pxfm 0.1.29 - Docs.rs

/*
 * // Copyright (c) Radzivon Bartoshyk 8/2025. All rights reserved.
 * //
 * // Redistribution and use in source and binary forms, with or without modification,
 * // are permitted provided that the following conditions are met:
 * //
 * // 1.  Redistributions of source code must retain the above copyright notice, this
 * // list of conditions and the following disclaimer.
 * //
 * // 2.  Redistributions in binary form must reproduce the above copyright notice,
 * // this list of conditions and the following disclaimer in the documentation
 * // and/or other materials provided with the distribution.
 * //
 * // 3.  Neither the name of the copyright holder nor the names of its
 * // contributors may be used to endorse or promote products derived from
 * // this software without specific prior written permission.
 * //
 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
 * // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/**
Taylor series for Y1 in extremums and zeros.

Generated by SageMath:

```python
mp.prec = 115
terms = 28
print(f"pub(crate) static Y1_COEFFS: [[(u64, u64); {terms}]; {len(y1_zeros)}] = [")

def get_constant_term(poly, y):
    for term in poly.operands():
        if term.is_constant():
            return term

def print_taylor_coeffs(poly, n):
    print("[")
    for i in range(0, n):
        coeff = poly[i]
        print_double_double("", RealField(115)(coeff))
        # print(f"{double_to_hex(coeff)},")
    print("],")

prev_zero = 0

for i in range(0, len(y1_zeros)):
    k_range = y1_zeros[i]
    range_diff = k_range - prev_zero

    x0 = mp.mpf(k_range)
    from mpmath import mp, bessely, taylor
    poly = taylor(lambda val: bessely(1, val), x0, terms)
    # print(poly)
    print_taylor_coeffs(poly, terms)
    prev_zero = y1_zeros[i]

print("];")
```
 */
pub(crate) static Y1_COEFFS: [[(u64, u64); 28]; 32] = [
    [
        (0x0000000000000000, 0x0000000000000000),
        (0xbc749367c4c05aaa, 0x3fe0aa48442f014b),
        (0xbc58e5288bbf5fe3, 0xbfbe56f82217b8f1),
        (0x3c45adcf3e0230ee, 0xbfa0d2af4e932386),
        (0xbc1aef581a20d1b6, 0xbf73a6dec37290aa),
        (0x3bea0fd3a3179817, 0x3f7e671c7d1196fd),
        (0x3bdbfdc1a54825cd, 0xbf65429dc5a45612),
        (0x3bf2b56b5db9ac40, 0x3f517ab4afac0735),
        (0x3bebebd87be68c3c, 0xbf40b2d877d5a29c),
        (0xbbcf3ef5ec675b9a, 0x3f2eea7bbb907646),
        (0xbbbc5481911cf1b3, 0xbf1c3fae3b0ad706),
        (0xbb97d87196deccbb, 0x3f09d174c9ccecd9),
        (0x3b9ce9bed2434862, 0xbef7956ad3fe9783),
        (0xbb81a3285733db7f, 0x3ee5865d11ebb14d),
        (0x3b7c0f8e48b356f0, 0xbed3a27f1fd4ac6e),
        (0xbb601bb903ea5d53, 0x3ec1e742c1cf6acb),
        (0xbb208185a8aebef4, 0xbeb051d134cb0a72),
        (0x3b2d22383a2945e9, 0x3e9dbea846629267),
        (0xbb2d0bd2365f955b, 0xbe8b1a1682f5eb1f),
        (0xbb17f54155dbfd8e, 0x3e78b0b08d8ccddf),
        (0x3b0c6ae86d8ad6fe, 0xbe667d8a7cc18981),
