pxfm/
asin_eval_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 */
29
30use crate::dyadic_float::{DyadicFloat128, DyadicSign};
31use crate::polyeval::f_polyeval16;
32
33// > procedure PRINTF128(a) {
34//   write("{");
35//   if (a < 0)
36//     then write("Sign::NEG, ") else write("Sign::Pos, ");
37//   a_exp = floor(log2(a)) + 1;
38//   write((a + 2 ^ a_exp) * 2 ^ -128);
39//   print("},");
40// };
41// > verbosity = 0;
42// > procedure ASIN_APPROX(N, Deg) {
43//     abs_error = 0;
44//     rel_error = 0;
45//     for i from 1 to N / 4 do {
46//       Q = fpminimax(asin(sqrt(i / N + x)) / sqrt(i / N + x), Deg,
47//                     [| 128... | ], [ -1 / (2 * N), 1 / (2 * N) ]);
48//       abs_err = dirtyinfnorm(asin(sqrt(i / N + x)) - sqrt(i / N + x) * Q,
49//                              [ -1 / (2 * N), 1 / (2 * N) ]);
50//       rel_err = dirtyinfnorm(asin(sqrt(i / N + x)) / sqrt(i / N + x) - Q,
51//                              [ -1 / (2 * N), 1 / (2 * N) ]);
52//       if (abs_err > abs_error) then abs_error = abs_err;
53//       if (rel_err > rel_error) then rel_error = rel_err;
54//       write("{");
55//       for j from 0 to Deg do PRINTF128(coeff(Q, j));
56//       print("},");
57//     };
58//     print("Absolute Errors:", abs_error);
59//     print("Relative Errors:", rel_error);
60//   };
61// > ASIN_APPROX(64, 15);
62// ...
63// Absolute Errors: 0x1.0b3...p-129
64// Relative Errors: 0x1.1db...p-128
65//
66// For k = 0, we use Taylor polynomial of asin(x)/x around x = 0.
67//   asin(x)/x ~ 1 + x^2/6 + (3 x^4)/40 + (5 x^6)/112 + (35 x^8)/1152 +
68//               + (63 x^10)/2816 + (231 x^12)/13312 + (143 x^14)/10240 +
69//               + (6435 x^16)/557056 + (12155 x^18)/1245184 +
70//               + (46189 x^20)/5505024 + (88179 x^22)/12058624 +
71//               + (676039 x^24)/104857600 + (1300075 x^26)/226492416 +
72//               + (5014575 x^28)/973078528 + (9694845 x^30)/2080374784.
73static ASIN_COEFFS_F128: [[DyadicFloat128; 16]; 17] = [
74    [
75        DyadicFloat128 {
76            sign: DyadicSign::Pos,
77            exponent: -127,
78            mantissa: 0x80000000_00000000_00000000_00000000_u128,
79        },
80        DyadicFloat128 {
81            sign: DyadicSign::Pos,
82            exponent: -130,
83            mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
84        },
85        DyadicFloat128 {
86            sign: DyadicSign::Pos,
87            exponent: -131,
88            mantissa: 0x99999999_99999999_99999999_9999999a_u128,
89        },
90        DyadicFloat128 {
91            sign: DyadicSign::Pos,
92            exponent: -132,
93            mantissa: 0xb6db6db6_db6db6db_6db6db6d_b6db6db7_u128,
94        },
95        DyadicFloat128 {
96            sign: DyadicSign::Pos,
97            exponent: -133,
98            mantissa: 0xf8e38e38_e38e38e3_8e38e38e_38e38e39_u128,
99        },
100        DyadicFloat128 {
101            sign: DyadicSign::Pos,
102            exponent: -133,
103            mantissa: 0xb745d174_5d1745d1_745d1745_d1745d17_u128,
104        },
105        DyadicFloat128 {
106            sign: DyadicSign::Pos,
107            exponent: -133,
108            mantissa: 0x8e276276_27627627_62762762_76276276_u128,
109        },
110        DyadicFloat128 {
111            sign: DyadicSign::Pos,
112            exponent: -134,
113            mantissa: 0xe4cccccc_cccccccc_cccccccc_cccccccd_u128,
114        },
115        DyadicFloat128 {
116            sign: DyadicSign::Pos,
117            exponent: -134,
118            mantissa: 0xbd43c3c3_c3c3c3c3_c3c3c3c3_c3c3c3c4_u128,
119        },
120        DyadicFloat128 {
121            sign: DyadicSign::Pos,
122            exponent: -134,
123            mantissa: 0x9fef286b_ca1af286_bca1af28_6bca1af3_u128,
124        },
125        DyadicFloat128 {
126            sign: DyadicSign::Pos,
127            exponent: -134,
128            mantissa: 0x89779e79_e79e79e7_9e79e79e_79e79e7a_u128,
129        },
130        DyadicFloat128 {
131            sign: DyadicSign::Pos,
132            exponent: -135,
133            mantissa: 0xef9de9bd_37a6f4de_9bd37a6f_4de9bd38_u128,
134        },
135        DyadicFloat128 {
136            sign: DyadicSign::Pos,
137            exponent: -135,
138            mantissa: 0xd3431eb8_51eb851e_b851eb85_1eb851ec_u128,
139        },
140        DyadicFloat128 {
141            sign: DyadicSign::Pos,
