range_set_blaze/

set.rs

#![allow(unexpected_cfgs)]
use core::cmp::max;
use core::mem;
use core::{
    cmp::Ordering,
    fmt,
    iter::FusedIterator,
    ops::{BitOr, BitOrAssign, Bound, RangeBounds, RangeInclusive},
};
use num_traits::{One, Zero};
#[cfg(all(not(coverage), feature = "std"))]
use std::{
    fs::File,
    io::{self, BufRead, BufReader},
    path::Path,
    str::FromStr,
};

use crate::alloc::string::ToString;
use crate::sorted_disjoint::RangeOnce;
use alloc::collections::{BTreeMap, btree_map};
use alloc::string::String;
use alloc::vec::Vec;
use gen_ops::gen_ops_ex;

use crate::ranges_iter::RangesIter;
use crate::unsorted_disjoint::{SortedDisjointWithLenSoFar, UnsortedDisjoint};
use crate::{Integer, prelude::*};
use crate::{IntoRangesIter, UnionIter};

// // FUTURE: use fn range to implement one-at-a-time intersection, difference, etc. and then add more inplace ops.

#[cfg(all(not(coverage), feature = "std"))]
#[allow(dead_code)]
#[doc(hidden)]
pub fn demo_read_ranges_from_file<P, T>(path: P) -> io::Result<RangeSetBlaze<T>>
where
    P: AsRef<Path>,
    T: FromStr + Integer,
{
    let lines = BufReader::new(File::open(&path)?).lines();

    let mut set = RangeSetBlaze::new();
    for line in lines {
        let line = line?;
        let mut split = line.split('\t');
        let start = split
            .next()
            .ok_or_else(|| io::Error::new(io::ErrorKind::InvalidData, "Missing start of range"))?
            .parse::<T>()
            .map_err(|_| io::Error::new(io::ErrorKind::InvalidData, "Invalid start of range"))?;
        let end = split
            .next()
            .ok_or_else(|| io::Error::new(io::ErrorKind::InvalidData, "Missing end of range"))?
            .parse::<T>()
            .map_err(|_| io::Error::new(io::ErrorKind::InvalidData, "Invalid end of range"))?;
        set.ranges_insert(start..=end);
    }

