/*

 * // 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.

 */

use crate::bessel::alpha1::{

    bessel_1_asympt_alpha, bessel_1_asympt_alpha_fast, bessel_1_asympt_alpha_hard,

};

use crate::bessel::beta1::{

    bessel_1_asympt_beta, bessel_1_asympt_beta_fast, bessel_1_asympt_beta_hard,

};

use crate::bessel::i0::bessel_rsqrt_hard;

use crate::bessel::y1_coeffs::Y1_COEFFS_REMEZ;

use crate::bessel::y1_coeffs_taylor::Y1_COEFFS;

use crate::bessel::y1f_coeffs::{Y1_ZEROS, Y1_ZEROS_VALUES};

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::dyadic_float::{DyadicFloat128, DyadicSign};

use crate::logs::log_dd_fast;

use crate::polyeval::{f_polyeval12, f_polyeval13, f_polyeval15, f_polyeval22, f_polyeval24};

use crate::rounding::CpuCeil;

use crate::sin_helper::{cos_dd_small, cos_dd_small_fast, cos_f128_small};

use crate::sincos_reduce::{AngleReduced, rem2pi_any, rem2pi_f128};

/// Bessel of the second kind of order 1 ( Y1 )

pub fn f_y1(x: f64) -> f64 {

    let ix = x.to_bits();

    if ix >= 0x7ffu64 << 52 || ix == 0 {

        // |x| == NaN, x == inf, |x| == 0, x < 0

        if ix.wrapping_shl(1) == 0 {

            // |x| == 0

            return f64::NEG_INFINITY;

        }

        if x.is_infinite() {

            if x.is_sign_negative() {

                return f64::NAN;

            }

            return 0.;

        }

        return x + f64::NAN; // x == NaN

    }

    let xb = x.to_bits();

    if xb <= 0x4049c00000000000u64 {

        // x <= 51.5

        if xb <= 0x4000000000000000u64 {

            // x <= 2

            if xb <= 0x3ff75c28f5c28f5cu64 {

                // x <= 1.46

                return y1_near_zero_fast(x);

            }

            // transient zone from 1.46 to 2 have bad behavior for log poly already,

            // and not yet good to be easily covered, thus it use its own poly

            return y1_transient_zone_fast(x);

        }

        return y1_small_argument_fast(x);

    }

    y1_asympt_fast(x)

}

/**

Generated by SageMath:

Evaluates:

y2 = -J1(x)*log(x) + 1/x * (1 - sum((-1)^m*(H(m)+H(m-1))/(2^m*m!*(m-1)!)*x^(2*m))

Y1(x) = 2/pi*(-y2(x)+(euler_gamma - log(2))*J1(x))

expressed as:

Y1(x)=log(x)*W1(x) - Z1(x) - 2/(pi*x)

```python

from sage.all import *

R = LaurentSeriesRing(RealField(300), 'x', default_prec=300)

x = R.gen()

N = 16  # Number of terms (adjust as needed)

gamma = RealField(300)(euler_gamma)

d2 = RealField(300)(2)

pi = RealField(300).pi()

log2 = RealField(300)(2).log()

def j_series(n, x):

    return sum([(-1)**m * (x/2)**(ZZ(n) + ZZ(2)*ZZ(m)) / (ZZ(m).factorial() * (ZZ(m) + ZZ(n)).factorial()) for m in range(N)])

J1_series = j_series(1, x)

def harmony(m):

    return sum(RealField(300)(1)/RealField(300)(k) for k in range(1, m+1))

def z_series(x):

    return sum([(-1)**m * (x)**(ZZ(2)*ZZ(m)) / (ZZ(2)**(2*m) * ZZ(m).factorial() * (ZZ(m) - ZZ(1)).factorial()) * (harmony(m) + harmony(m - 1)) for m in range(1, N)])

W1 = d2/pi * J1_series

Z1 = -(d2/(x*pi) * z_series(x) + d2/pi * gamma * J1_series(x) - d2/pi * log2 * J1_series(x))

def y1_full(x):

    return d2/pi * (J1_series(x) * x.log() - 1/x * ( 1 - z_series(x)) + (gamma - log2) * J1_series(x))

# see the series

print(W0)

print(Z0)

