pxfm/sin_cosf/
cosm1f.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_polyeval4;
31use crate::sin_cosf::sincosf_eval::sincosf_eval;
32
33/// Computes cos(x) - 1
34///
35/// ULP 0.5
36pub fn f_cosm1f(x: f32) -> f32 {
37    let x_abs = x.to_bits() & 0x7fff_ffffu32;
38    let x = f32::from_bits(x_abs);
39
40    // |x| <= pi/16
41    if x_abs <= 0x3e49_0fdbu32 {
42        let xd = x as f64;
43        // |x| < 0.000244141
44        if x_abs < 0x3980_0000u32 {
45            // Taylor expansion for small cos(x) - 1 ~ -x^2/2 + x^4/24 + O(x^6)
46            let x_sqr = xd * xd;
47            const R: f64 = 1. / 2.;
48            return (-x_sqr * R) as f32;
49        }
50
51        // Cosine
52        // Generated poly by Sollya:
53        // Polynomial cos(x) - 1 = x^2 * P(x^2)
54        //
55        // d = [0.0000000000001, pi/16];
56        // f_cosm1 = cos(x) - 1;
57        // Q = fpminimax(f_cosm1, [|2,4,6,8|], [|0, D...|], d);
58
59        let x2 = xd * xd;
60        let p = f_polyeval4(
61            x2,
62            f64::from_bits(0xbfe0000000000000),
63            f64::from_bits(0x3fa55555554ed21a),
64            f64::from_bits(0xbf56c16b981a61d0),
65            f64::from_bits(0x3ef9fc205e761f45),
66        );
67        return (p * x2) as f32;
68    }
69
70    if x_abs >= 0x7f80_0000u32 {
71        return x + f32::NAN;
72    }
73
74    // cos(x) - 1 = -2*sin^2(x/2)
75    // Hence we're computing sin using formula:
76    //   sin(x) = sin((k + y)*pi/32)
77    //          = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
78    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
79    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
80    // computed using degree-7 and degree-6 minimax polynomials generated by
81    // Sollya respectively.
82
83    let x_abs = (x * 0.5).to_bits();
84    let xd = f32::from_bits(x_abs) as f64;
85
86    let rs = sincosf_eval(xd, x_abs);
87    let sin_x_over_2 = f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k));
88    let sin_sqr = sin_x_over_2 * sin_x_over_2;
89    let cosm1x = -2. * sin_sqr;
90    cosm1x as f32
91}
92
93#[cfg(test)]
94mod tests {
95    use super::*;
96
97    #[test]
98    fn f_cosm1f_test() {
99        assert_eq!(f_cosm1f(0.00015928394), -1.2685687e-8);
100        assert_eq!(f_cosm1f(0.0), 0.0);
101        assert_eq!(f_cosm1f(std::f32::consts::PI), -2.);
102        assert_eq!(f_cosm1f(0.5), -0.122417435);
103        assert_eq!(f_cosm1f(0.7), -0.2351578);
104        assert_eq!(f_cosm1f(1.7), -1.1288445);
105        assert!(f_cosm1f(f32::INFINITY).is_nan());
106        assert!(f_cosm1f(f32::NEG_INFINITY).is_nan());
107        assert!(f_cosm1f(f32::NAN).is_nan());
108        assert_eq!(f_cosm1f(0.0002480338), -3.076038e-8);
109    }
110}
pxfm/sin_cosf/cosm1f.rs

pxfm/sin_cosf/
cosm1f.rs