    Ok(set)
}

/// A set of integers stored as sorted & disjoint ranges.
///
/// Internally, it stores the ranges in a cache-efficient [`BTreeMap`].
///
/// # Table of Contents
/// * [`RangeSetBlaze` Constructors](#rangesetblaze-constructors)
///    * [Performance](#constructor-performance)
///    * [Examples](struct.RangeSetBlaze.html#constructor-examples)
/// * [`RangeSetBlaze` Set Operations](#rangesetblaze-set-operations)
///    * [Performance](struct.RangeSetBlaze.html#set-operation-performance)
///    * [Examples](struct.RangeSetBlaze.html#set-operation-examples)
///  * [`RangeSetBlaze` Comparisons](#rangesetblaze-comparisons)
///  * [Additional Examples](#additional-examples)
///
/// # `RangeSetBlaze` Constructors
///
/// You can create `RangeSetBlaze`'s from unsorted and overlapping integers (or ranges).
/// However, if you know that your input is sorted and disjoint, you can speed up construction.
///
/// Here are the constructors, followed by a
/// description of the performance, and then some examples.
///
/// | Methods                                     | Input                        | Notes                    |
/// |---------------------------------------------|------------------------------|--------------------------|
/// | [`new`]/[`default`]                         |                              |                          |
/// | [`from_iter`][1]/[`collect`][1]             | integer iterator             |                          |
/// | [`from_iter`][2]/[`collect`][2]             | ranges iterator              |                          |
/// | [`from_slice`][5]                           | slice of integers            | Fast, but nightly-only  |
/// | [`from_sorted_disjoint`][3]/[`into_range_set_blaze`][3] | [`SortedDisjoint`] iterator |               |
/// | [`from`][5] /[`into`][5]                    | array of integers            |                          |
/// | [`from`][7]                                 | `RangeInclusive<T>`          |                          |
///
///
/// [`BTreeMap`]: alloc::collections::BTreeMap
/// [`new`]: RangeSetBlaze::new
/// [`default`]: RangeSetBlaze::default
/// [1]: struct.RangeSetBlaze.html#impl-FromIterator<T>-for-RangeSetBlaze<T>
/// [2]: struct.RangeSetBlaze.html#impl-FromIterator<RangeInclusive<T>>-for-RangeSetBlaze<T>
/// [3]: RangeSetBlaze::from_sorted_disjoint
/// [SortedDisjoint]: crate::SortedDisjoint.html#table-of-contents
/// [5]: RangeSetBlaze::from
/// [6]: RangeSetBlaze::from_slice()
/// [7]: #method.from-1
///
/// # Constructor Performance
///
/// The [`from_iter`][1]/[`collect`][1] constructors are designed to work fast on 'clumpy' data.
/// By 'clumpy', we mean that the number of ranges needed to represent the data is
/// small compared to the number of input integers. To understand this, consider the internals
/// of the constructors:
///
///  Internally, the `from_iter`/`collect` constructors take these steps:
/// * collect adjacent integers/ranges into disjoint ranges, O(*n₁*)
/// * sort the disjoint ranges by their `start`, O(*n₂* ln *n₂*)
/// * merge adjacent ranges, O(*n₂*)
/// * create a `BTreeMap` from the now sorted & disjoint ranges, O(*n₃* ln *n₃*)
///
/// where *n₁* is the number of input integers/ranges, *n₂* is the number of disjoint & unsorted ranges,
/// and *n₃* is the final number of sorted & disjoint ranges.
///
/// For example, an input of
///  *  `3, 2, 1, 4, 5, 6, 7, 0, 8, 8, 8, 100, 1`, becomes
///  * `0..=8, 100..=100, 1..=1`, and then
///  * `0..=8, 1..=1, 100..=100`, and finally
///  * `0..=8, 100..=100`.
///
/// What is the effect of clumpy data?
/// Notice that if *n₂* ≈ sqrt(*n₁*), then construction is O(*n₁*).
/// Indeed, as long as *n₂* ≤ *n₁*/ln(*n₁*), then construction is O(*n₁*).
/// Moreover, we'll see that set operations are O(*n₃*). Thus, if *n₃* ≈ sqrt(*n₁*) then set operations are O(sqrt(*n₁*)),
/// a quadratic improvement an O(*n₁*) implementation that ignores the clumps.
///
/// The [`from_slice`][5] constructor typically provides a constant-time speed up for array-like collections of clumpy integers.
/// On a representative benchmark, the speed up was 7×.
/// The method works by scanning the input for blocks of consecutive integers, and then using `from_iter` on the results.
/// Where available, it uses SIMD instructions. It is nightly only and enabled by the `from_slice` feature.
///
/// ## Constructor Examples
///
/// ```
/// use range_set_blaze::prelude::*;
///
/// // Create an empty set with 'new' or 'default'.
/// let a0 = RangeSetBlaze::<i32>::new();
/// let a1 = RangeSetBlaze::<i32>::default();
/// assert!(a0 == a1 && a0.is_empty());
///
/// // 'from_iter'/'collect': From an iterator of integers.
/// // Duplicates and out-of-order elements are fine.
/// let a0 = RangeSetBlaze::from_iter([3, 2, 1, 100, 1]);
/// let a1: RangeSetBlaze<i32> = [3, 2, 1, 100, 1].into_iter().collect();
/// assert!(a0 == a1 && a0.to_string() == "1..=3, 100..=100");
///
/// // 'from_iter'/'collect': From an iterator of inclusive ranges, start..=end.
/// // Overlapping, out-of-order, and empty ranges are fine.
/// #[allow(clippy::reversed_empty_ranges)]
/// let a0 = RangeSetBlaze::from_iter([1..=2, 2..=2, -10..=-5, 1..=0]);
/// #[allow(clippy::reversed_empty_ranges)]
/// let a1: RangeSetBlaze<i32> = [1..=2, 2..=2, -10..=-5, 1..=0].into_iter().collect();
/// assert!(a0 == a1 && a0.to_string() == "-10..=-5, 1..=2");
///
/// // 'from_slice': From any array-like collection of integers.
/// // Nightly-only, but faster than 'from_iter'/'collect' on integers.
/// #[cfg(feature = "from_slice")]
/// let a0 = RangeSetBlaze::from_slice(vec![3, 2, 1, 100, 1]);
/// #[cfg(feature = "from_slice")]
/// assert!(a0.to_string() == "1..=3, 100..=100");
///
/// // If we know the ranges are already sorted and disjoint,
/// // we can avoid work and use 'from_sorted_disjoint'/'into_range_set_blaze'.
/// let a0 = RangeSetBlaze::from_sorted_disjoint(CheckSortedDisjoint::new([-10..=-5, 1..=2]));
/// let a1: RangeSetBlaze<i32> = CheckSortedDisjoint::new([-10..=-5, 1..=2]).into_range_set_blaze();
/// assert!(a0 == a1 && a0.to_string() == "-10..=-5, 1..=2");
///
/// // For compatibility with `BTreeSet`, we also support
/// // 'from'/'into' from arrays of integers.
/// let a0 = RangeSetBlaze::from([3, 2, 1, 100, 1]);
/// let a1: RangeSetBlaze<i32> = [3, 2, 1, 100, 1].into();
/// assert!(a0 == a1 && a0.to_string() == "1..=3, 100..=100");
/// ```
///
/// # `RangeSetBlaze` Set Operations
///
/// You can perform set operations on `RangeSetBlaze`s using operators.
///
/// | Set Operation           | Operator          |  Multiway Method |
/// |-------------------|-------------------------|-------------------------|
/// | union             |  [`a` &#124; `b`]       | <code>[a, b, c].[union]()</code>`()` |
/// | intersection      |  [`a & b`]              | <code>[a, b, c].[intersection]()</code>`()` |
/// | difference        |  [`a - b`]              | *n/a* |
/// | symmetric difference|  [`a ^ b`]            | <code>[a, b, c].[symmetric_difference]()</code>`()` |
/// | complement        |  [`!a`]                 | *n/a* |
///
/// `RangeSetBlaze` also implements many other methods, such as [`insert`], [`pop_first`] and [`split_off`]. Many of
/// these methods match those of `BTreeSet`.
///
/// [`a` &#124; `b`]: struct.RangeSetBlaze.html#impl-BitOr-for-RangeSetBlaze<T>
/// [`a & b`]: struct.RangeSetBlaze.html#impl-BitAnd-for-RangeSetBlaze<T>
/// [`a - b`]: struct.RangeSetBlaze.html#impl-Sub-for-RangeSetBlaze<T>
/// [`a ^ b`]: struct.RangeSetBlaze.html#impl-BitXor-for-RangeSetBlaze<T>
/// [`!a`]: struct.RangeSetBlaze.html#method.not
/// [`union`]: trait.MultiwayRangeSetBlazeRef.html#method.union
/// [`intersection`]: trait.MultiwayRangeSetBlazeRef.html#method.intersection
/// [`symmetric_difference`]: trait.MultiwayRangeSetBlazeRef.html#method.symmetric_difference
/// [`insert`]: RangeSetBlaze::insert
/// [`pop_first`]: RangeSetBlaze::pop_first
/// [`split_off`]: RangeSetBlaze::split_off
/// [SortedDisjoint]: crate::SortedDisjoint.html#table-of-contents
///
///
/// ## Set Operation Performance
///
/// Every operation is implemented as
/// 1. a single pass over the sorted & disjoint ranges
/// 2. the construction of a new `RangeSetBlaze`
///
/// Thus, applying multiple operators creates intermediate
/// `RangeSetBlaze`'s. If you wish, you can avoid these intermediate
/// `RangeSetBlaze`'s by switching to the [`SortedDisjoint`] API. The last example below
/// demonstrates this.
///
/// ## Set Operation Examples
///
/// ```
/// use range_set_blaze::prelude::*;
///
/// let a = RangeSetBlaze::from_iter([1..=2, 5..=100]);
/// let b = RangeSetBlaze::from_iter([2..=6]);
///
/// // Union of two 'RangeSetBlaze's.
/// let result = &a | &b;
/// // Alternatively, we can take ownership via 'a | b'.
/// assert_eq!(result.to_string(), "1..=100");
///
/// // Intersection of two 'RangeSetBlaze's.
/// let result = &a & &b; // Alternatively, 'a & b'.
/// assert_eq!(result.to_string(), "2..=2, 5..=6");
///
/// // Set difference of two 'RangeSetBlaze's.
/// let result = &a - &b; // Alternatively, 'a - b'.
/// assert_eq!(result.to_string(), "1..=1, 7..=100");
///
/// // Symmetric difference of two 'RangeSetBlaze's.
/// let result = &a ^ &b; // Alternatively, 'a ^ b'.
/// assert_eq!(result.to_string(), "1..=1, 3..=4, 7..=100");
///
/// // complement of a 'RangeSetBlaze'.
/// let result = !&a; // Alternatively, '!a'.
/// assert_eq!(
///     result.to_string(),
///     "-2147483648..=0, 3..=4, 101..=2147483647"
/// );
///
/// // Multiway union of 'RangeSetBlaze's.
/// let c = RangeSetBlaze::from_iter([2..=2, 6..=200]);
/// let result = [&a, &b, &c].union();
/// assert_eq!(result.to_string(), "1..=200");
///
/// // Multiway intersection of 'RangeSetBlaze's.
/// let result = [&a, &b, &c].intersection();
/// assert_eq!(result.to_string(), "2..=2, 6..=6");
///
/// // Applying multiple operators
/// let result0 = &a - (&b | &c); // Creates an intermediate 'RangeSetBlaze'.
/// // Alternatively, we can use the 'SortedDisjoint' API and avoid the intermediate 'RangeSetBlaze'.
/// let result1 = RangeSetBlaze::from_sorted_disjoint(a.ranges() - (b.ranges() | c.ranges()));
/// assert!(result0 == result1 && result0.to_string() == "1..=1");
/// ```
/// # `RangeSetBlaze` Comparisons
///
/// We can compare `RangeSetBlaze`s using the following operators:
/// `<`, `<=`, `>`, `>=`.  Following the convention of `BTreeSet`,
/// these comparisons are lexicographic. See [`cmp`] for more examples.
///
/// Use the [`is_subset`] and [`is_superset`] methods to check if one `RangeSetBlaze` is a subset
/// or superset of another.
///
/// Use `==`, `!=` to check if two `RangeSetBlaze`s are equal or not.
///
/// [`BTreeSet`]: alloc::collections::BTreeSet
/// [`is_subset`]: RangeSetBlaze::is_subset
/// [`is_superset`]: RangeSetBlaze::is_superset
/// [`cmp`]: RangeSetBlaze::cmp
///
/// # Additional Examples
///
/// See the [module-level documentation] for additional examples.
///
/// [module-level documentation]: index.html
#[derive(Clone, Hash, PartialEq)]
pub struct RangeSetBlaze<T: Integer> {
    len: <T as Integer>::SafeLen,
    pub(crate) btree_map: BTreeMap<T, T>,
}

// impl default
impl<T: Integer> Default for RangeSetBlaze<T> {
    /// Creates an empty `RangeSetBlaze`.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set: RangeSetBlaze<i32> = RangeSetBlaze::default();
    /// assert!(set.is_empty());
    /// ```
    fn default() -> Self {
        Self {
            len: <T as Integer>::SafeLen::zero(),
            btree_map: BTreeMap::new(),
        }
    }
}

// FUTURE: Make all RangeSetBlaze iterators DoubleEndedIterator and ExactSizeIterator.
impl<T: Integer> fmt::Debug for RangeSetBlaze<T> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{}", self.ranges().into_string())
    }
}

impl<T: Integer> fmt::Display for RangeSetBlaze<T> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{}", self.ranges().into_string())
    }
}

impl<T: Integer> RangeSetBlaze<T> {
    /// Gets an iterator that visits the integer elements in the [`RangeSetBlaze`] in
    /// ascending and/or descending order. Double-ended.
    ///
    /// Also see the [`RangeSetBlaze::ranges`] method.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([1..=3]);
    /// let mut set_iter = set.iter();
    /// assert_eq!(set_iter.next(), Some(1));
    /// assert_eq!(set_iter.next(), Some(2));
    /// assert_eq!(set_iter.next(), Some(3));
    /// assert_eq!(set_iter.next(), None);
    /// ```
    ///
    /// Values returned by `.next()` are in ascending order.
    /// Values returned by `.next_back()` are in descending order.
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([3, 1, 2]);
    /// let mut set_iter = set.iter();
    /// assert_eq!(set_iter.next(), Some(1));
    /// assert_eq!(set_iter.next_back(), Some(3));
    /// assert_eq!(set_iter.next(), Some(2));
    /// assert_eq!(set_iter.next_back(), None);
    /// ```
    #[allow(clippy::iter_without_into_iter)]
    pub fn iter(&self) -> Iter<T, RangesIter<'_, T>> {
        // If the user asks for an iter, we give them a RangesIter iterator
        // and we iterate that one integer at a time.
        Iter {
            range_front: T::exhausted_range(),
            range_back: T::exhausted_range(),
            btree_set_iter: self.ranges(),
        }
    }

