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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural::InnerNatural::Small;
use crate::natural::Natural;
use crate::natural::arithmetic::gcd::extended_gcd::limbs_extended_gcd;
use crate::natural::arithmetic::sub::limbs_sub_same_length_in_place_right;
use malachite_base::num::arithmetic::traits::ModInverse;
use malachite_base::num::basic::traits::One;
fn mod_inverse_helper(x: Natural, m: Natural) -> Option<Natural> {
let mut xs = x.into_limbs_asc();
let mut ys = m.to_limbs_asc();
let len = ys.len();
xs.resize(len, 0);
let mut gs = vec![0; len];
let mut ss = vec![0; len + 1];
let (g_len, ss_sign) = limbs_extended_gcd(&mut gs, &mut ss, &mut xs, &mut ys);
gs.truncate(g_len);
if Natural::from_owned_limbs_asc(gs) != 1u32 {
return None;
}
if !ss_sign {
assert_eq!(ss.pop(), Some(0));
limbs_sub_same_length_in_place_right(&m.into_limbs_asc(), &mut ss);
}
Some(Natural::from_owned_limbs_asc(ss))
}
impl ModInverse for Natural {
type Output = Self;
/// Computes the multiplicative inverse of a [`Natural`] modulo another [`Natural`] $m$. The
/// input must be already reduced modulo $m$. Both [`Natural`]s are taken by value.
///
/// Returns `None` if $x$ and $m$ are not coprime.
///
/// $f(x, m) = y$, where $x, y < m$, $\gcd(x, y) = 1$, and $xy \equiv 1 \mod m$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// m.significant_bits())`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModInverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::from(3u32).mod_inverse(Natural::from(10u32)),
/// Some(Natural::from(7u32))
/// );
/// assert_eq!(Natural::from(4u32).mod_inverse(Natural::from(10u32)), None);
/// ```
fn mod_inverse(self, m: Self) -> Option<Self> {
assert_ne!(self, 0u32);
assert!(self < m, "self must be reduced mod m, but {self} >= {m}");
match (self, m) {
(x @ Self::ONE, _) => Some(x),
(Self(Small(x)), Self(Small(y))) => x.mod_inverse(y).map(Self::from),
(a, b) => mod_inverse_helper(a, b),
}
}
}
impl<'a> ModInverse<&'a Self> for Natural {
type Output = Self;
/// Computes the multiplicative inverse of a [`Natural`] modulo another [`Natural`] $m$. The
/// input must be already reduced modulo $m$. The first [`Natural`] is taken by value and the
/// second by reference.
///
/// Returns `None` if $x$ and $m$ are not coprime.
///
/// $f(x, m) = y$, where $x, y < m$, $\gcd(x, y) = 1$, and $xy \equiv 1 \mod m$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// m.significant_bits())`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModInverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::from(3u32).mod_inverse(&Natural::from(10u32)),
/// Some(Natural::from(7u32))
/// );
/// assert_eq!(Natural::from(4u32).mod_inverse(&Natural::from(10u32)), None);
/// ```
fn mod_inverse(self, m: &'a Self) -> Option<Self> {
assert_ne!(self, 0u32);
assert!(self < *m, "self must be reduced mod m, but {self} >= {m}");
match (self, m) {
(x @ Self::ONE, _) => Some(x),
(Self(Small(x)), Self(Small(y))) => x.mod_inverse(*y).map(Self::from),
(a, b) => mod_inverse_helper(a, b.clone()),
}
}
}
impl ModInverse<Natural> for &Natural {
type Output = Natural;
/// Computes the multiplicative inverse of a [`Natural`] modulo another [`Natural`] $m$. The
/// input must be already reduced modulo $m$. The first [`Natural`]s is taken by reference and
/// the second by value.
///
/// Returns `None` if $x$ and $m$ are not coprime.
///
/// $f(x, m) = y$, where $x, y < m$, $\gcd(x, y) = 1$, and $xy \equiv 1 \mod m$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// m.significant_bits())`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModInverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(3u32)).mod_inverse(Natural::from(10u32)),
/// Some(Natural::from(7u32))
/// );
/// assert_eq!(
/// (&Natural::from(4u32)).mod_inverse(Natural::from(10u32)),
/// None
/// );
/// ```
fn mod_inverse(self, m: Natural) -> Option<Natural> {
assert_ne!(*self, 0u32);
assert!(*self < m, "self must be reduced mod m, but {self} >= {m}");
match (self, m) {
(&Natural::ONE, _) => Some(Natural::ONE),
(Natural(Small(x)), Natural(Small(y))) => x.mod_inverse(y).map(Natural::from),
(a, b) => mod_inverse_helper(a.clone(), b),
}
}
}
impl ModInverse<&Natural> for &Natural {
type Output = Natural;
/// Computes the multiplicative inverse of a [`Natural`] modulo another [`Natural`] $m$. The
/// input must be already reduced modulo $m$. Both [`Natural`]s are taken by reference.
///
/// Returns `None` if $x$ and $m$ are not coprime.
///
/// $f(x, m) = y$, where $x, y < m$, $\gcd(x, y) = 1$, and $xy \equiv 1 \mod m$.
///
/// # Worst-case complexity
/// $T(n) = O(n (\log n)^2 \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// m.significant_bits())`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModInverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(3u32)).mod_inverse(&Natural::from(10u32)),
/// Some(Natural::from(7u32))
/// );
/// assert_eq!(
/// (&Natural::from(4u32)).mod_inverse(&Natural::from(10u32)),
/// None
/// );
/// ```
fn mod_inverse(self, m: &Natural) -> Option<Natural> {
assert_ne!(*self, 0u32);
assert!(self < m, "self must be reduced mod m, but {self} >= {m}");
match (self, m) {
(&Natural::ONE, _) => Some(Natural::ONE),
(Natural(Small(x)), Natural(Small(y))) => x.mod_inverse(*y).map(Natural::from),
(a, b) => mod_inverse_helper(a.clone(), b.clone()),
}
}
}