pxfm/bessel/
y0f_coeffs.rs

1/*
2 * // Copyright (c) Radzivon Bartoshyk 7/2025. 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
30/**
31Y0 zeros and extremums.
32Generated by SageMath:
33```python
34R120 = RealField(120)
35
36zeros = []
37
38mp.prec = 150
39
40step = mpf("0.1")
41epsilon = mpf("1e-35")
42x = mpf("1.25")
43
44previous_zero = R120(0)
45y0_zeros = []
46
47while x < mpf("76.0"):
48    f1 = bessely(0, x)
49    f2 = bessely(0, x + step)
50    if f1 * f2 < 0:
51        zero = findroot(lambda t: bessely(0, t), (x, x + step), solver='secant', tol=mp.mpf("1e-41"))
52        previous_zero = zero
53        y0_zeros.append(zero)
54    if previous_zero is not None and abs(x - mpf(f'{round(x)}')) < epsilon:
55        zeros.append(previous_zero)
56    x += step
57
58y0_extrema = []
59
60x = mpf("1.25")
61while x < mpf("76.0"):
62    d1 = mp.diff(lambda t: bessely(0, t), x)
63    d2 = mp.diff(lambda t: bessely(0, t), x + step)
64    if d1 * d2 < 0:
65        extremum = findroot(lambda t: mp.diff(lambda u: bessely(0, u), t), (x, x + step), solver='secant', tol=mp.mpf("1e-41"))
66        y0_extrema.append(extremum)
67    x += step
68
69# Print results
70for i, z in enumerate(j0_zeros):
71    print(f"Zero {i+1}: x ≈ {z}")
72
73print("Extrema (peaks/valleys) of Y0(x):")
74for e in y0_extrema:
75    print(f"nExtrema: {e}")
76
77y0_zeros.extend(y0_extrema)
78
79y0_zeros = sorted(y0_zeros)
80
81# Print results
82for i, z in enumerate(y0_zeros):
83    print(f"Peak or zero {i+1}: x ≈ {z}")
84
85print("")
86
87print("pub(crate) static Y0_ZEROS: [(u64, u64); 48] = [")
88print(f"(0x0, 0x0),")
89for z in y0_zeros:
90    k = split_double_double(z)
91    hi = double_to_hex(k[1])
92    lo = double_to_hex(k[0])
93    print(f"({lo}, {hi}),")
94
95print("];")
96```
97**/
98pub(crate) static Y0_ZEROS: [(u64, u64); 48] = [
99    (0x0, 0x0), // not really used, just a stab to avoid messing with indices
100    (0xbc8bd1e50d219bfd, 0x400193bed4dff243),
101    (0xbc9f06ae7804384e, 0x400fa9534d98569c),
102    (0x3cbdfe7bac228e8c, 0x4015b7fe4e87b02e),
103    (0xbc99774a495f56cf, 0x401c581dc4e72103),
104    (0x3cb479cc068d9046, 0x40213127ae6169b4),
105    (0xbcccb49ff791c495, 0x402471d735a47d58),
106    (0x3c80fc786ce06080, 0x40277f9138d43206),
107    (0xbcc7df81de86f24d, 0x402ab8e1c4a1e74a),
108    (0xbcc5e091a50f8e05, 0x402dcb7d88de848b),
109    (0x3cd25a237d12159b, 0x4030803c74003214),
110    (0xbcda1ee4c5487ede, 0x40320b1c695f1e3b),
111    (0xbcd8bf92d51fbaeb, 0x4033a42cdf5febd7),
112    (0x3cd391b14410528f, 0x40353025492188cd),
113    (0x3cdca75080cf53a8, 0x4036c832fd77ac07),
114    (0x3cb52f75f025b205, 0x403854fa303820ca),
115    (0xbcb03e052bd9c0af, 0x4039ec46f3e80146),
116    (0xbcbcf130fbea3b24, 0x403b79acee8cfb7d),
117    (0x3cd0aab17eca74b9, 0x403d106449616c4f),
118    (0xbc9e7a77047d6166, 0x403e9e480605283c),
119    (0x3ced2f18aa8a8f2f, 0x40401a4420e4abee),
120    (0xbce96beabef7ecf4, 0x4040e16907f8fb56),
121    (0xbca9dd1578036d11, 0x4041ac588c944279),
122    (0x3cd2481e87adfe57, 0x404273a7b35a7aff),
