diff --git a/src/bigint.rs b/src/bigint.rs
index d988959..5af89d4 100644
--- a/src/bigint.rs
+++ b/src/bigint.rs
@@ -189,7 +189,9 @@ impl Num for BigUint {}
 
 macro_rules! forward_val_val_binop {
     (impl $imp:ident for $res:ty, $method:ident) => {
-        impl $imp<$res, $res> for $res {
+        impl $imp<$res> for $res {
+            type Output = $res;
+
             #[inline]
             fn $method(self, other: $res) -> $res {
                 (&self).$method(&other)
@@ -200,7 +202,9 @@ macro_rules! forward_val_val_binop {
 
 macro_rules! forward_ref_val_binop {
     (impl $imp:ident for $res:ty, $method:ident) => {
-        impl<'a> $imp<$res, $res> for &'a $res {
+        impl<'a> $imp<$res> for &'a $res {
+            type Output = $res;
+
             #[inline]
             fn $method(self, other: $res) -> $res {
                 self.$method(&other)
@@ -211,7 +215,9 @@ macro_rules! forward_ref_val_binop {
 
 macro_rules! forward_val_ref_binop {
     (impl $imp:ident for $res:ty, $method:ident) => {
-        impl<'a> $imp<&'a $res, $res> for $res {
+        impl<'a> $imp<&'a $res> for $res {
+            type Output = $res;
+
             #[inline]
             fn $method(self, other: &$res) -> $res {
                 (&self).$method(other)
@@ -230,7 +236,9 @@ macro_rules! forward_all_binop {
 
 forward_all_binop!(impl BitAnd for BigUint, bitand);
 
-impl<'a, 'b> BitAnd<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> BitAnd<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn bitand(self, other: &BigUint) -> BigUint {
         BigUint::new(self.data.iter().zip(other.data.iter()).map(|(ai, bi)| *ai & *bi).collect())
@@ -239,7 +247,9 @@ impl<'a, 'b> BitAnd<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl BitOr for BigUint, bitor);
 
-impl<'a, 'b> BitOr<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> BitOr<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     fn bitor(self, other: &BigUint) -> BigUint {
         let zeros = ZERO_VEC.iter().cycle();
         let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
@@ -252,7 +262,9 @@ impl<'a, 'b> BitOr<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl BitXor for BigUint, bitxor);
 
-impl<'a, 'b> BitXor<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> BitXor<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     fn bitxor(self, other: &BigUint) -> BigUint {
         let zeros = ZERO_VEC.iter().cycle();
         let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
@@ -263,12 +275,16 @@ impl<'a, 'b> BitXor<&'b BigUint, BigUint> for &'a BigUint {
     }
 }
 
-impl Shl<uint, BigUint> for BigUint {
+impl Shl<uint> for BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn shl(self, rhs: uint) -> BigUint { (&self) << rhs }
 }
 
-impl<'a> Shl<uint, BigUint> for &'a BigUint {
+impl<'a> Shl<uint> for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn shl(self, rhs: uint) -> BigUint {
         let n_unit = rhs / BigDigit::BITS;
@@ -277,12 +293,16 @@ impl<'a> Shl<uint, BigUint> for &'a BigUint {
     }
 }
 
-impl Shr<uint, BigUint> for BigUint {
+impl Shr<uint> for BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn shr(self, rhs: uint) -> BigUint { (&self) >> rhs }
 }
 
-impl<'a> Shr<uint, BigUint> for &'a BigUint {
+impl<'a> Shr<uint> for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn shr(self, rhs: uint) -> BigUint {
         let n_unit = rhs / BigDigit::BITS;
@@ -308,7 +328,9 @@ impl Unsigned for BigUint {}
 
 forward_all_binop!(impl Add for BigUint, add);
 
-impl<'a, 'b> Add<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> Add<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     fn add(self, other: &BigUint) -> BigUint {
         let zeros = ZERO_VEC.iter().cycle();
         let (a, b) = if self.data.len() > other.data.len() { (self, other) } else { (other, self) };
@@ -327,7 +349,9 @@ impl<'a, 'b> Add<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl Sub for BigUint, sub);
 
-impl<'a, 'b> Sub<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> Sub<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     fn sub(self, other: &BigUint) -> BigUint {
         let new_len = cmp::max(self.data.len(), other.data.len());
         let zeros = ZERO_VEC.iter().cycle();
@@ -358,7 +382,9 @@ impl<'a, 'b> Sub<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl Mul for BigUint, mul);
 
