Vendor deprecated/unstable traits from std::num

This commit brings in a load of unstable and/or deprecated traits from
the `std::num` module. These traits provide for some degree of generic
programming over numeric types. They are not stable in `std` mostly
because we want more time to iterate on their design. Moving them to the
`num` crate allows existing code to keep using this functionality as we
do so.

Closes #74

src/traits.rs

@@ -11,10 +11,13 @@
 //! Numeric traits for generic mathematics
 
 use std::intrinsics;
-use std::ops::{Add, Div, Mul, Neg, Rem, Sub};
+use std::ops::{Add, Sub, Mul, Div, Rem, Neg};
+use std::ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
 use std::{usize, u8, u16, u32, u64};
 use std::{isize, i8, i16, i32, i64};
 use std::{f32, f64};
+use std::mem::size_of;
+use std::num::FpCategory;
 
 /// The base trait for numeric types
 pub trait Num: PartialEq + Zero + One
@@ -129,6 +132,7 @@ one_impl!(i64, 1i64);
 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<Output = Self> {
     /// Computes the absolute value.
@@ -478,3 +482,1786 @@ macro_rules! checkeddiv_uint_impl {
 }
 
 checkeddiv_uint_impl!(usize u8 u16 u32 u64);
+
+pub trait Int
+    : Num
+    + Clone
+    + NumCast
+    + PartialOrd + Ord
+    + Eq
+    + Not<Output=Self>
+    + BitAnd<Output=Self>
+    + BitOr<Output=Self>
+    + BitXor<Output=Self>
+    + Shl<usize, Output=Self>
+    + Shr<usize, Output=Self>
+    + CheckedAdd<Output=Self>
+    + CheckedSub<Output=Self>
+    + CheckedMul<Output=Self>
+    + CheckedDiv<Output=Self>
+    + Saturating
+{
+    /// Returns the smallest value that can be represented by this integer type.
+    fn min_value() -> Self;
+
+    /// Returns the largest value that can be represented by this integer type.
+    fn max_value() -> Self;
+
+    /// Returns the number of ones in the binary representation of `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0b01001100u8;
+    ///
+    /// assert_eq!(n.count_ones(), 3);
+    /// ```
+    fn count_ones(self) -> u32;
+
+    /// Returns the number of zeros in the binary representation of `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0b01001100u8;
+    ///
+    /// assert_eq!(n.count_zeros(), 5);
+    /// ```
+    fn count_zeros(self) -> u32;
+
+    /// Returns the number of leading zeros in the binary representation
+    /// of `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0b0101000u16;
+    ///
+    /// assert_eq!(n.leading_zeros(), 10);
+    /// ```
+    fn leading_zeros(self) -> u32;
+
+    /// Returns the number of trailing zeros in the binary representation
+    /// of `self`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0b0101000u16;
+    ///
+    /// assert_eq!(n.trailing_zeros(), 3);
+    /// ```
+    fn trailing_zeros(self) -> u32;
+
+    /// Shifts the bits to the left by a specified amount amount, `n`, wrapping
+    /// the truncated bits to the end of the resulting integer.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    /// let m = 0x3456789ABCDEF012u64;
+    ///
+    /// assert_eq!(n.rotate_left(12), m);
+    /// ```
+    fn rotate_left(self, n: u32) -> Self;
+
+    /// Shifts the bits to the right by a specified amount amount, `n`, wrapping
+    /// the truncated bits to the beginning of the resulting integer.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    /// let m = 0xDEF0123456789ABCu64;
+    ///
+    /// assert_eq!(n.rotate_right(12), m);
+    /// ```
+    fn rotate_right(self, n: u32) -> Self;
+
+    /// Reverses the byte order of the integer.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    /// let m = 0xEFCDAB8967452301u64;
+    ///
+    /// assert_eq!(n.swap_bytes(), m);
+    /// ```
+    fn swap_bytes(self) -> Self;
+
+    /// Convert an integer from big endian to the target's endianness.
+    ///
+    /// On big endian this is a no-op. On little endian the bytes are swapped.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    ///
+    /// if cfg!(target_endian = "big") {
+    ///     assert_eq!(Int::from_be(n), n)
+    /// } else {
+    ///     assert_eq!(Int::from_be(n), n.swap_bytes())
+    /// }
+    /// ```
+    fn from_be(x: Self) -> Self;
+
+    /// Convert an integer from little endian to the target's endianness.
+    ///
+    /// On little endian this is a no-op. On big endian the bytes are swapped.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    ///
+    /// if cfg!(target_endian = "little") {
+    ///     assert_eq!(Int::from_le(n), n)
+    /// } else {
+    ///     assert_eq!(Int::from_le(n), n.swap_bytes())
+    /// }
+    /// ```
+    fn from_le(x: Self) -> Self;
+
+    /// Convert `self` to big endian from the target's endianness.
+    ///
+    /// On big endian this is a no-op. On little endian the bytes are swapped.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    ///
+    /// if cfg!(target_endian = "big") {
+    ///     assert_eq!(n.to_be(), n)
+    /// } else {
+    ///     assert_eq!(n.to_be(), n.swap_bytes())
+    /// }
+    /// ```
+    fn to_be(self) -> Self;
+
+    /// Convert `self` to little endian from the target's endianness.
