range_collections/

range_set.rs

#![deny(missing_docs)]
#![allow(clippy::needless_lifetimes)]

//! A set of non-overlapping ranges
use crate::merge_state::{
    BoolOpMergeState, InPlaceMergeState, InPlaceMergeStateRef, MergeStateMut, SmallVecMergeState,
};
use binary_merge::{MergeOperation, MergeState};
use core::cmp::Ordering;
use core::fmt::Debug;
use core::ops::{
    BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Bound, Not, Range, RangeFrom,
    RangeTo, Sub, SubAssign,
};
use ref_cast::{ref_cast_custom, RefCastCustom};
use smallvec::{Array, SmallVec};
use std::borrow::Borrow;
use std::num::*;
use std::ops::{Deref, RangeBounds, RangeFull};
#[cfg(feature = "serde")]
use {
    core::{fmt, marker::PhantomData},
    serde::{
        de::{Deserialize, Deserializer, SeqAccess, Visitor},
        ser::{Serialize, SerializeSeq, Serializer},
    },
};

/// # A set of non-overlapping ranges
///
/// ```
/// # use range_collections::{RangeSet, RangeSet2};
/// let mut a: RangeSet2<i32> = RangeSet::from(10..);
/// let b: RangeSet2<i32> = RangeSet::from(1..5);
///
/// a |= b;
/// let r = !a;
/// ```
///
/// A data structure to represent a set of non-overlapping ranges of element type `T: RangeSetEntry`. It uses a `SmallVec<T>`
/// of sorted boundaries internally.
///
/// It can represent not just finite ranges but also ranges with unbounded end. Because it can represent
/// infinite ranges, it can also represent the set of all elements, and therefore all boolean operations including negation.
///
/// Adjacent ranges will be merged.
///
/// It provides very fast operations for set operations (&, |, ^) as well as for intersection tests (is_disjoint, is_subset).
///
/// In addition to the fast set operations that produce a new range set, it also supports the equivalent in-place operations.
///
/// # Complexity
///
/// Complexity is given separately for the number of comparisons and the number of copies, since sometimes you have
/// a comparison operation that is basically free (any of the primitive types), whereas sometimes you have a comparison
/// operation that is many orders of magnitude more expensive than a copy (long strings, arbitrary precision integers, ...)
///
/// ## Number of comparisons
///
/// |operation    | best      | worst     | remark
/// |-------------|-----------|-----------|--------
/// |negation     | 1         | O(N)      |
/// |union        | O(log(N)) | O(N)      | binary merge
/// |intersection | O(log(N)) | O(N)      | binary merge
/// |difference   | O(log(N)) | O(N)      | binary merge
/// |xor          | O(log(N)) | O(N)      | binary merge
/// |membership   | O(log(N)) | O(log(N)) | binary search
/// |is_disjoint  | O(log(N)) | O(N)      | binary merge with cutoff
/// |is_subset    | O(log(N)) | O(N)      | binary merge with cutoff
///
/// ## Number of copies
///
/// For creating new sets, obviously there needs to be at least one copy for each element of the result set, so the
/// complexity is always O(N). For in-place operations it gets more interesting. In case the number of elements of
/// the result being identical to the number of existing elements, there will be no copies and no allocations.
///
/// E.g. if the result just has some of the ranges of the left hand side extended or truncated, but the same number of boundaries,
/// there will be no allocations and no copies except for the changed boundaries themselves.
///
/// If the result has fewer boundaries than then lhs, there will be some copying but no allocations. Only if the result
/// is larger than the capacity of the underlying vector of the lhs will there be allocations.
///
/// |operation    | best      | worst     |
/// |-------------|-----------|-----------|
/// |negation     | 1         | 1         |
/// |union        | 1         | O(N)      |
/// |intersection | 1         | O(N)      |
/// |difference   | 1         | O(N)      |
/// |xor          | 1         | O(N)      |
///
/// # Testing
///
/// Testing is done by some simple smoke tests as well as quickcheck tests of the algebraic properties of the boolean operations.
pub struct RangeSet<A: Array>(SmallVec<A>);

impl<T, A: Array<Item = T>> Default for RangeSet<A> {
    fn default() -> Self {
        Self(Default::default())
    }
}

impl<T, A: Array<Item = T>> Deref for RangeSet<A> {
    type Target = RangeSetRef<T>;

    fn deref(&self) -> &Self::Target {
        RangeSetRef::new_unchecked_impl(&self.0)
    }
}

impl<T, A: Array<Item = T>> AsRef<RangeSetRef<T>> for RangeSet<A> {
    fn as_ref(&self) -> &RangeSetRef<T> {
        RangeSetRef::new_unchecked_impl(&self.0)
    }
}

impl<T, A: Array<Item = T>> Borrow<RangeSetRef<T>> for RangeSet<A> {
    fn borrow(&self) -> &RangeSetRef<T> {
        RangeSetRef::new_unchecked_impl(&self.0)
    }
}

/// Range that can be part of a range set
///
/// Start boundaries are always inclusive, end boundaries are exclusive.
/// Therefore some ranges types are not going to appear in a range set.
#[derive(Clone)]
pub enum RangeSetRange<T> {
    /// Closed range
    Range(Range<T>),
    /// Range with unbounded end
    RangeFrom(RangeFrom<T>),
}

impl<T: Clone> RangeSetRange<&T> {
    /// Maps a `RangeSetRange<&T>` to a `RangeSetRange<T>` by cloning start and end.
    pub fn cloned(&self) -> RangeSetRange<T> {
        match self {
            RangeSetRange::Range(r) => RangeSetRange::Range(r.start.clone()..r.end.clone()),
            RangeSetRange::RangeFrom(r) => RangeSetRange::RangeFrom(r.start.clone()..),
        }
    }
}

impl<T> From<Range<T>> for RangeSetRange<T> {
    fn from(r: Range<T>) -> Self {
        RangeSetRange::Range(r)
    }
}

impl<T> From<RangeFrom<T>> for RangeSetRange<T> {
    fn from(r: RangeFrom<T>) -> Self {
        RangeSetRange::RangeFrom(r)
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<RangeSetRange<T>> for RangeSet<A> {
    fn from(value: RangeSetRange<T>) -> Self {
        match value {
            RangeSetRange::Range(r) => RangeSet::from(r),
            RangeSetRange::RangeFrom(r) => RangeSet::from(r),
        }
    }
}

