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use crate::{DistributiveLattice, Domain, EuclideanDomain, IntegralDomain, Lattice, UnitaryRing};
use num::{BigInt, Integer, One, Signed, Zero};
#[derive(Clone, Debug, Default)]
pub struct Integers();
impl Domain for Integers {
type Elem = BigInt;
}
impl UnitaryRing for Integers {
fn zero(&self) -> Self::Elem {
Zero::zero()
}
fn neg(&self, elem: &Self::Elem) -> Self::Elem {
-elem
}
fn add(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
elem1 + elem2
}
fn one(&self) -> Self::Elem {
One::one()
}
fn mul(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
elem1 * elem2
}
}
impl IntegralDomain for Integers {}
impl EuclideanDomain for Integers {
fn quo_rem(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> (Self::Elem, Self::Elem) {
if elem2.is_zero() {
(BigInt::zero(), elem1.clone())
} else {
let (quo, rem) = elem1.div_rem(elem2);
if elem1.is_positive() && elem2.is_positive() {
let tmp = elem2 - &rem;
if rem > tmp {
return (quo + 1, -tmp);
}
} else if !elem1.is_positive() && !elem2.is_positive() {
let tmp = elem2 - &rem;
if rem <= tmp {
return (quo + 1, -tmp);
}
} else if elem1.is_positive() && !elem2.is_positive() {
let tmp = elem2 + &rem;
if -&rem < tmp {
return (quo - 1, tmp);
}
} else if !elem1.is_positive() && elem2.is_positive() {
let tmp = elem2 + &rem;
if -&rem >= tmp {
return (quo - 1, tmp);
}
}
(quo, rem)
}
}
fn is_multiple_of(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> bool {
if elem2.is_zero() {
elem1.is_zero()
} else {
elem1.is_multiple_of(elem2)
}
}
fn is_reduced(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> bool {
if elem2.is_zero() {
true
} else {
let elem1 = elem1 + elem1;
let elem2 = elem2.abs();
-&elem2 < elem1 && elem1 <= elem2
}
}
fn associate_repr(&self, elem: &Self::Elem) -> (Self::Elem, Self::Elem) {
if *elem < 0.into() {
(self.neg(elem), (-1).into())
} else {
(elem.clone(), 1.into())
}
}
}
impl Lattice for Integers {
fn meet(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
elem1.min(elem2).clone()
}
fn join(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> Self::Elem {
elem1.max(elem2).clone()
}
fn leq(&self, elem1: &Self::Elem, elem2: &Self::Elem) -> bool {
elem1 <= elem2
}
}
impl DistributiveLattice for Integers {}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn quo_rem() {
let ring = Integers();
for n in -40..40 {
let n: BigInt = n.into();
for m in -40..40 {
let m: BigInt = m.into();
let (q, r) = ring.quo_rem(&n, &m);
println!("n={}, m={}, q={}, r={}", n, m, q, r);
assert_eq!(n, &m * &q + &r);
assert!(r.abs() <= (&r + &m).abs());
assert!(r.abs() <= (&r - &m).abs());
assert!(m.is_zero() || &r + &r <= m.abs());
assert!(m.is_zero() || &r + &r > -m.abs());
assert_eq!(q, ring.quo(&n, &m));
assert_eq!(r, ring.rem(&n, &m));
assert_eq!(ring.is_zero(&r), ring.is_multiple_of(&n, &m));
assert_eq!(ring.is_zero(&q), ring.is_reduced(&n, &m));
}
}
assert_eq!(ring.rem(&0.into(), &2.into()), 0.into());
assert_eq!(ring.rem(&1.into(), &2.into()), 1.into());
assert_eq!(ring.rem(&0.into(), &3.into()), 0.into());
assert_eq!(ring.rem(&1.into(), &3.into()), 1.into());
assert_eq!(ring.rem(&2.into(), &3.into()), (-1).into());
assert_eq!(ring.rem(&0.into(), &4.into()), 0.into());
assert_eq!(ring.rem(&1.into(), &4.into()), 1.into());
assert_eq!(ring.rem(&2.into(), &4.into()), 2.into());
assert_eq!(ring.rem(&3.into(), &4.into()), (-1).into());
assert_eq!(ring.rem(&0.into(), &(-2).into()), 0.into());
assert_eq!(ring.rem(&1.into(), &(-2).into()), 1.into());
}
}