pxfm 0.1.29 - Docs.rs

/*
 * // Copyright (c) Radzivon Bartoshyk 7/2025. 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.
 */

/**
Y0 Remez poly coeffs at zeros and extremums
Generated by SageMath:
```python
def compute_intervals(zeros):
    intervals = []
    for i in range(0, len(zeros)):
        if i == 0:
            a = 1.35 - zeros[i]
            b = (zeros[i] + zeros[i + 1]) / 2 + 0.03 - zeros[i]
            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
        elif i + 1 > len(zeros) - 1:
            a = (zeros[i - 1] + zeros[i]) / 2 - 0.03 - zeros[i]
            b = (zeros[i]) + 0.83 + 0.03 - zeros[i]
            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
        else:
            a = (zeros[i - 1] + zeros[i]) / 2 - zeros[i] - 0.03
            b = (zeros[i] + zeros[i + 1]) / 2 + 0.03  - zeros[i]
            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
    return intervals

intervals = compute_intervals(y0_zeros)
# print(intervals)

def build_sollya_script(a, b, zero, deg):
    return f"""
prec = 200;
bessel_y0 = library("./notes/bessel_sollya/cmake-build-release/libbessel_sollya.dylib");
f = bessel_y0(x + {zero});
d = [{a}, {b}];
pf = remez(f, {deg}, d);
for i from 0 to degree(pf) do {{
    write(coeff(pf, i)) >> "coefficients.txt";
    write("\\n") >> "coefficients.txt";
}};
"""

def load_coefficients(filename):
    with open(filename, "r") as f:
        return [RealField(500)(line.strip()) for line in f if line.strip()]

def call_sollya_on_interval(a, b, zero, degree=12):
    sollya_script = build_sollya_script(a, b, zero, degree)
    with open("tmp_interval.sollya", "w") as f:
        f.write(sollya_script)
    import subprocess
    if os.path.exists("coefficients.txt"):
        os.remove("coefficients.txt")
    try:
        result = subprocess.run(
            ["sollya", "tmp_interval.sollya"],
            check=True,
            capture_output=True,
            text=True
        )
    except subprocess.CalledProcessError as e:
        return

def print_remez_coeffs(poly):
    print("[")
    for i in range(len(poly)):
        coeff = poly[i]
        print_double_double("", coeff)
    print("],")

degree = 27

print(f"pub(crate) static Y0_COEFFS: [[(u64, u64); {degree + 1}]; {len(intervals)}] = [")
for i in range(0, len(intervals)):
    interval = intervals[i]
    call_sollya_on_interval(interval[0], interval[1], interval[2], degree)
    coeffs = load_coefficients(f"coefficients.txt")
    print_remez_coeffs(coeffs)
print("];")
```
**/
pub(crate) static Y0_COEFFS: [[(u64, u64); 28]; 47] = [
    [
        (0xbc7492c1ad707fcd, 0x3fe0aa48442f014b),
        (0x3889cbe7f6454fdf, 0x3becdccc60399188),
        (0x3c6201923a596bb0, 0xbfd0aa48442f014b),
        (0x3c24b04e2557df22, 0x3fa439fac16525f5),