    /// Returns the first element in the set, if any.
    /// This element is always the minimum of all integer elements in the set.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    /// assert_eq!(set.first(), None);
    /// set.insert(1);
    /// assert_eq!(set.first(), Some(1));
    /// set.insert(2);
    /// assert_eq!(set.first(), Some(1));
    /// ```
    #[must_use]
    pub fn first(&self) -> Option<T> {
        self.btree_map.iter().next().map(|(x, _)| *x)
    }

    /// Returns the element in the set, if any, that is equal to
    /// the value.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([1, 2, 3]);
    /// assert_eq!(set.get(2), Some(2));
    /// assert_eq!(set.get(4), None);
    /// ```
    pub fn get(&self, value: T) -> Option<T> {
        if self.contains(value) {
            Some(value)
        } else {
            None
        }
    }

    /// Returns the last element in the set, if any.
    /// This element is always the maximum of all elements in the set.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    /// assert_eq!(set.last(), None);
    /// set.insert(1);
    /// assert_eq!(set.last(), Some(1));
    /// set.insert(2);
    /// assert_eq!(set.last(), Some(2));
    /// ```
    #[must_use]
    pub fn last(&self) -> Option<T> {
        self.btree_map.iter().next_back().map(|(_, x)| *x)
    }

    /// Create a [`RangeSetBlaze`] from a [`SortedDisjoint`] iterator.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let a0 = RangeSetBlaze::from_sorted_disjoint(CheckSortedDisjoint::new([-10..=-5, 1..=2]));
    /// let a1: RangeSetBlaze<i32> = CheckSortedDisjoint::new([-10..=-5, 1..=2]).into_range_set_blaze();
    /// assert!(a0 == a1 && a0.to_string() == "-10..=-5, 1..=2");
    /// ```
    pub fn from_sorted_disjoint<I>(iter: I) -> Self
    where
        I: SortedDisjoint<T>,
    {
        let mut iter_with_len = SortedDisjointWithLenSoFar::new(iter);
        let btree_map = (&mut iter_with_len).collect();
        Self {
            btree_map,
            len: iter_with_len.len_so_far(),
        }
    }

    /// Creates a [`RangeSetBlaze`] from a collection of integers. It is typically many
    /// times faster than [`from_iter`][1]/[`collect`][1].
    /// On a representative benchmark, the speed up was 7×.
    ///
    /// **Warning: Requires the nightly compiler. Also, you must enable the `from_slice`
    /// feature in your `Cargo.toml`. For example, with the command:**
    /// ```bash
    ///  cargo add range-set-blaze --features "from_slice"
    /// ```
    /// The function accepts any type that can be referenced as a slice of integers,
    /// including slices, arrays, and vectors. Duplicates and out-of-order elements are fine.
    ///
    /// Where available, this function leverages SIMD (Single Instruction, Multiple Data) instructions
    /// for performance optimization. To enable SIMD optimizations, compile with the Rust compiler
    /// (rustc) flag `-C target-cpu=native`. This instructs rustc to use the native instruction set
    /// of the CPU on the machine compiling the code, potentially enabling more SIMD optimizations.
    ///
    /// **Caution**: Compiling with `-C target-cpu=native` optimizes the binary for your current CPU architecture,
    /// which may lead to compatibility issues on other machines with different architectures.
    /// This is particularly important for distributing the binary or running it in varied environments.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a0 = RangeSetBlaze::from_slice(&[3, 2, 1, 100, 1]); // reference to a slice
    /// let a1 = RangeSetBlaze::from_slice([3, 2, 1, 100, 1]);   // array
    /// let a2 = RangeSetBlaze::from_slice(vec![3, 2, 1, 100, 1]); // vector
    /// assert!(a0 == a1 && a1 == a2 && a0.to_string() == "1..=3, 100..=100");
    /// ```
    /// [1]: struct.RangeSetBlaze.html#impl-FromIterator<T>-for-RangeSetBlaze<T>
    #[cfg(feature = "from_slice")]
    #[inline]
    pub fn from_slice(slice: impl AsRef<[T]>) -> Self {
        T::from_slice(slice)
    }

    #[allow(dead_code)]
    #[must_use]
    pub(crate) fn len_slow(&self) -> <T as Integer>::SafeLen {
        Self::btree_map_len(&self.btree_map)
    }

    /// Moves all elements from `other` into `self`, leaving `other` empty.
    ///
    /// # Performance
    /// It adds the integers in `other` to `self` in O(n log m) time, where n is the number of ranges in `other`
    /// and m is the number of ranges in `self`.
    /// When n is large, consider using `|` which is O(n+m) time.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut a = RangeSetBlaze::from_iter([1..=3]);
    /// let mut b = RangeSetBlaze::from_iter([3..=5]);
    ///
    /// a.append(&mut b);
    ///
    /// assert_eq!(a.len(), 5u64);
    /// assert_eq!(b.len(), 0u64);
    ///
    /// assert!(a.contains(1));
    /// assert!(a.contains(2));
    /// assert!(a.contains(3));
    /// assert!(a.contains(4));
    /// assert!(a.contains(5));
    ///
    /// ```
    pub fn append(&mut self, other: &mut Self) {
        for range in other.ranges() {
            self.internal_add(range);
        }
        other.clear();
    }

    /// Clears the set, removing all integer elements.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut v = RangeSetBlaze::new();
    /// v.insert(1);
    /// v.clear();
    /// assert!(v.is_empty());
    /// ```
    pub fn clear(&mut self) {
        self.btree_map.clear();
        self.len = <T as Integer>::SafeLen::zero();
    }

    /// Returns `true` if the set contains no elements.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut v = RangeSetBlaze::new();
    /// assert!(v.is_empty());
    /// v.insert(1);
    /// assert!(!v.is_empty());
    /// ```
    #[must_use]
    #[inline]
    pub fn is_empty(&self) -> bool {
        self.ranges_len() == 0
    }

    /// Returns `true` if the set contains all possible integers.
    ///
    /// For type `T`, this means covering the full domain from `T::min_value()` to `T::max_value()`.
    /// Complexity: O(1).
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut v = RangeSetBlaze::<u8>::new();
    /// assert!(!v.is_universal());
    ///
    /// let universal = !RangeSetBlaze::<u8>::new();
    /// assert!(universal.is_universal());
    /// ```
    #[must_use]
    #[inline]
    pub fn is_universal(&self) -> bool {
        self.ranges().is_universal()
    }

    /// Returns `true` if the set is a subset of another,
    /// i.e., `other` contains at least all the elements in `self`.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let sup = RangeSetBlaze::from_iter([1..=3]);
    /// let mut set = RangeSetBlaze::new();
    ///
    /// assert_eq!(set.is_subset(&sup), true);
    /// set.insert(2);
    /// assert_eq!(set.is_subset(&sup), true);
    /// set.insert(4);
    /// assert_eq!(set.is_subset(&sup), false);
    /// ```
    #[must_use]
    #[inline]
    pub fn is_subset(&self, other: &Self) -> bool {
        // Add a fast path
        if self.len() > other.len() {
            return false;
        }
        self.ranges().is_subset(other.ranges())
    }

    /// Returns `true` if the set is a superset of another,
    /// i.e., `self` contains at least all the elements in `other`.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let sub = RangeSetBlaze::from_iter([1, 2]);
    /// let mut set = RangeSetBlaze::new();
    ///
    /// assert_eq!(set.is_superset(&sub), false);
    ///
    /// set.insert(0);
    /// set.insert(1);
    /// assert_eq!(set.is_superset(&sub), false);
    ///
    /// set.insert(2);
    /// assert_eq!(set.is_superset(&sub), true);
    /// ```
    #[must_use]
    pub fn is_superset(&self, other: &Self) -> bool {
        other.is_subset(self)
    }

    /// Returns `true` if the set contains an element equal to the value.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([1, 2, 3]);
    /// assert_eq!(set.contains(1), true);
    /// assert_eq!(set.contains(4), false);
    /// ```
    pub fn contains(&self, value: T) -> bool {
        self.btree_map
            .range(..=value)
            .next_back()
            .is_some_and(|(_, end)| value <= *end)
    }