impl<T: Debug> Debug for RangeSetRange<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        match self {
            RangeSetRange::Range(r) => r.fmt(f),
            RangeSetRange::RangeFrom(r) => r.fmt(f),
        }
    }
}

impl<T> RangeBounds<T> for RangeSetRange<T> {
    fn start_bound(&self) -> Bound<&T> {
        match self {
            RangeSetRange::Range(r) => r.start_bound(),
            RangeSetRange::RangeFrom(r) => r.start_bound(),
        }
    }

    fn end_bound(&self) -> Bound<&T> {
        match self {
            RangeSetRange::Range(r) => r.end_bound(),
            RangeSetRange::RangeFrom(r) => r.end_bound(),
        }
    }
}

impl<A: Array> Clone for RangeSet<A>
where
    A::Item: Clone,
{
    fn clone(&self) -> Self {
        Self(self.0.clone())
    }
}

impl<A: Array, R: AsRef<RangeSetRef<A::Item>>> PartialEq<R> for RangeSet<A>
where
    A::Item: RangeSetEntry,
{
    fn eq(&self, that: &R) -> bool {
        self.boundaries() == that.as_ref().boundaries()
    }
}

impl<A: Array> Eq for RangeSet<A> where A::Item: Eq + RangeSetEntry {}

/// A range set that stores up to 2 boundaries inline
pub type RangeSet2<T> = RangeSet<[T; 2]>;

impl<T: Debug, A: Array<Item = T>> Debug for RangeSet<A> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "RangeSet{{")?;
        for (i, r) in self.iter().enumerate() {
            if i > 0 {
                write!(f, ", ")?;
            }
            write!(f, "{r:?}")?;
        }
        write!(f, "}}")
    }
}

/// Iterator for the ranges in a range set
pub struct Iter<'a, T>(&'a [T]);

impl<'a, T> Iterator for Iter<'a, T> {
    type Item = RangeSetRange<&'a T>;

    fn next(&mut self) -> Option<Self::Item> {
        let bounds = self.0;
        if !bounds.is_empty() {
            Some(if bounds.len() == 1 {
                self.0 = &bounds[1..];
                RangeSetRange::from(&bounds[0]..)
            } else {
                self.0 = &bounds[2..];
                RangeSetRange::from(&bounds[0]..&bounds[1])
            })
        } else {
            None
        }
    }
}

/// A reference to a range set
#[derive(Debug, PartialEq, Eq, PartialOrd, Ord, RefCastCustom)]
#[repr(transparent)]
pub struct RangeSetRef<T>([T]);

impl<T> Default for &RangeSetRef<T> {
    fn default() -> Self {
        RangeSetRef::new_unchecked_impl(&[])
    }
}

impl<T> RangeSetRef<T> {
    /// Create a new range set reference for an empty range set
    pub const fn empty() -> &'static Self {
        RangeSetRef::new_unchecked_impl(&[])
    }

    /// Create a new range set reference for a single boundary change
    ///
    /// This produces a RangeSetRef that goes from off before `value` to on at
    /// *and after* `value`.
    pub const fn single(value: &T) -> &Self {
        RangeSetRef::new_unchecked_impl(std::slice::from_ref(value))
    }

    /// Create a new range set reference
    ///
    /// This performs a check that the boundaries are strictly sorted.
    /// If you want to avoid this check, use `new_unchecked`
    /// (behind a feature flag because it is unsafe)
    pub fn new(boundaries: &[T]) -> Option<&Self>
    where
        T: Ord,
    {
        if is_strictly_sorted(boundaries) {
            Some(Self::new_unchecked_impl(boundaries))
        } else {
            None
        }
    }

    /// Split this range set into two parts `left`, `right` at position `at`,
    /// so that `left` is identical to `self` for all `x < at`
    /// and `right` is identical to `self` for all `x >= at`.
    ///
    /// More precisely:
    ///   contains(left, x) == contains(ranges, x) for x < at
    ///   contains(right, x) == contains(ranges, x) for x >= at
    ///
    /// This is not the same as limiting the ranges to the left or right of
    /// `at`, but it is much faster. It requires just a binary search and no
    /// allocations.
    pub fn split(&self, at: T) -> (&Self, &Self)
    where
        T: Ord,
    {
        let (left, right) = split(&self.0, at);
        (
            Self::new_unchecked_impl(left),
            Self::new_unchecked_impl(right),
        )
    }

    /// Create a new range set reference without checking that the boundaries are
    /// strictly sorted.
    #[cfg(feature = "new_unchecked")]
    pub const fn new_unchecked(boundaries: &[T]) -> &Self {
        Self::new_unchecked_impl(boundaries)
    }

    #[ref_cast_custom]
    const fn new_unchecked_impl(boundaries: &[T]) -> &Self;

    /// The boundaries of the range set, guaranteed to be strictly sorted
    pub const fn boundaries(&self) -> &[T] {
        &self.0
    }

    /// true if the value is contained in the range set
    pub fn contains(&self, value: &T) -> bool
    where
        T: Ord,
    {
        match self.boundaries().binary_search(value) {
            Ok(index) => !is_odd(index),
            Err(index) => is_odd(index),
        }
    }

    /// true if the range set is empty
    pub const fn is_empty(&self) -> bool {
        self.boundaries().is_empty()
    }

    /// true if the range set contains all values
    pub fn is_all(&self) -> bool
    where
        T: RangeSetEntry,
    {
        self.boundaries().len() == 1 && self.boundaries()[0].is_min_value()
    }

    /// true if this range set intersects from another range set
    ///
    /// This is just the opposite of `is_disjoint`, but is provided for
    /// better discoverability.
    pub fn intersects(&self, that: &RangeSetRef<T>) -> bool
    where
        T: Ord,
    {
        !self.is_disjoint(that)
    }

    /// true if this range set is disjoint from another range set
    pub fn is_disjoint(&self, that: &RangeSetRef<T>) -> bool
    where
        T: Ord,
    {
        !RangeSetBoolOpMergeState::merge(self.boundaries(), that.boundaries(), IntersectionOp::<0>)
    }

