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fix factorial(21) should not overflow when PostgreSQL returns a numeric answer #22306

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fix factorial(21) should not overflow when PostgreSQL returns a numeric answer #22306

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54e540c
fix factorial(21) should not overflow when PostgreSQL returns a numer…
xiedeyantu May 27, 2026
6fe8e83
fix
xiedeyantu May 30, 2026
9c9227a
fmt
xiedeyantu May 31, 2026
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159 changes: 121 additions & 38 deletions datafusion/functions/src/math/factorial.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -15,11 +15,12 @@
// specific language governing permissions and limitations
// under the License.

use arrow::array::{ArrayRef, AsArray, Int64Array};
use arrow::array::{ArrayRef, AsArray};
use std::sync::Arc;

use arrow::datatypes::DataType::Int64;
use arrow::datatypes::{DataType, Int64Type};
use arrow::datatypes::DataType::{Decimal256, Int64};
use arrow::datatypes::{DECIMAL256_MAX_PRECISION, DataType, Decimal256Type, Int64Type};
use arrow_buffer::i256;

use datafusion_common::{
Result, ScalarValue, exec_err, internal_err, utils::take_function_args,
Expand Down Expand Up @@ -63,6 +64,8 @@ impl FactorialFunc {
}
}

const FACTORIAL_RETURN_TYPE: DataType = Decimal256(DECIMAL256_MAX_PRECISION, 0);

impl ScalarUDFImpl for FactorialFunc {
fn name(&self) -> &str {
"factorial"
Expand All @@ -73,7 +76,7 @@ impl ScalarUDFImpl for FactorialFunc {
}

fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
Ok(Int64)
Ok(FACTORIAL_RETURN_TYPE)
}

fn invoke_with_args(&self, args: ScalarFunctionArgs) -> Result<ColumnarValue> {
Expand All @@ -82,13 +85,21 @@ impl ScalarUDFImpl for FactorialFunc {
match arg {
ColumnarValue::Scalar(scalar) => {
if scalar.is_null() {
return Ok(ColumnarValue::Scalar(ScalarValue::Int64(None)));
return Ok(ColumnarValue::Scalar(ScalarValue::Decimal256(
None,
DECIMAL256_MAX_PRECISION,
0,
)));
}

match scalar {
ScalarValue::Int64(Some(v)) => {
let result = compute_factorial(v)?;
Ok(ColumnarValue::Scalar(ScalarValue::Int64(Some(result))))
Ok(ColumnarValue::Scalar(ScalarValue::Decimal256(
Some(result),
DECIMAL256_MAX_PRECISION,
0,
)))
}
_ => {
internal_err!(
Expand All @@ -100,9 +111,10 @@ impl ScalarUDFImpl for FactorialFunc {
}
ColumnarValue::Array(array) => match array.data_type() {
Int64 => {
let result: Int64Array = array
let result = array
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@Jefffrey Jefffrey May 29, 2026

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we can keep the try_unary which should be much simpler, e.g.

                    let result = array
                        .as_primitive::<Int64Type>()
                        .try_unary::<_, Decimal256Type, _>(compute_factorial)?
                        .with_precision_and_scale(DECIMAL256_MAX_PRECISION, 0)?;
                    Ok(ColumnarValue::Array(Arc::new(result) as ArrayRef))

.as_primitive::<Int64Type>()
.try_unary(compute_factorial)?;
.try_unary::<_, Decimal256Type, _>(compute_factorial)?
.with_precision_and_scale(DECIMAL256_MAX_PRECISION, 0)?;
Ok(ColumnarValue::Array(Arc::new(result) as ArrayRef))
}
other => {
Expand All @@ -117,36 +129,107 @@ 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