-impl<'a, 'b> Mul<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> Mul<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     fn mul(self, other: &BigUint) -> BigUint {
         if self.is_zero() || other.is_zero() { return Zero::zero(); }
 
@@ -427,7 +453,9 @@ impl<'a, 'b> Mul<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl Div for BigUint, div);
 
-impl<'a, 'b> Div<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> Div<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn div(self, other: &BigUint) -> BigUint {
         let (q, _) = self.div_rem(other);
@@ -437,7 +465,9 @@ impl<'a, 'b> Div<&'b BigUint, BigUint> for &'a BigUint {
 
 forward_all_binop!(impl Rem for BigUint, rem);
 
-impl<'a, 'b> Rem<&'b BigUint, BigUint> for &'a BigUint {
+impl<'a, 'b> Rem<&'b BigUint> for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn rem(self, other: &BigUint) -> BigUint {
         let (_, r) = self.div_rem(other);
@@ -445,12 +475,16 @@ impl<'a, 'b> Rem<&'b BigUint, BigUint> for &'a BigUint {
     }
 }
 
-impl Neg<BigUint> for BigUint {
+impl Neg for BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn neg(self) -> BigUint { panic!() }
 }
 
-impl<'a> Neg<BigUint> for &'a BigUint {
+impl<'a> Neg for &'a BigUint {
+    type Output = BigUint;
+
     #[inline]
     fn neg(self) -> BigUint { panic!() }
 }
@@ -818,14 +852,14 @@ impl FromStrRadix for BigUint {
     }
 }
 
-impl<T: Iterator<BigUint>> AdditiveIterator<BigUint> for T {
+impl<T: Iterator<Item = BigUint>> AdditiveIterator<BigUint> for T {
     fn sum(self) -> BigUint {
         let init: BigUint = Zero::zero();
         self.fold(init, |acc, x| acc + x)
     }
 }
 
-impl<T: Iterator<BigUint>> MultiplicativeIterator<BigUint> for T {
+impl<T: Iterator<Item = BigUint>> MultiplicativeIterator<BigUint> for T {
     fn product(self) -> BigUint {
         let init: BigUint = One::one();
         self.fold(init, |acc, x| acc * x)
@@ -939,7 +973,9 @@ fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) {
 #[derive(PartialEq, PartialOrd, Eq, Ord, Copy, Clone, Show, RustcEncodable, RustcDecodable)]
 pub enum Sign { Minus, NoSign, Plus }
 
-impl Neg<Sign> for Sign {
+impl Neg for Sign {
+    type Output = Sign;
+
     /// Negate Sign value.
     #[inline]
     fn neg(self) -> Sign {
@@ -1015,24 +1051,32 @@ impl FromStr for BigInt {
 
 impl Num for BigInt {}
 
-impl Shl<uint, BigInt> for BigInt {
+impl Shl<uint> for BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn shl(self, rhs: uint) -> BigInt { (&self) << rhs }
 }
 
-impl<'a> Shl<uint, BigInt> for &'a BigInt {
+impl<'a> Shl<uint> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn shl(self, rhs: uint) -> BigInt {
         BigInt::from_biguint(self.sign, &self.data << rhs)
     }
 }
 
-impl Shr<uint, BigInt> for BigInt {
+impl Shr<uint> for BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn shr(self, rhs: uint) -> BigInt { (&self) >> rhs }
 }
 
-impl<'a> Shr<uint, BigInt> for &'a BigInt {
+impl<'a> Shr<uint> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn shr(self, rhs: uint) -> BigInt {
         BigInt::from_biguint(self.sign, &self.data >> rhs)
@@ -1088,7 +1132,9 @@ impl Signed for BigInt {
 
 forward_all_binop!(impl Add for BigInt, add);
 
-impl<'a, 'b> Add<&'b BigInt, BigInt> for &'a BigInt {
+impl<'a, 'b> Add<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn add(self, other: &BigInt) -> BigInt {
         match (self.sign, other.sign) {
@@ -1104,7 +1150,9 @@ impl<'a, 'b> Add<&'b BigInt, BigInt> for &'a BigInt {
 
 forward_all_binop!(impl Sub for BigInt, sub);
 