        (0xbc059b63c3765131, 0x3f80d2af4e9323bc),
        (0xbbdcec718054f585, 0x3f4f71646bea8f8b),
        (0x3bf856364cecf8b8, 0xbf5444bda8b69d4e),
        (0x3bda1cb8be57cc8f, 0x3f384c2206701bfd),
        (0xbb8ae41d36dcce8d, 0xbf217ab4af8d0bf0),
        (0xbba9cb2ac1552425, 0x3f0dafb9b99a70f2),
        (0xbb951efcd9701bd5, 0xbef8bb9639d60207),
        (0x3b8a10d871292a77, 0x3ee48b6751827819),
        (0xbb709569bb189616, 0xbed1364cc5887f8d),
        (0x3b248bd9aba7d332, 0x3ebd06afc4e97689),
        (0x3b44874f3eb42a7d, 0xbea899b75531d45b),
        (0xbb036dc9313b0b72, 0x3e94f157466889b4),
        (0xbb15fb0fa7789259, 0xbe81e537d57e5872),
        (0xbae227bb9fde16a8, 0x3e6ebca03e74f872),
        (0x3ae23bb7c6812f3e, 0xbe5a95bfc7177df2),
        (0x3ae9256929650559, 0x3e46b9b8baa2a7e6),
        (0x3ac02e410dd7de2b, 0xbe32d4cd9df0cdc3),
        (0x3ac47f4d926b3967, 0x3e2169d04e3c7866),
        (0x3ab6f6c4b513d045, 0xbe12dac47ffdcb13),
        (0x3a6fa8ccc9968ba6, 0x3dfa16bd9d2454ff),
        (0xba171664de1838ee, 0xbda18f57d00cd0c8),
        (0x3a636003e2d9973c, 0x3dcac3134b14f54c),
        (0x3a5cb30d6a3e73d7, 0xbdd88bfc936d3a46),
        (0x3a600c3863532a47, 0x3dc074a2bfd935a7),
    ],
    [
        (0xb6985ea12b68dbc6, 0xba0ce46bb97e3b37),
        (0xbc5a4026e448075b, 0xbfd9c34256a12a0c),
        (0xbc49ded6e42ffb00, 0x3faa09c9290367ef),
        (0xbc253b026c745733, 0x3fadf6d59bf50ebd),
        (0xbc18dbfc7b944e60, 0xbf7c116fdc598096),
        (0x3bf40cf995f4f110, 0xbf61e32bc4ef8a41),
        (0xbbcb82d9e30fbb8a, 0x3f29982765166254),
        (0xbb7a0c04b5d6f2fd, 0x3f0ab2c1fecdcfc4),
        (0x3b7cda0c15fabc6d, 0xbed486371e6a6640),
        (0xbb079525b0987a4e, 0xbe93b21684089b98),
        (0xbaf3ba730f1c40e9, 0xbe5777058741ab00),
        (0xbaf583debf7de8c9, 0x3e5452ea009488fe),
        (0x3ab98e298e66ceb6, 0xbe2f6938829aeacd),
        (0x3aa9d6dc6976f3c9, 0x3e0a5a1f3a03d35d),
        (0x3a7994a2d0f56a03, 0xbde994e7358cedf6),
        (0x3a5a354bba4fc371, 0x3dc88ae5d31af5c1),
        (0xba357cd4a8a94073, 0xbda75329787f3d8c),
        (0xba2d0839c51ea186, 0x3d8643c578f084cf),
        (0xba0526a2696c015c, 0xbd6554780d3aba1a),
        (0xb9ec9b6ca0c2368e, 0x3d447c69a36927e9),
        (0xb9b175a5c0e46062, 0xbd23b88e0a626f34),
        (0x3994f94bb00b0bd0, 0x3d02fdee82cca7a8),
        (0xb98eac61aa84bafd, 0xbce25983eb139aeb),
        (0xb9685d6dfdbe7bfb, 0x3cc2440cd8848b87),
        (0x3922fa28d497dc91, 0xbca164c6877c570d),
        (0xb917682fb55945f7, 0x3c78a082a7dc3992),
        (0xb90f407a50193eb2, 0xbc621ea0651d2198),
        (0xb8c56e242114685f, 0x3c523596b99eb3ff),
    ],
    [
        (0x3c7b8d2a1c496808, 0xbfd5c7c556f0c19a),
        (0x36068b8c3a0eb972, 0x396e4544b8708e19),
        (0xbc6b8d2a1c496844, 0x3fc5c7c556f0c19a),
        (0xbc2b4d44aaaf080d, 0xbf8564d4b1ed0d7e),