    /// true if this range set is a superset of another range set
    ///
    /// A range set is considered to be a superset of itself
    pub fn is_subset(&self, that: &RangeSetRef<T>) -> bool
    where
        T: Ord,
    {
        !RangeSetBoolOpMergeState::merge(self.boundaries(), that.boundaries(), DiffOp::<0>)
    }

    /// true if this range set is a subset of another range set
    ///
    /// A range set is considered to be a subset of itself
    pub fn is_superset(&self, that: &RangeSetRef<T>) -> bool
    where
        T: Ord,
    {
        !RangeSetBoolOpMergeState::merge(that.boundaries(), self.boundaries(), DiffOp::<0>)
    }

    /// iterate over all ranges in this range set
    pub fn iter(&self) -> Iter<T> {
        Iter(self.boundaries())
    }

    /// intersection
    pub fn intersection<A>(&self, that: &RangeSetRef<T>) -> RangeSet<A>
    where
        A: Array<Item = T>,
        T: Ord + Clone,
    {
        RangeSet::new_unchecked_impl(VecMergeState::merge(
            self.boundaries(),
            that.boundaries(),
            IntersectionOp::<{ usize::MAX }>,
        ))
    }

    /// union
    pub fn union<A>(&self, that: &RangeSetRef<T>) -> RangeSet<A>
    where
        A: Array<Item = T>,
        T: Ord + Clone,
    {
        RangeSet::new_unchecked_impl(VecMergeState::merge(
            self.boundaries(),
            that.boundaries(),
            UnionOp,
        ))
    }

    /// difference
    pub fn difference<A>(&self, that: &RangeSetRef<T>) -> RangeSet<A>
    where
        A: Array<Item = T>,
        T: Ord + Clone,
    {
        RangeSet::new_unchecked_impl(VecMergeState::merge(
            self.boundaries(),
            that.boundaries(),
            DiffOp::<{ usize::MAX }>,
        ))
    }

    /// symmetric difference (xor)
    pub fn symmetric_difference<A>(&self, that: &RangeSetRef<T>) -> RangeSet<A>
    where
        A: Array<Item = T>,
        T: Ord + Clone,
    {
        RangeSet::new_unchecked_impl(VecMergeState::merge(
            self.boundaries(),
            that.boundaries(),
            XorOp,
        ))
    }
}

#[cfg(feature = "rkyv")]
impl<T> Deref for ArchivedRangeSet<T> {
    type Target = RangeSetRef<T>;

    fn deref(&self) -> &Self::Target {
        RangeSetRef::new_unchecked(&self.0)
    }
}

#[cfg(feature = "rkyv")]
impl<T> AsRef<RangeSetRef<T>> for ArchivedRangeSet<T> {
    fn as_ref(&self) -> &RangeSetRef<T> {
        RangeSetRef::new_unchecked(&self.0)
    }
}

#[cfg(feature = "rkyv")]
impl<T> Borrow<RangeSetRef<T>> for ArchivedRangeSet<T> {
    fn borrow(&self) -> &RangeSetRef<T> {
        RangeSetRef::new_unchecked(&self.0)
    }
}

/// trait for types that can be entries of range sets
///
/// they must have an order and a minimum value.
pub trait RangeSetEntry: Ord {
    /// the minimum value for this type
    fn min_value() -> Self;

    /// checks if this is the minimum value
    ///
    /// this is to be able to check for minimum without having to create a value
    fn is_min_value(&self) -> bool;
}

macro_rules! entry_instance {
    ($t:tt) => {
        impl RangeSetEntry for $t {

            fn min_value() -> Self {
                $t::MIN
            }

            fn is_min_value(&self) -> bool {
                *self == $t::MIN
            }
        }
    };
    ($t:tt, $($rest:tt),+) => {
        entry_instance!($t);
        entry_instance!($( $rest ),*);
    }
}

macro_rules! non_zero_u_entry_instance {
    ($t:tt) => {
        impl RangeSetEntry for $t {

            fn min_value() -> Self {
                $t::new(1).unwrap()
            }

            fn is_min_value(&self) -> bool {
                *self == $t::new(1).unwrap()
            }
        }
    };
    ($t:tt, $($rest:tt),+) => {
        non_zero_u_entry_instance!($t);
        non_zero_u_entry_instance!($( $rest ),*);
    }
}

entry_instance!(u8, u16, u32, u64, u128, usize);
entry_instance!(i8, i16, i32, i64, i128, isize);
non_zero_u_entry_instance!(
    NonZeroU8,
    NonZeroU16,
    NonZeroU32,
    NonZeroU64,
    NonZeroU128,
    NonZeroUsize
);

impl<T: Ord> RangeSetEntry for Option<T> {
    fn min_value() -> Self {
        None
    }

    fn is_min_value(&self) -> bool {
        self.is_none()
    }
}

impl RangeSetEntry for String {
    fn min_value() -> Self {
        "".to_owned()
    }

    fn is_min_value(&self) -> bool {
        self.is_empty()
    }
}

impl RangeSetEntry for &str {
    fn min_value() -> Self {
        ""
    }

    fn is_min_value(&self) -> bool {
        self.is_empty()
    }
}

impl<T: Ord> RangeSetEntry for Vec<T> {
    fn min_value() -> Self {
        Vec::new()
    }

    fn is_min_value(&self) -> bool {
        self.is_empty()
    }
}

impl<T: Ord> RangeSetEntry for &[T] {
    fn min_value() -> Self {
        &[]
    }

    fn is_min_value(&self) -> bool {
        self.is_empty()
    }
}

impl<T, A: Array<Item = T>> RangeSet<A> {
    /// create a new range set from the given boundaries
    ///
    /// This performs a check that the boundaries are strictly sorted.
    /// If you want to avoid this check, use `new_unchecked`
    /// (behind a feature flag because it is unsafe)
    pub fn new(boundaries: SmallVec<A>) -> Option<Self>
    where
        A::Item: Ord,
    {
        if is_strictly_sorted(boundaries.as_ref()) {
            Some(Self::new_unchecked_impl(boundaries))
        } else {
            None
        }
    }

    /// Create a new range set reference without checking that the boundaries are
    /// strictly sorted.
    #[cfg(feature = "new_unchecked")]
    pub fn new_unchecked(boundaries: SmallVec<A>) -> Self {
        Self::new_unchecked_impl(boundaries)
    }

    /// note that this is private since it does not check the invariants!
    fn new_unchecked_impl(boundaries: SmallVec<A>) -> Self {
        RangeSet(boundaries)
    }