```

See ./notes/bessel_y1_taylor.ipynb for generation

**/

#[inline]

fn y1_near_zero_fast(x: f64) -> f64 {

    const W: [(u64, u64); 15] = [

        (0xbc76b01ec5417056, 0x3fd45f306dc9c883),

        (0x3c46b01ec5417056, 0xbfa45f306dc9c883),

        (0xbbfe40290701eb1e, 0x3f5b2995e7b7b604),

        (0xbba67fe4a5feb897, 0xbf021bb945252402),

        (0xbb0334914cdd2ba9, 0x3e9cf9286ea1d337),

        (0x3aab4f3c6d42c1f4, 0xbe2ee7a29824147f),

        (0xba407fb57ef4dc2c, 0x3db78be9987d036d),

        (0x39d2921e91b07dd0, 0xbd3ae90af76a4d0f),

        (0x395a28c8620dc90e, 0x3cb7eb97f85e7d62),

        (0xb8cf83f52abe45c5, 0xbc31028e3376648a),

        (0xb8441050c68ca435, 0x3ba3cb1e7d0c17e7),

        (0xb7ab072548a1aa43, 0xbb133191ed9f1eef),

        (0xb6f05192c2d9b6ee, 0x3a7f7f4b5e8ef7b0),

        (0x367ad65afe306d57, 0xb9e626e36cb3515d),

        (0xb5ea1c4136f8f230, 0x394b01153dce6810),

    ];

    let x2 = DoubleDouble::from_exact_mult(x, x);

    let w0 = f_polyeval12(

        x2.hi,

        f64::from_bits(W[3].1),

        f64::from_bits(W[4].1),

        f64::from_bits(W[5].1),

        f64::from_bits(W[6].1),

        f64::from_bits(W[7].1),

        f64::from_bits(W[8].1),

        f64::from_bits(W[9].1),

        f64::from_bits(W[10].1),

        f64::from_bits(W[11].1),

        f64::from_bits(W[12].1),

        f64::from_bits(W[13].1),

        f64::from_bits(W[14].1),

    );

    let mut w = DoubleDouble::mul_f64_add(x2, w0, DoubleDouble::from_bit_pair(W[2]));

    w = DoubleDouble::mul_add(x2, w, DoubleDouble::from_bit_pair(W[1]));

    w = DoubleDouble::mul_add(x2, w, DoubleDouble::from_bit_pair(W[0]));

    w = DoubleDouble::quick_mult_f64(w, x);

    const Z: [(u64, u64); 15] = [

        (0x3c61d7eb2e54cda1, 0x3fc91866143cbc8a),

        (0xbc2f9f7a0ce54a40, 0xbfabd3975c75b4a7),

        (0xbbf7659313f45e8c, 0x3f6835b97894be5b),

        (0x3b9cbcd40f1be7b9, 0xbf12c7dbffcde97d),

        (0xbb495d78778645b4, 0x3eb0a780ac776eac),

        (0xbae15be86455c1ab, 0xbe432e5a4ddeea30),

        (0xba5ad966c12f1e3c, 0x3dcf0ce34d2066a6),

        (0x39e9717155dc7521, 0xbd52a4e1aea45c18),

        (0x394f447fe5de1290, 0x3cd1474ade9154ac),

        (0xb8e1699d9009a7fc, 0xbc4978ba84f218c0),

        (0xb8505502096ead17, 0x3bbe9598c016378b),

        (0x37942b6c36b2c5f1, 0xbb2e7e5fcfc4b7b1),

        (0x37210853b78bd08a, 0x3a99a6c1266c116d),

        (0xb686c9639c9d976e, 0xba02738998fe7337),

        (0xb603b739ee04b9fe, 0x3966f58cd41b6d08),

    ];

    let z0 = f_polyeval12(

        x2.hi,

        f64::from_bits(Z[3].1),

        f64::from_bits(Z[4].1),

        f64::from_bits(Z[5].1),

        f64::from_bits(Z[6].1),

        f64::from_bits(Z[7].1),

        f64::from_bits(Z[8].1),

        f64::from_bits(Z[9].1),

        f64::from_bits(Z[10].1),

        f64::from_bits(Z[11].1),

        f64::from_bits(Z[12].1),

        f64::from_bits(Z[13].1),

        f64::from_bits(Z[14].1),

    );

    let mut z = DoubleDouble::mul_f64_add(x2, z0, DoubleDouble::from_bit_pair(Z[2]));

    z = DoubleDouble::mul_add(x2, z, DoubleDouble::from_bit_pair(Z[1]));

    z = DoubleDouble::mul_add(x2, z, DoubleDouble::from_bit_pair(Z[0]));

    z = DoubleDouble::quick_mult_f64(z, x);

    let w_log = log_dd_fast(x);

    const MINUS_TWO_OVER_PI: DoubleDouble =

        DoubleDouble::from_bit_pair((0x3c86b01ec5417056, 0xbfe45f306dc9c883));

    let m_two_over_pi_div_x: DoubleDouble;

    #[cfg(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    ))]

    {

        m_two_over_pi_div_x = DoubleDouble::div_dd_f64(MINUS_TWO_OVER_PI, x)

    }

    #[cfg(not(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    )))]

    {

        use crate::double_double::two_product_compatible;

        m_two_over_pi_div_x = if two_product_compatible(x) {

            DoubleDouble::div_dd_f64(MINUS_TWO_OVER_PI, x)

        } else {

            DoubleDouble::div_safe_dd_f64(MINUS_TWO_OVER_PI, x)

        };

