perf: optimize factorial function performance (#19575)

## Which issue does this PR close?

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- Closes #.

## Rationale for this change
benchmark
```
factorial_array         time:   [778.63 ns 783.03 ns 787.52 ns]
                        change: [−90.314% −90.211% −90.055%] (p = 0.00 < 0.05)
                        Performance has improved.

factorial_scalar        time:   [317.32 ns 319.36 ns 321.41 ns]
                        change: [−28.219% −27.508% −26.683%] (p = 0.00 < 0.05)
                        Performance has improved.
```
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## What changes are included in this PR?
1. factorial implementation from using loop to looking up precomputed
values.
2. using the `try_unary` kernel function on `PrimitiveArray`. (However,
since this isn’t `unary` function, it does not get vectorized execution)

and add benchmark
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## Are these changes tested?
Yes.
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## Are there any user-facing changes?
No.
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Author: getChan

datafusion/functions/Cargo.toml

@@ -299,3 +299,8 @@ required-features = ["unicode_expressions"]
 harness = false
 name = "left"
 required-features = ["unicode_expressions"]
+
+[[bench]]
+harness = false
+name = "factorial"
+required-features = ["math_expressions"]

datafusion/functions/benches/factorial.rs

@@ -0,0 +1,67 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+extern crate criterion;
+
+use arrow::array::Int64Array;
+use arrow::datatypes::{DataType, Field};
+use criterion::{Criterion, criterion_group, criterion_main};
+use datafusion_common::ScalarValue;
+use datafusion_common::config::ConfigOptions;
+use datafusion_expr::ScalarFunctionArgs;
+use datafusion_expr_common::columnar_value::ColumnarValue;
+use datafusion_functions::math::factorial;
+use std::hint::black_box;
+use std::sync::Arc;
+
+fn criterion_benchmark(c: &mut Criterion) {
+    let factorial = factorial();
+    let config_options = Arc::new(ConfigOptions::default());
+
+    let arr_args = vec![ColumnarValue::Array(Arc::new(Int64Array::from_iter(
+        (0..1024).map(|i| Some(i % 21)),
+    )))];
+    c.bench_function(&format!("{}_array", factorial.name()), |b| {
+        b.iter(|| {
+            let args_cloned = arr_args.clone();
+            black_box(factorial.invoke_with_args(ScalarFunctionArgs {
+                args: args_cloned,
+                arg_fields: vec![Field::new("a", DataType::Utf8, true).into()],
+                number_rows: arr_args.len(),
+                return_field: Field::new("f", DataType::Utf8, true).into(),
+                config_options: Arc::clone(&config_options),
+            }))
+        })
+    });
+
+    let scalar_args = vec![ColumnarValue::Scalar(ScalarValue::Int64(Some(20)))];
+    c.bench_function(&format!("{}_scalar", factorial.name()), |b| {
+        b.iter(|| {
+            let args_cloned = scalar_args.clone();
+            black_box(factorial.invoke_with_args(ScalarFunctionArgs {
+                args: args_cloned,
+                arg_fields: vec![Field::new("a", DataType::Utf8, true).into()],
+                number_rows: 1,
+                return_field: Field::new("f", DataType::Utf8, true).into(),
+                config_options: Arc::clone(&config_options),
+            }))
+        })
+    });
+}
+
+criterion_group!(benches, criterion_benchmark);
+criterion_main!(benches);

datafusion/functions/src/math/factorial.rs

@@ -15,18 +15,15 @@
 // specific language governing permissions and limitations
 // under the License.
 
-use arrow::{
-    array::{ArrayRef, Int64Array},
-    error::ArrowError,
-};
+use arrow::array::{ArrayRef, AsArray, Int64Array};
 use std::any::Any;
 use std::sync::Arc;
 
-use arrow::datatypes::DataType;
 use arrow::datatypes::DataType::Int64;
+use arrow::datatypes::{DataType, Int64Type};
 
 use crate::utils::make_scalar_function;
-use datafusion_common::{Result, arrow_datafusion_err, exec_err};
+use datafusion_common::{Result, exec_err};
 use datafusion_expr::{
     ColumnarValue, Documentation, ScalarFunctionArgs, ScalarUDFImpl, Signature,
     Volatility,
@@ -92,50 +89,77 @@ impl ScalarUDFImpl for FactorialFunc {
     }
 }
 
+const FACTORIALS: [i64; 21] = [
+    1,
+    1,
+    2,
+    6,
+    24,
+    120,
+    720,
+    5040,
+    40320,
+    362880,
+    3628800,
+    39916800,
+    479001600,
+    6227020800,
+    87178291200,
+    1307674368000,
+    20922789888000,
+    355687428096000,
+    6402373705728000,
+    121645100408832000,
+    2432902008176640000,
+]; // if return type changes, this constant needs to be updated accordingly
+
 /// Factorial SQL function
 fn factorial(args: &[ArrayRef]) -> Result<ArrayRef> {
     match args[0].data_type() {
         Int64 => {
-            let arg = downcast_named_arg!((&args[0]), "value", Int64Array);
-            Ok(arg
-                .iter()
-                .map(|a| match a {
-                    Some(a) => (2..=a)
-                        .try_fold(1i64, i64::checked_mul)
-                        .ok_or_else(|| {
-                            arrow_datafusion_err!(ArrowError::ComputeError(format!(
-                                "Overflow happened on FACTORIAL({a})"
-                            )))
-                        })
-                        .map(Some),
-                    _ => Ok(None),
-                })
-                .collect::<Result<Int64Array>>()
-                .map(Arc::new)? as ArrayRef)
+            let result: Int64Array =
+                args[0].as_primitive::<Int64Type>().try_unary(|a| {
+                    if a < 0 {
+                        Ok(1)
+                    } else if a < FACTORIALS.len() as i64 {
+                        Ok(FACTORIALS[a as usize])
+                    } else {
+                        exec_err!("Overflow happened on FACTORIAL({a})")
+                    }
+                })?;
+            Ok(Arc::new(result) as ArrayRef)
         }
         other => exec_err!("Unsupported data type {other:?} for function factorial."),
     }
 }
 
 #[cfg(test)]
 mod test {
-
-    use datafusion_common::cast::as_int64_array;
-
     use super::*;
+    use datafusion_common::cast::as_int64_array;
 
     #[test]
     fn test_factorial_i64() {
         let args: Vec<ArrayRef> = vec![
-            Arc::new(Int64Array::from(vec![0, 1, 2, 4])), // input
+            Arc::new(Int64Array::from(vec![0, 1, 2, 4, 20, -1])), // input
         ];
 
         let result = factorial(&args).expect("failed to initialize function factorial");
         let ints =
             as_int64_array(&result).expect("failed to initialize function factorial");
 
-        let expected = Int64Array::from(vec![1, 1, 2, 24]);
+        let expected = Int64Array::from(vec![1, 1, 2, 24, 2432902008176640000, 1]);
 
         assert_eq!(ints, &expected);
     }
+
+    #[test]
+    fn test_overflow() {
+        let args: Vec<ArrayRef> = vec![
+            Arc::new(Int64Array::from(vec![21])), // input
+        ];
+
+        let result = factorial(&args);
+        assert!(result.is_err());
+    }
 }

datafusion/sqllogictest/test_files/math.slt

@@ -795,7 +795,7 @@ select
 39 Decimal128(2, 1)
 
 # factorial overflow
-query error DataFusion error: Arrow error: Compute error: Overflow happened on FACTORIAL\(350943270\)
+query error DataFusion error: Execution error: Overflow happened on FACTORIAL\(350943270\)
 select FACTORIAL(350943270);
 
 statement ok