/*

 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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::common::f_fmla;

use crate::polyeval::f_polyeval5;

use crate::tangent::evalf::tanf_eval;

/// Computes tan

///

/// Max found ULP 0.4999999

#[inline]

pub fn f_tanf(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 x;

            }

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

            // is:

            //   |tan(x) - x| / |tan(x)| < |x^3| / (3|x|)

            //                           = x^2 / 3

            //                           < 2^-25

            //                           < epsilon(1)/2.

            #[cfg(any(

                all(

                    any(target_arch = "x86", target_arch = "x86_64"),

                    target_feature = "fma"

                ),

                target_arch = "aarch64"

            ))]

            {

                use crate::common::f_fmlaf;

                return f_fmlaf(x, f32::from_bits(0xb3000000), x);

            }

            #[cfg(not(any(

                all(

                    any(target_arch = "x86", target_arch = "x86_64"),

                    target_feature = "fma"

                ),

                target_arch = "aarch64"

            )))]

            {

                return f_fmla(xd, f64::from_bits(0xbe60000000000000), xd) as f32;

            }

        }

        let xsqr = xd * xd;

        /*

           Generated by Sollya:

           f_tan = tan(x)/x;

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

           See ./notes/tanf_at_zero.sollya

        */

        let p = f_polyeval5(

            xsqr,

            f64::from_bits(0x3ff0000000000000),

            f64::from_bits(0x3fd555555553d022),

            f64::from_bits(0x3fc111111ce442c1),

            f64::from_bits(0x3faba180a6bbdecd),

            f64::from_bits(0x3f969c0a88a0b71f),

        );

        return (xd * p) as f32;

    }

    if x_abs >= 0x7f80_0000u32 {

        return x + f32::NAN;

    }

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

    // tan(a+b) = (tan(a) + tan(b)) / (1 - 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 = 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.);

    (num / den) as f32

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn f_tanf_test() {

        assert_eq!(f_tanf(0.0), 0.0);

        assert_eq!(f_tanf(1.0), 1.5574077);

        assert_eq!(f_tanf(-1.0), -1.5574077);

        assert_eq!(f_tanf(10.0), 0.64836085);

        assert_eq!(f_tanf(-10.0), -0.64836085);

    }

}