fixing factorial negative values (#22278)

## Which issue does this PR close?

- Closes #22270

## Rationale for this change

PostgreSQL returns a domain error for `factorial` on negative inputs
(`ERROR: factorial of a negative number is undefined`). DataFusion
incorrectly returned `1` for negative values (e.g. `factorial(-1)`),
which breaks PostgreSQL-aligned SQL semantics and can silently produce
wrong results.

## What changes are included in this PR?

- **`factorial` (core / `datafusion-functions`):** Negative arguments
now fail with an execution error and message aligned with PostgreSQL:
`factorial of a negative number is undefined`, instead of returning `1`.
- **Documentation:** Updated the `#[user_doc]` description so it matches
behavior (non-negative inputs; error on negative values and on
overflow).
- **Tests:** Added a sqllogictest in `math.slt` that expects this error
for `factorial(-1)`.

**Note:** Spark’s `factorial` in `datafusion-spark` is unchanged
(PySpark-style nulls for out-of-domain values).

## Are these changes tested?

Yes. A sqllogictest was added in
`datafusion/sqllogictest/test_files/math.slt` for `SELECT
factorial(-1)`.

## Are there any user-facing changes?

Yes. `factorial` with a negative argument now errors at execution time
instead of returning `1`. This matches PostgreSQL and fixes incorrect
results; callers that relied on the old behavior would need to adjust.

No public Rust API breakage in exported types; behavior change is
SQL/UDF semantics for negative inputs.

---------

Co-authored-by: Raushan Prabhakar <ros@Raushans-MacBook-Air.local>
Co-authored-by: Kumar Ujjawal <ujjawalpathak6@gmail.com>

Author: 3 people

datafusion/functions/src/math/factorial.rs

@@ -32,7 +32,7 @@ use datafusion_macros::user_doc;
 
 #[user_doc(
     doc_section(label = "Math Functions"),
-    description = "Factorial. Returns 1 if value is less than 2.",
+    description = "Factorial of a non-negative integer. Errors if the argument is negative or the result overflows.",
     syntax_example = "factorial(numeric_expression)",
     sql_example = r#"```sql
 > SELECT factorial(5);
@@ -143,7 +143,7 @@ const FACTORIALS: [i64; 21] = [
 
 fn compute_factorial(n: i64) -> Result<i64> {
     if n < 0 {
-        Ok(1)
+        exec_err!("factorial of a negative number is undefined")
     } else if n < FACTORIALS.len() as i64 {
         Ok(FACTORIALS[n as usize])
     } else {

datafusion/sqllogictest/test_files/math.slt

@@ -826,6 +826,10 @@ select
 ----
 39 Decimal128(2, 1)
 
+# factorial negative (PostgreSQL-compatible domain error)
+query error DataFusion error: Execution error: factorial of a negative number is undefined
+select factorial(-1);
+
 # factorial overflow
 query error DataFusion error: Execution error: Overflow happened on FACTORIAL\(350943270\)
 select FACTORIAL(350943270);

docs/source/user-guide/sql/scalar_functions.md

@@ -420,7 +420,7 @@ exp(numeric_expression)
 
 ### `factorial`
 
-Factorial. Returns 1 if value is less than 2.
+Factorial of a non-negative integer. Errors if the argument is negative or the result overflows.
 
 ```sql
 factorial(numeric_expression)