pxfm 0.1.28

/*
 * // 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,
 * // 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.
 */
#![allow(clippy::too_many_arguments)]
use crate::bessel::j0f::j1f_rsqrt;
use crate::bessel::j1_coeffs::{J1_ZEROS, J1_ZEROS_VALUE};
use crate::bessel::j1f::{j1f_asympt_alpha, j1f_asympt_beta};
use crate::bessel::j1f_coeffs::J1F_COEFFS;
use crate::bessel::trigo_bessel::sin_small;
use crate::common::f_fmla;
use crate::double_double::DoubleDouble;
use crate::rounding::CpuCeil;
use crate::rounding::CpuRound;

pub(crate) trait JincpifBackend {
    fn fma(&self, x: f64, y: f64, z: f64) -> f64;
    fn round(&self, x: f64) -> f64;
    fn ceil(&self, x: f64) -> f64;
    fn polyeval6(&self, x: f64, a0: f64, a1: f64, a2: f64, a3: f64, a4: f64, a5: f64) -> f64;
    fn polyeval14(
        &self,
        x: f64,
        a0: f64,
        a1: f64,
        a2: f64,
        a3: f64,
        a4: f64,
        a5: f64,
        a6: f64,
        a7: f64,
        a8: f64,
        a9: f64,
        a10: f64,
        a11: f64,
        a12: f64,
        a13: f64,
    ) -> f64;
}

struct GenJincpifBackend {}

impl JincpifBackend for GenJincpifBackend {
    #[inline(always)]
    fn fma(&self, x: f64, y: f64, z: f64) -> f64 {
        f_fmla(x, y, z)
    }

    #[inline(always)]
    fn round(&self, x: f64) -> f64 {
        x.cpu_round()
    }

    #[inline(always)]
    fn ceil(&self, x: f64) -> f64 {
        x.cpu_ceil()
    }

    #[inline(always)]
    fn polyeval6(&self, x: f64, a0: f64, a1: f64, a2: f64, a3: f64, a4: f64, a5: f64) -> f64 {
        use crate::polyeval::f_polyeval6;
        f_polyeval6(x, a0, a1, a2, a3, a4, a5)
    }

    #[inline(always)]
    fn polyeval14(
        &self,
        x: f64,
        a0: f64,
        a1: f64,
        a2: f64,
        a3: f64,
        a4: f64,
        a5: f64,
        a6: f64,
        a7: f64,
        a8: f64,
        a9: f64,
        a10: f64,
        a11: f64,
        a12: f64,
        a13: f64,
    ) -> f64 {
        use crate::polyeval::f_polyeval14;
        f_polyeval14(
            x, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13,
        )
    }
}

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
struct FmaJincpifBackend {}

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
impl JincpifBackend for FmaJincpifBackend {
    #[inline(always)]
    fn fma(&self, x: f64, y: f64, z: f64) -> f64 {
        f64::mul_add(x, y, z)
    }

    #[inline(always)]
    fn round(&self, x: f64) -> f64 {
        x.round()
    }

    #[inline(always)]
    fn ceil(&self, x: f64) -> f64 {
        x.ceil()
    }

    #[inline(always)]
    fn polyeval6(&self, x: f64, a0: f64, a1: f64, a2: f64, a3: f64, a4: f64, a5: f64) -> f64 {
        use crate::polyeval::d_polyeval6;
        d_polyeval6(x, a0, a1, a2, a3, a4, a5)
    }

    #[inline(always)]
    fn polyeval14(
        &self,
        x: f64,
        a0: f64,
        a1: f64,
        a2: f64,
        a3: f64,
        a4: f64,
        a5: f64,
        a6: f64,
        a7: f64,
        a8: f64,
        a9: f64,
        a10: f64,
        a11: f64,
        a12: f64,
        a13: f64,
    ) -> f64 {
        use crate::polyeval::d_polyeval14;
        d_polyeval14(
            x, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13,
        )
    }
}

#[inline(always)]
fn jincpif_gen<B: JincpifBackend>(x: f32, backend: B) -> f32 {
    let ux = x.to_bits().wrapping_shl(1);
    if ux >= 0xffu32 << 24 || ux <= 0x6800_0000u32 {
        // |x| <= f32::EPSILON, |x| == inf, |x| == NaN
        if ux <= 0x6800_0000u32 {
            // |x| == 0
            return 1.;
        }
        if x.is_infinite() {
            return 0.;
        }
        return x + f32::NAN; // x == NaN
    }