+    ///
+    /// On little endian this is a no-op. On big endian the bytes are swapped.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// let n = 0x0123456789ABCDEFu64;
+    ///
+    /// if cfg!(target_endian = "little") {
+    ///     assert_eq!(n.to_le(), n)
+    /// } else {
+    ///     assert_eq!(n.to_le(), n.swap_bytes())
+    /// }
+    /// ```
+    fn to_le(self) -> Self;
+
+    /// Raises self to the power of `exp`, using exponentiation by squaring.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num::traits::Int;
+    ///
+    /// assert_eq!(2.pow(4), 16);
+    /// ```
+    fn pow(self, mut exp: u32) -> Self;
+}
+
+macro_rules! int_impl {
+    ($($T:ty)*) => ($(
+        impl Int for $T {
+            fn min_value() -> Self {
+                <$T>::min_value()
+            }
+
+            fn max_value() -> Self {
+                <$T>::max_value()
+            }
+
+            fn count_ones(self) -> u32 {
+                <$T>::count_ones(self)
+            }
+
+            fn count_zeros(self) -> u32 {
+                <$T>::count_zeros(self)
+            }
+
+            fn leading_zeros(self) -> u32 {
+                <$T>::leading_zeros(self)
+            }
+
+            fn trailing_zeros(self) -> u32 {
+                <$T>::trailing_zeros(self)
+            }
+
+            fn rotate_left(self, n: u32) -> Self {
+                <$T>::rotate_left(self, n)
+            }
+
+            fn rotate_right(self, n: u32) -> Self {
+                <$T>::rotate_right(self, n)
+            }
+
+            fn swap_bytes(self) -> Self {
+                <$T>::swap_bytes(self)
+            }
+
+            fn from_be(x: Self) -> Self {
+                <$T>::from_be(x)
+            }
+
+            fn from_le(x: Self) -> Self {
+                <$T>::from_le(x)
+            }
+
+            fn to_be(self) -> Self {
+                <$T>::to_be(self)
+            }
+
+            fn to_le(self) -> Self {
+                <$T>::to_le(self)
+            }
+
+            fn pow(self, exp: u32) -> Self {
+                <$T>::pow(self, exp)
+            }
+        }
+    )*)
+}
+
+int_impl!(u8 u16 u32 u64 usize i8 i16 i32 i64 isize);
+
+/// A generic trait for converting a value to a number.
+pub trait ToPrimitive {
+    /// Converts the value of `self` to an `isize`.
+    #[inline]
+    fn to_isize(&self) -> Option<isize> {
+        self.to_i64().and_then(|x| x.to_isize())
+    }
+
+    /// Converts the value of `self` to an `i8`.
+    #[inline]
+    fn to_i8(&self) -> Option<i8> {
+        self.to_i64().and_then(|x| x.to_i8())
+    }
+
+    /// Converts the value of `self` to an `i16`.
+    #[inline]
+    fn to_i16(&self) -> Option<i16> {
+        self.to_i64().and_then(|x| x.to_i16())
+    }
+
+    /// Converts the value of `self` to an `i32`.
+    #[inline]
+    fn to_i32(&self) -> Option<i32> {
+        self.to_i64().and_then(|x| x.to_i32())
+    }
+
+    /// Converts the value of `self` to an `i64`.
+    fn to_i64(&self) -> Option<i64>;
+
+    /// Converts the value of `self` to a `usize`.
+    #[inline]
+    fn to_usize(&self) -> Option<usize> {
+        self.to_u64().and_then(|x| x.to_usize())
+    }
+
+    /// Converts the value of `self` to an `u8`.
+    #[inline]
+    fn to_u8(&self) -> Option<u8> {
+        self.to_u64().and_then(|x| x.to_u8())
+    }
+
+    /// Converts the value of `self` to an `u16`.
+    #[inline]
+    fn to_u16(&self) -> Option<u16> {
+        self.to_u64().and_then(|x| x.to_u16())
+    }
+
+    /// Converts the value of `self` to an `u32`.
+    #[inline]
+    fn to_u32(&self) -> Option<u32> {
+        self.to_u64().and_then(|x| x.to_u32())
+    }
+
+    /// Converts the value of `self` to an `u64`.
+    #[inline]
+    fn to_u64(&self) -> Option<u64>;
+
+    /// Converts the value of `self` to an `f32`.
+    #[inline]
+    fn to_f32(&self) -> Option<f32> {
+        self.to_f64().and_then(|x| x.to_f32())
+    }
+
+    /// Converts the value of `self` to an `f64`.
+    #[inline]
+    fn to_f64(&self) -> Option<f64> {
+        self.to_i64().and_then(|x| x.to_f64())
+    }
+}
+
+macro_rules! impl_to_primitive_int_to_int {
+    ($SrcT:ty, $DstT:ty, $slf:expr) => (
+        {
+            if size_of::<$SrcT>() <= size_of::<$DstT>() {
+                Some($slf as $DstT)
+            } else {
+                let n = $slf as i64;
+                let min_value: $DstT = Int::min_value();
+                let max_value: $DstT = Int::max_value();
+                if min_value as i64 <= n && n <= max_value as i64 {
+                    Some($slf as $DstT)
+                } else {
+                    None
+                }
+            }
+        }
+    )
+}
+
+macro_rules! impl_to_primitive_int_to_uint {
+    ($SrcT:ty, $DstT:ty, $slf:expr) => (
+        {
+            let zero: $SrcT = Zero::zero();
+            let max_value: $DstT = Int::max_value();
+            if zero <= $slf && $slf as u64 <= max_value as u64 {
+                Some($slf as $DstT)
+            } else {
+                None
+            }
+        }
+    )
+}
+
+macro_rules! impl_to_primitive_int {
+    ($T:ty) => (
+        impl ToPrimitive for $T {
+            #[inline]
+            fn to_isize(&self) -> Option<isize> { impl_to_primitive_int_to_int!($T, isize, *self) }
+            #[inline]
+            fn to_i8(&self) -> Option<i8> { impl_to_primitive_int_to_int!($T, i8, *self) }
+            #[inline]
+            fn to_i16(&self) -> Option<i16> { impl_to_primitive_int_to_int!($T, i16, *self) }
+            #[inline]
