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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::{CheckedSqrt, UnsignedAbs};
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::integer::Integer;
impl CheckedSqrt for Rational {
type Output = Self;
/// Returns the the square root of a [`Rational`], or `None` if it is not a perfect square. The
/// [`Rational`] is taken by value.
///
/// $$
/// f(x) = \\begin{cases}
/// \operatorname{Some}(sqrt{x}) & \text{if} \\quad \sqrt{x} \in \mathbb{Q}, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is negative.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CheckedSqrt;
/// use malachite_base::strings::ToDebugString;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// Rational::from(99u8).checked_sqrt().to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// Rational::from(100u8).checked_sqrt().to_debug_string(),
/// "Some(10)"
/// );
/// assert_eq!(
/// Rational::from(101u8).checked_sqrt().to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// Rational::from_signeds(22, 7)
/// .checked_sqrt()
/// .to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// Rational::from_signeds(25, 9)
/// .checked_sqrt()
/// .to_debug_string(),
/// "Some(5/3)"
/// );
/// ```
fn checked_sqrt(self) -> Option<Self> {
assert!(self >= 0);
let (n, d) = self.into_numerator_and_denominator();
let sqrt_n;
let sqrt_d;
if n.significant_bits() <= d.significant_bits() {
sqrt_n = n.checked_sqrt()?;
sqrt_d = d.checked_sqrt()?;
} else {
sqrt_d = d.checked_sqrt()?;
sqrt_n = n.checked_sqrt()?;
}
Some(Self {
sign: sqrt_n >= 0,
numerator: sqrt_n,
denominator: sqrt_d,
})
}
}
impl CheckedSqrt for &Rational {
type Output = Rational;
/// Returns the the square root of a [`Rational`], or `None` if it is not a perfect square. The
/// [`Rational`] is taken by reference.
///
/// $$
/// f(x) = \\begin{cases}
/// \operatorname{Some}(sqrt{x}) & \text{if} \\quad \sqrt{x} \in \mathbb{Q}, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is negative.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CheckedSqrt;
/// use malachite_base::strings::ToDebugString;
/// use malachite_q::Rational;
///
/// assert_eq!(
/// (&Rational::from(99u8)).checked_sqrt().to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// (&Rational::from(100u8)).checked_sqrt().to_debug_string(),
/// "Some(10)"
/// );
/// assert_eq!(
/// (&Rational::from(101u8)).checked_sqrt().to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// (&Rational::from_signeds(22, 7))
/// .checked_sqrt()
/// .to_debug_string(),
/// "None"
/// );
/// assert_eq!(
/// (&Rational::from_signeds(25, 9))
/// .checked_sqrt()
/// .to_debug_string(),
/// "Some(5/3)"
/// );
/// ```
fn checked_sqrt(self) -> Option<Rational> {
let (n, d) = self.numerator_and_denominator_ref();
let sqrt_n;
let sqrt_d;
if n.significant_bits() <= d.significant_bits() {
sqrt_n = Integer::from_sign_and_abs_ref(*self >= 0, n).checked_sqrt()?;
sqrt_d = d.checked_sqrt()?;
} else {
sqrt_d = d.checked_sqrt()?;
sqrt_n = Integer::from_sign_and_abs_ref(*self >= 0, n).checked_sqrt()?;
}
Some(Rational {
sign: true,
numerator: sqrt_n.unsigned_abs(),
denominator: sqrt_d,
})
}
}