142            exponent: -135,
143            mantissa: 0xbc16ed09_7b425ed0_97b425ed_097b425f_u128,
144        },
145        DyadicFloat128 {
146            sign: DyadicSign::Pos,
147            exponent: -135,
148            mantissa: 0xa8dd1846_9ee58469_ee58469e_e58469ee_u128,
149        },
150        DyadicFloat128 {
151            sign: DyadicSign::Pos,
152            exponent: -135,
153            mantissa: 0x98b41def_7bdef7bd_ef7bdef7_bdef7bdf_u128,
154        },
155    ],
156    [
157        DyadicFloat128 {
158            sign: DyadicSign::Pos,
159            exponent: -127,
160            mantissa: 0x8055f060_94f0f05f_3ac3b927_50a701d9_u128,
161        },
162        DyadicFloat128 {
163            sign: DyadicSign::Pos,
164            exponent: -130,
165            mantissa: 0xad19c2ea_e3dd2429_8d04f71d_b965ee1b_u128,
166        },
167        DyadicFloat128 {
168            sign: DyadicSign::Pos,
169            exponent: -131,
170            mantissa: 0x9dfa882b_7b31af17_f9f19d33_0c45d24b_u128,
171        },
172        DyadicFloat128 {
173            sign: DyadicSign::Pos,
174            exponent: -132,
175            mantissa: 0xbedd3b58_c9e605ef_1404e1f0_4ba57940_u128,
176        },
177        DyadicFloat128 {
178            sign: DyadicSign::Pos,
179            exponent: -132,
180            mantissa: 0x83df2581_cb4fea82_b406f201_2fde6d5c_u128,
181        },
182        DyadicFloat128 {
183            sign: DyadicSign::Pos,
184            exponent: -133,
185            mantissa: 0xc534fe61_9b82dd16_ed5d8a43_f7710526_u128,
186        },
187        DyadicFloat128 {
188            sign: DyadicSign::Pos,
189            exponent: -133,
190            mantissa: 0x9b56fa62_88295ddf_ce8425fe_a04d733e_u128,
191        },
192        DyadicFloat128 {
193            sign: DyadicSign::Pos,
194            exponent: -134,
195            mantissa: 0xfdeddb19_4a030da7_27158080_d24caf46_u128,
196        },
197        DyadicFloat128 {
198            sign: DyadicSign::Pos,
199            exponent: -134,
200            mantissa: 0xd55827db_ff416ea8_042c4d8c_07cddeeb_u128,
201        },
202        DyadicFloat128 {
203            sign: DyadicSign::Pos,
204            exponent: -134,
205            mantissa: 0xb71d73a9_f2ba0688_5eaeeae9_413a0f5f_u128,
206        },
207        DyadicFloat128 {
208            sign: DyadicSign::Pos,
209            exponent: -134,
210            mantissa: 0x9fde87e2_ace91274_38f82666_d619c1ba_u128,
211        },
212        DyadicFloat128 {
213            sign: DyadicSign::Pos,
214            exponent: -134,
215            mantissa: 0x8d876557_5e4626a1_1b621336_93587847_u128,
216        },
217        DyadicFloat128 {
218            sign: DyadicSign::Pos,
219            exponent: -135,
220            mantissa: 0xfd801840_c8710595_6880fe13_a9657f8f_u128,
221        },
222        DyadicFloat128 {
223            sign: DyadicSign::Pos,
224            exponent: -135,
225            mantissa: 0xe54245a9_4c8c2ebb_30488494_64b0e34d_u128,
226        },
227        DyadicFloat128 {
228            sign: DyadicSign::Pos,
229            exponent: -135,
230            mantissa: 0xd11eb46f_4095a661_8890d123_15c96482_u128,
231        },
232        DyadicFloat128 {
233            sign: DyadicSign::Pos,
234            exponent: -135,
235            mantissa: 0xc01a4201_467fbc0b_960618d5_ec2adaa8_u128,
236        },
237    ],
238    [
239        DyadicFloat128 {
240            sign: DyadicSign::Pos,
241            exponent: -127,
242            mantissa: 0x80ad1cbe_7878de11_4293301c_11ce9d49_u128,
243        },
244        DyadicFloat128 {
245            sign: DyadicSign::Pos,
246            exponent: -130,
247            mantissa: 0xaf9ac0df_3d845544_0fe5e31b_9051d03e_u128,
248        },
249        DyadicFloat128 {
250            sign: DyadicSign::Pos,
251            exponent: -131,
252            mantissa: 0xa28ceef8_d7297e05_f94773ad_f4a695c6_u128,
253        },
254        DyadicFloat128 {
255            sign: DyadicSign::Pos,
256            exponent: -132,
257            mantissa: 0xc75a5b77_58b4b11d_396c68ad_6733022b_u128,
258        },
259        DyadicFloat128 {
260            sign: DyadicSign::Pos,
261            exponent: -132,
262            mantissa: 0x8bde42a1_084a6674_50c5bceb_005d4b62_u128,
263        },
264        DyadicFloat128 {
265            sign: DyadicSign::Pos,
266            exponent: -133,