+            fn to_i32(&self) -> Option<i32> { impl_to_primitive_int_to_int!($T, i32, *self) }
+            #[inline]
+            fn to_i64(&self) -> Option<i64> { impl_to_primitive_int_to_int!($T, i64, *self) }
+
+            #[inline]
+            fn to_usize(&self) -> Option<usize> { impl_to_primitive_int_to_uint!($T, usize, *self) }
+            #[inline]
+            fn to_u8(&self) -> Option<u8> { impl_to_primitive_int_to_uint!($T, u8, *self) }
+            #[inline]
+            fn to_u16(&self) -> Option<u16> { impl_to_primitive_int_to_uint!($T, u16, *self) }
+            #[inline]
+            fn to_u32(&self) -> Option<u32> { impl_to_primitive_int_to_uint!($T, u32, *self) }
+            #[inline]
+            fn to_u64(&self) -> Option<u64> { impl_to_primitive_int_to_uint!($T, u64, *self) }
+
+            #[inline]
+            fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
+            #[inline]
+            fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
+        }
+    )
+}
+
+impl_to_primitive_int! { isize }
+impl_to_primitive_int! { i8 }
+impl_to_primitive_int! { i16 }
+impl_to_primitive_int! { i32 }
+impl_to_primitive_int! { i64 }
+
+macro_rules! impl_to_primitive_uint_to_int {
+    ($DstT:ty, $slf:expr) => (
+        {
+            let max_value: $DstT = Int::max_value();
+            if $slf as u64 <= max_value as u64 {
+                Some($slf as $DstT)
+            } else {
+                None
+            }
+        }
+    )
+}
+
+macro_rules! impl_to_primitive_uint_to_uint {
+    ($SrcT:ty, $DstT:ty, $slf:expr) => (
+        {
+            if size_of::<$SrcT>() <= size_of::<$DstT>() {
+                Some($slf as $DstT)
+            } else {
+                let zero: $SrcT = Zero::zero();
+                let max_value: $DstT = Int::max_value();
+                if zero <= $slf && $slf as u64 <= max_value as u64 {
+                    Some($slf as $DstT)
+                } else {
+                    None
+                }
+            }
+        }
+    )
+}
+
+macro_rules! impl_to_primitive_uint {
+    ($T:ty) => (
+        impl ToPrimitive for $T {
+            #[inline]
+            fn to_isize(&self) -> Option<isize> { impl_to_primitive_uint_to_int!(isize, *self) }
+            #[inline]
+            fn to_i8(&self) -> Option<i8> { impl_to_primitive_uint_to_int!(i8, *self) }
+            #[inline]
+            fn to_i16(&self) -> Option<i16> { impl_to_primitive_uint_to_int!(i16, *self) }
+            #[inline]
+            fn to_i32(&self) -> Option<i32> { impl_to_primitive_uint_to_int!(i32, *self) }
+            #[inline]
+            fn to_i64(&self) -> Option<i64> { impl_to_primitive_uint_to_int!(i64, *self) }
+
+            #[inline]
+            fn to_usize(&self) -> Option<usize> {
+                impl_to_primitive_uint_to_uint!($T, usize, *self)
+            }
+            #[inline]
+            fn to_u8(&self) -> Option<u8> { impl_to_primitive_uint_to_uint!($T, u8, *self) }
+            #[inline]
+            fn to_u16(&self) -> Option<u16> { impl_to_primitive_uint_to_uint!($T, u16, *self) }
+            #[inline]
+            fn to_u32(&self) -> Option<u32> { impl_to_primitive_uint_to_uint!($T, u32, *self) }
+            #[inline]
+            fn to_u64(&self) -> Option<u64> { impl_to_primitive_uint_to_uint!($T, u64, *self) }
+
+            #[inline]
+            fn to_f32(&self) -> Option<f32> { Some(*self as f32) }
+            #[inline]
+            fn to_f64(&self) -> Option<f64> { Some(*self as f64) }
+        }
+    )
+}
+
+impl_to_primitive_uint! { usize }
+impl_to_primitive_uint! { u8 }
+impl_to_primitive_uint! { u16 }
+impl_to_primitive_uint! { u32 }
+impl_to_primitive_uint! { u64 }
+
+macro_rules! impl_to_primitive_float_to_float {
+    ($SrcT:ident, $DstT:ident, $slf:expr) => (
+        if size_of::<$SrcT>() <= size_of::<$DstT>() {
+            Some($slf as $DstT)
+        } else {
+            let n = $slf as f64;
+            let max_value: $SrcT = ::std::$SrcT::MAX;
+            if -max_value as f64 <= n && n <= max_value as f64 {
+                Some($slf as $DstT)
+            } else {
+                None
+            }
+        }
+    )
+}
+
+macro_rules! impl_to_primitive_float {
+    ($T:ident) => (
+        impl ToPrimitive for $T {
+            #[inline]
+            fn to_isize(&self) -> Option<isize> { Some(*self as isize) }
+            #[inline]
+            fn to_i8(&self) -> Option<i8> { Some(*self as i8) }
+            #[inline]
+            fn to_i16(&self) -> Option<i16> { Some(*self as i16) }
+            #[inline]
+            fn to_i32(&self) -> Option<i32> { Some(*self as i32) }
+            #[inline]
+            fn to_i64(&self) -> Option<i64> { Some(*self as i64) }
+
+            #[inline]
+            fn to_usize(&self) -> Option<usize> { Some(*self as usize) }
+            #[inline]
+            fn to_u8(&self) -> Option<u8> { Some(*self as u8) }
+            #[inline]
+            fn to_u16(&self) -> Option<u16> { Some(*self as u16) }
+            #[inline]
+            fn to_u32(&self) -> Option<u32> { Some(*self as u32) }
+            #[inline]
+            fn to_u64(&self) -> Option<u64> { Some(*self as u64) }
+
+            #[inline]
+            fn to_f32(&self) -> Option<f32> { impl_to_primitive_float_to_float!($T, f32, *self) }
+            #[inline]
+            fn to_f64(&self) -> Option<f64> { impl_to_primitive_float_to_float!($T, f64, *self) }
+        }
+    )
+}
+
+impl_to_primitive_float! { f32 }
+impl_to_primitive_float! { f64 }
+
+/// A generic trait for converting a number to a value.
