auto merge of #6110 : bjz/rust/numeric-traits, r=pcwalton

As discussed on issue #4819, I have created four new traits: `Algebraic`, `Trigonometric`, `Exponential` and `Hyperbolic`, and moved the appropriate methods into them from `Real`.

~~~rust
pub trait Algebraic {
    fn pow(&self, n: Self) -> Self;
    fn sqrt(&self) -> Self;
    fn rsqrt(&self) -> Self;
    fn cbrt(&self) -> Self;
    fn hypot(&self, other: Self) -> Self;
}

pub trait Trigonometric {
    fn sin(&self) -> Self;
    fn cos(&self) -> Self;
    fn tan(&self) -> Self;
    fn asin(&self) -> Self;
    fn acos(&self) -> Self;
    fn atan(&self) -> Self;
    fn atan2(&self, other: Self) -> Self;
}

pub trait Exponential {
    fn exp(&self) -> Self;
    fn exp2(&self) -> Self;
    fn expm1(&self) -> Self;
    fn log(&self) -> Self;
    fn log2(&self) -> Self;
    fn log10(&self) -> Self;
}

pub trait Hyperbolic: Exponential {
    fn sinh(&self) -> Self;
    fn cosh(&self) -> Self;
    fn tanh(&self) -> Self;
}
~~~

There was some discussion over whether we should shorten the names, for example `Trig` and `Exp`. No abbreviations have been agreed on yet, but this could be considered in the future.

Additionally, `Integer::divisible_by` has been renamed to `Integer::is_multiple_of`.

src/libstd/num/bigint.rs

@@ -428,7 +428,7 @@ fn lcm(&self, other: &BigUint) -> BigUint { ((*self * *other) / self.gcd(other))
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
+    fn is_multiple_of(&self, other: &BigUint) -> bool { (*self % *other).is_zero() }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]
@@ -973,7 +973,7 @@ fn lcm(&self, other: &BigInt) -> BigInt {
 
     /// Returns `true` if the number can be divided by `other` without leaving a remainder
     #[inline(always)]
-    fn divisible_by(&self, other: &BigInt) -> bool { self.data.divisible_by(&other.data) }
+    fn is_multiple_of(&self, other: &BigInt) -> bool { self.data.is_multiple_of(&other.data) }
 
     /// Returns `true` if the number is divisible by `2`
     #[inline(always)]

src/libstd/num/rational.rs

@@ -203,6 +203,9 @@ fn one() -> Ratio<T> {
     }
 }
 
+impl<T: Copy + Num + Ord>
+    Num for Ratio<T> {}
+
 /* Utils */
 impl<T: Copy + Num + Ord>
     Round for Ratio<T> {
@@ -242,6 +245,12 @@ fn fract(&self) -> Ratio<T> {
     }
 }
 
+impl<T: Copy + Num + Ord> Fractional for Ratio<T> {
+    #[inline]
+    fn recip(&self) -> Ratio<T> {
+        Ratio::new_raw(self.denom, self.numer)
+    }
+}
 
 /* String conversions */
 impl<T: ToStr> ToStr for Ratio<T> {
@@ -446,6 +455,15 @@ fn test_fract() {
         assert_eq!(_3_2.fract(), _1_2);
     }
 
+    #[test]
+    fn test_recip() {
+        assert_eq!(_1 * _1.recip(), _1);
+        assert_eq!(_2 * _2.recip(), _1);
+        assert_eq!(_1_2 * _1_2.recip(), _1);
+        assert_eq!(_3_2 * _3_2.recip(), _1);
+        assert_eq!(_neg1_2 * _neg1_2.recip(), _1);
+    }
+
     #[test]
     fn test_to_from_str() {
         fn test(r: Rational, s: ~str) {