267            mantissa: 0xd471cdae_e2f35a96_bd4bc513_e0ccdf2c_u128,
268        },
269        DyadicFloat128 {
270            sign: DyadicSign::Pos,
271            exponent: -133,
272            mantissa: 0xa9fc6fd5_d204a4e3_e609940c_6b991b67_u128,
273        },
274        DyadicFloat128 {
275            sign: DyadicSign::Pos,
276            exponent: -133,
277            mantissa: 0x8d242d97_ba12b492_e25c7e7c_0c3fcf60_u128,
278        },
279        DyadicFloat128 {
280            sign: DyadicSign::Pos,
281            exponent: -134,
282            mantissa: 0xf0f1ba74_b149afc3_2f0bbab5_a20c6199_u128,
283        },
284        DyadicFloat128 {
285            sign: DyadicSign::Pos,
286            exponent: -134,
287            mantissa: 0xd21b42fb_d8e9098d_19612692_9a043332_u128,
288        },
289        DyadicFloat128 {
290            sign: DyadicSign::Pos,
291            exponent: -134,
292            mantissa: 0xba5e5492_7896a3e7_193a74d5_78631587_u128,
293        },
294        DyadicFloat128 {
295            sign: DyadicSign::Pos,
296            exponent: -134,
297            mantissa: 0xa7a17ae7_fc707f45_910e7a5d_c95251f4_u128,
298        },
299        DyadicFloat128 {
300            sign: DyadicSign::Pos,
301            exponent: -134,
302            mantissa: 0x98889a6a_b0370464_50c950d3_61d79ed7_u128,
303        },
304        DyadicFloat128 {
305            sign: DyadicSign::Pos,
306            exponent: -134,
307            mantissa: 0x8c29330e_4318fd29_25c5b528_84e39e7c_u128,
308        },
309        DyadicFloat128 {
310            sign: DyadicSign::Pos,
311            exponent: -134,
312            mantissa: 0x81e7bf48_b25bc7c0_b9204a4f_d4f5fa8b_u128,
313        },
314        DyadicFloat128 {
315            sign: DyadicSign::Pos,
316            exponent: -135,
317            mantissa: 0xf2801b09_11bf0768_773996dd_5224d852_u128,
318        },
319    ],
320    [
321        DyadicFloat128 {
322            sign: DyadicSign::Pos,
323            exponent: -127,
324            mantissa: 0x81058e3e_f82ba622_ab81cd63_e1a91d57_u128,
325        },
326        DyadicFloat128 {
327            sign: DyadicSign::Pos,
328            exponent: -130,
329            mantissa: 0xb22e7055_c80dd354_8a2f2e8e_860d3f33_u128,
330        },
331        DyadicFloat128 {
332            sign: DyadicSign::Pos,
333            exponent: -131,
334            mantissa: 0xa753ce1a_7e3d1f57_247b37e6_03f93624_u128,
335        },
336        DyadicFloat128 {
337            sign: DyadicSign::Pos,
338            exponent: -132,
339            mantissa: 0xd05c5604_8eca8d18_dcdd76b7_f4b1f185_u128,
340        },
341        DyadicFloat128 {
342            sign: DyadicSign::Pos,
343            exponent: -132,
344            mantissa: 0x947cdd5e_f1d64df0_84f78df1_e2ecb854_u128,
345        },
346        DyadicFloat128 {
347            sign: DyadicSign::Pos,
348            exponent: -133,
349            mantissa: 0xe5218370_2ebbf6e8_3727a755_57843b93_u128,
350        },
351        DyadicFloat128 {
352            sign: DyadicSign::Pos,
353            exponent: -133,
354            mantissa: 0xba482553_383b92eb_186f78f1_8c35d6af_u128,
355        },
356        DyadicFloat128 {
357            sign: DyadicSign::Pos,
358            exponent: -133,
359            mantissa: 0x9d2b034a_7266c6a1_54b78a98_1a547429_u128,
360        },
361        DyadicFloat128 {
362            sign: DyadicSign::Pos,
363            exponent: -133,
364            mantissa: 0x8852f723_feea6046_e125f5a9_64e168e6_u128,
365        },
366        DyadicFloat128 {
367            sign: DyadicSign::Pos,
368            exponent: -134,
369            mantissa: 0xf19c9891_6c896c99_732052fe_5c54e992_u128,
370        },
371        DyadicFloat128 {
372            sign: DyadicSign::Pos,
373            exponent: -134,
374            mantissa: 0xd9cc81a5_c5ddf0f0_d651011e_a8ecd936_u128,
375        },
376        DyadicFloat128 {
377            sign: DyadicSign::Pos,
378            exponent: -134,
379            mantissa: 0xc7173169_dcb6095f_a6160847_b595aaff_u128,
380        },
381        DyadicFloat128 {
382            sign: DyadicSign::Pos,
383            exponent: -134,
384            mantissa: 0xb81cd3f6_4a422ebe_07aeb734_e4dcf3a1_u128,
385        },
386        DyadicFloat128 {
387            sign: DyadicSign::Pos,
388            exponent: -134,
389            mantissa: 0xabf01b1c_d15932aa_698d4382_512318a9_u128,
390        },
