/*

 * // 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::common::f_fmla;

use crate::exponents::core_expf;

use crate::logs::fast_logf;

use crate::polyeval::{f_estrin_polyeval8, f_polyeval3, f_polyeval4};

/// Modified exponentially scaled Bessel of the second kind of order 1

///

/// Computes K1(x)exp(x)

///

/// Max ULP 0.5

pub fn f_k1ef(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 {

            return f32::INFINITY;

        }

        if x.is_infinite() {

            return if x.is_sign_positive() { 0. } else { f32::NAN };

        }

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

    }

    let xb = x.to_bits();

    if xb <= 0x3f800000u32 {

        // x <= 1.0

        if xb <= 0x34000000u32 {

            // |x| <= f32::EPSILON

            let dx = x as f64;

            let leading_term = 1. / dx + 1.;

            if xb <= 0x3109705fu32 {

                // |x| <= 2e-9

                // taylor series for tiny K1(x)exp(x) ~ 1/x + 1 + O(x)

                return leading_term as f32;

            }

            // taylor series for small K1(x)exp(x) ~ 1/x+1+1/4 (1+2 EulerGamma-2 Log[2]+2 Log[x]) x + O(x^3)

            const C: f64 = f64::from_bits(0xbffd8773039049e8); // 1 + 2 EulerGamma-2 Log[2]

            let log_x = fast_logf(x);

            let r = f_fmla(log_x, 2., C);

            let w0 = f_fmla(dx * 0.25, r, leading_term);

            return w0 as f32;

        }

        return k1ef_small(x);

    }

    k1ef_asympt(x)

}

/**

Computes

I1(x) = x/2 * (1 + 1 * (x/2)^2 + (x/2)^4 * P((x/2)^2))

Generated by Woflram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=(BesselI[1,x]*2/x-1-1/2(x/2)^2)/(x/2)^4

g[z_]:=f[2 Sqrt[z]]

{err, approx}=MiniMaxApproximation[g[z],{z,{0.000000001,1},3,2},WorkingPrecision->60]

poly=Numerator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

poly=Denominator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

```

**/

#[inline]

fn i1f_small(x: f32) -> f64 {

    let dx = x as f64;

    let x_over_two = dx * 0.5;

    let x_over_two_sqr = x_over_two * x_over_two;

    let x_over_two_p4 = x_over_two_sqr * x_over_two_sqr;

    let p_num = f_polyeval4(

        x_over_two_sqr,

        f64::from_bits(0x3fb5555555555355),

        f64::from_bits(0x3f6ebf07f0dbc49b),

        f64::from_bits(0x3f1fdc02bf28a8d9),

        f64::from_bits(0x3ebb5e7574c700a6),

    );

    let p_den = f_polyeval3(

        x_over_two_sqr,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbfa39b64b6135b5a),

        f64::from_bits(0x3f3fa729bbe951f9),

    );

    let p = p_num / p_den;

    let p1 = f_fmla(0.5, x_over_two_sqr, 1.);

    let p2 = f_fmla(x_over_two_p4, p, p1);

    p2 * x_over_two

}

/**

Series for

f(x) := BesselK(1, x) - Log(x)*BesselI(1, x) - 1/x

Generated by Wolfram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=(BesselK[1, x]-Log[x]BesselI[1,x]-1/x)/x

g[z_]:=f[Sqrt[z]]

{err, approx}=MiniMaxApproximation[g[z],{z,{0.000000001,1},3,3},WorkingPrecision->60]

poly=Numerator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

poly=Denominator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

```

**/

#[inline]

fn k1ef_small(x: f32) -> f32 {

    let dx = x as f64;

    let rcp = 1. / dx;

    let x2 = dx * dx;

    let p_num = f_polyeval4(

        x2,

        f64::from_bits(0xbfd3b5b6028a83d6),

        f64::from_bits(0xbfb3fde2c83f7cca),

        f64::from_bits(0xbf662b2e5defbe8c),

        f64::from_bits(0xbefa2a63cc5c4feb),

    );

    let p_den = f_polyeval4(

        x2,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbf9833197207a7c6),

        f64::from_bits(0x3f315663bc7330ef),

        f64::from_bits(0xbeb9211958f6b8c3),

    );

    let p = p_num / p_den;

    let v_exp = core_expf(x);

    let lg = fast_logf(x);

    let v_i = i1f_small(x);

    let z = f_fmla(lg, v_i, rcp);

    let z0 = f_fmla(p, dx, z);

    (z0 * v_exp) as f32

}

/**

Generated by Wolfram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=Sqrt[x] Exp[x] BesselK[1,x]

g[z_]:=f[1/z]

{err, approx}=MiniMaxApproximation[g[z],{z,{0.000000001,1},7,7},WorkingPrecision->60]

poly=Numerator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

poly=Denominator[approx][[1]];

coeffs=CoefficientList[poly,z];

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

```

**/

#[inline]

fn k1ef_asympt(x: f32) -> f32 {

    let dx = x as f64;

    let recip = 1. / dx;

    let r_sqrt = j1f_rsqrt(dx);

    let p_num = f_estrin_polyeval8(

        recip,

        f64::from_bits(0x3ff40d931ff6270d),

        f64::from_bits(0x402d250670ed7a6c),

        f64::from_bits(0x404e517b9b494d38),

        f64::from_bits(0x405cb02b7433a838),

        f64::from_bits(0x405a03e606a1b871),

        f64::from_bits(0x4045c98d4308dbcd),

        f64::from_bits(0x401d115c4ce0540c),

        f64::from_bits(0x3fd4213e72b24b3a),

    );

    let p_den = f_estrin_polyeval8(

        recip,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0x402681096aa3a87d),

        f64::from_bits(0x404623ab8d72ceea),

        f64::from_bits(0x40530af06ea802b2),

        f64::from_bits(0x404d526906fb9cec),

        f64::from_bits(0x403281caca389f1b),

        f64::from_bits(0x3ffdb93996948bb4),

        f64::from_bits(0x3f9a009da07eb989),

    );

    let v = p_num / p_den;

    let pp = v * r_sqrt;

    pp as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_k1f() {

        assert_eq!(f_k1ef(0.00000000005423), 18439980000.0);

        assert_eq!(f_k1ef(0.0000000043123), 231894820.0);

        assert_eq!(f_k1ef(0.3), 4.125158);

        assert_eq!(f_k1ef(1.89), 1.0710458);

        assert_eq!(f_k1ef(5.89), 0.5477655);

        assert_eq!(f_k1ef(101.89), 0.12461915);

        assert_eq!(f_k1ef(0.), f32::INFINITY);

        assert_eq!(f_k1ef(-0.), f32::INFINITY);

        assert!(f_k1ef(-0.5).is_nan());

        assert!(f_k1ef(f32::NEG_INFINITY).is_nan());

        assert_eq!(f_k1ef(f32::INFINITY), 0.);

    }

}