-impl<'a, 'b> Sub<&'b BigInt, BigInt> for &'a BigInt {
+impl<'a, 'b> Sub<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn sub(self, other: &BigInt) -> BigInt {
         match (self.sign, other.sign) {
@@ -1124,7 +1172,9 @@ impl<'a, 'b> Sub<&'b BigInt, BigInt> for &'a BigInt {
 
 forward_all_binop!(impl Mul for BigInt, mul);
 
-impl<'a, 'b> Mul<&'b BigInt, BigInt> for &'a BigInt {
+impl<'a, 'b> Mul<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn mul(self, other: &BigInt) -> BigInt {
         match (self.sign, other.sign) {
@@ -1141,7 +1191,9 @@ impl<'a, 'b> Mul<&'b BigInt, BigInt> for &'a BigInt {
 
 forward_all_binop!(impl Div for BigInt, div);
 
-impl<'a, 'b> Div<&'b BigInt, BigInt> for &'a BigInt {
+impl<'a, 'b> Div<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn div(self, other: &BigInt) -> BigInt {
         let (q, _) = self.div_rem(other);
@@ -1151,7 +1203,9 @@ impl<'a, 'b> Div<&'b BigInt, BigInt> for &'a BigInt {
 
 forward_all_binop!(impl Rem for BigInt, rem);
 
-impl<'a, 'b> Rem<&'b BigInt, BigInt> for &'a BigInt {
+impl<'a, 'b> Rem<&'b BigInt> for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn rem(self, other: &BigInt) -> BigInt {
         let (_, r) = self.div_rem(other);
@@ -1159,12 +1213,16 @@ impl<'a, 'b> Rem<&'b BigInt, BigInt> for &'a BigInt {
     }
 }
 
-impl Neg<BigInt> for BigInt {
+impl Neg for BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn neg(self) -> BigInt { -&self }
 }
 
-impl<'a> Neg<BigInt> for &'a BigInt {
+impl<'a> Neg for &'a BigInt {
+    type Output = BigInt;
+
     #[inline]
     fn neg(self) -> BigInt {
         BigInt::from_biguint(self.sign.neg(), self.data.clone())
@@ -1496,14 +1554,14 @@ impl<R: Rng> RandBigInt for R {
     }
 }
 
-impl<T: Iterator<BigInt>> AdditiveIterator<BigInt> for T {
+impl<T: Iterator<Item = BigInt>> AdditiveIterator<BigInt> for T {
     fn sum(self) -> BigInt {
         let init: BigInt = Zero::zero();
         self.fold(init, |acc, x| acc + x)
     }
 }
 
-impl<T: Iterator<BigInt>> MultiplicativeIterator<BigInt> for T {
+impl<T: Iterator<Item = BigInt>> MultiplicativeIterator<BigInt> for T {
     fn product(self) -> BigInt {
         let init: BigInt = One::one();
         self.fold(init, |acc, x| acc * x)
diff --git a/src/complex.rs b/src/complex.rs
index e3872d7..b079a20 100644
--- a/src/complex.rs
+++ b/src/complex.rs
@@ -105,7 +105,9 @@ impl<T: Clone + FloatMath + Num> Complex<T> {
 
 macro_rules! forward_val_val_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<T: Clone + Num> $imp<Complex<T>, Complex<T>> for Complex<T> {
+        impl<T: Clone + Num> $imp<Complex<T>> for Complex<T> {
+            type Output = Complex<T>;
+
             #[inline]
             fn $method(self, other: Complex<T>) -> Complex<T> {
                 (&self).$method(&other)
@@ -116,7 +118,9 @@ macro_rules! forward_val_val_binop {
 
 macro_rules! forward_ref_val_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<'a, T: Clone + Num> $imp<Complex<T>, Complex<T>> for &'a Complex<T> {
+        impl<'a, T: Clone + Num> $imp<Complex<T>> for &'a Complex<T> {
+            type Output = Complex<T>;
+
             #[inline]
             fn $method(self, other: Complex<T>) -> Complex<T> {
                 self.$method(&other)
@@ -127,7 +131,9 @@ macro_rules! forward_ref_val_binop {
 
 macro_rules! forward_val_ref_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<'a, T: Clone + Num> $imp<&'a Complex<T>, Complex<T>> for Complex<T> {
+        impl<'a, T: Clone + Num> $imp<&'a Complex<T>> for Complex<T> {
+            type Output = Complex<T>;
+
             #[inline]
             fn $method(self, other: &Complex<T>) -> Complex<T> {
                 (&self).$method(other)
@@ -148,7 +154,9 @@ macro_rules! forward_all_binop {
 forward_all_binop!(impl Add, add);
 
