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#[inline(always)]
34fn tanf_gen_impl(x: f32) -> f32 {
35 let x_abs = x.to_bits() & 0x7fff_ffffu32;
36 let xd = x as f64;
37
38 // |x| < pi/32
39 if x_abs <= 0x3dc9_0fdbu32 {
40 // |x| < 0.000244141
41 if x_abs < 0x3980_0000u32 {
42 if x_abs == 0 {
43 return x;
44 }
45
46 // When |x| < 2^-12, the relative error of the approximation tan(x) ~ x
47 // is:
48 // |tan(x) - x| / |tan(x)| < |x^3| / (3|x|)
49 // = x^2 / 3
50 // < 2^-25
51 // < epsilon(1)/2.
52 #[cfg(any(
53 all(
54 any(target_arch = "x86", target_arch = "x86_64"),
55 target_feature = "fma"
56 ),
57 target_arch = "aarch64"
58 ))]
59 {
60 use crate::common::f_fmlaf;
61 return f_fmlaf(x, f32::from_bits(0xb3000000), x);
62 }
63 #[cfg(not(any(
64 all(
65 any(target_arch = "x86", target_arch = "x86_64"),
66 target_feature = "fma"
67 ),
68 target_arch = "aarch64"
69 )))]
70 {
71 return f_fmla(xd, f64::from_bits(0xbe60000000000000), xd) as f32;
72 }
73 }
74
75 let xsqr = xd * xd;
76
77 /*
78 Generated by Sollya:
79 f_tan = tan(x)/x;
80 Q = fpminimax(f_tan, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/32]);
81
82 See ./notes/tanf_at_zero.sollya
83 */
84 let p = f_polyeval5(
85 xsqr,
86 f64::from_bits(0x3ff0000000000000),
87 f64::from_bits(0x3fd555555553d022),
88 f64::from_bits(0x3fc111111ce442c1),
89 f64::from_bits(0x3faba180a6bbdecd),
90 f64::from_bits(0x3f969c0a88a0b71f),
91 );
92 return (xd * p) as f32;
93 }
94
95 if x_abs >= 0x7f80_0000u32 {
96 return x + f32::NAN;
97 }
98
99 // For |x| >= pi/32, we use the definition of tan(x) function:
100 // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
101 // tanf_eval returns:
102 // - rs.tan_y = tan(pi/32 * y) -> tangent of the remainder
103 // - rs.tan_k = tan(pi/32 * k) -> tan of the main angle multiple
104 let rs = tanf_eval(xd, x_abs);
105
106 // Then computing tan through identities
107 // num = tan(k*pi/32) + tan(y*pi/32)
108 let num = rs.tan_y + rs.tan_k;
109 // den = 1 - tan(k*pi/32) * tan(y*pi/32)
110 let den = f_fmla(rs.tan_y, -rs.tan_k, 1.);
111 (num / den) as f32
112}
113
114#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
115#[target_feature(enable = "avx", enable = "fma")]
116unsafe fn tanf_fma_impl(x: f32) -> f32 {
117 let x_abs = x.to_bits() & 0x7fff_ffffu32;
118 let xd = x as f64;
119
120 // |x| < pi/32
121 if x_abs <= 0x3dc9_0fdbu32 {
122 // |x| < 0.000244141
123 if x_abs < 0x3980_0000u32 {
124 if x_abs == 0 {
125 return x;
126 }
127
128 // When |x| < 2^-12, the relative error of the approximation tan(x) ~ x
129 // is:
130 // |tan(x) - x| / |tan(x)| < |x^3| / (3|x|)
131 // = x^2 / 3
132 // < 2^-25
133 // < epsilon(1)/2.
134 return f32::mul_add(x, f32::from_bits(0xb3000000), x);
135 }
136
137 let xsqr = xd * xd;
138
139 /*
140 Generated by Sollya:
141 f_tan = tan(x)/x;
142 Q = fpminimax(f_tan, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/32]);
143
144 See ./notes/tanf_at_zero.sollya
145 */
146 use crate::polyeval::d_polyeval5;
147 let p = d_polyeval5(
148 xsqr,
149 f64::from_bits(0x3ff0000000000000),
150 f64::from_bits(0x3fd555555553d022),
151 f64::from_bits(0x3fc111111ce442c1),
152 f64::from_bits(0x3faba180a6bbdecd),
153 f64::from_bits(0x3f969c0a88a0b71f),
154 );
155 return (xd * p) as f32;
156 }
157
158 if x_abs >= 0x7f80_0000u32 {
159 return x + f32::NAN;
160 }
161
162 // For |x| >= pi/32, we use the definition of tan(x) function:
163 // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
164 // tanf_eval returns:
165 // - rs.tan_y = tan(pi/32 * y) -> tangent of the remainder
166 // - rs.tan_k = tan(pi/32 * k) -> tan of the main angle multiple
167 use crate::tangent::evalf::tanf_eval_fma;
168 let rs = tanf_eval_fma(xd, x_abs);
169
170 // Then computing tan through identities
171 // num = tan(k*pi/32) + tan(y*pi/32)
172 let num = rs.tan_y + rs.tan_k;
173 // den = 1 - tan(k*pi/32) * tan(y*pi/32)
174 let den = f64::mul_add(rs.tan_y, -rs.tan_k, 1.);
175 (num / den) as f32
176}
177
178/// Computes tan
179///
180/// Max found ULP 0.4999999
181#[inline]
182pub fn f_tanf(x: f32) -> f32 {
183 #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
184 {
185 tanf_gen_impl(x)
186 }
187 #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
188 {
189 use std::sync::OnceLock;
190 static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
191 let q = EXECUTOR.get_or_init(|| {
192 if std::arch::is_x86_feature_detected!("avx")
193 && std::arch::is_x86_feature_detected!("fma")
194 {
195 tanf_fma_impl
196 } else {
197 tanf_gen_impl
198 }
199 });
200 unsafe { q(x) }
201 }
202}
203
204#[cfg(test)]
205mod tests {
206 use super::*;
207
208 #[test]
209 fn f_tanf_test() {
210 assert_eq!(f_tanf(0.0), 0.0);
211 assert_eq!(f_tanf(1.0), 1.5574077);
212 assert_eq!(f_tanf(-1.0), -1.5574077);
213 assert_eq!(f_tanf(10.0), 0.64836085);
214 assert_eq!(f_tanf(-10.0), -0.64836085);
215 }
216}