        (0xbaea87f82b9f7fa9, 0x3e547c0e174bc402),
        (0x3ae6655ff087a6b2, 0xbe42a7fb50d94c09),
        (0xba74f97124d12cda, 0x3e30fd661ade45f0),
        (0x3aad4c923a16d045, 0xbe1ef1655b283bca),
        (0x3aa6328133433e29, 0x3e0c2d21fe733c5f),
        (0xba292d7e82d617f2, 0xbdf9a7efb711afac),
        (0xba60d9e2266f470a, 0x3de75c3fc5194fe2),
    ],
    [
        (0x3c3c696f3eb0ae77, 0x3fdaabb4011ed330),
        (0x0000000000000000, 0x0000000000000000),
        (0xbc682b7fe4dd90ef, 0xbfc8b45babe797ba),
        (0x3bf255e280edf040, 0x3f8e147099a6f0ea),
        (0xbbfea368c6887e7f, 0x3f88c5af1eeb2d6b),
        (0xbbca04ffe9904e56, 0xbf4133fa47da52e2),
        (0xbbd3086cde21e2cb, 0xbf3bf8af93ff0b8c),
        (0xbbafa9018f253e3c, 0x3f021d64be62ccf9),
        (0x3b3a4d52bc5a61e1, 0x3eb44d2ce67b2d18),
        (0xbb48016de8c47acb, 0x3eb14c3ab2ad79cc),
        (0x3b28724eeca6e146, 0xbe9b8eee52e1ce01),
        (0xbb184699c450d4ac, 0x3e7a85f1a878746a),
        (0xbaf5fb00f2f338b7, 0xbe5bf86b3c89849b),
        (0x3adf14ae65986334, 0x3e3f01920a1ecb6b),
        (0xbac5a8492238e17f, 0xbe20fac544c5a674),
        (0x3a972f86dd69da9b, 0x3e02818841d3a289),
        (0xba686f565d0da109, 0xbde42b5ceddd3872),
        (0x3a540c6129af60a6, 0x3dc5f9472a38633d),
        (0xba4276328d0b688c, 0xbda7ed484e6442ee),
        (0xba23ab0f9748db4a, 0x3d8a0b10351f65a6),
        (0x39d5b91f2ce320af, 0xbd6c567ba5000a2c),
        (0x39e0b587d390388d, 0x3d4ed39e06bafa8a),
        (0xb9ca4dd40bbdfa57, 0xbd30c36f7f68d190),
        (0xb9ae9f2d1d6c950e, 0x3d123a81488a8c60),
        (0x39796d1b53f4c705, 0xbcf3d198a043957c),
        (0xb97e66e460933260, 0x3cd58b80d1da3cb2),
        (0xb95de7856c390662, 0xbcb76b414bca83a9),
        (0x3923face03bca6a1, 0x3c99742311b12a8a),
    ],
    [
        (0x0000000000000000, 0x0000000000000000),
        (0x3c7b8d2a1c496808, 0xbfd5c7c556f0c19a),
        (0xbc370c18fffb661e, 0x3fa00b9f8571ca1f),
        (0xbc4e4289c3acba27, 0x3faa15d92dfe3e27),
        (0xbbf5a3591cb63f33, 0xbf710a329e2c23fa),
        (0xbc0511883ce39919, 0xbf61be6db9923acf),
        (0x3bcb8759d4a0e5cd, 0x3f2337c7e138f484),
        (0x3ba7299907aec5c4, 0x3f085b940eb607f9),
        (0xbb2063eb830ecaea, 0xbec80619147b78f2),
        (0xbb4468879e6c349e, 0xbea255e6cf70cf33),
        (0xbafc601de5ef1462, 0x3e5b62cd02014989),
        (0xbad6adc77b77235d, 0x3e380b1aac007d1d),
        (0x3a624f45defeeef1, 0xbdfa7ee05a568fe6),
        (0xba283df15edc8775, 0x3d84065ca5f23bb5),
        (0xba2c1a2ebca15779, 0xbd93847684c7da93),
        (0x3a08225b40e694f7, 0x3d74980895b5067a),
        (0xb9eed81f16f01fb8, 0xbd4c00f7d6be89d7),
        (0xb9a4e2f268d1912d, 0x3d2402fd58efd6fd),
        (0x399973b6338a6d0f, 0xbcfded82b76f72f2),
        (0x3978023c06cffc92, 0x3cd6380d6ba31980),
        (0xb94735a17d43c8d2, 0xbcb06b38ec70e0a6),
        (0x3907f71a9df6b85b, 0x3c88443f14394c1d),
        (0xb8f01075b123018b, 0xbc61ee2105252260),
