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// numera::number::integer::z::integer
//
//!
//
use crate::number::{
integer::{z::*, Integer},
traits::ConstOne,
};
use devela::convert::az::CheckedAs;
#[cfg(not(feature = "std"))]
use crate::all::is_prime;
#[cfg(feature = "std")]
use crate::all::is_prime_sieve;
macro_rules! impl_integer {
(many: $($t:ident),+) => {
$( impl_integer![$t]; )+
};
($t:ident) => {
/// # Methods for all integers
impl $t {
/// Returns `true` if this integer is even.
#[inline]
#[must_use]
pub const fn is_even(&self) -> bool {
self.0 & 1 == 0
}
/// Returns `true` if this integer is odd.
#[inline]
#[must_use]
pub const fn is_odd(&self) -> bool {
!self.is_even()
}
/// Returns `true` if this integer is a multiple of the `other`.
#[inline]
#[must_use]
pub const fn is_multiple_of(&self, other: &Self) -> bool {
self.0 % other.0 == 0
}
/// Returns `true` if this integer is a divisor of the `other`.
#[inline]
#[must_use]
pub const fn is_divisor_of(&self, other: &Self) -> bool {
other.is_multiple_of(self)
}
/// Returns `true` if `self` and `other` are relative primes,
/// which means they have only 1 as their only common divisor.
///
/// # Notation
/// $a \perp b$.
#[inline]
#[must_use]
pub const fn is_coprime(&self, other: &Self) -> bool {
self.gcd(other).0 == Self::ONE.0
}
/// Returns the number of digits in base 10.
#[inline]
#[must_use]
pub const fn digits(&self) -> usize {
if let Some(n) = self.0.checked_ilog10() {
n as usize + 1
} else {
1
}
}
}
/// # Methods for non-negative integers
impl $t {
/// Returns `Some(true)` if this integer is prime, `Some(false)` if it's not
/// prime, or `None` if it can not be determined.
///
/// Returns `None` if this integer can't be represented as a [`usize`],
/// or as a [`u32`] in `no-std`.
#[inline]
pub fn is_prime(&self) -> Option<bool> {
#[cfg(feature = "std")]
return Some(is_prime_sieve((self.0).checked_as::<usize>()?));
#[cfg(not(feature = "std"))]
return Some(is_prime((self.0).checked_as::<u32>()?));
}
/// Calculates the *Greatest Common Divisor* of this integer and `other`.
#[inline]
#[must_use]
pub const fn gcd(&self, other: &Self) -> Self {
let (mut a, mut b) = (self.0, other.0);
while b != 0 {
let temp = b;
b = a % b;
a = temp;
}
$t(a)
}
/// Calculates the *Lowest Common Multiple* of this integer and `other`.
#[inline]
#[must_use]
pub const fn lcm(&self, other: &Self) -> Self {
$t(self.0 * other.0 / self.gcd(other).0)
}
}
impl Integer for $t {
#[inline]
fn integer_is_even(&self) -> bool {
self.is_even()
}
#[inline]
fn integer_is_multiple_of(&self, other: &Self) -> bool {
self.is_multiple_of(&other)
}
#[inline]
fn integer_is_prime(&self) -> Option<bool> {
self.is_prime()
}
#[inline]
fn integer_gcd(&self, other: &Self) -> Option<Self> {
Some(self.gcd(other))
}
#[inline]
fn integer_lcm(&self, other: &Self) -> Option<Self> {
Some(self.lcm(other))
}
#[inline]
fn integer_digits(&self) -> usize {
self.digits()
}
}
};
}
impl_integer![many: Integer8, Integer16, Integer32, Integer64, Integer128];
#[cfg(feature = "dashu-int")]
mod big {
use crate::number::integer::{is_prime_sieve, z::IntegerBig, Integer};
use dashu_int::{ops::Gcd, IBig, UBig};
/// # Methods for all integers
impl IntegerBig {
/// Returns `true` if this integer is even.
#[inline]
#[must_use]
pub fn is_even(&self) -> bool {
&self.0 & IBig::ONE == IBig::ZERO
}
/// Returns `true` if this integer is odd.
#[inline]
#[must_use]
pub fn is_odd(&self) -> bool {
!self.is_even()
}
/// Returns `true` if this integer is a multiple of the `other`.
