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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::InnerFloat::{Finite, Infinity, NaN, Zero};
use crate::{ComparableFloat, ComparableFloatRef, Float};
use core::cmp::Ordering::{self, *};
use malachite_base::num::comparison::traits::{OrdAbs, PartialOrdAbs};
impl PartialOrdAbs for Float {
/// Compares the absolute values of two [`Float`]s.
///
/// This implementation follows the IEEE 754 standard. `NaN` is not comparable to anything, not
/// even itself. [`Float`]s with different precisions are equal if they represent the same
/// numeric value.
///
/// For different comparison behavior that provides a total order, consider using
/// [`ComparableFloat`] or [`ComparableFloatRef`].
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// 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, NaN, NegativeInfinity, NegativeOne, NegativeZero, One, OneHalf, Zero,
/// };
/// use malachite_base::num::comparison::traits::PartialOrdAbs;
/// use malachite_float::Float;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(Float::NAN.partial_cmp_abs(&Float::NAN), None);
/// assert_eq!(
/// Float::ZERO.partial_cmp_abs(&Float::NEGATIVE_ZERO),
/// Some(Equal)
/// );
/// assert_eq!(
/// Float::ONE.partial_cmp_abs(&Float::one_prec(100)),
/// Some(Equal)
/// );
/// assert!(Float::INFINITY.gt_abs(&Float::ONE));
/// assert!(Float::NEGATIVE_INFINITY.gt_abs(&Float::ONE));
/// assert!(Float::ONE_HALF.lt_abs(&Float::ONE));
/// assert!(Float::ONE_HALF.lt_abs(&Float::NEGATIVE_ONE));
/// ```
fn partial_cmp_abs(&self, other: &Self) -> Option<Ordering> {
match (self, other) {
(float_nan!(), _) | (_, float_nan!()) => None,
(float_either_infinity!(), float_either_infinity!())
| (float_either_zero!(), float_either_zero!()) => Some(Equal),
(float_either_infinity!(), _) | (_, float_either_zero!()) => Some(Greater),
(_, float_either_infinity!()) | (float_either_zero!(), _) => Some(Less),
(
Self(Finite {
exponent: e_x,
significand: x,
..
}),
Self(Finite {
exponent: e_y,
significand: y,
..
}),
) => Some(e_x.cmp(e_y).then_with(|| x.cmp_normalized_no_shift(y))),
}
}
}
impl<'a> OrdAbs for ComparableFloatRef<'a> {
/// Compares the absolute values of two [`ComparableFloatRef`]s.
///
/// This implementation does not follow the IEEE 754 standard. This is how
/// [`ComparableFloatRef`]s are ordered by absolute value, from least to greatest:
/// - NaN
/// - Positive and negative zero
/// - Nonzero finite floats
/// - $\infty$ and $-\infty$
///
/// For different comparison behavior that follows the IEEE 754 standard, consider just using
/// [`Float`].
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// 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, NaN, NegativeInfinity, NegativeOne, NegativeZero, One, OneHalf, Zero,
/// };
/// use malachite_base::num::comparison::traits::PartialOrdAbs;
/// use malachite_float::{ComparableFloatRef, Float};
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// ComparableFloatRef(&Float::NAN).partial_cmp_abs(&ComparableFloatRef(&Float::NAN)),
/// Some(Equal)
/// );
/// assert_eq!(
/// ComparableFloatRef(&Float::ZERO)
/// .partial_cmp_abs(&ComparableFloatRef(&Float::NEGATIVE_ZERO)),
/// Some(Equal)
/// );
/// assert!(ComparableFloatRef(&Float::ONE).lt_abs(&ComparableFloatRef(&Float::one_prec(100))));
/// assert!(ComparableFloatRef(&Float::INFINITY).gt_abs(&ComparableFloatRef(&Float::ONE)));
/// assert!(
/// ComparableFloatRef(&Float::NEGATIVE_INFINITY).gt_abs(&ComparableFloatRef(&Float::ONE))
/// );
/// assert!(ComparableFloatRef(&Float::ONE_HALF).lt_abs(&ComparableFloatRef(&Float::ONE)));
/// assert!(
/// ComparableFloatRef(&Float::ONE_HALF).lt_abs(&ComparableFloatRef(&Float::NEGATIVE_ONE))
/// );
/// ```
#[allow(clippy::match_same_arms)]
fn cmp_abs(&self, other: &Self) -> Ordering {
match (&self.0, &other.0) {
(float_nan!(), float_nan!())
| (float_either_infinity!(), float_either_infinity!())
| (float_either_zero!(), float_either_zero!()) => Equal,
(float_either_infinity!(), _) | (_, float_nan!()) => Greater,
(_, float_either_infinity!()) | (float_nan!(), _) => Less,
(float_either_zero!(), _) => Less,
(_, float_either_zero!()) => Greater,
(
Float(Finite {
exponent: e_x,
precision: p_x,
significand: x,
..
}),
Float(Finite {
exponent: e_y,
precision: p_y,
significand: y,
..
}),
) => e_x
.cmp(e_y)
.then_with(|| x.cmp_normalized_no_shift(y))
.then_with(|| p_x.cmp(p_y)),
}
}
}
impl PartialOrdAbs for ComparableFloatRef<'_> {
/// Compares the absolute values of two [`ComparableFloatRef`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp_abs(&self, other: &ComparableFloatRef) -> Option<Ordering> {
Some(self.cmp_abs(other))
}
}
impl OrdAbs for ComparableFloat {
/// Compares the absolute values of two [`ComparableFloat`]s.
///
/// This implementation does not follow the IEEE 754 standard. This is how [`ComparableFloat`]s
/// are ordered by absolute value, from least to greatest:
/// - NaN
/// - Positive and negative zero
/// - Nonzero finite floats
/// - $\infty$ and $-\infty$
///
/// For different comparison behavior that follows the IEEE 754 standard, consider just using
/// [`Float`].
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// 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, NaN, NegativeInfinity, NegativeOne, NegativeZero, One, OneHalf, Zero,
/// };
/// use malachite_base::num::comparison::traits::PartialOrdAbs;
/// use malachite_float::{ComparableFloat, Float};
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// ComparableFloat(Float::NAN).partial_cmp_abs(&ComparableFloat(Float::NAN)),
/// Some(Equal)
/// );
/// assert_eq!(
/// ComparableFloat(Float::ZERO).partial_cmp_abs(&ComparableFloat(Float::NEGATIVE_ZERO)),
/// Some(Equal)
/// );
/// assert!(ComparableFloat(Float::ONE).lt_abs(&ComparableFloat(Float::one_prec(100))));
/// assert!(ComparableFloat(Float::INFINITY).gt_abs(&ComparableFloat(Float::ONE)));
/// assert!(ComparableFloat(Float::NEGATIVE_INFINITY).gt_abs(&ComparableFloat(Float::ONE)));
/// assert!(ComparableFloat(Float::ONE_HALF).lt_abs(&ComparableFloat(Float::ONE)));
/// assert!(ComparableFloat(Float::ONE_HALF).lt_abs(&ComparableFloat(Float::NEGATIVE_ONE)));
/// ```
#[inline]
fn cmp_abs(&self, other: &Self) -> Ordering {
self.as_ref().cmp_abs(&other.as_ref())
}
}
impl PartialOrdAbs for ComparableFloat {
/// Compares the absolute values of two [`ComparableFloatRef`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp_abs(&self, other: &Self) -> Option<Ordering> {
Some(self.as_ref().cmp_abs(&other.as_ref()))
}
}