123    (0xbce9c3dd43e59158, 0x40433e6ecf5cb221),
124    (0x3cda8ffacaac8461, 0x404405e18393afb5),
125    (0xbce753b7fcd5250c, 0x4044d0867ec213f3),
126    (0x3cbfe463face2c1c, 0x4045981787d668db),
127    (0x3cec2eb6ee3e4c70, 0x4046629f4e1e0321),
128    (0xbce26390f25f01cb, 0x40472a4a85cc317e),
129    (0xbcaafdee84ced526, 0x4047f4b904dc9a53),
130    (0xbcdcc667e557a177, 0x4048bc7b10ed3960),
131    (0x3cebbca9a96dc1aa, 0x404986d378522b70),
132    (0x3cb377717d2f36f7, 0x404a4ea9997b5eaa),
133    (0xbcedf185c89a4066, 0x404b18ee87b4e700),
134    (0xbcc68a841a2af000, 0x404be0d6766d13de),
135    (0x3ced8a878e90eda4, 0x404cab0a1968b221),
136    (0x3cddcc8dd083c434, 0x404d7301ec2bf16e),
137    (0xbceb5c58b22794af, 0x404e3d2619226875),
138    (0xbce5919b54336657, 0x404f052c3146d1da),
139    (0xbc87b54cc765fd11, 0x404fcf4276983013),
140    (0xbcf389f975d9dfa2, 0x40504baab8e42f8f),
141    (0xbce195534d06b08a, 0x4050b0af92483bf5),
142    (0xbcd4e0ffa0b9d2e9, 0x405114bee8d0f4bd),
143    (0xbcf1c076cb371565, 0x405179be0c18f0e1),
144    (0x3cf5d0de43102daa, 0x4051ddd2b7398636),
145    (0xbce8a4f19e47d0be, 0x405242cca44048f8),
146    (0x3ceb379dbe48b8f5, 0x4052a6e6306f1d08),
147];
148
149/**
150Zeros and extremums solved values for Y0
151
152Generated by MPFR:
153```text
154let mut arr = vec![];
155for zeros in Y0_ZEROS.iter() {
156    if zeros.1 == 0 {
157        arr.push(0);
158    } else {
159        let mpfr = Float::with_val(107, f64::from_bits(zeros.1)).y0();
160        arr.push(mpfr.to_f64().to_bits());
161    }
162}
163println!(
164    "arr: [{}]",
165    arr.iter()
166        .map(|x| format!("0x{:016x}", x))
167        .collect::<Vec<_>>()
168        .join(", ")
169);
170```
171**/
172pub(crate) static Y0_ZEROS_VALUES: [u64; 48] = [
173    0x0000000000000000,
174    0x3fe0aa48442f014b,
175    0xbc88fa8956b4b481,
176    0xbfd5c7c556f0c19a,
177    0x3c7e91b198d39ce2,
178    0x3fd15f993fceab5c,
179    0xbcacabd7c823bf21,
180    0xbfcdc14ea14e89f9,
181    0x3ca4d9fe48a91cef,
182    0x3fca7022be084d99,
183    0x3cacd827f6c074a2,
184    0xbfc80781c32422e7,
185    0x3cb1d336c8b0a153,
186    0x3fc62d94d97e859c,
187    0x3cb3296749aaf800,
188    0xbfc4b2a38f1ab9b4,
189    0x3c845d52c7c075b2,
190    0x3fc37aaceac987b9,
191    0x3ca3bc249963d4c1,
192    0xbfc2740819f1caaa,
193    0xbcc069eacea8ff0b,
194    0x3fc192f2627a74e3,
195    0xbc7bc4fd81e2b2c5,
196    0xbfc0cf3ee98f769b,
197    0x3cba82b3a8997d82,
198    0x3fc0230ba90f2871,
199    0xbcb71414f52d813b,
200    0xbfbf13fb0c0e6fcd,
201    0xbcbae2d399eafcc6,
202    0x3fbe018dac1c17e3,
203    0xbc78e44442565953,
204    0xbfbd09b21e36c0bd,
205    0xbcb8c779e4075b10,
206    0x3fbc2861347b1b39,
207    0xbcb9f6a4816aab2e,
208    0xbfbb5a622198a72c,
209    0xbcb8e727b71a083d,
210    0x3fba9d183bc04545,
211    0xbcb67533047d83fb,
212    0xbfb9ee5eee1a97c6,
213    0x3c52f9257b962770,
214    0x3fb94c6f5898708b,
215    0xbcab7916830bd3b8,
216    0xbfb8b5ccb03d459b,
217    0x3cbb1b180f8e9062,
218    0x3fb829356c2fb67c,
219    0xbcb267f22477b55d,
220    0xbfb7a597eb76a5e3,