391        DyadicFloat128 {
392            sign: DyadicSign::Pos,
393            exponent: -134,
394            mantissa: 0xa1f1cf1b_d889a1ac_7120ca2f_bbbc1745_u128,
395        },
396        DyadicFloat128 {
397            sign: DyadicSign::Pos,
398            exponent: -134,
399            mantissa: 0x99a1b838_e38fbf11_429a4350_76b7d191_u128,
400        },
401    ],
402    [
403        DyadicFloat128 {
404            sign: DyadicSign::Pos,
405            exponent: -127,
406            mantissa: 0x815f4e70_5c3e68f2_e84ed170_78211dfd_u128,
407        },
408        DyadicFloat128 {
409            sign: DyadicSign::Pos,
410            exponent: -130,
411            mantissa: 0xb4d5a992_de1ac4da_16fe6024_3a6cc371_u128,
412        },
413        DyadicFloat128 {
414            sign: DyadicSign::Pos,
415            exponent: -131,
416            mantissa: 0xac526184_bd558c65_66642dce_edc4b04a_u128,
417        },
418        DyadicFloat128 {
419            sign: DyadicSign::Pos,
420            exponent: -132,
421            mantissa: 0xd9ed9b03_46ec0bab_429ea221_4774bbc1_u128,
422        },
423        DyadicFloat128 {
424            sign: DyadicSign::Pos,
425            exponent: -132,
426            mantissa: 0x9dca410c_1efaeb74_87956685_dd5fe848_u128,
427        },
428        DyadicFloat128 {
429            sign: DyadicSign::Pos,
430            exponent: -133,
431            mantissa: 0xf76e411b_a926fc02_7f942265_9c39a882_u128,
432        },
433        DyadicFloat128 {
434            sign: DyadicSign::Pos,
435            exponent: -133,
436            mantissa: 0xcc71b004_eeb60c0f_1d387f76_44b46bf8_u128,
437        },
438        DyadicFloat128 {
439            sign: DyadicSign::Pos,
440            exponent: -133,
441            mantissa: 0xaf527a40_6f1084fb_5019904e_d12d384d_u128,
442        },
443        DyadicFloat128 {
444            sign: DyadicSign::Pos,
445            exponent: -133,
446            mantissa: 0x9a9304b0_d8a9de19_e1803691_269be22c_u128,
447        },
448        DyadicFloat128 {
449            sign: DyadicSign::Pos,
450            exponent: -133,
451            mantissa: 0x8b3d37c0_dbde09ef_342ddf4f_e80dd3fb_u128,
452        },
453        DyadicFloat128 {
454            sign: DyadicSign::Pos,
455            exponent: -134,
456            mantissa: 0xff2e9111_3a961c78_92297bab_cc257804_u128,
457        },
458        DyadicFloat128 {
459            sign: DyadicSign::Pos,
460            exponent: -134,
461            mantissa: 0xed1fb643_f2ca31c1_b0a1553a_e077285a_u128,
462        },
463        DyadicFloat128 {
464            sign: DyadicSign::Pos,
465            exponent: -134,
466            mantissa: 0xdeeb0f5e_81ad5e30_78d79ae3_83be1c18_u128,
467        },
468        DyadicFloat128 {
469            sign: DyadicSign::Pos,
470            exponent: -134,
471            mantissa: 0xd3a13ba6_8ce9abfc_a66eb1fd_c0c760fd_u128,
472        },
473        DyadicFloat128 {
474            sign: DyadicSign::Pos,
475            exponent: -134,
476            mantissa: 0xcaa8c381_d44bb44f_0ab25126_9a5fae10_u128,
477        },
478        DyadicFloat128 {
479            sign: DyadicSign::Pos,
480            exponent: -134,
481            mantissa: 0xc36fb2c4_244401cf_10dd8a39_78ccbf7f_u128,
482        },
483    ],
484    [
485        DyadicFloat128 {
486            sign: DyadicSign::Pos,
487            exponent: -127,
488            mantissa: 0x81ba6750_6064f4dd_08015b7c_713688f0_u128,
489        },
490        DyadicFloat128 {
491            sign: DyadicSign::Pos,
492            exponent: -130,
493            mantissa: 0xb791524b_d975fdd1_584037b7_103b42ca_u128,
494        },
495        DyadicFloat128 {
496            sign: DyadicSign::Pos,
497            exponent: -131,
498            mantissa: 0xb18c26c5_3ced9856_db5bc672_cc95a64f_u128,
499        },
500        DyadicFloat128 {
501            sign: DyadicSign::Pos,
502            exponent: -132,
503            mantissa: 0xe4199ce5_d25be89b_4a0ad208_da77022d_u128,
504        },
505        DyadicFloat128 {
506            sign: DyadicSign::Pos,
507            exponent: -132,
508            mantissa: 0xa7d77999_0f80e3e9_7e97e9d1_0e337550_u128,
509        },
510        DyadicFloat128 {
511            sign: DyadicSign::Pos,
512            exponent: -132,
513            mantissa: 0x85c3e039_8959c95b_e6e1e87f_7e6636b1_u128,
514        },
515        DyadicFloat128 {
