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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::integer::conversion::to_twos_complement_limbs::limbs_twos_complement_in_place;
use crate::natural::InnerNatural::{Large, Small};
use crate::natural::arithmetic::add::limbs_slice_add_limb_in_place;
use crate::natural::arithmetic::mod_power_of_2::limbs_slice_mod_power_of_2_in_place;
use crate::natural::arithmetic::mul::mul_low::limbs_mul_low_same_length;
use crate::natural::{Natural, bit_to_limb_count_ceiling};
use crate::platform::Limb;
use malachite_base::num::arithmetic::traits::{ModPowerOf2Inverse, Parity};
use malachite_base::num::basic::integers::PrimitiveInt;
use malachite_base::num::basic::traits::One;
use malachite_base::num::logic::traits::SignificantBits;
// - out should be just long enough for `pow` bits.
// - xs should have the same length as out.
// - scratch should be at least twice as long as out.
// - out should be filled with zeros.
fn limbs_mod_power_of_2_inverse(out: &mut [Limb], xs: &[Limb], pow: u64, scratch: &mut [Limb]) {
let len = out.len();
split_into_chunks_mut!(scratch, len, [scratch_0, scratch_1], _unused);
let mut limb_pow = 1;
out[0] = xs[0].mod_power_of_2_inverse(Limb::WIDTH).unwrap();
while limb_pow < len {
limb_pow <<= 1;
if limb_pow > len {
limb_pow = len;
}
let out_lo = &mut out[..limb_pow];
let scratch_0_lo = &mut scratch_0[..limb_pow];
let scratch_1_lo = &mut scratch_1[..limb_pow];
limbs_mul_low_same_length(scratch_0_lo, out_lo, &xs[..limb_pow]);
limbs_twos_complement_in_place(scratch_0_lo);
limbs_slice_add_limb_in_place(scratch_0_lo, 2);
limbs_mul_low_same_length(scratch_1_lo, scratch_0_lo, out_lo);
out_lo.copy_from_slice(scratch_1_lo);
}
limbs_slice_mod_power_of_2_in_place(out, pow);
}
#[allow(clippy::unnecessary_wraps)]
fn mod_power_of_2_inverse_helper(xs: &[Limb], pow: u64) -> Option<Natural> {
let len = xs.len();
let mut big_scratch = vec![0; len * 3];
let (out, scratch) = big_scratch.split_at_mut(len);
limbs_mod_power_of_2_inverse(out, xs, pow, scratch);
big_scratch.truncate(len);
Some(Natural::from_owned_limbs_asc(big_scratch))
}
impl ModPowerOf2Inverse for Natural {
type Output = Self;
/// Computes the multiplicative inverse of a [`Natural`] modulo $2^k$. The input must be already
/// reduced modulo $2^k$. The [`Natural`] is taken by value.
///
/// Returns `None` if $x$ is even.
///
/// $f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Inverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::from(3u32).mod_power_of_2_inverse(8),
/// Some(Natural::from(171u32))
/// );
/// assert_eq!(Natural::from(4u32).mod_power_of_2_inverse(8), None);
/// ```
fn mod_power_of_2_inverse(self, pow: u64) -> Option<Self> {
assert_ne!(self, 0u32);
assert!(
self.significant_bits() <= pow,
"self must be reduced mod 2^pow, but {self} >= 2^{pow}"
);
match (self, pow) {
(Self::ONE, _) => Some(Self::ONE),
(x, _) if x.even() => None,
(Self(Small(x)), pow) if pow <= Limb::WIDTH => {
x.mod_power_of_2_inverse(pow).map(Self::from)
}
(Self(Small(x)), pow) => {
let len = bit_to_limb_count_ceiling(pow);
let mut xs = vec![0; len];
xs[0] = x;
mod_power_of_2_inverse_helper(&xs, pow)
}
(Self(Large(mut xs)), pow) => {
let len = bit_to_limb_count_ceiling(pow);
xs.resize(len, 0);
mod_power_of_2_inverse_helper(&xs, pow)
}
}
}
}
impl ModPowerOf2Inverse for &Natural {
type Output = Natural;
/// Computes the multiplicative inverse of a [`Natural`] modulo $2^k$. The input must be already
/// reduced modulo $2^k$. The [`Natural`] is taken by reference.
///
/// Returns `None` if $x$ is even.
///
/// $f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Panics
/// Panics if `self` is 0 or if `self` is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Inverse;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(3u32)).mod_power_of_2_inverse(8),
/// Some(Natural::from(171u32))
/// );
/// assert_eq!((&Natural::from(4u32)).mod_power_of_2_inverse(8), None);
/// ```
fn mod_power_of_2_inverse(self, pow: u64) -> Option<Natural> {
assert_ne!(*self, 0u32);
assert!(
self.significant_bits() <= pow,
"self must be reduced mod 2^pow, but {self} >= 2^{pow}"
);
match (self, pow) {
(&Natural::ONE, _) => Some(Natural::ONE),
(x, _) if x.even() => None,
(Natural(Small(x)), pow) if pow <= Limb::WIDTH => {
x.mod_power_of_2_inverse(pow).map(Natural::from)
}
(Natural(Small(x)), pow) => {
let mut xs = vec![0; bit_to_limb_count_ceiling(pow)];
xs[0] = *x;
mod_power_of_2_inverse_helper(&xs, pow)
}
(Natural(Large(xs)), pow) => {
let mut xs = xs.clone();
xs.resize(bit_to_limb_count_ceiling(pow), 0);
mod_power_of_2_inverse_helper(&xs, pow)
}
}
}
}