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

// Copyright 2006 The Android Open Source Project
// Copyright 2020 Yevhenii Reizner
//
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

use crate::floating_point::f32_as_2s_compliment;

#[allow(missing_docs)]
pub const SCALAR_MAX: f32 = 3.402823466e+38;
#[allow(missing_docs)]
pub const SCALAR_NEARLY_ZERO: f32 = 1.0 / (1 << 12) as f32;
#[allow(missing_docs)]
pub const SCALAR_ROOT_2_OVER_2: f32 = 0.707106781;

/// Float number extension methods.
///
/// Mainly for internal use. Do not rely on it!
#[allow(missing_docs)]
pub trait Scalar {
    fn half(self) -> Self;
    fn ave(self, other: Self) -> Self;
    fn sqr(self) -> Self;
    fn invert(self) -> Self;
    fn bound(self, min: Self, max: Self) -> Self;
    fn is_nearly_equal(self, other: Self) -> bool;
    fn is_nearly_zero(self) -> bool;
    fn is_nearly_zero_within_tolerance(self, tolerance: Self) -> bool;
    fn almost_dequal_ulps(self, other: Self) -> bool;
}

impl Scalar for f32 {
    fn half(self) -> f32 {
        self * 0.5
    }

    fn ave(self, other: Self) -> f32 {
        (self + other) * 0.5
    }

    fn sqr(self) -> f32 {
        self * self
    }

    fn invert(self) -> f32 {
        1.0 / self
    }

    // Works just like SkTPin, returning `max` for NaN/inf
    /// A non-panicking clamp.
    fn bound(self, min: Self, max: Self) -> Self {
        max.min(self).max(min)
    }

    fn is_nearly_equal(self, other: Self) -> bool {
        (self - other).abs() <= SCALAR_NEARLY_ZERO
    }

    fn is_nearly_zero(self) -> bool {
        self.is_nearly_zero_within_tolerance(SCALAR_NEARLY_ZERO)
    }

    fn is_nearly_zero_within_tolerance(self, tolerance: Self) -> bool {
        debug_assert!(tolerance >= 0.0);
        self.abs() <= tolerance
    }

    // From SkPathOpsTypes.
    fn almost_dequal_ulps(self, other: Self) -> bool {
        const ULPS_EPSILON: i32 = 16;
        let a_bits = f32_as_2s_compliment(self);
        let b_bits = f32_as_2s_compliment(other);
        // Find the difference in ULPs.
        a_bits < b_bits + ULPS_EPSILON && b_bits < a_bits + ULPS_EPSILON
    }
}

#[allow(missing_docs)]
#[cfg(all(not(feature = "std"), feature = "no-std-float"))]
pub trait NoStdFloat {
    fn trunc(self) -> Self;
    fn sqrt(self) -> Self;
    fn abs(self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn ceil(self) -> Self;
    fn floor(self) -> Self;
    fn round(self) -> Self;
    fn powf(self, y: Self) -> Self;
    fn acos(self) -> Self;
}

#[cfg(all(not(feature = "std"), feature = "no-std-float"))]
impl NoStdFloat for f32 {
    fn trunc(self) -> Self {
        libm::truncf(self)
    }
    fn sqrt(self) -> Self {
        libm::sqrtf(self)
    }
    fn abs(self) -> Self {
        libm::fabsf(self)
    }
    fn sin(self) -> Self {
        libm::sinf(self)
    }
    fn cos(self) -> Self {
        libm::cosf(self)
    }
    fn ceil(self) -> Self {
        libm::ceilf(self)
    }
    fn floor(self) -> Self {
        libm::floorf(self)
    }
    fn round(self) -> Self {
        libm::roundf(self)
    }
    fn powf(self, y: Self) -> Self {
        libm::powf(self, y)
    }
    fn acos(self) -> Self {
        libm::acosf(self)
    }
}

#[cfg(all(not(feature = "std"), feature = "no-std-float"))]
impl NoStdFloat for f64 {
    fn trunc(self) -> Self {
        libm::trunc(self)
    }
    fn sqrt(self) -> Self {
        libm::sqrt(self)
    }
    fn abs(self) -> Self {
        libm::fabs(self)
    }
    fn sin(self) -> Self {
        libm::sin(self)
    }
    fn cos(self) -> Self {
        libm::cos(self)
    }
    fn ceil(self) -> Self {
        libm::ceil(self)
    }
    fn floor(self) -> Self {
        libm::floor(self)
    }
    fn round(self) -> Self {
        libm::round(self)
    }
    fn powf(self, y: Self) -> Self {
        libm::pow(self, y)
    }
    fn acos(self) -> Self {
        libm::acos(self)
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn bound() {
        assert_eq!(f32::NAN.bound(0.0, 1.0), 1.0);
        assert_eq!(f32::INFINITY.bound(0.0, 1.0), 1.0);
        assert_eq!(f32::NEG_INFINITY.bound(0.0, 1.0), 0.0);
        assert_eq!(f32::EPSILON.bound(0.0, 1.0), f32::EPSILON);
        assert_eq!(0.5.bound(0.0, 1.0), 0.5);
        assert_eq!((-1.0).bound(0.0, 1.0), 0.0);
        assert_eq!(2.0.bound(0.0, 1.0), 1.0);
    }
}