+pub trait FromPrimitive: Sized {
+    /// Convert an `isize` to return an optional value of this type. If the
+    /// value cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_isize(n: isize) -> Option<Self> {
+        FromPrimitive::from_i64(n as i64)
+    }
+
+    /// Convert an `i8` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_i8(n: i8) -> Option<Self> {
+        FromPrimitive::from_i64(n as i64)
+    }
+
+    /// Convert an `i16` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_i16(n: i16) -> Option<Self> {
+        FromPrimitive::from_i64(n as i64)
+    }
+
+    /// Convert an `i32` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_i32(n: i32) -> Option<Self> {
+        FromPrimitive::from_i64(n as i64)
+    }
+
+    /// Convert an `i64` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    fn from_i64(n: i64) -> Option<Self>;
+
+    /// Convert a `usize` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_usize(n: usize) -> Option<Self> {
+        FromPrimitive::from_u64(n as u64)
+    }
+
+    /// Convert an `u8` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_u8(n: u8) -> Option<Self> {
+        FromPrimitive::from_u64(n as u64)
+    }
+
+    /// Convert an `u16` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_u16(n: u16) -> Option<Self> {
+        FromPrimitive::from_u64(n as u64)
+    }
+
+    /// Convert an `u32` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_u32(n: u32) -> Option<Self> {
+        FromPrimitive::from_u64(n as u64)
+    }
+
+    /// Convert an `u64` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    fn from_u64(n: u64) -> Option<Self>;
+
+    /// Convert a `f32` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_f32(n: f32) -> Option<Self> {
+        FromPrimitive::from_f64(n as f64)
+    }
+
+    /// Convert a `f64` to return an optional value of this type. If the
+    /// type cannot be represented by this value, the `None` is returned.
+    #[inline]
+    fn from_f64(n: f64) -> Option<Self> {
+        FromPrimitive::from_i64(n as i64)
+    }
+}
+
+macro_rules! impl_from_primitive {
+    ($T:ty, $to_ty:ident) => (
+        #[allow(deprecated)]
+        impl FromPrimitive for $T {
+            #[inline] fn from_i8(n: i8) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_i16(n: i16) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_i32(n: i32) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_i64(n: i64) -> Option<$T> { n.$to_ty() }
+
+            #[inline] fn from_u8(n: u8) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_u16(n: u16) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_u32(n: u32) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_u64(n: u64) -> Option<$T> { n.$to_ty() }
+
+            #[inline] fn from_f32(n: f32) -> Option<$T> { n.$to_ty() }
+            #[inline] fn from_f64(n: f64) -> Option<$T> { n.$to_ty() }
+        }
+    )
+}
+
+impl_from_primitive! { isize, to_isize }
+impl_from_primitive! { i8, to_i8 }
+impl_from_primitive! { i16, to_i16 }
+impl_from_primitive! { i32, to_i32 }
+impl_from_primitive! { i64, to_i64 }
+impl_from_primitive! { usize, to_usize }
+impl_from_primitive! { u8, to_u8 }
+impl_from_primitive! { u16, to_u16 }
+impl_from_primitive! { u32, to_u32 }
+impl_from_primitive! { u64, to_u64 }
+impl_from_primitive! { f32, to_f32 }
+impl_from_primitive! { f64, to_f64 }
+
+/// Cast from one machine scalar to another.
+///
+/// # Examples
+///
+/// ```
+/// use num;
+///
+/// let twenty: f32 = num::traits::cast(0x14).unwrap();
+/// assert_eq!(twenty, 20f32);
+/// ```
+///
+#[inline]
+pub fn cast<T: NumCast,U: NumCast>(n: T) -> Option<U> {
+    NumCast::from(n)
+}
+
+/// An interface for casting between machine scalars.
+pub trait NumCast: ToPrimitive {
+    /// Creates a number from another value that can be converted into
+    /// a primitive via the `ToPrimitive` trait.
+    fn from<T: ToPrimitive>(n: T) -> Option<Self>;
+}
+
+macro_rules! impl_num_cast {
+    ($T:ty, $conv:ident) => (
+        impl NumCast for $T {
+            #[inline]
+            #[allow(deprecated)]
+            fn from<N: ToPrimitive>(n: N) -> Option<$T> {
+                // `$conv` could be generated using `concat_idents!`, but that
+                // macro seems to be broken at the moment
+                n.$conv()
+            }
+        }
+    )
+}
+
+impl_num_cast! { u8,    to_u8 }
+impl_num_cast! { u16,   to_u16 }
+impl_num_cast! { u32,   to_u32 }
+impl_num_cast! { u64,   to_u64 }
+impl_num_cast! { usize,  to_usize }
+impl_num_cast! { i8,    to_i8 }
+impl_num_cast! { i16,   to_i16 }
+impl_num_cast! { i32,   to_i32 }
+impl_num_cast! { i64,   to_i64 }
+impl_num_cast! { isize,   to_isize }
+impl_num_cast! { f32,   to_f32 }
+impl_num_cast! { f64,   to_f64 }
+
+pub trait Float
+    : Num
+    + Clone
+    + NumCast
+    + PartialOrd
+{
+    /// Returns the `NaN` value.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let nan: f32 = Float::nan();
+    ///
+    /// assert!(nan.is_nan());
+    /// ```
+    fn nan() -> Self;
+    /// Returns the infinite value.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f32;
+    ///
+    /// let infinity: f32 = Float::infinity();
+    ///
+    /// assert!(infinity.is_infinite());
+    /// assert!(!infinity.is_finite());
+    /// assert!(infinity > f32::MAX);
+    /// ```
+    fn infinity() -> Self;
+    /// Returns the negative infinite value.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f32;
+    ///
+    /// let neg_infinity: f32 = Float::neg_infinity();
+    ///
+    /// assert!(neg_infinity.is_infinite());
+    /// assert!(!neg_infinity.is_finite());
+    /// assert!(neg_infinity < f32::MIN);
+    /// ```
+    fn neg_infinity() -> Self;
+    /// Returns `-0.0`.