fn compute_factorial(n: i64) -> Result<i64> {
const FACTORIALS: [i256; 57] = [
i256::from_parts(1, 0),
i256::from_parts(1, 0),
i256::from_parts(2, 0),
i256::from_parts(6, 0),
i256::from_parts(24, 0),
i256::from_parts(120, 0),
i256::from_parts(720, 0),
i256::from_parts(5040, 0),
i256::from_parts(40320, 0),
i256::from_parts(362880, 0),
i256::from_parts(3628800, 0),
i256::from_parts(39916800, 0),
i256::from_parts(479001600, 0),
i256::from_parts(6227020800, 0),
i256::from_parts(87178291200, 0),
i256::from_parts(1307674368000, 0),
i256::from_parts(20922789888000, 0),
i256::from_parts(355687428096000, 0),
i256::from_parts(6402373705728000, 0),
i256::from_parts(121645100408832000, 0),
i256::from_parts(2432902008176640000, 0),
i256::from_parts(51090942171709440000, 0),
i256::from_parts(1124000727777607680000, 0),
i256::from_parts(25852016738884976640000, 0),
i256::from_parts(620448401733239439360000, 0),
i256::from_parts(15511210043330985984000000, 0),
i256::from_parts(403291461126605635584000000, 0),
i256::from_parts(10888869450418352160768000000, 0),
i256::from_parts(304888344611713860501504000000, 0),
i256::from_parts(8841761993739701954543616000000, 0),
i256::from_parts(265252859812191058636308480000000, 0),
i256::from_parts(8222838654177922817725562880000000, 0),
i256::from_parts(263130836933693530167218012160000000, 0),
i256::from_parts(8683317618811886495518194401280000000, 0),
i256::from_parts(295232799039604140847618609643520000000, 0),
i256::from_parts(124676958757991025765413114570153656320, 30),
i256::from_parts(64699745315476902531002227912544878592, 1093),
i256::from_parts(11914008226076149403460180741783027712, 40448),
i256::from_parts(112449945669955213868112260755986841600, 1537025),
i256::from_parts(302159478076991779295882880302268284928, 59943987),
i256::from_parts(176496280846824950617203951978843996160, 2397759515),
i256::from_parts(90417809380115242574495275065471401984, 98308140136),
i256::from_parts(54441957834517090031680871000348557312, 4128941885723),
i256::from_parts(299309985358604090582029808424378695680, 177544501086095),
i256::from_parts(238909412782918374001076488265470574592, 7811958047788218),
i256::from_parts(202170200682234462683829141561361301504, 351538112150469841),
i256::from_parts(
112205324517446769945026111164878159872,
16170753158921612713,
),
i256::from_parts(
169414748505921235465608113272750342144,
760025398469315797526,
),
i256::from_parts(
305413489102634642691573466161347559424,
36481219126527158281271,
),
i256::from_parts(
333119188428743562961991722339997319168,
1787579737199830755782322,
),
i256::from_parts(
322405809232131901857604960274991808512,
89378986859991537789116148,
),
i256::from_parts(
109142658633680748495871817299708084224,
4558328329859568427244923596,
),
i256::from_parts(
230900378216383506371340780676528996352,
237033073152697558216736027008,
),
i256::from_parts(
327837203235479616462950115744149405696,
12562752877092970585487009431459,
),
i256::from_parts(
8525894827099188903826663732120911872,
678388655363020411616298509298838,
),
i256::from_parts(
128641848569516926247091897834881941504,
37311376044966122638896418011436091,
),
i256::from_parts(
58013814553240137106279522686256283648,
2089437058518102867778199408640421117,
),
];

fn compute_factorial(n: i64) -> Result<i256> {
if n < 0 {
exec_err!("factorial of a negative number is undefined")
} else if n < FACTORIALS.len() as i64 {
Ok(FACTORIALS[n as usize])
} else {
exec_err!("Overflow happened on FACTORIAL({n})")
return exec_err!("factorial of a negative number is undefined");
}

if let Some(value) = FACTORIALS.get(n as usize) {
return Ok(*value);
}

exec_err!("Overflow happened on FACTORIAL({n})")
}
24 changes: 21 additions & 3 deletions datafusion/sqllogictest/test_files/scalar.slt
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Original file line number Diff line number Diff line change
Expand Up @@ -461,19 +461,37 @@ select round(exp(a), 5), round(exp(e), 5), round(exp(f), 5) from signed_integers
## factorial

# factorial scalar function
query III rowsort
query RRR rowsort
select factorial(0), factorial(10), factorial(15);
----
1 3628800 1307674368000

query TR
select arrow_typeof(factorial(21)), factorial(21);
----
Decimal256(76, 0) 51090942171709440000

query R
select factorial(21);
----
51090942171709440000

query TR
select arrow_typeof(factorial(56)), factorial(56);
----
Decimal256(76, 0) 710998587804863451854045647463724949736497978881168458687447040000000000000

query error DataFusion error: Execution error: Overflow happened on FACTORIAL\(57\)
select factorial(57);

# factorial scalar nulls
query I rowsort
query R rowsort
select factorial(null);
----
NULL

# factorial with columns
query III rowsort
query RRR rowsort
select factorial(a), factorial(e), factorial(f) from unsigned_integers;
----
1 24 3628800
Expand Down
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