pxfm/hyperbolic/
sinhf.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, f_fmlaf};
30use crate::round_ties_even::RoundTiesEven;
31
32static TB: [u64; 32] = [
33    0x3fe0000000000000,
34    0x3fe059b0d3158574,
35    0x3fe0b5586cf9890f,
36    0x3fe11301d0125b51,
37    0x3fe172b83c7d517b,
38    0x3fe1d4873168b9aa,
39    0x3fe2387a6e756238,
40    0x3fe29e9df51fdee1,
41    0x3fe306fe0a31b715,
42    0x3fe371a7373aa9cb,
43    0x3fe3dea64c123422,
44    0x3fe44e086061892d,
45    0x3fe4bfdad5362a27,
46    0x3fe5342b569d4f82,
47    0x3fe5ab07dd485429,
48    0x3fe6247eb03a5585,
49    0x3fe6a09e667f3bcd,
50    0x3fe71f75e8ec5f74,
51    0x3fe7a11473eb0187,
52    0x3fe82589994cce13,
53    0x3fe8ace5422aa0db,
54    0x3fe93737b0cdc5e5,
55    0x3fe9c49182a3f090,
56    0x3fea5503b23e255d,
57    0x3feae89f995ad3ad,
58    0x3feb7f76f2fb5e47,
59    0x3fec199bdd85529c,
60    0x3fecb720dcef9069,
61    0x3fed5818dcfba487,
62    0x3fedfc97337b9b5f,
63    0x3feea4afa2a490da,
64    0x3fef50765b6e4540,
65];
66
67#[cold]
68fn sinhf_accurate(z: f64, ia: f64, sp: u64, sm: u64) -> f32 {
69    const CH: [u64; 7] = [
70        0x3ff0000000000000,
71        0x3f962e42fefa39ef,
72        0x3f2ebfbdff82c58f,
73        0x3ebc6b08d702e0ed,
74        0x3e43b2ab6fb92e5e,
75        0x3dc5d886e6d54203,
76        0x3d4430976b8ce6ef,
77    ];
78    const ILN2H: f64 = f64::from_bits(0x4047154765000000);
79    const ILN2L: f64 = f64::from_bits(0x3e55c17f0bbbe880);
80    let h = f_fmla(ILN2L, z, f_fmla(ILN2H, z, -ia));
81    let h2 = h * h;
82
83    let q0 = f_fmla(h2, f64::from_bits(CH[6]), f64::from_bits(CH[4]));
84    let q1 = f_fmla(h2, f64::from_bits(CH[2]), f64::from_bits(CH[0]));
85
86    let te = f_fmla(h2 * h2, q0, q1);
87
88    let q2 = f_fmla(h2, f64::from_bits(CH[5]), f64::from_bits(CH[3]));
89
90    let to = f_fmla(h2, q2, f64::from_bits(CH[1]));
91
92    let b0 = f_fmla(h, to, te);
93    let b1 = f_fmla(-h, to, te);
94
95    f_fmla(f64::from_bits(sp), b0, -f64::from_bits(sm) * b1) as f32
96}
97
98/// Huperbolic sine function
99///
100/// Max found ULP 0.4954563
101#[inline]
102pub fn f_sinhf(x: f32) -> f32 {
103    const C: [u64; 4] = [
104        0x3ff0000000000000,
105        0x3f962e42fef4c4e7,
106        0x3f2ebfd1b232f475,
107        0x3ebc6b19384ecd93,
108    ];
109
110    const ST: [(u32, u32, u32); 1] = [(0x74250bfeu32, 0x3a1285ff, 0x2d800000)];
111    const ILN2: f64 = f64::from_bits(0x40471547652b82fe);
112    let t = x.to_bits();
113    let z: f64 = x as f64;
114    let ux = t.wrapping_shl(1);
115    if ux > 0x8565a9f8u32 {
116        // |x| > 89.416
117        let sgn = f32::copysign(2.0, x);
118        if ux >= 0xff000000u32 {
119            if ux.wrapping_shl(8) != 0 {
120                return x + x;
121            } // nan
122            return sgn * f32::INFINITY; // +-inf
123        }
124        let r = sgn * f64::from_bits(0x47efffffe0000000) as f32;
125
126        return r;
127    }
128    if ux < 0x7c000000u32 {
129        // |x| < 0.125
130        if ux <= 0x74250bfeu32 {
131            // |x| <= 0.000558942
132            if ux < 0x66000000u32 {
133                // |x| < 5.96046e-08
134                return f_fmlaf(x, x.abs(), x);
135            }
136            if ST[0].0 == ux {
137                let sgn = f32::copysign(1.0, x);
138                return f_fmlaf(sgn, f32::from_bits(ST[0].1), sgn * f32::from_bits(ST[0].2));
139            }
140            return f_fmlaf(x * f64::from_bits(0x3fc5555560000000) as f32, x * x, x);
141        }
142        const CP: [u64; 4] = [
143            0x3fc5555555555555,
144            0x3f811111111146e1,
145            0x3f2a01a00930dda6,
146            0x3ec71f92198aa6e9,
147        ];
148        let z2 = z * z;
149        let z4 = z2 * z2;
150
151        let w0 = f_fmla(z2, f64::from_bits(CP[3]), f64::from_bits(CP[2]));
152        let w1 = f_fmla(z2, f64::from_bits(CP[1]), f64::from_bits(CP[0]));
153        let w2 = f_fmla(z4, w0, w1);
154
155        return f_fmla(z2 * z, w2, z) as f32;
156    }
157    let a = ILN2 * z;
158    let ia = a.round_ties_even_finite();
159    let h = a - ia;
160    let h2 = h * h;
161    let ja = (ia + f64::from_bits(0x4338000000000000)).to_bits();
162    let jp: i64 = ja as i64;
163    let jm = -jp;
164    let sp = TB[(jp & 31) as usize].wrapping_add(jp.wrapping_shr(5).wrapping_shl(52) as u64);
165    let sm = TB[(jm & 31) as usize].wrapping_add(jm.wrapping_shr(5).wrapping_shl(52) as u64);
166    let te = f_fmla(h2, f64::from_bits(C[2]), f64::from_bits(C[0]));
167    let to = f_fmla(h2, f64::from_bits(C[3]), f64::from_bits(C[1]));
168    let rp = f64::from_bits(sp) * f_fmla(h, to, te);
169    let rm = f64::from_bits(sm) * f_fmla(-h, to, te);
170    let r = rp - rm;
171    let ub = r;
172    let lb = r - f64::from_bits(0x3de4e406496685f4) * r;
173    // Ziv's accuracy test
174    if ub != lb {
175        return sinhf_accurate(z, ia, sp, sm);
176    }
177    ub as f32
178}
179
180#[cfg(test)]
181mod tests {
182    use super::*;
183
184    #[test]
185    fn test_sinhf() {
186        assert_eq!(f_sinhf(-0.5), -0.5210953);
187        assert_eq!(f_sinhf(0.5), 0.5210953);
188        assert_eq!(f_sinhf(7.), 548.3161);
189    }
190}
pxfm/hyperbolic/sinhf.rs

pxfm/hyperbolic/
sinhf.rs
