feat: Addressed comments for adding modular division algorithm

math/modular_division.cpp

@@ -1,7 +1,7 @@
 /**
  * @file
- * @brief Division of two numbers under modulo
+ * @brief An algorithm to divide two numbers under modulo p [Modular 
- *
+ * Division](https://www.geeksforgeeks.org/modular-division)
  * @details To calculate division of two numbers under modulo p
  * Modulo operator is not distributive under division, therefore
  * we first have to calculate the inverse of divisor using
@@ -15,64 +15,67 @@
  * NOTE: For the existence of inverse of 'b', 'b' and 'p' must be coprime
  * For simplicity we take p as prime
  * Time Complexity: O(log(b))
- *
  * Example: ( 24 / 3 ) % 5 => 8 % 5 = 3 --- (i)
             Now the inverse of 3 is 2
             (24 * 2) % 5 = (24 % 5) * (2 % 5) = (4 * 2) % 5 = 3 --- (ii)
             (i) and (ii) are equal hence the answer is correct.
-
- *
  * @see modular_inverse_fermat_little_theorem.cpp, modular_exponentiation.cpp
- *
  * @author [Shubham Yadav](https://github.com/shubhamamsa)
  */
 
-#include <cassert>
+#include <cassert>   /// for assert
-#include <iostream>
+#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
+   * @namespace modular_division
-   * modular exponentiation.
+   * @brief Functions for Modular Division implementation
-   * @param a integer base
-   * @param b unsigned integer exponent
-   * @param c integer modulo
-   * @return a raised to power b modulo c
    */
-  int power(int a, int b, int c) {
+  namespace modular_division {
-      int ans = 1;  /// Initialize the answer to be returned
+    /**
-      a = a % c;         /// Update a if it is more than or equal to c
+     * @brief This function calculates a raised to exponent b under modulo c using
-      if (a == 0) {
+     * modular exponentiation.
-          return 0;  /// In case a is divisible by c;
+     * @param a integer base
-      }
+     * @param b unsigned integer exponent
-      while (b > 0) {
+     * @param c integer modulo
-          /// If b is odd, multiply a with answer
+     * @return a raised to power b modulo c
-          if (b & 1) {
+     */
-              ans = ((ans % c) * (a % c)) % c;
+    uint64_t power(uint64_t a, uint64_t b, uint64_t c) {
-          }
+        uint64_t ans = 1;  /// Initialize the answer to be returned
-          /// b must be even now
+        a = a % c;         /// Update a if it is more than or equal to c
-          b = b >> 1;  /// b = b/2
+        if (a == 0) {
-          a = ((a % c) * (a % c)) % c;
+            return 0;  /// In case a is divisible by c;
-      }
+        }
-      return ans;
+        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;
+    }
 
-  /**
+    /**
-   * @brief This function calculates modular division
+     * @brief This function calculates modular division
-   * @param a integer dividend
+     * @param a integer dividend
-   * @param b integer divisor
+     * @param b integer divisor
-   * @param p integer modulo
+     * @param p integer modulo
-   * @return a/b modulo c
+     * @return a/b modulo c
-   */
+     */
-  int mod_division(int a, int b, int p)	{
+    uint64_t mod_division(uint64_t a, uint64_t b, uint64_t p)	{
-      int inverse = power(b, p-2, p)%p;  /// Calculate the inverse of b
+        uint64_t inverse = power(b, p-2, p)%p;  /// Calculate the inverse of b
-      int result = ((a%p)*(inverse%p))%p;   /// Calculate the final result
+        uint64_t result = ((a%p)*(inverse%p))%p;   /// Calculate the final result
-      return result;
+        return result;
-  }
+    }
-}
+  } // namespace modular_division
+}   // namespace math
 
 /**
  * Function for testing power function.
@@ -80,19 +83,19 @@ namespace math {
  * @returns `void`
  */
 static void test() {
-    int test_case_1 = math::mod_division(8, 2, 2);
+    uint64_t test_case_1 = math::modular_division::mod_division(8, 2, 2);
     assert(test_case_1 == 0);
     std::cout << "Test 1 Passed!" << std::endl;
-    int test_case_2 = math::mod_division(15, 3, 7);
+    uint64_t test_case_2 = math::modular_division::mod_division(15, 3, 7);
     assert(test_case_2 == 5);
     std::cout << "Test 2 Passed!" << std::endl;
-    int test_case_3 = math::mod_division(10, 5, 2);
+    uint64_t test_case_3 = math::modular_division::mod_division(10, 5, 2);
     assert(test_case_3 == 0);
     std::cout << "Test 3 Passed!" << std::endl;
-    int test_case_4 = math::mod_division(81, 3, 5);
+    uint64_t test_case_4 = math::modular_division::mod_division(81, 3, 5);
     assert(test_case_4 == 2);
     std::cout << "Test 4 Passed!" << std::endl;
-    int test_case_5 = math::mod_division(12848, 73, 29);
+    uint64_t test_case_5 = math::modular_division::mod_division(12848, 73, 29);
     assert(test_case_5 == 2);
     std::cout << "Test 5 Passed!" << std::endl;
 }