221];
222
223/**
224Taylor series at different zeros and extremums for Y0
225Generated by SageMath:
226```python
227def compute_intervals(zeros):
228    intervals = []
229    for i in range(0, len(zeros)):
230        if i == 0:
231            a = 2 - zeros[i]
232            b = (zeros[i] + zeros[i + 1]) / 2 + 0.05 - zeros[i]
233            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
234        elif i + 1 > len(zeros) - 1:
235            a = (zeros[i - 1] + zeros[i]) / 2 - 0.05 - zeros[i]
236            b = (zeros[i]) + 0.83 + 0.05 - zeros[i]
237            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
238        else:
239            a = (zeros[i - 1] + zeros[i]) / 2 - zeros[i] - 0.05
240            b = (zeros[i] + zeros[i + 1]) / 2 + 0.05  - zeros[i]
241            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
242    return intervals
243
244intervals = compute_intervals(y0_zeros)
245print(intervals)
246
247def build_sollya_script(a, b, zero, deg):
248    return f"""
249prec = 500;
250bessel_y0 = library("./notes/bessel_sollya/cmake-build-release/libbessel_sollya.dylib");
251f = bessel_y0(x + {zero});
252d = [{a}, {b}];
253pf = remez(f, {deg}, d);
254for i from 0 to degree(pf) do {{
255    write(coeff(pf, i)) >> "coefficients.txt";
256    write("\\n") >> "coefficients.txt";
257}};
258"""
259
260def load_coefficients(filename):
261    with open(filename, "r") as f:
262        return [RR(line.strip()) for line in f if line.strip()]
263
264def call_sollya_on_interval(a, b, zero, degree=12):
265    sollya_script = build_sollya_script(a, b, zero, degree)
266    with open("tmp_interval.sollya", "w") as f:
267        f.write(sollya_script)
268    import subprocess
269    if os.path.exists("coefficients.txt"):
270        os.remove("coefficients.txt")
271    try:
272        result = subprocess.run(
273            ["sollya", "tmp_interval.sollya"],
274            check=True,
275            capture_output=True,
276            text=True
277        )
278    except subprocess.CalledProcessError as e:
279        return
280
281degree = 17
282
283print(f"pub(crate) static Y0F_COEFFS: [[u64;{degree + 1}]; {len(intervals)}] = [")
284for i in range(0, len(intervals)):
285    interval = intervals[i]
286    call_sollya_on_interval(interval[0], interval[1], interval[2], degree)
287    coeffs = load_coefficients(f"coefficients.txt")
288    print("[")
289    for c in coeffs:
290        print(double_to_hex(c) + ",")
291    print("],")
292print("];")
293```
294**/
295pub(crate) static Y0F_COEFFS: [[u64; 18]; 47] = [
296    [
297        0x3fe0aa48442f014b,
298        0xbc009e915c2e5f95,
299        0xbfd0aa48442f0143,
300        0x3fa439fac165257c,
301        0x3f80d2af4e929791,
302        0x3f4f71646c0dc646,
303        0xbf5444bda7f2ee4c,
304        0x3f384c21f1d0de42,
305        0xbf217ab4d69ab0db,
306        0x3f0dafc989c8ea40,
307        0xbef8bbefbac0d893,
308        0x3ee48ac7a622784f,
309        0xbed1245593770ad0,
310        0x3ebc28878607b687,
311        0xbea585c089718cc9,
312        0x3e8b7ad75bd333d8,
