pxfm 0.1.29

/*
 * // 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 zeros and extremums.
Generated by SageMath:
```python
R120 = RealField(120)

zeros = []

mp.prec = 150

step = mpf("0.1")
epsilon = mpf("1e-35")
x = mpf("1.25")

previous_zero = R120(0)
y0_zeros = []

while x < mpf("76.0"):
    f1 = bessely(0, x)
    f2 = bessely(0, x + step)
    if f1 * f2 < 0:
        zero = findroot(lambda t: bessely(0, t), (x, x + step), solver='secant', tol=mp.mpf("1e-41"))
        previous_zero = zero
        y0_zeros.append(zero)
    if previous_zero is not None and abs(x - mpf(f'{round(x)}')) < epsilon:
        zeros.append(previous_zero)
    x += step

y0_extrema = []

x = mpf("1.25")
while x < mpf("76.0"):
    d1 = mp.diff(lambda t: bessely(0, t), x)
    d2 = mp.diff(lambda t: bessely(0, t), x + step)
    if d1 * d2 < 0:
        extremum = findroot(lambda t: mp.diff(lambda u: bessely(0, u), t), (x, x + step), solver='secant', tol=mp.mpf("1e-41"))
        y0_extrema.append(extremum)
    x += step

# Print results
for i, z in enumerate(j0_zeros):
    print(f"Zero {i+1}: x ≈ {z}")

print("Extrema (peaks/valleys) of Y0(x):")
for e in y0_extrema:
    print(f"nExtrema: {e}")

y0_zeros.extend(y0_extrema)

y0_zeros = sorted(y0_zeros)

# Print results
for i, z in enumerate(y0_zeros):
    print(f"Peak or zero {i+1}: x ≈ {z}")

print("")

print("pub(crate) static Y0_ZEROS: [(u64, u64); 48] = [")
print(f"(0x0, 0x0),")
for z in y0_zeros:
    k = split_double_double(z)
    hi = double_to_hex(k[1])
    lo = double_to_hex(k[0])
    print(f"({lo}, {hi}),")

print("];")
```
**/
pub(crate) static Y0_ZEROS: [(u64, u64); 48] = [
    (0x0, 0x0), // not really used, just a stab to avoid messing with indices
    (0xbc8bd1e50d219bfd, 0x400193bed4dff243),
    (0xbc9f06ae7804384e, 0x400fa9534d98569c),
    (0x3cbdfe7bac228e8c, 0x4015b7fe4e87b02e),
    (0xbc99774a495f56cf, 0x401c581dc4e72103),
    (0x3cb479cc068d9046, 0x40213127ae6169b4),
    (0xbcccb49ff791c495, 0x402471d735a47d58),
    (0x3c80fc786ce06080, 0x40277f9138d43206),
    (0xbcc7df81de86f24d, 0x402ab8e1c4a1e74a),
    (0xbcc5e091a50f8e05, 0x402dcb7d88de848b),
    (0x3cd25a237d12159b, 0x4030803c74003214),
    (0xbcda1ee4c5487ede, 0x40320b1c695f1e3b),
    (0xbcd8bf92d51fbaeb, 0x4033a42cdf5febd7),
    (0x3cd391b14410528f, 0x40353025492188cd),
    (0x3cdca75080cf53a8, 0x4036c832fd77ac07),
    (0x3cb52f75f025b205, 0x403854fa303820ca),
    (0xbcb03e052bd9c0af, 0x4039ec46f3e80146),
    (0xbcbcf130fbea3b24, 0x403b79acee8cfb7d),
    (0x3cd0aab17eca74b9, 0x403d106449616c4f),
    (0xbc9e7a77047d6166, 0x403e9e480605283c),
    (0x3ced2f18aa8a8f2f, 0x40401a4420e4abee),
    (0xbce96beabef7ecf4, 0x4040e16907f8fb56),
    (0xbca9dd1578036d11, 0x4041ac588c944279),
    (0x3cd2481e87adfe57, 0x404273a7b35a7aff),
    (0xbce9c3dd43e59158, 0x40433e6ecf5cb221),
    (0x3cda8ffacaac8461, 0x404405e18393afb5),
    (0xbce753b7fcd5250c, 0x4044d0867ec213f3),
    (0x3cbfe463face2c1c, 0x4045981787d668db),
    (0x3cec2eb6ee3e4c70, 0x4046629f4e1e0321),
    (0xbce26390f25f01cb, 0x40472a4a85cc317e),
    (0xbcaafdee84ced526, 0x4047f4b904dc9a53),
    (0xbcdcc667e557a177, 0x4048bc7b10ed3960),
    (0x3cebbca9a96dc1aa, 0x404986d378522b70),
    (0x3cb377717d2f36f7, 0x404a4ea9997b5eaa),
    (0xbcedf185c89a4066, 0x404b18ee87b4e700),
