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use crate::{interval::*, simd::*};
impl Interval {
/// Returns $\hull(\self ∪ \rhs)$, the tightest interval that contains both `self` and `rhs` as its subsets.
///
/// | | $\rhs = ∅$ | $\rhs = \[c, d\]$ |
/// | :----------------: | :--------: | :------------------------------------: |
/// | $\self = ∅$ | $∅$ | $\[c, d\]$ |
/// | $\self = \[a, b\]$ | $\[a, b\]$ | $\[\min \set{a, c}, \max \set{b, d}\]$ |
#[must_use]
pub fn convex_hull(self, rhs: Self) -> Self {
if self.is_empty() {
return rhs;
}
if rhs.is_empty() {
return self;
}
// [min(a, c), max(b, d)]
// = [-min(a, c); max(b, d)] = [max(-a, -c); max(b, d)] = .max([-a; b], [-c; d])
Self {
rep: max(self.rep, rhs.rep),
}
}
/// Returns $\self ∩ \rhs$, the intersection of `self` and `rhs`.
///
/// | | $\rhs = ∅$ | $\rhs = \[c, d\]$ |
/// | :----------------: | :--------: | :------------------------------------: |
/// | $\self = ∅$ | $∅$ | $∅$ |
/// | $\self = \[a, b\]$ | $∅$ | $\[\max \set{a, c}, \min \set{b, d}\]$ |
#[must_use]
pub fn intersection(self, rhs: Self) -> Self {
if self.either_empty(rhs) {
return Self::EMPTY;
}
// [max(a, c), min(b, d)]
// = [-max(a, c); min(b, d)] = [min(-a, -c); min(b, d)] = .min([-a; b], [-c; d])
let i = Self {
rep: min(self.rep, rhs.rep),
};
if i.inf_raw() > i.sup_raw() {
Self::EMPTY
} else {
i
}
}
}
macro_rules! impl_dec {
($f:ident) => {
#[doc = concat!("Applies [`Interval::", stringify!($f), "`] to the interval parts of `self` and `rhs`")]
/// and returns the result decorated with [`Decoration::Trv`].
///
/// A NaI is returned if `self` or `rhs` is NaI.
#[must_use]
pub fn $f(self, rhs: Self) -> Self {
if self.is_nai() || rhs.is_nai() {
return Self::NAI;
}
Self::new_unchecked(self.x.$f(rhs.x), Decoration::Trv)
}
};
}
impl DecInterval {
impl_dec!(convex_hull);
impl_dec!(intersection);
}
#[cfg(test)]
mod tests {
use crate::*;
use DecInterval as DI;
use Interval as I;
#[test]
fn empty() {
assert_eq!(I::EMPTY.convex_hull(I::PI), I::PI);
assert_eq!(I::PI.convex_hull(I::EMPTY), I::PI);
assert!(I::EMPTY.intersection(I::PI).is_empty());
assert!(I::PI.intersection(I::EMPTY).is_empty());
assert_eq!(DI::EMPTY.convex_hull(DI::PI), DI::PI);
assert_eq!(DI::PI.convex_hull(DI::EMPTY), DI::PI);
assert!(DI::EMPTY.intersection(DI::PI).is_empty());
assert!(DI::PI.intersection(DI::EMPTY).is_empty());
}
#[test]
fn nai() {
assert!(DI::NAI.convex_hull(DI::PI).is_nai());
assert!(DI::PI.convex_hull(DI::NAI).is_nai());
assert!(DI::NAI.intersection(DI::PI).is_nai());
assert!(DI::PI.intersection(DI::NAI).is_nai());
}
}