pxfm/sin_cosf/
sincf.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;
30use crate::polyeval::f_polyeval5;
31use crate::sin_cosf::sincosf_eval::sincosf_eval;
32
33/// Computes sinc(x)
34///
35/// Max found ULP 0.5
36pub fn f_sincf(x: f32) -> f32 {
37    let x_abs = x.to_bits() & 0x7fff_ffffu32;
38    let xd = x as f64;
39
40    // |x| <= pi/16
41    if x_abs <= 0x3e49_0fdbu32 {
42        // |x| < 0.000443633
43        if x_abs < 0x39e8_9769u32 {
44            if x_abs == 0u32 {
45                // For signed zeros.
46                return 1.;
47            }
48            /*
49            Generated by Sollya:
50            f = sin(x) / x;
51
52            d = [0.0; 0.000443633];
53            pf = fpminimax(f, [|0, 2|], [|1, D...|], d, relative, floating);
54
55            See ./notes/sincf.sollya
56             */
57            return f_fmla(
58                xd * xd,
59                f64::from_bits(0xbfc555555265f618),
60                f64::from_bits(0x3ff0000000000000),
61            ) as f32;
62        }
63
64        let xsqr = xd * xd;
65
66        /*
67        Generated by Sollya:
68        f_sinpi_16 = sin(x)/x;
69        Q = fpminimax(f_sinpi_16, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/16]);
70
71        See ./notes/sincosf.sollya
72         */
73        let p = f_polyeval5(
74            xsqr,
75            f64::from_bits(0x3ff0000000000000),
76            f64::from_bits(0xbfc55555555554c6),
77            f64::from_bits(0x3f81111111085e65),
78            f64::from_bits(0xbf2a019f70fb4d4f),
79            f64::from_bits(0x3ec718d179815e74),
80        );
81        return p as f32;
82    }
83
84    if x_abs >= 0x7f80_0000u32 {
85        return x + f32::NAN;
86    }
87
88    // Formula:
89    //   sin(x) = sin((k + y)*pi/32)
90    //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
91    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
92    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
93    // computed using degree-7 and degree-6 minimax polynomials generated by
94    // Sollya respectively.
95
96    let rs = sincosf_eval(xd, x_abs);
97    let v_sin = f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k));
98    (v_sin / xd) as f32
99}
100
101#[cfg(test)]
102mod tests {
103    use super::*;
104
105    #[test]
106    fn test_f_sincf() {
107        assert_eq!(f_sincf(-7.991783e37), -1.1754942946874968e-38);
108        assert_eq!(f_sincf(-8.04695e37), 1.1754942974913884e-38);
109        assert_eq!(f_sincf(-0.00044236073), 0.9999999673861641);
110        assert_eq!(f_sincf(0.0), 1.0);
111        assert_eq!(f_sincf(0.2), 0.99334663);
112        assert!(f_sincf(f32::INFINITY).is_nan());
113        assert!(f_sincf(f32::NEG_INFINITY).is_nan());
114    }
115}
pxfm/sin_cosf/sincf.rs

pxfm/sin_cosf/
sincf.rs
