From 4944d4c8b1dc00231209d24f26374dfc96d2c429 Mon Sep 17 00:00:00 2001
From: Krishna Vedala <krishna.vedala@ieee.org>
Date: Wed, 27 May 2020 14:07:18 -0400
Subject: [PATCH] documentation for eulers_totient_function.cpp

---
 math/eulers_totient_function.cpp | 62 ++++++++++++++++++++------------
 1 file changed, 39 insertions(+), 23 deletions(-)

diff --git a/math/eulers_totient_function.cpp b/math/eulers_totient_function.cpp
index 31ced5a51..e7f6fbf7f 100644
--- a/math/eulers_totient_function.cpp
+++ b/math/eulers_totient_function.cpp
@@ -1,28 +1,37 @@
-/// C++ Program to find Euler Totient Function
-#include<iostream>
-
-/*
+/**
+ * @file
+ * @brief C++ Program to find
+ * [Euler's Totient](https://en.wikipedia.org/wiki/Euler%27s_totient_function)
+ * function
+ *
  * Euler Totient Function is also known as phi function.
- * phi(n) = phi(p1^a1).phi(p2^a2)...
- * where p1, p2,... are prime factors of n.
- * 3 Euler's properties:
- * 1. phi(prime_no) = prime_no-1
- * 2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
- * 3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.
+ * \f[\phi(n) =
+ * \phi\left({p_1}^{a_1}\right)\cdot\phi\left({p_2}^{a_2}\right)\ldots\f] where
+ * \f$p_1\f$, \f$p_2\f$, \f$\ldots\f$ are prime factors of n.
+ * <br/>3 Euler's properties:
+ * 1. \f$\phi(n) = n-1\f$
+ * 2. \f$\phi(n^k) = n^k - n^{k-1}\f$
+ * 3. \f$\phi(a,b) = \phi(a)\cdot\phi(b)\f$ where a and b are relative primes.
+ *
  * Applying this 3 properties on the first equation.
- * phi(n) = n. (1-1/p1). (1-1/p2). ...
- * where p1,p2... are prime factors.
- * Hence Implementation in O(sqrt(n)).
- * phi(100) = 40
- * phi(1) = 1
- * phi(17501) = 15120
- * phi(1420) = 560
+ * \f[\phi(n) =
+ * n\cdot\left(1-\frac{1}{p_1}\right)\cdot\left(1-\frac{1}{p_2}\right)\cdots\f]
+ * where \f$p_1\f$,\f$p_2\f$... are prime factors.
+ * Hence Implementation in \f$O\left(\sqrt{n}\right)\f$.
+ * <br/>Some known values are:
+ * * \f$\phi(100) = 40\f$
+ * * \f$\phi(1) = 1\f$
+ * * \f$\phi(17501) = 15120\f$
+ * * \f$\phi(1420) = 560\f$
  */
+#include <cstdlib>
+#include <iostream>
 
-// Function to caculate Euler's totient phi
-int phiFunction(int n) {
-    int result = n;
-    for (int i = 2; i * i <= n; i++) {
+/** Function to caculate Euler's totient phi
+ */
+uint64_t phiFunction(uint64_t n) {
+    uint64_t result = n;
+    for (uint64_t i = 2; i * i <= n; i++) {
         if (n % i == 0) {
             while (n % i == 0) {
                 n /= i;
@@ -34,8 +43,15 @@ int phiFunction(int n) {
     return result;
 }
 
-int main() {
-    int n;
+/// Main function
+int main(int argc, char *argv[]) {
+    uint64_t n;
+    if (argc < 2) {
+        std::cout << "Enter the number: ";
+    } else {
+        n = strtoull(argv[1], nullptr, 10);
+    }
     std::cin >> n;
     std::cout << phiFunction(n);
+    return 0;
 }