core_math_rs/f16/
cbrt.rs

1/* Correctly-rounded cubic root of binary16 value.
2
3Copyright (c) 2025 Maxence Ponsardin.
4
5This file is ported from the CORE-MATH project
6(https://core-math.gitlabpages.inria.fr/).
7
8Permission is hereby granted, free of charge, to any person obtaining a copy
9of this software and associated documentation files (the "Software"), to deal
10in the Software without restriction, including without limitation the rights
11to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
12copies of the Software, and to permit persons to whom the Software is
13furnished to do so, subject to the following conditions:
14
15The above copyright notice and this permission notice shall be included in all
16copies or substantial portions of the Software.
17
18THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
19IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
20FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
21AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
22LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
23OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
24SOFTWARE.
25*/
26
27use hexf::hexf32 as h;
28
29pub fn cr_cbrtf16(x: f16) -> f16 {
30    const TM: [u16; 16] = [
31        0x00, 0xff, 0xff, 0xff, 0x33, 0x1c, 0x32, 0xff, 0xff, 0xff, 0xff, 0x00, 0xff, 0xff, 0xff,
32        0x10,
33    ];
34    const TE: [u16; 16] = [0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0];
35    const TF: [u16; 16] = [
36        0x3c00, 0, 0, 0, 0x3d80, 0x3f00, 0x3c80, 0, 0, 0, 0, 0x3e00, 0, 0, 0, 0x3d00,
37    ];
38
39    let t = x;
40    let mut tu = t.to_bits();
41    let xf = f32::from(x);
42    let xu = xf.to_bits();
43    if u32::from(TM[((xu >> 19) % 16) as usize]) == ((xu >> 13) % 64) {
44        // exact cases (not supported by cbrtf)
45        let expo = ((xu & 0x7fffffff) >> 23) as i32;
46        if (i32::from(TE[((xu >> 19) % 16) as usize]) == ((expo + 2) % 3))
47            && (
48                // @juntyr: guard against exponent for NaN and infinity
49                (expo & 0xff) != 0xff
50                // @juntyr
51            )
52        {
53            tu = u32::from(tu & 0x8000)
54                .wrapping_add(
55                    (((expo - 127 - i32::from(TE[((xu >> 19) % 16) as usize])) / 3) as u32) << 10,
56                )
57                .wrapping_add(u32::from(TF[((xu >> 19) % 16) as usize])) as u16;
58            return f16::from_bits(tu);
59        }
60    }
61    if (tu & 0x03ff) == 0x0151 {
62        // only wrong case is 0x1.544pk with k = 1 mod 3
63        let expo = i32::from((tu & 0x7fff) >> 10);
64        if ((expo % 3) == 1) && (expo < 31) {
65            // avoid sNaN and k != 1 mod 3
66            tu = ((((expo - 16) / 3 + 15) << 10) + 0x018b + i32::from((tu >> 15) << 15)) as u16;
67            return (f32::from(f16::from_bits(tu)) + h!("0x1p-16") * (f32::from(tu >> 15) - 0.5))
68                as f16;
69        }
70    }
71    // TODO: which cbrt should be called here?
72    xf.cbrt() as f16
73}
74
75#[cfg(test)]
76mod tests {
77    #[test]
78    fn exhaustive() {
79        for b in 0..=u16::MAX {
80            let x = f16::from_bits(b);
81            let y1 = super::cr_cbrtf16(x);
82            let y2 = core_math::cbrtf16(x);
83            assert_eq!(
84                y1.to_bits(),
85                y2.to_bits(),
86                "cbrtf16({x} @ {b:#04x}) = ({y1} @ {y1b:#04x}) vs ({y2} @ {y2b:#04x})",
87                y1b = y1.to_bits(),
88                y2b = y2.to_bits()
89            );
90        }
91    }
92
93    #[test]
94    fn edge() {
95        assert_eq!(
96            super::cr_cbrtf16(-f16::NAN).to_bits(),
97            (-f16::NAN).to_bits()
98        );
99        assert_eq!(super::cr_cbrtf16(-f16::INFINITY), -f16::INFINITY);
100        assert_eq!(super::cr_cbrtf16(-1.0), -1.0);
101        assert_eq!(super::cr_cbrtf16(-0.0).to_bits(), (-0.0_f16).to_bits());
102        assert_eq!(super::cr_cbrtf16(0.0).to_bits(), (0.0_f16).to_bits());
103        assert_eq!(super::cr_cbrtf16(1.0), 1.0);
104        assert_eq!(super::cr_cbrtf16(f16::INFINITY), f16::INFINITY);
105        assert_eq!(super::cr_cbrtf16(f16::NAN).to_bits(), (f16::NAN).to_bits());
106    }
107}
core_math_rs/f16/cbrt.rs

core_math_rs/f16/
cbrt.rs
