/*

 * // 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::polyeval::{

    f_estrin_polyeval5, f_estrin_polyeval7, f_estrin_polyeval8, f_polyeval6, f_polyeval10,

};

/// Modified exponentially scaled Bessel of the first kind of order 0

///

/// Computes exp(-|x|)*I0(x)

///

/// Max ULP 0.5

pub fn f_i0ef(x: f32) -> f32 {

    let ux = x.to_bits().wrapping_shl(1);

    if ux >= 0xffu32 << 24 || ux == 0 {

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

        if ux == 0 {

            // |x| == 0

            return 1.;

        }

        if x.is_infinite() {

            return 0.;

        }

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

    }

    let xb = x.to_bits() & 0x7fff_ffff;

    if xb <= 0x40f00000u32 {

        // |x| <= 7.5

        let core_expf = core_expf(-f32::from_bits(xb));

        if xb < 0x3f800000u32 {

            if xb <= 0x34000000u32 {

                // |x| <= f32::EPSILON

                // taylor series for I0(x) * exp(-x) ~ 1 - x + O(x^2)

                return 1. - x;

            }

            // |x| < 1

            return i0f_small(f32::from_bits(xb), core_expf);

        } else if xb <= 0x40600000u32 {

            // |x| <= 3.5

            return i0ef_1_to_3p5(f32::from_bits(xb), core_expf);

        } else if xb <= 0x40c00000u32 {

            // |x| <= 6

            return i0f_3p5_to_6(f32::from_bits(xb), core_expf);

        }

        return i0f_6_to_7p5(f32::from_bits(xb), core_expf);

    }

    i0ef_asympt(f32::from_bits(xb))

}

/**

How polynomial is obtained described at [i0f_1_to_7p5].

Computes I0(x) as follows:

I0(x) = 1 + (x/2)^2 * P(x)

This method valid only [0;1]

Generated by Wolfram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=(BesselI[0,x]-1)/(x/2)^2

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

{err, approx}=MiniMaxApproximation[g[z],{z,{0.0000001,1},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]

pub(crate) fn i0f_small(x: f32, v_exp: f64) -> f32 {

    let dx = x as f64;

    const C: f64 = 1. / 4.;

    let eval_x = dx * dx * C;

    let p = f_estrin_polyeval7(

        eval_x,

        f64::from_bits(0x3ff000000000013a),

        f64::from_bits(0x3fcffffffffc20b6),

        f64::from_bits(0x3f9c71c71e6cd6a2),

        f64::from_bits(0x3f5c71c65b0af15f),

        f64::from_bits(0x3f1234796fceb081),

        f64::from_bits(0x3ec0280faf31678c),

        f64::from_bits(0x3e664fd494223545),

    );

    (f_fmla(p, eval_x, 1.) * v_exp) as f32

}

/**

Computes I0.

/// Valid only on interval [1;3.5]

as rational approximation I0 = 1 + (x/2)^2 * Pn((x/2)^2)/Qm((x/2)^2))

