pxfm/
sinmx.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::double_double::DoubleDouble;
31use crate::polyeval::f_estrin_polyeval5;
32use crate::sin::{range_reduction_small, sincos_eval};
33use crate::sin_helper::sincos_eval_dd;
34use crate::sin_table::SIN_K_PI_OVER_128;
35use crate::sincos_reduce::LargeArgumentReduction;
36
37#[cold]
38#[inline(never)]
39fn sinmx_accurate(y: DoubleDouble, sin_k: DoubleDouble, cos_k: DoubleDouble, x: f64) -> f64 {
40    let r_sincos = sincos_eval_dd(y);
41
42    // k is an integer and -pi / 256 <= y <= pi / 256.
43    // Then sin(x) = sin((k * pi/128 + y)
44    //             = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)
45
46    let sin_k_cos_y = DoubleDouble::quick_mult(r_sincos.v_cos, sin_k);
47    let cos_k_sin_y = DoubleDouble::quick_mult(r_sincos.v_sin, cos_k);
48
49    let mut rr = DoubleDouble::full_dd_add(sin_k_cos_y, cos_k_sin_y);
50    rr = DoubleDouble::full_add_f64(rr, -x);
51    rr.to_f64()
52}
53
54#[cold]
55fn sinmx_near_zero_hard(x: f64) -> f64 {
56    const C: [(u64, u64); 8] = [
57        (0xb37137ef120d4bbd, 0xb6db8d4e2aa9f813),
58        (0xbc6555555554e720, 0xbfc5555555555555),
59        (0x3c01110fff8e3ea0, 0x3f81111111111111),
60        (0xbb6314569388b856, 0xbf2a01a01a01a01a),
61        (0xbb61f946e615f3cd, 0x3ec71de3a556c723),
62        (0x3a8998bc94bd3bf0, 0xbe5ae64567f2d4df),
63        (0xba702e73490290eb, 0x3de61245e54b6747),
64        (0xba0182df5b1ffd4c, 0xbd6ae4894bb27213),
65    ];
66    let x2 = DoubleDouble::from_exact_mult(x, x);
67    let mut p = DoubleDouble::mul_add(
68        x2,
69        DoubleDouble::from_bit_pair(C[7]),
70        DoubleDouble::from_bit_pair(C[6]),
71    );
72    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[5]));
73    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[4]));
74    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[3]));
75    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[2]));
76    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[1]));
77    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[0]));
78    p = DoubleDouble::quick_mult_f64(p, x);
79    p.to_f64()
80}
81
82/// Computes sin(x) - x
83///
84/// ULP 0.5
85pub fn f_sinmx(x: f64) -> f64 {
86    let x_e = (x.to_bits() >> 52) & 0x7ff;
87    const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;
88
89    let y: DoubleDouble;
90    let k;
91
92    let mut argument_reduction = LargeArgumentReduction::default();
93
94    // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)
95    if x_e < E_BIAS + 16 {
96        if x_e < E_BIAS - 6 {
97            // |x| < 2^-6
98            if x_e < E_BIAS - 32 {
99                // |x| < 2^-32
100                // Signed zeros.