    /// Returns `true` if `self` has no elements in common with `other`.
    /// This is equivalent to checking for an empty intersection.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=3]);
    /// let mut b = RangeSetBlaze::new();
    ///
    /// assert_eq!(a.is_disjoint(&b), true);
    /// b.insert(4);
    /// assert_eq!(a.is_disjoint(&b), true);
    /// b.insert(1);
    /// assert_eq!(a.is_disjoint(&b), false);
    /// ```
    #[must_use]
    #[inline]
    pub fn is_disjoint(&self, other: &Self) -> bool {
        self.ranges().is_disjoint(other.ranges())
    }

    fn delete_extra(&mut self, internal_range: &RangeInclusive<T>) {
        let (start, end) = internal_range.clone().into_inner();
        let mut after = self.btree_map.range_mut(start..);
        let (start_after, end_after) = after
            .next()
            .expect("Real assert: there will always be a next");
        debug_assert!(start == *start_after && end == *end_after);

        let mut end_new = end;
        let delete_list = after
            .map_while(|(start_delete, end_delete)| {
                // must check this in two parts to avoid overflow
                if *start_delete <= end || *start_delete <= end.add_one() {
                    end_new = max(end_new, *end_delete);
                    self.len -= T::safe_len(&(*start_delete..=*end_delete));
                    Some(*start_delete)
                } else {
                    None
                }
            })
            .collect::<Vec<_>>();
        if end_new > end {
            self.len += T::safe_len(&(end..=end_new.sub_one()));
            *end_after = end_new;
        }
        for start in delete_list {
            self.btree_map.remove(&start);
        }
    }

    /// Adds a value to the set.
    ///
    /// Returns whether the value was newly inserted. That is:
    ///
    /// - If the set did not previously contain an equal value, `true` is
    ///   returned.
    /// - If the set already contained an equal value, `false` is returned, and
    ///   the entry is not updated.
    ///
    /// # Performance
    /// Inserting n items will take in O(n log m) time, where n is the number of inserted items and m is the number of ranges in `self`.
    /// When n is large, consider using `|` which is O(n+m) time.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    ///
    /// assert_eq!(set.insert(2), true);
    /// assert_eq!(set.insert(2), false);
    /// assert_eq!(set.len(), 1u64);
    /// ```
    pub fn insert(&mut self, value: T) -> bool {
        let len_before = self.len;
        self.internal_add(value..=value);
        self.len != len_before
    }

    /// Constructs an iterator over a sub-range of elements in the set.
    ///
    /// Not to be confused with [`RangeSetBlaze::ranges`], which returns an iterator over the ranges in the set.
    ///
    /// The simplest way is to use the range syntax `min..max`, thus `range(min..max)` will
    /// yield elements from min (inclusive) to max (exclusive).
    /// The range may also be entered as `(Bound<T>, Bound<T>)`, so for example
    /// `range((Excluded(4), Included(10)))` will yield a left-exclusive, right-inclusive
    /// range from 4 to 10.
    ///
    /// # Panics
    ///
    /// Panics if range `start > end`.
    /// Panics if range `start == end` and both bounds are `Excluded`.
    ///
    /// # Performance
    ///
    /// Although this could be written to run in time O(ln(n)) in the number of ranges, it is currently O(n) in the number of ranges.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// use core::ops::Bound::Included;
    ///
    /// let mut set = RangeSetBlaze::new();
    /// set.insert(3);
    /// set.insert(5);
    /// set.insert(8);
    /// for elem in set.range((Included(4), Included(8))) {
    ///     println!("{elem}");
    /// }
    /// assert_eq!(Some(5), set.range(4..).next());
    /// ```
    pub fn range<R>(&self, range: R) -> IntoIter<T>
    where
        R: RangeBounds<T>,
    {
        let (start, end) = extract_range(range);
        assert!(
            start <= end,
            "start (inclusive) must be less than or equal to end (inclusive)"
        );

        let bounds = CheckSortedDisjoint::new([start..=end]);
        Self::from_sorted_disjoint(self.ranges() & bounds).into_iter()
    }

    /// Adds a range to the set.
    ///
    /// Returns whether any values where newly inserted. That is:
    ///
    /// - If the set did not previously contain some value in the range, `true` is
    ///   returned.
    /// - If the set already contained every value in the range, `false` is returned, and
    ///   the entry is not updated.
    ///
    /// # Performance
    /// Inserting n items will take in O(n log m) time, where n is the number of inserted items and m is the number of ranges in `self`.
    /// When n is large, consider using `|` which is O(n+m) time.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    ///
    /// assert_eq!(set.ranges_insert(2..=5), true);
    /// assert_eq!(set.ranges_insert(5..=6), true);
    /// assert_eq!(set.ranges_insert(3..=4), false);
    /// assert_eq!(set.len(), 5u64);
    /// ```
    pub fn ranges_insert<R>(&mut self, range: R) -> bool
    where
        R: RangeBounds<T>,
    {
        let len_before = self.len;
        let (start, end) = extract_range(range);
        self.internal_add(start..=end);
        self.len != len_before
    }

    /// If the set contains an element equal to the value, removes it from the
    /// set and drops it. Returns whether such an element was present.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    ///
    /// set.insert(2);
    /// assert!(set.remove(2));
    /// assert!(!set.remove(2));
    /// ```
    pub fn remove(&mut self, value: T) -> bool {
        // The code can have only one mutable reference to self.btree_map.
        let Some((start_ref, end_ref)) = self.btree_map.range_mut(..=value).next_back() else {
            return false;
        };

        let end = *end_ref;
        if end < value {
            return false;
        }
        let start = *start_ref;
        // special case if in range and start strictly less than value
        if start < value {
            *end_ref = value.sub_one();
            // special, special case if value == end
            if value == end {
                self.len -= <T::SafeLen>::one();
                return true;
            }
        }
        self.len -= <T::SafeLen>::one();
        if start == value {
            self.btree_map.remove(&start);
        }
        if value < end {
            self.btree_map.insert(value.add_one(), end);
        }
        true
    }

    /// Splits the collection into two at the value. Returns a new collection
    /// with all elements greater than or equal to the value.
    ///
    /// # Examples
    ///
    /// Basic usage:
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut a = RangeSetBlaze::new();
    /// a.insert(1);
    /// a.insert(2);
    /// a.insert(3);
    /// a.insert(17);
    /// a.insert(41);
    ///
    /// let b = a.split_off(3);
    ///
    /// assert_eq!(a, RangeSetBlaze::from_iter([1, 2]));
    /// assert_eq!(b, RangeSetBlaze::from_iter([3, 17, 41]));
    /// ```
    #[must_use]
    pub fn split_off(&mut self, key: T) -> Self {
        let old_len = self.len;
        let old_btree_len = self.btree_map.len();
        let mut new_btree = self.btree_map.split_off(&key);
        let Some(last_entry) = self.btree_map.last_entry() else {
            // Left is empty
            self.len = T::SafeLen::zero();
            return Self {
                btree_map: new_btree,
                len: old_len,
            };
        };

        let end = *last_entry.get();
        if end < key {
            // The split is clean
            let (a_len, b_len) = self.two_element_lengths(old_btree_len, &new_btree, old_len);
            self.len = a_len;
            return Self {
                btree_map: new_btree,
                len: b_len,
            };
        }

        // The split is not clean, so we must move some keys from the end of self to the start of b.
        *(last_entry.into_mut()) = key.sub_one();
        new_btree.insert(key, end);
        let (a_len, b_len) = self.two_element_lengths(old_btree_len, &new_btree, old_len);
        self.len = a_len;
        Self {
            btree_map: new_btree,
            len: b_len,
        }
    }

    // Find the len of the smaller btree_map and then the element len of self & b.
    fn two_element_lengths(
        &self,
        old_btree_len: usize,
        new_btree: &BTreeMap<T, T>,
        mut old_len: <T as Integer>::SafeLen,
    ) -> (<T as Integer>::SafeLen, <T as Integer>::SafeLen) {
        if old_btree_len / 2 < new_btree.len() {
            let a_len = Self::btree_map_len(&self.btree_map);
            old_len -= a_len;
            (a_len, old_len)
        } else {
            let b_len = Self::btree_map_len(new_btree);
            old_len -= b_len;
            (old_len, b_len)
        }
    }

    fn btree_map_len(btree_map: &BTreeMap<T, T>) -> T::SafeLen {
        btree_map
            .iter()
            .fold(<T as Integer>::SafeLen::zero(), |acc, (start, end)| {
                acc + T::safe_len(&(*start..=*end))
            })
    }