    }

    if m_two_over_pi_div_x.hi.is_infinite() {

        return f64::NEG_INFINITY;

    }

    let zvp = DoubleDouble::mul_add(w, w_log, -z);

    let p = DoubleDouble::add(m_two_over_pi_div_x, zvp);

    let err = f_fmla(

        p.hi,

        f64::from_bits(0x3c30000000000000), // 2^-60

        f64::from_bits(0x3be0000000000000), // 2^-65

    );

    let ub = p.hi + (p.lo + err);

    let lb = p.hi + (p.lo - err);

    if ub == lb {

        return p.to_f64();

    }

    y1_near_zero(x, w_log)

}

/**

Generated by SageMath:

Evaluates:

y2 = -J1(x)*log(x) + 1/x * (1 - sum((-1)^m*(H(m)+H(m-1))/(2^m*m!*(m-1)!)*x^(2*m))

Y1(x) = 2/pi*(-y2(x)+(euler_gamma - log(2))*J1(x))

expressed as:

Y1(x)=log(x)*W1(x) - Z1(x) - 2/(pi*x)

```python

from sage.all import *

R = LaurentSeriesRing(RealField(300), 'x', default_prec=300)

x = R.gen()

N = 16  # Number of terms (adjust as needed)

gamma = RealField(300)(euler_gamma)

d2 = RealField(300)(2)

pi = RealField(300).pi()

log2 = RealField(300)(2).log()

def j_series(n, x):

    return sum([(-1)**m * (x/2)**(ZZ(n) + ZZ(2)*ZZ(m)) / (ZZ(m).factorial() * (ZZ(m) + ZZ(n)).factorial()) for m in range(N)])

J1_series = j_series(1, x)

def harmony(m):

    return sum(RealField(300)(1)/RealField(300)(k) for k in range(1, m+1))

def z_series(x):

    return sum([(-1)**m * (x)**(ZZ(2)*ZZ(m)) / (ZZ(2)**(2*m) * ZZ(m).factorial() * (ZZ(m) - ZZ(1)).factorial()) * (harmony(m) + harmony(m - 1)) for m in range(1, N)])

W1 = d2/pi * J1_series

Z1 = -(d2/(x*pi) * z_series(x) + d2/pi * gamma * J1_series(x) - d2/pi * log2 * J1_series(x))

def y1_full(x):

    return d2/pi * (J1_series(x) * x.log() - 1/x * ( 1 - z_series(x)) + (gamma - log2) * J1_series(x))

# see the series

print(W0)

print(Z0)

```

See ./notes/bessel_y1_taylor.ipynb for generation

**/

#[cold]

#[inline(never)]

fn y1_near_zero(x: f64, w_log: DoubleDouble) -> f64 {

    const W: [(u64, u64); 15] = [

        (0xbc76b01ec5417056, 0x3fd45f306dc9c883),

        (0x3c46b01ec5417056, 0xbfa45f306dc9c883),

        (0xbbfe40290701eb1e, 0x3f5b2995e7b7b604),

        (0xbba67fe4a5feb897, 0xbf021bb945252402),

        (0xbb0334914cdd2ba9, 0x3e9cf9286ea1d337),

        (0x3aab4f3c6d42c1f4, 0xbe2ee7a29824147f),

        (0xba407fb57ef4dc2c, 0x3db78be9987d036d),

        (0x39d2921e91b07dd0, 0xbd3ae90af76a4d0f),

        (0x395a28c8620dc90e, 0x3cb7eb97f85e7d62),

        (0xb8cf83f52abe45c5, 0xbc31028e3376648a),

        (0xb8441050c68ca435, 0x3ba3cb1e7d0c17e7),

        (0xb7ab072548a1aa43, 0xbb133191ed9f1eef),

        (0xb6f05192c2d9b6ee, 0x3a7f7f4b5e8ef7b0),

        (0x367ad65afe306d57, 0xb9e626e36cb3515d),

        (0xb5ea1c4136f8f230, 0x394b01153dce6810),

    ];

    let x2 = DoubleDouble::from_exact_mult(x, x);

    let mut w = f_polyeval15(

        x2,

        DoubleDouble::from_bit_pair(W[0]),

        DoubleDouble::from_bit_pair(W[1]),

        DoubleDouble::from_bit_pair(W[2]),

        DoubleDouble::from_bit_pair(W[3]),

        DoubleDouble::from_bit_pair(W[4]),

        DoubleDouble::from_bit_pair(W[5]),

        DoubleDouble::from_bit_pair(W[6]),

        DoubleDouble::from_bit_pair(W[7]),

        DoubleDouble::from_bit_pair(W[8]),

        DoubleDouble::from_bit_pair(W[9]),

        DoubleDouble::from_bit_pair(W[10]),

        DoubleDouble::from_bit_pair(W[11]),

        DoubleDouble::from_bit_pair(W[12]),

        DoubleDouble::from_bit_pair(W[13]),

        DoubleDouble::from_bit_pair(W[14]),

    );

