/*

 * // 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

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 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE

 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

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 */

use crate::bessel::i0f::i0f_small;

use crate::common::f_fmla;

use crate::exponents::core_expf;

use crate::logs::fast_logf;

use crate::polyeval::{f_estrin_polyeval7, f_estrin_polyeval8};

/// Modified Bessel of the second kind of order 0

///

/// Max ULP 0.5

///

/// This method have exactly one exception which is not correctly rounded with FMA.

pub fn f_k0f(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 >= 0x42cbc4fbu32 {

        // x > 101.88473

        return 0.;

    }

    if xb <= 0x3f800000u32 {

        if xb <= 0x34000000u32 {

            // |x| < f32::EPSILON

            // taylor series for K0(x) ~ -euler_gamma + log(2) - log(x)

            let log_x = fast_logf(x);

            const EULER_GAMMA_PLUS_LOG2: f64 = f64::from_bits(0x3fbdadb014541eb2);

            return (-log_x + EULER_GAMMA_PLUS_LOG2) as f32;

        }

        // x <= 1.0

        return k0f_small(x);

    }

    k0f_asympt(x)

}

/**

K0(x) + log(x) * I0(x) = P(x^2)

hence

K0(x) = P(x^2) - log(x)*I0(x)

Polynomial generated by Wolfram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=BesselK[0,x]+Log[x]BesselI[0,x]

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

{err, approx}=MiniMaxApproximation[g[z],{z,{0.000000001,1},6,0},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}]]

```

**/

#[inline]

fn k0f_small(x: f32) -> f32 {

    let v_log = fast_logf(x);

    let i0 = i0f_small(x);

    let dx = x as f64;

    let p = f_estrin_polyeval7(

        dx * dx,

        f64::from_bits(0x3fbdadb014541ece),

        f64::from_bits(0x3fd1dadb01453e9c),

        f64::from_bits(0x3f99dadb01491ac7),

        f64::from_bits(0x3f4bb90e82a4f609),

        f64::from_bits(0x3eef4749ebd25b10),

        f64::from_bits(0x3e85d5b5668593af),

        f64::from_bits(0x3e15233b0788618b),

    );

    let c = f_fmla(-i0, v_log, p);

    c as f32

}

/**

Generated in Wolfram

Computes sqrt(x)*exp(x)*K0(x)=Pn(1/x)/Qm(1/x)

hence

K0(x) = Pn(1/x)/Qm(1/x) / (sqrt(x) * exp(x))

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=Sqrt[x] Exp[x] BesselK[0,x]

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

{err, approx}=MiniMaxApproximation[g[z],{z,{0.0000000000001,1},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 k0f_asympt(x: f32) -> f32 {

    let dx = x as f64;

    let recip = 1. / dx;

    let e = core_expf(x);

    let r_sqrt = dx.sqrt();

    let p_num = f_estrin_polyeval8(

        recip,

        f64::from_bits(0x3ff40d931ff62701),

        f64::from_bits(0x402d8410a62d9c17),

        f64::from_bits(0x404e9f1804dd7e54),

        f64::from_bits(0x405c076822dcd255),

        f64::from_bits(0x4057379c6932949f),

        f64::from_bits(0x403ffd64a0bd54b7),

        f64::from_bits(0x400cc53ed733fd97),

        f64::from_bits(0x3faf8cc8756944eb),

    );

    let p_den = f_estrin_polyeval8(

        recip,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0x4027ccde1d27ffc9),

        f64::from_bits(0x40492418136fb90f),

        f64::from_bits(0x4057be8a00983906),

        f64::from_bits(0x4054cc77d2379b76),

        f64::from_bits(0x403fd218713ec08d),

        f64::from_bits(0x4011c77649d3f65f),

        f64::from_bits(0x3fc2080a59e87324),

    );

    let v = p_num / p_den;

    let pp = v / (e * r_sqrt);

    pp as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_k0f() {

        assert_eq!(f_k0f(2.034804e-5), 10.918458);

        assert_eq!(f_k0f(0.010260499), 4.695535);

        assert_eq!(f_k0f(0.3260499), 1.2965646);

        assert_eq!(f_k0f(0.72341), 0.636511734);

        assert_eq!(f_k0f(0.), f32::INFINITY);

        assert_eq!(f_k0f(-0.), f32::INFINITY);

        assert!(f_k0f(-0.5).is_nan());

        assert!(f_k0f(f32::NEG_INFINITY).is_nan());

        assert_eq!(f_k0f(f32::INFINITY), 0.);

    }

}