313        0xbe68a20d8d3d57a5,
314        0x3e362c70b36d12a4,
315    ],
316    [
317        0x3bf75cf88f1b7237,
318        0xbfd9c34256a12a0c,
319        0x3faa09c9290367ec,
320        0x3fadf6d59bf50e4b,
321        0xbf7c116fdc597e2f,
322        0xbf61e32bc4eef0b0,
323        0x3f29982765136b27,
324        0x3f0ab2c1fd5871c0,
325        0xbed486371d6e71eb,
326        0xbe93b212b9208b3e,
327        0xbe577700c20e01fd,
328        0x3e545234fb052f6a,
329        0xbe2f6a5f736d8c82,
330        0x3e0a8134a3ddd47f,
331        0xbde9666a74f1504a,
332        0x3dc63b75b90c0da3,
333        0xbdaa991122c61028,
334        0x3d930f1a31e30006,
335    ],
336    [
337        0xbfd5c7c556f0c19a,
338        0xbbc44b457ab6a440,
339        0x3fc5c7c556f0c19a,
340        0xbf8564d4b1ed0d7e,
341        0xbf8a15d92dfe3e28,
342        0x3f4b438430469f6e,
343        0x3f37a8924cc2fcab,
344        0xbef5f69b4a89930d,
345        0xbed85b940ebd0c07,
346        0x3e955ac0f4e7f8ab,
347        0x3e6d563e284b0072,
348        0xbe23eac267e6cf3c,
349        0xbe00077161c32b55,
350        0x3dc04d965b688847,
351        0xbd45e4f4886f7d51,
352        0x3d5501605dba787a,
353        0xbd363e6119f047ec,
354        0x3d096861e7e8004b,
355    ],
356    [
357        0xbb236a0ad5bec7c3,
358        0x3fd334cca0697a5b,
359        0xbf95aef611fc4d57,
360        0xbfa8969c64cbf452,
361        0x3f6b2f14a95527cb,
362        0x3f61d35e85fde2a4,
363        0xbf226dd71e391c65,
364        0xbf08177e4fe524db,
365        0x3ec6a9227352b13b,
366        0x3ea34aa757412911,
367        0xbe60a2814d2e238a,
368        0xbe3442a3d67717ae,
369        0x3defa6c448c9759c,
370        0x3dbf14eacd6e3a21,
371        0xbd771434b676ae83,
372        0xbd406a106470261f,
373        0x3cf2c5324aed291b,
374        0x3cc47f208256e17f,
375    ],
376    [
377        0x3fd15f993fceab5c,
378        0xbb597aaa5d4472ea,
379        0xbfc15f993fceab5c,
380        0x3f758ef6efbed797,
381        0x3f86395dfe49fcd4,
382        0xbf3fb15104a41c03,
383        0xbf35f88a11d55641,
384        0x3eef37d226a827fd,
385        0x3ed6f7bab104d878,
386        0xbe8f0c45a3868f32,
387        0xbe6dfe11ded99f62,
388        0x3e2311adc6046d1a,
389        0x3dfad34dd085ee0f,
390        0xbdafdc85833041dc,
391        0xbd819463fb6a5c22,
392        0x3d33a4c369438250,
393        0x3d014560b8776112,
394        0xbcb2ae15d3a41e47,
395    ],
396    [
397        0x3b12ba7db6ce5807,
398        0xbfcff635cc72b9f1,
399        0x3f89036451ff57c5,
400        0x3fa4e667a71556af,
401        0xbf60325ee41e910c,
402        0xbf5fe23914fb9128,
403        0x3f17f84d7c50e49e,
404        0x3f06afdd57be1e75,
405        0xbec04053abf415e2,
406        0xbea2aea9ec4954d7,
407        0x3e593eb9f19579b5,
408        0x3e3428a3a4917f21,
409        0xbde99d8be9e4cd5a,
410        0xbdbec9815ee61f19,
411        0x3d7260f619cb637c,
412        0x3d418f963ce687db,
413        0xbcf38a6e7195daa0,
414        0xbcbf332d386dfb1b,
415    ],
416    [
417        0xbfcdc14ea14e89f9,
418        0x3b52ef4e10970973,
