feat: add cumulative_prod specification

PR-URL: #793
Closes: #598

Author: kgryte

Diff for: spec/draft/API_specification/statistical_functions.rst

@@ -18,6 +18,7 @@ Objects in API
    :toctree: generated
    :template: method.rst
 
+   cumulative_prod
    cumulative_sum
    max
    mean

Diff for: src/array_api_stubs/_draft/statistical_functions.py

@@ -1,9 +1,71 @@
-__all__ = ["cumulative_sum", "max", "mean", "min", "prod", "std", "sum", "var"]
+__all__ = [
+    "cumulative_sum",
+    "cumulative_prod",
+    "max",
+    "mean",
+    "min",
+    "prod",
+    "std",
+    "sum",
+    "var",
+]
 
 
 from ._types import Optional, Tuple, Union, array, dtype
 
 
+def cumulative_prod(
+    x: array,
+    /,
+    *,
+    axis: Optional[int] = None,
+    dtype: Optional[dtype] = None,
+    include_initial: bool = False,
+) -> array:
+    """
+    Calculates the cumulative product of elements in the input array ``x``.
+
+    Parameters
+    ----------
+    x: array
+        input array. Should have one or more dimensions (axes). Should have a numeric data type.
+    axis: Optional[int]
+        axis along which a cumulative product must be computed. If ``axis`` is negative, the function must determine the axis along which to compute a cumulative product by counting from the last dimension.
+
+        If ``x`` is a one-dimensional array, providing an ``axis`` is optional; however, if ``x`` has more than one dimension, providing an ``axis`` is required.
+
+    dtype: Optional[dtype]
+        data type of the returned array. If ``None``, the returned array must have the same data type as ``x``, unless ``x`` has an integer data type supporting a smaller range of values than the default integer data type (e.g., ``x`` has an ``int16`` or ``uint32`` data type and the default integer data type is ``int64``). In those latter cases:
+
+        -   if ``x`` has a signed integer data type (e.g., ``int16``), the returned array must have the default integer data type.
+        -   if ``x`` has an unsigned integer data type (e.g., ``uint16``), the returned array must have an unsigned integer data type having the same number of bits as the default integer data type (e.g., if the default integer data type is ``int32``, the returned array must have a ``uint32`` data type).
+
+        If the data type (either specified or resolved) differs from the data type of ``x``, the input array should be cast to the specified data type before computing the product (rationale: the ``dtype`` keyword argument is intended to help prevent overflows). Default: ``None``.
+
+    include_initial: bool
+        boolean indicating whether to include the initial value as the first value in the output. By convention, the initial value must be the multiplicative identity (i.e., one). Default: ``False``.
+
+    Returns
+    -------
+    out: array
+        an array containing the cumulative products. The returned array must have a data type as described by the ``dtype`` parameter above.
+
+        Let ``N`` be the size of the axis along which to compute the cumulative product. The returned array must have a shape determined according to the following rules:
+
+        -   if ``include_initial`` is ``True``, the returned array must have the same shape as ``x``, except the size of the axis along which to compute the cumulative product must be ``N+1``.
+        -   if ``include_initial`` is ``False``, the returned array must have the same shape as ``x``.
+
+    Notes
+    -----
+
+    -   When ``x`` is a zero-dimensional array, behavior is unspecified and thus implementation-defined.
+
+    **Special Cases**
+
+    For both real-valued and complex floating-point operands, special cases must be handled as if the operation is implemented by successive application of :func:`~array_api.multiply`.
+    """
+
+
 def cumulative_sum(
     x: array,
     /,