    /// Removes and returns the element in the set, if any, that is equal to
    /// the value.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::from_iter([1, 2, 3]);
    /// assert_eq!(set.take(2), Some(2));
    /// assert_eq!(set.take(2), None);
    /// ```
    pub fn take(&mut self, value: T) -> Option<T> {
        if self.remove(value) {
            Some(value)
        } else {
            None
        }
    }

    /// Adds a value to the set, replacing the existing element, if any, that is
    /// equal to the value. Returns the replaced element.
    ///
    /// Note: This is very similar to `insert`. It is included for consistency with [`BTreeSet`].
    ///
    /// [`BTreeSet`]: alloc::collections::BTreeSet
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    /// assert!(set.replace(5).is_none());
    /// assert!(set.replace(5).is_some());
    /// ```
    pub fn replace(&mut self, value: T) -> Option<T> {
        if self.insert(value) {
            None
        } else {
            Some(value)
        }
    }

    // https://stackoverflow.com/questions/49599833/how-to-find-next-smaller-key-in-btreemap-btreeset
    // https://stackoverflow.com/questions/35663342/how-to-modify-partially-remove-a-range-from-a-btreemap
    pub(crate) fn internal_add(&mut self, range: RangeInclusive<T>) {
        let (start, end) = range.clone().into_inner();
        if end < start {
            return;
        }
        // FUTURE: would be nice of BTreeMap to have a partition_point function that returns two iterators
        let mut before = self.btree_map.range_mut(..=start).rev();
        if let Some((start_before, end_before)) = before.next() {
            // Must check this in two parts to avoid overflow
            if (*end_before)
                .checked_add_one()
                .is_some_and(|end_before_succ| end_before_succ < start)
            {
                self.internal_add2(&range);
            } else if *end_before < end {
                self.len += T::safe_len(&(*end_before..=end.sub_one()));
                *end_before = end;
                let start_before = *start_before;
                self.delete_extra(&(start_before..=end));
            } else {
                // completely contained, so do nothing
            }
        } else {
            self.internal_add2(&range);
        }
    }

    #[inline]
    fn internal_add2(&mut self, internal_range: &RangeInclusive<T>) {
        let (start, end) = internal_range.clone().into_inner();
        let was_there = self.btree_map.insert(start, end);
        debug_assert!(was_there.is_none()); // real assert
        self.delete_extra(internal_range);
        self.len += T::safe_len(internal_range);
    }

    /// Returns the number of elements in the set.
    ///
    /// The number is allowed to be very, very large.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let mut v = RangeSetBlaze::new();
    /// assert_eq!(v.len(), 0u64);
    /// v.insert(1);
    /// assert_eq!(v.len(), 1u64);
    ///
    /// let v = RangeSetBlaze::from_iter([
    ///     -170_141_183_460_469_231_731_687_303_715_884_105_728i128..=10,
    ///     -10..=170_141_183_460_469_231_731_687_303_715_884_105_726,
    /// ]);
    /// assert_eq!(
    ///     v.len(),
    ///     UIntPlusOne::UInt(340282366920938463463374607431768211455)
    /// );
    /// ```
    #[must_use]
    pub const fn len(&self) -> <T as Integer>::SafeLen {
        self.len
    }

    /// Makes a new, empty [`RangeSetBlaze`].
    ///
    /// # Examples
    ///
    /// ```
    /// # #![allow(unused_mut)]
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set: RangeSetBlaze<i32> = RangeSetBlaze::new();
    /// ```
    #[must_use]
    #[inline]
    pub fn new() -> Self {
        Self {
            btree_map: BTreeMap::new(),
            len: <T as Integer>::SafeLen::zero(),
        }
    }

    /// Removes the first element from the set and returns it, if any.
    /// The first element is always the minimum element in the set.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    ///
    /// set.insert(1);
    /// while let Some(n) = set.pop_first() {
    ///     assert_eq!(n, 1);
    /// }
    /// assert!(set.is_empty());
    /// ```
    pub fn pop_first(&mut self) -> Option<T> {
        if let Some(entry) = self.btree_map.first_entry() {
            let (start, end) = entry.remove_entry();
            self.len -= T::safe_len(&(start..=end));
            if start != end {
                let start = start.add_one();
                self.btree_map.insert(start, end);
                self.len += T::safe_len(&(start..=end));
            }
            Some(start)
        } else {
            None
        }
    }

    /// Removes the last value from the set and returns it, if any.
    /// The last value is always the maximum value in the set.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::new();
    ///
    /// set.insert(1);
    /// while let Some(n) = set.pop_last() {
    ///     assert_eq!(n, 1);
    /// }
    /// assert!(set.is_empty());
    /// ```
    pub fn pop_last(&mut self) -> Option<T> {
        let mut entry = self.btree_map.last_entry()?;
        let start = *entry.key();
        let end = entry.get_mut();
        let result = *end;
        self.len -= T::safe_len(&(start..=*end));
        if start == *end {
            entry.remove_entry();
        } else {
            (*end).assign_sub_one();
            self.len += T::safe_len(&(start..=*end));
        }
        Some(result)
    }

    /// An iterator that visits the ranges in the [`RangeSetBlaze`],
    /// i.e., the integers as sorted & disjoint ranges. Double-ended.
    ///
    /// Also see [`RangeSetBlaze::iter`] and [`RangeSetBlaze::into_ranges`].
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([10..=20, 15..=25, 30..=40]);
    /// let mut ranges = set.ranges();
    /// assert_eq!(ranges.next(), Some(10..=25));
    /// assert_eq!(ranges.next(), Some(30..=40));
    /// assert_eq!(ranges.next(), None);
    /// ```
    ///
    /// Values returned by the iterator are returned in ascending order:
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([30..=40, 15..=25, 10..=20]);
    /// let mut ranges = set.ranges();
    /// assert_eq!(ranges.next(), Some(10..=25));
    /// assert_eq!(ranges.next(), Some(30..=40));
    /// assert_eq!(ranges.next(), None);
    /// ```
    pub fn ranges(&self) -> RangesIter<'_, T> {
        RangesIter {
            iter: self.btree_map.iter(),
        }
    }

    /// An iterator that moves out the ranges in the [`RangeSetBlaze`],
    /// i.e., the integers as sorted & disjoint ranges.
    ///
    /// Also see [`RangeSetBlaze::into_iter`] and [`RangeSetBlaze::ranges`].
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut ranges = RangeSetBlaze::from_iter([10..=20, 15..=25, 30..=40]).into_ranges();
    /// assert_eq!(ranges.next(), Some(10..=25));
    /// assert_eq!(ranges.next(), Some(30..=40));
    /// assert_eq!(ranges.next(), None);
    /// ```
    ///
    /// Values returned by the iterator are returned in ascending order:
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut ranges = RangeSetBlaze::from_iter([30..=40, 15..=25, 10..=20]).into_ranges();
    /// assert_eq!(ranges.next(), Some(10..=25));
    /// assert_eq!(ranges.next(), Some(30..=40));
    /// assert_eq!(ranges.next(), None);
    /// ```
    pub fn into_ranges(self) -> IntoRangesIter<T> {
        IntoRangesIter {
            iter: self.btree_map.into_iter(),
        }
    }

    /// Deprecated. Use `RangeSetBlaze::to_string` instead.
    #[deprecated(since = "0.2.0", note = "Use `RangeSetBlaze::to_string` instead.")]
    pub fn into_string(&self) -> String {
        self.to_string()
    }

    // FUTURE BTreeSet some of these as 'const' but it uses unstable. When stable, add them here and elsewhere.