101                if x == 0.0 {
102                    return x;
103                }
104
105                // For |x| < 2^-32, taylor series sin(x) - x ~ -x^3/6
106                let x2 = x * x;
107                let c = f_fmla(
108                    x2,
109                    f64::from_bits(0x3f81111111111111),
110                    f64::from_bits(0xbfc5555555555555),
111                ) * x2;
112                return c * x;
113            }
114
115            // Generated by Sollya:
116            // d = [2^-26, pi/16];
117            // f_sinmx = (sin(x) - x)/x;
118            // Q = fpminimax(f_sinmx, [|0, 2, 4, 6, 8, 10, 12|], [|127, 127, D...|], d);
119            let x2 = DoubleDouble::from_exact_mult(x, x);
120            let p = f_estrin_polyeval5(
121                x2.hi,
122                f64::from_bits(0x3f81111111111111),
123                f64::from_bits(0xbf2a01a01a019d2f),
124                f64::from_bits(0x3ec71de3a5269512),
125                f64::from_bits(0xbe5ae642b76ba0f5),
126                f64::from_bits(0x3de6035da3c7eaed),
127            );
128            let mut c = DoubleDouble::mul_f64_add(
129                x2,
130                p,
131                DoubleDouble::from_bit_pair((0xbc655542976eb2af, 0xbfc5555555555555)),
132            );
133            c = DoubleDouble::mul_add(
134                x2,
135                c,
136                DoubleDouble::from_bit_pair((0x34b215c35dc9e9be, 0xb832bde584573661)),
137            );
138            c = DoubleDouble::quick_mult_f64(c, x);
139            let err = f_fmla(
140                x2.hi,
141                f64::from_bits(0x3cc0000000000000), // 2^-51
142                f64::from_bits(0x3bc0000000000000), // 2^-67
143            );
144            let ub = c.hi + (c.lo + err);
145            let lb = c.hi + (c.lo - err);
146            if ub == lb {
147                return c.to_f64();
148            }
149            return sinmx_near_zero_hard(x);
150        }
151        // // Small range reduction.
152        (y, k) = range_reduction_small(x);
153    } else {
154        // Inf or NaN
155        if x_e > 2 * E_BIAS {
156            // sin(+-Inf) = NaN
157            return x + f64::NAN;
158        }
159
160        // Large range reduction.
161        (k, y) = argument_reduction.reduce(x);
162    }
163
164    let r_sincos = sincos_eval(y);
165
166    // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).
167    let sk = SIN_K_PI_OVER_128[(k & 255) as usize];
168    let ck = SIN_K_PI_OVER_128[((k.wrapping_add(64)) & 255) as usize];
169
170    let sin_k = DoubleDouble::from_bit_pair(sk);
171    let cos_k = DoubleDouble::from_bit_pair(ck);
172
173    let sin_k_cos_y = DoubleDouble::quick_mult(r_sincos.v_cos, sin_k);
174    let cos_k_sin_y = DoubleDouble::quick_mult(r_sincos.v_sin, cos_k);
175
176    // sin_k_cos_y is always >> cos_k_sin_y
177    let mut rr = DoubleDouble::from_exact_add(sin_k_cos_y.hi, cos_k_sin_y.hi);
178    rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;
179
180    rr = DoubleDouble::from_exact_add(rr.hi, rr.lo);
181    rr = DoubleDouble::full_add_f64(rr, -x);
182
183    let rlp = rr.lo + r_sincos.err;
184    let rlm = rr.lo - r_sincos.err;
185
186    let r_upper = rr.hi + rlp; // (rr.lo + ERR);
187    let r_lower = rr.hi + rlm; // (rr.lo - ERR);
188
189    // Ziv's accuracy test
190    if r_upper == r_lower {
191        return rr.to_f64();
192    }
193
194    sinmx_accurate(y, sin_k, cos_k, x)
195}
196
197#[cfg(test)]
198mod tests {
199    use super::*;
200
201    #[test]
202    fn f_sinf_test() {
203        assert_eq!(f_sinmx(0.0), 0.0);
204        assert_eq!(f_sinmx(1.0), -0.1585290151921035);
205        assert_eq!(f_sinmx(0.3), -0.0044797933386604245);
206        assert_eq!(f_sinmx(-1.0), 0.1585290151921035);
207        assert_eq!(f_sinmx(-0.3), 0.0044797933386604245);
208        assert_eq!(f_sinmx(std::f64::consts::PI / 2.), -0.5707963267948966);
209        assert!(f_sinmx(f64::INFINITY).is_nan());
210        assert!(f_sinmx(f64::NEG_INFINITY).is_nan());
211    }
212}
pxfm/sinmx.rs

pxfm/
sinmx.rs