419        0x3fbdc14ea14e89f9,
420        0xbf6b037fe9cf2a52,
421        0xbf8367d7d608e4ba,
422        0x3f34abef5636e4f9,
423        0x3f33d8a66122924a,
424        0xbee5cfe92a1a2ead,
425        0xbed571814a1a8669,
426        0x3e87414e33ccd6d7,
427        0x3e6ca7069e37c5b4,
428        0xbe1e0b3a74e3f35e,
429        0xbdfa15dd188a976e,
430        0x3daa33983e3b34b5,
431        0x3d8141656fbf9e02,
432        0xbd3089bd5153b08a,
433        0xbd01345e91fc8d5c,
434        0x3cb05566655c2807,
435    ],
436    [
437        0xbb10bed1f7905ee9,
438        0x3fcbf32a27594007,
439        0xbf80bc2d84e65214,
440        0xbfa26cab38a8b368,
441        0x3f55f03e47165d72,
442        0x3f5caaa76e34992d,
443        0xbf10c5f18c46d00f,
444        0xbf04f0af7d46cd82,
445        0x3eb7d1e28094a46b,
446        0x3ea1ad073122cd33,
447        0xbe536021c88affe4,
448        0xbe3371ae6cd96849,
449        0x3de46ce028e7c109,
450        0x3dbe235dc856ef66,
451        0xbd6e401d592ca47a,
452        0xbd415f37788a98a4,
453        0x3cf078a1b34fa822,
454        0x3cbefbc3ca8cda9f,
455    ],
456    [
457        0x3fca7022be084d99,
458        0xbb4ddca3665cb95a,
459        0xbfba7022be084d99,
460        0x3f62ee079d020b12,
461        0x3f8163191c30aa62,
462        0xbf2d7806ea72fc7a,
463        0xbf320f95702b1d3e,
464        0x3ee006108822968d,
465        0x3ed3e398cbc455aa,
466        0xbe81bbe181c8bfbe,
467        0xbe6b0f89b78908bf,
468        0x3e17c3f85c062f0a,
469        0x3df902361639d835,
470        0xbda56494e7b59641,
471        0xbd80bde23236fbba,
472        0x3d2bbbd3bb25cf30,
473        0x3d00d7f96ac5af92,
474        0xbcabe3861f527a48,
475    ],
476    [
477        0x3b0d39acdbc38af2,
478        0xbfc925c35988ee29,
479        0x3f7862549367591e,
480        0x3fa0a4512039d6a2,
481        0xbf5013b38cfb9292,
482        0xbf5a24a1215f6684,
483        0x3f08f91421377f72,
484        0x3f035d17cec01753,
485        0xbeb2283a93110ac0,
486        0xbea099e713932038,
487        0x3e4e5de01dbe7d10,
488        0x3e3288585522eec4,
489        0xbde0730be51a22c7,
490        0xbdbd174416e1daeb,
491        0x3d68f810d9b70d7c,
492        0x3d40f177553ea68b,
493        0xbcebc58c79d9f1a6,
494        0xbcbe6305e9d630f0,
495    ],
496    [
497        0xbfc80781c32422e7,
498        0x3b483f69e003254a,
499        0x3fb80781c32422e7,
500        0xbf5c6923374d561f,
501        0xbf7fbe6df840847f,
502        0x3f264f4711a85f1d,
503        0x3f309ff42b0d7a58,
504        0xbed8a60685a59ae7,
505        0xbed282d26a74a669,
506        0x3e7bdb57a88d9298,
507        0x3e697d9c12695952,
508        0xbe131aa86bece7b9,
509        0xbdf7d486a4891297,
510        0x3da197f4a31bb9d7,
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1023        0xbf22e052707cc843,
1024        0x3eb18a5da77ee010,
1025        0x3ec5846b622f2fd0,
1026        0xbe54b17e97b8ccc9,
1027        0xbe5e7f7666f84ced,
1028        0x3dedeb50538393d5,
1029        0x3ded72e1f6ccd5a2,
1030        0xbd7d3e0b2d7b598f,
1031        0xbd749b384c86d390,
1032        0x3d049ebe7a682354,