    (0xbcc68a841a2af000, 0x404be0d6766d13de),
    (0x3ced8a878e90eda4, 0x404cab0a1968b221),
    (0x3cddcc8dd083c434, 0x404d7301ec2bf16e),
    (0xbceb5c58b22794af, 0x404e3d2619226875),
    (0xbce5919b54336657, 0x404f052c3146d1da),
    (0xbc87b54cc765fd11, 0x404fcf4276983013),
    (0xbcf389f975d9dfa2, 0x40504baab8e42f8f),
    (0xbce195534d06b08a, 0x4050b0af92483bf5),
    (0xbcd4e0ffa0b9d2e9, 0x405114bee8d0f4bd),
    (0xbcf1c076cb371565, 0x405179be0c18f0e1),
    (0x3cf5d0de43102daa, 0x4051ddd2b7398636),
    (0xbce8a4f19e47d0be, 0x405242cca44048f8),
    (0x3ceb379dbe48b8f5, 0x4052a6e6306f1d08),
];

/**
Zeros and extremums solved values for Y0

Generated by MPFR:
```text
let mut arr = vec![];
for zeros in Y0_ZEROS.iter() {
    if zeros.1 == 0 {
        arr.push(0);
    } else {
        let mpfr = Float::with_val(107, f64::from_bits(zeros.1)).y0();
        arr.push(mpfr.to_f64().to_bits());
    }
}
println!(
    "arr: [{}]",
    arr.iter()
        .map(|x| format!("0x{:016x}", x))
        .collect::<Vec<_>>()
        .join(", ")
);
```
**/
pub(crate) static Y0_ZEROS_VALUES: [u64; 48] = [
    0x0000000000000000,
    0x3fe0aa48442f014b,
    0xbc88fa8956b4b481,
    0xbfd5c7c556f0c19a,
    0x3c7e91b198d39ce2,
    0x3fd15f993fceab5c,
    0xbcacabd7c823bf21,
    0xbfcdc14ea14e89f9,
    0x3ca4d9fe48a91cef,
    0x3fca7022be084d99,
    0x3cacd827f6c074a2,
    0xbfc80781c32422e7,
    0x3cb1d336c8b0a153,
    0x3fc62d94d97e859c,
    0x3cb3296749aaf800,
    0xbfc4b2a38f1ab9b4,
    0x3c845d52c7c075b2,
    0x3fc37aaceac987b9,
    0x3ca3bc249963d4c1,
    0xbfc2740819f1caaa,
    0xbcc069eacea8ff0b,
    0x3fc192f2627a74e3,
    0xbc7bc4fd81e2b2c5,
    0xbfc0cf3ee98f769b,
    0x3cba82b3a8997d82,
    0x3fc0230ba90f2871,
    0xbcb71414f52d813b,
    0xbfbf13fb0c0e6fcd,
    0xbcbae2d399eafcc6,
    0x3fbe018dac1c17e3,
    0xbc78e44442565953,
    0xbfbd09b21e36c0bd,
    0xbcb8c779e4075b10,
    0x3fbc2861347b1b39,
    0xbcb9f6a4816aab2e,
    0xbfbb5a622198a72c,
    0xbcb8e727b71a083d,
    0x3fba9d183bc04545,
    0xbcb67533047d83fb,
    0xbfb9ee5eee1a97c6,
    0x3c52f9257b962770,
    0x3fb94c6f5898708b,
    0xbcab7916830bd3b8,
    0xbfb8b5ccb03d459b,
    0x3cbb1b180f8e9062,
    0x3fb829356c2fb67c,
    0xbcb267f22477b55d,
    0xbfb7a597eb76a5e3,
];

/**
Taylor series at different zeros and extremums for Y0
Generated by SageMath:
```python
def compute_intervals(zeros):
    intervals = []
    for i in range(0, len(zeros)):
        if i == 0:
            a = 2 - zeros[i]
            b = (zeros[i] + zeros[i + 1]) / 2 + 0.05 - 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 - 0.05 - zeros[i]
            b = (zeros[i]) + 0.83 + 0.05 - zeros[i]
            intervals.append((RealField(18)(a), RealField(18)(b), RealField(110)(zeros[i])))
        else:
            a = (zeros[i - 1] + zeros[i]) / 2 - zeros[i] - 0.05
            b = (zeros[i] + zeros[i + 1]) / 2 + 0.05  - 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 = 500;
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 [RR(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

degree = 17

print(f"pub(crate) static Y0F_COEFFS: [[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("[")
    for c in coeffs:
        print(double_to_hex(c) + ",")
    print("],")
print("];")
```
**/
pub(crate) static Y0F_COEFFS: [[u64; 18]; 47] = [