    /// iterate over all ranges in this range set
    pub fn iter(&self) -> Iter<T> {
        Iter(self.0.as_ref())
    }

    /// get the boundaries in this range set as a SmallVec
    pub fn into_inner(self) -> SmallVec<A> {
        self.0
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> RangeSet<A> {
    fn from_range_until(a: T) -> Self {
        let mut t = SmallVec::new();
        if !a.is_min_value() {
            t.push(T::min_value());
            t.push(a);
        }
        Self::new_unchecked_impl(t)
    }
    fn from_range_from(a: T) -> Self {
        let mut t = SmallVec::new();
        t.push(a);
        Self::new_unchecked_impl(t)
    }
    /// the empty range set
    pub fn empty() -> Self {
        Self(SmallVec::new())
    }
    /// a range set containing all values
    pub fn all() -> Self {
        Self::from_range_from(T::min_value())
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> RangeSet<A> {
    /// intersection in place
    pub fn intersection_with(&mut self, that: &RangeSetRef<T>) {
        InPlaceMergeStateRef::merge(
            &mut self.0,
            &that.boundaries(),
            IntersectionOp::<{ usize::MAX }>,
        );
    }
    /// union in place
    pub fn union_with(&mut self, that: &RangeSetRef<T>) {
        InPlaceMergeStateRef::merge(&mut self.0, &that.boundaries(), UnionOp);
    }
    /// difference in place
    pub fn difference_with(&mut self, that: &RangeSetRef<T>) {
        InPlaceMergeStateRef::merge(&mut self.0, &that.boundaries(), DiffOp::<{ usize::MAX }>);
    }
    /// symmetric difference in place (xor)
    pub fn symmetric_difference_with(&mut self, that: &RangeSetRef<T>) {
        InPlaceMergeStateRef::merge(&mut self.0, &that.boundaries(), XorOp);
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<bool> for RangeSet<A> {
    fn from(value: bool) -> Self {
        if value {
            Self::all()
        } else {
            Self::empty()
        }
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> RangeSet<A> {
    fn from_range(a: Range<T>) -> Self {
        if a.start < a.end {
            let mut t = SmallVec::new();
            t.push(a.start);
            t.push(a.end);
            Self::new_unchecked_impl(t)
        } else {
            Self::empty()
        }
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<Range<T>> for RangeSet<A> {
    fn from(value: Range<T>) -> Self {
        Self::from_range(value)
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<RangeFrom<T>> for RangeSet<A> {
    fn from(value: RangeFrom<T>) -> Self {
        Self::from_range_from(value.start)
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<RangeTo<T>> for RangeSet<A> {
    fn from(value: RangeTo<T>) -> Self {
        Self::from_range_until(value.end)
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> From<RangeFull> for RangeSet<A> {
    fn from(_: RangeFull) -> Self {
        Self::all()
    }
}

/// compute the intersection of this range set with another, producing a new range set
///
/// &forall; t &isin; T, r(t) = a(t) & b(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitAnd<RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitand(self, that: RangeSet<A>) -> Self::Output {
        self.intersection(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitAnd<&RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitand(self, that: &RangeSet<A>) -> Self::Output {
        self.intersection(that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitAnd<RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitand(self, that: RangeSet<A>) -> Self::Output {
        self.intersection(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitAnd<&RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitand(self, that: &RangeSet<A>) -> Self::Output {
        self.intersection(that)
    }
}

impl<T: Ord, A: Array<Item = T>> BitAndAssign for RangeSet<A> {
    fn bitand_assign(&mut self, that: Self) {
        InPlaceMergeState::merge(&mut self.0, that.0, IntersectionOp::<{ usize::MAX }>);
    }
}

/// compute the union of this range set with another, producing a new range set
///
/// &forall; t &isin; T, r(t) = a(t) | b(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitOr<RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitor(self, that: RangeSet<A>) -> Self::Output {
        self.union(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitOr<&RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitor(self, that: &RangeSet<A>) -> Self::Output {
        self.union(that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitOr<RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitor(self, that: RangeSet<A>) -> Self::Output {
        self.union(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitOr<&RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitor(self, that: &RangeSet<A>) -> Self::Output {
        self.union(that)
    }
}

impl<T: Ord, A: Array<Item = T>> BitOrAssign for RangeSet<A> {
    fn bitor_assign(&mut self, that: Self) {
        InPlaceMergeState::merge(&mut self.0, that.0, UnionOp);
    }
}

/// compute the exclusive or of this range set with another, producing a new range set
///
/// &forall; t &isin; T, r(t) = a(t) ^ b(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitXor<RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitxor(self, that: RangeSet<A>) -> Self::Output {
        self.symmetric_difference(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitXor<&RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitxor(self, that: &RangeSet<A>) -> Self::Output {
        self.symmetric_difference(that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitXor<RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitxor(self, that: RangeSet<A>) -> Self::Output {
        self.symmetric_difference(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> BitXor<&RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn bitxor(self, that: &RangeSet<A>) -> Self::Output {
        self.symmetric_difference(that)
    }
}

impl<T: RangeSetEntry, A: Array<Item = T>> BitXorAssign for RangeSet<A> {
    fn bitxor_assign(&mut self, that: Self) {
        InPlaceMergeState::merge(&mut self.0, that.0, XorOp);
    }
}

/// compute the difference of this range set with another, producing a new range set
///
/// &forall; t &isin; T, r(t) = a(t) & !b(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Sub<RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn sub(self, that: RangeSet<A>) -> Self::Output {
        self.difference(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Sub<&RangeSet<A>> for RangeSet<A> {
    type Output = RangeSet<A>;
    fn sub(self, that: &RangeSet<A>) -> Self::Output {
        self.difference(that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Sub<RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn sub(self, that: RangeSet<A>) -> Self::Output {
        self.difference(&that)
    }
}

impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Sub<&RangeSet<A>> for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn sub(self, that: &RangeSet<A>) -> Self::Output {
        self.difference(that)
    }
}

impl<T: Ord, A: Array<Item = T>> SubAssign for RangeSet<A> {
    fn sub_assign(&mut self, that: Self) {
        InPlaceMergeState::merge(&mut self.0, that.0, DiffOp::<{ usize::MAX }>);
    }
}