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

    if ax < 0x429533c2u32 {
        // |x| < 74.60109
        if ax <= 0x3e800000u32 {
            // |x| < 0.25
            return jincf_near_zero(f32::from_bits(ax), &backend);
        }
        let scaled_pix = f32::from_bits(ax) * std::f32::consts::PI; // just test boundaries
        if scaled_pix < 74.60109 {
            return jincpif_small_argument(f32::from_bits(ax), &backend);
        }
    }

    jincpif_asympt(f32::from_bits(ax), &backend) as f32
}

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
#[target_feature(enable = "avx", enable = "fma")]
unsafe fn jincpif_fma_impl(x: f32) -> f32 {
    jincpif_gen(x, FmaJincpifBackend {})
}

/// Normalized jinc 2*J1(PI\*x)/(pi\*x)
///
pub fn f_jincpif(x: f32) -> f32 {
    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
    {
        jincpif_gen(x, GenJincpifBackend {})
    }
    #[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")
            {
                jincpif_fma_impl
            } else {
                fn def_jincpif(x: f32) -> f32 {
                    jincpif_gen(x, GenJincpifBackend {})
                }
                def_jincpif
            }
        });
        unsafe { q(x) }
    }
}

#[inline(always)]
fn jincf_near_zero<B: JincpifBackend>(x: f32, backend: &B) -> f32 {
    let dx = x as f64;
    // Generated in Wolfram Mathematica:
    // <<FunctionApproximations`
    // ClearAll["Global`*"]
    // f[x_]:=2*BesselJ[1,x*Pi]/(x*Pi)
    // {err,approx}=MiniMaxApproximation[f[z],{z,{2^-23,0.3},5,5},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}]]
    let p_num = backend.polyeval6(
        dx,
        f64::from_bits(0x3ff0000000000002),
        f64::from_bits(0xbfe46cd1822a5aa0),
        f64::from_bits(0xbfee583c923dc6f4),
        f64::from_bits(0x3fe3834f47496519),
        f64::from_bits(0x3fc8118468756e6f),
        f64::from_bits(0xbfbfaff09f13df88),
    );
    let p_den = backend.polyeval6(
        dx,
        f64::from_bits(0x3ff0000000000000),
        f64::from_bits(0xbfe46cd1822a4cb0),
        f64::from_bits(0x3fd2447a026f477a),
        f64::from_bits(0xbfc6bdf2192404e5),
        f64::from_bits(0x3fa0cf182218e448),
        f64::from_bits(0xbf939ab46c3f7a7d),
    );
    (p_num / p_den) as f32
}

/// This method on small range searches for nearest zero or extremum.
/// Then picks stored series expansion at the point end evaluates the poly at the point.
#[inline(always)]
fn jincpif_small_argument<B: JincpifBackend>(ox: f32, backend: &B) -> f32 {
    const PI: f64 = f64::from_bits(0x400921fb54442d18);
    let x = ox as f64 * PI;
    let x_abs = f64::from_bits(x.to_bits() & 0x7fff_ffff_ffff_ffff);

    // let avg_step = 74.60109 / 47.0;
    // let inv_step = 1.0 / avg_step;

    const INV_STEP: f64 = 0.6300176043004198;

    let inv_scale = x;

    let fx = x_abs * INV_STEP;
    const J1_ZEROS_COUNT: f64 = (J1_ZEROS.len() - 1) as f64;
    let idx0 = unsafe { fx.min(J1_ZEROS_COUNT).to_int_unchecked::<usize>() };
    let idx1 = unsafe {
        backend
            .ceil(fx)
            .min(J1_ZEROS_COUNT)
            .to_int_unchecked::<usize>()
    };

    let found_zero0 = DoubleDouble::from_bit_pair(J1_ZEROS[idx0]);
    let found_zero1 = DoubleDouble::from_bit_pair(J1_ZEROS[idx1]);

    let dist0 = (found_zero0.hi - x_abs).abs();
    let dist1 = (found_zero1.hi - x_abs).abs();

    let (found_zero, idx, dist) = if dist0 < dist1 {
        (found_zero0, idx0, dist0)
    } else {
        (found_zero1, idx1, dist1)
    };

