/*

 * // 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;

static OFF: [f32; 8] = [0.0, 0.5, 1.0, 0.5, -0.0, -0.5, -1.0, -0.5];

static SGNF: [f32; 2] = [1., -1.];

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

#[inline(always)]

fn atan2pif_gen_impl<Q: Fn(f64, f64, f64) -> f64>(y: f32, x: f32, fma: Q) -> f32 {

    let tx = x.to_bits();

    let ty: u32 = y.to_bits();

    let ux: u32 = tx;

    let uy: u32 = ty;

    let ax: u32 = ux & 0x7fff_ffff;

    let ay = uy & 0x7fff_ffff;

    if ay >= (0xff << 23) || ax >= (0xff << 23) {

        if ay > (0xff << 23) {

            return x + y;

        } // nan

        if ax > (0xff << 23) {

            return x + y;

        } // nan

        let yinf = ay == (0xff << 23);

        let xinf = ax == (0xff << 23);

        if yinf & xinf {

            return if (ux >> 31) != 0 {

                0.75 * SGNF[(uy >> 31) as usize]

            } else {

                0.25 * SGNF[(uy >> 31) as usize]

            };

        }

        if xinf {

            return if (ux >> 31) != 0 {

                SGNF[(uy >> 31) as usize]

            } else {

                0.0 * SGNF[(uy >> 31) as usize]

            };

        }

        if yinf {

            return 0.5 * SGNF[(uy >> 31) as usize];

        }

    }

    if ay == 0 {

        if (ay | ax) == 0 {

            let i: u32 = (uy >> 31) * 4 + (ux >> 31) * 2;

            return OFF[i as usize];

        }

        if (ux >> 31) == 0 {

            return 0.0 * SGNF[(uy >> 31) as usize];

        }

    }

    if ax == ay {

        static S: [f32; 4] = [0.25, 0.75, -0.25, -0.75];

        let i = (uy >> 31) * 2 + (ux >> 31);

        return S[i as usize];

    }

    let gt: usize = (ay > ax) as usize;

    let i: u32 = (uy >> 31) * 4 + (ux >> 31) * 2 + gt as u32;

    let zx = x as f64;

    let zy = y as f64;

    static M: [f64; 2] = [0., 1.];

    let mut z = fma(M[gt], zx, M[1 - gt] * zy) / fma(M[gt], zy, M[1 - gt] * zx);

    const CN: [u64; 7] = [

        0x3fd45f306dc9c883,

        0x3fe988d83a142ada,

        0x3fe747bebf492057,

        0x3fd2cc5645094ff3,

        0x3faa0521c711ab66,

        0x3f6881b8058b9a0d,

        0x3efb16ff514a0af0,

    ];

    let mut r = f64::from_bits(CN[0]);

    let z2 = z * z;

    z *= SGN[gt];

    // avoid spurious underflow in the polynomial evaluation excluding tiny arguments

    if z2 > f64::from_bits(0x3c90000000000000) {

        let z4 = z2 * z2;

        let z8 = z4 * z4;

        let mut cn0 = fma(z2, f64::from_bits(CN[1]), r);

        let cn2 = fma(z2, f64::from_bits(CN[3]), f64::from_bits(CN[2]));

        let mut cn4 = fma(z2, f64::from_bits(CN[5]), f64::from_bits(CN[4]));

        let cn6 = f64::from_bits(CN[6]);

        cn0 += z4 * cn2;

        cn4 += z4 * cn6;

        cn0 += z8 * cn4;

        const CD: [u64; 7] = [

            0x3ff0000000000000,

            0x4006b8b143a3f6da,

            0x4008421201d18ed5,

            0x3ff8221d086914eb,

            0x3fd670657e3a07ba,

            0x3fa0f4951fd1e72d,

            0x3f4b3874b8798286,

        ];

        let mut cd0 = fma(z2, f64::from_bits(CD[1]), f64::from_bits(CD[0]));

        let cd2 = fma(z2, f64::from_bits(CD[3]), f64::from_bits(CD[2]));

        let mut cd4 = fma(z2, f64::from_bits(CD[5]), f64::from_bits(CD[4]));

        let cd6 = f64::from_bits(CD[6]);

        cd0 = fma(z4, cd2, cd0);

        cd4 = fma(z4, cd6, cd4);

        cd0 = fma(z8, cd4, cd0);

        r = cn0 / cd0;

    }

    fma(z, r, OFF[i as usize] as f64) as f32

}

Unexecuted instantiation: pxfm::tangent::atan2pif::atan2pif_gen_impl::<<f64>::mul_add>

Unexecuted instantiation: pxfm::tangent::atan2pif::atan2pif_gen_impl::<pxfm::common::f_fmla>

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]

#[target_feature(enable = "avx", enable = "fma")]

unsafe fn atan2pif_fma_impl(y: f32, x: f32) -> f32 {

    atan2pif_gen_impl(y, x, f64::mul_add)

}

/// Computes atan(x/y) / PI

///

/// Max found ULP 0.5

#[inline]

pub fn f_atan2pif(y: f32, x: f32) -> f32 {

    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]

    {

        atan2pif_gen_impl(y, x, f_fmla)

    }

    #[cfg(any(target_arch = "x86", target_arch = "x86_64"))]

    {

        use std::sync::OnceLock;

        static EXECUTOR: OnceLock<unsafe fn(f32, f32) -> f32> = OnceLock::new();

        let q = EXECUTOR.get_or_init(|| {

            if std::arch::is_x86_feature_detected!("avx")

                && std::arch::is_x86_feature_detected!("fma")

            {

                atan2pif_fma_impl

            } else {

                fn def_atan2pif(y: f32, x: f32) -> f32 {

                    atan2pif_gen_impl(y, x, f_fmla)

                }

                def_atan2pif

            }

        });

        unsafe { q(y, x) }

    }

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_atan2pif() {

        assert_eq!(f_atan2pif(0.32131, 0.987565), 0.10012555);

        assert_eq!(f_atan2pif(532.32131, 12.987565), 0.49223542);

        assert_eq!(f_atan2pif(-754.32131, 12.987565), -0.494520042);

    }

}