/*

 * // 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::j0f::j1f_rsqrt;

use crate::bessel::j1f::{j1f_asympt_alpha, j1f_asympt_beta};

use crate::bessel::trigo_bessel::cos_small;

use crate::bessel::y1f_coeffs::{Y1_ZEROS, Y1_ZEROS_VALUES, Y1F_COEFFS};

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::logs::fast_logf;

use crate::polyeval::{f_polyeval10, f_polyeval18, f_polyeval19};

use crate::rounding::CpuCeil;

use crate::sincos_reduce::rem2pif_any;

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

///

/// Max ULP 0.5

pub fn f_y1f(x: f32) -> f32 {

    let ux = x.to_bits();

    if ux >= 0xffu32 << 23 || ux == 0 {

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

        if ux.wrapping_shl(1) == 0 {

            // |x| == 0

            return f32::NEG_INFINITY;

        }

        if x.is_infinite() {

            if x.is_sign_negative() {

                return f32::NAN;

            }

            return 0.;

        }

        return x + f32::NAN; // x == NaN

    }

    let xb = x.to_bits();

    if xb <= 0x424e0000u32 {

        // x <= 51.5

        if xb <= 0x40000000u32 {

            // x <= 2

            if xb <= 0x3fb5c28fu32 {

                // x <= 1.42

                return y1f_near_zero(x);

            }

            // transient zone from 1.42 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_area(x);

        }

        return y1f_small_argument_path(x);

    }

    // Exceptions

    let bx = x.to_bits();

    if bx == 0x47037a3d {

        return f32::from_bits(0x2deededb);

    } else if bx == 0x65ce46e4 {

        return f32::from_bits(0x9eed85c4);

    } else if bx == 0x6bf68a7b {

        return f32::from_bits(0x9dc70a09);

    } else if bx == 0x76d84625 {

        return f32::from_bits(0x15d7a68b);

    } else if bx == 0x7e3dcda0 {

        return f32::from_bits(0x12b81111);

    }

    y1f_asympt(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))

# see the series

print(W0)