/// compute the negation of this range set
///
/// &forall; t &isin; T, r(t) = !a(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Not for RangeSet<A> {
    type Output = RangeSet<A>;
    fn not(mut self) -> Self::Output {
        match self.0.first() {
            Some(x) if x.is_min_value() => {
                self.0.remove(0);
            }
            _ => {
                self.0.insert(0, T::min_value());
            }
        }
        self
    }
}

/// compute the negation of this range set
///
/// &forall; t &isin; T, r(t) = !a(t)
impl<T: RangeSetEntry + Clone, A: Array<Item = T>> Not for &RangeSet<A> {
    type Output = RangeSet<A>;
    fn not(self) -> Self::Output {
        self ^ &RangeSet::all()
    }
}

struct RangeSetBoolOpMergeState<'a, T> {
    inner: BoolOpMergeState<'a, T, T>,
}

impl<'a, T> RangeSetBoolOpMergeState<'a, T> {
    fn merge<O: MergeOperation<Self>>(a: &'a [T], b: &'a [T], o: O) -> bool {
        let mut state = Self {
            inner: BoolOpMergeState::new(a, b),
        };
        o.merge(&mut state);
        state.inner.result()
    }
}

impl<'a, T> MergeStateMut for RangeSetBoolOpMergeState<'a, T> {
    fn advance_a(&mut self, n: usize, copy: bool) -> bool {
        self.inner.advance_a(n, copy)
    }
    fn advance_b(&mut self, n: usize, copy: bool) -> bool {
        self.inner.advance_b(n, copy)
    }
    fn ac(&self) -> bool {
        self.inner.ac()
    }
    fn bc(&self) -> bool {
        self.inner.bc()
    }
}

impl<'a, T> MergeState for RangeSetBoolOpMergeState<'a, T> {
    type A = T;
    type B = T;
    fn a_slice(&self) -> &[T] {
        self.inner.a_slice()
    }
    fn b_slice(&self) -> &[T] {
        self.inner.b_slice()
    }
}

struct VecMergeState<'a, T, A: Array> {
    inner: SmallVecMergeState<'a, T, T, A>,
}

impl<'a, T: Clone, A: Array<Item = T>> VecMergeState<'a, T, A> {
    fn merge<O: MergeOperation<Self>>(a: &'a [T], b: &'a [T], o: O) -> SmallVec<A> {
        let mut state = Self {
            inner: SmallVecMergeState::new(a, b, SmallVec::new()),
        };
        o.merge(&mut state);
        state.inner.result()
    }
}

impl<'a, T: Clone, A: Array<Item = T>> MergeStateMut for VecMergeState<'a, T, A> {
    fn advance_a(&mut self, n: usize, copy: bool) -> bool {
        self.inner.advance_a(n, copy)
    }
    fn advance_b(&mut self, n: usize, copy: bool) -> bool {
        self.inner.advance_b(n, copy)
    }

    fn ac(&self) -> bool {
        self.inner.ac()
    }

    fn bc(&self) -> bool {
        self.inner.bc()
    }
}

impl<'a, T, A: Array<Item = T>> MergeState for VecMergeState<'a, T, A> {
    type A = T;
    type B = T;
    fn a_slice(&self) -> &[T] {
        self.inner.a_slice()
    }
    fn b_slice(&self) -> &[T] {
        self.inner.b_slice()
    }
}

#[cfg(feature = "serde")]
impl<T: Serialize, A: Array<Item = T>> Serialize for RangeSet<A> {
    fn serialize<S: Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error> {
        let mut map = serializer.serialize_seq(Some(self.0.len()))?;
        for x in self.0.iter() {
            map.serialize_element(x)?;
        }
        map.end()
    }
}

#[cfg(feature = "serde")]
impl<'de, T: Deserialize<'de> + Ord, A: Array<Item = T>> Deserialize<'de> for RangeSet<A> {
    fn deserialize<D: Deserializer<'de>>(deserializer: D) -> Result<Self, D::Error> {
        deserializer.deserialize_seq(RangeSetVisitor {
            phantom: PhantomData,
        })
    }
}

#[cfg(feature = "serde")]
struct RangeSetVisitor<T, A> {
    phantom: PhantomData<(T, A)>,
}

#[cfg(feature = "serde")]
impl<'de, T, A: Array<Item = T>> Visitor<'de> for RangeSetVisitor<T, A>
where
    T: Deserialize<'de> + Ord,
{
    type Value = RangeSet<A>;

    fn expecting(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
        formatter.write_str("a sequence")
    }

    fn visit_seq<B>(self, mut seq: B) -> Result<Self::Value, B::Error>
    where
        B: SeqAccess<'de>,
    {
        let len = seq.size_hint().unwrap_or(0);
        let mut boundaries: SmallVec<A> = SmallVec::with_capacity(len);
        while let Some(value) = seq.next_element::<A::Item>()? {
            boundaries.push(value);
        }
        boundaries.sort();
        boundaries.dedup();
        Ok(RangeSet(boundaries))
    }
}

#[cfg(feature = "rkyv")]
impl<T, A> rkyv::Archive for RangeSet<A>
where
    T: rkyv::Archive,
    A: Array<Item = T>,
{
    type Archived = ArchivedRangeSet<<T as rkyv::Archive>::Archived>;

    type Resolver = rkyv::vec::VecResolver;

    unsafe fn resolve(&self, pos: usize, resolver: Self::Resolver, out: *mut Self::Archived) {
        rkyv::vec::ArchivedVec::resolve_from_slice(
            self.0.as_slice(),
            pos,
            resolver,
            &mut (*out).0 as *mut rkyv::vec::ArchivedVec<<T as rkyv::Archive>::Archived>,
        );
    }
}

#[cfg(feature = "rkyv")]
impl<T, S, A> rkyv::Serialize<S> for RangeSet<A>
where
    T: rkyv::Archive + rkyv::Serialize<S>,
    S: rkyv::ser::ScratchSpace + rkyv::ser::Serializer,
    A: Array<Item = T>,
{
    fn serialize(&self, serializer: &mut S) -> Result<Self::Resolver, S::Error> {
        rkyv::vec::ArchivedVec::serialize_from_slice(self.0.as_ref(), serializer)
    }
}

