TheAlgorithms-C-Plus-Plus/math/modular_exponentiation.cpp

/**
 * @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 <iostream> /// for io operations
#include <cassert>  /// for assert

/**
 * @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*a) % c; 
			}
			/// b must be even now 
			b = b>>1;       		/// b = b/2 
			a = (a*a) % c; 
		}
		return ans; 
	}

}  // namespace math 

/**
 * Function for testing power function.
 * test cases and assert statement.
 * @returns `void`
*/
static void test()
{
	int test_case_1 = math::power(2,5,13);
	assert(test_case_1==6);
	std::cout<<"Test 1 Passed!"<<std::endl;
	
	int test_case_2 = math::power(14,7,15);
	assert(test_case_2==14);
	std::cout<<"Test 2 Passed!"<<std::endl;
	
	int test_case_3 = math::power(8,15,41);
	assert(test_case_3==32);
	std::cout<<"Test 3 Passed!"<<std::endl;
	
	int test_case_4 = math::power(27,2,5);
	assert(test_case_4==4);
	std::cout<<"Test 4 Passed!"<<std::endl;
	
	int 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; 
}