[types] Make math ops macros even more generic -- implement them for cross types too!

Still need to write tests for this though.

types/src/number/arith.rs

@@ -3,7 +3,7 @@
  */
 
 use std::ops::{Add, Div, Mul, Sub, Rem};
-use number::{Int, Irr};
+use number::{Int, Irr, Number};
 
 pub trait GCD {
     /// Find the greatest common divisor of `self` and another number.
@@ -17,24 +17,19 @@ pub trait LCM {
 
 macro_rules! impl_newtype_arith_op {
     ($id:ident, $opt:ident, $opm:ident, $op:tt) => {
-        impl $opt for $id {
+        impl<T> $opt<T> for $id where T: Number + Into<$id> {
             type Output = $id;
             #[inline]
-            fn $opm(self, rhs: $id) -> Self::Output {
+            fn $opm(self, rhs: T) -> Self::Output {
+                let rhs: $id = rhs.into();
                 $id(self.0 $op rhs.0)
             }
         }
-        impl<'a> $opt<$id> for &'a $id {
+        impl<'a, T> $opt<T> for &'a $id where T: Number + Into<$id> {
             type Output = $id;
             #[inline]
-            fn $opm(self, rhs: $id) -> Self::Output {
-                $id(self.0 $op rhs.0)
-            }
-        }
-        impl<'a, 'b> $opt<&'a $id> for &'b $id {
-            type Output = $id;
-            #[inline]
-            fn $opm(self, rhs: &$id) -> Self::Output {
+            fn $opm(self, rhs: T) -> Self::Output {
+                let rhs: $id = rhs.into();
                 $id(self.0 $op rhs.0)
             }
         }

types/src/number/frac.rs

@@ -32,6 +32,10 @@ impl Frac {
         Frac::new(Int(p), Int(q))
     }
 
+    pub fn quotient(&self) -> f64 {
+        self.p.0 as f64 / self.q.0 as f64
+    }
+
     fn reduced(self) -> Frac {
         let gcd = self.p.gcd(self.q);
         Frac { p: self.p / gcd, q: self.q / gcd }
@@ -77,6 +81,12 @@ impl fmt::Display for Frac {
     }
 }
 
+impl From<Int> for Frac {
+    fn from(i: Int) -> Frac {
+        Frac{p: i, q: Int(1)}
+    }
+}
+
 impl Mul for Frac {
     type Output = Frac;
     fn mul(self, rhs: Self) -> Self::Output {

types/src/number/integer.rs

@@ -5,8 +5,8 @@
 use std::any::Any;
 use std::fmt;
 use number::arith::{GCD, LCM};
-use number::{Frac, Number};
 use object::{Obj, Object};
+use super::{Frac, Number};
 
 #[derive(Copy, Clone, Debug, Eq, Ord, PartialEq, PartialOrd)]
 pub struct Int(pub i64);

types/src/number/irr.rs

@@ -20,9 +20,14 @@ impl fmt::Display for Irr {
     }
 }
 
-impl Object for Irr {
-    fn as_any(&self) -> &Any { self }
-    fn as_num(&self) -> Option<&Number> { Some(self) }
+impl From<Int> for Irr {
+    fn from(i: Int) -> Irr { Irr(i.0 as f64) }
+}
+
+impl From<Frac> for Irr {
+    fn from(f: Frac) -> Irr {
+        Irr(f.quotient())
+    }
 }
 
 impl Number for Irr {
@@ -46,6 +51,11 @@ impl Number for Irr {
     fn is_zero(&self) -> bool { self.0 == 0.0 }
 }
 
+impl Object for Irr {
+    fn as_any(&self) -> &Any { self }
+    fn as_num(&self) -> Option<&Number> { Some(self) }
+}
+
 impl PartialEq<Obj> for Irr {
     fn eq<'a>(&self, rhs: &'a Obj) -> bool {
         match rhs.obj().and_then(Object::as_num) {

types/src/number/mod.rs

@@ -11,13 +11,13 @@
 //! Integer can be cast as a Rational (by putting its value over 1), but a Rational like 1/2 cannot
 //! be represented as an Integer.
 
+use object::Object;
+
 mod arith;
 mod frac;
 mod integer;
 mod irr;
 
-use object::Object;
-
 pub use self::frac::Frac;
 pub use self::integer::Int;
 pub use self::irr::Irr;