#[cfg(feature = "rkyv")]
impl<T, A, D> rkyv::Deserialize<RangeSet<A>, D> for ArchivedRangeSet<T::Archived>
where
    T: rkyv::Archive,
    A: Array<Item = T>,
    D: rkyv::Fallible + ?Sized,
    [T::Archived]: rkyv::DeserializeUnsized<[T], D>,
{
    fn deserialize(&self, deserializer: &mut D) -> Result<RangeSet<A>, D::Error> {
        // todo: replace this with SmallVec once smallvec support for rkyv lands on crates.io
        let boundaries: Vec<T> = self.0.deserialize(deserializer)?;
        Ok(RangeSet(boundaries.into()))
    }
}

/// Archived version of a RangeSet
#[cfg(feature = "rkyv")]
#[repr(transparent)]
pub struct ArchivedRangeSet<T>(rkyv::vec::ArchivedVec<T>);

#[cfg(feature = "rkyv")]
impl<T: Debug> Debug for ArchivedRangeSet<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "ArchivedRangeSet{{")?;
        for (i, r) in self.iter().enumerate() {
            if i > 0 {
                write!(f, ", ")?;
            }
            write!(f, "{r:?}")?;
        }
        write!(f, "}}")
    }
}

/// Validation error for a range set
#[cfg(feature = "rkyv_validated")]
#[derive(Debug)]
pub enum ArchivedRangeSetError {
    /// error with the individual fields of the ArchivedRangeSet, e.g a NonZeroU64 with a value of 0
    ValueCheckError,
    /// boundaries were not properly ordered
    OrderCheckError,
}

#[cfg(feature = "rkyv_validated")]
impl std::error::Error for ArchivedRangeSetError {}

#[cfg(feature = "rkyv_validated")]
impl std::fmt::Display for ArchivedRangeSetError {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        write!(f, "{:?}", self)
    }
}

#[cfg(feature = "rkyv_validated")]
impl<C: ?Sized, T> bytecheck::CheckBytes<C> for ArchivedRangeSet<T>
where
    T: Ord,
    bool: bytecheck::CheckBytes<C>,
    rkyv::vec::ArchivedVec<T>: bytecheck::CheckBytes<C>,
{
    type Error = ArchivedRangeSetError;
    unsafe fn check_bytes<'a>(
        value: *const Self,
        context: &mut C,
    ) -> Result<&'a Self, Self::Error> {
        let boundaries = &(*value).0;
        rkyv::vec::ArchivedVec::<T>::check_bytes(boundaries, context)
            .map_err(|_| ArchivedRangeSetError::ValueCheckError)?;
        if !boundaries
            .iter()
            .zip(boundaries.iter().skip(1))
            .all(|(a, b)| a < b)
        {
            return Err(ArchivedRangeSetError::OrderCheckError);
        };
        Ok(&*value)
    }
}

struct UnionOp;
struct XorOp;
struct IntersectionOp<const T: usize>;
struct DiffOp<const T: usize>;

impl<T: Ord, M: MergeStateMut<A = T, B = T>> MergeOperation<M> for UnionOp {
    fn from_a(&self, m: &mut M, n: usize) -> bool {
        m.advance_a(n, !m.bc())
    }
    fn from_b(&self, m: &mut M, n: usize) -> bool {
        m.advance_b(n, !m.ac())
    }
    fn collision(&self, m: &mut M) -> bool {
        m.advance_both(m.ac() == m.bc())
    }
    fn cmp(&self, a: &T, b: &T) -> Ordering {
        a.cmp(b)
    }
}

impl<T: Ord, M: MergeStateMut<A = T, B = T>, const X: usize> MergeOperation<M>
    for IntersectionOp<X>
{
    fn from_a(&self, m: &mut M, n: usize) -> bool {
        m.advance_a(n, m.bc())
    }
    fn from_b(&self, m: &mut M, n: usize) -> bool {
        m.advance_b(n, m.ac())
    }
    fn collision(&self, m: &mut M) -> bool {
        m.advance_both(m.ac() == m.bc())
    }
    fn cmp(&self, a: &T, b: &T) -> Ordering {
        a.cmp(b)
    }
    const MCM_THRESHOLD: usize = X;
}

impl<T: Ord, M: MergeStateMut<A = T, B = T>, const X: usize> MergeOperation<M> for DiffOp<X> {
    fn from_a(&self, m: &mut M, n: usize) -> bool {
        m.advance_a(n, !m.bc())
    }
    fn from_b(&self, m: &mut M, n: usize) -> bool {
        m.advance_b(n, m.ac())
    }
    fn collision(&self, m: &mut M) -> bool {
        m.advance_both(m.ac() != m.bc())
    }
    fn cmp(&self, a: &T, b: &T) -> Ordering {
        a.cmp(b)
    }
    const MCM_THRESHOLD: usize = X;
}

impl<T: Ord, M: MergeStateMut<A = T, B = T>> MergeOperation<M> for XorOp {
    fn from_a(&self, m: &mut M, n: usize) -> bool {
        m.advance_a(n, true)
    }
    fn from_b(&self, m: &mut M, n: usize) -> bool {
        m.advance_b(n, true)
    }
    fn collision(&self, m: &mut M) -> bool {
        m.advance_both(false)
    }
    fn cmp(&self, a: &T, b: &T) -> Ordering {
        a.cmp(b)
    }
}

#[inline]
fn is_odd(x: usize) -> bool {
    (x & 1) != 0
}

#[inline]
fn is_even(x: usize) -> bool {
    (x & 1) == 0
}

fn is_strictly_sorted<T: Ord>(ranges: &[T]) -> bool {
    for i in 0..ranges.len().saturating_sub(1) {
        if ranges[i] >= ranges[i + 1] {
            return false;
        }
    }
    true
}