516            sign: DyadicSign::Pos,
517            exponent: -133,
518            mantissa: 0xe0b90ecd_95f7e6eb_a675bae0_628bd214_u128,
519        },
520        DyadicFloat128 {
521            sign: DyadicSign::Pos,
522            exponent: -133,
523            mantissa: 0xc3edb6b4_ed0a684c_c7a3ee4d_f1dcd3f9_u128,
524        },
525        DyadicFloat128 {
526            sign: DyadicSign::Pos,
527            exponent: -133,
528            mantissa: 0xafa274d2_e66e1f61_9e8ab3c7_7221214e_u128,
529        },
530        DyadicFloat128 {
531            sign: DyadicSign::Pos,
532            exponent: -133,
533            mantissa: 0xa0dd903d_e110b71a_8a1fc9df_cc080308_u128,
534        },
535        DyadicFloat128 {
536            sign: DyadicSign::Pos,
537            exponent: -133,
538            mantissa: 0x95e2f38c_60441961_72b90625_e3a37573_u128,
539        },
540        DyadicFloat128 {
541            sign: DyadicSign::Pos,
542            exponent: -133,
543            mantissa: 0x8d9fe38f_2c705139_029f857c_9f628b2b_u128,
544        },
545        DyadicFloat128 {
546            sign: DyadicSign::Pos,
547            exponent: -133,
548            mantissa: 0x8762410a_4967a974_6b609e83_7c025a39_u128,
549        },
550        DyadicFloat128 {
551            sign: DyadicSign::Pos,
552            exponent: -133,
553            mantissa: 0x82b220be_d9ec0e5a_9ce9af7c_c65c94b9_u128,
554        },
555        DyadicFloat128 {
556            sign: DyadicSign::Pos,
557            exponent: -134,
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565    ],
566    [
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730    [
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1024            exponent: -132,
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1034            exponent: -132,
1035            mantissa: 0xdc0aeb56_ca679f92_3b3c44d8_99b1add7_u128,
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1039            exponent: -132,
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1044            exponent: -132,
1045            mantissa: 0xfb5e3897_5a5c8f62_280a90dc_9ebe9107_u128,
1046        },
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1049            exponent: -131,
1050            mantissa: 0x88301d81_b38f225d_2226ab7e_df342d90_u128,
1051        },
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1054            exponent: -131,
1055            mantissa: 0x949e3465_e4a8aef7_46311182_5fc3fde8_u128,
1056        },
1057    ],
1058    [
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1063        },
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1066            exponent: -130,
1067            mantissa: 0xcd47ac90_3c311c2b_98dd7493_4656d210_u128,
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1071            exponent: -131,
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1073        },
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1076            exponent: -131,
1077            mantissa: 0xa086fafa_c220fb73_9939cae3_2d69683f_u128,
1078        },
1079        DyadicFloat128 {
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1081            exponent: -131,
1082            mantissa: 0x855b5efa_f6963d73_e4664cb1_d43f03a9_u128,
1083        },
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1086            exponent: -132,
1087            mantissa: 0xf05c9774_fe0de25c_ccf1c1df_d2ed9941_u128,
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1091            exponent: -132,
1092            mantissa: 0xe484a941_19639229_f06ae955_f8edc7d1_u128,
1093        },
1094        DyadicFloat128 {
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1096            exponent: -132,
1097            mantissa: 0xe1a32bb2_52ca122c_bf2f0904_cfc476cb_u128,
1098        },
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1101            exponent: -132,
1102            mantissa: 0xe528e091_7bb8a01a_9218ce3e_1e85af60_u128,
1103        },
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1106            exponent: -132,
1107            mantissa: 0xeddd556a_faa2d46f_e91c61fa_adf12aec_u128,
1108        },
1109        DyadicFloat128 {
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1111            exponent: -132,
1112            mantissa: 0xfb390fa3_15e9d55f_5683c0c4_c7719f81_u128,
1113        },
1114        DyadicFloat128 {
1115            sign: DyadicSign::Pos,
1116            exponent: -131,
