## C++, math, double_factorial.cpp

``````/**
* @file
* @brief Compute [double
* factorial](https://en.wikipedia.org/wiki/Double_factorial): \f\$n!!\f\$
*
* Double factorial of a non-negative integer `n`, is defined as the product of
* all the integers from 1 to n that have the same parity (odd or even) as n.
* <br/>It is also called as semifactorial of a number and is denoted by
* \f\$n!!\f\$
*/

#include <cassert>
#include <iostream>

/** Compute double factorial using iterative method
*/
uint64_t double_factorial_iterative(uint64_t n) {
uint64_t res = 1;
for (uint64_t i = n;; i -= 2) {
if (i == 0 || i == 1)
return res;
res *= i;
}
return res;
}

/** Compute double factorial using resursive method.
* <br/>Recursion can be costly for large numbers.
*/
uint64_t double_factorial_recursive(uint64_t n) {
if (n <= 1)
return 1;
return n * double_factorial_recursive(n - 2);
}

/** Wrapper to run tests using both recursive and iterative implementations.
* The checks are only valid in debug builds due to the use of `assert()`
* statements.
* \param [in] n number to check double factorial for
* \param [in] expected expected result
*/
void test(uint64_t n, uint64_t expected) {
assert(double_factorial_iterative(n) == expected);
assert(double_factorial_recursive(n) == expected);
}

/**
* Test implementations
*/
void tests() {
std::cout << "Test 1:\t n=5\t...";
test(5, 15);
std::cout << "passed\n";

std::cout << "Test 2:\t n=15\t...";
test(15, 2027025);
std::cout << "passed\n";

std::cout << "Test 3:\t n=0\t...";
test(0, 1);
std::cout << "passed\n";
}

/**
* Main function
*/
int main() {
tests();
return 0;
}
``````