 // (a + i b) + (c + i d) == (a + c) + i (b + d)
-impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>, Complex<T>> for &'a Complex<T> {
+impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>> for &'a Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn add(self, other: &Complex<T>) -> Complex<T> {
         Complex::new(self.re.clone() + other.re.clone(),
@@ -159,7 +167,9 @@ impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>, Complex<T>> for &'a Complex<T>
 forward_all_binop!(impl Sub, sub);
 
 // (a + i b) - (c + i d) == (a - c) + i (b - d)
-impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>, Complex<T>> for &'a Complex<T> {
+impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>> for &'a Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn sub(self, other: &Complex<T>) -> Complex<T> {
         Complex::new(self.re.clone() - other.re.clone(),
@@ -170,7 +180,9 @@ impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>, Complex<T>> for &'a Complex<T>
 forward_all_binop!(impl Mul, mul);
 
 // (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)
-impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>, Complex<T>> for &'a Complex<T> {
+impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>> for &'a Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn mul(self, other: &Complex<T>) -> Complex<T> {
         Complex::new(self.re.clone() * other.re.clone() - self.im.clone() * other.im.clone(),
@@ -182,7 +194,9 @@ forward_all_binop!(impl Div, div);
 
 // (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d)
 //   == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)]
-impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>, Complex<T>> for &'a Complex<T> {
+impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>> for &'a Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn div(self, other: &Complex<T>) -> Complex<T> {
         let norm_sqr = other.norm_sqr();
@@ -191,12 +205,16 @@ impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>, Complex<T>> for &'a Complex<T>
     }
 }
 
-impl<T: Clone + Num> Neg<Complex<T>> for Complex<T> {
+impl<T: Clone + Num> Neg for Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn neg(self) -> Complex<T> { -&self }
 }
 
-impl<'a, T: Clone + Num> Neg<Complex<T>> for &'a Complex<T> {
+impl<'a, T: Clone + Num> Neg for &'a Complex<T> {
+    type Output = Complex<T>;
+
     #[inline]
     fn neg(self) -> Complex<T> {
         Complex::new(-self.re.clone(), -self.im.clone())
@@ -234,14 +252,18 @@ impl<T: fmt::Show + Num + PartialOrd + Clone> fmt::Show for Complex<T> {
     }
 }
 
-impl<A: Clone + Num, T: Iterator<Complex<A>>> AdditiveIterator<Complex<A>> for T {
+impl<A, T> AdditiveIterator<Complex<A>> for T
+    where A: Clone + Num, T: Iterator<Item = Complex<A>>
+{
     fn sum(self) -> Complex<A> {
         let init: Complex<A> = Zero::zero();
         self.fold(init, |acc, x| acc + x)
     }
 }
 
-impl<A: Clone + Num, T: Iterator<Complex<A>>> MultiplicativeIterator<Complex<A>> for T {
+impl<A, T> MultiplicativeIterator<Complex<A>> for T
+    where A: Clone + Num, T: Iterator<Item = Complex<A>>
+{
     fn product(self) -> Complex<A> {
         let init: Complex<A> = One::one();
         self.fold(init, |acc, x| acc * x)
diff --git a/src/integer.rs b/src/integer.rs
index 006ea3c..a44b552 100644
--- a/src/integer.rs
+++ b/src/integer.rs
@@ -15,8 +15,7 @@ use std::ops::{Div, Rem};
 use {Num, Signed};
 
 pub trait Integer: Sized + Num + PartialOrd
-                 + Div<Self, Self>
-                 + Rem<Self, Self> {
+                 + Div<Self, Output = Self> + Rem<Self, Output = Self> {
     /// Floored integer division.
     ///
     /// # Examples
diff --git a/src/iter.rs b/src/iter.rs
index fd75721..ecf0fd2 100644
--- a/src/iter.rs
+++ b/src/iter.rs
@@ -36,12 +36,18 @@ pub struct Range<A> {
 /// }
 /// ```
 #[inline]
-pub fn range<A: Add<A, A> + PartialOrd + Clone + One>(start: A, stop: A) -> Range<A> {
+pub fn range<A>(start: A, stop: A) -> Range<A>
+    where A: Add<A, Output = A> + PartialOrd + Clone + One
+{
     Range{state: start, stop: stop, one: One::one()}
 }
 
