fix: fit armstrong_number.cpp to guidelines

Author: realstealthninja

Diff for: math/armstrong_number.cpp

@@ -1,22 +1,28 @@
 /**
- * @file
- * \brief Program to check if a number is an [Armstrong/Narcissistic
- * number](https://en.wikipedia.org/wiki/Narcissistic_number) in decimal system.
- *
- * \details
- * Armstrong number or [Narcissistic
- * number](https://en.wikipedia.org/wiki/Narcissistic_number) is a number that
- * is the sum of its own digits raised to the power of the number of digits.
- * @author iamnambiar
+* @file
+* @brief Program to check if a number is an [Armstrong/Narcissistic
+* number](https://en.wikipedia.org/wiki/Narcissistic_number) in decimal system.
+*
+* @details
+* Armstrong number or [Narcissistic
+* number](https://en.wikipedia.org/wiki/Narcissistic_number) is a number that
+* is the sum of its own digits raised to the power of the number of digits.
+*
+* let n be the narcissistic number,
+* \f[F_b(n) = \sum_{i=0}^{k-1}d_{i}^{k}\f] for
+* \f$ b > 1 F_b : \N \to \N \f$ where
+* \f$ k = \lfloor log_b n\rfloor is the number of digits in the number in base \f$b\f$, and
+* \f$ d_i = \frac{n mod b^{i+1} - n mod b^{i}}{b^{i}} \f$
+*
+* @author [Neeraj Cherkara](https://github.com/iamnambiar)
  */
-#include <cassert>
-#include <cmath>
-#include <iostream>
+#include <cassert> /// for assert
+#include <cmath> /// for std::pow
 
 /**
- * Function to calculate the total number of digits in the number.
- * @param num Number
- * @return Total number of digits.
+* @brief Function to calculate the total number of digits in the number.
+* @param num Number
+* @return Total number of digits.
  */
 int number_of_digits(int num) {
     int total_digits = 0;
@@ -28,16 +34,17 @@ int number_of_digits(int num) {
 }
 
 /**
- * Function to check whether the number is armstrong number or not.
- * @param num Number
- * @return `true` if the number is armstrong.
- * @return `false` if the number is not armstrong.
+* @brief Function to check whether the number is armstrong number or not.
+* @param number to be checked
+* @return `true` if the number is armstrong.
+* @return `false` if the number is not armstrong.
  */
 bool is_armstrong(int number) {
-    // If the number is less than 0, then it is not a armstrong number.
+    // If the number is less than 0, then it is not an armstrong number.
     if (number < 0) {
         return false;
     }
+
     int sum = 0;
     int temp = number;
     // Finding the total number of digits in the number
@@ -46,17 +53,17 @@ bool is_armstrong(int number) {
         int rem = temp % 10;
         // Finding each digit raised to the power total digit and add it to the
         // total sum
-        sum = sum + std::pow(rem, total_digits);
+        sum += static_cast<int>(std::pow(rem, total_digits));
         temp = temp / 10;
     }
     return number == sum;
 }
 
 /**
- * Function for testing the is_armstrong() function
- * with all the test cases.
+* @brief Self-test implementations
+* @returns void
  */
-void test() {
+static void test() {
     // is_armstrong(370) returns true.
     assert(is_armstrong(370) == true);
     // is_armstrong(225) returns false.
@@ -72,9 +79,10 @@ void test() {
 }
 
 /**
- * Main Function
+* @brief Main Function
+* @returns 0 on exit
  */
 int main() {
-    test();
+    test(); // run self-test implementations
     return 0;
 }