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    #[cfg(feature = "num-complex")]
    use num_complex::Complex;
    #[cfg(not(feature = "std"))]
    use num_traits::float::FloatCore;
    use std::{cell, mem};

    use AbsDiffEq;

    /// Equality comparisons between two numbers using both the absolute difference and ULPs
    /// (Units in Last Place) based comparisons.
    pub trait UlpsEq<Rhs = Self>: AbsDiffEq<Rhs>
    where
        Rhs: ?Sized,
    {
        /// The default ULPs to tolerate when testing values that are far-apart.
        ///
        /// This is used when no `max_ulps` value is supplied to the `ulps_eq` macro.
        fn default_max_ulps() -> u32;

        /// A test for equality that uses units in the last place (ULP) if the values are far apart.
        fn ulps_eq(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool;

        /// The inverse of `ApproxEq::ulps_eq`.
        fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
            !Self::ulps_eq(self, other, epsilon, max_ulps)
        }
    }

    ///////////////////////////////////////////////////////////////////////////////////////////////////
    // Base implementations
    ///////////////////////////////////////////////////////////////////////////////////////////////////

    // Implementation based on: [Comparing Floating Point Numbers, 2012 Edition]
    // (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
    macro_rules! impl_ulps_eq {
        ($T:ident, $U:ident) => {
            impl UlpsEq for $T {
                #[inline]
                fn default_max_ulps() -> u32 {
                    4
                }

                #[inline]
                fn ulps_eq(&self, other: &$T, epsilon: $T, max_ulps: u32) -> bool {
                    // For when the numbers are really close together
                    if $T::abs_diff_eq(self, other, epsilon) {
                        return true;
                    }

                    // Trivial negative sign check
                    if self.signum() != other.signum() {
                        return false;
                    }

                    // ULPS difference comparison
                    let int_self: $U = unsafe { mem::transmute(*self) };
                    let int_other: $U = unsafe { mem::transmute(*other) };

                    $U::abs(int_self - int_other) <= max_ulps as $U
                }
            }
        };
    }

    impl_ulps_eq!(f32, i32);
    impl_ulps_eq!(f64, i64);

    ///////////////////////////////////////////////////////////////////////////////////////////////////
    // Derived implementations
    ///////////////////////////////////////////////////////////////////////////////////////////////////

    impl<'a, T: UlpsEq + ?Sized> UlpsEq for &'a T {
        #[inline]
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &&'a T, epsilon: T::Epsilon, max_ulps: u32) -> bool {
            T::ulps_eq(*self, *other, epsilon, max_ulps)
        }
    }

    impl<'a, T: UlpsEq + ?Sized> UlpsEq for &'a mut T {
        #[inline]
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &&'a mut T, epsilon: T::Epsilon, max_ulps: u32) -> bool {
            T::ulps_eq(*self, *other, epsilon, max_ulps)
        }
    }

    impl<T: UlpsEq + Copy> UlpsEq for cell::Cell<T> {
        #[inline]
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &cell::Cell<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
            T::ulps_eq(&self.get(), &other.get(), epsilon, max_ulps)
        }
    }

    impl<T: UlpsEq + ?Sized> UlpsEq for cell::RefCell<T> {
        #[inline]
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &cell::RefCell<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
            T::ulps_eq(&self.borrow(), &other.borrow(), epsilon, max_ulps)
        }
    }

    impl<A, B> UlpsEq<[B]> for [A]
    where
        A: UlpsEq<B>,
        A::Epsilon: Clone,
    {
        #[inline]
        fn default_max_ulps() -> u32 {
            A::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &[B], epsilon: A::Epsilon, max_ulps: u32) -> bool {
            self.len() == other.len()
                && Iterator::zip(self.iter(), other)
                    .all(|(x, y)| A::ulps_eq(x, y, epsilon.clone(), max_ulps.clone()))
        }
    }

    #[cfg(feature = "num-complex")]
    impl<T: UlpsEq> UlpsEq for Complex<T>
    where
        T::Epsilon: Clone,
    {
        #[inline]
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }

        #[inline]
        fn ulps_eq(&self, other: &Complex<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
            T::ulps_eq(&self.re, &other.re, epsilon.clone(), max_ulps)
                && T::ulps_eq(&self.im, &other.im, epsilon.clone(), max_ulps)
        }
    }

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