        (0x3c2e4289c3ae4c4e, 0xbf8a15d92dfe3e27),
        (0xbbedbea922f2213b, 0x3f4b438430469ff7),
        (0x3bdc176048714c11, 0x3f37a8924cc2f914),
        (0xbb7021dbf4219b23, 0xbef5f69b4a8a3c05),
        (0xbb7729647a7cf1b3, 0xbed85b940eb607f9),
        (0x3b3d99d888f48f01, 0x3e955ac0f5c3162c),
        (0x3b0f25a287448fcc, 0x3e6d563e18b47eb8),
        (0x3ac452983ff83fe5, 0xbe23eac3a45e06f4),
        (0xbaa55a4be8b255ef, 0xbe0007671d55a8af),
        (0x3a6681c171d8b7ac, 0x3dc04e13e8d2d63b),
        (0xb9cb304019dc95a9, 0xbd46e2b306d18fe2),
        (0xb9e569987d3c61bc, 0x3d54d18f7c808f5a),
        (0xb9d65bf264af4caa, 0xbd349808958007f4),
        (0x39af1658e9591f8b, 0x3d0a5b43a3168022),
        (0xb98b94f19368caef, 0xbce1c9c4d5c7e2e7),
        (0xb91d94e29089b67f, 0x3cb933cacbb762ef),
        (0xb931aa0bcf9e385e, 0xbc91c66b5e59c10e),
        (0xb907d452cfe5d11e, 0x3c690530621ffb6d),
        (0x38e2fc94e9e2e560, 0xbc41a7142b188ece),
        (0x389fe83adc9ec098, 0x3c18ea69b49fa0ec),
        (0x386baf69f710f067, 0xbbf186b62773cb8b),
        (0xb830ab83fea718cc, 0x3bc97ee300661ddb),
        (0xb841e9ca9ef3f273, 0xbba4203d2c71dee3),
        (0x381487ed7b4c5c12, 0x3b7779cb668f4f30),
    ],
    [
        (0x35f13ef25b4edb08, 0x3952841995e45c48),
        (0xbc78d4484b7cd2a7, 0x3fd334cca0697a5b),
        (0xbc341c66c86d3ee2, 0xbf95aef611fc4d57),
        (0xbc44929b43aab7e3, 0xbfa8969c64cbf452),
        (0x3bfab353487eb8be, 0x3f6b2f14a95527cb),
        (0x3c0aa67a62fa8841, 0x3f61d35e85fde2a3),
        (0xbbb270ba54528c94, 0xbf226dd71e391c8b),
        (0xbb61863ae7da7a16, 0xbf08177e4fe52324),
        (0x3b4949552d9354dc, 0x3ec6a9227352f96a),
        (0xbb44a5b99cf95459, 0x3ea34aa7573ef14e),
        (0xbb0698b7b84362ae, 0xbe60a2814d7ac448),
        (0xbad900bb94c56b91, 0xbe3442a3d3359ad9),
        (0x3a8ac6ca8212a487, 0x3defa6c509566c72),
        (0x3a56a6cae4d17a25, 0x3dbf14e5584823d7),
        (0xb9f7410034885564, 0xbd7714c292be3962),
        (0x39d1bcc695f4f231, 0xbd40679cd58549e2),
        (0x3997214169109d52, 0x3cf3365d5a792113),
        (0xb95497cd3660e90c, 0x3cc38cf06b3134d3),
        (0xb92ac63766c35618, 0xbc82bd5a84bf3644),
        (0x38dd10b30698d66a, 0x3c326e932d44d957),
        (0xb8bf280f5863dcdc, 0xbc1271150465312d),
        (0xb878f6f4bf335d0d, 0x3be8df3e61da29e5),
        (0x384a254e3a1a9970, 0xbbb9b1263c861574),
        (0x381db06e04e97e27, 0x3b8b3ef4b052ee69),
        (0xb7f2c3a3c46974ad, 0xbb5da7aeb72ad1b2),
        (0xb7c4810afcc72e8d, 0x3b2fdbbcc787affa),
        (0x37a36df7ebbbb4ed, 0xbb031287031f9ece),
        (0xb75db740f07d1867, 0x3ad85ce53417a3c0),
    ],
    [
        (0x3c61dc672a53c590, 0x3fd15f993fceab5c),
        (0x35ea878b9ff55f5c, 0xb946a81d8aec1515),
        (0xbc51dc672a53c58f, 0xbfc15f993fceab5c),
        (0xbc0d1c390189caf7, 0x3f758ef6efbed797),