    w = DoubleDouble::quick_mult_f64(w, x);

    const Z: [(u64, u64); 15] = [

        (0x3c61d7eb2e54cda1, 0x3fc91866143cbc8a),

        (0xbc2f9f7a0ce54a40, 0xbfabd3975c75b4a7),

        (0xbbf7659313f45e8c, 0x3f6835b97894be5b),

        (0x3b9cbcd40f1be7b9, 0xbf12c7dbffcde97d),

        (0xbb495d78778645b4, 0x3eb0a780ac776eac),

        (0xbae15be86455c1ab, 0xbe432e5a4ddeea30),

        (0xba5ad966c12f1e3c, 0x3dcf0ce34d2066a6),

        (0x39e9717155dc7521, 0xbd52a4e1aea45c18),

        (0x394f447fe5de1290, 0x3cd1474ade9154ac),

        (0xb8e1699d9009a7fc, 0xbc4978ba84f218c0),

        (0xb8505502096ead17, 0x3bbe9598c016378b),

        (0x37942b6c36b2c5f1, 0xbb2e7e5fcfc4b7b1),

        (0x37210853b78bd08a, 0x3a99a6c1266c116d),

        (0xb686c9639c9d976e, 0xba02738998fe7337),

        (0xb603b739ee04b9fe, 0x3966f58cd41b6d08),

    ];

    let mut z = f_polyeval15(

        x2,

        DoubleDouble::from_bit_pair(Z[0]),

        DoubleDouble::from_bit_pair(Z[1]),

        DoubleDouble::from_bit_pair(Z[2]),

        DoubleDouble::from_bit_pair(Z[3]),

        DoubleDouble::from_bit_pair(Z[4]),

        DoubleDouble::from_bit_pair(Z[5]),

        DoubleDouble::from_bit_pair(Z[6]),

        DoubleDouble::from_bit_pair(Z[7]),

        DoubleDouble::from_bit_pair(Z[8]),

        DoubleDouble::from_bit_pair(Z[9]),

        DoubleDouble::from_bit_pair(Z[10]),

        DoubleDouble::from_bit_pair(Z[11]),

        DoubleDouble::from_bit_pair(Z[12]),

        DoubleDouble::from_bit_pair(Z[13]),

        DoubleDouble::from_bit_pair(Z[14]),

    );

    z = DoubleDouble::quick_mult_f64(z, x);

    const MINUS_TWO_OVER_PI: DoubleDouble =

        DoubleDouble::from_bit_pair((0x3c86b01ec5417056, 0xbfe45f306dc9c883));

    let m_two_over_pi_div_x: DoubleDouble;

    #[cfg(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    ))]

    {

        m_two_over_pi_div_x = DoubleDouble::div_dd_f64(MINUS_TWO_OVER_PI, x)

    }

    #[cfg(not(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    )))]

    {

        use crate::double_double::two_product_compatible;

        m_two_over_pi_div_x = if two_product_compatible(x) {

            DoubleDouble::div_dd_f64(MINUS_TWO_OVER_PI, x)

        } else {

            DoubleDouble::div_safe_dd_f64(MINUS_TWO_OVER_PI, x)

        };

    }

    if m_two_over_pi_div_x.hi.is_infinite() {

        return f64::NEG_INFINITY;

    }

    let zvp = DoubleDouble::mul_add(w, w_log, -z);

    DoubleDouble::full_dd_add(m_two_over_pi_div_x, zvp).to_f64()

}

#[inline]

fn y1_transient_zone_fast(x: f64) -> f64 {

    /*

    <<FunctionApproximations`

    ClearAll["Global`*"]

    f[x_]:= BesselY[1,x + 2.1971413260310170351490335626990]

    {approx,error} =MiniMaxApproximation[f[x],{x,{1.42 -  2.1971413260310170351490335626990, 2-  2.1971413260310170351490335626990 },27,0},WorkingPrecision->120]

    poly=error[[1]];

    coeffs=CoefficientList[poly,x];

    TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50}, ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]

