pxfm/
sincos_dyadic.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::dyadic_float::{DyadicFloat128, DyadicSign};
30use crate::round::RoundFinite;
31use crate::sincos_reduce_tables::ONE_TWENTY_EIGHT_OVER_PI;
32
33pub(crate) fn range_reduction_small_f128(x: f64) -> DyadicFloat128 {
34    const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
35        sign: DyadicSign::Pos,
36        exponent: -133,
37        mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
38    };
39    const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
40    let prod_hi = x * ONE_TWENTY_EIGHT_OVER_PI_D;
41    let kd = prod_hi.round_finite();
42
43    let mk_f128 = DyadicFloat128::new_from_f64(-kd);
44    let x_f128 = DyadicFloat128::new_from_f64(x);
45    let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
46    let p_hi = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
47    let p_mid = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
48    let p_lo = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
49    let s_hi = p_hi.quick_add(&mk_f128);
50    let s_lo = p_mid.quick_add(&p_lo);
51    let y = s_hi.quick_add(&s_lo);
52    y.quick_mul(&PI_OVER_128_F128)
53}
54
55pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, i64) {
56    const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
57        sign: DyadicSign::Pos,
58        exponent: -133,
59        mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
60    };
61    const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
62    let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
63    let kd = prod_hi.round_finite();
64
65    let mk_f128 = DyadicFloat128::new_from_f64(-kd);
66    let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
67    let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
68    let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
69    let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
70    let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
71    let s_hi = p_hi.quick_add(&mk_f128);
72    let s_lo = p_mid.quick_add(&p_lo);
73    let y = (s_hi + s_lo) + p_lo_lo;
74    (y.quick_mul(&PI_OVER_128_F128), kd as i64)
75}
76
77// pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, u64) {
78//     const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
79//         sign: DyadicSign::Pos,
80//         exponent: -133,
81//         mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
82//     };
83//     const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
84//     let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
85//     let kd = prod_hi.round();
86//
87//     let mk_f128 = DyadicFloat128::new_from_f64(-kd);
88//     let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
89//     let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
90//     let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
91//     let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
92//     let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
93//     let s_hi = p_hi.quick_add(&mk_f128);
94//     let s_lo = p_mid.quick_add(&p_lo);
95//     let s_lo_lo = p_lo_lo.quick_add(&p_lo_lo);
96//     let y = s_hi.quick_add(&s_lo).quick_add(&s_lo_lo);
97//     (y.quick_mul(&PI_OVER_128_F128), (kd as i64) as u64)
98// }
99
100pub(crate) struct SinCosDyadic {
101    pub(crate) v_sin: DyadicFloat128,
102    pub(crate) v_cos: DyadicFloat128,
103}
104
105#[cold]
106pub(crate) fn sincos_eval_dyadic(u: &DyadicFloat128) -> SinCosDyadic {
107    let u_sq = u.quick_mul(u);
108
109    // sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
110    static SIN_COEFFS: [DyadicFloat128; 7] = [
111        DyadicFloat128 {
112            sign: DyadicSign::Pos,
113            exponent: -127,
114            mantissa: 0x80000000_00000000_00000000_00000000_u128,
115        }, // 1
116        DyadicFloat128 {
117            sign: DyadicSign::Neg,
118            exponent: -130,
119            mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
120        }, // -1/3!
121        DyadicFloat128 {
122            sign: DyadicSign::Pos,
123            exponent: -134,
124            mantissa: 0x88888888_88888888_88888888_88888889_u128,
125        }, // 1/5!
126        DyadicFloat128 {
127            sign: DyadicSign::Neg,
128            exponent: -140,
129            mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
130        }, // -1/7!
131        DyadicFloat128 {
132            sign: DyadicSign::Pos,
133            exponent: -146,
134            mantissa: 0xb8ef1d2a_b6399c7d_560e4472_800b8ef2_u128,
135        }, // 1/9!
136        DyadicFloat128 {
137            sign: DyadicSign::Neg,
138            exponent: -153,
139            mantissa: 0xd7322b3f_aa271c7f_3a3f25c1_bee38f10_u128,
140        }, // -1/11!
141        DyadicFloat128 {
142            sign: DyadicSign::Pos,
143            exponent: -160,
144            mantissa: 0xb092309d_43684be5_1c198e91_d7b4269e_u128,
145        }, // 1/13!
