auto merge of #6041 : bjz/rust/numeric-traits, r=brson

As part of the numeric trait reform (see issue #4819), I have added the following traits to `core::num` and implemented them for the appropriate types:

~~~rust
pub trait Signed: Num
                + Neg<Self> {
    fn abs(&self) -> Self;
    fn signum(&self) -> Self;
    fn is_positive(&self) -> bool;
    fn is_negative(&self) -> bool;
}

pub trait Unsigned: Num {}

pub trait Natural: Num
                 + Ord
                 + Quot<Self,Self>
                 + Rem<Self,Self> {
    fn div(&self, other: Self) -> Self;
    fn modulo(&self, other: Self) -> Self;
    fn div_mod(&self, other: Self) -> (Self,Self);
    fn quot_rem(&self, other: Self) -> (Self,Self);

    fn gcd(&self, other: Self) -> Self;
    fn lcm(&self, other: Self) -> Self;
    fn divisible_by(&self, other: Self) -> bool;
    fn is_even(&self) -> bool;
    fn is_odd(&self) -> bool;
}
~~~

I have not implemented `Natural` for `BigInt` and `BigUInt` because they're a little over my head. Help with this would be most appreciated.

1 files changed, 25 insertions, 8 deletions

diff --git a/src/libstd/num/bigint.rs b/src/libstd/num/bigint.rs
index ee9749af532..5f0fd76640a 100644
--- a/src/libstd/num/bigint.rs
+++ b/src/libstd/num/bigint.rs
@@ -154,6 +154,8 @@ impl One for BigUint {
     pub fn one() -> BigUint { BigUint::new(~[1]) }
 }
 
+impl Unsigned for BigUint {}
+
 impl Add<BigUint, BigUint> for BigUint {
     fn add(&self, other: &BigUint) -> BigUint {
         let new_len = uint::max(self.data.len(), other.data.len());
@@ -469,11 +471,8 @@ pub impl BigUint {
     }
 
     fn is_zero(&self) -> bool { self.data.is_empty() }
+
     fn is_not_zero(&self) -> bool { !self.data.is_empty() }
-    fn is_positive(&self) -> bool { self.is_not_zero() }
-    fn is_negative(&self) -> bool { false }
-    fn is_nonpositive(&self) -> bool { self.is_zero() }
-    fn is_nonnegative(&self) -> bool { true }
 
     fn to_uint(&self) -> uint {
         match self.data.len() {
@@ -693,6 +692,27 @@ impl One for BigInt {
     }
 }
 
+impl Signed for BigInt {
+    fn abs(&self) -> BigInt {
+        match self.sign {
+            Plus | Zero => copy *self,
+            Minus => BigInt::from_biguint(Plus, copy self.data)
+        }
+    }
+
+    fn signum(&self) -> BigInt {
+        match self.sign {
+            Plus  => BigInt::from_biguint(Plus, One::one()),
+            Minus => BigInt::from_biguint(Minus, One::one()),
+            Zero  => Zero::zero(),
+        }
+    }
+
+    fn is_positive(&self) -> bool { self.sign == Plus }
+
+    fn is_negative(&self) -> bool { self.sign == Minus }
+}
+
 impl Add<BigInt, BigInt> for BigInt {
     fn add(&self, other: &BigInt) -> BigInt {
         match (self.sign, other.sign) {
@@ -888,11 +908,8 @@ pub impl BigInt {
     }
 
     fn is_zero(&self) -> bool { self.sign == Zero }
+
     fn is_not_zero(&self) -> bool { self.sign != Zero }
-    fn is_positive(&self) -> bool { self.sign == Plus }
-    fn is_negative(&self) -> bool { self.sign == Minus }
-    fn is_nonpositive(&self) -> bool { self.sign != Plus }
-    fn is_nonnegative(&self) -> bool { self.sign != Minus }
 
     fn to_uint(&self) -> uint {
         match self.sign {