+    ///
+    /// ```
+    /// use num::traits::{Zero, Float};
+    ///
+    /// let inf: f32 = Float::infinity();
+    /// let zero: f32 = Zero::zero();
+    /// let neg_zero: f32 = Float::neg_zero();
+    ///
+    /// assert_eq!(zero, neg_zero);
+    /// assert_eq!(7.0f32/inf, zero);
+    /// assert_eq!(zero * 10.0, zero);
+    /// ```
+    fn neg_zero() -> Self;
+
+    /// Returns the smallest finite value that this type can represent.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x: f64 = Float::min_value();
+    ///
+    /// assert_eq!(x, f64::MIN);
+    /// ```
+    fn min_value() -> Self;
+
+    /// Returns the largest finite value that this type can represent.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x: f64 = Float::max_value();
+    /// assert_eq!(x, f64::MAX);
+    /// ```
+    fn max_value() -> Self;
+
+    /// Returns `true` if this value is `NaN` and false otherwise.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let nan = f64::NAN;
+    /// let f = 7.0;
+    ///
+    /// assert!(nan.is_nan());
+    /// assert!(!f.is_nan());
+    /// ```
+    fn is_nan(self) -> bool;
+
+    /// Returns `true` if this value is positive infinity or negative infinity and
+    /// false otherwise.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f32;
+    ///
+    /// let f = 7.0f32;
+    /// let inf: f32 = Float::infinity();
+    /// let neg_inf: f32 = Float::neg_infinity();
+    /// let nan: f32 = f32::NAN;
+    ///
+    /// assert!(!f.is_infinite());
+    /// assert!(!nan.is_infinite());
+    ///
+    /// assert!(inf.is_infinite());
+    /// assert!(neg_inf.is_infinite());
+    /// ```
+    fn is_infinite(self) -> bool;
+
+    /// Returns `true` if this number is neither infinite nor `NaN`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f32;
+    ///
+    /// let f = 7.0f32;
+    /// let inf: f32 = Float::infinity();
+    /// let neg_inf: f32 = Float::neg_infinity();
+    /// let nan: f32 = f32::NAN;
+    ///
+    /// assert!(f.is_finite());
+    ///
+    /// assert!(!nan.is_finite());
+    /// assert!(!inf.is_finite());
+    /// assert!(!neg_inf.is_finite());
+    /// ```
+    fn is_finite(self) -> bool;
+
+    /// Returns `true` if the number is neither zero, infinite,
+    /// [subnormal][subnormal], or `NaN`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f32;
+    ///
+    /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
+    /// let max = f32::MAX;
+    /// let lower_than_min = 1.0e-40_f32;
+    /// let zero = 0.0f32;
+    ///
+    /// assert!(min.is_normal());
+    /// assert!(max.is_normal());
+    ///
+    /// assert!(!zero.is_normal());
+    /// assert!(!f32::NAN.is_normal());
+    /// assert!(!f32::INFINITY.is_normal());
+    /// // Values between `0` and `min` are Subnormal.
+    /// assert!(!lower_than_min.is_normal());
+    /// ```
+    /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
+    fn is_normal(self) -> bool;
+
+    /// Returns the floating point category of the number. If only one property
+    /// is going to be tested, it is generally faster to use the specific
+    /// predicate instead.
+    ///
+    /// ```
+    /// # #![feature(core)]
+    /// use std::num::{Float, FpCategory};
+    /// use std::f32;
+    ///
+    /// let num = 12.4f32;
+    /// let inf = f32::INFINITY;
+    ///
+    /// assert_eq!(num.classify(), FpCategory::Normal);
+    /// assert_eq!(inf.classify(), FpCategory::Infinite);
+    /// ```
+    fn classify(self) -> FpCategory;
+
+    /// Returns the largest integer less than or equal to a number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 3.99;
+    /// let g = 3.0;
+    ///
+    /// assert_eq!(f.floor(), 3.0);
+    /// assert_eq!(g.floor(), 3.0);
+    /// ```
+    fn floor(self) -> Self;
+
+    /// Returns the smallest integer greater than or equal to a number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 3.01;
+    /// let g = 4.0;
+    ///
+    /// assert_eq!(f.ceil(), 4.0);
+    /// assert_eq!(g.ceil(), 4.0);
+    /// ```
+    fn ceil(self) -> Self;
+
+    /// Returns the nearest integer to a number. Round half-way cases away from
+    /// `0.0`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 3.3;
+    /// let g = -3.3;
+    ///
+    /// assert_eq!(f.round(), 3.0);
+    /// assert_eq!(g.round(), -3.0);
+    /// ```
+    fn round(self) -> Self;
+
+    /// Return the integer part of a number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 3.3;
+    /// let g = -3.7;
+    ///
+    /// assert_eq!(f.trunc(), 3.0);
+    /// assert_eq!(g.trunc(), -3.0);
+    /// ```
+    fn trunc(self) -> Self;
+
+    /// Returns the fractional part of a number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 3.5;
+    /// let y = -3.5;
+    /// let abs_difference_x = (x.fract() - 0.5).abs();
+    /// let abs_difference_y = (y.fract() - (-0.5)).abs();
+    ///
+    /// assert!(abs_difference_x < 1e-10);
+    /// assert!(abs_difference_y < 1e-10);
+    /// ```
+    fn fract(self) -> Self;
+
+    /// Computes the absolute value of `self`. Returns `Float::nan()` if the
+    /// number is `Float::nan()`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = 3.5;
+    /// let y = -3.5;
+    ///
+    /// let abs_difference_x = (x.abs() - x).abs();
+    /// let abs_difference_y = (y.abs() - (-y)).abs();
+    ///
+    /// assert!(abs_difference_x < 1e-10);
+    /// assert!(abs_difference_y < 1e-10);
+    ///
+    /// assert!(f64::NAN.abs().is_nan());
+    /// ```
+    fn abs(self) -> Self;
+
+    /// Returns a number that represents the sign of `self`.