    /// Returns the number of sorted & disjoint ranges in the set.
    ///
    /// # Example
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// // We put in three ranges, but they are not sorted & disjoint.
    /// let set = RangeSetBlaze::from_iter([10..=20, 15..=25, 30..=40]);
    /// // After RangeSetBlaze sorts & 'disjoint's them, we see two ranges.
    /// assert_eq!(set.ranges_len(), 2);
    /// assert_eq!(set.to_string(), "10..=25, 30..=40");
    /// ```
    #[must_use]
    pub fn ranges_len(&self) -> usize {
        self.btree_map.len()
    }

    /// Retains only the elements specified by the predicate.
    ///
    /// In other words, remove all integers `t` for which `f(&t)` returns `false`.
    /// The integer elements are visited in ascending order.
    ///
    /// Because if visits every element in every range, it is expensive compared to
    /// [`RangeSetBlaze::ranges_retain`].
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::from_iter([1..=6]);
    /// // Keep only the even numbers.
    /// set.retain(|k| k % 2 == 0);
    /// assert_eq!(set, RangeSetBlaze::from_iter([2, 4, 6]));
    /// ```
    pub fn retain<F>(&mut self, mut f: F)
    where
        F: FnMut(&T) -> bool,
    {
        *self = self.iter().filter(|t| f(t)).collect();
    }

    /// Retains only the ranges specified by the predicate.
    ///
    /// In other words, remove all ranges `r` for which `f(&r)` returns `false`.
    /// The ranges are visited in ascending order.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let mut set = RangeSetBlaze::from_iter([1..=6, 10..=15]);
    /// // Keep only the ranges starting before 10.
    /// set.ranges_retain(|range| range.start() < &10);
    /// assert_eq!(set, RangeSetBlaze::from_iter([1..=6]));
    /// ```
    pub fn ranges_retain<F>(&mut self, mut f: F)
    where
        F: FnMut(&RangeInclusive<T>) -> bool,
    {
        self.btree_map.retain(|start, end| {
            let range = *start..=*end;
            if f(&range) {
                true
            } else {
                self.len -= T::safe_len(&range);
                false
            }
        });
    }
}

// We create a RangeSetBlaze from an iterator of integers or integer ranges by
// 1. turning them into a UnionIter (internally, it collects into intervals and sorts by start).
// 2. Turning the SortedDisjoint into a BTreeMap.
impl<T: Integer> FromIterator<T> for RangeSetBlaze<T> {
    /// Create a [`RangeSetBlaze`] from an iterator of integers. Duplicates and out-of-order elements are fine.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a0 = RangeSetBlaze::from_iter([3, 2, 1, 100, 1]);
    /// let a1: RangeSetBlaze<i32> = [3, 2, 1, 100, 1].into_iter().collect();
    /// assert!(a0 == a1 && a0.to_string() == "1..=3, 100..=100");
    /// ```
    fn from_iter<I>(iter: I) -> Self
    where
        I: IntoIterator<Item = T>,
    {
        iter.into_iter().map(|x| x..=x).collect()
    }
}

impl<'a, T: Integer> FromIterator<&'a T> for RangeSetBlaze<T> {
    /// Create a [`RangeSetBlaze`] from an iterator of integers references. Duplicates and out-of-order elements are fine.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a0 = RangeSetBlaze::from_iter(vec![3, 2, 1, 100, 1]);
    /// let a1: RangeSetBlaze<i32> = vec![3, 2, 1, 100, 1].into_iter().collect();
    /// assert!(a0 == a1 && a0.to_string() == "1..=3, 100..=100");
    /// ```
    fn from_iter<I>(iter: I) -> Self
    where
        I: IntoIterator<Item = &'a T>,
    {
        iter.into_iter().map(|x| *x..=*x).collect()
    }
}

impl<T: Integer> FromIterator<RangeInclusive<T>> for RangeSetBlaze<T> {
    /// Create a [`RangeSetBlaze`] from an iterator of inclusive ranges, `start..=end`.
    /// Overlapping, out-of-order, and empty ranges are fine.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// #[allow(clippy::reversed_empty_ranges)]
    /// let a0 = RangeSetBlaze::from_iter([1..=2, 2..=2, -10..=-5, 1..=0]);
    /// #[allow(clippy::reversed_empty_ranges)]
    /// let a1: RangeSetBlaze<i32> = [1..=2, 2..=2, -10..=-5, 1..=0].into_iter().collect();
    /// assert!(a0 == a1 && a0.to_string() == "-10..=-5, 1..=2");
    /// ```
    fn from_iter<I>(iter: I) -> Self
    where
        I: IntoIterator<Item = RangeInclusive<T>>,
    {
        let union_iter: UnionIter<T, _> = iter.into_iter().collect();
        Self::from_sorted_disjoint(union_iter)
    }
}

impl<'a, T: Integer> FromIterator<&'a RangeInclusive<T>> for RangeSetBlaze<T> {
    /// Create a [`RangeSetBlaze`] from an iterator of inclusive ranges, `start..=end`.
    /// Overlapping, out-of-order, and empty ranges are fine.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// #[allow(clippy::reversed_empty_ranges)]
    /// let vec_range = vec![1..=2, 2..=2, -10..=-5, 1..=0];
    /// let a0 = RangeSetBlaze::from_iter(&vec_range);
    /// let a1: RangeSetBlaze<i32> = vec_range.iter().collect();
    /// assert!(a0 == a1 && a0.to_string() == "-10..=-5, 1..=2");
    /// ```
    fn from_iter<I>(iter: I) -> Self
    where
        I: IntoIterator<Item = &'a RangeInclusive<T>>,
    {
        let union_iter: UnionIter<T, _> = iter.into_iter().cloned().collect();
        Self::from_sorted_disjoint(union_iter)
    }
}

impl<T: Integer, const N: usize> From<[T; N]> for RangeSetBlaze<T> {
    /// For compatibility with [`BTreeSet`] you may create a [`RangeSetBlaze`] from an array of integers.
    ///
    /// *For more about constructors and performance, see [`RangeSetBlaze` Constructors](struct.RangeSetBlaze.html#rangesetblaze-constructors).*
    ///
    /// [`BTreeSet`]: alloc::collections::BTreeSet
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a0 = RangeSetBlaze::from([3, 2, 1, 100, 1]);
    /// let a1: RangeSetBlaze<i32> = [3, 2, 1, 100, 1].into();
    /// assert!(a0 == a1 && a0.to_string() == "1..=3, 100..=100")
    /// ```
    #[cfg(not(feature = "from_slice"))]
    fn from(arr: [T; N]) -> Self {
        arr.into_iter().collect()
    }
    #[cfg(feature = "from_slice")]
    fn from(arr: [T; N]) -> Self {
        Self::from_slice(arr)
    }
}

impl<T: Integer> From<RangeInclusive<T>> for RangeSetBlaze<T> {
    /// Construct a [`RangeSetBlaze<T>`] directly from a [`RangeInclusive<T>`].
    fn from(value: RangeInclusive<T>) -> Self {
        Self::from_sorted_disjoint(RangeOnce::new(value))
    }
}

gen_ops_ex!(
    <T>;
    types ref RangeSetBlaze<T>, ref RangeSetBlaze<T> => RangeSetBlaze<T>;

    /// Intersects the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Either, neither, or both inputs may be borrowed.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=2, 5..=100]);
    /// let b = RangeSetBlaze::from_iter([2..=6]);
    /// let result = &a & &b; // Alternatively, 'a & b'.
    /// assert_eq!(result.to_string(), "2..=2, 5..=6");
    /// ```
    for & call |a: &RangeSetBlaze<T>, b: &RangeSetBlaze<T>| {
        (a.ranges() & b.ranges()).into_range_set_blaze()
    };

    /// Symmetric difference the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Either, neither, or both inputs may be borrowed.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=2, 5..=100]);
    /// let b = RangeSetBlaze::from_iter([2..=6]);
    /// let result = &a ^ &b; // Alternatively, 'a ^ b'.
    /// assert_eq!(result.to_string(), "1..=1, 3..=4, 7..=100");
    /// ```
    for ^ call |a: &RangeSetBlaze<T>, b: &RangeSetBlaze<T>| {
        a.ranges().symmetric_difference(b.ranges()).into_range_set_blaze()
    };

    /// Difference the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Either, neither, or both inputs may be borrowed.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=2, 5..=100]);
    /// let b = RangeSetBlaze::from_iter([2..=6]);
    /// let result = &a - &b; // Alternatively, 'a - b'.
    /// assert_eq!(result.to_string(), "1..=1, 7..=100");
    /// ```
    for - call |a: &RangeSetBlaze<T>, b: &RangeSetBlaze<T>| {
        (a.ranges() - b.ranges()).into_range_set_blaze()
    };
    where T: Integer //Where clause for all impl's
);

gen_ops_ex!(
    <T>;
    types ref RangeSetBlaze<T> => RangeSetBlaze<T>;

    /// Complement the contents of a [`RangeSetBlaze`].
    ///
    /// The input may be borrowed or not.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::prelude::*;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=2, 5..=100]);
    /// let result = !&a; // Alternatively, '!a'.
    /// assert_eq!(
    ///     result.to_string(),
    ///     "-2147483648..=0, 3..=4, 101..=2147483647"
    /// );
    /// ```
    for ! call |a: &RangeSetBlaze<T>| {
        (!a.ranges()).into_range_set_blaze()
    };

    where T: Integer //Where clause for all impl's
);

