 +138,6 @@ pub fn add_one(args: &[ColumnarValue]) -> Result<ArrayRef> {
 }
 ```
 
-For brevity, we'll skipped some error handling, but e.g. you may want to check that `args.len()` is the expected number of arguments.
-
 This "works" in isolation, i.e. if you have a slice of `ArrayRef`s, you can call `add_one` and it will return a new `ArrayRef` with 1 added to each value.
 
 ```rust
@@ -74,11 +152,10 @@ assert_eq!(result, &Int64Array::from(vec![Some(2), None, Some(4)]));
 
 The challenge however is that DataFusion doesn't know about this function. We need to register it with DataFusion so that it can be used in the context of a query.
 
-### Registering a Scalar UDF
+#### Registering a Scalar UDF
 
 To register a Scalar UDF, you need to wrap the function implementation in a [`ScalarUDF`] struct and then register it with the `SessionContext`.
 DataFusion provides the [`create_udf`] and helper functions to make this easier.
-There is a lower level API with more functionality but is more complex, that is documented in [`advanced_udf.rs`].
 
 ```rust
 use datafusion::logical_expr::{Volatility, create_udf};