print(Z0)

```

See ./notes/bessel_y1_taylor.ipynb for generation

**/

#[inline]

fn y1f_near_zero(x: f32) -> f32 {

    const W: [u64; 10] = [

        0x3fd45f306dc9c883,

        0xbfa45f306dc9c883,

        0x3f5b2995e7b7b604,

        0xbf021bb945252402,

        0x3e9cf9286ea1d337,

        0xbe2ee7a29824147f,

        0x3db78be9987d036d,

        0xbd3ae90af76a4d0f,

        0x3cb7eb97f85e7d62,

        0xbc31028e3376648a,

    ];

    let dx = x as f64;

    let x2 = dx * dx;

    let w0 = f_polyeval10(

        x2,

        f64::from_bits(W[0]),

        f64::from_bits(W[1]),

        f64::from_bits(W[2]),

        f64::from_bits(W[3]),

        f64::from_bits(W[4]),

        f64::from_bits(W[5]),

        f64::from_bits(W[6]),

        f64::from_bits(W[7]),

        f64::from_bits(W[8]),

        f64::from_bits(W[9]),

    ) * dx;

    const Z: [u64; 10] = [

        0x3fc91866143cbc8a,

        0xbfabd3975c75b4a7,

        0x3f6835b97894be5b,

        0xbf12c7dbffcde97d,

        0x3eb0a780ac776eac,

        0xbe432e5a4ddeea30,

        0x3dcf0ce34d2066a6,

        0xbd52a4e1aea45c18,

        0x3cd1474ade9154ac,

        0xbc4978ba84f218c0,

    ];

    let z0 = f_polyeval10(

        x2,

        f64::from_bits(Z[0]),

        f64::from_bits(Z[1]),

        f64::from_bits(Z[2]),

        f64::from_bits(Z[3]),

        f64::from_bits(Z[4]),

        f64::from_bits(Z[5]),

        f64::from_bits(Z[6]),

        f64::from_bits(Z[7]),

        f64::from_bits(Z[8]),

        f64::from_bits(Z[9]),

    ) * dx;

    let w_log = fast_logf(x);

    const TWO_OVER_PI: f64 = f64::from_bits(0x3fe45f306dc9c883);

    let recip = 1. / dx;

    let z = f_fmla(w0, w_log, -z0);

    f_fmla(recip, -TWO_OVER_PI, z) as f32

}

#[inline]

fn y1_transient_area(x: f32) -> f32 {

    let dx = x as f64;

    // first Y0 bessel zero

    const ZERO: DoubleDouble =

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

    let r = (dx - ZERO.hi) - ZERO.lo;

    /*

        Poly generated by Wolfram Matematica:

        <<FunctionApproximations`

        ClearAll["Global`*"]

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

        {approx,error} = MiniMaxApproximation[f[x],{x,{1.42 - 2.1971413260310170351490335626990, 2 - 2.1971413260310170351490335626990 },17,0},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}]]

    */

    let p = f_polyeval18(

        r,

        f64::from_bits(0x3d9b15a8283b069b),

        f64::from_bits(0x3fe0aa484455fd09),

        f64::from_bits(0xbfbe56f80802fa38),

        f64::from_bits(0xbfa0d2ac9d0409ad),

        f64::from_bits(0xbf73a619b3551650),

        f64::from_bits(0x3f7e6c480057ecbb),

        f64::from_bits(0xbf650dc773a5df4d),

        f64::from_bits(0x3f531e9ccab7d4da),

        f64::from_bits(0xbf29b76999169b0e),

        f64::from_bits(0x3f509c829abceaf7),

        f64::from_bits(0x3f575aee5697c4d8),

        f64::from_bits(0x3f63f7f9598be176),

        f64::from_bits(0x3f67a6ae61541282),

        f64::from_bits(0x3f665e6d3de19021),

        f64::from_bits(0x3f5ee8837b9197f6),

        f64::from_bits(0x3f4e6924f270fd7e),

        f64::from_bits(0x3f32ca61e5b74925),

        f64::from_bits(0x3f0725735bc3890b),

    );

    p as f32

}

/// 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]

fn y1f_small_argument_path(x: f32) -> f32 {

    let x_abs = x as 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_abs * 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).abs();

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

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

        (found_zero0, idx0, dist0)

    } else {

        (found_zero1, idx1, dist1)

    };

    if idx == 0 {

        // Really should not happen here, but if it is then to log expansion

        return y1f_near_zero(x);

    }

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

    if dist == 0. {

        return f64::from_bits(Y1_ZEROS_VALUES[idx]) as f32;

    }

    let c = &Y1F_COEFFS[idx - 1];

    let r = (x_abs - found_zero.hi) - found_zero.lo;

    let p = f_polyeval19(

        r,

        f64::from_bits(c[0]),

        f64::from_bits(c[1]),

        f64::from_bits(c[2]),

        f64::from_bits(c[3]),

        f64::from_bits(c[4]),

        f64::from_bits(c[5]),

        f64::from_bits(c[6]),

        f64::from_bits(c[7]),

        f64::from_bits(c[8]),

        f64::from_bits(c[9]),

        f64::from_bits(c[10]),

        f64::from_bits(c[11]),

        f64::from_bits(c[12]),

        f64::from_bits(c[13]),

        f64::from_bits(c[14]),

        f64::from_bits(c[15]),

        f64::from_bits(c[16]),

        f64::from_bits(c[17]),

        f64::from_bits(c[18]),

    );

    p as f32

}

/*

   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]

fn y1f_asympt(x: f32) -> f32 {

    let dx = x as f64;

    let alpha = j1f_asympt_alpha(dx);

    let beta = j1f_asympt_beta(dx);

    let angle = rem2pif_any(x);

    const SQRT_2_OVER_PI: f64 = f64::from_bits(0x3fe9884533d43651);

    const MPI_OVER_4: f64 = f64::from_bits(0xbfe921fb54442d18);

    let x0pi34 = MPI_OVER_4 - alpha;

    let r0 = angle + x0pi34;

    let m_cos = -cos_small(r0);

    let z0 = beta * m_cos;

    let scale = SQRT_2_OVER_PI * j1f_rsqrt(dx);

    (scale * z0) as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_bessel_zero() {

        assert_eq!(f_y1f(700.76), 0.024876066);

        assert_eq!(f_y1f(35.76), 0.121432826);

        assert_eq!(f_y1f(1.76), -0.24787569);

        assert_eq!(f_y1f(0.87), -0.9030042);

        assert_eq!(f_y1f(f32::INFINITY), 0.0);

        assert!(f_y1f(f32::NEG_INFINITY).is_nan());

        assert!(f_y1f(f32::NAN).is_nan());

    }

}