+    ///
+    /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()`
+    /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()`
+    /// - `Float::nan()` if the number is `Float::nan()`
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let f = 3.5;
+    ///
+    /// assert_eq!(f.signum(), 1.0);
+    /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
+    ///
+    /// assert!(f64::NAN.signum().is_nan());
+    /// ```
+    fn signum(self) -> Self;
+
+    /// Returns `true` if `self` is positive, including `+0.0` and
+    /// `Float::infinity()`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let nan: f64 = f64::NAN;
+    ///
+    /// let f = 7.0;
+    /// let g = -7.0;
+    ///
+    /// assert!(f.is_sign_positive());
+    /// assert!(!g.is_sign_positive());
+    /// // Requires both tests to determine if is `NaN`
+    /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
+    /// ```
+    fn is_sign_positive(self) -> bool;
+
+    /// Returns `true` if `self` is negative, including `-0.0` and
+    /// `Float::neg_infinity()`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let nan = f64::NAN;
+    ///
+    /// let f = 7.0;
+    /// let g = -7.0;
+    ///
+    /// assert!(!f.is_sign_negative());
+    /// assert!(g.is_sign_negative());
+    /// // Requires both tests to determine if is `NaN`.
+    /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
+    /// ```
+    fn is_sign_negative(self) -> bool;
+
+    /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
+    /// error. This produces a more accurate result with better performance than
+    /// a separate multiplication operation followed by an add.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let m = 10.0;
+    /// let x = 4.0;
+    /// let b = 60.0;
+    ///
+    /// // 100.0
+    /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn mul_add(self, a: Self, b: Self) -> Self;
+    /// Take the reciprocal (inverse) of a number, `1/x`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 2.0;
+    /// let abs_difference = (x.recip() - (1.0/x)).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn recip(self) -> Self;
+
+    /// Raise a number to an integer power.
+    ///
+    /// Using this function is generally faster than using `powf`
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 2.0;
+    /// let abs_difference = (x.powi(2) - x*x).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn powi(self, n: i32) -> Self;
+
+    /// Raise a number to a floating point power.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 2.0;
+    /// let abs_difference = (x.powf(2.0) - x*x).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn powf(self, n: Self) -> Self;
+
+    /// Take the square root of a number.
+    ///
+    /// Returns NaN if `self` is a negative number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let positive = 4.0;
+    /// let negative = -4.0;
+    ///
+    /// let abs_difference = (positive.sqrt() - 2.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// assert!(negative.sqrt().is_nan());
+    /// ```
+    fn sqrt(self) -> Self;
+
+    /// Returns `e^(self)`, (the exponential function).
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let one = 1.0;
+    /// // e^1
+    /// let e = one.exp();
+    ///
+    /// // ln(e) - 1 == 0
+    /// let abs_difference = (e.ln() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn exp(self) -> Self;
+
+    /// Returns `2^(self)`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 2.0;
+    ///
+    /// // 2^2 - 4 == 0
+    /// let abs_difference = (f.exp2() - 4.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn exp2(self) -> Self;
+
+    /// Returns the natural logarithm of the number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let one = 1.0;
+    /// // e^1
+    /// let e = one.exp();
+    ///
+    /// // ln(e) - 1 == 0
+    /// let abs_difference = (e.ln() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn ln(self) -> Self;
+
+    /// Returns the logarithm of the number with respect to an arbitrary base.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let ten = 10.0;
+    /// let two = 2.0;
+    ///
+    /// // log10(10) - 1 == 0
+    /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
+    ///
+    /// // log2(2) - 1 == 0
+    /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
+    ///
+    /// assert!(abs_difference_10 < 1e-10);
+    /// assert!(abs_difference_2 < 1e-10);
+    /// ```
+    fn log(self, base: Self) -> Self;
+
+    /// Returns the base 2 logarithm of the number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let two = 2.0;
+    ///
+    /// // log2(2) - 1 == 0
+    /// let abs_difference = (two.log2() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn log2(self) -> Self;
+
+    /// Returns the base 10 logarithm of the number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let ten = 10.0;
+    ///
+    /// // log10(10) - 1 == 0
+    /// let abs_difference = (ten.log10() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn log10(self) -> Self;
+
+    /// Convert radians to degrees.
+    ///
+    /// ```
+    /// # #![feature(std_misc, core)]
+    /// use num::traits::Float;
+    /// use std::f64::consts;
+    ///
+    /// let angle = consts::PI;
+    ///
+    /// let abs_difference = (angle.to_degrees() - 180.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn to_degrees(self) -> Self;
+
+    /// Convert degrees to radians.
+    ///
+    /// ```
+    /// # #![feature(std_misc, core)]
+    /// use num::traits::Float;
+    /// use std::f64::consts;
+    ///
+    /// let angle = 180.0;
+    ///
+    /// let abs_difference = (angle.to_radians() - consts::PI).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn to_radians(self) -> Self;
+
+    /// Returns the maximum of the two numbers.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 1.0;
+    /// let y = 2.0;
+    ///
+    /// assert_eq!(x.max(y), y);
+    /// ```
+    fn max(self, other: Self) -> Self;
+
+    /// Returns the minimum of the two numbers.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 1.0;
+    /// let y = 2.0;
+    ///
+    /// assert_eq!(x.min(y), x);
+    /// ```
+    fn min(self, other: Self) -> Self;
+
+    /// The positive difference of two numbers.
