/*

 * // 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

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 * // 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

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 */

use crate::bessel::j0f::j1f_rsqrt;

use crate::common::f_fmla;

use crate::exponents::core_expf;

use crate::polyeval::{f_estrin_polyeval7, f_estrin_polyeval9, f_polyeval10};

/// Modified Bessel of the first kind of order 1

///

/// Max ULP 0.5

pub fn f_i1f(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 0.;

        }

        if x.is_infinite() {

            return if x.is_sign_positive() {

                f32::INFINITY

            } else {

                f32::NEG_INFINITY

            };

        }

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

    }

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

    if xb > 0x42b7d001 {

        // x > 91.906261

        return if x.is_sign_negative() {

            f32::NEG_INFINITY

        } else {

            f32::INFINITY

        };

    }

    static SIGN: [f64; 2] = [1., -1.];

    let sign_scale = SIGN[x.is_sign_negative() as usize];

    if xb <= 0x40f80000u32 {

        // |x| <= 7.75

        if xb <= 0x34000000u32 {

            // |x| <= f32::EPSILON

            // taylor series for I1(x) ~ x/2 + O(x^3)

            return x * 0.5;

        }

        return i1f_small(f32::from_bits(xb), sign_scale) as f32;

    }

    i1f_asympt(f32::from_bits(xb), sign_scale)

}

/**

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,{0.000000001,7.75},6,6},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 i1f_small(x: f32, sign_scale: f64) -> 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_estrin_polyeval7(

        x_over_two_sqr,

        f64::from_bits(0x3fb5555555555555),

        f64::from_bits(0x3f706cdccca396c4),

        f64::from_bits(0x3f23f9e12bdbba92),

        f64::from_bits(0x3ec8e39208e926b2),

        f64::from_bits(0x3e62e53b433c42ff),

        f64::from_bits(0x3def7cb16d10fb46),

        f64::from_bits(0x3d6747cd73d9d783),

    );

    let p_den = f_estrin_polyeval7(

        x_over_two_sqr,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xbfa2075f77b54885),

        f64::from_bits(0x3f438c6d797c29f5),

        f64::from_bits(0xbeda57e2a258c6da),

        f64::from_bits(0x3e677e777c569432),

        f64::from_bits(0xbdea9212a96babc1),

        f64::from_bits(0x3d5e183186d5d782),

    );

    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 * sign_scale

}

/**

Asymptotic expansion for I1.

Computes:

sqrt(x) * exp(-x) * I1(x) = Pn(1/x)/Qn(1/x)

hence:

I1(x) = Pn(1/x)/Qm(1/x)*exp(x)/sqrt(x)

Generated by Wolfram Mathematica:

```text

<<FunctionApproximations`

ClearAll["Global`*"]

f[x_]:=Sqrt[x] Exp[-x] BesselI[1,x]

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

{err, approx,err1}=MiniMaxApproximation[g[z],{z,{1/91.9,1/7.75},9,8},WorkingPrecision->60]

poly=Numerator[approx];

coeffs=CoefficientList[poly,z];

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

poly=Denominator[approx];

coeffs=CoefficientList[poly,z];

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

```

**/

#[inline]

fn i1f_asympt(x: f32, sign_scale: f64) -> f32 {

    let dx = x as f64;

    let recip = 1. / dx;

    let p_num = f_polyeval10(

        recip,

        f64::from_bits(0x3fd9884533d43711),

        f64::from_bits(0xc0309c047537243a),

        f64::from_bits(0x4073bdb14a29bf68),

        f64::from_bits(0xc0aaf9eca14d15af),

        f64::from_bits(0x40d6c629318a9e42),

        f64::from_bits(0xc0f7bee33088a4b0),

        f64::from_bits(0x410d018cef093ee2),

        f64::from_bits(0xc111f32b325d3fe4),

        f64::from_bits(0x4100dddad80e0b42),

        f64::from_bits(0xc0c96006c91a00e2),

    );

    let p_den = f_estrin_polyeval9(

        recip,

        f64::from_bits(0x3ff0000000000000),

        f64::from_bits(0xc044a11d10bae889),

        f64::from_bits(0x408843069497d993),

        f64::from_bits(0xc0c058710de4b9b9),

        f64::from_bits(0x40eb0d97f71420ae),

        f64::from_bits(0xc10b55d181ef9ea1),

        f64::from_bits(0x411f9413e1932a48),

        f64::from_bits(0xc1213bff5bc7d2d6),

        f64::from_bits(0x4105c53e92d9b9c0),

    );

    let z = p_num / p_den;

    let e = core_expf(x);

    let r_sqrt = j1f_rsqrt(dx);

    (z * r_sqrt * e * sign_scale) as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_i1f() {

        assert!(f_i1f(f32::NAN).is_nan());

        assert!(f_i1f(f32::INFINITY).is_infinite());

        assert!(f_i1f(f32::NEG_INFINITY).is_infinite());

        assert_eq!(f_i1f(0.), 0.);

        assert_eq!(f_i1f(1.), 0.5651591);

        assert_eq!(f_i1f(-1.), -0.5651591);

        assert_eq!(f_i1f(9.), 1030.9147);

        assert_eq!(f_i1f(-9.), -1030.9147);

    }

}