pxfm/tangent/
tanf.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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::tangent::evalf::tanf_eval;
32
33/// Computes tan
34///
35/// Max found ULP 0.4999999
36#[inline]
37pub fn f_tanf(x: f32) -> f32 {
38    let x_abs = x.to_bits() & 0x7fff_ffffu32;
39    let xd = x as f64;
40
41    // |x| < pi/32
42    if x_abs <= 0x3dc9_0fdbu32 {
43        // |x| < 0.000244141
44        if x_abs < 0x3980_0000u32 {
45            if x_abs == 0 {
46                return x;
47            }
48
49            // When |x| < 2^-12, the relative error of the approximation tan(x) ~ x
50            // is:
51            //   |tan(x) - x| / |tan(x)| < |x^3| / (3|x|)
52            //                           = x^2 / 3
53            //                           < 2^-25
54            //                           < epsilon(1)/2.
55            #[cfg(any(
56                all(
57                    any(target_arch = "x86", target_arch = "x86_64"),
58                    target_feature = "fma"
59                ),
60                all(target_arch = "aarch64", target_feature = "neon")
61            ))]
62            {
63                use crate::common::f_fmlaf;
64                return f_fmlaf(x, f32::from_bits(0xb3000000), x);
65            }
66            #[cfg(not(any(
67                all(
68                    any(target_arch = "x86", target_arch = "x86_64"),
69                    target_feature = "fma"
70                ),
71                all(target_arch = "aarch64", target_feature = "neon")
72            )))]
73            {
74                return f_fmla(xd, f64::from_bits(0xbe60000000000000), xd) as f32;
75            }
76        }
77
78        let xsqr = xd * xd;
79
80        /*
81           Generated by Sollya:
82           f_tan = tan(x)/x;
83           Q = fpminimax(f_tan, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/32]);
84
85           See ./notes/tanf_at_zero.sollya
86        */
87        let p = f_polyeval5(
88            xsqr,
89            f64::from_bits(0x3ff0000000000000),
90            f64::from_bits(0x3fd555555553d022),
91            f64::from_bits(0x3fc111111ce442c1),
92            f64::from_bits(0x3faba180a6bbdecd),
93            f64::from_bits(0x3f969c0a88a0b71f),
94        );
95        return (xd * p) as f32;
96    }
97
98    if x_abs >= 0x7f80_0000u32 {
99        return x + f32::NAN;
100    }
101
102    // For |x| >= pi/32, we use the definition of tan(x) function:
103    // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
104    // tanf_eval returns:
105    // - rs.tan_y = tan(pi/32 * y)          -> tangent of the remainder
106    // - rs.tan_k = tan(pi/32 * k)          -> tan of the main angle multiple
107    let rs = tanf_eval(xd, x_abs);
108
109    // Then computing tan through identities
110    // num = tan(k*pi/32) + tan(y*pi/32)
111    let num = rs.tan_y + rs.tan_k;
112    // den = 1 - tan(k*pi/32) * tan(y*pi/32)
113    let den = f_fmla(rs.tan_y, -rs.tan_k, 1.);
114    (num / den) as f32
115}
116
117#[cfg(test)]
118mod tests {
119    use super::*;
120
121    #[test]
122    fn f_tanf_test() {
123        assert_eq!(f_tanf(0.0), 0.0);
124        assert_eq!(f_tanf(1.0), 1.5574077);
125        assert_eq!(f_tanf(-1.0), -1.5574077);
126        assert_eq!(f_tanf(10.0), 0.64836085);
127        assert_eq!(f_tanf(-10.0), -0.64836085);
128    }
129}
pxfm/tangent/tanf.rs

pxfm/tangent/
tanf.rs