// Implementing `IntoIterator` for `&RangeSetBlaze` because BTreeSet does.
impl<'a, T: Integer> IntoIterator for &'a RangeSetBlaze<T> {
    type Item = T;
    type IntoIter = Iter<T, RangesIter<'a, T>>;
    fn into_iter(self) -> Self::IntoIter {
        self.iter()
    }
}

impl<T: Integer> IntoIterator for RangeSetBlaze<T> {
    type Item = T;
    type IntoIter = IntoIter<T>;

    /// Gets an iterator for moving out the [`RangeSetBlaze`]'s integer contents.
    /// Double-ended.
    ///
    /// # Examples
    ///
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let set = RangeSetBlaze::from_iter([1, 2, 3, 4]);
    ///
    /// let v: Vec<_> = set.into_iter().collect();
    /// assert_eq!(v, [1, 2, 3, 4]);
    ///
    /// let set = RangeSetBlaze::from_iter([1, 2, 3, 4]);
    /// let v: Vec<_> = set.into_iter().rev().collect();
    /// assert_eq!(v, [4, 3, 2, 1]);
    /// ```
    fn into_iter(self) -> IntoIter<T> {
        IntoIter {
            option_range_front: None,
            option_range_back: None,
            btree_map_into_iter: self.btree_map.into_iter(),
        }
    }
}

/// An iterator over the integer elements of a [`RangeSetBlaze`]. Double-ended.
///
/// This `struct` is created by the [`iter`] method on [`RangeSetBlaze`]. See its
/// documentation for more.
///
/// [`iter`]: RangeSetBlaze::iter
#[must_use = "iterators are lazy and do nothing unless consumed"]
#[derive(Clone, Debug)]
#[allow(clippy::struct_field_names)]
pub struct Iter<T, I>
where
    T: Integer,
    I: SortedDisjoint<T>,
{
    btree_set_iter: I,
    // FUTURE: here and elsewhere, when core::iter:Step is available could
    // FUTURE: use RangeInclusive as an iterator (with exhaustion) rather than needing an Option
    range_front: RangeInclusive<T>,
    range_back: RangeInclusive<T>,
}

impl<T: Integer, I> FusedIterator for Iter<T, I> where I: SortedDisjoint<T> + FusedIterator {}

impl<T: Integer, I> Iterator for Iter<T, I>
where
    I: SortedDisjoint<T>,
{
    type Item = T;
    fn next(&mut self) -> Option<T> {
        // return the next integer (if any) from range_front
        if let Some(next_item) = T::range_next(&mut self.range_front) {
            return Some(next_item);
        }

        // if range_front is exhausted, get the next range from the btree_set_iter and its next integer
        if let Some(next_range) = self.btree_set_iter.next() {
            debug_assert!(next_range.start() <= next_range.end()); // real assert
            self.range_front = next_range;
            return T::range_next(&mut self.range_front); // will never be None
        }

        // if that doesn't work, move the back range to the front and get the next integer (if any)
        self.range_front = mem::replace(&mut self.range_back, T::exhausted_range());
        T::range_next(&mut self.range_front)
    }

    // We'll have at least as many integers as intervals. There could be more that usize MAX
    // The option_range field could increase the number of integers, but we can ignore that.
    fn size_hint(&self) -> (usize, Option<usize>) {
        let (low, _high) = self.btree_set_iter.size_hint();
        (low, None)
    }
}

impl<T: Integer, I> DoubleEndedIterator for Iter<T, I>
where
    I: SortedDisjoint<T> + DoubleEndedIterator,
{
    fn next_back(&mut self) -> Option<Self::Item> {
        // return the next_back integer (if any) from range_back
        if let Some(next_item) = T::range_next_back(&mut self.range_back) {
            return Some(next_item);
        }

        // if the range_back is exhausted, get the next_back range from the btree_set_iter and its next_back integer
        if let Some(next_back_range) = self.btree_set_iter.next_back() {
            debug_assert!(next_back_range.start() <= next_back_range.end()); // real assert
            self.range_back = next_back_range;
            return T::range_next_back(&mut self.range_back); // will never be None
        }

        // if that doesn't work, move the front range to the back and get the next back integer (if any)
        self.range_back = mem::replace(&mut self.range_front, T::exhausted_range());
        T::range_next_back(&mut self.range_back)
    }
}

/// An iterator over the integer elements of a [`RangeSetBlaze`]. Double-ended.
///
/// This `struct` is created by the [`into_iter`] method on [`RangeSetBlaze`]. See its
/// documentation for more.
///
/// [`into_iter`]: RangeSetBlaze::into_iter
#[must_use = "iterators are lazy and do nothing unless consumed"]
#[derive(Debug)]
#[allow(clippy::struct_field_names)]
pub struct IntoIter<T: Integer> {
    option_range_front: Option<RangeInclusive<T>>,
    option_range_back: Option<RangeInclusive<T>>,
    btree_map_into_iter: btree_map::IntoIter<T, T>,
}

impl<T: Integer> FusedIterator for IntoIter<T> {}

impl<T: Integer> Iterator for IntoIter<T> {
    type Item = T;

    fn next(&mut self) -> Option<Self::Item> {
        let range = self
            .option_range_front
            .take()
            .or_else(|| {
                self.btree_map_into_iter
                    .next()
                    .map(|(start, end)| start..=end)
            })
            .or_else(|| self.option_range_back.take())?;

        let (start, end) = range.into_inner();
        debug_assert!(start <= end);
        if start < end {
            self.option_range_front = Some(start.add_one()..=end);
        }
        Some(start)
    }

    // We'll have at least as many integers as intervals. There could be more that usize MAX
    // the option_range field could increase the number of integers, but we can ignore that.
    fn size_hint(&self) -> (usize, Option<usize>) {
        let (low, _high) = self.btree_map_into_iter.size_hint();
        (low, None)
    }
}

impl<T: Integer> DoubleEndedIterator for IntoIter<T> {
    fn next_back(&mut self) -> Option<Self::Item> {
        let range = self
            .option_range_back
            .take()
            .or_else(|| {
                self.btree_map_into_iter
                    .next_back()
                    .map(|(start, end)| start..=end)
            })
            .or_else(|| self.option_range_front.take())?;

        let (start, end) = range.into_inner();
        debug_assert!(start <= end);
        if start < end {
            self.option_range_back = Some(start..=end.sub_one());
        }

        Some(end)
    }
}

impl<T: Integer> Extend<T> for RangeSetBlaze<T> {
    /// Extends the [`RangeSetBlaze`] with the contents of an Integer iterator.
    ///
    /// Integers are added one-by-one. There is also a version
    /// that takes a range iterator.
    ///
    /// The [`|=`](RangeSetBlaze::bitor_assign) operator extends a [`RangeSetBlaze`]
    /// from another [`RangeSetBlaze`]. It is never slower
    /// than  [`RangeSetBlaze::extend`] and often several times faster.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// a.extend([5, 0, 0, 3, 4, 10]);
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    ///
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// let mut b = RangeSetBlaze::from_iter([5, 0, 0, 3, 4, 10]);
    /// a |= b;
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    #[inline]
    fn extend<I>(&mut self, iter: I)
    where
        I: IntoIterator<Item = T>,
    {
        let iter = iter.into_iter();
        for range in UnsortedDisjoint::new(iter.map(|x| x..=x)) {
            self.internal_add(range);
        }
    }
}

impl<T: Integer> BitOrAssign<&Self> for RangeSetBlaze<T> {
    /// Adds the contents of another [`RangeSetBlaze`] to this one.
    ///
    /// Passing the right-hand side by ownership rather than borrow
    /// will allow a many-times faster speed up when the
    /// right-hand side is much larger than the left-hand side.
    ///
    /// Also, this operation is never slower than [`RangeSetBlaze::extend`] and
    /// can often be many times faster.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// let mut b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// a |= &b;
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    fn bitor_assign(&mut self, other: &Self) {
        let b_len = other.ranges_len();
        if b_len == 0 {
            return;
        }
        let a_len = self.ranges_len();
        if a_len == 0 {
            *self = other.clone();
            return;
        }
        let a_len_log2: usize = a_len
            .ilog2()
            .try_into() // u32 → usize
            .expect(
                "ilog2 result always fits in usize on our targets so this will be optimized away",
            );

