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    #[cfg(feature = "decimal")]
    use decimal::d128;
    use std::cmp::{Ordering, PartialOrd};

    /// A set where every two elements have an infimum (i.e. greatest lower bound).
    pub trait MeetSemilattice: Sized {
        /// Returns the meet (aka. infimum) of two values.
        fn meet(&self, other: &Self) -> Self;
    }

    /// A set where every two elements have a supremum (i.e. smallest upper bound).
    pub trait JoinSemilattice: Sized {
        /// Returns the join (aka. supremum) of two values.
        fn join(&self, other: &Self) -> Self;
    }

    /// Partially orderable sets where every two elements have a supremum and infimum.
    pub trait Lattice: MeetSemilattice + JoinSemilattice + PartialOrd {
        /// Returns the infimum and the supremum simultaneously.
        #[inline]
        fn meet_join(&self, other: &Self) -> (Self, Self) {
            (self.meet(other), self.join(other))
        }

        /// Return the minimum of `self` and `other` if they are comparable.
        #[inline]
        fn partial_min<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
            if let Some(ord) = self.partial_cmp(other) {
                match ord {
                    Ordering::Greater => Some(other),
                    _ => Some(self),
                }
            } else {
                None
            }
        }

        /// Return the maximum of `self` and `other` if they are comparable.
        #[inline]
        fn partial_max<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
            if let Some(ord) = self.partial_cmp(other) {
                match ord {
                    Ordering::Less => Some(other),
                    _ => Some(self),
                }
            } else {
                None
            }
        }

        /// Sorts two values in increasing order using a partial ordering.
        #[inline]
        fn partial_sort2<'a>(&'a self, other: &'a Self) -> Option<(&'a Self, &'a Self)> {
            if let Some(ord) = self.partial_cmp(other) {
                match ord {
                    Ordering::Less => Some((self, other)),
                    _ => Some((other, self)),
                }
            } else {
                None
            }
        }

        /// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
        /// `min` or `max`.
        #[inline]
        fn partial_clamp<'a>(&'a self, min: &'a Self, max: &'a Self) -> Option<&'a Self> {
            if let (Some(cmp_min), Some(cmp_max)) = (self.partial_cmp(min), self.partial_cmp(max)) {
                if cmp_min == Ordering::Less {
                    Some(min)
                } else if cmp_max == Ordering::Greater {
                    Some(max)
                } else {
                    Some(self)
                }
            } else {
                None
            }
        }
    }

    macro_rules! impl_lattice(
        ($($T:ident),*) => {$(
            impl MeetSemilattice for $T {
                #[inline]
                fn meet(&self, other: &Self) -> Self {
                    if *self <= *other {
                        *self
                    }
                    else {
                        *other
                    }
                }
            }

            impl JoinSemilattice for $T {
                #[inline]
                fn join(&self, other: &Self) -> Self {
                    if *self >= *other {
                        *self
                    }
                    else {
                        *other
                    }
                }
            }

            impl Lattice for $T {
                #[inline]
                fn meet_join(&self, other: &Self) -> (Self, Self) {
                    if *self >= *other {
                        (*other, *self)
                    }
                    else {
                        (*self, *other)
                    }
                }
            }
        )*}
    );

    impl_lattice!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize, f32, f64);
    #[cfg(feature = "decimal")]
    impl_lattice!(d128);

    impl<N: MeetSemilattice> MeetSemilattice for num_complex::Complex<N> {
        #[inline]
        fn meet(&self, other: &Self) -> Self {
            Self {
                re: self.re.meet(&other.re),
                im: self.im.meet(&other.im),
            }
        }
    }

    impl<N: JoinSemilattice> JoinSemilattice for num_complex::Complex<N> {
        #[inline]
        fn join(&self, other: &Self) -> Self {
            Self {
                re: self.re.join(&other.re),
                im: self.im.join(&other.im),
            }
        }
    }

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