     */

    const C: [(u64, u64); 28] = [

        (0x38d23216c8eac2ee, 0x3c631de77e55e9b0),

        (0x3c77f3a6718f8e03, 0x3fe0aa48442f0150),

        (0xbc52b77d09be8679, 0xbfbe56f82217b33a),

        (0x3c237af39fc9d759, 0xbfa0d2af4e922afe),

        (0xbc08241e95389bc3, 0xbf73a6dec2f9f739),

        (0x3c18eac6a35acd63, 0x3f7e671c82a1c956),

        (0x3be0a0f3c8908083, 0xbf65429d5dbc3bb0),

        (0x3be217fa58861600, 0x3f517abad71c26c0),

        (0x3bebc327d6c65514, 0xbf40b28b4ef33a56),

        (0xbbcb597d6bdd5992, 0x3f2ef0d150ec9934),

        (0x3bb1a480de696e07, 0xbf1c0758a86844be),

        (0xbb9c6ea6352ab84e, 0x3f0b7c88b58d9ef3),

        (0x3b7dbb78dfd868a9, 0xbee97ef9519bdcfd),

        (0xbb8d4519030f499d, 0x3f04815f08e7ad5e),

        (0x3bbbd70e1480e260, 0x3f10f348483b57bc),

        (0x3b7117cf4d2b6f3c, 0x3f231914389bb1bb),

        (0x3b8ca48beaf6a58d, 0x3f30b29e838345b4),

        (0x3bccfac65ce17cf9, 0x3f39a69e98f61897),

        (0xbbeae7e3065b09c9, 0x3f40b9511666fcf0),

        (0xbbe5cbddf691e7e6, 0x3f428cd8388e634b),

        (0xbbd91372412d1e1b, 0x3f414ba048d9e1d5),

        (0xbbb0781a70c6f715, 0x3f3acdcf66f1de95),

        (0xbba3ae83fd425494, 0x3f30f44ae6620bba),

        (0x3bc001d75da77b74, 0x3f21154a0a1f2161),

        (0xbb91c9afb1a1b874, 0x3f0a687b664cbac6),

        (0x3b8e0a06b9444963, 0x3eed7c3cbb4ba5d8),

        (0x3b4f0e9dfc915934, 0x3ec53ca23fdd0999),

        (0xbb0409258f8ffca8, 0x3e8de620acb51b2d),

    ];

    // this poly relative to first zero

    const ZERO: DoubleDouble =

        DoubleDouble::from_bit_pair((0xbc8bd1e50d219bfd, 0x400193bed4dff243));

    let mut r = DoubleDouble::full_add_f64(-ZERO, x);

    r = DoubleDouble::from_exact_add(r.hi, r.lo);

    let p0 = f_polyeval24(

        r.to_f64(),

        f64::from_bits(C[4].1),

        f64::from_bits(C[5].1),

        f64::from_bits(C[6].1),

        f64::from_bits(C[7].1),

        f64::from_bits(C[8].1),

        f64::from_bits(C[9].1),

        f64::from_bits(C[10].1),

        f64::from_bits(C[11].1),

        f64::from_bits(C[12].1),

        f64::from_bits(C[13].1),

        f64::from_bits(C[14].1),

        f64::from_bits(C[15].1),

        f64::from_bits(C[16].1),

        f64::from_bits(C[17].1),

        f64::from_bits(C[18].1),

        f64::from_bits(C[19].1),

        f64::from_bits(C[20].1),

        f64::from_bits(C[21].1),

        f64::from_bits(C[22].1),

        f64::from_bits(C[23].1),

        f64::from_bits(C[24].1),

        f64::from_bits(C[25].1),

        f64::from_bits(C[26].1),

        f64::from_bits(C[27].1),

    );

    let mut p = DoubleDouble::mul_f64_add(r, p0, DoubleDouble::from_bit_pair(C[3]));

    p = DoubleDouble::mul_add(p, r, DoubleDouble::from_bit_pair(C[2]));

    p = DoubleDouble::mul_add(p, r, DoubleDouble::from_bit_pair(C[1]));

    p = DoubleDouble::mul_add(p, r, DoubleDouble::from_bit_pair(C[0]));

    let err = f_fmla(

        p.hi,

        f64::from_bits(0x3c50000000000000), // 2^-58

        f64::from_bits(0x3b90000000000000), // 2^-70

    );

    let ub = p.hi + (p.lo + err);

    let lb = p.hi + (p.lo - err);

    if ub == lb {

        return p.to_f64();

    }

    y1_transient_zone(x)

}

fn y1_transient_zone(x: f64) -> f64 {

    /*

    <<FunctionApproximations`

    ClearAll["Global`*"]

    f[x_]:= BesselY[1,x + 2.1971413260310170351490335626990]

    {approx,error} =MiniMaxApproximation[f[x],{x,{1.42 -  2.1971413260310170351490335626990, 2-  2.1971413260310170351490335626990 },27,0},WorkingPrecision->120]

    poly=error[[1]];

    coeffs=CoefficientList[poly,x];

    TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50}, ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]

