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    use core::num::Wrapping;
    use core::ops::Neg;

    use float::FloatCore;
    use Num;

    /// Useful functions for signed numbers (i.e. numbers that can be negative).
    pub trait Signed: Sized + Num + Neg<Output = Self> {
        /// Computes the absolute value.
        ///
        /// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`.
        ///
        /// For signed integers, `::MIN` will be returned if the number is `::MIN`.
        fn abs(&self) -> Self;

        /// The positive difference of two numbers.
        ///
        /// Returns `zero` if the number is less than or equal to `other`, otherwise the difference
        /// between `self` and `other` is returned.
        fn abs_sub(&self, other: &Self) -> Self;

        /// Returns the sign of the number.
        ///
        /// For `f32` and `f64`:
        ///
        /// * `1.0` if the number is positive, `+0.0` or `INFINITY`
        /// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
        /// * `NaN` if the number is `NaN`
        ///
        /// For signed integers:
        ///
        /// * `0` if the number is zero
        /// * `1` if the number is positive
        /// * `-1` if the number is negative
        fn signum(&self) -> Self;

        /// Returns true if the number is positive and false if the number is zero or negative.
        fn is_positive(&self) -> bool;

        /// Returns true if the number is negative and false if the number is zero or positive.
        fn is_negative(&self) -> bool;
    }

    macro_rules! signed_impl {
        ($($t:ty)*) => ($(
            impl Signed for $t {
                #[inline]
                fn abs(&self) -> $t {
                    if self.is_negative() { -*self } else { *self }
                }

                #[inline]
                fn abs_sub(&self, other: &$t) -> $t {
                    if *self <= *other { 0 } else { *self - *other }
                }

                #[inline]
                fn signum(&self) -> $t {
                    match *self {
                        n if n > 0 => 1,
                        0 => 0,
                        _ => -1,
                    }
                }

                #[inline]
                fn is_positive(&self) -> bool { *self > 0 }

                #[inline]
                fn is_negative(&self) -> bool { *self < 0 }
            }
        )*)
    }

    signed_impl!(isize i8 i16 i32 i64);

    #[cfg(has_i128)]
    signed_impl!(i128);

    impl<T: Signed> Signed for Wrapping<T>
    where
        Wrapping<T>: Num + Neg<Output = Wrapping<T>>,
    {
        #[inline]
        fn abs(&self) -> Self {
            Wrapping(self.0.abs())
        }

        #[inline]
        fn abs_sub(&self, other: &Self) -> Self {
            Wrapping(self.0.abs_sub(&other.0))
        }

        #[inline]
        fn signum(&self) -> Self {
            Wrapping(self.0.signum())
        }

        #[inline]
        fn is_positive(&self) -> bool {
            self.0.is_positive()
        }

        #[inline]
        fn is_negative(&self) -> bool {
            self.0.is_negative()
        }
    }

    macro_rules! signed_float_impl {
        ($t:ty) => {
            impl Signed for $t {
                /// Computes the absolute value. Returns `NAN` if the number is `NAN`.
                #[inline]
                fn abs(&self) -> $t {
                    FloatCore::abs(*self)
                }

                /// The positive difference of two numbers. Returns `0.0` if the number is
                /// less than or equal to `other`, otherwise the difference between`self`
                /// and `other` is returned.
                #[inline]
                fn abs_sub(&self, other: &$t) -> $t {
                    if *self <= *other {
                        0.
                    } else {
                        *self - *other
                    }
                }

                /// # Returns
                ///
                /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
                /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
                /// - `NAN` if the number is NaN
                #[inline]
                fn signum(&self) -> $t {
                    FloatCore::signum(*self)
                }

                /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
                #[inline]
                fn is_positive(&self) -> bool {
                    FloatCore::is_sign_positive(*self)
                }

                /// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
                #[inline]
                fn is_negative(&self) -> bool {
                    FloatCore::is_sign_negative(*self)
                }
            }
        };
    }

    signed_float_impl!(f32);
    signed_float_impl!(f64);

    /// Computes the absolute value.
    ///
    /// For `f32` and `f64`, `NaN` will be returned if the number is `NaN`
    ///
    /// For signed integers, `::MIN` will be returned if the number is `::MIN`.
    #[inline(always)]
    pub fn abs<T: Signed>(value: T) -> T {
        value.abs()
    }

    /// The positive difference of two numbers.
    ///
    /// Returns zero if `x` is less than or equal to `y`, otherwise the difference
    /// between `x` and `y` is returned.
    #[inline(always)]
    pub fn abs_sub<T: Signed>(x: T, y: T) -> T {
        x.abs_sub(&y)
    }

    /// Returns the sign of the number.
    ///
    /// For `f32` and `f64`:
    ///
    /// * `1.0` if the number is positive, `+0.0` or `INFINITY`
    /// * `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
    /// * `NaN` if the number is `NaN`
    ///
    /// For signed integers:
    ///
    /// * `0` if the number is zero
    /// * `1` if the number is positive
    /// * `-1` if the number is negative
    #[inline(always)]
    pub fn signum<T: Signed>(value: T) -> T {
        value.signum()
    }

    /// A trait for values which cannot be negative
    pub trait Unsigned: Num {}

    macro_rules! empty_trait_impl {
        ($name:ident for $($t:ty)*) => ($(
            impl $name for $t {}
        )*)
    }

    empty_trait_impl!(Unsigned for usize u8 u16 u32 u64);
    #[cfg(has_i128)]
    empty_trait_impl!(Unsigned for u128);

    impl<T: Unsigned> Unsigned for Wrapping<T> where Wrapping<T>: Num {}

    #[test]
    fn unsigned_wrapping_is_unsigned() {
        fn require_unsigned<T: Unsigned>(_: &T) {}
        require_unsigned(&Wrapping(42_u32));
    }
    /*
    // Commenting this out since it doesn't compile on Rust 1.8,
    // because on this version Wrapping doesn't implement Neg and therefore can't
    // implement Signed.
    #[test]
    fn signed_wrapping_is_signed() {
        fn require_signed<T: Signed>(_: &T) {}
        require_signed(&Wrapping(-42));
    }
    */

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