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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 core::cmp::Ordering::*;
use malachite_base::num::arithmetic::traits::{
CeilingLogBase2, CheckedLogBase2, FloorLogBase2, IsPowerOf2,
};
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
impl Rational {
/// Returns the floor of the base-2 logarithm of the absolute value of a nonzero [`Rational`].
///
/// $f(x) = \lfloor\log_2 |x|\rfloor$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is zero.
///
/// # Examples
/// ```
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(3u32).floor_log_base_2_abs(), 1);
/// assert_eq!(Rational::from_signeds(1, 3).floor_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(1, 4).floor_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(1, 5).floor_log_base_2_abs(), -3);
///
/// assert_eq!(Rational::from(-3).floor_log_base_2_abs(), 1);
/// assert_eq!(Rational::from_signeds(-1, 3).floor_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(-1, 4).floor_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(-1, 5).floor_log_base_2_abs(), -3);
/// ```
pub fn floor_log_base_2_abs(&self) -> i64 {
let exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Less {
exponent - 1
} else {
exponent
}
}
/// Returns the ceiling of the base-2 logarithm of the absolute value of a nonzero [`Rational`].
///
/// $f(x) = \lfloor\log_2 |x|\rfloor$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` less than or equal to zero.
///
/// # Examples
/// ```
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(3u32).ceiling_log_base_2_abs(), 2);
/// assert_eq!(Rational::from_signeds(1, 3).ceiling_log_base_2_abs(), -1);
/// assert_eq!(Rational::from_signeds(1, 4).ceiling_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(1, 5).ceiling_log_base_2_abs(), -2);
///
/// assert_eq!(Rational::from(-3).ceiling_log_base_2_abs(), 2);
/// assert_eq!(Rational::from_signeds(-1, 3).ceiling_log_base_2_abs(), -1);
/// assert_eq!(Rational::from_signeds(-1, 4).ceiling_log_base_2_abs(), -2);
/// assert_eq!(Rational::from_signeds(-1, 5).ceiling_log_base_2_abs(), -2);
/// ```
pub fn ceiling_log_base_2_abs(&self) -> i64 {
let exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Greater {
exponent + 1
} else {
exponent
}
}
}
impl FloorLogBase2 for &Rational {
type Output = i64;
/// Returns the floor of the base-2 logarithm of a positive [`Rational`].
///
/// $f(x) = \lfloor\log_2 x\rfloor$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` less than or equal to zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::FloorLogBase2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(3u32).floor_log_base_2(), 1);
/// assert_eq!(Rational::from_signeds(1, 3).floor_log_base_2(), -2);
/// assert_eq!(Rational::from_signeds(1, 4).floor_log_base_2(), -2);
/// assert_eq!(Rational::from_signeds(1, 5).floor_log_base_2(), -3);
/// ```
#[inline]
fn floor_log_base_2(self) -> i64 {
assert!(*self > 0u32);
self.floor_log_base_2_abs()
}
}
impl CeilingLogBase2 for &Rational {
type Output = i64;
/// Returns the ceiling of the base-2 logarithm of a positive [`Rational`].
///
/// $f(x) = \lfloor\log_2 x\rfloor$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` less than or equal to zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CeilingLogBase2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(3u32).ceiling_log_base_2(), 2);
/// assert_eq!(Rational::from_signeds(1, 3).ceiling_log_base_2(), -1);
/// assert_eq!(Rational::from_signeds(1, 4).ceiling_log_base_2(), -2);
/// assert_eq!(Rational::from_signeds(1, 5).ceiling_log_base_2(), -2);
/// ```
#[inline]
fn ceiling_log_base_2(self) -> i64 {
assert!(*self > 0u32);
self.ceiling_log_base_2_abs()
}
}
impl CheckedLogBase2 for &Rational {
type Output = i64;
/// Returns the base-2 logarithm of a positive [`Rational`]. If the [`Rational`] is not a power
/// of 2, then `None` is returned.
///
/// $$
/// f(x) = \\begin{cases}
/// \operatorname{Some}(\log_2 x) & \text{if} \\quad \log_2 x \in \Z, \\\\
/// \operatorname{None} & \textrm{otherwise}.
/// \\end{cases}
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `self` is less than or equal to zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CheckedLogBase2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from(3u32).checked_log_base_2(), None);
/// assert_eq!(Rational::from_signeds(1, 3).checked_log_base_2(), None);
/// assert_eq!(Rational::from_signeds(1, 4).checked_log_base_2(), Some(-2));
/// assert_eq!(Rational::from_signeds(1, 5).checked_log_base_2(), None);
/// ```
fn checked_log_base_2(self) -> Option<i64> {
assert!(*self > 0u32);
if self.denominator == 1u32 && self.numerator.is_power_of_2() {
Some(i64::exact_from(self.numerator.significant_bits()) - 1)
} else if self.numerator == 1u32 && self.denominator.is_power_of_2() {
Some(1 - i64::exact_from(self.denominator.significant_bits()))
} else {
None
}
}
}