#### Modular Exponentiation

```/**
* @file
* @brief C++ Program for Modular Exponentiation Iteratively.
* @details The task is to calculate the value of an integer a raised to an
* integer exponent b under modulo c.
* @note The time complexity of this approach is O(log b).
*
* Example:
* (4^3) % 5 (where ^ stands for exponentiation and % for modulo)
* (4*4*4) % 5
* (4 % 5) * ( (4*4) % 5 )
* 4 * (16 % 5)
* 4 * 1
* 4
* We can also verify the result as 4^3 is 64 and 64 modulo 5 is 4
*
* @author [Shri2206](https://github.com/Shri2206)
*/
#include <cassert>   /// for assert
#include <iostream>  /// for io operations

/**
* @namespace math
* @brief Mathematical algorithms
*/
namespace math {
/**
* @brief This function calculates a raised to exponent b under modulo c using
* modular exponentiation.
* @param a integer base
* @param b unsigned integer exponent
* @param c integer modulo
* @return a raised to power b modulo c
*/
uint64_t power(uint64_t a, uint64_t b, uint64_t c) {
uint64_t ans = 1;  /// Initialize the answer to be returned
a = a % c;         /// Update a if it is more than or equal to c
if (a == 0) {
return 0;  /// In case a is divisible by c;
}
while (b > 0) {
/// If b is odd, multiply a with answer
if (b & 1) {
ans = ((ans % c) * (a % c)) % c;
}
/// b must be even now
b = b >> 1;  /// b = b/2
a = ((a % c) * (a % c)) % c;
}
return ans;
}

}  // namespace math

/**
* Function for testing power function.
* test cases and assert statement.
* @returns `void`
*/
static void test() {
uint32_t test_case_1 = math::power(2, 5, 13);
assert(test_case_1 == 6);
std::cout << "Test 1 Passed!" << std::endl;

uint32_t test_case_2 = math::power(14, 7, 15);
assert(test_case_2 == 14);
std::cout << "Test 2 Passed!" << std::endl;

uint64_t test_case_3 = math::power(8, 15, 41);
assert(test_case_3 == 32);
std::cout << "Test 3 Passed!" << std::endl;

uint64_t test_case_4 = math::power(27, 2, 5);
assert(test_case_4 == 4);
std::cout << "Test 4 Passed!" << std::endl;

uint16_t test_case_5 = math::power(7, 3, 6);
assert(test_case_5 == 1);
std::cout << "Test 5 Passed!" << std::endl;
}

/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test();  // execute the tests
return 0;
}
```  