    [
        0x3fe0aa48442f014b,
        0xbc009e915c2e5f95,
        0xbfd0aa48442f0143,
        0x3fa439fac165257c,
        0x3f80d2af4e929791,
        0x3f4f71646c0dc646,
        0xbf5444bda7f2ee4c,
        0x3f384c21f1d0de42,
        0xbf217ab4d69ab0db,
        0x3f0dafc989c8ea40,
        0xbef8bbefbac0d893,
        0x3ee48ac7a622784f,
        0xbed1245593770ad0,
        0x3ebc28878607b687,
        0xbea585c089718cc9,
        0x3e8b7ad75bd333d8,
        0xbe68a20d8d3d57a5,
        0x3e362c70b36d12a4,
    ],
    [
        0x3bf75cf88f1b7237,
        0xbfd9c34256a12a0c,
        0x3faa09c9290367ec,
        0x3fadf6d59bf50e4b,
        0xbf7c116fdc597e2f,
        0xbf61e32bc4eef0b0,
        0x3f29982765136b27,
        0x3f0ab2c1fd5871c0,
        0xbed486371d6e71eb,
        0xbe93b212b9208b3e,
        0xbe577700c20e01fd,
        0x3e545234fb052f6a,
        0xbe2f6a5f736d8c82,
        0x3e0a8134a3ddd47f,
        0xbde9666a74f1504a,
        0x3dc63b75b90c0da3,
        0xbdaa991122c61028,
        0x3d930f1a31e30006,
    ],
    [
        0xbfd5c7c556f0c19a,
        0xbbc44b457ab6a440,
        0x3fc5c7c556f0c19a,
        0xbf8564d4b1ed0d7e,
        0xbf8a15d92dfe3e28,
        0x3f4b438430469f6e,
        0x3f37a8924cc2fcab,
        0xbef5f69b4a89930d,
        0xbed85b940ebd0c07,
        0x3e955ac0f4e7f8ab,
        0x3e6d563e284b0072,
        0xbe23eac267e6cf3c,
        0xbe00077161c32b55,
        0x3dc04d965b688847,
        0xbd45e4f4886f7d51,
        0x3d5501605dba787a,
        0xbd363e6119f047ec,
        0x3d096861e7e8004b,
    ],
    [
        0xbb236a0ad5bec7c3,
        0x3fd334cca0697a5b,
        0xbf95aef611fc4d57,
        0xbfa8969c64cbf452,
        0x3f6b2f14a95527cb,
        0x3f61d35e85fde2a4,
        0xbf226dd71e391c65,
        0xbf08177e4fe524db,
        0x3ec6a9227352b13b,
        0x3ea34aa757412911,
        0xbe60a2814d2e238a,
        0xbe3442a3d67717ae,
        0x3defa6c448c9759c,
        0x3dbf14eacd6e3a21,
        0xbd771434b676ae83,
        0xbd406a106470261f,
        0x3cf2c5324aed291b,
        0x3cc47f208256e17f,
    ],
    [
        0x3fd15f993fceab5c,
        0xbb597aaa5d4472ea,
        0xbfc15f993fceab5c,
        0x3f758ef6efbed797,
        0x3f86395dfe49fcd4,
        0xbf3fb15104a41c03,
        0xbf35f88a11d55641,
        0x3eef37d226a827fd,
        0x3ed6f7bab104d878,
        0xbe8f0c45a3868f32,
        0xbe6dfe11ded99f62,
        0x3e2311adc6046d1a,
        0x3dfad34dd085ee0f,
        0xbdafdc85833041dc,
        0xbd819463fb6a5c22,
        0x3d33a4c369438250,
        0x3d014560b8776112,
        0xbcb2ae15d3a41e47,
    ],
    [
        0x3b12ba7db6ce5807,
        0xbfcff635cc72b9f1,
        0x3f89036451ff57c5,
        0x3fa4e667a71556af,
        0xbf60325ee41e910c,
        0xbf5fe23914fb9128,
        0x3f17f84d7c50e49e,
        0x3f06afdd57be1e75,
        0xbec04053abf415e2,
        0xbea2aea9ec4954d7,
        0x3e593eb9f19579b5,
        0x3e3428a3a4917f21,
        0xbde99d8be9e4cd5a,
        0xbdbec9815ee61f19,
        0x3d7260f619cb637c,
        0x3d418f963ce687db,
        0xbcf38a6e7195daa0,
        0xbcbf332d386dfb1b,
    ],
    [
        0xbfcdc14ea14e89f9,
        0x3b52ef4e10970973,
        0x3fbdc14ea14e89f9,
        0xbf6b037fe9cf2a52,
        0xbf8367d7d608e4ba,
        0x3f34abef5636e4f9,
