pxfm/sin_cosf/
cosf.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#[inline(always)]
34fn cosf_gen_impl(x: f32) -> f32 {
35    let x_abs = x.to_bits() & 0x7fff_ffffu32;
36    let x = f32::from_bits(x_abs);
37    let xd = x as f64;
38
39    // |x| <= pi/16
40    if x_abs <= 0x3e49_0fdbu32 {
41        // |x| < 0.000244141
42        if x_abs < 0x3980_0000u32 {
43            #[cfg(any(
44                all(
45                    any(target_arch = "x86", target_arch = "x86_64"),
46                    target_feature = "fma"
47                ),
48                target_arch = "aarch64"
49            ))]
50            {
51                use crate::common::f_fmlaf;
52                return f_fmlaf(x, f32::from_bits(0xb3000000), 1.);
53            }
54            #[cfg(not(any(
55                all(
56                    any(target_arch = "x86", target_arch = "x86_64"),
57                    target_feature = "fma"
58                ),
59                target_arch = "aarch64"
60            )))]
61            {
62                return f_fmla(xd, f64::from_bits(0xbe60000000000000), 1.) as f32;
63            }
64        }
65
66        // Cosine
67        // Generated poly by Sollya:
68        // f_cos_16 = cos(x);
69        //
70        // Q = fpminimax(f_cos_16, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/16]);
71        // See ./notes/cosf.sollya
72
73        let x2 = xd * xd;
74        let p = f_polyeval5(
75            x2,
76            f64::from_bits(0x3ff0000000000000),
77            f64::from_bits(0xbfdffffffffffcea),
78            f64::from_bits(0x3fa55555553d611a),
79            f64::from_bits(0xbf56c16b2e26561a),
80            f64::from_bits(0x3ef9faa67b9da80b),
81        );
82        return p as f32;
83    }
84
85    if x_abs >= 0x7f80_0000u32 {
86        return x + f32::NAN;
87    }
88
89    // Formula:
90    //   cos(x) = cos((k + y)*pi/32)
91    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
92    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
93    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
94    // computed using degree-7 and degree-6 minimax polynomials generated by
95    // Sollya respectively.
96    // Combine the results with the sine of sum formula:
97    //   cos(x) = cos((k + y)*pi/32)
98    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
99    //          = cosm1_y * cos_k + sin_y * sin_k
100    //          = (cosm1_y * cos_k + cos_k) + sin_y * sin_k
101
102    let rs = sincosf_eval(xd, x_abs);
103    f_fmla(rs.sin_y, -rs.sin_k, f_fmla(rs.cosm1_y, rs.cos_k, rs.cos_k)) as f32
104}
105
106#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
107#[target_feature(enable = "avx", enable = "fma")]
108unsafe fn cosf_fma_impl(x: f32) -> f32 {
109    let x_abs = x.to_bits() & 0x7fff_ffffu32;
110    let x = f32::from_bits(x_abs);
111    let xd = x as f64;
112
113    // |x| <= pi/16
114    if x_abs <= 0x3e49_0fdbu32 {
115        // |x| < 0.000244141
116        if x_abs < 0x3980_0000u32 {
117            return f32::mul_add(x, f32::from_bits(0xb3000000), 1.);
118        }
119
120        // Cosine
121        // Generated poly by Sollya:
122        // f_cos_16 = cos(x);
123        //
124        // Q = fpminimax(f_cos_16, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/16]);
125        // See ./notes/cosf.sollya
126
127        let x2 = xd * xd;
128        use crate::polyeval::d_polyeval5;
129        let p = d_polyeval5(
130            x2,
131            f64::from_bits(0x3ff0000000000000),
132            f64::from_bits(0xbfdffffffffffcea),
133            f64::from_bits(0x3fa55555553d611a),
134            f64::from_bits(0xbf56c16b2e26561a),
135            f64::from_bits(0x3ef9faa67b9da80b),
136        );
137        return p as f32;
138    }
139
140    if x_abs >= 0x7f80_0000u32 {
141        return x + f32::NAN;
142    }
143
144    // Formula:
145    //   cos(x) = cos((k + y)*pi/32)
146    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
147    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
148    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
149    // computed using degree-7 and degree-6 minimax polynomials generated by
150    // Sollya respectively.
151    // Combine the results with the sine of sum formula:
152    //   cos(x) = cos((k + y)*pi/32)
153    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
154    //          = cosm1_y * cos_k + sin_y * sin_k
155    //          = (cosm1_y * cos_k + cos_k) + sin_y * sin_k
156    use crate::sin_cosf::sincosf_eval::sincosf_eval_fma;
157    let rs = sincosf_eval_fma(xd, x_abs);
158    f64::mul_add(
159        rs.sin_y,
160        -rs.sin_k,
161        f64::mul_add(rs.cosm1_y, rs.cos_k, rs.cos_k),
162    ) as f32
163}
164
165/// Computes cosine function
166///
167/// ULP 0.5
168///
169#[inline]
170pub fn f_cosf(x: f32) -> f32 {
171    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
172    {
173        cosf_gen_impl(x)
174    }
175    #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
176    {
177        use std::sync::OnceLock;
178        static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
179        let q = EXECUTOR.get_or_init(|| {
180            if std::arch::is_x86_feature_detected!("avx")
181                && std::arch::is_x86_feature_detected!("fma")
182            {
183                cosf_fma_impl
184            } else {
185                cosf_gen_impl
186            }
187        });
188        unsafe { q(x) }
189    }
190}
191
192#[cfg(test)]
193mod tests {
194    use super::*;
195
196    #[test]
197    fn f_cosf_test() {
198        assert_eq!(f_cosf(0.0), 1.0);
199        assert_eq!(f_cosf(std::f32::consts::PI), -1f32);
200        assert_eq!(f_cosf(0.5), 0.87758255);
201        assert_eq!(f_cosf(0.7), 0.7648422);
202        assert_eq!(f_cosf(1.7), -0.12884454);
203        assert!(f_cosf(f32::INFINITY).is_nan());
204        assert!(f_cosf(f32::NEG_INFINITY).is_nan());
205        assert!(f_cosf(f32::NAN).is_nan());
206        assert_eq!(f_cosf(0.0002480338), 0.9999999692396206);
207    }
208}
pxfm/sin_cosf/cosf.rs

pxfm/sin_cosf/
cosf.rs