146    ];
147
148    // cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
149    static COS_COEFFS: [DyadicFloat128; 7] = [
150        DyadicFloat128 {
151            sign: DyadicSign::Pos,
152            exponent: -127,
153            mantissa: 0x80000000_00000000_00000000_00000000_u128,
154        }, // 1.0
155        DyadicFloat128 {
156            sign: DyadicSign::Neg,
157            exponent: -128,
158            mantissa: 0x80000000_00000000_00000000_00000000_u128,
159        }, // 1/2
160        DyadicFloat128 {
161            sign: DyadicSign::Pos,
162            exponent: -132,
163            mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
164        }, // 1/4!
165        DyadicFloat128 {
166            sign: DyadicSign::Neg,
167            exponent: -137,
168            mantissa: 0xb60b60b6_0b60b60b_60b60b60_b60b60b6_u128,
169        }, // 1/6!
170        DyadicFloat128 {
171            sign: DyadicSign::Pos,
172            exponent: -143,
173            mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
174        }, // 1/8!
175        DyadicFloat128 {
176            sign: DyadicSign::Neg,
177            exponent: -149,
178            mantissa: 0x93f27dbb_c4fae397_780b69f5_333c725b_u128,
179        }, // 1/10!
180        DyadicFloat128 {
181            sign: DyadicSign::Pos,
182            exponent: -156,
183            mantissa: 0x8f76c77f_c6c4bdaa_26d4c3d6_7f425f60_u128,
184        }, // 1/12!
185    ];
186
187    let mut sin_u = SIN_COEFFS[6];
188    for i in (0..7).rev() {
189        sin_u = sin_u * u_sq + SIN_COEFFS[i];
190    }
191    sin_u = sin_u * *u;
192
193    let mut cos_u = COS_COEFFS[6];
194    for i in (0..7).rev() {
195        cos_u = cos_u * u_sq + COS_COEFFS[i];
196    }
197
198    SinCosDyadic {
199        v_sin: sin_u,
200        v_cos: cos_u,
201    }
202}
203
204/*
205   Sage math:
206   # Sin K PI over 128
207   R = RealField(128)
208   π = R.pi()
209
210   def format_hex(value):
211       l = hex(value)[2:]
212       n = 4
213       x = [l[i:i + n] for i in range(0, len(l), n)]
214       return "0x" + "_".join(x) + "_u128"
215
216   def print_dyadic(value):
217       (s, m, e) = RealField(128)(value).sign_mantissa_exponent();
218       print("DyadicFloat128 {")
219       print(f"    sign: DyadicSign::{'Pos' if s >= 0 else 'Neg'},")
220       print(f"    exponent: {e},")
221       print(f"    mantissa: {format_hex(m)},")
222       print("},")
223
224   # Generate array entries
225   print("pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [")
226   for k in range(65):
227       value = R(k) * π / 128
228       print_dyadic(value.sin())
229
230   print("];")
231*/
232pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [
233    DyadicFloat128 {
234        sign: DyadicSign::Pos,
235        exponent: 0,
236        mantissa: 0x0_u128,
237    },
238    DyadicFloat128 {
239        sign: DyadicSign::Pos,
240        exponent: -133,
241        mantissa: 0xc90a_afbd_1b33_efc9_c539_edcb_fda0_cf2c_u128,
242    },
243    DyadicFloat128 {
244        sign: DyadicSign::Pos,
245        exponent: -132,
246        mantissa: 0xc8fb_2f88_6ec0_9f37_6a17_954b_2b7c_5171_u128,
247    },
248    DyadicFloat128 {
249        sign: DyadicSign::Pos,
250        exponent: -131,
251        mantissa: 0x96a9_0496_70cf_ae65_f775_7409_4d3c_35c4_u128,
252    },
