/*

 * // 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,

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 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 */

use crate::common::f_fmla;

use crate::polyeval::f_polyeval5;

/// Computes cotangent

///

/// Max found ULP 0.4999999

#[inline]

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

    let x_abs = x.to_bits() & 0x7fff_ffffu32;

    let xd = x as f64;

    // |x| < pi/32

    if x_abs <= 0x3dc9_0fdbu32 {

        // |x| < 0.000244141

        if x_abs < 0x3980_0000u32 {

            if x_abs == 0 {

                return 1. / x;

            }

            // When |x| < 2^-12, the relative error of the approximation cot(x)

            // is:

            let ddx = x as f64;

            let dx = 1. / ddx;

            // taylor order 3

            return f_fmla(ddx, f64::from_bits(0xbfd5555555555555), dx) as f32;

        }

        let xsqr = xd * xd;

        /*

           Generated by Sollya:

           f_cotf = x/tan(x);

           Q = fpminimax(f_cotf, [|0, 2, 4, 6, 8|], [|1, D...|], [0, pi/32]);

           See ./notes/cotf.sollya

        */

        let p = f_polyeval5(

            xsqr,

            f64::from_bits(0x3ff0000000000000),

            f64::from_bits(0xbfd5555555555466),

            f64::from_bits(0xbf96c16c16fb8937),

            f64::from_bits(0xbf6156688756cd43),

            f64::from_bits(0xbf2bce669d7cd742),

        );

        return (p / xd) as f32;

    }

    if x_abs >= 0x7f80_0000u32 {

        return x + f32::NAN;

    }

    // For |x| >= pi/32, we use the definition of cot(x) function:

    // cot(a+b) = (1 - tan(a)tan(b)) / (tan(a) + tan(b))

    // tanf_eval returns:

    // - rs.tan_y = tan(pi/32 * y)          -> tangent of the remainder

    // - rs.tan_k = tan(pi/32 * k)          -> tan of the main angle multiple

    let rs = crate::tangent::evalf::tanf_eval(xd, x_abs);

    // Then computing tan through identities

    // num = tan(k*pi/32) + tan(y*pi/32)

    let num = rs.tan_y + rs.tan_k;

    // den = 1 - tan(k*pi/32) * tan(y*pi/32)

    let den = f_fmla(rs.tan_y, -rs.tan_k, 1.);

    (den / num) as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn cotf_test() {

        assert_eq!(f_cotf(0.0010348097), 966.36084);

        assert_eq!(f_cotf(0.0020286469), 492.93872);

        assert_eq!(f_cotf(-0.0020286469), -492.93872);

        assert_eq!(f_cotf(1.0020286469), 0.63923126);

        assert_eq!(f_cotf(-1.0020286469), -0.63923126);

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

        assert_eq!(f_cotf(-0.0), f32::NEG_INFINITY);

        assert!(f_cotf(f32::INFINITY).is_nan());

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

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

    }

}