Generated by Wolram Mathematica:

```python

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=(BesselI[0,x]-1)/(x/2)^2

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

{err, approx}=MiniMaxApproximation[g[z],{z,{1,3.5},5,4},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 i0ef_1_to_3p5(x: f32, v_exp: f64) -> f32 {

    let dx = x as f64;

    const C: f64 = 1. / 4.;

    let eval_x = dx * dx * C;

    let p_num = f_polyeval6(

        eval_x,

        f64::from_bits(0x3feffffffffffb69),

        f64::from_bits(0x3fc9ed7bd9dc97a7),

        f64::from_bits(0x3f915c14693c842e),

        f64::from_bits(0x3f45c6dc6a719e42),

        f64::from_bits(0x3eeacb79eba725f7),

        f64::from_bits(0x3e7b51e2acfc4355),

    );

    let p_den = f_estrin_polyeval5(

        eval_x,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbfa84a10988f28eb),

        f64::from_bits(0x3f50f5599197a4be),

        f64::from_bits(0xbeea420cf9b13b1b),

        f64::from_bits(0x3e735d0c1eb6ed7d),

    );

    (f_fmla(p_num / p_den, eval_x, 1.) * v_exp) as f32

}

// Valid only on interval [6;7]

// Generated by Wolfram Mathematica:

// <<FunctionApproximations`

// ClearAll["Global`*"]

// f[x_]:=(BesselI[0,x]-1)/(x/2)^2

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

// {err, approx}=MiniMaxApproximation[g[z],{z,{6,7},7,6},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 i0f_6_to_7p5(x: f32, v_exp: f64) -> f32 {

    let dx = x as f64;

    const C: f64 = 1. / 4.;

    let eval_x = dx * dx * C;

    let p_num = f_estrin_polyeval8(

        eval_x,

        f64::from_bits(0x3fefffffffffff7d),

        f64::from_bits(0x3fcb373b00569ccf),

        f64::from_bits(0x3f939069c3363b81),

        f64::from_bits(0x3f4c2095c90c66b3),

        f64::from_bits(0x3ef6713f648413db),

        f64::from_bits(0x3e947efa2f9936b4),

        f64::from_bits(0x3e2486a182f49420),

        f64::from_bits(0x3da213034a33de33),

    );

    let p_den = f_estrin_polyeval7(

        eval_x,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbfa32313fea59d9e),

        f64::from_bits(0x3f460594c2ec6706),

        f64::from_bits(0xbedf725fb714690f),

        f64::from_bits(0x3e6d9cb39b19555c),

        f64::from_bits(0xbdf1900e3abcb7a6),

        f64::from_bits(0x3d64a21a2ea78ef6),

    );

    (f_fmla(p_num / p_den, eval_x, 1.) * v_exp) as f32

}

// Valid only on interval [3.5;6]

// Generated in Wolfram Mathematica:

// <<FunctionApproximations`

// ClearAll["Global`*"]

// f[x_]:=(BesselI[0,x]-1)/(x/2)^2

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

// {err, approx}=MiniMaxApproximation[g[z],{z,{3.5,6},5,5},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 i0f_3p5_to_6(x: f32, v_exp: f64) -> f32 {

    let dx = x as f64;

    const C: f64 = 1. / 4.;

    let eval_x = dx * dx * C;

    let p_num = f_polyeval6(

        eval_x,

        f64::from_bits(0x3feffffffffd9550),

        f64::from_bits(0x3fc97e18ee033fb4),

        f64::from_bits(0x3f90b3199079bce1),

        f64::from_bits(0x3f442c300a425372),

        f64::from_bits(0x3ee7831030ae18ca),

        f64::from_bits(0x3e76387d67354932),

    );

    let p_den = f_polyeval6(

        eval_x,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbfaa079c484e406a),

        f64::from_bits(0x3f5452098f1556fb),

        f64::from_bits(0xbef33efb4a8128ac),

        f64::from_bits(0x3e865996e19448ca),

        f64::from_bits(0xbe09acbb64533c3e),

    );

    (f_fmla(p_num / p_den, eval_x, 1.) * v_exp) as f32

}

/**

Asymptotic expansion for I0.

Computes:

sqrt(x) * exp(-x) * I0(x) = Pn(1/x)/Qn(1/x)

hence:

I0(x)exp(-x) = Pn(1/x)/Qm(1/x)/sqrt(x)

Generated by Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=Sqrt[x] Exp[-x] BesselI[0,x]

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

{err,approx}=MiniMaxApproximation[g[z],{z,{2^-33,1/7.5},9,9},WorkingPrecision->70]

num=Numerator[approx][[1]];

den=Denominator[approx][[1]];

poly=num;

coeffs=CoefficientList[poly,z];

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

poly=den;

coeffs=CoefficientList[poly,z];

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

```

**/

#[inline]

fn i0ef_asympt(x: f32) -> f32 {

    let dx = x as f64;

    let recip = 1. / dx;

    let p_num = f_polyeval10(

        recip,

        f64::from_bits(0x3fd9884533d4364f),

        f64::from_bits(0xc02ed6c9269921a7),

        f64::from_bits(0x4070ee77ffed64a5),

        f64::from_bits(0xc0a4ffd558b06889),

        f64::from_bits(0x40cf2633e2840f6f),

        f64::from_bits(0xc0ea813a9ba42b84),

        f64::from_bits(0x40f569bf5d63eb8c),

        f64::from_bits(0xc0b3138874cdd180),

        f64::from_bits(0xc0fa3152ed485937),

        f64::from_bits(0x40ddaccbed454f47),

    );

    let p_den = f_polyeval10(

        recip,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xc0436352c350b88c),

        f64::from_bits(0x40855eaa17b05edd),

        f64::from_bits(0xc0baa46f155bd266),

        f64::from_bits(0x40e3e9fd90a2e695),

        f64::from_bits(0xc1012dc621dfc1e8),

        f64::from_bits(0x410cafeea713e8ce),

        f64::from_bits(0xc0e0a3ee0077d7f7),

        f64::from_bits(0xc110bcced6a39e9e),

        f64::from_bits(0x40f9a1e4a91be4d6),

    );

    let z = p_num / p_den;

    let r_sqrt = j1f_rsqrt(dx);

    (z * r_sqrt) as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_i0f() {

        assert!(f_i0ef(f32::NAN).is_nan());

        assert_eq!(f_i0ef(f32::NEG_INFINITY), 0.);

        assert_eq!(f_i0ef(f32::INFINITY), 0.);

        assert_eq!(f_i0ef(1.), 0.4657596);

        assert_eq!(f_i0ef(5.), 0.1835408);

        assert_eq!(f_i0ef(16.), 0.100544125);

        assert_eq!(f_i0ef(32.), 0.070804186);

        assert_eq!(f_i0ef(92.0), 0.04164947);

        assert_eq!(f_i0ef(0.), 1.0);

        assert_eq!(f_i0ef(28.), 0.075736605);

        assert_eq!(f_i0ef(-28.), 0.075736605);

        assert_eq!(f_i0ef(-32.), 0.070804186);

        assert_eq!(f_i0ef(-92.0), 0.04164947);

        assert_eq!(f_i0ef(-0.), 1.0);

    }

}