1117            mantissa: 0x868e5fa4_15597c8f_7c42a262_8f2d6332_u128,
1118        },
1119        DyadicFloat128 {
1120            sign: DyadicSign::Pos,
1121            exponent: -131,
1122            mantissa: 0x91d79767_a3d037f9_cd84ead5_c0714310_u128,
1123        },
1124        DyadicFloat128 {
1125            sign: DyadicSign::Pos,
1126            exponent: -131,
1127            mantissa: 0x9fa6a035_915bc052_377a8abb_faf4e3c6_u128,
1128        },
1129        DyadicFloat128 {
1130            sign: DyadicSign::Pos,
1131            exponent: -131,
1132            mantissa: 0xb04edefd_6ac2a93e_ec33e6f6_3d53e7c2_u128,
1133        },
1134        DyadicFloat128 {
1135            sign: DyadicSign::Pos,
1136            exponent: -131,
1137            mantissa: 0xc416980d_dc5c186b_7bdcded6_97ea5844_u128,
1138        },
1139    ],
1140    [
1141        DyadicFloat128 {
1142            sign: DyadicSign::Pos,
1143            exponent: -127,
1144            mantissa: 0x84c8fd4d_ffdf9fc6_bdd7ebca_88183d7b_u128,
1145        },
1146        DyadicFloat128 {
1147            sign: DyadicSign::Pos,
1148            exponent: -130,
1149            mantissa: 0xd0cf0544_11dbf845_cb6eeae5_bc980e2f_u128,
1150        },
1151        DyadicFloat128 {
1152            sign: DyadicSign::Pos,
1153            exponent: -131,
1154            mantissa: 0xe5bb9480_7ce0eaca_74300a46_8398e944_u128,
1155        },
1156        DyadicFloat128 {
1157            sign: DyadicSign::Pos,
1158            exponent: -131,
1159            mantissa: 0xa92a18f8_d611860b_5f2ef8c6_8e8ca002_u128,
1160        },
1161        DyadicFloat128 {
1162            sign: DyadicSign::Pos,
1163            exponent: -131,
1164            mantissa: 0x8f2e1684_17eb4e6c_1ec44b9b_e4b1c3e5_u128,
1165        },
1166        DyadicFloat128 {
1167            sign: DyadicSign::Pos,
1168            exponent: -131,
1169            mantissa: 0x837f1764_0ee8f416_8694b4a1_c647af0c_u128,
1170        },
1171        DyadicFloat128 {
1172            sign: DyadicSign::Pos,
1173            exponent: -132,
1174            mantissa: 0xfed7e2a9_05a5190e_b7d70a61_a24ad801_u128,
1175        },
1176        DyadicFloat128 {
1177            sign: DyadicSign::Pos,
1178            exponent: -131,
1179            mantissa: 0x803f29ff_dc6fd2bc_3c3c4b50_a9dc860c_u128,
1180        },
1181        DyadicFloat128 {
1182            sign: DyadicSign::Pos,
1183            exponent: -131,
1184            mantissa: 0x84c61e09_b8aa35e4_96239f9c_b1d00b3c_u128,
1185        },
1186        DyadicFloat128 {
1187            sign: DyadicSign::Pos,
1188            exponent: -131,
1189            mantissa: 0x8c7ed311_f77980d6_842ddf90_6a68a0bc_u128,
1190        },
1191        DyadicFloat128 {
1192            sign: DyadicSign::Pos,
1193            exponent: -131,
1194            mantissa: 0x9746077b_d397c2d1_038a4744_a76f5fb5_u128,
1195        },
1196        DyadicFloat128 {
1197            sign: DyadicSign::Pos,
1198            exponent: -131,
1199            mantissa: 0xa5341277_c4185ace_54f26328_322158e8_u128,
1200        },
1201        DyadicFloat128 {
1202            sign: DyadicSign::Pos,
1203            exponent: -131,
1204            mantissa: 0xb68d78f5_0972f6de_9189aa23_d3ecefc2_u128,
1205        },
1206        DyadicFloat128 {
1207            sign: DyadicSign::Pos,
1208            exponent: -131,
1209            mantissa: 0xcbbcefc2_15bade4e_f1d36947_c8b6e460_u128,
1210        },
1211        DyadicFloat128 {
1212            sign: DyadicSign::Pos,
1213            exponent: -131,
1214            mantissa: 0xe564a459_c851390d_d45a4748_f29f182b_u128,
1215        },
1216        DyadicFloat128 {
1217            sign: DyadicSign::Pos,
1218            exponent: -130,
1219            mantissa: 0x820ea28b_c89662c3_2a64ccdc_efb2b259_u128,
1220        },
1221    ],
1222    [
1223        DyadicFloat128 {
1224            sign: DyadicSign::Pos,
1225            exponent: -127,
1226            mantissa: 0x85324d39_f30f9174_ac0d817e_9c744b0b_u128,
1227        },
1228        DyadicFloat128 {
1229            sign: DyadicSign::Pos,
1230            exponent: -130,
1231            mantissa: 0xd476186e_49c47f3a_a71f8886_7f9f21c4_u128,
1232        },
1233        DyadicFloat128 {
1234            sign: DyadicSign::Pos,
1235            exponent: -131,
1236            mantissa: 0xede08f54_a830e87b_07881700_65e57b6c_u128,
1237        },
1238        DyadicFloat128 {