 // FIXME: rust-lang/rust#10414: Unfortunate type bound
-impl<A: Add<A, A> + PartialOrd + Clone + ToPrimitive> Iterator<A> for Range<A> {
+impl<A> Iterator for Range<A>
+    where A: Add<A, Output = A> + PartialOrd + Clone + ToPrimitive
+{
+    type Item = A;
+
     #[inline]
     fn next(&mut self) -> Option<A> {
         if self.state < self.stop {
@@ -88,7 +94,9 @@ impl<A: Add<A, A> + PartialOrd + Clone + ToPrimitive> Iterator<A> for Range<A> {
 
 /// `Integer` is required to ensure the range will be the same regardless of
 /// the direction it is consumed.
-impl<A: Integer + PartialOrd + Clone + ToPrimitive> DoubleEndedIterator<A> for Range<A> {
+impl<A> DoubleEndedIterator for Range<A>
+    where A: Integer + PartialOrd + Clone + ToPrimitive
+{
     #[inline]
     fn next_back(&mut self) -> Option<A> {
         if self.stop > self.state {
@@ -109,12 +117,17 @@ pub struct RangeInclusive<A> {
 
 /// Return an iterator over the range [start, stop]
 #[inline]
-pub fn range_inclusive<A: Add<A, A> + PartialOrd + Clone + One>(start: A, stop: A)
-    -> RangeInclusive<A> {
+pub fn range_inclusive<A>(start: A, stop: A) -> RangeInclusive<A>
+    where A: Add<A, Output = A> + PartialOrd + Clone + One
+{
     RangeInclusive{range: range(start, stop), done: false}
 }
 
-impl<A: Add<A, A> + PartialOrd + Clone + ToPrimitive> Iterator<A> for RangeInclusive<A> {
+impl<A> Iterator for RangeInclusive<A>
+    where A: Add<A, Output = A> + PartialOrd + Clone + ToPrimitive
+{
+    type Item = A;
+
     #[inline]
     fn next(&mut self) -> Option<A> {
         match self.range.next() {
@@ -146,8 +159,9 @@ impl<A: Add<A, A> + PartialOrd + Clone + ToPrimitive> Iterator<A> for RangeInclu
     }
 }
 
-impl<A: Sub<A, A> + Integer + PartialOrd + Clone + ToPrimitive> DoubleEndedIterator<A>
-    for RangeInclusive<A> {
+impl<A> DoubleEndedIterator for RangeInclusive<A>
+    where A: Sub<A, Output = A> + Integer + PartialOrd + Clone + ToPrimitive
+{
     #[inline]
     fn next_back(&mut self) -> Option<A> {
         if self.range.stop > self.range.state {
@@ -174,13 +188,18 @@ pub struct RangeStep<A> {
 
 /// Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.
 #[inline]
-pub fn range_step<A: CheckedAdd + PartialOrd +
-                  Clone + Zero>(start: A, stop: A, step: A) -> RangeStep<A> {
+pub fn range_step<A>(start: A, stop: A, step: A) -> RangeStep<A>
+    where A: CheckedAdd + PartialOrd + Clone + Zero
+{
     let rev = step < Zero::zero();
     RangeStep{state: start, stop: stop, step: step, rev: rev}
 }
 
-impl<A: CheckedAdd + PartialOrd + Clone> Iterator<A> for RangeStep<A> {
+impl<A> Iterator for RangeStep<A>
+    where A: CheckedAdd + PartialOrd + Clone
+{
+    type Item = A;
+
     #[inline]
     fn next(&mut self) -> Option<A> {
         if (self.rev && self.state > self.stop) || (!self.rev && self.state < self.stop) {
@@ -208,13 +227,18 @@ pub struct RangeStepInclusive<A> {
 
