pxfm 0.1.29

/*
 * // 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;
use crate::cube_roots::cbrt::{CbrtBackend, GenericCbrtBackend};

#[inline(always)]
pub(crate) fn halley_refine_d(x: f64, a: f64) -> f64 {
    let tx = x * x * x;
    x * f_fmla(2., a, tx) / f_fmla(2., tx, a)
}

#[inline(always)]
#[allow(unused)]
pub(crate) fn halley_refine_d_fma(x: f64, a: f64) -> f64 {
    let tx = x * x * x;
    x * f64::mul_add(2., a, tx) / f64::mul_add(2., tx, a)
}

#[inline(always)]
const fn halley_refine(x: f32, a: f32) -> f32 {
    let tx = x * x * x;
    x * (tx + 2f32 * a) / (2f32 * tx + a)
}

/// Cbrt for given value for const context.
/// This is simplified version just to make a good approximation on const context.
#[inline]
pub const fn cbrtf(x: f32) -> f32 {
    let u = x.to_bits();
    let au = u.wrapping_shl(1);
    if au < (1u32 << 24) || au >= (0xffu32 << 24) {
        if au >= (0xffu32 << 24) {
            return x + x; /* inf, nan */
        }
        if au == 0 {
            return x; /* +-0 */
        }
    }

    const B1: u32 = 709958130;
    let mut t: f32;
    let mut ui: u32 = x.to_bits();
    let mut hx: u32 = ui & 0x7fffffff;

    hx = (hx / 3).wrapping_add(B1);
    ui &= 0x80000000;
    ui |= hx;

    t = f32::from_bits(ui);
    t = halley_refine(t, x);
    halley_refine(t, x)
}

#[inline(always)]
fn cbrtf_gen_impl<B: CbrtBackend>(x: f32, backend: B) -> f32 {
    let u = x.to_bits();
    let au = u.wrapping_shl(1);
    if au < (1u32 << 24) || au >= (0xffu32 << 24) {
        if au >= (0xffu32 << 24) {
            return x + x; /* inf, nan */
        }
        if au == 0 {
            return x; /* +-0 */
        }
    }

    let mut ui: u32 = x.to_bits();
    let mut hx: u32 = ui & 0x7fffffff;

    if hx < 0x00800000 {
        /* zero or subnormal? */
        if hx == 0 {
            return x; /* cbrt(+-0) is itself */
        }
        const TWO_EXP_24: f32 = f32::from_bits(0x4b800000);
        ui = (x * TWO_EXP_24).to_bits();
        hx = ui & 0x7fffffff;
        const B2: u32 = 642849266;
        hx = (hx / 3).wrapping_add(B2);
    } else {
        const B1: u32 = 709958130;
        hx = (hx / 3).wrapping_add(B1);
    }
    ui &= 0x80000000;
    ui |= hx;

    let mut t = f32::from_bits(ui) as f64;
    let dx = x as f64;
    t = backend.halley(t, dx);
    backend.halley(t, dx) as f32
}

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
#[target_feature(enable = "avx", enable = "fma")]
unsafe fn cbrtf_fma_impl(x: f32) -> f32 {
    use crate::cube_roots::cbrt::FmaCbrtBackend;
    cbrtf_gen_impl(x, FmaCbrtBackend {})
}

/// Computes cube root
///
/// Peak ULP on 64 bit = 0.49999577
#[inline]
pub fn f_cbrtf(x: f32) -> f32 {
    #[cfg(not(any(target_arch = "x86", target_arch = "x86_64")))]
    {
        cbrtf_gen_impl(x, GenericCbrtBackend {})
    }
    #[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")
            {
                cbrtf_fma_impl
            } else {
                fn def_cbrt(x: f32) -> f32 {
                    cbrtf_gen_impl(x, GenericCbrtBackend {})
                }
                def_cbrt
            }
        });
        unsafe { q(x) }
    }
}

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

    #[test]
    fn test_fcbrtf() {
        assert_eq!(f_cbrtf(0.0), 0.0);
        assert_eq!(f_cbrtf(-27.0), -3.0);
        assert_eq!(f_cbrtf(27.0), 3.0);
        assert_eq!(f_cbrtf(64.0), 4.0);
        assert_eq!(f_cbrtf(-64.0), -4.0);
        assert_eq!(f_cbrtf(f32::NEG_INFINITY), f32::NEG_INFINITY);
        assert_eq!(f_cbrtf(f32::INFINITY), f32::INFINITY);
        assert!(f_cbrtf(f32::NAN).is_nan());
    }
}