1239            sign: DyadicSign::Pos,
1240            exponent: -131,
1241            mantissa: 0xb271b8eb_309963ee_89187c73_0b92f7d5_u128,
1242        },
1243        DyadicFloat128 {
1244            sign: DyadicSign::Pos,
1245            exponent: -131,
1246            mantissa: 0x99f0011d_95d3a6dd_282bd00a_db808151_u128,
1247        },
1248        DyadicFloat128 {
1249            sign: DyadicSign::Pos,
1250            exponent: -131,
1251            mantissa: 0x9021134e_02b479e7_3aabf9bb_b7ab6cf3_u128,
1252        },
1253        DyadicFloat128 {
1254            sign: DyadicSign::Pos,
1255            exponent: -131,
1256            mantissa: 0x8e673bf2_f11db54a_909c4c72_6389499f_u128,
1257        },
1258        DyadicFloat128 {
1259            sign: DyadicSign::Pos,
1260            exponent: -131,
1261            mantissa: 0x9226a371_88dd55f7_bfe21777_4a42a7ae_u128,
1262        },
1263        DyadicFloat128 {
1264            sign: DyadicSign::Pos,
1265            exponent: -131,
1266            mantissa: 0x9a4d78fc_9df79d9a_44609c02_a625808a_u128,
1267        },
1268        DyadicFloat128 {
1269            sign: DyadicSign::Pos,
1270            exponent: -131,
1271            mantissa: 0xa68335fb_41d2d91c_e7bbd2a3_31a1d17b_u128,
1272        },
1273        DyadicFloat128 {
1274            sign: DyadicSign::Pos,
1275            exponent: -131,
1276            mantissa: 0xb6d89c39_28d0cb26_809d4df6_e55cba1a_u128,
1277        },
1278        DyadicFloat128 {
1279            sign: DyadicSign::Pos,
1280            exponent: -131,
1281            mantissa: 0xcba71468_9177fc2d_7f23df2f_37226488_u128,
1282        },
1283        DyadicFloat128 {
1284            sign: DyadicSign::Pos,
1285            exponent: -131,
1286            mantissa: 0xe5846de8_44833ae9_34416c87_0315eb9e_u128,
1287        },
1288        DyadicFloat128 {
1289            sign: DyadicSign::Pos,
1290            exponent: -130,
1291            mantissa: 0x82a07032_64e6226b_200d94a1_66fc7951_u128,
1292        },
1293        DyadicFloat128 {
1294            sign: DyadicSign::Pos,
1295            exponent: -130,
1296            mantissa: 0x9602695c_b6fa8886_68ca0cba_b59ea683_u128,
1297        },
1298        DyadicFloat128 {
1299            sign: DyadicSign::Pos,
1300            exponent: -130,
1301            mantissa: 0xad7d185a_ab3d14dd_d908a7b1_c57352bb_u128,
1302        },
1303    ],
1304    [
1305        DyadicFloat128 {
1306            sign: DyadicSign::Pos,
1307            exponent: -127,
1308            mantissa: 0x859d78fa_4405d8fa_287dbc69_95d0975e_u128,
1309        },
1310        DyadicFloat128 {
1311            sign: DyadicSign::Pos,
1312            exponent: -130,
1313            mantissa: 0xd83ea3bc_131d6baa_67c51d88_4c4dae01_u128,
1314        },
1315        DyadicFloat128 {
1316            sign: DyadicSign::Pos,
1317            exponent: -131,
1318            mantissa: 0xf6790edb_df07342b_aad85870_167af128_u128,
1319        },
1320        DyadicFloat128 {
1321            sign: DyadicSign::Pos,
1322            exponent: -131,
1323            mantissa: 0xbc6daa33_12be0f85_bc7fa753_52b10a83_u128,
1324        },
1325        DyadicFloat128 {
1326            sign: DyadicSign::Pos,
1327            exponent: -131,
1328            mantissa: 0xa5bd41bc_9c986b13_1af2542e_92aacb59_u128,
1329        },
1330        DyadicFloat128 {
1331            sign: DyadicSign::Pos,
1332            exponent: -131,
1333            mantissa: 0x9e4358bc_24e04364_b4539b76_e444b790_u128,
1334        },
1335        DyadicFloat128 {
1336            sign: DyadicSign::Pos,
1337            exponent: -131,
1338            mantissa: 0x9f7fc21b_dca1f2b5_f3f6d44b_c5a37626_u128,
1339        },
1340        DyadicFloat128 {
1341            sign: DyadicSign::Pos,
1342            exponent: -131,
1343            mantissa: 0xa6fd793c_0b9c44c1_30a518cc_66b5e511_u128,
1344        },
1345        DyadicFloat128 {
1346            sign: DyadicSign::Pos,
1347            exponent: -131,
1348            mantissa: 0xb3dccfac_cd1592b3_bcd6b7c0_9749993d_u128,
1349        },
1350        DyadicFloat128 {
1351            sign: DyadicSign::Pos,
1352            exponent: -131,
1353            mantissa: 0xc6056c3a_4a5f329a_48f1429d_27f930fc_u128,
1354        },
1355        DyadicFloat128 {
1356            sign: DyadicSign::Pos,
1357            exponent: -131,
1358            mantissa: 0xddd9e529_858a4502_6e7f3d1c_1e7dcb89_u128,
