Add new function gcd_lcm for calculating the gcd and lcm simultaneously (performance)

src/lib.rs

@@ -95,6 +95,21 @@ pub trait Integer: Sized + Num + PartialOrd + Ord + Eq {
  /// ~~~
  fn lcm(&self, other: &Self) -> Self;
 
+ /// Greatest Common Divisor (GCD) and
+ /// Lowest Common Multiple (LCM) simultaneously.
+ ///
+ /// More efficient than calling `gcd` and `lcm`
+ /// individually for identical inputs.
+ /// 
+ /// # Examples
+ ///
+ /// ~~~
+ /// # use num_integer::Integer;
+ /// assert_eq!(10.gcd_lcm(&4), (2, 20));
+ /// assert_eq!(8.gcd_lcm(&9), (1, 72));
+ /// ~~~
+ fn gcd_lcm(&self, other: &Self) -> (Self, Self);
+
  /// Deprecated, use `is_multiple_of` instead.
  fn divides(&self, other: &Self) -> bool;
 
@@ -206,6 +221,13 @@ pub fn lcm<T: Integer>(x: T, y: T) -> T {
  x.lcm(&y)
 }
 
+/// Calculates the Greatest Common Divisor (GCD) and
+/// Lowest Common Multiple (LCM) of the number and `other`.
+#[inline(always)]
+pub fn gcd_lcm<T: Integer>(x: T, y: T) -> (T, T) {
+ x.gcd_lcm(&y)
+}
+
 macro_rules! impl_integer_for_isize {
  ($T:ty, $test_mod:ident) => (
  impl Integer for $T {
@@ -297,6 +319,16 @@ macro_rules! impl_integer_for_isize {
  (*self * (*other / self.gcd(other))).abs()
  }
 
+ /// Calculates the Greatest Common Divisor (GCD) and 
+ /// Lowest Common Multiple (LCM) of the number and `other`.
+ #[inline]
+ fn gcd_lcm(&self, other: &Self) -> (Self, Self) {
+ let gcd = self.gcd(other);
+ // should not have to recalculate abs
+ let lcm = (*self * (*other / gcd)).abs();
+ (gcd, lcm)
+ }
+
  /// Deprecated, use `is_multiple_of` instead.
  #[inline]
  fn divides(&self, other: &Self) -> bool {
@@ -475,6 +507,15 @@ macro_rules! impl_integer_for_isize {
  assert_eq!((11 as $T).lcm(&5), 55 as $T);
  }
 
+ #[test]
+ fn test_gcd_lcm() {
+ for i in 1..=255 {
+ for j in 0..=255 {
+ assert_eq!(i.gcd_lcm(&j), (i.gcd(&j), i.lcm(&j)));
+ }
+ }
+ }
+
  #[test]
  fn test_even() {
  assert_eq!((-4 as $T).is_even(), true);
@@ -560,6 +601,15 @@ macro_rules! impl_integer_for_usize {
  *self * (*other / self.gcd(other))
  }
 
+ /// Calculates the Greatest Common Divisor (GCD) and 
+ /// Lowest Common Multiple (LCM) of the number and `other`.
+ #[inline]
+ fn gcd_lcm(&self, other: &Self) -> (Self, Self) {
+ let gcd = self.gcd(other);
+ let lcm = *self * (*other / gcd);
+ (gcd, lcm)
+ }
+
  /// Deprecated, use `is_multiple_of` instead.
  #[inline]
  fn divides(&self, other: &Self) -> bool {
@@ -653,6 +703,15 @@ macro_rules! impl_integer_for_usize {
  assert_eq!((15 as $T).lcm(&17), 255 as $T);
  }
 
+ #[test]
+ fn test_gcd_lcm() {
+ for i in 1..=255 {
+ for j in 0..=255 {
+ assert_eq!(i.gcd_lcm(&j), (i.gcd(&j), i.lcm(&j)));
+ }
+ }
+ }
+
  #[test]
  fn test_is_multiple_of() {
  assert!((6 as $T).is_multiple_of(&(6 as $T)));