+    ///
+    /// * If `self <= other`: `0:0`
+    /// * Else: `self - other`
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 3.0;
+    /// let y = -3.0;
+    ///
+    /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
+    /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
+    ///
+    /// assert!(abs_difference_x < 1e-10);
+    /// assert!(abs_difference_y < 1e-10);
+    /// ```
+    fn abs_sub(self, other: Self) -> Self;
+
+    /// Take the cubic root of a number.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 8.0;
+    ///
+    /// // x^(1/3) - 2 == 0
+    /// let abs_difference = (x.cbrt() - 2.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn cbrt(self) -> Self;
+
+    /// Calculate the length of the hypotenuse of a right-angle triangle given
+    /// legs of length `x` and `y`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 2.0;
+    /// let y = 3.0;
+    ///
+    /// // sqrt(x^2 + y^2)
+    /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn hypot(self, other: Self) -> Self;
+
+    /// Computes the sine of a number (in radians).
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = f64::consts::PI/2.0;
+    ///
+    /// let abs_difference = (x.sin() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn sin(self) -> Self;
+
+    /// Computes the cosine of a number (in radians).
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = 2.0*f64::consts::PI;
+    ///
+    /// let abs_difference = (x.cos() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn cos(self) -> Self;
+
+    /// Computes the tangent of a number (in radians).
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = f64::consts::PI/4.0;
+    /// let abs_difference = (x.tan() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-14);
+    /// ```
+    fn tan(self) -> Self;
+
+    /// Computes the arcsine of a number. Return value is in radians in
+    /// the range [-pi/2, pi/2] or NaN if the number is outside the range
+    /// [-1, 1].
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let f = f64::consts::PI / 2.0;
+    ///
+    /// // asin(sin(pi/2))
+    /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn asin(self) -> Self;
+
+    /// Computes the arccosine of a number. Return value is in radians in
+    /// the range [0, pi] or NaN if the number is outside the range
+    /// [-1, 1].
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let f = f64::consts::PI / 4.0;
+    ///
+    /// // acos(cos(pi/4))
+    /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn acos(self) -> Self;
+
+    /// Computes the arctangent of a number. Return value is in radians in the
+    /// range [-pi/2, pi/2];
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let f = 1.0;
+    ///
+    /// // atan(tan(1))
+    /// let abs_difference = (f.tan().atan() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn atan(self) -> Self;
+
+    /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
+    ///
+    /// * `x = 0`, `y = 0`: `0`
+    /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
+    /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
+    /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let pi = f64::consts::PI;
+    /// // All angles from horizontal right (+x)
+    /// // 45 deg counter-clockwise
+    /// let x1 = 3.0;
+    /// let y1 = -3.0;
+    ///
+    /// // 135 deg clockwise
+    /// let x2 = -3.0;
+    /// let y2 = 3.0;
+    ///
+    /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
+    /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
+    ///
+    /// assert!(abs_difference_1 < 1e-10);
+    /// assert!(abs_difference_2 < 1e-10);
+    /// ```
+    fn atan2(self, other: Self) -> Self;
+
+    /// Simultaneously computes the sine and cosine of the number, `x`. Returns
+    /// `(sin(x), cos(x))`.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = f64::consts::PI/4.0;
+    /// let f = x.sin_cos();
+    ///
+    /// let abs_difference_0 = (f.0 - x.sin()).abs();
+    /// let abs_difference_1 = (f.1 - x.cos()).abs();
+    ///
+    /// assert!(abs_difference_0 < 1e-10);
+    /// assert!(abs_difference_0 < 1e-10);
+    /// ```
+    fn sin_cos(self) -> (Self, Self);
+
+    /// Returns `e^(self) - 1` in a way that is accurate even if the
+    /// number is close to zero.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 7.0;
+    ///
+    /// // e^(ln(7)) - 1
+    /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn exp_m1(self) -> Self;
+
+    /// Returns `ln(1+n)` (natural logarithm) more accurately than if
+    /// the operations were performed separately.
+    ///
+    /// ```
+    /// # #![feature(std_misc, core)]
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let x = f64::consts::E - 1.0;
+    ///
+    /// // ln(1 + (e - 1)) == ln(e) == 1
+    /// let abs_difference = (x.ln_1p() - 1.0).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn ln_1p(self) -> Self;
+
+    /// Hyperbolic sine function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let e = f64::consts::E;
+    /// let x = 1.0;
+    ///
+    /// let f = x.sinh();
+    /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
+    /// let g = (e*e - 1.0)/(2.0*e);
+    /// let abs_difference = (f - g).abs();
+    ///
+    /// assert!(abs_difference < 1e-10);
+    /// ```
+    fn sinh(self) -> Self;
+
+    /// Hyperbolic cosine function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let e = f64::consts::E;
+    /// let x = 1.0;
+    /// let f = x.cosh();
+    /// // Solving cosh() at 1 gives this result
+    /// let g = (e*e + 1.0)/(2.0*e);
+    /// let abs_difference = (f - g).abs();
+    ///
+    /// // Same result
+    /// assert!(abs_difference < 1.0e-10);
+    /// ```
+    fn cosh(self) -> Self;
+
+    /// Hyperbolic tangent function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let e = f64::consts::E;
+    /// let x = 1.0;
+    ///
+    /// let f = x.tanh();
+    /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
+    /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
+    /// let abs_difference = (f - g).abs();
+    ///
+    /// assert!(abs_difference < 1.0e-10);
+    /// ```
+    fn tanh(self) -> Self;
+
+    /// Inverse hyperbolic sine function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 1.0;
+    /// let f = x.sinh().asinh();
+    ///
+    /// let abs_difference = (f - x).abs();
+    ///
+    /// assert!(abs_difference < 1.0e-10);
+    /// ```
+    fn asinh(self) -> Self;
+
+    /// Inverse hyperbolic cosine function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    ///
+    /// let x = 1.0;
+    /// let f = x.cosh().acosh();
+    ///
+    /// let abs_difference = (f - x).abs();
+    ///
+    /// assert!(abs_difference < 1.0e-10);
+    /// ```
+    fn acosh(self) -> Self;
+
+    /// Inverse hyperbolic tangent function.