1033        0x3cf5a2123b57dec6,
1034        0xbc8662ce26072b62,
1035    ],
1036    [
1037        0x3ae97c92b0497970,
1038        0xbfba4407dac72297,
1039        0x3f4bcba4dec1da44,
1040        0x3f91803c65cafdfb,
1041        0xbf2283df2b3e4a6d,
1042        0xbf4bf695e89259cd,
1043        0x3edd8f3759122cea,
1044        0x3ef54246c8e04206,
1045        0xbe867111bc8e08a2,
1046        0xbe92d72a1f62d131,
1047        0x3e23d9ca3e4f40f9,
1048        0x3e25d74a6df26826,
1049        0xbdb6f4b3a86a00b8,
1050        0xbdb1d6f951aed310,
1051        0x3d42b1828de6ffa0,
1052        0x3d35a1d54468858d,
1053        0xbcc655ad620318bd,
1054        0xbcb40c27591e7a1a,
1055    ],
1056    [
1057        0xbfb9ee5eee1a97c6,
1058        0x3b22e5c966133b1c,
1059        0x3fa9ee5eee1a97c6,
1060        0xbf31d55d93e59bd7,
1061        0xbf7146219394a99c,
1062        0x3efc7d32bb646e2e,
1063        0x3f226599aed4f1b4,
1064        0xbeb03ba58ec85e6f,
1065        0xbec4f9e3961b9170,
1066        0x3e5328d4dc364807,
1067        0x3e5dbda7ac1d3f8b,
1068        0xbdebb7c2f5dfce50,
1069        0xbdecbac1e6849bc9,
1070        0x3d7b1c39328db702,
1071        0x3d741cdba002ff38,
1072        0xbd0321f9e5a1aec7,
1073        0xbcf520545c68186a,
1074        0x3c84ca30f2d8fe34,
1075    ],
1076    [
1077        0xbae7aaec85700fa6,
1078        0x3fb99be73fa3efcc,
1079        0xbf49c3248da75775,
1080        0xbf91107147eda800,
1081        0x3f212980be9d8520,
1082        0x3f4b44e1221e6051,
1083        0xbedb67b78c1dd966,
1084        0xbef4bc49e9b5bceb,
1085        0x3e84d02ffb8b7772,
1086        0x3e9261c31456c932,
1087        0xbe226b4006e91d9d,
1088        0xbe25512519fb5144,
1089        0x3db5500f2545f2d3,
1090        0x3db16b4e5f84ad48,
1091        0xbd415e211f9e7a0f,
1092        0xbd3521ed4cbd2b27,
1093        0x3cc4c4800c50a30c,
1094        0x3cb39810921b4be9,
1095    ],
1096    [
1097        0x3fb94c6f5898708b,
1098        0xbb219499b2c197ca,
1099        0xbfa94c6f5898708b,
1100        0x3f308f4f1b8fb0dc,
1101        0x3f70da931c776c71,
1102        0xbefa7550d2940f2e,
1103        0xbf21f3b978a47cde,
1104        0x3eae28ea0247325a,
1105        0x3ec47930aec7652a,
1106        0xbe51ce32c4f61fb7,
1107        0xbe5d0950e94a9be9,
1108        0x3de9c5a164496f38,
1109        0x3dec0f17151563cb,
1110        0xbd79390150c5d3eb,
1111        0xbd73a6c5157c0de8,
1112        0x3d01d041a270134c,
1113        0x3cf4a6c2b9e9b4e9,
1114        0xbc835f05ebdf3e12,
1115    ],
1116    [
1117        0x3ae60bdc6a36e0e5,
1118        0xbfb8ffc9b9a131f6,
1119        0x3f47f724314bb99d,
1120        0x3f90a89c5d1074ba,
1121        0xbf1feeaeb33465e7,
1122        0xbf4a9fba36a7a08e,
1123        0x3ed980034770f358,
1124        0x3ef43fa4bb8cba45,
1125        0xbe835f40f3a33db9,
1126        0xbe91f465ba2910f8,
1127        0x3e212688f6f9e1b4,
1128        0x3e24d3f7e3ce0c1a,
1129        0xbdb3daee33c4651d,
1130        0xbdb106a0ff5e7529,
1131        0x3d40309d2f92ac42,
1132        0x3d34aa09772c258a,
1133        0xbcc35f72aaef208c,
1134        0xbcb32afd4e360d62,
1135    ],