        (0xb8b57669955b81a8, 0x3c3a7c72c37961bf),
        (0xb8954dc89e6e0348, 0xbc138e5e595f9137),
        (0xb87ee16a4e8bff5b, 0x3becdf0d22c4f792),
        (0xb86abb1732ed43be, 0xbbc54e9dcbced4f1),
        (0xb82e4e62e1a676d6, 0x3b9f718438e6ba2f),
    ],
    [
        (0xbc583acf6511df31, 0xbfd36732d4b96094),
        (0x0000000000000000, 0x0000000000000000),
        (0xbc5b435291c33433, 0x3fc3001c8002caf8),
        (0x3c085153ba2c907f, 0xbf7bf5a03bab4999),
        (0x3c28d66c540219c4, 0xbf8751ea028c1953),
        (0x3be6d2f429037cfc, 0x3f423874cd8d0401),
        (0xbbb4d7b925522373, 0x3f364f6610d64939),
        (0xbb9920eb782e7608, 0xbef02978de3838b9),
        (0x3b66c8e5402ae5c0, 0xbed72f0766d0d591),
        (0x3b20b724f28fabb4, 0x3e8f2081874c7e33),
        (0xbafe89c3eab7b761, 0x3e6defd5dce00666),
        (0x3ab712e9adc751d5, 0xbe2205c6fe8f26fd),
        (0xba90a1fcff20092c, 0xbdfb6432e005a435),
        (0xba40d93a2f6bee54, 0x3db0289fce476883),
        (0xba2c7d1344d3ff23, 0x3d80778a2d37fe43),
        (0x39a7b4208bcbde0d, 0xbd29723fe5684800),
        (0xb9a84df62153f4f5, 0xbd082f3f70663f33),
        (0xb91998f4a32b0e4b, 0x3cc7a09f40ec7306),
        (0x39256931314bf68c, 0xbc85319ec342127c),
        (0x38fd4eda573e2499, 0x3c62d63483483be2),
        (0xb8a4a42a37750699, 0xbc38c3ecf9381019),
        (0x3893811d88a13751, 0x3c0ba15f09ca6382),
        (0xb8653a606cd73ccb, 0xbbdf92174ea83693),
        (0x385bcb6c1b8ec617, 0x3bb25604c3a40365),
        (0xb82168dd0f69d5f1, 0xbb853b55eb1a54fe),
        (0xb7e96fc33c8ede98, 0x3b5889d72e8200c6),
        (0xb7b3762a6112ab36, 0xbb2c5b6e1cc194ec),
        (0xb78614198a535866, 0x3b0061d24b95ed7a),
    ],
    [
        (0x0000000000000000, 0x0000000000000000),
        (0x3c61dc672a53c590, 0x3fd15f993fceab5c),
        (0xbc1455aa7db14f38, 0xbf902b3933cf21b1),
        (0x3c443ede64b782d9, 0xbfa6395dfe49fcd4),
        (0x3be10ad2b71b9820, 0x3f63ced2a2e69180),
        (0x3c0f30cad7e0ebe8, 0x3f607a678d6000bb),
        (0x3baf8fd02659f1ef, 0xbf1b50d7e1d32020),
        (0x3b91fb17827843f5, 0xbf06f7bab104f355),
        (0xbb60ab92724984c7, 0x3ec176e72bf94b8f),
        (0x3b31557f6e92a4a7, 0x3ea2becb2b6bbc6d),
        (0x3aea30e9dd0c4fab, 0xbe5a384eebfe1367),
        (0xbad27d53b702d9ee, 0xbe341e7a923c3a90),
        (0x3a8be8710ba9cded, 0x3de9e3284f5dd101),
        (0xba5a7ff332888842, 0x3dbec40b623ea350),
        (0x3a1bb0f2b7e06e32, 0xbd726868b83f8d7d),
        (0xb9d127448ae5dbb8, 0xbd416f7ae80cad77),
        (0xb98b4267f56d6b60, 0x3cf318658ecb9bd5),
        (0x394a28f7ccb2ac45, 0x3cbfacabdbabe483),
        (0xb8fdeb4ca08fc098, 0xbc713cc1f6930364),
        (0x38c8e1a7a7c446ff, 0xbc33cb94044d8aee),
        (0x3846a7a1323190de, 0x3bda22029099f534),
        (0x385ab5c5889916dc, 0x3bb47d9b88989e97),
        (0x381dfc385d309d52, 0xbb745299177606ed),
        (0x37def84f6911654b, 0x3b3503d9701ead82),
        (0x3757dbc183f5d86f, 0xbb08176b7514ca80),
