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// Copyright © 2024 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::InnerFloat::{Finite, Infinity, NaN, Zero};
use crate::{significand_bits, Float};
use core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::Sign;
use malachite_base::num::comparison::traits::PartialOrdAbs;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_q::Rational;

impl PartialOrdAbs<Rational> for Float {
    /// Compares the absolute values of a [`Float`] and a [`Rational`].
    ///
    /// NaN is not comparable to any [`Rational`]. Infinity and negative infinity are greater in
    /// absolute value than any [`Rational`]. Both the [`Float`] zero and the [`Float`] negative
    /// zero are equal to the [`Rational`] zero.
    ///
    /// # 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 `max(self.significant_bits(),
    /// other.significant_bits())`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::basic::traits::{Infinity, NegativeInfinity};
    /// use malachite_base::num::comparison::traits::PartialOrdAbs;
    /// use malachite_float::Float;
    /// use malachite_q::Rational;
    ///
    /// assert!(Float::from(80).lt_abs(&Rational::from(100)));
    /// assert!(Float::from(-80).lt_abs(&Rational::from(-100)));
    /// assert!(Float::INFINITY.gt_abs(&Rational::from(100)));
    /// assert!(Float::NEGATIVE_INFINITY.gt_abs(&Rational::from(-100)));
    /// assert!(Float::from(1.0f64 / 3.0).lt_abs(&Rational::from_unsigneds(1u8, 3)));
    /// ```
    fn partial_cmp_abs(&self, other: &Rational) -> Option<Ordering> {
        match (self, other) {
            (float_nan!(), _) => None,
            (float_either_infinity!(), _) => Some(Greater),
            (float_either_zero!(), y) => Some(if *y == 0 { Equal } else { Less }),
            (
                Float(Finite {
                    exponent: e_x,
                    significand: significand_x,
                    ..
                }),
                y,
            ) => Some(if *y == 0u32 {
                Greater
            } else {
                let ord_cmp = (e_x - 1).cmp(&y.floor_log_base_2_abs());
                if ord_cmp == Equal {
                    let shift = e_x - i64::exact_from(significand_bits(significand_x));
                    let abs_shift = shift.unsigned_abs();
                    match shift.sign() {
                        Equal => {
                            (significand_x * other.denominator_ref()).cmp(other.numerator_ref())
                        }
                        Greater => ((significand_x * other.denominator_ref()) << abs_shift)
                            .cmp(other.numerator_ref()),
                        Less => {
                            let n_trailing_zeros = significand_x.trailing_zeros().unwrap();
                            if abs_shift <= n_trailing_zeros {
                                ((significand_x >> abs_shift) * other.denominator_ref())
                                    .cmp(other.numerator_ref())
                            } else {
                                ((significand_x >> n_trailing_zeros) * other.denominator_ref())
                                    .cmp(&(other.numerator_ref() << (abs_shift - n_trailing_zeros)))
                            }
                        }
                    }
                } else {
                    ord_cmp
                }
            }),
        }
    }
}

impl PartialOrdAbs<Float> for Rational {
    /// Compares the absolute values of a [`Rational`] and a [`Float`].
    ///
    /// No [`Rational`] is comparable to NaN. Every [`Rational`] is smaller in absolute value than
    /// infinity and negative infinity. The [`Rational`] zero is equal to both the [`Float`] zero
    /// and the [`Float`] negative zero.
    ///
    /// # 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 `max(self.significant_bits(),
    /// other.significant_bits())`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::basic::traits::{Infinity, NegativeInfinity};
    /// use malachite_base::num::comparison::traits::PartialOrdAbs;
    /// use malachite_float::Float;
    /// use malachite_q::Rational;
    ///
    /// assert!(Rational::from(100).gt_abs(&Float::from(80)));
    /// assert!(Rational::from(-100).gt_abs(&Float::from(-80)));
    /// assert!(Rational::from(100).lt_abs(&Float::INFINITY));
    /// assert!(Rational::from(-100).lt_abs(&Float::NEGATIVE_INFINITY));
    /// assert!(Rational::from_unsigneds(1u8, 3).gt_abs(&Float::from(1.0f64 / 3.0)));
    /// ```
    #[inline]
    fn partial_cmp_abs(&self, other: &Float) -> Option<Ordering> {
        other.partial_cmp_abs(self).map(Ordering::reverse)
    }
}