pxfm/tangent/
atanpif.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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#[inline(always)]
32fn atanpif_gen_impl<Q: Fn(f64, f64, f64) -> f64>(x: f32, fma: Q) -> f32 {
33    let t = x.to_bits();
34    let e: i32 = ((t >> 23) & 0xff) as i32;
35    let gt = e >= 127;
36    if e > 127 + 24 {
37        // |x| >= 2^25
38        let f = f32::copysign(0.5, x);
39        if e == 0xff {
40            if (t.wrapping_shl(9)) != 0 {
41                return x + x;
42            } // nan
43            return f; // inf
44        }
45        // Warning: 0x1.45f306p-2f / x underflows for |x| >= 0x1.45f306p+124
46        return if x.abs() >= f32::from_bits(0x7da2f983) {
47            f - f32::copysign(f32::from_bits(0x32800000), x)
48        } else {
49            f - f32::from_bits(0x3ea2f983) / x
50        };
51    }
52    let mut z = x as f64;
53    if e < 127 - 13 {
54        // |x| < 2^-13
55        let sx = z * f64::from_bits(0x3fd45f306dc9c883);
56        if e < 127 - 25 {
57            // |x| < 2^-25
58            return sx as f32;
59        }
60        let zz0 = sx - (f64::from_bits(0x3fd5555555555555) * sx) * (x as f64 * x as f64);
61        return zz0 as f32;
62    }
63    let ax = t & 0x7fff_ffff;
64    if ax == 0x3fa267ddu32 {
65        return f32::copysign(f32::from_bits(0x3e933802), x)
66            - f32::copysign(f32::from_bits(0x24000000), x);
67    };
68    if ax == 0x3f693531u32 {
69        return f32::copysign(f32::from_bits(0x3e70d331), x)
70            + f32::copysign(f32::from_bits(0x31800000), x);
71    };
72    if ax == 0x3f800000u32 {
73        return f32::copysign(f32::from_bits(0x3e800000), x);
74    };
75    if gt {
76        z = 1. / z;
77    }
78    let z2 = z * z;
79    let z4 = z2 * z2;
80    let z8 = z4 * z4;
81    const CN: [u64; 6] = [
82        0x3fd45f306dc9c882,
83        0x3fe733b561bc23d5,
84        0x3fe28d9805bdfbf2,
85        0x3fc8c3ba966ae287,
86        0x3f994a7f81ee634b,
87        0x3f4a6bbf6127a6df,
88    ];
89    let mut cn0 = fma(z2, f64::from_bits(CN[1]), f64::from_bits(CN[0]));
90    let cn2 = fma(z2, f64::from_bits(CN[3]), f64::from_bits(CN[2]));
91    let cn4 = fma(z2, f64::from_bits(CN[5]), f64::from_bits(CN[4]));
92    cn0 += z4 * cn2;
93    cn0 += z8 * cn4;
94    cn0 *= z;
95
96    const CD: [u64; 7] = [
97        0x3ff0000000000000,
98        0x4004e3b3ecc2518f,
99        0x4003ef4a360ff063,
100        0x3ff0f1dc55bad551,
101        0x3fc8da0fecc018a4,
102        0x3f88fa87803776bf,
103        0x3f1dadf2ca0acb43,
104    ];
105
106    let mut cd0 = fma(z2, f64::from_bits(CD[1]), f64::from_bits(CD[0]));
107    let cd2 = fma(z2, f64::from_bits(CD[3]), f64::from_bits(CD[2]));
108    let mut cd4 = fma(z2, f64::from_bits(CD[5]), f64::from_bits(CD[4]));
109    let cd6 = f64::from_bits(CD[6]);
110    cd0 += z4 * cd2;
111    cd4 += z4 * cd6;
112    cd0 = fma(z8, cd4, cd0);
113    let mut r = cn0 / cd0;
114    if gt {
115        r = f64::copysign(0.5, z) - r;
116    }
117    r as f32
118}
119
120#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
121#[target_feature(enable = "avx", enable = "fma")]
122unsafe fn atanpif_fma_impl(x: f32) -> f32 {
123    atanpif_gen_impl(x, f64::mul_add)
124}
125
126/// Computes atan(x)/PI
127///
128/// Max ULP 0.5
129#[inline]
130pub fn f_atanpif(x: f32) -> f32 {
131    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
132    {
133        atanpif_gen_impl(x, f_fmla)
134    }
135    #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
136    {
137        use std::sync::OnceLock;
138        static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
139        let q = EXECUTOR.get_or_init(|| {
140            if std::arch::is_x86_feature_detected!("avx")
141                && std::arch::is_x86_feature_detected!("fma")
142            {
143                atanpif_fma_impl
144            } else {
145                fn def_atanpif(x: f32) -> f32 {
146                    atanpif_gen_impl(x, f_fmla)
147                }
148                def_atanpif
149            }
150        });
151        unsafe { q(x) }
152    }
153}
154
155#[cfg(test)]
156mod tests {
157    use super::*;
158    #[test]
159    fn test_atanpif() {
160        assert_eq!(f_atanpif(0.0), 0.0);
161        assert_eq!(f_atanpif(1.0), 0.25);
162        assert_eq!(f_atanpif(1.5), 0.31283295);
163        assert_eq!(f_atanpif(-1.0), -0.25);
164        assert_eq!(f_atanpif(-1.5), -0.31283295);
165    }
166}
pxfm/tangent/atanpif.rs

pxfm/tangent/
atanpif.rs
