int_interval/

u8.rs

use crate::res::{OneTwo, ZeroOneTwo};

#[cfg(test)]
mod between_tests;
#[cfg(test)]
mod convex_hull_tests;
#[cfg(test)]
mod difference_tests;
#[cfg(test)]
mod intersection_tests;
#[cfg(test)]
mod symmetric_difference_tests;
#[cfg(test)]
mod minkowski_tests;
#[cfg(test)]
mod union_tests;

#[derive(Copy, Clone, Debug, Eq, PartialEq, Hash)]
pub struct U8CO {
    start: u8,
    end_excl: u8,
}

// ------------------------------------------------------------
// low-level api: construction / accessors / predicates
// ------------------------------------------------------------

mod construction_accessors_predicates {

    use super::*;

    impl U8CO {
        #[inline]
        pub const fn try_new(start: u8, end_excl: u8) -> Option<Self> {
            if start < end_excl {
                Some(Self { start, end_excl })
            } else {
                None
            }
        }

        #[inline]
        pub(super) const fn new_unchecked(start: u8, end_excl: u8) -> Self {
            debug_assert!(start < end_excl);
            Self { start, end_excl }
        }

        #[inline]
        pub const fn start(self) -> u8 {
            self.start
        }

        #[inline]
        pub const fn end_excl(self) -> u8 {
            self.end_excl
        }

        #[inline]
        pub const fn end_incl(self) -> u8 {
            // u8_low_bound =< start < end_excl
            self.end_excl - 1
        }

        #[inline]
        pub const fn len(self) -> u8 {
            self.end_excl - self.start
        }

        #[inline]
        pub const fn contains(self, x: u8) -> bool {
            self.start <= x && x < self.end_excl
        }

        #[inline]
        pub const fn iter(self) -> core::ops::Range<u8> {
            self.start..self.end_excl
        }

        #[inline]
        pub const fn intersects(self, other: Self) -> bool {
            !(self.end_excl <= other.start || other.end_excl <= self.start)
        }

        #[inline]
        pub const fn is_adjacent(self, other: Self) -> bool {
            self.end_excl == other.start || other.end_excl == self.start
        }

        #[inline]
        pub const fn is_contiguous_with(self, other: Self) -> bool {
            self.intersects(other) || self.is_adjacent(other)
        }
    }
}

// ------------------------------------------------------------
// interval algebra api: intersection / convex_hull / between / union / difference / symmetric_difference
// ------------------------------------------------------------

mod interval_algebra {

    use super::*;

    impl U8CO {
        /// Returns the intersection of two intervals.
        ///
        /// If the intervals do not overlap, returns `None`.
        #[inline]
        pub const fn intersection(self, other: Self) -> Option<Self> {
            let start = if self.start >= other.start {
                self.start
            } else {
                other.start
            };

            let end_excl = if self.end_excl <= other.end_excl {
                self.end_excl
            } else {
                other.end_excl
            };

            Self::try_new(start, end_excl)
        }

        /// Returns the convex hull (smallest interval containing both) of two intervals.
        ///
        /// Always returns a valid `U8CO`.
        #[inline]
        pub const fn convex_hull(self, other: Self) -> Self {
            let start = if self.start <= other.start {
                self.start
            } else {
                other.start
            };

            let end_excl = if self.end_excl >= other.end_excl {
                self.end_excl
            } else {
                other.end_excl
            };

            Self { start, end_excl }
        }

        /// Returns the interval strictly between two intervals.
        ///
        /// If the intervals are contiguous or overlap, returns `None`.
        #[inline]
        pub const fn between(self, other: Self) -> Option<Self> {
            let (left, right) = if self.start <= other.start {
                (self, other)
            } else {
                (other, self)
            };

            Self::try_new(left.end_excl, right.start)
        }

        /// Returns the union of two intervals.
        ///
        /// - If intervals are contiguous or overlapping, returns `One` containing the merged interval.
        /// - Otherwise, returns `Two` containing both intervals in ascending order.
        #[inline]
        pub const fn union(self, other: Self) -> OneTwo<Self> {
            if self.is_contiguous_with(other) {
                OneTwo::One(self.convex_hull(other))
            } else if self.start <= other.start {
                OneTwo::Two(self, other)
            } else {
                OneTwo::Two(other, self)
            }
        }

        /// Returns the difference of two intervals (self - other).
        ///
        /// - If no overlap, returns `One(self)`.
        /// - If partial overlap, returns `One` or `Two` depending on remaining segments.
        /// - If fully contained, returns `Zero`.
        #[inline]
        pub const fn difference(self, other: Self) -> ZeroOneTwo<Self> {
            match self.intersection(other) {
                None => ZeroOneTwo::One(self),
                Some(inter) => {
                    let left = Self::try_new(self.start, inter.start);
                    let right = Self::try_new(inter.end_excl, self.end_excl);

                    match (left, right) {
                        (None, None) => ZeroOneTwo::Zero,
                        (Some(x), None) | (None, Some(x)) => ZeroOneTwo::One(x),
                        (Some(x), Some(y)) => ZeroOneTwo::Two(x, y),
                    }
                }
            }
        }

