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
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185

use core::cell;
#[cfg(feature = "num-complex")]
use num_complex::Complex;

/// Equality that is defined using the absolute difference of two numbers.
pub trait AbsDiffEq<Rhs = Self>: PartialEq<Rhs>
where
    Rhs: ?Sized,
{
    /// Used for specifying relative comparisons.
    type Epsilon;

    /// The default tolerance to use when testing values that are close together.
    ///
    /// This is used when no `epsilon` value is supplied to the [`abs_diff_eq!`], [`relative_eq!`],
    /// or [`ulps_eq!`] macros.
    fn default_epsilon() -> Self::Epsilon;

    /// A test for equality that uses the absolute difference to compute the approximate
    /// equality of two numbers.
    fn abs_diff_eq(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool;

    /// The inverse of [`AbsDiffEq::abs_diff_eq`].
    fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool {
        !Self::abs_diff_eq(self, other, epsilon)
    }
}

///////////////////////////////////////////////////////////////////////////////////////////////////
// Base implementations
///////////////////////////////////////////////////////////////////////////////////////////////////

macro_rules! impl_unsigned_abs_diff_eq {
    ($T:ident, $default_epsilon:expr) => {
        impl AbsDiffEq for $T {
            type Epsilon = $T;

            #[inline]
            fn default_epsilon() -> $T {
                $default_epsilon
            }

            #[inline]
            fn abs_diff_eq(&self, other: &$T, epsilon: $T) -> bool {
                (if self > other {
                    self - other
                } else {
                    other - self
                }) <= epsilon
            }
        }
    };
}

impl_unsigned_abs_diff_eq!(u8, 0);
impl_unsigned_abs_diff_eq!(u16, 0);
impl_unsigned_abs_diff_eq!(u32, 0);
impl_unsigned_abs_diff_eq!(u64, 0);
impl_unsigned_abs_diff_eq!(usize, 0);

macro_rules! impl_signed_abs_diff_eq {
    ($T:ident, $default_epsilon:expr) => {
        impl AbsDiffEq for $T {
            type Epsilon = $T;

            #[inline]
            fn default_epsilon() -> $T {
                $default_epsilon
            }

            #[inline]
            #[allow(unused_imports)]
            fn abs_diff_eq(&self, other: &$T, epsilon: $T) -> bool {
                use num_traits::float::FloatCore;
                $T::abs(self - other) <= epsilon
            }
        }
    };
}

impl_signed_abs_diff_eq!(i8, 0);
impl_signed_abs_diff_eq!(i16, 0);
impl_signed_abs_diff_eq!(i32, 0);
impl_signed_abs_diff_eq!(i64, 0);
impl_signed_abs_diff_eq!(isize, 0);
impl_signed_abs_diff_eq!(f32, core::f32::EPSILON);
impl_signed_abs_diff_eq!(f64, core::f64::EPSILON);

///////////////////////////////////////////////////////////////////////////////////////////////////
// Derived implementations
///////////////////////////////////////////////////////////////////////////////////////////////////

impl<'a, T: AbsDiffEq + ?Sized> AbsDiffEq for &'a T {
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> T::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &&'a T, epsilon: T::Epsilon) -> bool {
        T::abs_diff_eq(*self, *other, epsilon)
    }
}

impl<'a, T: AbsDiffEq + ?Sized> AbsDiffEq for &'a mut T {
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> T::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &&'a mut T, epsilon: T::Epsilon) -> bool {
        T::abs_diff_eq(*self, *other, epsilon)
    }
}

impl<T: AbsDiffEq + Copy> AbsDiffEq for cell::Cell<T> {
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> T::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &cell::Cell<T>, epsilon: T::Epsilon) -> bool {
        T::abs_diff_eq(&self.get(), &other.get(), epsilon)
    }
}

impl<T: AbsDiffEq + ?Sized> AbsDiffEq for cell::RefCell<T> {
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> T::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &cell::RefCell<T>, epsilon: T::Epsilon) -> bool {
        T::abs_diff_eq(&self.borrow(), &other.borrow(), epsilon)
    }
}

impl<A, B> AbsDiffEq<[B]> for [A]
where
    A: AbsDiffEq<B>,
    A::Epsilon: Clone,
{
    type Epsilon = A::Epsilon;

    #[inline]
    fn default_epsilon() -> A::Epsilon {
        A::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &[B], epsilon: A::Epsilon) -> bool {
        self.len() == other.len()
            && Iterator::zip(self.iter(), other).all(|(x, y)| A::abs_diff_eq(x, y, epsilon.clone()))
    }
}

#[cfg(feature = "num-complex")]
impl<T: AbsDiffEq> AbsDiffEq for Complex<T>
where
    T::Epsilon: Clone,
{
    type Epsilon = T::Epsilon;

    #[inline]
    fn default_epsilon() -> T::Epsilon {
        T::default_epsilon()
    }

    #[inline]
    fn abs_diff_eq(&self, other: &Complex<T>, epsilon: T::Epsilon) -> bool {
        T::abs_diff_eq(&self.re, &other.re, epsilon.clone())
            && T::abs_diff_eq(&self.im, &other.im, epsilon)
    }
}