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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::Rational;
use malachite_base::num::arithmetic::traits::{Average, AverageAssign};
impl Average<Self> for Rational {
type Output = Self;
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking both by value.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// f(x, y) = \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Average;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// Rational::ONE_HALF
/// .average(Rational::from_signeds(1, 3))
/// .to_string(),
/// "5/12"
/// );
/// assert_eq!(
/// Rational::from_signeds(22, 7)
/// .average(Rational::from_signeds(-22, 7))
/// .to_string(),
/// "0"
/// );
/// assert_eq!(
/// Rational::from(3).average(Rational::from(4)).to_string(),
/// "7/2"
/// );
/// ```
#[inline]
fn average(self, other: Self) -> Self {
(self + other) >> 1u32
}
}
impl Average<&Self> for Rational {
type Output = Self;
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking the first by value and
/// the second by reference.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// f(x, y) = \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Average;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// Rational::ONE_HALF
/// .average(&Rational::from_signeds(1, 3))
/// .to_string(),
/// "5/12"
/// );
/// assert_eq!(
/// Rational::from_signeds(22, 7)
/// .average(&Rational::from_signeds(-22, 7))
/// .to_string(),
/// "0"
/// );
/// assert_eq!(
/// Rational::from(3).average(&Rational::from(4)).to_string(),
/// "7/2"
/// );
/// ```
#[inline]
fn average(self, other: &Self) -> Self {
(self + other) >> 1u32
}
}
impl Average<Rational> for &Rational {
type Output = Rational;
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking the first by reference
/// and the second by value.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// f(x, y) = \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Average;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// (&Rational::ONE_HALF)
/// .average(Rational::from_signeds(1, 3))
/// .to_string(),
/// "5/12"
/// );
/// assert_eq!(
/// (&Rational::from_signeds(22, 7))
/// .average(Rational::from_signeds(-22, 7))
/// .to_string(),
/// "0"
/// );
/// assert_eq!(
/// (&Rational::from(3)).average(Rational::from(4)).to_string(),
/// "7/2"
/// );
/// ```
#[inline]
fn average(self, other: Rational) -> Rational {
(self + other) >> 1u32
}
}
impl Average<&Rational> for &Rational {
type Output = Rational;
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking both by reference.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// f(x, y) = \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Average;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// (&Rational::ONE_HALF)
/// .average(&Rational::from_signeds(1, 3))
/// .to_string(),
/// "5/12"
/// );
/// assert_eq!(
/// (&Rational::from_signeds(22, 7))
/// .average(&Rational::from_signeds(-22, 7))
/// .to_string(),
/// "0"
/// );
/// assert_eq!(
/// (&Rational::from(3)).average(&Rational::from(4)).to_string(),
/// "7/2"
/// );
/// ```
#[inline]
fn average(self, other: &Rational) -> Rational {
(self + other) >> 1u32
}
}
impl AverageAssign<Self> for Rational {
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking the [`Rational`] on the
/// right-hand side by value and replacing the first [`Rational`] with it.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// x \gets \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AverageAssign;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// let mut x = Rational::ONE_HALF;
/// x.average_assign(Rational::from_signeds(1, 3));
/// assert_eq!(x.to_string(), "5/12");
/// ```
#[inline]
fn average_assign(&mut self, other: Self) {
*self += other;
*self >>= 1u32;
}
}
impl AverageAssign<&Self> for Rational {
/// Computes the average (arithmetic mean) of two [`Rational`]s, taking the [`Rational`] on the
/// right-hand side by reference and replacing the first [`Rational`] with it.
///
/// The result is always exact, so no rounding is involved.
///
/// $$
/// x \gets \frac{x + y}{2}.
/// $$
///
/// # 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(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AverageAssign;
/// use malachite_base::num::basic::traits::OneHalf;
/// use malachite_q::Rational;
///
/// let mut x = Rational::ONE_HALF;
/// x.average_assign(&Rational::from_signeds(1, 3));
/// assert_eq!(x.to_string(), "5/12");
/// ```
#[inline]
fn average_assign(&mut self, other: &Self) {
*self += other;
*self >>= 1u32;
}
}