chore: import upstream snapshot with attribution

math/eulers_totient_function.cpp

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+/**
+ * @file
+ * @brief Implementation of [Euler's
+ * Totient](https://en.wikipedia.org/wiki/Euler%27s_totient_function)
+ * @description
+ * Euler Totient Function is also known as phi function.
+ * \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.
+ * \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$\phi(1420) = 560\f$
+ * @author [Mann Mehta](https://github.com/mann2108)
+ */
+
+#include <cassert>   /// for assert
+#include <cstdint>
+#include <iostream>  /// for IO operations
+
+/**
+ * @brief Mathematical algorithms
+ * @namespace
+ */
+namespace math {
+/**
+ * @brief Function to calculate Euler's Totient
+ * @param n the number to find the Euler's Totient of
+ */
+uint64_t phiFunction(uint64_t n) {
+    uint64_t result = n;
+    for (uint64_t i = 2; i * i <= n; i++) {
+        if (n % i != 0)
+            continue;
+        while (n % i == 0) n /= i;
+
+        result -= result / i;
+    }
+    if (n > 1)
+        result -= result / n;
+
+    return result;
+}
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    assert(math::phiFunction(1) == 1);
+    assert(math::phiFunction(2) == 1);
+    assert(math::phiFunction(10) == 4);
+    assert(math::phiFunction(123456) == 41088);
+    assert(math::phiFunction(808017424794) == 263582333856);
+    assert(math::phiFunction(3141592) == 1570792);
+    assert(math::phiFunction(27182818) == 12545904);
+
+    std::cout << "All tests have successfully passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();
+    return 0;
+}