253    DyadicFloat128 {
254        sign: DyadicSign::Pos,
255        exponent: -131,
256        mantissa: 0xc8bd_35e1_4da1_5f0e_c739_6c89_4bbf_7389_u128,
257    },
258    DyadicFloat128 {
259        sign: DyadicSign::Pos,
260        exponent: -131,
261        mantissa: 0xfab2_72b5_4b98_71a2_7047_29ae_56d7_8a37_u128,
262    },
263    DyadicFloat128 {
264        sign: DyadicSign::Pos,
265        exponent: -130,
266        mantissa: 0x9640_8374_7309_d113_000a_89a1_1e07_c1ff_u128,
267    },
268    DyadicFloat128 {
269        sign: DyadicSign::Pos,
270        exponent: -130,
271        mantissa: 0xaf10_a224_59fe_32a6_3fee_f3bb_58b1_f10d_u128,
272    },
273    DyadicFloat128 {
274        sign: DyadicSign::Pos,
275        exponent: -130,
276        mantissa: 0xc7c5_c1e3_4d30_55b2_5cc8_c00e_4fcc_d850_u128,
277    },
278    DyadicFloat128 {
279        sign: DyadicSign::Pos,
280        exponent: -130,
281        mantissa: 0xe05c_1353_f27b_17e5_0ebc_61ad_e6ca_83cc_u128,
282    },
283    DyadicFloat128 {
284        sign: DyadicSign::Pos,
285        exponent: -130,
286        mantissa: 0xf8cf_cbd9_0af8_d57a_4221_dc4b_a772_598d_u128,
287    },
288    DyadicFloat128 {
289        sign: DyadicSign::Pos,
290        exponent: -129,
291        mantissa: 0x888e_9315_8fb3_bb04_9841_56f5_5334_4306_u128,
292    },
293    DyadicFloat128 {
294        sign: DyadicSign::Pos,
295        exponent: -129,
296        mantissa: 0x94a0_3176_acf8_2d45_ae4b_a773_da6b_f754_u128,
297    },
298    DyadicFloat128 {
299        sign: DyadicSign::Pos,
300        exponent: -129,
301        mantissa: 0xa09a_e4a0_bb30_0a19_2f89_5f44_a303_cc0b_u128,
302    },
303    DyadicFloat128 {
304        sign: DyadicSign::Pos,
305        exponent: -129,
306        mantissa: 0xac7c_d3ad_58fe_e7f0_811f_9539_84ef_f83e_u128,
307    },
308    DyadicFloat128 {
309        sign: DyadicSign::Pos,
310        exponent: -129,
311        mantissa: 0xb844_2987_d22c_f576_9cc3_ef36_746d_e3b8_u128,
312    },
313    DyadicFloat128 {
314        sign: DyadicSign::Pos,
315        exponent: -129,
316        mantissa: 0xc3ef_1535_754b_168d_3122_c2a5_9efd_dc37_u128,
317    },
318    DyadicFloat128 {
319        sign: DyadicSign::Pos,
320        exponent: -129,
321        mantissa: 0xcf7b_ca1d_476c_516d_a812_90bd_baad_62e4_u128,
322    },
323    DyadicFloat128 {
324        sign: DyadicSign::Pos,
325        exponent: -129,
326        mantissa: 0xdae8_804f_0ae6_015b_362c_b974_182e_3030_u128,
327    },
328    DyadicFloat128 {
329        sign: DyadicSign::Pos,
330        exponent: -129,
331        mantissa: 0xe633_74c9_8e22_f0b4_2872_ce1b_fc7a_d1cc_u128,
332    },
333    DyadicFloat128 {
334        sign: DyadicSign::Pos,
335        exponent: -129,
336        mantissa: 0xf15a_e9c0_37b1_d8f0_6c48_e9e3_420b_0f1d_u128,
337    },
338    DyadicFloat128 {
339        sign: DyadicSign::Pos,
340        exponent: -129,
341        mantissa: 0xfc5d_26df_c4d5_cfda_27c0_7c91_1290_b8d1_u128,
342    },
343    DyadicFloat128 {
344        sign: DyadicSign::Pos,
345        exponent: -128,
346        mantissa: 0x839c_3cc9_17ff_6cb4_bfd7_9717_f288_0abf_u128,
347    },
348    DyadicFloat128 {
349        sign: DyadicSign::Pos,
350        exponent: -128,
351        mantissa: 0x88f5_9aa0_da59_1421_b892_ca83_61d8_c84c_u128,
352    },
353    DyadicFloat128 {
354        sign: DyadicSign::Pos,
355        exponent: -128,