/// Split a strictly ordered sequence of boundaries `ranges` into two parts
/// `left`, `right` at position `at`, so that
///   contains(left, x) == contains(ranges, x) for x < at
///   contains(right, x) == contains(ranges, x) for x >= at
///
/// The returned slices are guaranteed to be minimal. The left slice will contain
/// no boundaries after the split point, and the right slice will contain at most
/// one boundary before the split point.
#[inline]
fn split<T: Ord>(ranges: &[T], at: T) -> (&[T], &[T]) {
    let l = ranges.len();
    let res = ranges.binary_search(&at);
    match res {
        Ok(i) if is_even(i) => {
            // left will be an even size, so we can just cut it off
            (&ranges[..i], &ranges[i..])
        }
        Err(i) if is_even(i) => {
            // right will be an even size, so we can just cut it off
            (&ranges[..i], &ranges[i..])
        }
        Ok(i) => {
            // left will be an odd size, so we need to add one if possible
            //
            // since i is an odd value, it indicates going to false at the
            // split point, and we don't need to have it in right.
            let sp = i.saturating_add(1).min(l);
            (&ranges[..i], &ranges[sp..])
        }
        Err(i) => {
            // left will be an odd size, so we add one if possible
            //
            // i is an odd value, so right is true at the split point, and
            // we need to add one value before the split point to right.
            // hence the saturating_sub(1).
            (&ranges[..i], &ranges[i.saturating_sub(1)..])
        }
    }
}

/// For a strictly ordered sequence of boundaries `ranges`, checks if the
/// value at `at` is true.
#[allow(dead_code)]
fn contains<T: Ord>(boundaries: &[T], value: &T) -> bool {
    match boundaries.binary_search(value) {
        Ok(index) => !is_odd(index),
        Err(index) => is_odd(index),
    }
}

/// Check if a sequence of boundaries `ranges` intersects with a range
#[allow(dead_code)]
fn intersects<T: Ord>(boundaries: &[T], range: Range<T>) -> bool {
    let (_, remaining) = split(boundaries, range.start);
    let (remaining, _) = split(remaining, range.end);
    // remaining is not the intersection but can be larger.
    // But if remaining is empty, then we know that the intersection is empty.
    !remaining.is_empty()
}

#[cfg(test)]
mod util_tests {
    use std::{collections::BTreeSet, ops::Range};

    use super::*;
    use proptest::prelude::*;

    fn test_points(boundaries: impl IntoIterator<Item = u64>) -> BTreeSet<u64> {
        let mut res = BTreeSet::new();
        for x in boundaries {
            res.insert(x.saturating_sub(1));
            res.insert(x);
            res.insert(x.saturating_add(1));
        }
        res
    }

    fn test_boundaries() -> impl Strategy<Value = (Vec<u64>, u64)> {
        proptest::collection::vec(any::<u64>(), 0..100).prop_flat_map(|mut v| {
            v.sort();
            v.dedup();
            // split point should occasionally be outside of the range
            let max_split = v
                .iter()
                .max()
                .cloned()
                .unwrap_or_default()
                .saturating_add(2);
            (Just(v), 0..max_split)
        })
    }

    proptest! {
        #[test]
        fn test_split((boundaries, at) in test_boundaries()) {
            let (left, right) = split(&boundaries, at);
            for x in test_points(boundaries.clone()) {
                // test that split does what it promises
                if x < at {
                    prop_assert_eq!(contains(left, &x), contains(&boundaries, &x), "left must be like boundaries for x < at");
                } else {
                    prop_assert_eq!(contains(right, &x), contains(&boundaries, &x), "right must be like boundaries for x >= at");
                }
                // test that split is not just returning the input, but minimal parts
                let nr = right.iter().filter(|x| x < &&at).count();
                prop_assert!(nr <= 1, "there must be at most one boundary before the split point");
                let nl = left.iter().filter(|x| x >= &&at).count();
                prop_assert!(nl == 0, "there must be no boundaries after the split point");
            }
        }
    }

    #[test]
    fn test_split_0() {
        #[allow(clippy::type_complexity)]
        let cases: Vec<(&[u64], u64, (&[u64], &[u64]))> = vec![
            (&[0, 2], 0, (&[], &[0, 2])),
            (&[0, 2], 2, (&[0], &[])),
            (&[0, 2, 4], 2, (&[0], &[4])),
            (&[0, 2, 4], 4, (&[0, 2], &[4])),
            (&[0, 2, 4, 8], 2, (&[0], &[4, 8])),
            (&[0, 2, 4, 8], 4, (&[0, 2], &[4, 8])),
            (&[0, 2, 4, 8], 3, (&[0, 2], &[4, 8])),
            (&[0, 2, 4, 8], 6, (&[0, 2, 4], &[4, 8])),
        ];
        for (ranges, pos, (left, right)) in cases {
            assert_eq!(split(ranges, pos), (left, right));
        }
    }

    #[test]
    fn test_intersects_0() {
        let cases: Vec<(&[u64], Range<u64>, bool)> = vec![
            (&[0, 2], 0..2, true),
            (&[0, 2], 2..4, false),
            (&[0, 2, 4, 8], 0..2, true),
            (&[0, 2, 4, 8], 2..4, false),
            (&[0, 2, 4, 8], 4..8, true),
            (&[0, 2, 4, 8], 8..12, false),
        ];
        for (ranges, range, expected) in cases {
            assert_eq!(intersects(ranges, range), expected);
        }
    }

    #[test]
    fn contains_0() {
        let cases: Vec<(&[u64], u64, bool)> = vec![
            (&[0, 2], 0, true),
            (&[0, 2], 1, true),
            (&[0, 2], 2, false),
            (&[0, 2, 4, 8], 3, false),
            (&[0, 2, 4, 8], 4, true),
        ];
        for (ranges, pos, expected) in cases {
            assert_eq!(contains(ranges, &pos), expected);
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use num_traits::{Bounded, PrimInt};
    use obey::*;
    use quickcheck::*;
    use std::collections::BTreeSet;
    use std::ops::RangeBounds;

    impl<T: RangeSetEntry + Clone, A: Array<Item = T>> RangeSet<A> {
        fn from_range_bounds<R: RangeBounds<T>>(r: R) -> std::result::Result<Self, ()> {
            match (r.start_bound(), r.end_bound()) {
                (Bound::Unbounded, Bound::Unbounded) => Ok(Self::all()),
                (Bound::Unbounded, Bound::Excluded(b)) => Ok(Self::from_range_until(b.clone())),
                (Bound::Included(a), Bound::Unbounded) => Ok(Self::from_range_from(a.clone())),
                (Bound::Included(a), Bound::Excluded(b)) => Ok(Self::from_range(Range {
                    start: a.clone(),
                    end: b.clone(),
                })),
                _ => Err(()),
            }
        }
    }

    impl<T: Arbitrary + Ord, A: Array<Item = T> + Clone + 'static> Arbitrary for RangeSet<A> {
        fn arbitrary<G: Gen>(g: &mut G) -> Self {
            let mut boundaries: Vec<T> = Arbitrary::arbitrary(g);
            boundaries.truncate(4);
            boundaries.sort();
            boundaries.dedup();
            Self::new_unchecked_impl(boundaries.into())
        }
    }