        /// Returns the symmetric difference of two intervals.
        ///
        /// Equivalent to `(self - other) ∪ (other - self)`.
        /// - If intervals do not overlap, returns `Two(self, other)` in order.
        /// - If intervals partially overlap, returns remaining non-overlapping segments as `One` or `Two`.
        #[inline]
        pub const fn symmetric_difference(self, other: Self) -> ZeroOneTwo<Self> {
            match self.intersection(other) {
                None => {
                    if self.start <= other.start {
                        ZeroOneTwo::Two(self, other)
                    } else {
                        ZeroOneTwo::Two(other, self)
                    }
                }
                Some(inter) => {
                    let hull = self.convex_hull(other);
                    let left = Self::try_new(hull.start, inter.start);
                    let right = Self::try_new(inter.end_excl, hull.end_excl);

                    match (left, right) {
                        (None, None) => ZeroOneTwo::Zero,
                        (Some(x), None) | (None, Some(x)) => ZeroOneTwo::One(x),
                        (Some(x), Some(y)) => ZeroOneTwo::Two(x, y),
                    }
                }
            }
        }
    }
}

// ------------------------------------------------------------
// Module: Minkowski arithmetic for U8CO
// Provides checked Minkowski operations for intervals
// ------------------------------------------------------------

pub mod minkowski {
    use super::U8CO;

    // --------------------------------------------------------
    // Interval-to-interval Minkowski operations
    // --------------------------------------------------------
    impl U8CO {
        /// Minkowski addition: [a_start, a_end) + [b_start, b_end)
        #[inline]
        pub const fn minkowski_add(self, other: Self) -> Option<Self> {
            match self.start.checked_add(other.start) {
                Some(start) => match self.end_incl().checked_add(other.end_incl()) {
                    Some(end_incl) => match end_incl.checked_add(1) {
                        Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                        None => None,
                    },
                    None => None,
                },
                None => None,
            }
        }

        /// Minkowski subtraction: [a_start, a_end) - [b_start, b_end)
        #[inline]
        pub const fn minkowski_sub(self, other: Self) -> Option<Self> {
            match self.start.checked_sub(other.end_incl()) {
                Some(start) => match self.end_incl().checked_sub(other.start) {
                    Some(end_incl) => match end_incl.checked_add(1) {
                        Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                        None => None,
                    },
                    None => None,
                },
                None => None,
            }
        }

        /// Minkowski multiplication: [a_start, a_end) * [b_start, b_end)
        #[inline]
        pub const fn minkowski_mul(self, other: Self) -> Option<Self> {
            match self.start.checked_mul(other.start) {
                Some(start) => match self.end_incl().checked_mul(other.end_incl()) {
                    Some(end_incl) => match end_incl.checked_add(1) {
                        Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                        None => None,
                    },
                    None => None,
                },
                None => None,
            }
        }

        /// Minkowski division: [a_start, a_end) / [b_start, b_end)
        #[inline]
        pub const fn minkowski_div(self, other: Self) -> Option<Self> {
            if other.start == 0 {
                return None; // avoid division by zero
            }
            match self.start.checked_div(other.end_incl()) {
                Some(start) => match self.end_incl().checked_div(other.start) {
                    Some(end_incl) => match end_incl.checked_add(1) {
                        Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                        None => None,
                    },
                    None => None,
                },
                None => None,
            }
        }
    }

    // --------------------------------------------------------
    // Interval-to-scalar Minkowski operations
    // --------------------------------------------------------
    impl U8CO {
        /// Add a scalar to an interval: [start, end) + n
        #[inline]
        pub const fn minkowski_add_n(self, n: u8) -> Option<Self> {
            match self.start.checked_add(n) {
                Some(start) => match self.end_excl.checked_add(n) {
                    Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                    None => None,
                },
                None => None,
            }
        }

        /// Subtract a scalar from an interval: [start, end) - n
        #[inline]
        pub const fn minkowski_sub_n(self, n: u8) -> Option<Self> {
            match self.start.checked_sub(n) {
                Some(start) => match self.end_excl.checked_sub(n) {
                    Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                    None => None,
                },
                None => None,
            }
        }

        /// Multiply an interval by a scalar: [start, end) * n
        #[inline]
        pub const fn minkowski_mul_n(self, n: u8) -> Option<Self> {
            match self.start.checked_mul(n) {
                Some(start) => match self.end_incl().checked_mul(n) {
                    Some(end_incl) => match end_incl.checked_add(1) {
                        Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                        None => None,
                    },
                    None => None,
                },
                None => None,
            }
        }

        /// Divide an interval by a scalar: [start, end) / n
        #[inline]
        pub const fn minkowski_div_n(self, n: u8) -> Option<Self> {
            if n == 0 {
                return None; // avoid division by zero
            }
            let start = self.start / n;
            let end_incl = self.end_incl() / n;
            match end_incl.checked_add(1) {
                Some(end_excl) => Some(Self::new_unchecked(start, end_excl)),
                None => None,
            }
        }
    }
}