     */

    const C: [(u64, u64); 28] = [

        (0x38d23216c8eac2ee, 0x3c631de77e55e9b0),

        (0x3c77f3a6718f8e03, 0x3fe0aa48442f0150),

        (0xbc52b77d09be8679, 0xbfbe56f82217b33a),

        (0x3c237af39fc9d759, 0xbfa0d2af4e922afe),

        (0xbc08241e95389bc3, 0xbf73a6dec2f9f739),

        (0x3c18eac6a35acd63, 0x3f7e671c82a1c956),

        (0x3be0a0f3c8908083, 0xbf65429d5dbc3bb0),

        (0x3be217fa58861600, 0x3f517abad71c26c0),

        (0x3bebc327d6c65514, 0xbf40b28b4ef33a56),

        (0xbbcb597d6bdd5992, 0x3f2ef0d150ec9934),

        (0x3bb1a480de696e07, 0xbf1c0758a86844be),

        (0xbb9c6ea6352ab84e, 0x3f0b7c88b58d9ef3),

        (0x3b7dbb78dfd868a9, 0xbee97ef9519bdcfd),

        (0xbb8d4519030f499d, 0x3f04815f08e7ad5e),

        (0x3bbbd70e1480e260, 0x3f10f348483b57bc),

        (0x3b7117cf4d2b6f3c, 0x3f231914389bb1bb),

        (0x3b8ca48beaf6a58d, 0x3f30b29e838345b4),

        (0x3bccfac65ce17cf9, 0x3f39a69e98f61897),

        (0xbbeae7e3065b09c9, 0x3f40b9511666fcf0),

        (0xbbe5cbddf691e7e6, 0x3f428cd8388e634b),

        (0xbbd91372412d1e1b, 0x3f414ba048d9e1d5),

        (0xbbb0781a70c6f715, 0x3f3acdcf66f1de95),

        (0xbba3ae83fd425494, 0x3f30f44ae6620bba),

        (0x3bc001d75da77b74, 0x3f21154a0a1f2161),

        (0xbb91c9afb1a1b874, 0x3f0a687b664cbac6),

        (0x3b8e0a06b9444963, 0x3eed7c3cbb4ba5d8),

        (0x3b4f0e9dfc915934, 0x3ec53ca23fdd0999),

        (0xbb0409258f8ffca8, 0x3e8de620acb51b2d),

    ];

    // this poly relative to first zero

    const ZERO: DoubleDouble =

        DoubleDouble::from_bit_pair((0xbc8bd1e50d219bfd, 0x400193bed4dff243));

    let r = DoubleDouble::full_add_f64(-ZERO, x);

    let p0 = f_polyeval13(

        r.to_f64(),

        f64::from_bits(C[15].1),

        f64::from_bits(C[16].1),

        f64::from_bits(C[17].1),

        f64::from_bits(C[18].1),

        f64::from_bits(C[19].1),

        f64::from_bits(C[20].1),

        f64::from_bits(C[21].1),

        f64::from_bits(C[22].1),

        f64::from_bits(C[23].1),

        f64::from_bits(C[24].1),

        f64::from_bits(C[25].1),

        f64::from_bits(C[26].1),

        f64::from_bits(C[27].1),

    );

    let mut p_e = DoubleDouble::mul_f64_add(r, p0, DoubleDouble::from_bit_pair(C[14]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[13]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[12]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[11]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[10]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[9]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[8]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[7]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[6]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[5]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[4]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[3]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[2]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[1]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(C[0]));

    let p = DoubleDouble::from_exact_add(p_e.hi, p_e.lo);

    let err = f_fmla(

        p.hi,

        f64::from_bits(0x3c20000000000000), // 2^-61

        f64::from_bits(0x3a90000000000000), // 2^-86

    );

    let ub = p.hi + (p.lo + err);

    let lb = p.hi + (p.lo - err);

    if ub == lb {

        return p.to_f64();

    }

    y1_transient_hard(x)

}

#[cold]

#[inline(never)]

fn y1_transient_hard(x: f64) -> f64 {

    /*

    <<FunctionApproximations`

    ClearAll["Global`*"]

    f[x_]:= BesselY[1,x + 2.1971413260310170351490335626990]

    {approx,error} =MiniMaxApproximation[f[x],{x,{1.42 -  2.1971413260310170351490335626990, 2-  2.1971413260310170351490335626990 },27,0},WorkingPrecision->120]

    poly=error[[1]];

    coeffs=CoefficientList[poly,x];

    TableForm[Table[Row[{"'",NumberForm[coeffs[[i+1]],{50,50}, ExponentFunction->(Null&)],"',"}],{i,0,Length[coeffs]-1}]]

     */

    pub(crate) static C: [DyadicFloat128; 28] = [

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -184,

            mantissa: 0x98ef3bf2_af4d8048_c85b23ab_0bb72488_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -128,

            mantissa: 0x85524221_780a817f_3a6718f8_e03513ec_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -131,

            mantissa: 0xf2b7c110_bd99d256_efa137d0_cf1f7988_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -132,

            mantissa: 0x86957a74_9157ef64_286301b1_453792e2_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -135,

            mantissa: 0x9d36f617_cfb9c982_41e95389_bc32e8c2_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -135,

            mantissa: 0xf338e415_0e4ab31d_58d46b59_ac6792eb_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -136,

            mantissa: 0xaa14eaed_e1dd7f7a_f861bb7b_fbe6acb5_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -137,

            mantissa: 0x8bd5d6b8_e1360121_7fa58861_5ff9b614_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -138,

