pxfm/sin_cosf/
sincpif.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 9/2025. 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, is_integerf};
30use crate::polyeval::f_polyeval5;
31use crate::sin_cosf::sincosf_eval::sincospif_eval;
32
33#[inline(always)]
34fn sincpif_gen_impl(x: f32) -> f32 {
35    let x_abs = x.to_bits() & 0x7fff_ffffu32;
36    let xd = x as f64;
37
38    if x_abs <= 0x3d80_0000u32 {
39        // |x| <= 1/16
40        if x_abs < 0x3580_2126u32 {
41            // |x| < 0.0000009546391
42            if x_abs == 0u32 {
43                // Signed zeros.
44                return 1.;
45            }
46
47            // Small values approximated with Taylor poly
48            // sincpi(x) ~ 1 - x^2*Pi^2/6 + O(x^4)
49            #[cfg(any(
50                all(
51                    any(target_arch = "x86", target_arch = "x86_64"),
52                    target_feature = "fma"
53                ),
54                target_arch = "aarch64"
55            ))]
56            {
57                use crate::common::f_fmlaf;
58                const M_SQR_PI_OVER_6: f32 = f32::from_bits(0xbfd28d33);
59                return f_fmlaf(x, M_SQR_PI_OVER_6 * x, 1.);
60            }
61            #[cfg(not(any(
62                all(
63                    any(target_arch = "x86", target_arch = "x86_64"),
64                    target_feature = "fma"
65                ),
66                target_arch = "aarch64"
67            )))]
68            {
69                const M_SQR_PI_OVER_6: f64 = f64::from_bits(0xbffa51a6625307d3);
70                let x2 = xd * xd;
71                let p = f_fmla(x2, M_SQR_PI_OVER_6, 1.);
72                return p as f32;
73            }
74        }
75
76        let xsqr = xd * xd;
77
78        // Generated by Sollya:
79        // d = [0, 1/16];
80        // f_sincpif = sin(y*pi)/(y*pi);
81        // Q = fpminimax(f_sincpif, [|0, 2, 4, 6, 8|], [|D...|], d, relative, floating);
82        // See ./notes/sincpif.sollya
83        let p = f_polyeval5(
84            xsqr,
85            f64::from_bits(0x3ff0000000000000),
86            f64::from_bits(0xbffa51a662530723),
87            f64::from_bits(0x3fe9f9cb401e8e85),
88            f64::from_bits(0xbfc86a8da89c9234),
89            f64::from_bits(0x3f9ac0a16798157e),
90        );
91        return p as f32;
92    }
93
94    // Numbers greater or equal to 2^23 are always integers or NaN
95    // integers are always 0
96    if x_abs >= 0x4b00_0000u32 || is_integerf(x) {
97        if x_abs >= 0x7f80_0000u32 {
98            return x + f32::NAN;
99        }
100        return if x.is_sign_negative() { -0. } else { 0. };
101    }
102
103    const PI: f64 = f64::from_bits(0x400921fb54442d18);
104    let rs = sincospif_eval(xd);
105    let sf = f_fmla(rs.sin_y, rs.cos_k, f_fmla(rs.cosm1_y, rs.sin_k, rs.sin_k));
106    (sf / (PI * xd)) as f32
107}
108
109#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
110#[target_feature(enable = "avx", enable = "fma")]
111unsafe fn sincpif_fma_impl(x: f32) -> f32 {
112    let x_abs = x.to_bits() & 0x7fff_ffffu32;
113    let xd = x as f64;
114
115    if x_abs <= 0x3d80_0000u32 {
116        // |x| <= 1/16
117        if x_abs < 0x3580_2126u32 {
118            // |x| < 0.0000009546391
119            if x_abs == 0u32 {
120                // Signed zeros.
121                return 1.;
122            }
123
124            // Small values approximated with Taylor poly
125            // sincpi(x) ~ 1 - x^2*Pi^2/6 + O(x^4)
126            const M_SQR_PI_OVER_6: f32 = f32::from_bits(0xbfd28d33);
127            return f32::mul_add(x, M_SQR_PI_OVER_6 * x, 1.);
128        }
129
130        let xsqr = xd * xd;
131
132        // Generated by Sollya:
133        // d = [0, 1/16];
134        // f_sincpif = sin(y*pi)/(y*pi);
135        // Q = fpminimax(f_sincpif, [|0, 2, 4, 6, 8|], [|D...|], d, relative, floating);
136        // See ./notes/sincpif.sollya
137        use crate::polyeval::d_polyeval5;
138        let p = d_polyeval5(
139            xsqr,
140            f64::from_bits(0x3ff0000000000000),
141            f64::from_bits(0xbffa51a662530723),
142            f64::from_bits(0x3fe9f9cb401e8e85),
143            f64::from_bits(0xbfc86a8da89c9234),
144            f64::from_bits(0x3f9ac0a16798157e),
145        );
146        return p as f32;
147    }
148
149    // Numbers greater or equal to 2^23 are always integers or NaN
150    // integers are always 0
151    if x_abs >= 0x4b00_0000u32 || x == x.round_ties_even() {
152        if x_abs >= 0x7f80_0000u32 {
153            return x + f32::NAN;
154        }
155        return if x.is_sign_negative() { -0. } else { 0. };
156    }
157
158    const PI: f64 = f64::from_bits(0x400921fb54442d18);
159    use crate::sin_cosf::sincosf_eval::sincospif_eval_fma;
160    let rs = sincospif_eval_fma(xd);
161    let sf = f64::mul_add(
162        rs.sin_y,
163        rs.cos_k,
164        f64::mul_add(rs.cosm1_y, rs.sin_k, rs.sin_k),
165    );
166    (sf / (PI * xd)) as f32
167}
168
169/// Computes sin(PI\*x)/(PI\*x)
170///
171/// Produces normalized sinc.
172///
173/// ulp 0.5
174pub fn f_sincpif(x: f32) -> f32 {
175    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
176    {
177        sincpif_gen_impl(x)
178    }
179    #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
180    {
181        use std::sync::OnceLock;
182        static EXECUTOR: OnceLock<unsafe fn(f32) -> f32> = OnceLock::new();
183        let q = EXECUTOR.get_or_init(|| {
184            if std::arch::is_x86_feature_detected!("avx")
185                && std::arch::is_x86_feature_detected!("fma")
186            {
187                sincpif_fma_impl
188            } else {
189                sincpif_gen_impl
190            }
191        });
192        unsafe { q(x) }
193    }
194}
195
196#[cfg(test)]
197mod tests {
198    use super::*;
199
200    #[test]
201    fn test_sincpif_eval() {
202        assert_eq!(f_sincpif(1.0), 0.);
203        assert_eq!(f_sincpif(2.0), 0.);
204        assert_eq!(f_sincpif(3.0), 0.);
205        assert_eq!(f_sincpif(0.0543242), 0.99515265);
206        assert_eq!(f_sincpif(0.002134242), 0.9999925);
207        assert_eq!(f_sincpif(0.00000005421321), 1.0);
208        assert!(f_sincpif(f32::INFINITY).is_nan());
209        assert!(f_sincpif(f32::NEG_INFINITY).is_nan());
210        assert!(f_sincpif(f32::NAN).is_nan());
211    }
212}
pxfm/sin_cosf/sincpif.rs

pxfm/sin_cosf/
sincpif.rs
