pxfm/sin_cosf/cscf.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_polyeval3, f_polyeval5};
31use crate::sin_cosf::sincosf_eval::sincosf_eval;
32
33#[inline(always)]
34fn cscf_gen_impl(x: f32) -> f32 {
35 let x_abs = x.to_bits() & 0x7fff_ffffu32;
36 let xd = x as f64;
37
38 // |x| <= pi/16
39 if x_abs <= 0x3e49_0fdbu32 {
40 // |x| < 0.000443633
41 if x_abs < 0x39e8_9769u32 {
42 if x_abs == 0u32 {
43 // For signed zeros.
44 return if x.is_sign_negative() {
45 f32::NEG_INFINITY
46 } else {
47 f32::INFINITY
48 };
49 }
50 let dx = x as f64;
51 let c_term = 1. / dx;
52 let x2 = dx * dx;
53 // Maclaurin series
54 // 1/x + x/6 + (7 x^3)/360 + (31 x^5)/15120 + O(x^7)
55 let p = f_polyeval3(
56 x2,
57 f64::from_bits(0x3fc5555555555555),
58 f64::from_bits(0x3f93e93e93e93e94),
59 f64::from_bits(0x3f60b2463814bc5f),
60 );
61 return f_fmla(dx, p, c_term) as f32;
62 }
63
64 let xsqr = xd * xd;
65
66 /*
67 Generated by Sollya:
68 f = 1 / sin(x) - 1/x;
69
70 d = [0.000443633; pi/16];
71 pf = fpminimax(f, [|1, 3, 5, 7, 9|], [|D...|], d, relative, floating);
72
73 See ./notes/cscf.sollya
74 */
75
76 let p = f_polyeval5(
77 xsqr,
78 f64::from_bits(0x3fc5555555555562),
79 f64::from_bits(0x3f93e93e93e730a3),
80 f64::from_bits(0x3f60cbb77382ae6f),
81 f64::from_bits(0x3f2b85bfd4188934),
82 f64::from_bits(0x3ef697a32ebe822d),
83 );
84 return f_fmla(xd, p, 1. / xd) as f32;
85 }
86
87 if x_abs >= 0x7f80_0000u32 {
88 return x + f32::NAN;
89 }
90
91 // Formula:
92 // sin(x) = sin((k + y)*pi/32)
93 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
94 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
95 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
96 // computed using degree-7 and degree-6 minimax polynomials generated by
97 // Sollya respectively.
98
99 let rs = sincosf_eval(xd, x_abs);
100 (1. / f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k))) as f32
101}
102
103#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
104#[target_feature(enable = "avx", enable = "fma")]
105unsafe fn cscf_fma_impl(x: f32) -> f32 {
106 let x_abs = x.to_bits() & 0x7fff_ffffu32;
107 let xd = x as f64;
108
109 // |x| <= pi/16
110 if x_abs <= 0x3e49_0fdbu32 {
111 // |x| < 0.000443633
112 if x_abs < 0x39e8_9769u32 {
113 if x_abs == 0u32 {
114 // For signed zeros.
115 return if x.is_sign_negative() {
116 f32::NEG_INFINITY
117 } else {
118 f32::INFINITY
119 };
120 }
121 let dx = x as f64;
122 let c_term = 1. / dx;
123 let x2 = dx * dx;
124 // Maclaurin series
125 // 1/x + x/6 + (7 x^3)/360 + (31 x^5)/15120 + O(x^7)
126 use crate::polyeval::d_polyeval3;
127 let p = d_polyeval3(
128 x2,
129 f64::from_bits(0x3fc5555555555555),
130 f64::from_bits(0x3f93e93e93e93e94),
131 f64::from_bits(0x3f60b2463814bc5f),
132 );
133 return f64::mul_add(dx, p, c_term) as f32;
134 }
135
136 let xsqr = xd * xd;
137
138 /*
139 Generated by Sollya:
140 f = 1 / sin(x) - 1/x;
141
142 d = [0.000443633; pi/16];
143 pf = fpminimax(f, [|1, 3, 5, 7, 9|], [|D...|], d, relative, floating);
144
145 See ./notes/cscf.sollya
146 */
147 use crate::polyeval::d_polyeval5;
148 let p = d_polyeval5(
149 xsqr,
150 f64::from_bits(0x3fc5555555555562),
151 f64::from_bits(0x3f93e93e93e730a3),
152 f64::from_bits(0x3f60cbb77382ae6f),
153 f64::from_bits(0x3f2b85bfd4188934),
154 f64::from_bits(0x3ef697a32ebe822d),
155 );
156 return f64::mul_add(xd, p, 1. / xd) as f32;
157 }
158
159 if x_abs >= 0x7f80_0000u32 {
160 return x + f32::NAN;
161 }
162
163 // Formula:
164 // sin(x) = sin((k + y)*pi/32)
165 // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
166 // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
167 // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
168 // computed using degree-7 and degree-6 minimax polynomials generated by
169 // Sollya respectively.
170 use crate::sin_cosf::sincosf_eval::sincosf_eval_fma;
171 let rs = sincosf_eval_fma(xd, x_abs);
172 (1. / f64::mul_add(
173 rs.sin_y,
174 rs.cos_k,
175 f64::mul_add(rs.cosm1_y, rs.sin_k, rs.sin_k),
176 )) as f32
177}
178
179/// Cosecant ( 1 / sin(x) )
180///
181/// ULP 0.5
182#[inline]
183pub fn f_cscf(x: f32) -> f32 {
184 #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
185 {
186 cscf_gen_impl(x)
187 }
188 #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
189 {
190 use std::sync::OnceLock;
191 static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
192 let q = EXECUTOR.get_or_init(|| {
193 if std::arch::is_x86_feature_detected!("avx")
194 && std::arch::is_x86_feature_detected!("fma")
195 {
196 cscf_fma_impl
197 } else {
198 cscf_gen_impl
199 }
200 });
201 unsafe { q(x) }
202 }
203}
204
205#[cfg(test)]
206mod tests {
207 use super::*;
208
209 #[test]
210 fn f_cscf_test() {
211 assert_eq!(f_cscf(0.04915107), 20.353632);
212 assert_eq!(f_cscf(0.5), 2.0858297);
213 assert_eq!(f_cscf(0.07), 14.297387);
214 assert_eq!(f_cscf(3.6171106e-5), 27646.375);
215 assert_eq!(f_cscf(-5.535772e-10), -1806432800.0);
216 assert_eq!(f_cscf(0.0), f32::INFINITY);
217 assert_eq!(f_cscf(-0.0), f32::NEG_INFINITY);
218 assert_eq!(f_cscf(-1.0854926e-19), -9.2124077e18);
219 }
220}