            mantissa: 0x85945a77_99d2ac87_9b052735_5d7f5f59_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -140,

            mantissa: 0xf7868a87_64c99c94_d0528454_cdccd44c_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -141,

            mantissa: 0xe03ac543_4225edcb_6fe432d2_3f11a8b0_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -142,

            mantissa: 0xdbe445ac_6cf79639_159cad54_7b1eda7c_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Neg,

            exponent: -144,

            mantissa: 0xcbf7ca8c_dee7e624_48720279_75757a17_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -142,

            mantissa: 0xa40af847_3d6aef15_d737e785_b3163322_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -141,

            mantissa: 0x879a4241_dabde37a_e1c2901c_4c06b1dc_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -140,

            mantissa: 0x98c8a1c4_dd8dd811_17cf4d2b_6f3c3910_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -139,

            mantissa: 0x8594f41c_1a2da01c_a48beaf6_a58cef9f_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -139,

            mantissa: 0xcd34f4c7_b0c4b9cf_ac65ce17_cf940c9c_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -138,

            mantissa: 0x85ca88b3_37e77ca3_039f349e_c6ddb06d_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -138,

            mantissa: 0x9466c1c4_731a5546_84412dc3_033a8ee7_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -138,

            mantissa: 0x8a5d0246_cf0ea66e_c8dbed2e_1e50b14f_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -139,

            mantissa: 0xd66e7b37_8ef4a77c_3f2c79c8_4757a40d_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -139,

            mantissa: 0x87a25733_105dcfb1_45f00af6_adb11b5f_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -140,

            mantissa: 0x88aa5050_f90b0a00_3aebb4ef_6e7e9ce1_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -142,

            mantissa: 0xd343db32_65d62ee3_6504e5e4_78c55965_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -144,

            mantissa: 0xebe1e5da_5d2ec3c1_40d72889_2c57e483_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -146,

            mantissa: 0xa9e511fe_e84cc8f8_74efe48a_c9a09ebc_u128,

        },

        DyadicFloat128 {

            sign: DyadicSign::Pos,

            exponent: -150,

            mantissa: 0xef310565_a8d9675f_b6d38380_1abf92a6_u128,

        },

    ];

    const ZERO: DyadicFloat128 = DyadicFloat128 {

        sign: DyadicSign::Pos,

        exponent: -126,

        mantissa: 0x8c9df6a6_ff921721_70d796f3_2017e155_u128,

    };

    let r = DyadicFloat128::new_from_f64(x) - ZERO;

    let mut p = C[27];

    for i in (0..27).rev() {

        p = r * p + C[i];

    }

    p.fast_as_f64()

}

/// This method on small range searches for nearest zero or extremum.

/// Then picks stored series expansion at the point end evaluates the poly at the point.

#[inline]

pub(crate) fn y1_small_argument_fast(x: f64) -> f64 {

    // let avg_step = 51.03 / 33.0;

    // let inv_step = 1.0 / avg_step;

    //

    // println!("inv_step {}", inv_step);

    const INV_STEP: f64 = 0.6466784244562023;

    let fx = x * INV_STEP;

    const Y1_ZEROS_COUNT: f64 = (Y1_ZEROS.len() - 1) as f64;

    let idx0 = unsafe { fx.min(Y1_ZEROS_COUNT).to_int_unchecked::<usize>() };

    let idx1 = unsafe {

        fx.cpu_ceil()

            .min(Y1_ZEROS_COUNT)

            .to_int_unchecked::<usize>()

    };

    let found_zero0 = DoubleDouble::from_bit_pair(Y1_ZEROS[idx0]);

    let found_zero1 = DoubleDouble::from_bit_pair(Y1_ZEROS[idx1]);

    let dist0 = (found_zero0.hi - x).abs();

    let dist1 = (found_zero1.hi - x).abs();

    let (found_zero, idx, dist) = if dist0 < dist1 {

        (found_zero0, idx0, dist0)

    } else {

        (found_zero1, idx1, dist1)

    };

    if idx == 0 {

        return y1_near_zero_fast(x);

    }

    let close_to_zero = dist.abs() < 1e-3;

    let c = if close_to_zero {

        &Y1_COEFFS[idx - 1]

    } else {

        &Y1_COEFFS_REMEZ[idx - 1]

    };

    let r = DoubleDouble::full_add_f64(-found_zero, x);

    // We hit exact zero, value, better to return it directly

    if dist == 0. {

        return f64::from_bits(Y1_ZEROS_VALUES[idx]);

