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use std::convert::{TryFrom, TryInto};
use core::ops::{Rem, RemAssign};
use analysis::ordered::*;
use algebra::*;
auto!{
pub trait CastPrimInt =
TryFrom<i8> + TryFrom<u8> + TryInto<i8> + TryInto<u8> +
TryFrom<i16> + TryFrom<u16> + TryInto<i16> + TryInto<u16> +
TryFrom<i32> + TryFrom<u32> + TryInto<i32> + TryInto<u32> +
TryFrom<i64> + TryFrom<u64> + TryInto<i64> + TryInto<u64> +
TryFrom<i128> + TryFrom<u128> + TryInto<i128> + TryInto<u128>;
}
pub trait IntegerSubset: Ord + Eq + Clone + CastPrimInt
+ EuclideanSemidomain
+ Primality
+ ArchimedeanSemiring
+ Sub<Self, Output=Self> + Div<Self, Output=Self> + Rem<Self, Output=Self>
+ SubAssign<Self> + DivAssign<Self> + RemAssign<Self>
{
type Signed: Integer + IntegerSubset<Signed=Self::Signed, Unsigned=Self::Unsigned>;
type Unsigned: Natural + IntegerSubset<Signed=Self::Signed, Unsigned=Self::Unsigned>;
fn as_signed(&self) -> Self::Signed;
fn as_unsigned(&self) -> Self::Unsigned;
#[inline] fn two() -> Self { Self::one()+Self::one() }
#[inline] fn mul_two(self) -> Self { self * Self::two() }
#[inline] fn div_two(self) -> Self { self / Self::two() }
#[inline] fn even(&self) -> bool {(Self::one()+Self::one()).divides(self.clone())}
#[inline] fn odd(&self) -> bool {!self.even()}
}
pub trait Natural: IntegerSubset<Unsigned=Self> {}
pub trait Integer: IntegerSubset<Signed=Self> + Ring {}
macro_rules! impl_int_subset {
(@unit $self:ident @unsigned) => {*$self==1};
(@unit $self:ident @signed) => {*$self==1 || *$self == -1 };
(@factors $factors:ident $self:ident @unsigned) => {};
(@factors $factors:ident $self:ident @signed) => {
if *$self < 0 {
$factors.push(-1);
}
};
(@neg $self:ident @unsigned) => {false};
(@neg $self:ident @signed) => {*$self < 0 };
(@abs $self:ident $name:ident @unsigned) => {$self};
(@abs $self:ident $name:ident @signed) => {($self as $name).abs() };
($name:ident:$signed:ident:$unsigned:ident $($tt:tt)*) => {
impl Divisibility for $name {
#[inline] fn unit(&self) -> bool{ impl_int_subset!(@unit self $($tt)*) }
#[inline] fn inverse(self) -> Option<Self>
{if self.unit() { Option::Some(self) }else {Option::None} }
#[inline] fn divides(self, rhs: Self) -> bool { (rhs % self) == 0}
#[inline] fn divide(self, rhs: Self) -> Option<Self> {
let (q, r) = self.div_alg(rhs);
if r==0 {Some(q)} else {None}
}
}
impl NoZeroDivisors for $name {}
impl GCD for $name {
#[inline] fn lcm(self, rhs: Self) -> Self { (self*rhs) / self.gcd(rhs) }
#[inline] fn gcd(self, rhs: Self) -> Self{ euclidean(self, rhs) }
}
impl UniquelyFactorizable for $name {}
#[cfg(std)]
impl Factorizable for $name {
fn factors(&self) -> Vec<Self> {
let mut factors = Vec::new();
let mut a:$name = *self;
if a==0 || a==1 {
factors.push(*self);
}else{
let mut i:$name = 2;
let mut start = true;
while a!=1 {
let (q, r) = (a as $name).div_alg(i.clone());
if r==0 {
a = q;
factors.push(i);
}else {
if i*i >= a {
factors.push(a);
}else {
if start {
i = 3;
start = false;
} else {
i = i + 2;
}
}
}
}
}
impl_int_subset!( @factors factors self $($tt)*);
factors
}
}
impl EuclideanDiv for $name {
type Naturals = $unsigned;
#[inline] fn euclid_norm(&self) -> $unsigned {self.abs().as_unsigned()}
#[inline] fn div_euc(self, rhs: Self) -> Self {(self / rhs)}
#[inline] fn rem_euc(self, rhs: Self) -> Self {(self % rhs)}
#[inline] fn div_alg(self, rhs: Self) -> (Self, Self) {(self / rhs, self % rhs)}
}
impl IntegerSubset for $name {
type Signed = $signed;
type Unsigned = $unsigned;
#[inline] fn as_signed(&self) -> $signed { *self as $signed }
#[inline] fn as_unsigned(&self) -> $unsigned {
if cfg!(debug_assertions) && self.negative() {
panic!("Cannot make unsigned: {} < 0", self)
} else {
*self as $unsigned
}
}
#[inline] fn two() -> Self { 2 }
#[inline] fn mul_two(self) -> Self { self << 1 }
#[inline] fn div_two(self) -> Self { self >> 1 }
#[inline] fn even(&self) -> bool { (*self & 1) == 0 }
#[inline] fn odd(&self) -> bool { (*self & 1) == 1 }
}
}
}
macro_rules! impl_int {
($($s:ident:$u:ident)*) => {
$(
impl Bezout for $s {
#[inline]
fn bezout_coefficients(self, rhs: Self) -> (Self, Self) {
let (x, y, _g) = extended_euclidean(self, rhs);
(x, y)
}
#[inline] fn bezout_with_gcd(self, rhs: Self) -> (Self, Self, Self) { extended_euclidean(self, rhs) }
}
impl_int_subset!($u:$s:$u @unsigned);
impl_int_subset!($s:$s:$u @signed);
impl Natural for $u {}
impl Integer for $s {}
)*
};
}
macro_rules! impl_primality {
($($t:ident:$hp:ident)*) => {$(
impl Primality for $t {
#[inline] fn irreducible(&self) -> bool { self.prime() }
#[inline] fn prime(&self) -> bool { miller_rabin(*self as $hp) }
}
)*}
}
impl_int!(i8:u8 i16:u16 i32:u32 i64:u64 i128:u128 isize:usize);
impl_primality!(i8:u16 i16:u32 i32:u64 i64:u128 i128:u128 isize:u128);
impl_primality!(u8:u16 u16:u32 u32:u64 u64:u128 u128:u128 usize:u128);