 /// Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.
 #[inline]
-pub fn range_step_inclusive<A: CheckedAdd + PartialOrd + Clone + Zero>(start: A, stop: A,
-                                                                step: A) -> RangeStepInclusive<A> {
+pub fn range_step_inclusive<A>(start: A, stop: A, step: A) -> RangeStepInclusive<A>
+    where A: CheckedAdd + PartialOrd + Clone + Zero
+{
     let rev = step < Zero::zero();
     RangeStepInclusive{state: start, stop: stop, step: step, rev: rev, done: false}
 }
 
-impl<A: CheckedAdd + PartialOrd + Clone + PartialEq> Iterator<A> for RangeStepInclusive<A> {
+impl<A> Iterator for RangeStepInclusive<A>
+    where A: CheckedAdd + PartialOrd + Clone + PartialEq
+{
+    type Item = A;
+
     #[inline]
     fn next(&mut self) -> Option<A> {
         if !self.done && ((self.rev && self.state >= self.stop) ||
@@ -249,7 +273,9 @@ mod tests {
             fn to_u64(&self) -> Option<u64> { None }
         }
 
-        impl Add<Foo, Foo> for Foo {
+        impl Add<Foo> for Foo {
+            type Output = Foo;
+
             fn add(self, _: Foo) -> Foo {
                 Foo
             }
@@ -273,7 +299,9 @@ mod tests {
             }
         }
 
-        impl Mul<Foo, Foo> for Foo {
+        impl Mul<Foo> for Foo {
+            type Output = Foo;
+
             fn mul(self, _: Foo) -> Foo {
                 Foo
             }
diff --git a/src/lib.rs b/src/lib.rs
index 58ef857..fd5106f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -45,6 +45,7 @@
 //!
 //! [newt]: https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
 
+#![feature(associated_types)]
 #![feature(macro_rules)]
 #![feature(default_type_params)]
 #![feature(slicing_syntax)]
@@ -123,7 +124,7 @@ pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
 /// assert_eq!(num::pow(2i, 4), 16);
 /// ```
 #[inline]
-pub fn pow<T: Clone + One + Mul<T, T>>(mut base: T, mut exp: uint) -> T {
+pub fn pow<T: Clone + One + Mul<T, Output = T>>(mut base: T, mut exp: uint) -> T {
     if exp == 1 { base }
     else {
         let mut acc = one::<T>();
diff --git a/src/rational.rs b/src/rational.rs
index 7bb587b..8210d97 100644
--- a/src/rational.rs
+++ b/src/rational.rs
@@ -216,7 +216,7 @@ macro_rules! cmp_impl {
     };
     // return something other than a Ratio<T>
     (impl $imp:ident, $($method:ident -> $res:ty),*) => {
-        impl<T: Clone + Mul<T,T> + $imp> $imp for Ratio<T> {
+        impl<T: Clone + Mul<T, Output = T> + $imp> $imp for Ratio<T> {
             $(
                 #[inline]
                 fn $method(&self, other: &Ratio<T>) -> $res {
@@ -234,7 +234,9 @@ cmp_impl!(impl Ord, cmp -> cmp::Ordering);
 
 macro_rules! forward_val_val_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<T: Clone + Integer + PartialOrd> $imp<Ratio<T>, Ratio<T>> for Ratio<T> {
+        impl<T: Clone + Integer + PartialOrd> $imp<Ratio<T>> for Ratio<T> {
+            type Output = Ratio<T>;
+
             #[inline]
             fn $method(self, other: Ratio<T>) -> Ratio<T> {
                 (&self).$method(&other)
@@ -245,7 +247,9 @@ macro_rules! forward_val_val_binop {
 
 macro_rules! forward_ref_val_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<'a, T: Clone + Integer + PartialOrd> $imp<Ratio<T>, Ratio<T>> for &'a Ratio<T> {
+        impl<'a, T: Clone + Integer + PartialOrd> $imp<Ratio<T>> for &'a Ratio<T> {
+            type Output = Ratio<T>;
+
             #[inline]
             fn $method(self, other: Ratio<T>) -> Ratio<T> {
                 self.$method(&other)
@@ -256,7 +260,9 @@ macro_rules! forward_ref_val_binop {
 
