fix:fit binary-exponent.cpp to guidelines

math/binary_exponent.cpp

@@ -2,6 +2,7 @@
  * @file
  * @brief C++ Program to find Binary Exponent Iteratively and Recursively.
  *
+ * @details
  * Calculate \f$a^b\f$ in \f$O(\log(b))\f$ by converting \f$b\f$ to a
  * binary number. Binary exponentiation is also known as exponentiation by
  * squaring.
@@ -19,53 +20,117 @@
  * \f}
  * Hence to calculate 2^10 we only need to multiply \f$2^8\f$ and \f$2^2\f$
  * skipping \f$2^1\f$ and \f$2^4\f$.
+ *
+ * @author [Mann Mehta](https://github.com/mann2108)
+ * @author [ewd00010](https://github.com/ewd00010)
  */
 
-#include <iostream>
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
 
-/// Recursive function to calculate exponent in \f$O(\log(n))\f$ using binary
-/// exponent.
-int binExpo(int a, int b) {
-    if (b == 0) {
+/**
+ * @brief Mathematical algorithms
+ * @namespace
+ */
+namespace math {
+/**
+ * @brief Recursive function to calculate exponent in \f$O(\log(n))\f$ using
+ * binary exponent.
+ * @param a base number
+ * @param b exponent number
+ * @return 1 if the exponent number is 0 the return value will always be 1
+ * @return (res * res * a) if modulo 2 of exponential is 0
+ * @return (res * res) if modulo 2 of exponential is 1
+ */
+int64_t binExpo_recursive(int64_t a, uint64_t b) {
+    /*!
+     * Provided that b != 0, this function recursively calls itself, until an
+     * instance of it returns 1 (which eventually occurs due to b/2 for each
+     * call to binExpo). This triggers a chain reaction eventually leading
+     * back to the original call to binExpo returning. This works like a
+     * building a russian doll, first figure out however dolls you want to use (
+     * say, until a call to binExpo returns 1 ) and then assemble the dolls (
+     * with each return, res gets exponentially bigger )
+     */
+    if (b == 0 || a == 1) {
         return 1;
+    } else if(b == 1 || a == 0){
+        return a;
     }
-    int res = binExpo(a, b / 2);
+
+    int64_t res = binExpo_recursive(a, b / 2);
     if (b % 2) {
         return res * res * a;
     } else {
         return res * res;
     }
 }
 
-/// Iterative function to calculate exponent in \f$O(\log(n))\f$ using binary
-/// exponent.
-int binExpo_alt(int a, int b) {
-    int res = 1;
-    while (b > 0) {
+/**
+ * @brief Iterative function to calculate exponent in \f$O(\log(n))\f$ using
+ * binary
+ + exponent.
+ * @param a base number
+ * @param b exponential number
+ * @return res if the exponential number is >= 0
+ */
+int64_t binExpo_iterative(int64_t a, uint64_t b) {
+    /*!
+     * Provided b > 0, this function iteratively multiples the value res. Each
+     * iteration of the while loop, checks if the exponential number is binary,
+     * if so res is multiplied by the current value of a, for that iteration.
+     * Additionally, a is multiplied by itself and b is halved by itself.
+     */
+    if (b == 0 || a == 1) {
+        return 1;
+    } else if(b == 1 || a == 0){
+        return a;
+    }
+
+    int64_t res = 1;
+    while (b > 0) {  // if b is not a valid exponent
         if (b % 2) {
             res = res * a;
         }
         a = a * a;
-        b /= 2;
+        b >>= 1;
     }
     return res;
 }
+}  // namespace math
 
-/// Main function
-int main() {
-    int a, b;
-    /// Give two numbers a, b
-    std::cin >> a >> b;
-    if (a == 0 && b == 0) {
-        std::cout << "Math error" << std::endl;
-    } else if (b < 0) {
-        std::cout << "Exponent must be positive !!" << std::endl;
-    } else {
-        int resRecurse = binExpo(a, b);
-        /// int resIterate = binExpo_alt(a, b);
+/**
+ * @brief Self-test implementation
+ * @returns void
+ */
+static void tests() {
+    assert(math::binExpo_recursive(0, 1) == 0);
+    assert(math::binExpo_recursive(1, 0) == 1);
+    assert(math::binExpo_recursive(746584, 0) == 1);
+    assert(math::binExpo_recursive(1, 1) == 1);
+    assert(math::binExpo_recursive(2938374, 1) == 2938374);
+    assert(math::binExpo_recursive(3, 7) == 2187);
+    assert(math::binExpo_recursive(-31, 5) == -28629151);
+    assert(math::binExpo_recursive(0, 0) == 1);
+    assert(math::binExpo_recursive(1, 20) == 1);
 
-        /// Result of a^b (where '^' denotes exponentiation)
-        std::cout << resRecurse << std::endl;
-        /// std::cout << resIterate << std::endl;
-    }
+    assert(math::binExpo_iterative(0, 1) == 0);
+    assert(math::binExpo_iterative(1, 0) == 1);
+    assert(math::binExpo_iterative(746584, 0) == 1);
+    assert(math::binExpo_iterative(1, 1) == 1);
+    assert(math::binExpo_iterative(2938374, 1) == 2938374);
+    assert(math::binExpo_iterative(3, 7) == 2187);
+    assert(math::binExpo_iterative(-31, 5) == -28629151);
+    assert(math::binExpo_iterative(0, 0) == 1);
+    assert(math::binExpo_iterative(1, 20) == 1);
+    std::cout << "All tests have successfully passed!" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    tests();  // run self-test implementations
+    return 0;
 }