        0x3f33d8a66122924a,
        0xbee5cfe92a1a2ead,
        0xbed571814a1a8669,
        0x3e87414e33ccd6d7,
        0x3e6ca7069e37c5b4,
        0xbe1e0b3a74e3f35e,
        0xbdfa15dd188a976e,
        0x3daa33983e3b34b5,
        0x3d8141656fbf9e02,
        0xbd3089bd5153b08a,
        0xbd01345e91fc8d5c,
        0x3cb05566655c2807,
    ],
    [
        0xbb10bed1f7905ee9,
        0x3fcbf32a27594007,
        0xbf80bc2d84e65214,
        0xbfa26cab38a8b368,
        0x3f55f03e47165d72,
        0x3f5caaa76e34992d,
        0xbf10c5f18c46d00f,
        0xbf04f0af7d46cd82,
        0x3eb7d1e28094a46b,
        0x3ea1ad073122cd33,
        0xbe536021c88affe4,
        0xbe3371ae6cd96849,
        0x3de46ce028e7c109,
        0x3dbe235dc856ef66,
        0xbd6e401d592ca47a,
        0xbd415f37788a98a4,
        0x3cf078a1b34fa822,
        0x3cbefbc3ca8cda9f,
    ],
    [
        0x3fca7022be084d99,
        0xbb4ddca3665cb95a,
        0xbfba7022be084d99,
        0x3f62ee079d020b12,
        0x3f8163191c30aa62,
        0xbf2d7806ea72fc7a,
        0xbf320f95702b1d3e,
        0x3ee006108822968d,
        0x3ed3e398cbc455aa,
        0xbe81bbe181c8bfbe,
        0xbe6b0f89b78908bf,
        0x3e17c3f85c062f0a,
        0x3df902361639d835,
        0xbda56494e7b59641,
        0xbd80bde23236fbba,
        0x3d2bbbd3bb25cf30,
        0x3d00d7f96ac5af92,
        0xbcabe3861f527a48,
    ],
    [
        0x3b0d39acdbc38af2,
        0xbfc925c35988ee29,
        0x3f7862549367591e,
        0x3fa0a4512039d6a2,
        0xbf5013b38cfb9292,
        0xbf5a24a1215f6684,
        0x3f08f91421377f72,
        0x3f035d17cec01753,
        0xbeb2283a93110ac0,
        0xbea099e713932038,
        0x3e4e5de01dbe7d10,
        0x3e3288585522eec4,
        0xbde0730be51a22c7,
        0xbdbd174416e1daeb,
        0x3d68f810d9b70d7c,
        0x3d40f177553ea68b,
        0xbcebc58c79d9f1a6,
        0xbcbe6305e9d630f0,
    ],
    [
        0xbfc80781c32422e7,
        0x3b483f69e003254a,
        0x3fb80781c32422e7,
        0xbf5c6923374d561f,
        0xbf7fbe6df840847f,
        0x3f264f4711a85f1d,
        0x3f309ff42b0d7a58,
        0xbed8a60685a59ae7,
        0xbed282d26a74a669,
        0x3e7bdb57a88d9298,
        0x3e697d9c12695952,
        0xbe131aa86bece7b9,
        0xbdf7d486a4891297,
        0x3da197f4a31bb9d7,
        0x3d801da2d1e74508,
        0xbd2749f32e6b29e4,
        0xbd005a3044bf379a,
        0x3ca7cdb1346a2761,
    ],
    [
        0xbb095b0f9cce8be6,
        0x3fc70c4f66cab47f,
        0xbf72c6731071e936,
        0xbf9e924b85a17361,
        0x3f48d6c364d92082,
        0x3f58247b02d6b0f6,
        0xbf037612593855eb,
        0xbf0206da232a2b7e,
        0x3eacaf84db86b79e,
        0x3e9f367117733794,
        0xbe48654affaeff8a,
        0xbe3199ec88cf0125,
        0x3ddaeb1a0e170f3e,
        0x3dbbe67c38767c0a,
        0xbd64cda59f058a2d,
        0xbd406490f1401c35,
        0x3ce7873ddbd2ecb8,
        0x3cbd9254c745332c,
    ],
    [
        0x3fc62d94d97e859c,
        0xbb4423d84fd9daf1,
        0xbfb62d94d97e859c,
        0x3f565481b55eaefb,
        0x3f7d5f857a2a6107,
        0xbf21a015a2ccb791,
        0xbf2eeb4eafd8612c,
        0x3ed3a7b79e4d8384,
        0x3ed154ed4598b648,
        0xbe767f762ea5d48d,
        0xbe680ec1e0075865,
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