        (0x3726e80a82be2e11, 0x3ad863cb123482cb),
        (0xb7400c9d5c314e72, 0xbaa6552586051784),
        (0xb6ed950d76fdf6bc, 0x3a74afbafce97c21),
    ],
    [
        (0xbc64f19a2762f5ae, 0x3fd00ef3745e0e3c),
        (0x0000000000000000, 0x0000000000000000),
        (0xbc2a5ca3437ac1c3, 0xbfbfcdacdda138f2),
        (0x3c19a8e604f93931, 0x3f706cc34cd829fa),
        (0x3c01d3813b5701a3, 0x3f84641bb10c16cb),
        (0x3bbd08ac252b4932, 0xbf37fac943e2a16d),
        (0xbbd98c55ed55e5ec, 0xbf34769ed32e14a2),
        (0xbb8b665d8b88b73b, 0x3ee80608ecda1520),
        (0xbb7d207258864fea, 0x3ed5cc8242d77e79),
        (0x3b2f5c5f133a954a, 0xbe888c8f253923cc),
        (0xbb0d50fa8d8c7a72, 0xbe6ce5908c1f1376),
        (0x3abc19806933366e, 0x3e1ed1625825eeeb),
        (0x3a969b1553c1a884, 0x3dfa30d624f10edf),
        (0x3a41711a2b894301, 0xbdaa50765ef82dbe),
        (0x39ef8b9861fc6da9, 0xbd814cd364ef8287),
        (0xb9bec99ce5124af1, 0x3d306199db2399a2),
        (0x39a24cb0ca5a627f, 0x3d0164150f087360),
        (0xb90883d74ed9e2a1, 0xbcaefb1085d3b5a6),
        (0x390110bd90901ca7, 0xbc7ba1419f5a6f40),
        (0x389f7ac7f08169b1, 0x3c27638ccf29c1b0),
        (0xb89f51222b4b42bb, 0x3bf18a62dccdca9d),
        (0xb83b3be96059d0b4, 0xbb9b54a4a2d7343a),
        (0x38017f10a44ce3ed, 0xbb635931e0eacdee),
        (0x37be3118e01854ca, 0x3b1036817e50e3af),
        (0xb7657afa36f3f4a9, 0x3aca87e3e3debd9e),
        (0x36c384606510e7f7, 0xba44ec6558f8bb31),
        (0x36c308ed950cf583, 0xba4d684c0820785d),
        (0xb6acfa02e081161c, 0x3a0f0d58bca1c41b),
    ],
    [
        (0x0000000000000000, 0x0000000000000000),
        (0x3c54d14c77bc1691, 0xbfcdc14ea14e89f9),
        (0x3c2340bd04e7df4a, 0x3f84429fef5b5fbd),
        (0x3c4f19a8f5b1379e, 0x3fa367d7d608e4ba),
        (0xbbf4eb6bddef363a, 0xbf59d6eb2bc49e35),
        (0xbba2f121221c388c, 0xbf5dc4f991b3db86),
        (0x3bbf047b90425584, 0x3f1315ec04d6e6bc),
        (0x3b9087e84c57d2ad, 0x3f0571814a1aa301),
        (0x3b2795eb85278f1d, 0xbeba2977fa42f227),
        (0x3b3f92ddd9da4ad7, 0xbea1e86423086328),
        (0x3aff19e1c5d9e237, 0x3e54a7b82d41f690),
        (0xbad0197985af09ca, 0x3e3390660a1bb74c),
        (0x3a8a68e5322dab0d, 0xbde549e8b3ed12f4),
        (0x3a500e54fb5a85ec, 0xbdbe32cf77b347a3),
        (0xb9d3ea446c95f85a, 0x3d6eff58d55a39fb),
        (0x39d1c41d97727556, 0x3d415e5c0af749d4),
        (0x3994a6959d259d8b, 0xbcf0d67f939f4917),
        (0x3951f0d6f37c7a4e, 0xbcbef3f2afde9972),
        (0xb8ce371e6c4a5fb7, 0x3c6c60ed345061d2),
        (0xb8ce6598cd4716cf, 0x3c360519c76d6d8a),
        (0xb868ddc08c092699, 0xbbe324831e767061),
        (0x3820a7a0186edebf, 0xbba99201cd6f64ed),
        (0xb7d50b99e3cbd8ed, 0x3b55120660d9db07),
        (0x37bd05b3e6de1af6, 0x3b18d03fd947900e),
        (0x373b419f47dccb93, 0xbac397b2f45393ab),
        (0x371a75815e071b8c, 0xba840af84bf4566b),
        (0x36c253d300be5f73, 0x3a2d23b6405995b9),
