pxfm/sin_cosf/
sinmxf.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 sin(x) - x
34pub fn f_sinmxf(x: f32) -> f32 {
35    let x_abs = x.to_bits() & 0x7fff_ffffu32;
36    let xd = x as f64;
37    let ax: u32 = x.to_bits().wrapping_shl(1);
38    if ax == 0 || ax >= 0xffu32 << 24 {
39        if x_abs == 0u32 {
40            // For signed zeros.
41            return x;
42        }
43        return f32::NAN; // x == inf or x == NaN
44    }
45
46    // |x| <= pi/16
47    if x_abs <= 0x3e49_0fdbu32 {
48        // |x| < 0.000443633
49        if x_abs < 0x39e8_9769u32 {
50            // sin(x) - x ~ -x^3/6 + x^5/120 + O(x^7)
51            let dx = x as f64;
52            let x2 = dx * dx;
53            let c = f_fmla(
54                x2,
55                f64::from_bits(0x3f81111111111111),
56                f64::from_bits(0xbfc5555555555555),
57            ) * x2;
58            return (c * dx) as f32;
59        }
60
61        let xsqr = xd * xd;
62
63        // Generated by Sollya:
64        // d = [2^-10, pi/16];
65        // f_sinmx = (sin(x) - x)/x;
66        // Q = fpminimax(f_sinmx, [|0, 2, 4, 6, 8|], [|D...|], d);
67        // See ./notes/sinmxf.sollya
68        let p = f_polyeval5(
69            xsqr,
70            f64::from_bits(0xbb8f6a339382f07f),
71            f64::from_bits(0xbfc5555555555545),
72            f64::from_bits(0x3f811111110ddf5c),
73            f64::from_bits(0xbf2a019fb330c620),
74            f64::from_bits(0x3ec719bc2a614884),
75        );
76        return (xd * p) as f32;
77    }
78
79    // Formula:
80    //   sin(x) = sin((k + y)*pi/32)
81    //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
82    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
83    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
84    // computed using degree-7 and degree-6 minimax polynomials generated by
85    // Sollya respectively.
86
87    let rs = sincosf_eval(xd, x_abs);
88    let sinx = f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k));
89    (sinx - xd) as f32
90}
91
92#[cfg(test)]
93mod tests {
94    use super::*;
95
96    #[test]
97    fn f_sinf_test() {
98        assert_eq!(f_sinmxf(0.00016344387), -0.00000000000072770376);
99        assert_eq!(f_sinmxf(0.0), 0.0);
100        assert_eq!(f_sinmxf(-0.0), 0.0);
101        assert_eq!(f_sinmxf(1.0), -0.15852901);
102        assert_eq!(f_sinmxf(0.3), -0.004479794);
103        assert_eq!(f_sinmxf(-1.0), 0.15852901);
104        assert_eq!(f_sinmxf(-0.3), 0.004479794);
105        assert_eq!(f_sinmxf(std::f32::consts::PI / 2.), -0.5707964);
106        assert!(f_sinmxf(f32::INFINITY).is_nan());
107        assert!(f_sinmxf(f32::NEG_INFINITY).is_nan());
108        assert!(f_sinmxf(f32::NAN).is_nan());
109    }
110}
pxfm/sin_cosf/sinmxf.rs

pxfm/sin_cosf/
sinmxf.rs
