implement operator overloading for comparision operators

src/rational.rs

@@ -1,6 +1,7 @@
 //! # Rational Numbers (fractions)
 
 use crate::num::*;
+use std::cmp::{Ord, Ordering, PartialOrd};
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 /// Type representing a fraction
@@ -104,7 +105,65 @@ impl<T: Unsigned> Frac<T> {
     }
 }
 
-impl<T: Unsigned + Mul<Output = T>> Mul for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> PartialOrd
+    for Frac<T>
+{
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+
+    fn lt(&self, other: &Self) -> bool {
+        self.cmp(other) == Ordering::Less
+    }
+
+    fn le(&self, other: &Self) -> bool {
+        self == other || self.cmp(other) == Ordering::Less
+    }
+
+    fn gt(&self, other: &Self) -> bool {
+        self.cmp(other) == Ordering::Greater
+    }
+
+    fn ge(&self, other: &Self) -> bool {
+        self == other || self.cmp(other) == Ordering::Greater
+    }
+}
+
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Ord
+    for Frac<T>
+{
+    fn cmp(&self, other: &Self) -> Ordering {
+        if self.sign == other.sign {
+            if self.denom == other.denom {
+                return self.numer.cmp(&other.numer);
+            } else {
+                let gcd = T::gcd(self.denom, other.denom);
+                let x = gcd / self.denom;
+                let y = gcd / self.denom;
+                let mut a = self.clone();
+                let mut b = other.clone();
+
+                a.numer *= x;
+                a.denom *= x;
+
+                b.numer *= y;
+                b.denom *= y;
+
+                a.numer.cmp(&b.numer)
+            }
+        } else {
+            if self.sign == Sign::Positive {
+                return Ordering::Greater;
+            } else {
+                return Ordering::Less;
+            }
+        }
+    }
+}
+
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Mul
+    for Frac<T>
+{
     type Output = Self;
 
     fn mul(self, rhs: Self) -> Self {
@@ -116,13 +175,17 @@ impl<T: Unsigned + Mul<Output = T>> Mul for Frac<T> {
     }
 }
 
-impl<T: Unsigned + Mul<Output = T>> MulAssign for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> MulAssign
+    for Frac<T>
+{
     fn mul_assign(&mut self, rhs: Self) {
         *self = self.clone() * rhs
     }
 }
 
-impl<T: Unsigned + Mul<Output = T>> Div for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Div
+    for Frac<T>
+{
     type Output = Self;
 
     fn div(self, rhs: Self) -> Self {
@@ -134,13 +197,17 @@ impl<T: Unsigned + Mul<Output = T>> Div for Frac<T> {
     }
 }
 
-impl<T: Unsigned + Mul<Output = T>> DivAssign for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> DivAssign
+    for Frac<T>
+{
     fn div_assign(&mut self, rhs: Self) {
         *self = self.clone() / rhs
     }
 }
 
-impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> Add for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Add
+    for Frac<T>
+{
     type Output = Self;
 
     fn add(self, rhs: Self) -> Self::Output {
@@ -150,9 +217,9 @@ impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> Add for
         // If the sign of one input differs,
         // subtraction is equivalent
         if self.sign != rhs.sign {
-            if a.numer > b.numer {
+            if a > b {
                 return a - b;
-            } else if a.numer < b.numer {
+            } else if a < b {
                 return b - a;
             }
         }
@@ -176,20 +243,25 @@ impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> Add for
     }
 }
 
-impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T>> AddAssign for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> AddAssign
+    for Frac<T>
+{
     fn add_assign(&mut self, rhs: Self) {
         *self = self.clone() + rhs
     }
 }
 
-impl<T: Unsigned + Sub<Output = T> + Mul<Output = T>> Sub for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> Sub
+    for Frac<T>
+{
     type Output = Self;
 
     fn sub(self, rhs: Self) -> Self::Output {
-        // Set the larger argument as `a`
         let a = self;
         let b = rhs;
 
+        // @TODO handle sign "overflow" conditions
+
         if a.denom != b.denom {
             let numer = (a.numer * b.denom) - (b.numer * a.denom);
             let denom = a.denom * b.denom;
@@ -206,7 +278,9 @@ impl<T: Unsigned + Sub<Output = T> + Mul<Output = T>> Sub for Frac<T> {
     }
 }
 
-impl<T: Unsigned + Sub<Output = T> + Mul<Output = T>> SubAssign for Frac<T> {
+impl<T: Unsigned + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T>> SubAssign
+    for Frac<T>
+{
     fn sub_assign(&mut self, rhs: Self) {
         *self = self.clone() - rhs
     }
@@ -247,8 +321,8 @@ mod tests {
     #[test]
     fn sub_test() {
         assert_eq!(frac!(1 / 6), frac!(1 / 2) - frac!(1 / 3));
-        // assert_eq!(frac!(1), frac!(1/3) - -frac!(2/3), "1/3 - -2/3");
-        // assert_eq!(-frac!(1 / 1), -frac!(2 / 3) - frac!(1 / 3), "-2/3 - 1/3");
+        // assert_eq!(frac!(1), frac!(1 / 3) - -frac!(2 / 3), "1/3 - -2/3");
+        // assert_eq!(-frac!(1), -frac!(2 / 3) - frac!(1 / 3), "-2/3 - 1/3");
     }
 
     #[test]