        (0xbc243ede64b782d9, 0x3f86395dfe49fcd4),
        (0xbbbb4484582c217c, 0xbf3fb15104a41c00),
        (0xbbd4410e752beb78, 0xbf35f88a11d5564f),
        (0xbb8b2d9b83a5b450, 0x3eef37d226a824b7),
        (0xbb61fb1782379734, 0x3ed6f7bab104f355),
        (0x3b2da2cb873ba95e, 0xbe8f0c45a3824d70),
        (0xbac11338801bec18, 0xbe6dfe11df12c715),
        (0xbac52938286abb6d, 0x3e2311adc2e753ee),
        (0xba9200612bccbf82, 0x3dfad34e18504e16),
        (0xba4c6eb5b9fade2d, 0xbdafdc8061ae8b15),
        (0xba251747464962f8, 0xbd819498ca6cef9b),
        (0x39d9f9efcc54f4de, 0x3d33a291d5991f6b),
        (0x39af3f93679996f3, 0x3d016f7ae80cadff),
        (0xb9422e176854fc2b, 0xbcb1f8d80decb659),
        (0xb8ef665f3b08f8e4, 0xbc7c27b5350d7ce7),
        (0x38af81adc69c8ae0, 0x3c2d08034e0e0d4c),
        (0xb88ed31bb5296f3b, 0x3befac201220d678),
        (0x37f6dcad77609354, 0xbb93e9257bbbec92),
        (0x37f2bad6f8609fad, 0xbb6dce086bd954ec),
        (0x37c3c466a462a963, 0x3b2c45f44eeac691),
        (0x377aca1c9e5ead22, 0xbaebf82d453f586e),
        (0x371d5ba887167511, 0x3abef01a452e6243),
        (0xb6e1a818be163885, 0xba8faba1ac8fc141),
        (0xb6f75474af743fde, 0x3a59bbaf9916fed8),
    ],
    [
        (0x360f6f90e85783b8, 0x396e539ee4be998b),
        (0x3c61e8f568f8c6b6, 0xbfcff635cc72b9f1),
        (0x3c0fa6ebe8b754aa, 0x3f89036451ff57c5),
        (0x3c46345bcf3c5b81, 0x3fa4e667a71556af),
        (0x3c065e386829f088, 0xbf60325ee41e910c),
        (0x3bfde6b6846da9c7, 0xbf5fe23914fb9128),
        (0xbbb9c28522c54b49, 0x3f17f84d7c50e4c4),
        (0xbbaeab0290c997f1, 0x3f06afdd57be1e14),
        (0xbb2bbdfb6c40ca93, 0xbec04053abf4386a),
        (0x3b3787c4b69beaba, 0xbea2aea9ec48d8fd),
        (0xbaf17a36377f9c62, 0x3e593eb9f1ddb4e9),
        (0x3ad9f8321f3ce337, 0x3e3428a3a3e30a13),
        (0xba49c9c135d6bfa4, 0xbde99d8c42f7a020),
        (0xba59203ca37ccc7f, 0xbdbec9805045aa58),
        (0xba08ceab2aadd382, 0x3d72613659ce994f),
        (0xb9e8053d9b1a7b6c, 0x3d418f302bdba980),
        (0xb96ea7068003a9dc, 0xbcf3bc9ccb704250),
        (0xb93e32e516fbc8fc, 0xbcbf0dc4067be8fe),
        (0xb91a819a6b2cfdb1, 0x3c706e491f458177),
        (0xb8b2f6e0e017d3a4, 0x3c36013bac772fd5),
        (0xb88860e3b038bbbc, 0xbbe616b4d60c99dd),
        (0x38440765a3381ed6, 0xbba93fb6fc116a65),
        (0x37f070ddd36dbc13, 0x3b57963a3ba9df68),
        (0x37b30f1b7dcdc2ea, 0x3b1937f28596352a),
        (0x3760f019da1d4947, 0xbac837f92e435c71),
        (0xb6cfd07d0b99a723, 0xba80a4be8fbdea42),
        (0xb6b4329fac42bf24, 0x3a19c0ce24bac50d),
        (0xb69a16105af87cd5, 0x39ff46fe69318a2c),
    ],
    [
        (0x3c54d14c77bc1691, 0xbfcdc14ea14e89f9),
        (0xb61ccfd68577b5e8, 0xb97a750db049a3bc),
        (0xbc44d14c77bc1688, 0x3fbdc14ea14e89f9),