 macro_rules! forward_val_ref_binop {
     (impl $imp:ident, $method:ident) => {
-        impl<'a, T: Clone + Integer + PartialOrd> $imp<&'a Ratio<T>, Ratio<T>> for Ratio<T> {
+        impl<'a, T: Clone + Integer + PartialOrd> $imp<&'a Ratio<T>> for Ratio<T> {
+            type Output = Ratio<T>;
+
             #[inline]
             fn $method(self, other: &Ratio<T>) -> Ratio<T> {
                 (&self).$method(other)
@@ -276,8 +282,11 @@ macro_rules! forward_all_binop {
 /* Arithmetic */
 forward_all_binop!(impl Mul, mul);
 // a/b * c/d = (a*c)/(b*d)
-impl<'a, 'b, T: Clone + Integer + PartialOrd>
-    Mul<&'b Ratio<T>, Ratio<T>> for &'a Ratio<T> {
+impl<'a, 'b, T> Mul<&'b Ratio<T>> for &'a Ratio<T>
+    where T: Clone + Integer + PartialOrd
+{
+
+        type Output = Ratio<T>;
     #[inline]
     fn mul(self, rhs: &Ratio<T>) -> Ratio<T> {
         Ratio::new(self.numer.clone() * rhs.numer.clone(), self.denom.clone() * rhs.denom.clone())
@@ -286,8 +295,11 @@ impl<'a, 'b, T: Clone + Integer + PartialOrd>
 
 forward_all_binop!(impl Div, div);
 // (a/b) / (c/d) = (a*d)/(b*c)
-impl<'a, 'b, T: Clone + Integer + PartialOrd>
-    Div<&'b Ratio<T>, Ratio<T>> for &'a Ratio<T> {
+impl<'a, 'b, T> Div<&'b Ratio<T>> for &'a Ratio<T>
+    where T: Clone + Integer + PartialOrd
+{
+    type Output = Ratio<T>;
+
     #[inline]
     fn div(self, rhs: &Ratio<T>) -> Ratio<T> {
         Ratio::new(self.numer.clone() * rhs.denom.clone(), self.denom.clone() * rhs.numer.clone())
@@ -299,7 +311,8 @@ macro_rules! arith_impl {
     (impl $imp:ident, $method:ident) => {
         forward_all_binop!(impl $imp, $method);
         impl<'a, 'b, T: Clone + Integer + PartialOrd>
-            $imp<&'b Ratio<T>,Ratio<T>> for &'a Ratio<T> {
+            $imp<&'b Ratio<T>> for &'a Ratio<T> {
+            type Output = Ratio<T>;
             #[inline]
             fn $method(self, rhs: &Ratio<T>) -> Ratio<T> {
                 Ratio::new((self.numer.clone() * rhs.denom.clone()).$method(self.denom.clone() * rhs.numer.clone()),
@@ -318,14 +331,20 @@ arith_impl!(impl Sub, sub);
 // a/b % c/d = (a*d % b*c)/(b*d)
 arith_impl!(impl Rem, rem);
 
-impl<T: Clone + Integer + PartialOrd>
-    Neg<Ratio<T>> for Ratio<T> {
+impl<T> Neg for Ratio<T>
+    where T: Clone + Integer + PartialOrd
+{
+    type Output = Ratio<T>;
+
     #[inline]
     fn neg(self) -> Ratio<T> { -&self }
 }
 
-impl<'a, T: Clone + Integer + PartialOrd>
-    Neg<Ratio<T>> for &'a Ratio<T> {
+impl<'a, T> Neg for &'a Ratio<T>
+    where T: Clone + Integer + PartialOrd
+{
+    type Output = Ratio<T>;
+
     #[inline]
     fn neg(self) -> Ratio<T> {
         Ratio::new_raw(-self.numer.clone(), self.denom.clone())
@@ -437,14 +456,18 @@ impl<T: FromStrRadix + Clone + Integer + PartialOrd>
     }
 }
 
-impl<A: Clone + Integer + PartialOrd, T: Iterator<Ratio<A>>> AdditiveIterator<Ratio<A>> for T {
+impl<A, T> AdditiveIterator<Ratio<A>> for T
+    where A: Clone + Integer + PartialOrd, T: Iterator<Item = Ratio<A>>
+{
     fn sum(self) -> Ratio<A> {
         let init: Ratio<A> = Zero::zero();
         self.fold(init, |acc, x| acc + x)
     }
 }
 