        (0x365d14598eec4332, 0x39ee07cb3c4c18f5),
    ],
    [
        (0xbc5a8046704071bd, 0xbfcc075da85beb4f),
        (0x0000000000000000, 0x0000000000000000),
        (0xbc53b0c30f3f6eaa, 0x3fbbdeb6ff9f55e1),
        (0x3bef54869c1812be, 0xbf661eefb74da882),
        (0xbc20492140a086db, 0xbf8229ea914b846e),
        (0xbbc9a664ae9a2c1e, 0x3f30cbcc6778fd37),
        (0xbbd8078d46437190, 0x3f32aa59f5091f7b),
        (0xbb7b81f3aff07289, 0xbee1c15d5251ae6a),
        (0x3b707e9f1d7b7e6a, 0xbed4583f15abd692),
        (0xbb2cc9b93ff3f6ce, 0x3e831d151a1284aa),
        (0x3b0aa58bdebda7d1, 0x3e6b74e57c226d3c),
        (0x3abe0f534111cac9, 0xbe19044f1378d3e4),
        (0xba92c7e898648f68, 0xbdf93b1ec7cafe33),
        (0x3a314e62ad0639ef, 0x3da61a4e89bf8438),
        (0x3a298cd71751f9aa, 0x3d80d430f7e78fff),
        (0xb9c643be1c5347dd, 0xbd2c3b0a8f7a7b0e),
        (0xb9608e40ab9aafb9, 0xbd010e773677ab43),
        (0x3946ed856edf6b25, 0x3cab59410f7e6f10),
        (0xb8e86e49965ef8df, 0x3c7b2e693f06a801),
        (0xb8bd6df9232d394a, 0xbc24d1b6b5dbdd8a),
        (0x389d45bfc9e28c95, 0xbbf17c6418e80b27),
        (0x38330cb81415d134, 0x3b999a3de4a881f9),
        (0x38014861b029a2c1, 0x3b628ca7ea60d3ed),
        (0x3763e7968eedb33e, 0xbb09f8cd292fbd53),
        (0xb772e1ee82abca63, 0xbad0840446d9db33),
        (0x36eac14fda382bcb, 0x3a7627f31e8af8f1),
        (0x36d03dd271f85894, 0x3a38fffe9d4c8a9c),
        (0x368992b4a1b37e32, 0xb9e006ef0777e888),
    ],
    [
        (0x0000000000000000, 0x0000000000000000),
        (0x3c57ba12cd0fc91f, 0x3fca7022be084d99),
        (0xbc17334559c5138c, 0xbf7c650b6b83109a),
        (0xbc4d0f8f36713120, 0xbfa163191c30aa62),
        (0x3bbcf7c95031f425, 0x3f526b045287ddca),
        (0xbbf7b71420f279ea, 0x3f5b17602840abf5),
        (0xbb99a95b35521d32, 0xbf0c0a9cee3c842a),
        (0xbb91505ce3b29a78, 0xbf03e398cbc472ea),
        (0x3b5125ae0677178c, 0x3eb3f35db1ff1b8e),
        (0xbb4e582cdfc5009b, 0x3ea0e9b612dbd385),
        (0x3ae57a34bc6cd52d, 0xbe5056babcd9632b),
        (0x3ad18fdd63164b8f, 0xbe32c1a8c8f963a5),
        (0xb9e37fef15ca364c, 0x3de161b6aa9fde63),
        (0xba4ed1a8c48bfaf3, 0x3dbd4caa1e0162bc),
        (0xba0907496979f354, 0xbd69fdda132e53b1),
        (0x39dc92d876d25063, 0xbd4101c31e1df223),
        (0xb980f5f389d54392, 0x3cecdc25a81e55f3),
        (0xb9476a7e07116985, 0x3cbe87025cca1380),
        (0x38f93a72b93872b3, 0xbc68c602211c7544),
        (0xb8dd598494fb4eb0, 0xbc35d4a3a29a7da9),
        (0x387e1025298516ea, 0x3be0f3be0d4b8ee0),
        (0x3829d1ee76262ed4, 0x3ba97a197d3cf12a),
        (0xb7f42ff2642fd193, 0xbb52f220fc5e4bf1),
        (0xb79a001d511e0971, 0xbb18bb200c3f6737),
        (0xb75720aadc56d8cc, 0x3ac1a0fc9e585d08),
        (0xb6f810019c65facf, 0x3a8449eb5d1ccd0b),
        (0x36c0524fdb6e5bf4, 0xba2bc209d14d289f),
        (0xb663781b8b017ac7, 0xb9ec816d53cd34ad),
    ],
    [
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