#[inline]
#[must_use]
pub fn is_multiple_of(&self, other: &Self) -> bool {
&self.0 % &other.0 == IBig::ZERO
}
/// Returns `true` if this integer is a divisor of the `other`.
#[inline]
#[must_use]
pub fn is_divisor_of(&self, other: &Self) -> bool {
other.is_multiple_of(self)
}
/// Returns `true` if `self` and `other` are relative primes,
/// which means they have only 1 as their only common divisor.
///
/// # Notation
/// $a \perp b$.
#[inline]
#[must_use]
pub fn is_coprime(&self, other: &Self) -> bool {
self.0.clone().gcd(&other.0) == UBig::ONE
}
/// Returns the number of digits in base 10.
#[inline]
#[must_use]
pub fn digits(&self) -> usize {
self.0.to_string().len()
}
}
/// # Methods for non-negative integers
impl IntegerBig {
/// Returns `Some(true)` if this integer is prime, `Some(false)` if it's not
/// prime, or `None` if it can not be determined.
///
/// Returns `None` if this integer can't be represented as a [`usize`].
//
// IMPROVE: use an algorithm for big numbers.
#[inline]
pub fn is_prime(&self) -> Option<bool> {
Some(is_prime_sieve(usize::try_from(&self.0).ok()?))
}
/// Calculates the *Greatest Common Divisor* of this integer and `other`.
#[inline]
#[must_use]
pub fn gcd(&self, other: &Self) -> Self {
Self(self.0.clone().gcd(&other.0).into())
}
/// Calculates the *Lowest Common Multiple* of this integer and `other`.
#[inline]
#[must_use]
pub fn lcm(&self, other: &Self) -> Self {
IntegerBig(&self.0 * &other.0 / self.gcd(other).0)
}
}
impl Integer for IntegerBig {
#[inline]
fn integer_is_even(&self) -> bool {
self.is_even()
}
#[inline]
fn integer_is_multiple_of(&self, other: &Self) -> bool {
self.is_multiple_of(other)
}
#[inline]
fn integer_is_prime(&self) -> Option<bool> {
self.is_prime()
}
#[inline]
fn integer_gcd(&self, other: &Self) -> Option<Self> {
Some(self.gcd(other))
}
#[inline]
fn integer_lcm(&self, other: &Self) -> Option<Self> {
Some(self.lcm(other))
}
#[inline]
fn integer_digits(&self) -> usize {
self.digits()
}
}
}
#[cfg(test)]
mod tests {
use crate::all::*;
#[test]
fn z_impl_integer() -> NumeraResult<()> {
/* parity */
assert_eq![true, Z8::new(5).is_odd()];
assert_eq![true, Z8::new(-1).is_odd()];
assert_eq![true, Z8::new(6).is_even()];
assert_eq![true, Z8::new(0).is_even()];
/* factors */
assert_eq![true, Z8::new(10).is_multiple_of(&Z8::new(10))];
assert_eq![true, Z8::new(10).is_multiple_of(&Z8::new(5))];
assert_eq![true, Z8::new(10).is_multiple_of(&Z8::new(2))];
assert_eq![true, Z8::new(10).is_multiple_of(&Z8::new(1))];
assert_eq![false, Z8::new(10).is_multiple_of(&Z8::new(3))];
assert_eq![true, Z8::new(1).is_divisor_of(&Z8::new(10))];
assert_eq![true, Z8::new(2).is_divisor_of(&Z8::new(10))];
assert_eq![true, Z8::new(5).is_divisor_of(&Z8::new(10))];
assert_eq![true, Z8::new(10).is_divisor_of(&Z8::new(10))];
assert_eq![false, Z8::new(3).is_divisor_of(&Z8::new(10))];
/* primality */
// absolute primality
assert_eq![Some(true), Z8::new(5).is_prime()];
assert_eq![Some(false), Z8::new(6).is_prime()];
assert_eq![None, Z128::MAX.is_prime()];
// relative primality
assert_eq![true, Z8::new(5).is_coprime(&Z8::new(11))];
assert_eq![false, Z8::new(5).is_coprime(&Z8::new(10))];
/* LCM, GCD */
assert_eq![Z32::new(30), Z32::new(10).lcm(&Z32::new(15))];
assert_eq![Z32::new(5), Z32::new(10).gcd(&Z32::new(15))];
Ok(())
}
}