pxfm/sin_cosf/
secf.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_polyeval6;
31use crate::sin_cosf::sincosf_eval::sincosf_eval;
32
33/// Computes secant ( 1 / cos(x) )
34///
35/// Max found ULP 0.5
36#[inline]
37pub fn f_secf(x: f32) -> f32 {
38    let x_abs = x.to_bits() & 0x7fff_ffffu32;
39    let x = f32::from_bits(x_abs);
40    let xd = x as f64;
41
42    // |x| <= pi/16
43    if x_abs <= 0x3e49_0fdbu32 {
44        // |x| < 0.000244141
45        if x_abs < 0x3980_0000u32 {
46            // taylor series for sec(x) ~ 1 + x^2/2 + O(x^4)
47            // for such small interval just doing 2 first coefficients from taylor series
48            // FMA availability is mandatory to perform it in f32 without upcasting to f64.
49            #[cfg(any(
50                all(
51                    any(target_arch = "x86", target_arch = "x86_64"),
52                    target_feature = "fma"
53                ),
54                all(target_arch = "aarch64", target_feature = "neon")
55            ))]
56            {
57                use crate::common::f_fmlaf;
58                return f_fmlaf(x, x * f32::from_bits(0x3f000000), 1.);
59            }
60            #[cfg(not(any(
61                all(
62                    any(target_arch = "x86", target_arch = "x86_64"),
63                    target_feature = "fma"
64                ),
65                all(target_arch = "aarch64", target_feature = "neon")
66            )))]
67            {
68                let x2 = xd * xd;
69                return f_fmla(x2, f64::from_bits(0x3fe0000000000000), 1.) as f32;
70            }
71        }
72
73        // Secant
74        // Generated poly by Sollya:
75        // f = 1 / cos(x);
76        // d = [0.000244141; pi/16];
77        // pf = fpminimax(f, [|0, 2, 4, 6, 8, 10|], [|1, D...|], d, relative, floating);
78        //
79        // See ./notes/secf.sollya
80
81        let x2 = xd * xd;
82        let p = f_polyeval6(
83            x2,
84            f64::from_bits(0x3ff0000000000000),
85            f64::from_bits(0x3fe000000001c0fb),
86            f64::from_bits(0x3fcaaaaaa0b8a71b),
87            f64::from_bits(0x3fb5b06437bc5a13),
88            f64::from_bits(0x3fa192a33a9fca4f),
89            f64::from_bits(0x3f8dde280c29af37),
90        );
91        return p as f32;
92    }
93
94    if x_abs >= 0x7f80_0000u32 {
95        return x + f32::NAN;
96    }
97
98    // Formula:
99    //   cos(x) = cos((k + y)*pi/32)
100    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
101    // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
102    // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
103    // computed using degree-7 and degree-6 minimax polynomials generated by
104    // Sollya respectively.
105    // Combine the results with the sine of sum formula:
106    //   cos(x) = cos((k + y)*pi/32)
107    //          = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
108    //          = cosm1_y * cos_k + sin_y * sin_k
109    //          = (cosm1_y * cos_k + cos_k) + sin_y * sin_k
110    // then sec(x) = 1/cos(x)
111
112    let rs = sincosf_eval(xd, x_abs);
113    (1. / f_fmla(rs.sin_y, -rs.sin_k, f_fmla(rs.cosm1_y, rs.cos_k, rs.cos_k))) as f32
114}
115
116#[cfg(test)]
117mod tests {
118    use super::*;
119
120    #[test]
121    fn test_f_secf() {
122        assert_eq!(f_secf(0.0), 1.0);
123        assert_eq!(f_secf(0.5), 1.139494);
124        assert_eq!(f_secf(-0.5), 1.139494);
125        assert_eq!(f_secf(1.5), 14.136833);
126        assert_eq!(f_secf(-1.5), 14.136833);
127        assert!(f_secf(f32::INFINITY).is_nan());
128        assert!(f_secf(f32::NEG_INFINITY).is_nan());
129        assert!(f_secf(f32::NAN).is_nan());
130    }
131}
pxfm/sin_cosf/secf.rs

pxfm/sin_cosf/
secf.rs