        if b_len * (a_len_log2 + 1) < a_len + b_len {
            for (start, end) in &other.btree_map {
                self.internal_add(*start..=*end);
            }
        } else {
            *self = (self.ranges() | other.ranges()).into_range_set_blaze();
        }
    }
}

impl<T: Integer> BitOrAssign<Self> for RangeSetBlaze<T> {
    /// Adds the contents of another [`RangeSetBlaze`] to this one.
    ///
    /// Passing the right-hand side by ownership rather than borrow
    /// will allow a many-times faster speed up when the
    /// right-hand side is much larger than the left-hand side.
    ///
    /// Also, this operation is never slower than [`RangeSetBlaze::extend`] and
    /// can often be many times faster.
    ///
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// let mut b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// a |= b;
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    fn bitor_assign(&mut self, mut other: Self) {
        let a_len = self.ranges_len();
        let b_len = other.ranges_len();
        if b_len <= a_len {
            *self |= &other;
        } else {
            other |= &*self;
            *self = other;
        }
    }
}

impl<T: Integer> BitOr<Self> for RangeSetBlaze<T> {
    /// Unions the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Passing ownership rather than borrow sometimes allows a many-times
    /// faster speed up.
    ///
    /// Also see [`a |= b`](RangeSetBlaze::bitor_assign).
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let a = RangeSetBlaze::from_iter([1..=4]);
    /// let b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// let union = a | b; // Alternatively, '&a | &b', etc.
    /// assert_eq!(union, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    type Output = Self;
    fn bitor(mut self, other: Self) -> Self {
        self |= other;
        self
    }
}

impl<T: Integer> BitOr<&Self> for RangeSetBlaze<T> {
    /// Unions the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Passing ownership rather than borrow sometimes allows a many-times
    /// faster speed up.
    ///
    /// Also see [`a |= b`](RangeSetBlaze::bitor_assign).
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let a = RangeSetBlaze::from_iter([1..=4]);
    /// let b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// let union = a | &b;  // Alternatively, 'a | b', etc.
    /// assert_eq!(union, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    type Output = Self;
    fn bitor(mut self, other: &Self) -> Self {
        self |= other;
        self
    }
}

impl<T: Integer> BitOr<RangeSetBlaze<T>> for &RangeSetBlaze<T> {
    type Output = RangeSetBlaze<T>;
    /// Unions the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Passing ownership rather than borrow sometimes allows a many-times
    /// faster speed up.
    ///
    /// Also see [`a |= b`](RangeSetBlaze::bitor_assign).
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let a = RangeSetBlaze::from_iter([1..=4]);
    /// let b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// let union = &a | b;  // Alternatively, 'a | b', etc.
    /// assert_eq!(union, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    fn bitor(self, mut other: RangeSetBlaze<T>) -> RangeSetBlaze<T> {
        other |= self;
        other
    }
}

impl<T: Integer> BitOr<&RangeSetBlaze<T>> for &RangeSetBlaze<T> {
    type Output = RangeSetBlaze<T>;
    /// Unions the contents of two [`RangeSetBlaze`]'s.
    ///
    /// Passing ownership rather than borrow sometimes allows a many-times
    /// faster speed up.
    ///
    /// Also see [`a |= b`](RangeSetBlaze::bitor_assign).
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let a = RangeSetBlaze::from_iter([1..=4]);
    /// let b = RangeSetBlaze::from_iter([0..=0, 3..=5, 10..=10]);
    /// let union = &a | &b;  // Alternatively, 'a | b', etc.
    /// assert_eq!(union, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    fn bitor(self, other: &RangeSetBlaze<T>) -> RangeSetBlaze<T> {
        if other.ranges_len() == 0 {
            return self.clone();
        }
        if self.ranges_len() == 0 {
            return other.clone();
        }
        (self.ranges() | other.ranges()).into_range_set_blaze()
    }
}

impl<T: Integer> Extend<RangeInclusive<T>> for RangeSetBlaze<T> {
    /// Extends the [`RangeSetBlaze`] with the contents of a
    /// range iterator.
    ///
    /// Elements are added one-by-one. There is also a version
    /// that takes an integer iterator.
    ///
    /// The [`|=`](RangeSetBlaze::bitor_assign) operator extends a [`RangeSetBlaze`]
    /// from another [`RangeSetBlaze`]. It is never slower
    ///  than  [`RangeSetBlaze::extend`] and often several times faster.
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// a.extend([5..=5, 0..=0, 0..=0, 3..=4, 10..=10]);
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    ///
    /// let mut a = RangeSetBlaze::from_iter([1..=4]);
    /// let b = RangeSetBlaze::from_iter([5..=5, 0..=0, 0..=0, 3..=4, 10..=10]);
    /// a |= b;
    /// assert_eq!(a, RangeSetBlaze::from_iter([0..=5, 10..=10]));
    /// ```
    #[inline]
    fn extend<I>(&mut self, iter: I)
    where
        I: IntoIterator<Item = RangeInclusive<T>>,
    {
        let iter = iter.into_iter();
        let iter = UnsortedDisjoint::new(iter);
        for range in iter {
            self.internal_add(range);
        }
    }
}

impl<T: Integer> Ord for RangeSetBlaze<T> {
    /// We define a total ordering on `RangeSetBlaze`. Following the convention of
    /// [`BTreeSet`], the ordering is lexicographic, *not* by subset/superset.
    ///
    /// [`BTreeSet`]: alloc::collections::BTreeSet
    ///
    /// # Examples
    /// ```
    /// use range_set_blaze::RangeSetBlaze;
    ///
    /// let a = RangeSetBlaze::from_iter([1..=3, 5..=7]);
    /// let b = RangeSetBlaze::from_iter([2..=2]);
    /// assert!(a < b); // Lexicographic comparison
    /// assert!(b.is_subset(&a)); // Subset comparison
    /// // More lexicographic comparisons
    /// assert!(a <= b);
    /// assert!(b > a);
    /// assert!(b >= a);
    /// assert!(a != b);
    /// assert!(a == a);
    /// use core::cmp::Ordering;
    /// assert_eq!(a.cmp(&b), Ordering::Less);
    /// assert_eq!(a.partial_cmp(&b), Some(Ordering::Less));
    /// ```
    #[inline]
    fn cmp(&self, other: &Self) -> Ordering {
        // slow one by one: return self.iter().cmp(other.iter());

        // fast by ranges:
        let mut a = self.ranges();
        let mut b = other.ranges();
        let mut a_rx = a.next();
        let mut b_rx = b.next();
        loop {
            match (a_rx, b_rx) {
                (Some(a_r), Some(b_r)) => {
                    let cmp_start = a_r.start().cmp(b_r.start());
                    if cmp_start != Ordering::Equal {
                        return cmp_start;
                    }
                    let cmp_end = a_r.end().cmp(b_r.end());
                    match cmp_end {
                        Ordering::Equal => {
                            a_rx = a.next();
                            b_rx = b.next();
                        }
                        Ordering::Less => {
                            a_rx = a.next();
                            b_rx = Some((*a_r.end()).add_one()..=*b_r.end());
                        }
                        Ordering::Greater => {
                            a_rx = Some((*b_r.end()).add_one()..=*a_r.end());
                            b_rx = b.next();
                        }
                    }
                }
                (Some(_), None) => return Ordering::Greater,
                (None, Some(_)) => return Ordering::Less,
                (None, None) => return Ordering::Equal,
            }
        }
    }
}

impl<T: Integer> PartialOrd for RangeSetBlaze<T> {
    #[inline]
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

impl<T: Integer> Eq for RangeSetBlaze<T> {}

/// Extracts the start and end of a range from a `RangeBounds`.
///
/// Empty ranges are allowed.
#[allow(clippy::redundant_pub_crate)]
#[inline]
pub(crate) fn extract_range<T: Integer, R>(range: R) -> (T, T)
where
    R: RangeBounds<T>,
{
    let start = match range.start_bound() {
        Bound::Included(n) => *n,
        Bound::Excluded(n) => {
            assert!(
                *n < T::max_value(),
                "inclusive start must be <= T::max_safe_value()"
            );
            n.add_one()
        }
        Bound::Unbounded => T::min_value(),
    };
    let end = match range.end_bound() {
        Bound::Included(n) => *n,
        Bound::Excluded(n) => {
            assert!(
                *n > T::min_value(),
                "inclusive end must be >= T::min_value()"
            );
            n.sub_one()
        }
        Bound::Unbounded => T::max_value(),
    };
    (start, end)
}