1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
// 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::Float;
use crate::InnerFloat::{Finite, Zero};
use core::cmp::Ordering::*;
use malachite_base::num::arithmetic::traits::UnsignedAbs;
use malachite_base::num::basic::signeds::PrimitiveSigned;
use malachite_base::num::basic::unsigneds::PrimitiveUnsigned;
use malachite_base::num::comparison::traits::EqAbs;
use malachite_nz::natural::Natural;
fn float_eq_abs_unsigned<T: PrimitiveUnsigned>(x: &Float, y: &T) -> bool
where
Natural: From<T>,
{
match x {
float_either_zero!() => *y == T::ZERO,
Float(Finite {
exponent,
significand,
..
}) => {
*y != T::ZERO
&& *exponent >= 0
&& y.significant_bits() == u64::from(exponent.unsigned_abs())
&& significand.cmp_normalized(&Natural::from(*y)) == Equal
}
_ => false,
}
}
macro_rules! impl_eq_abs_unsigned {
($t: ident) => {
impl EqAbs<$t> for Float {
/// Determines whether the absolute value of a [`Float`] is equal to an unsigned
/// primitive integer.
///
/// $\infty$, $-\infty$, and NaN are not equal to any primitive integer. Both the
/// [`Float`] zero and the [`Float`] negative zero are equal to the integer zero.
///
/// # 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()`.
///
/// # Examples
/// See [here](super::partial_eq_primitive_int#partial_eq).
#[inline]
fn eq_abs(&self, other: &$t) -> bool {
float_eq_abs_unsigned(self, other)
}
}
impl EqAbs<Float> for $t {
/// Determines whether an unsigned primitive integer is equal to the absolute value of a
/// [`Float`].
///
/// No primitive integer is equal to $\infty$, $-\infty$, or NaN. The integer zero is
/// equal to both the [`Float`] zero and the [`Float`] negative zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
///
/// # Examples
/// See [here](super::partial_eq_primitive_int#partial_eq).
#[inline]
fn eq_abs(&self, other: &Float) -> bool {
other.eq_abs(self)
}
}
};
}
apply_to_unsigneds!(impl_eq_abs_unsigned);
fn float_eq_abs_signed<T: PrimitiveSigned>(x: &Float, y: &T) -> bool
where
Natural: From<<T as UnsignedAbs>::Output>,
{
match x {
float_either_zero!() => *y == T::ZERO,
Float(Finite {
exponent,
significand,
..
}) => {
*y != T::ZERO
&& *exponent >= 0
&& y.significant_bits() == u64::from(exponent.unsigned_abs())
&& significand.cmp_normalized(&Natural::from(y.unsigned_abs())) == Equal
}
_ => false,
}
}
macro_rules! impl_eq_abs_signed {
($t: ident) => {
impl EqAbs<$t> for Float {
/// Determines whether the absolute value of a [`Float`] is equal to the absolute value
/// of a signed primitive integer.
///
/// $\infty$, $-\infty$, and NaN are not equal to any primitive integer. Both the
/// [`Float`] zero and the [`Float`] negative zero are equal to the integer zero.
///
/// # 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()`.
///
/// # Examples
/// See [here](super::eq_abs#eq_abs).
#[inline]
fn eq_abs(&self, other: &$t) -> bool {
float_eq_abs_signed(self, other)
}
}
impl EqAbs<Float> for $t {
/// Determines whether the absolute value of a signed primitive integer is equal to the
/// absolute value of a [`Float`].
///
/// No primitive integer is equal to $\infty$, $-\infty$, or NaN. The integer zero is
/// equal to both the [`Float`] zero and the [`Float`] negative zero.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `other.significant_bits()`.
///
/// # Examples
/// See [here](super::eq_abs#eq_abs).
#[inline]
fn eq_abs(&self, other: &Float) -> bool {
other.eq_abs(self)
}
}
};
}
apply_to_signeds!(impl_eq_abs_signed);