    if idx == 0 {
        return jincf_near_zero(ox, backend);
    }

    // We hit exact zero, value, better to return it directly
    if dist == 0. {
        return (f64::from_bits(J1_ZEROS_VALUE[idx]) / inv_scale * 2.) as f32;
    }

    let c = &J1F_COEFFS[idx - 1];

    let r = (x_abs - found_zero.hi) - found_zero.lo;

    let p = backend.polyeval14(
        r,
        f64::from_bits(c[0]),
        f64::from_bits(c[1]),
        f64::from_bits(c[2]),
        f64::from_bits(c[3]),
        f64::from_bits(c[4]),
        f64::from_bits(c[5]),
        f64::from_bits(c[6]),
        f64::from_bits(c[7]),
        f64::from_bits(c[8]),
        f64::from_bits(c[9]),
        f64::from_bits(c[10]),
        f64::from_bits(c[11]),
        f64::from_bits(c[12]),
        f64::from_bits(c[13]),
    );

    (p / inv_scale * 2.) as f32
}

/*
   Evaluates:
   J1 = sqrt(2/(PI*x)) * beta(x) * cos(x - 3*PI/4 - alpha(x))
   discarding 1*PI/2 using identities gives:
   J1 = sqrt(2/(PI*x)) * beta(x) * sin(x - PI/4 - alpha(x))

   to avoid squashing small (-PI/4 - alpha(x)) into a large x actual expansion is:

   J1 = sqrt(2/(PI*x)) * beta(x) * sin((x mod 2*PI) - PI/4 - alpha(x))
*/
#[inline(always)]
pub(crate) fn jincpif_asympt<B: JincpifBackend>(x: f32, backend: &B) -> f64 {
    const PI: f64 = f64::from_bits(0x400921fb54442d18);

    let dox = x as f64;
    let dx = dox * PI;

    let alpha = j1f_asympt_alpha(dx);
    let beta = j1f_asympt_beta(dx);

    // argument reduction assuming x here value is already multiple of PI.
    // k = round((x*Pi) / (pi*2))
    let kd = backend.round(dox * 0.5);
    //  y = (x * Pi) - k * 2
    let angle = backend.fma(kd, -2., dox) * PI;

    // 2^(3/2)/(Pi^2)
    // reduce argument 2*sqrt(2/(PI*(x*PI))) = 2*sqrt(2)/PI
    // adding additional pi from division then 2*sqrt(2)/PI^2
    const Z2_3_2_OVER_PI_SQR: f64 = f64::from_bits(0x3fd25751e5614413);
    const MPI_OVER_4: f64 = f64::from_bits(0xbfe921fb54442d18);

    let x0pi34 = MPI_OVER_4 - alpha;
    let r0 = angle + x0pi34;

    let m_sin = sin_small(r0);

    let z0 = beta * m_sin;
    let scale = Z2_3_2_OVER_PI_SQR * j1f_rsqrt(dox);

    let j1pix = scale * z0;
    j1pix / dox
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_jincpif() {
        assert_eq!(f_jincpif(-102.59484), 0.00024380769);
        assert_eq!(f_jincpif(102.59484), 0.00024380769);
        assert_eq!(f_jincpif(100.08199), -0.00014386141);
        assert_eq!(f_jincpif(0.27715185), 0.9081822);
        assert_eq!(f_jincpif(0.007638072), 0.99992806);
        assert_eq!(f_jincpif(-f32::EPSILON), 1.0);
        assert_eq!(f_jincpif(f32::EPSILON), 1.0);
        assert_eq!(
            f_jincpif(0.000000000000000000000000000000000000008827127),
            1.0
        );
        assert_eq!(f_jincpif(5.4), -0.010821743);
        assert_eq!(
            f_jincpif(77.743162408196766932633181568235159),
            -0.00041799102
        );
        assert_eq!(
            f_jincpif(-77.743162408196766932633181568235159),
            -0.00041799102
        );
        assert_eq!(
            f_jincpif(84.027189586293545175976760219782591),
            -0.00023927793
        );
        assert_eq!(f_jincpif(f32::INFINITY), 0.);
        assert_eq!(f_jincpif(f32::NEG_INFINITY), 0.);
        assert!(f_jincpif(f32::NAN).is_nan());
        assert_eq!(f_jincpif(-1.7014118e38), -0.0);
    }
}