356        mantissa: 0x8e39_d9cd_7346_4364_bba4_cfec_bff5_4868_u128,
357    },
358    DyadicFloat128 {
359        sign: DyadicSign::Pos,
360        exponent: -128,
361        mantissa: 0x9368_2a66_e896_f544_b178_2191_1e71_c16e_u128,
362    },
363    DyadicFloat128 {
364        sign: DyadicSign::Pos,
365        exponent: -128,
366        mantissa: 0x987f_bfe7_0b81_a708_19ce_c845_ac87_a5c6_u128,
367    },
368    DyadicFloat128 {
369        sign: DyadicSign::Pos,
370        exponent: -128,
371        mantissa: 0x9d7f_d149_0285_c9e3_e25e_3954_9638_ae67_u128,
372    },
373    DyadicFloat128 {
374        sign: DyadicSign::Pos,
375        exponent: -128,
376        mantissa: 0xa267_9928_48ee_b0c0_3b51_67ee_359a_234e_u128,
377    },
378    DyadicFloat128 {
379        sign: DyadicSign::Pos,
380        exponent: -128,
381        mantissa: 0xa736_55df_1f2f_489e_149f_6e75_9934_68a2_u128,
382    },
383    DyadicFloat128 {
384        sign: DyadicSign::Pos,
385        exponent: -128,
386        mantissa: 0xabeb_49a4_6764_fd15_1bec_da80_89c1_a94c_u128,
387    },
388    DyadicFloat128 {
389        sign: DyadicSign::Pos,
390        exponent: -128,
391        mantissa: 0xb085_baa8_e966_f6da_e4ca_d00d_5c94_bcd1_u128,
392    },
393    DyadicFloat128 {
394        sign: DyadicSign::Pos,
395        exponent: -128,
396        mantissa: 0xb504_f333_f9de_6484_597d_89b3_754a_be9f_u128,
397    },
398    DyadicFloat128 {
399        sign: DyadicSign::Pos,
400        exponent: -128,
401        mantissa: 0xb968_41bf_7ffc_b21a_9de1_e3b2_2b8b_f4db_u128,
402    },
403    DyadicFloat128 {
404        sign: DyadicSign::Pos,
405        exponent: -128,
406        mantissa: 0xbdae_f913_557d_76f0_ac85_320f_528d_6d5c_u128,
407    },
408    DyadicFloat128 {
409        sign: DyadicSign::Pos,
410        exponent: -128,
411        mantissa: 0xc1d8_705f_fcbb_6e90_bdf0_715c_b8b2_0bd7_u128,
412    },
413    DyadicFloat128 {
414        sign: DyadicSign::Pos,
415        exponent: -128,
416        mantissa: 0xc5e4_0358_a8ba_05a7_43da_25d9_9267_326b_u128,
417    },
418    DyadicFloat128 {
419        sign: DyadicSign::Pos,
420        exponent: -128,
421        mantissa: 0xc9d1_124c_931f_da7a_8335_241b_e169_3225_u128,
422    },
423    DyadicFloat128 {
424        sign: DyadicSign::Pos,
425        exponent: -128,
426        mantissa: 0xcd9f_023f_9c3a_059e_23af_31db_7179_a4a9_u128,
427    },
428    DyadicFloat128 {
429        sign: DyadicSign::Pos,
430        exponent: -128,
431        mantissa: 0xd14d_3d02_313c_0eed_744f_ea20_e8ab_ef92_u128,
432    },
433    DyadicFloat128 {
434        sign: DyadicSign::Pos,
435        exponent: -128,
436        mantissa: 0xd4db_3148_750d_1819_f630_e8b6_dac8_3e68_u128,
437    },
438    DyadicFloat128 {
439        sign: DyadicSign::Pos,
440        exponent: -128,
441        mantissa: 0xd848_52c0_a80f_fcdb_24b9_fe00_6635_74a4_u128,
442    },
443    DyadicFloat128 {
444        sign: DyadicSign::Pos,
445        exponent: -128,
446        mantissa: 0xdb94_1a28_cb71_ec87_2c19_b632_53da_43fb_u128,
447    },
448    DyadicFloat128 {
449        sign: DyadicSign::Pos,
450        exponent: -128,
451        mantissa: 0xdebe_0563_7ca9_4cfb_4b19_aa71_fec3_ae6c_u128,
452    },
453    DyadicFloat128 {
454        sign: DyadicSign::Pos,
455        exponent: -128,
456        mantissa: 0xe1c5_978c_05ed_8691_f4e8_a837_2f8c_5810_u128,