    }

    let p = f_polyeval22(

        r.hi,

        f64::from_bits(c[6].1),

        f64::from_bits(c[7].1),

        f64::from_bits(c[8].1),

        f64::from_bits(c[9].1),

        f64::from_bits(c[10].1),

        f64::from_bits(c[11].1),

        f64::from_bits(c[12].1),

        f64::from_bits(c[13].1),

        f64::from_bits(c[14].1),

        f64::from_bits(c[15].1),

        f64::from_bits(c[16].1),

        f64::from_bits(c[17].1),

        f64::from_bits(c[18].1),

        f64::from_bits(c[19].1),

        f64::from_bits(c[20].1),

        f64::from_bits(c[21].1),

        f64::from_bits(c[22].1),

        f64::from_bits(c[23].1),

        f64::from_bits(c[24].1),

        f64::from_bits(c[25].1),

        f64::from_bits(c[26].1),

        f64::from_bits(c[27].1),

    );

    let mut z = DoubleDouble::mul_f64_add(r, p, DoubleDouble::from_bit_pair(c[5]));

    z = DoubleDouble::mul_add(z, r, DoubleDouble::from_bit_pair(c[4]));

    z = DoubleDouble::mul_add(z, r, DoubleDouble::from_bit_pair(c[3]));

    z = DoubleDouble::mul_add(z, r, DoubleDouble::from_bit_pair(c[2]));

    z = DoubleDouble::mul_add(z, r, DoubleDouble::from_bit_pair(c[1]));

    z = DoubleDouble::mul_add(z, r, DoubleDouble::from_bit_pair(c[0]));

    let p = z;

    let err = f_fmla(

        p.hi,

        f64::from_bits(0x3c60000000000000), // 2^-57

        f64::from_bits(0x3c20000000000000), // 2^-61

    );

    let ub = p.hi + (p.lo + err);

    let lb = p.hi + (p.lo - err);

    if ub == lb {

        return p.to_f64();

    }

    y0_small_argument_moderate(r, c)

}

fn y0_small_argument_moderate(r: DoubleDouble, c0: &[(u64, u64); 28]) -> f64 {

    let c = &c0[15..];

    let p0 = f_polyeval13(

        r.to_f64(),

        f64::from_bits(c[0].1),

        f64::from_bits(c[1].1),

        f64::from_bits(c[2].1),

        f64::from_bits(c[3].1),

        f64::from_bits(c[4].1),

        f64::from_bits(c[5].1),

        f64::from_bits(c[6].1),

        f64::from_bits(c[7].1),

        f64::from_bits(c[8].1),

        f64::from_bits(c[9].1),

        f64::from_bits(c[10].1),

        f64::from_bits(c[11].1),

        f64::from_bits(c[12].1),

    );

    let c = c0;

    let mut p_e = DoubleDouble::mul_f64_add(r, p0, DoubleDouble::from_bit_pair(c[14]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[13]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[12]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[11]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[10]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[9]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[8]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[7]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[6]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[5]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[4]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[3]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[2]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[1]));

    p_e = DoubleDouble::mul_add(p_e, r, DoubleDouble::from_bit_pair(c[0]));

    let p = DoubleDouble::from_exact_add(p_e.hi, p_e.lo);

    let err = f_fmla(

        p.hi,

        f64::from_bits(0x3c30000000000000), // 2^-60

        f64::from_bits(0x3bf0000000000000), // 2^-64

    );

    let ub = p.hi + (p.lo + err);

    let lb = p.hi + (p.lo - err);

    if ub == lb {

        return p.to_f64();

    }

    y1_small_argument_hard(r, c)

}

#[cold]

#[inline(never)]

fn y1_small_argument_hard(r: DoubleDouble, c: &[(u64, u64); 28]) -> f64 {

    // if we're too close to zero taylor will converge faster and more accurate,

    // since remez, minimax and other almost cannot polynomial optimize near zero

    let mut p = DoubleDouble::from_bit_pair(c[27]);

    for i in (0..27).rev() {

        p = DoubleDouble::mul_add(r, p, DoubleDouble::from_bit_pair(c[i]));

        p = DoubleDouble::from_exact_add(p.hi, p.lo);

    }

    p.to_f64()

}

/*

   Evaluates:

   Y1 = sqrt(2/(PI*x)) * beta(x) * sin(x - 3*PI/4 - alpha(x))

   Discarding 1/2*PI gives:

   Y1 = sqrt(2/(PI*x)) * beta(x) * (-cos(x - PI/4 - alpha(x)))

*/

#[inline]

pub(crate) fn y1_asympt_fast(x: f64) -> f64 {

    const SQRT_2_OVER_PI: DoubleDouble = DoubleDouble::new(

        f64::from_bits(0xbc8cbc0d30ebfd15),

        f64::from_bits(0x3fe9884533d43651),

    );

    const MPI_OVER_4: DoubleDouble = DoubleDouble::new(

        f64::from_bits(0xbc81a62633145c07),

        f64::from_bits(0xbfe921fb54442d18),

    );

    let recip = if x.to_bits() > 0x7fd000000000000u64 {

        DoubleDouble::quick_mult_f64(DoubleDouble::from_exact_div_fma(4.0, x), 0.25)