pxfm/cube_roots/
rcbrtf.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 8/2025. All rights reserved.
3 * //
4 * // Redistribution and use in source and binary forms, with or without modification,
5 * // are permitted provided that the following conditions are met:
6 * //
7 * // 1.  Redistributions of source code must retain the above copyright notice, this
8 * // list of conditions and the following disclaimer.
9 * //
10 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
11 * // this list of conditions and the following disclaimer in the documentation
12 * // and/or other materials provided with the distribution.
13 * //
14 * // 3.  Neither the name of the copyright holder nor the names of its
15 * // contributors may be used to endorse or promote products derived from
16 * // this software without specific prior written permission.
17 * //
18 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29use crate::common::f_fmla;
30
31// // y1 = y0 * (2+x*y0^3)/(1+2*x*y0^3)
32// #[inline(always)]
33// fn halley_refine_d(x: f64, a: f64) -> f64 {
34//     let tx = x * x * x;
35//     x * f_fmla(tx, a, 2.0) / f_fmla(2. * a, tx, 1.0)
36// }
37
38#[inline(always)]
39fn rapshon_refine_inv_cbrt(x: f64, a: f64) -> f64 {
40    x * f_fmla(-1. / 3. * a, x * x * x, 4. / 3.)
41}
42
43#[inline(always)]
44#[allow(unused)]
45fn rapshon_refine_inv_cbrt_fma(x: f64, a: f64) -> f64 {
46    x * f64::mul_add(-1. / 3. * a, x * x * x, 4. / 3.)
47}
48
49// y1 = y0(k1 − c(k2 − k3c), c = x*y0*y0*y0
50// k1 = 14/9 , k2 = 7/9 , k3 = 2/9
51#[inline(always)]
52fn halleys_div_free(x: f64, a: f64) -> f64 {
53    const K3: f64 = 2. / 9.;
54    const K2: f64 = 7. / 9.;
55    const K1: f64 = 14. / 9.;
56    let c = a * x * x * x;
57    let mut y = f_fmla(-K3, c, K2);
58    y = f_fmla(-c, y, K1);
59    y * x
60}
61
62#[inline(always)]
63#[allow(unused)]
64fn halleys_div_free_fma(x: f64, a: f64) -> f64 {
65    const K3: f64 = 2. / 9.;
66    const K2: f64 = 7. / 9.;
67    const K1: f64 = 14. / 9.;
68    let c = a * x * x * x;
69    let mut y = f64::mul_add(-K3, c, K2);
70    y = f64::mul_add(-c, y, K1);
71    y * x
72}
73
74#[inline(always)]
75fn rcbrtf_gen_impl<Halley: Fn(f64, f64) -> f64, NewtonRaphson: Fn(f64, f64) -> f64>(
76    x: f32,
77    halley: Halley,
78    rapshon: NewtonRaphson,
79) -> f32 {
80    let u = x.to_bits();
81    let au = u.wrapping_shl(1);
82    if au < (1u32 << 24) || au >= (0xffu32 << 24) {
83        if x.is_infinite() {
84            return if x.is_sign_negative() { -0.0 } else { 0.0 };
85        }
86        if au >= (0xffu32 << 24) {
87            return x + x; /* inf, nan */
88        }
89        if x == 0. {
90            return if x.is_sign_positive() {
91                f32::INFINITY
92            } else {
93                f32::NEG_INFINITY
94            }; /* +-inf */
95        }
96    }
97
98    let mut ui: u32 = x.to_bits();
99    let mut hx: u32 = ui & 0x7fffffff;
100
101    if hx < 0x00800000 {
102        /* zero or subnormal? */
103        if hx == 0 {
104            return x; /* cbrt(+-0) is itself */
105        }
106        const TWO_EXP_24: f32 = f32::from_bits(0x4b800000);
107        ui = (x * TWO_EXP_24).to_bits();
108        hx = ui & 0x7fffffff;
109        const B: u32 = 0x54a21d2au32 + (8u32 << 23);
110        hx = B.wrapping_sub(hx / 3);
111    } else {
112        hx = 0x54a21d2au32.wrapping_sub(hx / 3);
113    }
114    ui &= 0x80000000;
115    ui |= hx;
116
117    let t = f32::from_bits(ui) as f64;
118    let dx = x as f64;
119    let mut t = halley(t, dx);
120    t = halley(t, dx);
121    t = rapshon(t, dx);
122    t as f32
123}
124
125#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
126#[target_feature(enable = "avx", enable = "fma")]
127unsafe fn rcbrtf_fma_impl(x: f32) -> f32 {
128    rcbrtf_gen_impl(x, halleys_div_free_fma, rapshon_refine_inv_cbrt_fma)
129}
130
131/// Computes 1/cbrt(x)
132///
133/// ULP 0.5
134#[inline]
135pub fn f_rcbrtf(x: f32) -> f32 {
136    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
137    {
138        rcbrtf_gen_impl(x, halleys_div_free, rapshon_refine_inv_cbrt)
139    }
140    #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
141    {
142        use std::sync::OnceLock;
143        static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
144        let q = EXECUTOR.get_or_init(|| {
145            if std::arch::is_x86_feature_detected!("avx")
146                && std::arch::is_x86_feature_detected!("fma")
147            {
148                rcbrtf_fma_impl
149            } else {
150                fn def_rcbrtf(x: f32) -> f32 {
151                    rcbrtf_gen_impl(x, halleys_div_free, rapshon_refine_inv_cbrt)
152                }
153                def_rcbrtf
154            }
155        });
156        unsafe { q(x) }
157    }
158}
159
160#[cfg(test)]
161mod tests {
162    use super::*;
163
164    #[test]
165    fn test_fcbrtf() {
166        assert_eq!(f_rcbrtf(0.0), f32::INFINITY);
167        assert_eq!(f_rcbrtf(-0.0), f32::NEG_INFINITY);
168        assert_eq!(f_rcbrtf(-27.0), -1. / 3.);
169        assert_eq!(f_rcbrtf(27.0), 1. / 3.);
170        assert_eq!(f_rcbrtf(64.0), 0.25);
171        assert_eq!(f_rcbrtf(-64.0), -0.25);
172        assert_eq!(f_rcbrtf(f32::NEG_INFINITY), -0.0);
173        assert_eq!(f_rcbrtf(f32::INFINITY), 0.0);
174        assert!(f_rcbrtf(f32::NAN).is_nan());
175    }
176}
pxfm/cube_roots/rcbrtf.rs

pxfm/cube_roots/
rcbrtf.rs
