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
use crate::{classify::*, interval::*, simd::*};
impl Interval {
/// Returns the absolute value of `self`.
///
/// The domain and the range of the point function are:
///
/// | Domain | Range |
/// | ------ | --------- |
/// | $\R$ | $\[0, ∞)$ |
#[must_use]
pub fn abs(self) -> Self {
use IntervalClass::*;
match self.classify() {
E | P0 | P1 | Z => self,
M => {
// [0, max(-a, b)] = [0; max(-a, b)]
let x = self.rep; // [-a; b]
let r = max(x, swap(x)); // [max(-a, b); _]
Self {
rep: shuffle02(splat(0.0), r),
}
}
N0 | N1 => {
// [-b, -a] = [b; -a]
Self {
rep: swap(self.rep),
}
}
}
}
/// Returns the maximum of `self` and `rhs`.
///
/// The domain and the range of the point function are:
///
/// | Domain | Range |
/// | ------ | ----- |
/// | $\R^2$ | $\R$ |
#[must_use]
pub fn max(self, rhs: Self) -> Self {
if HAS_MAXIMUM {
// [max(a, c), max(b, d)] = [-max(a, c); max(b, d)] = [min(-a, -c); max(b, d)]
let min = minimum(self.rep, rhs.rep); // [min(-a, -c); min(b, d)]
let max = maximum(self.rep, rhs.rep); // [max(-a, -c); max(b, d)]
Self {
rep: shuffle03(min, max),
}
} else {
if self.either_empty(rhs) {
return Self::EMPTY;
}
let min = min(self.rep, rhs.rep);
let max = max(self.rep, rhs.rep);
Self {
rep: shuffle03(min, max),
}
}
}
/// Returns the minimum of `self` and `rhs`.
///
/// The domain and the range of the point function are:
///
/// | Domain | Range |
/// | ------ | ----- |
/// | $\R^2$ | $\R$ |
#[must_use]
pub fn min(self, rhs: Self) -> Self {
if HAS_MAXIMUM {
// [min(a, c), min(b, d)] = [-min(a, c); min(b, d)] = [max(-a, -c); min(b, d)]
let max = maximum(self.rep, rhs.rep); // [max(-a, -c); max(b, d)]
let min = minimum(self.rep, rhs.rep); // [min(-a, -c); min(b, d)]
Self {
rep: shuffle03(max, min),
}
} else {
if self.either_empty(rhs) {
return Self::EMPTY;
}
let max = max(self.rep, rhs.rep);
let min = min(self.rep, rhs.rep);
Self {
rep: shuffle03(max, min),
}
}
}
}
impl DecInterval {
/// The decorated version of [`Interval::abs`].
///
/// A NaI is returned if `self` is NaI.
#[must_use]
pub fn abs(self) -> Self {
if self.is_nai() {
return self;
}
Self::set_dec(self.x.abs(), self.d)
}
/// The decorated version of [`Interval::max`].
///
/// A NaI is returned if `self` or `rhs` is NaI.
#[must_use]
pub fn max(self, rhs: Self) -> Self {
if self.is_nai() {
return self;
}
Self::set_dec(self.x.max(rhs.x), self.d.min(rhs.d))
}
/// The decorated version of [`Interval::min`].
///
/// A NaI is returned if `self` or `rhs` is NaI.
#[must_use]
pub fn min(self, rhs: Self) -> Self {
if self.is_nai() {
return self;
}
Self::set_dec(self.x.min(rhs.x), self.d.min(rhs.d))
}
}
#[cfg(test)]
mod tests {
use crate::*;
use DecInterval as DI;
use Interval as I;
#[test]
fn empty() {
assert!(I::EMPTY.abs().is_empty());
assert!(I::EMPTY.max(I::PI).is_empty());
assert!(I::PI.max(I::EMPTY).is_empty());
assert!(I::EMPTY.min(I::PI).is_empty());
assert!(I::PI.min(I::EMPTY).is_empty());
assert!(DI::EMPTY.abs().is_empty());
assert!(DI::EMPTY.max(DI::PI).is_empty());
assert!(DI::PI.max(DI::EMPTY).is_empty());
assert!(DI::EMPTY.min(DI::PI).is_empty());
assert!(DI::PI.min(DI::EMPTY).is_empty());
}
#[test]
fn nai() {
assert!(DI::NAI.abs().is_nai());
assert!(DI::NAI.max(DI::PI).is_nai());
assert!(DI::PI.max(DI::NAI).is_nai());
assert!(DI::NAI.min(DI::PI).is_nai());
assert!(DI::PI.min(DI::NAI).is_nai());
}
}