+    ///
+    /// ```
+    /// use num::traits::Float;
+    /// use std::f64;
+    ///
+    /// let e = f64::consts::E;
+    /// let f = e.tanh().atanh();
+    ///
+    /// let abs_difference = (f - e).abs();
+    ///
+    /// assert!(abs_difference < 1.0e-10);
+    /// ```
+    fn atanh(self) -> Self;
+}
+
+macro_rules! float_impl {
+    ($($T:ident)*) => ($(
+        impl Float for $T {
+            fn nan() -> Self {
+                ::std::$T::NAN
+            }
+
+            fn infinity() -> Self {
+                ::std::$T::INFINITY
+            }
+
+            fn neg_infinity() -> Self {
+                ::std::$T::NEG_INFINITY
+            }
+
+            fn neg_zero() -> Self {
+                -0.0
+            }
+
+            fn min_value() -> Self {
+                ::std::$T::MIN
+            }
+
+            fn max_value() -> Self {
+                ::std::$T::MAX
+            }
+
+            fn is_nan(self) -> bool {
+                <$T>::is_nan(self)
+            }
+
+            fn is_infinite(self) -> bool {
+                <$T>::is_infinite(self)
+            }
+
+            fn is_finite(self) -> bool {
+                <$T>::is_finite(self)
+            }
+
+            fn is_normal(self) -> bool {
+                <$T>::is_normal(self)
+            }
+
+            fn classify(self) -> FpCategory {
+                <$T>::classify(self)
+            }
+
+            fn floor(self) -> Self {
+                <$T>::floor(self)
+            }
+
+            fn ceil(self) -> Self {
+                <$T>::ceil(self)
+            }
+
+            fn round(self) -> Self {
+                <$T>::round(self)
+            }
+
+            fn trunc(self) -> Self {
+                <$T>::trunc(self)
+            }
+
+            fn fract(self) -> Self {
+                <$T>::fract(self)
+            }
+
+            fn abs(self) -> Self {
+                <$T>::abs(self)
+            }
+
+            fn signum(self) -> Self {
+                <$T>::signum(self)
+            }
+
+            fn is_sign_positive(self) -> bool {
+                <$T>::is_sign_positive(self)
+            }
+
+            fn is_sign_negative(self) -> bool {
+                <$T>::is_sign_negative(self)
+            }
+
+            fn mul_add(self, a: Self, b: Self) -> Self {
+                <$T>::mul_add(self, a, b)
+            }
+
+            fn recip(self) -> Self {
+                <$T>::recip(self)
+            }
+
+            fn powi(self, n: i32) -> Self {
+                <$T>::powi(self, n)
+            }
+
+            fn powf(self, n: Self) -> Self {
+                <$T>::powf(self, n)
+            }
+
+            fn sqrt(self) -> Self {
+                <$T>::sqrt(self)
+            }
+
+            fn exp(self) -> Self {
+                <$T>::exp(self)
+            }
+
+            fn exp2(self) -> Self {
+                <$T>::exp2(self)
+            }
+
+            fn ln(self) -> Self {
+                <$T>::ln(self)
+            }
+
+            fn log(self, base: Self) -> Self {
+                <$T>::log(self, base)
+            }
+
+            fn log2(self) -> Self {
+                <$T>::log2(self)
+            }
+
+            fn log10(self) -> Self {
+                <$T>::log10(self)
+            }
+
+            fn to_degrees(self) -> Self {
+                <$T>::to_degrees(self)
+            }
+
+            fn to_radians(self) -> Self {
+                <$T>::to_radians(self)
+            }
+
+            fn max(self, other: Self) -> Self {
+                <$T>::max(self, other)
+            }
+
+            fn min(self, other: Self) -> Self {
+                <$T>::min(self, other)
+            }
+
+            fn abs_sub(self, other: Self) -> Self {
+                <$T>::abs_sub(self, other)
+            }
+
+            fn cbrt(self) -> Self {
+                <$T>::cbrt(self)
+            }
+
+            fn hypot(self, other: Self) -> Self {
+                <$T>::hypot(self, other)
+            }
+
+            fn sin(self) -> Self {
+                <$T>::sin(self)
+            }
+
+            fn cos(self) -> Self {
+                <$T>::cos(self)
+            }
+
+            fn tan(self) -> Self {
+                <$T>::tan(self)
+            }
+
+            fn asin(self) -> Self {
+                <$T>::asin(self)
+            }
+
+            fn acos(self) -> Self {
+                <$T>::acos(self)
+            }
+
+            fn atan(self) -> Self {
+                <$T>::atan(self)
+            }
+
+            fn atan2(self, other: Self) -> Self {
+                <$T>::atan2(self, other)
+            }
+
+            fn sin_cos(self) -> (Self, Self) {
+                <$T>::sin_cos(self)
+            }
+
+            fn exp_m1(self) -> Self {
+                <$T>::exp_m1(self)
+            }
+
+            fn ln_1p(self) -> Self {
+                <$T>::ln_1p(self)
+            }
+
+            fn sinh(self) -> Self {
+                <$T>::sinh(self)
+            }
+
+            fn cosh(self) -> Self {
+                <$T>::cosh(self)
+            }
+
+            fn tanh(self) -> Self {
+                <$T>::tanh(self)
+            }
+
+            fn asinh(self) -> Self {
+                <$T>::asinh(self)
+            }
+
+            fn acosh(self) -> Self {
+                <$T>::acosh(self)
+            }
+
+            fn atanh(self) -> Self {
+                <$T>::atanh(self)
+            }
+
+        }
+    )*)
+}
+
+float_impl!(f32 f64);