1136    [
1137        0xbfb8b5ccb03d459b,
1138        0x3b206ac337f71f68,
1139        0x3fa8b5ccb03d459b,
1140        0xbf2edc98b92fedf3,
1141        0xbf70767d524cea88,
1142        0x3ef8a85a847c89c6,
1143        0x3f2189afaa2bffb7,
1144        0xbeac1d231a69bf1e,
1145        0xbec40139bdbc767b,
1146        0x3e509a6859cb8509,
1147        0x3e5c60fc5f4b173c,
1148        0xbde80ad395bd719c,
1149        0xbdeb6e94ec333a76,
1150        0x3d778adf7d6d4ffb,
1151        0x3d7338227f2ea5d9,
1152        0xbd00a328a2899a4a,
1153        0xbcf4349a4535eb0d,
1154        0x3c821ac1fe027675,
1155    ],
1156    [
1157        0xbae4990a795d52df,
1158        0x3fb86e51bb2ee24d,
1159        0xbf465e3bad214eb8,
1160        0xbf9047d6ed159c31,
1161        0x3f1dce4a381ce24d,
1162        0x3f4a05b93842da9a,
1163        0xbed7ce3df60b0e4e,
1164        0xbef3cb50138cce39,
1165        0x3e8216e84a5d9f52,
1166        0x3e918e354c013832,
1167        0xbe2005492fe9c63e,
1168        0xbe245ed4a343a749,
1169        0x3db28e2e71c56d3c,
1170        0x3db0a83f8589bb9d,
1171        0xbd3e46baa33f452c,
1172        0xbd3439690ccae646,
1173        0x3cc2201c8a30e9e6,
1174        0x3cb2c44f88828341,
1175    ],
1176    [
1177        0x3fb829356c2fb67c,
1178        0xbb1ebe6fec859455,
1179        0xbfa829356c2fb67c,
1180        0x3f2cd964e5e4caa0,
1181        0x3f70190ce66b97c3,
1182        0xbef70d5fd8bad7b8,
1183        0xbf2126a150469af1,
1184        0x3eaa49ea858153dd,
1185        0x3ec3910f5c157962,
1186        0xbe4f0f4bdbe6f9e5,
1187        0xbe5bc36977db17fb,
1188        0x3de67f295d55fdea,
1189        0x3dead81ba8b0c52f,
1190        0xbd760a13803ef42a,
1191        0xbd72d03bf820c54e,
1192        0x3cff2ad7c1434050,
1193        0x3cf3c92e07a03306,
1194        0xbc80f7d055471199,
1195    ],
1196    [
1197        0x3ae34bfa6ed120b4,
1198        0xbfb7e656ed57a0d1,
1199        0x3f44f0cfc62eb61c,
1200        0x3f8fdaba63e9c655,
1201        0xbf1be7bad1c50546,
1202        0xbf4975ac0770c98d,
1203        0x3ed64a6af83ba812,
1204        0x3ef35e6b41b6d769,
1205        0xbe80f12d050da9bf,
1206        0xbe912e744222d16c,
1207        0x3e1e04a8c0124324,
1208        0x3e23f0ed5e3ac1ab,
1209        0xbdb163fd1599c398,
1210        0xbdb04f8ecba977f7,
1211        0x3d3c639575076eb9,
1212        0x3d33cf61a84aa254,
1213        0xbcc101368b088743,
1214        0xbcb26377b4c35c24,
1215    ],
1216    [
1217        0xbfb7a597eb76a5e3,
1218        0x3b53aefe167f1294,
1219        0x3fa7a597eb76a5e3,
1220        0xbf2b0bd9eb615315,
1221        0xbf6f831b9629acd2,
1222        0x3ef59d1c40c95bc4,
1223        0x3f20c9d35d4be179,
1224        0xbea8a711bec6b4b0,
1225        0xbec327e42f38db9e,
1226        0x3e4d225aa909ad2f,
1227        0x3e5b2f83a8f0f85c,
1228        0xbde51bef24cad6b5,
1229        0xbdea4ab13337518e,
1230        0x3d74b0547a699854,
1231        0x3d726e6cf385d626,
1232        0xbcfd56db39ddf26a,
1233        0xbcf362be01af446b,
1234        0x3c82edb1a6e2242c,
1235    ],
1236];
pxfm/bessel/y0f_coeffs.rs

pxfm/bessel/
y0f_coeffs.rs
