1515# specific language governing permissions and limitations
1616# under the License.
1717
18- from collections .abc import Callable , Iterable , Sequence , Mapping
18+ from collections .abc import Callable , Hashable , Iterable , Sequence , Mapping
1919from typing import Literal , TypeAlias , TypeVar , Any , ParamSpec
2020
2121import numpy as np
@@ -654,7 +654,7 @@ def round(
654654def round_to_multiple (
655655 x : _NumericScalarT | _NumericArrayT | list | Expression ,
656656 / ,
657- multiple : int = 0 ,
657+ multiple : int | float | NumericScalar = 1. 0 ,
658658 round_mode : Literal [
659659 "down" ,
660660 "up" ,
@@ -1521,7 +1521,7 @@ def local_timestamp(
15211521def random (
15221522 n : int ,
15231523 * ,
1524- initializer : Literal [ "system" ] | int = "system" ,
1524+ initializer : Hashable = "system" ,
15251525 options : RandomOptions | None = None ,
15261526 memory_pool : lib .MemoryPool | None = None ,
15271527) -> lib .DoubleArray : ...
@@ -1533,7 +1533,7 @@ def random(
15331533def cumulative_sum (
15341534 values : _NumericArrayT | ArrayLike | Expression ,
15351535 / ,
1536- start : lib .Scalar | None = None ,
1536+ start : int | float | lib .Scalar | None = None ,
15371537 * ,
15381538 skip_nulls : bool = False ,
15391539 options : CumulativeSumOptions | None = None ,
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