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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::Integer;
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{
BalancedModPowerOf2, IsPowerOf2, ModPowerOf2, NegModPowerOf2,
};
use malachite_base::num::basic::traits::Zero;
use malachite_base::num::logic::traits::BitAccess;
// The balanced remainder modulo $2^k$ of a number whose ordinary remainder is `r`. It is `r` when
// `r` is at most $2^{k-1}$, and $r - 2^k$ otherwise; `r` exceeds $2^{k-1}$ exactly when bit $k - 1$
// is set and `r` is not $2^{k-1}$ itself.
pub(crate) fn balanced_from_mod_power_of_2(r: Natural, pow: u64) -> Integer {
if pow == 0 {
Integer::ZERO
} else if r.get_bit(pow - 1) && !r.is_power_of_2() {
-Integer::from(r.neg_mod_power_of_2(pow))
} else {
Integer::from(r)
}
}
impl BalancedModPowerOf2 for Natural {
type Output = Integer;
/// Divides a [`Natural`] by $2^k$, returning the balanced remainder: the representative of
/// `self` modulo $2^k$ that is closest to zero. The [`Natural`] is taken by value.
///
/// The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which
/// determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so
/// the result may be negative and is returned as an [`Integer`]. This is
/// [`balanced_mod`](malachite_base::num::arithmetic::traits::BalancedMod::balanced_mod) with
/// modulus $2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(19u32).balanced_mod_power_of_2(3), 3);
/// // 7 is more than half of 8, so the representative closest to zero is negative
/// assert_eq!(Natural::from(23u32).balanced_mod_power_of_2(3), -1);
/// // exactly half the modulus stays positive
/// assert_eq!(Natural::from(20u32).balanced_mod_power_of_2(3), 4);
/// ```
#[inline]
fn balanced_mod_power_of_2(self, pow: u64) -> Integer {
balanced_from_mod_power_of_2(self.mod_power_of_2(pow), pow)
}
}
impl BalancedModPowerOf2 for &Natural {
type Output = Integer;
/// Divides a [`Natural`] by $2^k$, returning the balanced remainder: the representative of
/// `self` modulo $2^k$ that is closest to zero. The [`Natural`] is taken by reference.
///
/// See the [`BalancedModPowerOf2`] documentation for details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::from(19u32)).balanced_mod_power_of_2(3), 3);
/// assert_eq!((&Natural::from(23u32)).balanced_mod_power_of_2(3), -1);
/// assert_eq!((&Natural::from(20u32)).balanced_mod_power_of_2(3), 4);
/// ```
#[inline]
fn balanced_mod_power_of_2(self, pow: u64) -> Integer {
balanced_from_mod_power_of_2(self.mod_power_of_2(pow), pow)
}
}