Add Euler's Totient function implementation

Author: allansomensi

DIRECTORY.md

@@ -194,6 +194,7 @@
     * [Doomsday](https://github.com/TheAlgorithms/Rust/blob/master/src/math/doomsday.rs)
     * [Elliptic Curve](https://github.com/TheAlgorithms/Rust/blob/master/src/math/elliptic_curve.rs)
     * [Euclidean Distance](https://github.com/TheAlgorithms/Rust/blob/master/src/math/euclidean_distance.rs)
+    * [Euler Totient](https://github.com/TheAlgorithms/Rust/blob/master/src/math/euler_totient.rs)
     * [Exponential Linear Unit](https://github.com/TheAlgorithms/Rust/blob/master/src/math/exponential_linear_unit.rs)
     * [Extended Euclidean Algorithm](https://github.com/TheAlgorithms/Rust/blob/master/src/math/extended_euclidean_algorithm.rs)
     * [Factorial](https://github.com/TheAlgorithms/Rust/blob/master/src/math/factorial.rs)

src/math/euler_totient.rs

@@ -0,0 +1,45 @@
+/// ## Euler's Totient (`φ(n)`)
+///
+/// Calculate the **Euler's Totient** function of a given number `n`.
+///
+/// Wikipedia: https://en.wikipedia.org/wiki/Euler%27s_totient_function
+pub fn euler_totient(mut n: i64) -> i64 {
+    let mut result = n;
+
+    if n <= 0 {
+        panic!("Must be a positive integer!");
+    }
+
+    for i in 2..=n.isqrt() {
+        if n % i == 0 {
+            while n % i == 0 {
+                n /= i;
+            }
+            result -= result / i;
+        }
+    }
+
+    if n > 1 {
+        result -= result / n;
+    }
+
+    result
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_euler_totient() {
+        assert_eq!(euler_totient(1), 1);
+        assert_eq!(euler_totient(325), 240);
+        assert_eq!(euler_totient(746), 372);
+        assert_eq!(euler_totient(3_639), 2_424);
+        assert_eq!(euler_totient(98_354), 49_176);
+        assert_eq!(euler_totient(123_456), 41_088);
+        assert_eq!(euler_totient(493_123_235), 347_518_080);
+        assert_eq!(euler_totient(945_243_784_032), 315_074_904_192);
+        assert_eq!(euler_totient(372_036_854_775_808), 185_661_377_740_800);
+    }
+}

src/math/mod.rs

@@ -19,6 +19,7 @@ mod decimal_to_fraction;
 mod doomsday;
 mod elliptic_curve;
 mod euclidean_distance;
+mod euler_totient;
 mod exponential_linear_unit;
 mod extended_euclidean_algorithm;
 pub mod factorial;
@@ -103,6 +104,7 @@ pub use self::decimal_to_fraction::decimal_to_fraction;
 pub use self::doomsday::get_week_day;
 pub use self::elliptic_curve::EllipticCurve;
 pub use self::euclidean_distance::euclidean_distance;
+pub use self::euler_totient::euler_totient;
 pub use self::exponential_linear_unit::exponential_linear_unit;
 pub use self::extended_euclidean_algorithm::extended_euclidean_algorithm;
 pub use self::factorial::{factorial, factorial_bigmath, factorial_recursive};