457    },
458    DyadicFloat128 {
459        sign: DyadicSign::Pos,
460        exponent: -128,
461        mantissa: 0xe4aa_5909_a08f_a7b4_1227_85ae_67f5_515c_u128,
462    },
463    DyadicFloat128 {
464        sign: DyadicSign::Pos,
465        exponent: -128,
466        mantissa: 0xe76b_d7a1_e63b_9786_1251_2952_9d48_a92f_u128,
467    },
468    DyadicFloat128 {
469        sign: DyadicSign::Pos,
470        exponent: -128,
471        mantissa: 0xea09_a68a_6e49_cd62_15ad_45b4_a1b5_e823_u128,
472    },
473    DyadicFloat128 {
474        sign: DyadicSign::Pos,
475        exponent: -128,
476        mantissa: 0xec83_5e79_946a_3145_7e61_0231_ac1d_6181_u128,
477    },
478    DyadicFloat128 {
479        sign: DyadicSign::Pos,
480        exponent: -128,
481        mantissa: 0xeed8_9db6_6611_e307_86f8_c20f_b664_b01b_u128,
482    },
483    DyadicFloat128 {
484        sign: DyadicSign::Pos,
485        exponent: -128,
486        mantissa: 0xf109_0827_b437_25fd_6712_7db3_5b28_7315_u128,
487    },
488    DyadicFloat128 {
489        sign: DyadicSign::Pos,
490        exponent: -128,
491        mantissa: 0xf314_4762_4708_8f74_a548_6bdc_455d_56a3_u128,
492    },
493    DyadicFloat128 {
494        sign: DyadicSign::Pos,
495        exponent: -128,
496        mantissa: 0xf4fa_0ab6_316e_d2ec_163c_5c7f_03b7_18c5_u128,
497    },
498    DyadicFloat128 {
499        sign: DyadicSign::Pos,
500        exponent: -128,
501        mantissa: 0xf6ba_073b_424b_19e8_2c79_1f59_cc1f_fc23_u128,
502    },
503    DyadicFloat128 {
504        sign: DyadicSign::Pos,
505        exponent: -128,
506        mantissa: 0xf853_f7dc_9186_b952_c7ad_c6b4_9888_91ba_u128,
507    },
508    DyadicFloat128 {
509        sign: DyadicSign::Pos,
510        exponent: -128,
511        mantissa: 0xf9c7_9d63_272c_4628_4504_ae08_d19b_2981_u128,
512    },
513    DyadicFloat128 {
514        sign: DyadicSign::Pos,
515        exponent: -128,
516        mantissa: 0xfb14_be7f_bae5_8156_2172_a361_fd2a_722f_u128,
517    },
518    DyadicFloat128 {
519        sign: DyadicSign::Pos,
520        exponent: -128,
521        mantissa: 0xfc3b_27d3_8a5d_49ab_2567_78ff_cb5c_1769_u128,
522    },
523    DyadicFloat128 {
524        sign: DyadicSign::Pos,
525        exponent: -128,
526        mantissa: 0xfd3a_abf8_4528_b50b_eae6_bd95_1c1d_abbd_u128,
527    },
528    DyadicFloat128 {
529        sign: DyadicSign::Pos,
530        exponent: -128,
531        mantissa: 0xfe13_2387_0cfe_9a3d_90cd_1d95_9db6_74ef_u128,
532    },
533    DyadicFloat128 {
534        sign: DyadicSign::Pos,
535        exponent: -128,
536        mantissa: 0xfec4_6d1e_8929_2cf0_4139_0efd_c726_e9ef_u128,
537    },
538    DyadicFloat128 {
539        sign: DyadicSign::Pos,
540        exponent: -128,
541        mantissa: 0xff4e_6d68_0c41_d0a9_0f66_8633_f1ab_858a_u128,
542    },
543    DyadicFloat128 {
544        sign: DyadicSign::Pos,
545        exponent: -128,
546        mantissa: 0xffb1_0f1b_cb6b_ef1d_421e_8eda_af59_453e_u128,
547    },
548    DyadicFloat128 {
549        sign: DyadicSign::Pos,
550        exponent: -128,
551        mantissa: 0xffec_4304_2668_65d9_5657_5523_6696_1732_u128,
552    },
553    DyadicFloat128 {
554        sign: DyadicSign::Pos,
555        exponent: -127,
556        mantissa: 0x8000_0000_0000_0000_0000_0000_0000_0000_u128,
557    },
558];
pxfm/sincos_dyadic.rs

pxfm/
sincos_dyadic.rs
