pxfm/sin_cosf/
cospif.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::{is_integerf, is_odd_integerf};
30use crate::polyeval::f_polyeval5;
31use crate::sin_cosf::argument_reduction_pi::ArgumentReducerPi;
32use crate::sin_cosf::sincosf_eval::{cospif_eval, sinpif_eval};
33
34/// Computes cos(PI*x)
35///
36/// Max ULP 0.5
37#[inline]
38pub fn f_cospif(x: f32) -> f32 {
39    let x_abs = x.to_bits() & 0x7fff_ffffu32;
40    let x = f32::from_bits(x_abs);
41    let xd = x as f64;
42
43    // |x| <= 1/16
44    if x_abs <= 0x3d80_0000u32 {
45        // |x| < 0.00000009546391
46        if x_abs < 0x38a2_f984u32 {
47            #[cfg(any(
48                all(
49                    any(target_arch = "x86", target_arch = "x86_64"),
50                    target_feature = "fma"
51                ),
52                all(target_arch = "aarch64", target_feature = "neon")
53            ))]
54            {
55                use crate::common::f_fmlaf;
56                return f_fmlaf(x, f32::from_bits(0xb3000000), 1.);
57            }
58            #[cfg(not(any(
59                all(
60                    any(target_arch = "x86", target_arch = "x86_64"),
61                    target_feature = "fma"
62                ),
63                all(target_arch = "aarch64", target_feature = "neon")
64            )))]
65            {
66                use crate::common::f_fmla;
67                return f_fmla(xd, f64::from_bits(0xbe60000000000000), 1.) as f32;
68            }
69        }
70
71        // Cos(x*PI)
72        // Generated poly by Sollya:
73        // d = [0, 1/16];
74        // f_cos = cos(y*pi);
75        // Q = fpminimax(f_cos, [|0, 2, 4, 6, 8|], [|D...|], d, relative, floating);
76        //
77        // See ./notes/cospif.sollya
78
79        let x2 = xd * xd;
80        let p = f_polyeval5(
81            x2,
82            f64::from_bits(0x3ff0000000000000),
83            f64::from_bits(0xc013bd3cc9be43f7),
84            f64::from_bits(0x40103c1f08091fe0),
85            f64::from_bits(0xbff55d3ba3d94835),
86            f64::from_bits(0x3fce173c2a00e74e),
87        );
88        return p as f32;
89    }
90
91    // Numbers greater or equal to 2^23 are always integers or NaN
92    if x_abs >= 0x4b00_0000u32 || is_integerf(x) {
93        if x_abs >= 0x7f80_0000u32 {
94            return x + f32::NAN;
95        }
96        if x_abs < 0x4b80_0000u32 {
97            static CF: [f32; 2] = [1., -1.];
98            return CF[is_odd_integerf(x) as usize];
99        }
100        return 1.;
101    }
102
103    // We're computing cos(y) after argument reduction then return valid value
104    // based on quadrant
105    let reducer = ArgumentReducerPi { x: x as f64 };
106    let (y, k) = reducer.reduce_0p25();
107    // Decide based on quadrant what kernel function to use
108    (match k & 3 {
109        0 => cospif_eval(y),
110        1 => sinpif_eval(-y),
111        2 => -cospif_eval(y),
112        _ => sinpif_eval(y),
113    }) as f32
114}
115
116#[cfg(test)]
117mod tests {
118    use super::*;
119
120    #[test]
121    fn test_f_cospif() {
122        assert_eq!(f_cospif(1.), -1.);
123        assert_eq!(f_cospif(-3.5), 0.0);
124        assert_eq!(f_cospif(3.), -1.);
125        assert_eq!(f_cospif(-3.), -1.);
126        assert_eq!(f_cospif(2.), 1.);
127        assert_eq!(f_cospif(-2.), 1.);
128        assert_eq!(f_cospif(115.30706), -0.5696978);
129        assert!(f_cospif(f32::INFINITY).is_nan());
130        assert!(f_cospif(f32::NAN).is_nan());
131        assert!(f_cospif(f32::NEG_INFINITY).is_nan());
132    }
133}
pxfm/sin_cosf/cospif.rs

pxfm/sin_cosf/
cospif.rs