1359        },
1360        DyadicFloat128 {
1361            sign: DyadicSign::Pos,
1362            exponent: -131,
1363            mantissa: 0xfc1bccee_dc8d2567_1721c468_6f7f53ec_u128,
1364        },
1365        DyadicFloat128 {
1366            sign: DyadicSign::Pos,
1367            exponent: -130,
1368            mantissa: 0x90f2bb21_5cdbe7e2_f9ef8e12_059cc66a_u128,
1369        },
1370        DyadicFloat128 {
1371            sign: DyadicSign::Pos,
1372            exponent: -130,
1373            mantissa: 0xa857d5df_5b4da940_15ce4e95_7201fc79_u128,
1374        },
1375        DyadicFloat128 {
1376            sign: DyadicSign::Pos,
1377            exponent: -130,
1378            mantissa: 0xc54119c0_10c02bf4_d87ece17_1ef85c5f_u128,
1379        },
1380        DyadicFloat128 {
1381            sign: DyadicSign::Pos,
1382            exponent: -130,
1383            mantissa: 0xe8c50ebc_880356de_2c1f4c42_9ee9748f_u128,
1384        },
1385    ],
1386    [
1387        DyadicFloat128 {
1388            sign: DyadicSign::Pos,
1389            exponent: -127,
1390            mantissa: 0x860a91c1_6b9b2c23_2dd99707_ab3d688b_u128,
1391        },
1392        DyadicFloat128 {
1393            sign: DyadicSign::Pos,
1394            exponent: -130,
1395            mantissa: 0xdc2a86b1_5fdb645d_ea2781dd_25555f49_u128,
1396        },
1397        DyadicFloat128 {
1398            sign: DyadicSign::Pos,
1399            exponent: -131,
1400            mantissa: 0xff8def07_d1e514d7_b2e8ebb6_5c3afe5e_u128,
1401        },
1402        DyadicFloat128 {
1403            sign: DyadicSign::Pos,
1404            exponent: -131,
1405            mantissa: 0xc72f9d5b_4fb559e3_20db92e3_a5ae3f73_u128,
1406        },
1407        DyadicFloat128 {
1408            sign: DyadicSign::Pos,
1409            exponent: -131,
1410            mantissa: 0xb2b5f45b_1d26f4dd_0b210309_fb68914f_u128,
1411        },
1412        DyadicFloat128 {
1413            sign: DyadicSign::Pos,
1414            exponent: -131,
1415            mantissa: 0xae1cbaae_c7b55465_4da858f5_47e62a37_u128,
1416        },
1417        DyadicFloat128 {
1418            sign: DyadicSign::Pos,
1419            exponent: -131,
1420            mantissa: 0xb30f3998_10202a0d_a52ec085_a7d63289_u128,
1421        },
1422        DyadicFloat128 {
1423            sign: DyadicSign::Pos,
1424            exponent: -131,
1425            mantissa: 0xbf51f27f_b7aff89d_dc24e2aa_208d2054_u128,
1426        },
1427        DyadicFloat128 {
1428            sign: DyadicSign::Pos,
1429            exponent: -131,
1430            mantissa: 0xd250735e_87d0b527_6f99bcc9_bd6fc717_u128,
1431        },
1432        DyadicFloat128 {
1433            sign: DyadicSign::Pos,
1434            exponent: -131,
1435            mantissa: 0xec543ec2_bddb2efb_36d9ce81_a7c84336_u128,
1436        },
1437        DyadicFloat128 {
1438            sign: DyadicSign::Pos,
1439            exponent: -130,
1440            mantissa: 0x871f73e3_298ef45c_eed83998_2bc731b9_u128,
1441        },
1442        DyadicFloat128 {
1443            sign: DyadicSign::Pos,
1444            exponent: -130,
1445            mantissa: 0x9cbb5447_af8574f1_21fa4cda_93d82b7e_u128,
1446        },
1447        DyadicFloat128 {
1448            sign: DyadicSign::Pos,
1449            exponent: -130,
1450            mantissa: 0xb7f5a6c0_430a347f_11b22cde_91de0885_u128,
1451        },
1452        DyadicFloat128 {
1453            sign: DyadicSign::Pos,
1454            exponent: -130,
1455            mantissa: 0xda153cc4_14abdb96_840df7c2_3299fec0_u128,
1456        },
1457        DyadicFloat128 {
1458            sign: DyadicSign::Pos,
1459            exponent: -129,
1460            mantissa: 0x826c129b_3e4a2612_b2cd11f1_4d2ba60c_u128,
1461        },
1462        DyadicFloat128 {
1463            sign: DyadicSign::Pos,
1464            exponent: -129,
1465            mantissa: 0x9d19c289_fc0e8aa4_f351418b_b760ce90_u128,
1466        },
1467    ],
1468];
1469
1470#[cold]
1471pub(crate) fn asin_eval_dyadic(u: DyadicFloat128, idx: usize) -> DyadicFloat128 {
1472    let coeffs = ASIN_COEFFS_F128[idx];
1473    f_polyeval16(
1474        u, coeffs[0], coeffs[1], coeffs[2], coeffs[3], coeffs[4], coeffs[5], coeffs[6], coeffs[7],
1475        coeffs[8], coeffs[9], coeffs[10], coeffs[11], coeffs[12], coeffs[13], coeffs[14],
1476        coeffs[15],
1477    )
1478}
pxfm/asin_eval_dyadic.rs

pxfm/
asin_eval_dyadic.rs
