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//! Number traits and utilities.
use core::{
mem,
ops::{
Add, AddAssign, Div, DivAssign, Mul, MulAssign, Rem, RemAssign, Sub,
SubAssign,
},
};
pub mod rational;
//NOTE: these should probably be broken up a bunch; they're only implemented
// this way because i didn't really need much else to implement
// rationals. ideally we should break them up on the lines of rings,
// groups, fields, unique factorization domains, principal ideal domains,
// ordered rings, etc. this would make further extensions to
// functionality in azimuth easier.
/// Integer.
pub trait Integer:
Eq
+ Ord
+ Mul<Output = Self>
+ Div<Output = Self>
+ Add<Output = Self>
+ Sub<Output = Self>
+ Rem<Output = Self>
+ MulAssign
+ DivAssign
+ AddAssign
+ SubAssign
+ RemAssign
+ Sized
+ Copy
+ Clone
{
//NOTE: `Neg` is neglected here as the primary purpose of this trait is
// to abstract over integers for the `Rational` type. as stated
// above, i'd like to adjust the way all of this works anyway for
// future extensions, but for now, we don't really need it.
//NOTE: `Copy` is required for now as bignum support is not a requirement
// yet and this makes implementation simpler.
/// Additive identity.
const ZERO: Self;
/// Multiplicative identity.
const ONE: Self;
/// Maximum attainable value.
const MAX: Self;
/// Minimum attainable value.
const MIN: Self;
/// Calculates the greatest common divisor of this number and another
fn gcd(&self, rhs: &Self) -> Self;
}
/// Helper macro for the implementation of `Integer`
macro_rules! integer_impl {
($type:ty, $zero:expr, $one:expr, $max:expr, $min:expr) => {
impl Integer for $type {
const ZERO: Self = $zero;
const ONE: Self = $one;
const MAX: Self = $max;
const MIN: Self = $min;
#[inline]
fn gcd(&self, rhs: &Self) -> Self {
let mut m = *self;
let mut n = *rhs;
if m < n {
mem::swap(&mut m, &mut n);
}
while n != 0 {
let t = n;
n = m % n;
m = t;
}
m
}
}
};
}
integer_impl!(i8, 0, 1, i8::MAX, i8::MIN);
integer_impl!(i16, 0, 1, i16::MAX, i16::MIN);
integer_impl!(i32, 0, 1, i32::MAX, i32::MIN);
integer_impl!(i64, 0, 1, i64::MAX, i64::MIN);
integer_impl!(i128, 0, 1, i128::MAX, i128::MIN);
integer_impl!(u8, 0, 1, u8::MAX, u8::MIN);
integer_impl!(u16, 0, 1, u16::MAX, u16::MIN);
integer_impl!(u32, 0, 1, u32::MAX, u32::MIN);
integer_impl!(u64, 0, 1, u64::MAX, u64::MIN);
integer_impl!(u128, 0, 1, u128::MAX, u128::MIN);
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