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
/*
* // Copyright (c) Radzivon Bartoshyk 4/2025. All rights reserved.
* //
* // Redistribution and use in source and binary forms, with or without modification,
* // are permitted provided that the following conditions are met:
* //
* // 1. Redistributions of source code must retain the above copyright notice, this
* // list of conditions and the following disclaimer.
* //
* // 2. Redistributions in binary form must reproduce the above copyright notice,
* // this list of conditions and the following disclaimer in the documentation
* // and/or other materials provided with the distribution.
* //
* // 3. Neither the name of the copyright holder nor the names of its
* // contributors may be used to endorse or promote products derived from
* // this software without specific prior written permission.
* //
* // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
use crate::common::f_fmla;
#[inline(always)]
fn halley_refine_d(x: f64, a: f64) -> f64 {
let tx = x * x * x;
x * f_fmla(2., a, tx) / f_fmla(2., tx, a)
}
#[inline(always)]
const fn halley_refine(x: f32, a: f32) -> f32 {
let tx = x * x * x;
x * (tx + 2f32 * a) / (2f32 * tx + a)
}
/// Computes Cube Root
#[inline]
pub const fn cbrtf(x: f32) -> f32 {
let u = x.to_bits();
let au = u.wrapping_shl(1);
if au < (1u32 << 24) || au >= (0xffu32 << 24) {
if au >= (0xffu32 << 24) {
return x + x; /* inf, nan */
}
if au == 0 {
return x; /* +-0 */
}
}
const B1: u32 = 709958130;
let mut t: f32;
let mut ui: u32 = x.to_bits();
let mut hx: u32 = ui & 0x7fffffff;
hx = (hx / 3).wrapping_add(B1);
ui &= 0x80000000;
ui |= hx;
t = f32::from_bits(ui);
t = halley_refine(t, x);
halley_refine(t, x)
}
/// Computes Cube Root using FMA
///
/// Peak ULP on 64 bit = 0.49999577
#[inline]
pub fn f_cbrtf(x: f32) -> f32 {
let u = x.to_bits();
let au = u.wrapping_shl(1);
if au < (1u32 << 24) || au >= (0xffu32 << 24) {
if au >= (0xffu32 << 24) {
return x + x; /* inf, nan */
}
if au == 0 {
return x; /* +-0 */
}
}
let mut ui: u32 = x.to_bits();
let mut hx: u32 = ui & 0x7fffffff;
if hx < 0x00800000 {
/* zero or subnormal? */
if hx == 0 {
return x; /* cbrt(+-0) is itself */
}
const X1P24: f32 = f32::from_bits(0x4b800000);
ui = (x * X1P24).to_bits();
hx = ui & 0x7fffffff;
const B2: u32 = 642849266;
hx = hx / 3 + B2;
} else {
const B1: u32 = 709958130;
hx = hx / 3 + B1;
}
ui &= 0x80000000;
ui |= hx;
let mut t = f32::from_bits(ui) as f64;
t = halley_refine_d(t, x as f64);
halley_refine_d(t, x as f64) as f32
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_fcbrtf() {
assert_eq!(f_cbrtf(0.0), 0.0);
assert_eq!(f_cbrtf(-27.0), -3.0);
assert_eq!(f_cbrtf(27.0), 3.0);
assert_eq!(f_cbrtf(f32::NEG_INFINITY), f32::NEG_INFINITY);
assert_eq!(f_cbrtf(f32::INFINITY), f32::INFINITY);
assert!(f_cbrtf(f32::NAN).is_nan());
}
}