```  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
```
```#[cfg(feature = "decimal")]
use decimal::d128;
use std::cmp::{Ordering, PartialOrd};

/// A set where every two elements have an infimum (i.e. greatest lower bound).
pub trait MeetSemilattice: Sized {
/// Returns the meet (aka. infimum) of two values.
fn meet(&self, other: &Self) -> Self;
}

/// A set where every two elements have a supremum (i.e. smallest upper bound).
pub trait JoinSemilattice: Sized {
/// Returns the join (aka. supremum) of two values.
fn join(&self, other: &Self) -> Self;
}

/// Partially orderable sets where every two elements have a supremum and infimum.
pub trait Lattice: MeetSemilattice + JoinSemilattice + PartialOrd {
/// Returns the infimum and the supremum simultaneously.
#[inline]
fn meet_join(&self, other: &Self) -> (Self, Self) {
(self.meet(other), self.join(other))
}

/// Return the minimum of `self` and `other` if they are comparable.
#[inline]
fn partial_min<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
if let Some(ord) = self.partial_cmp(other) {
match ord {
Ordering::Greater => Some(other),
_ => Some(self),
}
} else {
None
}
}

/// Return the maximum of `self` and `other` if they are comparable.
#[inline]
fn partial_max<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
if let Some(ord) = self.partial_cmp(other) {
match ord {
Ordering::Less => Some(other),
_ => Some(self),
}
} else {
None
}
}

/// Sorts two values in increasing order using a partial ordering.
#[inline]
fn partial_sort2<'a>(&'a self, other: &'a Self) -> Option<(&'a Self, &'a Self)> {
if let Some(ord) = self.partial_cmp(other) {
match ord {
Ordering::Less => Some((self, other)),
_ => Some((other, self)),
}
} else {
None
}
}

/// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
/// `min` or `max`.
#[inline]
fn partial_clamp<'a>(&'a self, min: &'a Self, max: &'a Self) -> Option<&'a Self> {
if let (Some(cmp_min), Some(cmp_max)) = (self.partial_cmp(min), self.partial_cmp(max)) {
if cmp_min == Ordering::Less {
Some(min)
} else if cmp_max == Ordering::Greater {
Some(max)
} else {
Some(self)
}
} else {
None
}
}
}

macro_rules! impl_lattice(
(\$(\$T:ident),*) => {\$(
impl MeetSemilattice for \$T {
#[inline]
fn meet(&self, other: &Self) -> Self {
if *self <= *other {
*self
}
else {
*other
}
}
}

impl JoinSemilattice for \$T {
#[inline]
fn join(&self, other: &Self) -> Self {
if *self >= *other {
*self
}
else {
*other
}
}
}

impl Lattice for \$T {
#[inline]
fn meet_join(&self, other: &Self) -> (Self, Self) {
if *self >= *other {
(*other, *self)
}
else {
(*self, *other)
}
}
}
)*}
);

impl_lattice!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize, f32, f64);
#[cfg(feature = "decimal")]
impl_lattice!(d128);

impl<N: MeetSemilattice> MeetSemilattice for num_complex::Complex<N> {
#[inline]
fn meet(&self, other: &Self) -> Self {
Self {
re: self.re.meet(&other.re),
im: self.im.meet(&other.im),
}
}
}

impl<N: JoinSemilattice> JoinSemilattice for num_complex::Complex<N> {
#[inline]
fn join(&self, other: &Self) -> Self {
Self {
re: self.re.join(&other.re),
im: self.im.join(&other.im),
}
}
}
```