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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, *};
impl PartialOrd for Float {
/// Compares two [`Float`]s.
///
/// This implementation follows the IEEE 754 standard. `NaN` is not comparable to anything, not
/// even itself. Positive zero is equal to negative zero. [`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_float::Float;
/// use std::cmp::Ordering::*;
///
/// assert_eq!(Float::NAN.partial_cmp(&Float::NAN), None);
/// assert_eq!(Float::ZERO.partial_cmp(&Float::NEGATIVE_ZERO), Some(Equal));
/// assert_eq!(Float::ONE.partial_cmp(&Float::one_prec(100)), Some(Equal));
/// assert!(Float::INFINITY > Float::ONE);
/// assert!(Float::NEGATIVE_INFINITY < Float::ONE);
/// assert!(Float::ONE_HALF < Float::ONE);
/// assert!(Float::ONE_HALF > Float::NEGATIVE_ONE);
/// ```
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
match (self, other) {
(float_nan!(), _) | (_, float_nan!()) => None,
(float_infinity!(), float_infinity!())
| (float_negative_infinity!(), float_negative_infinity!())
| (float_either_zero!(), float_either_zero!()) => Some(Equal),
(float_infinity!(), _) | (_, float_negative_infinity!()) => Some(Greater),
(float_negative_infinity!(), _) | (_, float_infinity!()) => Some(Less),
(Self(Finite { sign, .. }), float_either_zero!()) => {
Some(if *sign { Greater } else { Less })
}
(float_either_zero!(), Self(Finite { sign, .. })) => {
Some(if *sign { Less } else { Greater })
}
(
Self(Finite {
sign: s_x,
exponent: e_x,
significand: x,
..
}),
Self(Finite {
sign: s_y,
exponent: e_y,
significand: y,
..
}),
) => Some(s_x.cmp(s_y).then_with(|| {
let abs_cmp = e_x.cmp(e_y).then_with(|| x.cmp_normalized_no_shift(y));
if *s_x { abs_cmp } else { abs_cmp.reverse() }
})),
}
}
}
impl<'a> Ord for ComparableFloatRef<'a> {
/// Compares two [`ComparableFloatRef`]s.
///
/// This implementation does not follow the IEEE 754 standard. This is how
/// [`ComparableFloatRef`]s are ordered, least to greatest:
/// - $-\infty$
/// - Negative nonzero finite floats
/// - Negative zero
/// - NaN
/// - Positive zero
/// - Positive nonzero finite floats
/// - $\infty$
///
/// When comparing two finite floats with the same numeric value but different precisions, the
/// one with greater precision is ordered to be further from zero.
///
/// 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_float::{ComparableFloatRef, Float};
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// ComparableFloatRef(&Float::NAN).partial_cmp(&ComparableFloatRef(&Float::NAN)),
/// Some(Equal)
/// );
/// assert!(ComparableFloatRef(&Float::ZERO) > ComparableFloatRef(&Float::NEGATIVE_ZERO));
/// assert!(ComparableFloatRef(&Float::ONE) < ComparableFloatRef(&Float::one_prec(100)));
/// assert!(ComparableFloatRef(&Float::INFINITY) > ComparableFloatRef(&Float::ONE));
/// assert!(ComparableFloatRef(&Float::NEGATIVE_INFINITY) < ComparableFloatRef(&Float::ONE));
/// assert!(ComparableFloatRef(&Float::ONE_HALF) < ComparableFloatRef(&Float::ONE));
/// assert!(ComparableFloatRef(&Float::ONE_HALF) > ComparableFloatRef(&Float::NEGATIVE_ONE));
/// ```
fn cmp(&self, other: &Self) -> Ordering {
match (&self.0, &other.0) {
(float_nan!(), float_nan!())
| (float_infinity!(), float_infinity!())
| (float_negative_infinity!(), float_negative_infinity!()) => Equal,
(Float(Zero { sign: s_x }), Float(Zero { sign: s_y })) => s_x.cmp(s_y),
(float_infinity!(), _) | (_, float_negative_infinity!()) => Greater,
(float_negative_infinity!(), _) | (_, float_infinity!()) => Less,
(Float(NaN | Zero { .. }), Float(Finite { sign, .. }))
| (Float(NaN), Float(Zero { sign })) => {
if *sign {
Less
} else {
Greater
}
}
(Float(Finite { sign, .. } | Zero { sign }), Float(NaN))
| (Float(Finite { sign, .. }), Float(Zero { .. })) => {
if *sign {
Greater
} else {
Less
}
}
(
Float(Finite {
sign: s_x,
exponent: e_x,
precision: p_x,
significand: x,
}),
Float(Finite {
sign: s_y,
exponent: e_y,
precision: p_y,
significand: y,
}),
) => s_x.cmp(s_y).then_with(|| {
let abs_cmp = e_x
.cmp(e_y)
.then_with(|| x.cmp_normalized_no_shift(y))
.then_with(|| p_x.cmp(p_y));
if *s_x { abs_cmp } else { abs_cmp.reverse() }
}),
}
}
}
impl PartialOrd for ComparableFloatRef<'_> {
/// Compares two [`ComparableFloatRef`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp(&self, other: &ComparableFloatRef) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl Ord for ComparableFloat {
/// Compares two [`ComparableFloat`]s.
///
/// This implementation does not follow the IEEE 754 standard. This is how [`ComparableFloat`]s
/// are ordered, least to greatest:
/// - $-\infty$
/// - Negative nonzero finite floats
/// - Negative zero
/// - NaN
/// - Positive zero
/// - Positive nonzero finite floats
/// - $\infty$
///
/// When comparing two finite floats with the same numeric value but different precisions, the
/// one with greater precision is ordered to be further from zero.
///
/// 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_float::{ComparableFloat, Float};
/// use std::cmp::Ordering::*;
///
/// assert_eq!(
/// ComparableFloat(Float::NAN).partial_cmp(&ComparableFloat(Float::NAN)),
/// Some(Equal)
/// );
/// assert!(ComparableFloat(Float::ZERO) > ComparableFloat(Float::NEGATIVE_ZERO));
/// assert!(ComparableFloat(Float::ONE) < ComparableFloat(Float::one_prec(100)));
/// assert!(ComparableFloat(Float::INFINITY) > ComparableFloat(Float::ONE));
/// assert!(ComparableFloat(Float::NEGATIVE_INFINITY) < ComparableFloat(Float::ONE));
/// assert!(ComparableFloat(Float::ONE_HALF) < ComparableFloat(Float::ONE));
/// assert!(ComparableFloat(Float::ONE_HALF) > ComparableFloat(Float::NEGATIVE_ONE));
/// ```
#[inline]
fn cmp(&self, other: &Self) -> Ordering {
self.as_ref().cmp(&other.as_ref())
}
}
#[allow(clippy::non_canonical_partial_ord_impl)]
impl PartialOrd for ComparableFloat {
/// Compares two [`ComparableFloat`]s.
///
/// See the documentation for the [`Ord`] implementation.
#[inline]
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.as_ref().cmp(&other.as_ref()))
}
}