-impl<A: Clone + Integer + PartialOrd, T: Iterator<Ratio<A>>> MultiplicativeIterator<Ratio<A>> for T {
+impl<A, T> MultiplicativeIterator<Ratio<A>> for T
+    where A: Clone + Integer + PartialOrd, T: Iterator<Item = Ratio<A>>
+{
     fn product(self) -> Ratio<A> {
         let init: Ratio<A> = One::one();
         self.fold(init, |acc, x| acc * x)
diff --git a/src/traits.rs b/src/traits.rs
index a0b77fb..c76380a 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -18,12 +18,8 @@ use std::{f32, f64};
 
 /// The base trait for numeric types
 pub trait Num: PartialEq + Zero + One
-             + Neg<Self>
-             + Add<Self,Self>
-             + Sub<Self,Self>
-             + Mul<Self,Self>
-             + Div<Self,Self>
-             + Rem<Self,Self> {}
+    + Neg<Output = Self> + Add<Output = Self> + Sub<Output = Self>
+    + Mul<Output = Self> + Div<Output = Self> + Rem<Output = Self> {}
 
 macro_rules! trait_impl {
     ($name:ident for $($t:ty)*) => ($(
@@ -40,7 +36,7 @@ trait_impl!(Num for uint u8 u16 u32 u64 int i8 i16 i32 i64 f32 f64);
 /// This trait can be automatically be derived using `#[deriving(Zero)]`
 /// attribute. If you choose to use this, make sure that the laws outlined in
 /// the documentation for `Zero::zero` still hold.
-pub trait Zero: Add<Self, Self> {
+pub trait Zero: Add<Self, Output = Self> {
     /// Returns the additive identity element of `Self`, `0`.
     ///
     /// # Laws
@@ -90,7 +86,7 @@ zero_impl!(f32, 0.0f32);
 zero_impl!(f64, 0.0f64);
 
 /// Defines a multiplicative identity element for `Self`.
-pub trait One: Mul<Self, Self> {
+pub trait One: Mul<Self, Output = Self> {
     /// Returns the multiplicative identity element of `Self`, `1`.
     ///
     /// # Laws
@@ -134,7 +130,7 @@ one_impl!(f32, 1.0f32);
 one_impl!(f64, 1.0f64);
 
 /// Useful functions for signed numbers (i.e. numbers that can be negative).
-pub trait Signed: Num + Neg<Self> {
+pub trait Signed: Num + Neg<Output = Self> {
     /// Computes the absolute value.
     ///
     /// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`.
@@ -328,7 +324,7 @@ impl<T: CheckedAdd + CheckedSub + Zero + PartialOrd + Bounded> Saturating for T
 }
 
 /// Performs addition that returns `None` instead of wrapping around on overflow.
-pub trait CheckedAdd: Add<Self, Self> {
+pub trait CheckedAdd: Add<Self, Output = Self> {
     /// Adds two numbers, checking for overflow. If overflow happens, `None` is returned.
     ///
     /// # Example
@@ -389,7 +385,7 @@ checked_impl!(CheckedAdd, checked_add, i32, intrinsics::i32_add_with_overflow);
 checked_impl!(CheckedAdd, checked_add, i64, intrinsics::i64_add_with_overflow);
 
 /// Performs subtraction that returns `None` instead of wrapping around on underflow.
-pub trait CheckedSub: Sub<Self, Self> {
+pub trait CheckedSub: Sub<Self, Output = Self> {
     /// Subtracts two numbers, checking for underflow. If underflow happens, `None` is returned.
     ///
     /// # Example
@@ -424,7 +420,7 @@ checked_impl!(CheckedSub, checked_sub, i64, intrinsics::i64_sub_with_overflow);
 
 /// Performs multiplication that returns `None` instead of wrapping around on underflow or
 /// overflow.
-pub trait CheckedMul: Mul<Self, Self> {
+pub trait CheckedMul: Mul<Self, Output = Self> {
     /// Multiplies two numbers, checking for underflow or overflow. If underflow or overflow
     /// happens, `None` is returned.
     ///
@@ -460,7 +456,7 @@ checked_impl!(CheckedMul, checked_mul, i64, intrinsics::i64_mul_with_overflow);
 
 /// Performs division that returns `None` instead of panicking on division by zero and instead of
 /// wrapping around on underflow and overflow.
-pub trait CheckedDiv: Div<Self, Self> {
+pub trait CheckedDiv: Div<Self, Output = Self> {
     /// Divides two numbers, checking for underflow, overflow and division by zero. If any of that
     /// happens, `None` is returned.
     ///