    /// A range set can be seen as a set of elements, even though it does not actually contain the elements
    impl<E: PrimInt + RangeSetEntry + Clone, A: Array<Item = E>> TestSamples<E, bool> for RangeSet<A> {
        fn samples(&self, res: &mut BTreeSet<E>) {
            res.insert(<E as Bounded>::min_value());
            for x in self.0.iter().cloned() {
                res.insert(x.saturating_sub(E::one()));
                res.insert(x);
                res.insert(x.saturating_add(E::one()));
            }
            res.insert(E::max_value());
        }

        fn at(&self, elem: E) -> bool {
            self.contains(&elem)
        }
    }
    type Test = RangeSet<[i64; 4]>;

    #[test]
    fn smoke_test() {
        let x: Test = Test::from(0..10);
        println!(
            "{:?} {:?} {:?} {:?} {:?}",
            x,
            x.contains(&0),
            x.contains(&1),
            x.contains(&9),
            x.contains(&10)
        );

        let y: Test = Test::from(..10);
        let z: Test = Test::from(20..);

        let r: Test = (&x).bitor(&z);

        println!("{:?} {:?} {:?} {:?}", x, y, z, r);

        let r2: Test = &x & &y;
        let r3: Test = &x | &y;
        let r4 = y.is_disjoint(&z);
        let r5 = (&y).bitand(&z);

        println!("{:?}", r2);
        println!("{:?}", r3);
        println!("{:?} {:?}", r4, r5);
    }

    #[cfg(feature = "serde")]
    #[quickcheck]
    fn range_seq_serde(a: Test) -> bool {
        let bytes = serde_cbor::to_vec(&a).unwrap();
        let b: Test = serde_cbor::from_slice(&bytes).unwrap();
        a == b
    }

    #[cfg(feature = "rkyv")]
    #[quickcheck]
    fn range_seq_rkyv_unvalidated(a: Test) -> bool {
        use rkyv::*;
        use ser::Serializer;
        let mut serializer = ser::serializers::AllocSerializer::<256>::default();
        serializer.serialize_value(&a).unwrap();
        let bytes = serializer.into_serializer().into_inner();
        let archived = unsafe { rkyv::archived_root::<Test>(&bytes) };
        let deserialized: Test = archived.deserialize(&mut Infallible).unwrap();
        a == deserialized
    }

    #[cfg(feature = "rkyv_validated")]
    #[quickcheck]
    fn range_seq_rkyv_validated(a: Test) -> bool {
        use rkyv::*;
        use ser::Serializer;
        let mut serializer = ser::serializers::AllocSerializer::<256>::default();
        serializer.serialize_value(&a).unwrap();
        let bytes = serializer.into_serializer().into_inner();
        let archived = rkyv::check_archived_root::<Test>(&bytes).unwrap();
        let deserialized: Test = archived.deserialize(&mut Infallible).unwrap();
        a == deserialized
    }

    #[cfg(feature = "rkyv_validated")]
    #[test]
    fn range_seq_rkyv_errors() {
        use rkyv::*;
        use std::num::NonZeroU64;

        // deserialize a boolean value of 2, must produce an error!
        let mut bytes = AlignedVec::new();
        bytes.extend_from_slice(&hex::decode("000000000000000002000000").unwrap());
        assert!(rkyv::check_archived_root::<Test>(&bytes).is_err());

        // deserialize wrongly ordered range set, must produce an error
        let mut bytes = AlignedVec::new();
        bytes.extend_from_slice(
            &hex::decode("02000000000000000100000000000000f0ffffff0200000000000000").unwrap(),
        );
        assert!(rkyv::check_archived_root::<Test>(&bytes).is_err());

        // deserialize wrong value (0 for a NonZeroU64), must produce an error
        let mut bytes = AlignedVec::new();
        bytes.extend_from_slice(
            &hex::decode("00000000000000000100000000000000f0ffffff0200000000000000").unwrap(),
        );
        assert!(rkyv::check_archived_root::<RangeSet2<NonZeroU64>>(&bytes).is_err());
    }

    #[quickcheck]
    fn ranges_consistent(a: Test) -> bool {
        let mut b = Test::empty();
        for e in a.iter() {
            let e = e.cloned();
            b |= Test::from_range_bounds(e).unwrap();
        }
        a == b
    }

    #[quickcheck]
    fn is_disjoint_sample(a: Test, b: Test) -> bool {
        let res = binary_property_test(&a, &b, a.is_disjoint(&b), |a, b| !(a & b));
        if !res {
            println!("{:?} {:?} {:?}", a, b, a.is_disjoint(&b));
        }
        res
    }

    #[quickcheck]
    fn is_subset_sample(a: Test, b: Test) -> bool {
        binary_property_test(&a, &b, a.is_subset(&b), |a, b| !a | b)
    }

    #[quickcheck]
    fn negation_check(a: RangeSet2<i64>) -> bool {
        unary_element_test(&a, !a.clone(), |x| !x)
    }

    #[quickcheck]
    fn union_check(a: RangeSet2<i64>, b: RangeSet2<i64>) -> bool {
        binary_element_test(&a, &b, &a | &b, |a, b| a | b)
    }

    #[quickcheck]
    fn intersection_check(a: RangeSet2<i64>, b: RangeSet2<i64>) -> bool {
        binary_element_test(&a, &b, &a & &b, |a, b| a & b)
    }

    #[quickcheck]
    fn xor_check(a: RangeSet2<i64>, b: RangeSet2<i64>) -> bool {
        binary_element_test(&a, &b, &a ^ &b, |a, b| a ^ b)
    }

    #[quickcheck]
    fn difference_check(a: RangeSet2<i64>, b: RangeSet2<i64>) -> bool {
        binary_element_test(&a, &b, &a - &b, |a, b| a & !b)
    }

    bitop_assign_consistent!(Test);
    bitop_symmetry!(Test);
    bitop_empty!(Test);
    bitop_sub_not_all!(Test);
    set_predicate_consistent!(Test);
}