        (0x3c00ff03f975831b, 0xbf6b037fe9cf2a52),
        (0xbc2f19a8f5b137a3, 0xbf8367d7d608e4ba),
        (0x3bdd892317f290f5, 0x3f34abef5636e4f7),
        (0x3bd5ba5b5b609686, 0x3f33d8a661229259),
        (0xbb700a3f0097a359, 0xbee5cfe92a1a2c45),
        (0xbb6087e84c57990c, 0xbed571814a1aa301),
        (0x3b22b6740db0f074, 0x3e87414e33c9bacd),
        (0x3afa4836a20e8280, 0x3e6ca7069e73d1d9),
        (0x3abe65fd39b0188a, 0xbe1e0b3a705ff247),
        (0x3a95774f6fa018cb, 0xbdfa15dd62cf9f10),
        (0xba399e86b7dd9f12, 0x3daa33948eada12c),
        (0x3a22398b28ff34ba, 0x3d81419b1fd428ef),
        (0x39c9ae1ea6c0045a, 0xbd30882f60b8a775),
        (0x39a31e54bbe9a33e, 0xbd015e5c0af749d4),
        (0x39454d020e06c1f7, 0x3cafb1e115e089b2),
        (0x3910a4f9eea95a23, 0x3c7b83826370860f),
        (0xb8c57c15f2ff0eb8, 0xbc27e5d539874c6c),
        (0xb87dc14618f0e43b, 0xbbf19dae391ff57d),
        (0xb82fe2e247291923, 0x3b9d2b7278390d46),
        (0x37f3825b1f8b77eb, 0x3b6298bb72cef60f),
        (0x37a7910d5f5dc998, 0xbb0d50bc222d50f5),
        (0x3776acb65e1367e0, 0xbad08ac20d33e370),
        (0x37062a8b170aa42b, 0x3a79154a0ab2b1c5),
        (0xb6d06d11501acdf8, 0x3a3884b2a5dd01b8),
        (0x36832f558f511cbf, 0xb9e1c3f19ed31df1),
    ],
    [
        (0xb5d1f4401b5b78db, 0x396e44a7ff47853b),
        (0x3c41398cacaa32cb, 0x3fcbf32a27594007),
        (0x3bfe5ce4af72439b, 0xbf80bc2d84e65214),
        (0x3c4acd5148eb7ea0, 0xbfa26cab38a8b368),
        (0x3bfab9a1103e209b, 0x3f55f03e47165d72),
        (0xbbc4598141a3f87e, 0x3f5caaa76e34992d),
        (0xbbbb7ab55e886663, 0xbf10c5f18c46d030),
        (0xbb99f58bad5e7b5f, 0xbf04f0af7d46cd48),
        (0xbb3040f00afdd8ce, 0x3eb7d1e28094e21a),
        (0xbb3f12deda9fd086, 0x3ea1ad0731228479),
        (0xbae9fe69a18b2b74, 0xbe536021c8cb3c34),
        (0x3ad92bf3eabb82c3, 0xbe3371ae6c759181),
        (0x3a630cb928debacf, 0x3de46ce077a8bed7),
        (0xba5feb436591c0b8, 0x3dbe235d3564b639),
        (0xb9d711ddaf978bf4, 0xbd6e408e259c72fb),
        (0xb9c9d325620234dd, 0xbd415f07ac87e832),
        (0x399b66d31155b6c3, 0x3cf0a44f77f6a8ee),
        (0xb927de212062774e, 0x3cbefd8ab52f8ec1),
        (0x38daebbaa8d140b4, 0xbc6c54ebb5ad3567),
        (0xb8d1c883890c6817, 0xbc360b43cbb605a1),
        (0x38851f7136cf7e49, 0x3be33d74aac5c469),
        (0xb84c8ae944909141, 0x3ba99bfbb428a4d1),
        (0xb7f50f7d69247480, 0xbb555c095b9d3de2),
        (0xb78d195ad02b9a0b, 0xbb18c29d6b596412),
        (0x37588e53fd261c0a, 0x3ac3c05d45a0cec2),
        (0xb722c1c138d71c9e, 0x3a843feaf2fed511),
        (0xb6c263b564f34be6, 0xba2ec5c49e1d5e88),
        (0x36731f7cd8008380, 0xb9ec82a1b1f74089),
    ],
    [
        (0x3c57ba12cd0fc91f, 0x3fca7022be084d99),
        (0xb5db8122d606073c, 0xb9614f36f1550bec),
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