/*

 * // Copyright (c) Radzivon Bartoshyk 4/2025. 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, f_fmlaf};

#[inline(always)]

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

    const PI2: f64 = f64::from_bits(0x3ff921fb54442d18);

    let t = x.to_bits();

    let e = (t >> 23) & 0xff;

    let gt = e >= 127;

    let ta = t & 0x7fffffff;

    if ta >= 0x4c700518u32 {

        // |x| >= 6.29198e+07

        if ta > 0x7f800000u32 {

            return x + x;

        } // nan

        return f32::copysign(PI2 as f32, x); // inf or |x| >= 6.29198e+07

    }

    if e < 127 - 13 {

        // |x| < 2^-13

        if e < 127 - 25 {

            // |x| < 2^-25

            if t << 1 == 0 {

                return x;

            }

            let res = f_fmlaf(-x, x.abs(), x);

            return res;

        }

        return f_fmlaf(-f64::from_bits(0x3fd5555560000000) as f32 * x, x * x, x);

    }

    /* now |x| >= 0.00012207 */

    let mut z = x as f64;

    if gt {

        z = 1.0 / z;

    } /* gt is non-zero for |x| >= 1 */

    let z2 = z * z;

    let z4 = z2 * z2;

    let z8 = z4 * z4;

    /* polynomials generated using rminimax

       (https://gitlab.inria.fr/sfilip/rminimax) with the following command:

       ./ratapprox --function="atan(x)" --dom=[0.000122070,1] --num=[x,x^3,x^5,x^7,x^9,x^11,x^13] --den=[1,x^2,x^4,x^6,x^8,x^10,x^12] --output=atanf.sollya --log

       (see output atanf.sollya)

       The coefficient cd[0] was slightly reduced from the original value

       0.330005 to avoid an exceptional case for |x| = 0.069052

       and rounding to nearest.

    */

    const CN: [u64; 7] = [

        0x3fd51eccde075d67,

        0x3fea76bb5637f2f2,

        0x3fe81e0eed20de88,

        0x3fd376c8ca67d11d,

        0x3faaec7b69202ac6,

        0x3f69561899acc73e,

        0x3efbf9fa5b67e600,

    ];

    const CD: [u64; 7] = [

        0x3fd51eccde075d66,

        0x3fedfbdd7b392d28,

        0x3ff0000000000000,

        0x3fdfd22bf0e89b54,

        0x3fbd91ff8b576282,

        0x3f8653ea99fc9bb0,

        0x3f31e7fcc202340a,

    ];

    let mut cn0 = fma(z2, f64::from_bits(CN[1]), f64::from_bits(CN[0]));

    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 = fma(z4, cn2, cn0);

    cn4 = fma(z4, cn6, cn4);

    cn0 = fma(z8, cn4, cn0);

    cn0 *= z;

    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);

    let r = cn0 / cd0;

    if !gt {

        return r as f32;

    } /* for |x| < 1, (float) r is correctly rounded */

    const PI_OVER2_H: f64 = f64::from_bits(0x3ff9000000000000);

    const PI_OVER2_L: f64 = f64::from_bits(0x3f80fdaa22168c23);

    /* now r approximates atan(1/x), we use atan(x) + atan(1/x) = sign(x)*pi/2,

    where PI_OVER2_H + PI_OVER2_L approximates pi/2.

    With sign(z)*L + (-r + sign(z)*H), it fails for x=0x1.98c252p+12 and

    rounding upward.

    With sign(z)*PI - r, where PI is a double approximation of pi to nearest,

    it fails for x=0x1.ddf9f6p+0 and rounding upward. */

    ((f64::copysign(PI_OVER2_L, z) - r) + f64::copysign(PI_OVER2_H, z)) as f32

}

Unexecuted instantiation: pxfm::tangent::atanf::atanf_gen_impl::<<f64>::mul_add>

Unexecuted instantiation: pxfm::tangent::atanf::atanf_gen_impl::<pxfm::common::f_fmla>

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

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

unsafe fn atanf_fma_impl(x: f32) -> f32 {

    atanf_gen_impl(x, f64::mul_add)

}

/// Computes atan

///

/// Max found ULP 0.49999973

#[inline]

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

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

    {

        atanf_gen_impl(x, f_fmla)

    }

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

    {

        use std::sync::OnceLock;

        static EXECUTOR: OnceLock<unsafe fn(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")

            {

                atanf_fma_impl

            } else {

                fn def_atanf(x: f32) -> f32 {

                    atanf_gen_impl(x, f_fmla)

                }

                def_atanf

            }

        });

        unsafe { q(x) }

    }

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn f_atan_test() {

        assert!(

            (f_atanf(1.0) - std::f32::consts::PI / 4f32).abs() < 1e-6,

            "Invalid result {}",

            f_atanf(1f32)

        );

        assert!(

            (f_atanf(2f32) - 1.107148717794090503017065f32).abs() < 1e-6,

            "Invalid result {}",

            f_atanf(2f32)

        );

        assert!(

            (f_atanf(5f32) - 1.3734007669450158608612719264f32).abs() < 1e-6,

            "Invalid result {}",

            f_atanf(5f32)

        );

    }

}