#### Double Factorial

R
```def double_factorial_recursive(n: int) -> int:
"""
Compute double factorial using recursive method.
Recursion can be costly for large numbers.

To learn about the theory behind this algorithm:
https://en.wikipedia.org/wiki/Double_factorial

>>> from math import prod
>>> all(double_factorial_recursive(i) == prod(range(i, 0, -2)) for i in range(20))
True
>>> double_factorial_recursive(0.1)
Traceback (most recent call last):
...
ValueError: double_factorial_recursive() only accepts integral values
>>> double_factorial_recursive(-1)
Traceback (most recent call last):
...
ValueError: double_factorial_recursive() not defined for negative values
"""
if not isinstance(n, int):
raise ValueError("double_factorial_recursive() only accepts integral values")
if n < 0:
raise ValueError("double_factorial_recursive() not defined for negative values")
return 1 if n <= 1 else n * double_factorial_recursive(n - 2)

def double_factorial_iterative(num: int) -> int:
"""
Compute double factorial using iterative method.

To learn about the theory behind this algorithm:
https://en.wikipedia.org/wiki/Double_factorial

>>> from math import prod
>>> all(double_factorial_iterative(i) == prod(range(i, 0, -2)) for i in range(20))
True
>>> double_factorial_iterative(0.1)
Traceback (most recent call last):
...
ValueError: double_factorial_iterative() only accepts integral values
>>> double_factorial_iterative(-1)
Traceback (most recent call last):
...
ValueError: double_factorial_iterative() not defined for negative values
"""
if not isinstance(num, int):
raise ValueError("double_factorial_iterative() only accepts integral values")
if num < 0:
raise ValueError("double_factorial_iterative() not defined for negative values")
value = 1
for i in range(num, 0, -2):
value *= i
return value

if __name__ == "__main__":
import doctest

doctest.testmod()
```