/* SPDX-License-Identifier: MIT */

/* origin: core-math/src/binary64/cbrt/cbrt.c

 * Copyright (c) 2021-2022 Alexei Sibidanov.

 * Ported to Rust in 2025 by Trevor Gross.

 */

use super::Float;

use super::support::{FpResult, Round, cold_path};

/// Compute the cube root of the argument.

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]

pub fn cbrt(x: f64) -> f64 {

    cbrt_round(x, Round::Nearest).val

}

pub fn cbrt_round(x: f64, round: Round) -> FpResult<f64> {

    const ESCALE: [f64; 3] = [

        1.0,

        hf64!("0x1.428a2f98d728bp+0"), /* 2^(1/3) */

        hf64!("0x1.965fea53d6e3dp+0"), /* 2^(2/3) */

    ];

    /* the polynomial c0+c1*x+c2*x^2+c3*x^3 approximates x^(1/3) on [1,2]

    with maximal error < 9.2e-5 (attained at x=2) */

    const C: [f64; 4] = [

        hf64!("0x1.1b0babccfef9cp-1"),

        hf64!("0x1.2c9a3e94d1da5p-1"),

        hf64!("-0x1.4dc30b1a1ddbap-3"),

        hf64!("0x1.7a8d3e4ec9b07p-6"),

    ];

    let u0: f64 = hf64!("0x1.5555555555555p-2");

    let u1: f64 = hf64!("0x1.c71c71c71c71cp-3");

    let rsc = [1.0, -1.0, 0.5, -0.5, 0.25, -0.25];

    let off = [hf64!("0x1p-53"), 0.0, 0.0, 0.0];

    /* rm=0 for rounding to nearest, and other values for directed roundings */

    let hx: u64 = x.to_bits();

    let mut mant: u64 = hx & f64::SIG_MASK;

    let sign: u64 = hx >> 63;

    let mut e: u32 = (hx >> f64::SIG_BITS) as u32 & f64::EXP_SAT;

    if ((e + 1) & f64::EXP_SAT) < 2 {

        cold_path();

        let ix: u64 = hx & !f64::SIGN_MASK;

        /* 0, inf, nan: we return x + x instead of simply x,

        to that for x a signaling NaN, it correctly triggers

        the invalid exception. */

        if e == f64::EXP_SAT || ix == 0 {

            return FpResult::ok(x + x);

        }

        let nz = ix.leading_zeros() - 11; /* subnormal */

        mant <<= nz;

        mant &= f64::SIG_MASK;

        e = e.wrapping_sub(nz - 1);

    }

    e = e.wrapping_add(3072);

    let cvt1: u64 = mant | (0x3ffu64 << 52);

    let mut cvt5: u64 = cvt1;

    let et: u32 = e / 3;

    let it: u32 = e % 3;

    /* 2^(3k+it) <= x < 2^(3k+it+1), with 0 <= it <= 3 */

    cvt5 += u64::from(it) << f64::SIG_BITS;

    cvt5 |= sign << 63;

    let zz: f64 = f64::from_bits(cvt5);

    /* cbrt(x) = cbrt(zz)*2^(et-1365) where 1 <= zz < 8 */

    let mut isc: u64 = ESCALE[it as usize].to_bits(); // todo: index

    isc |= sign << 63;

    let cvt2: u64 = isc;

    let z: f64 = f64::from_bits(cvt1);

    /* cbrt(zz) = cbrt(z)*isc, where isc encodes 1, 2^(1/3) or 2^(2/3),

    and 1 <= z < 2 */

    let r: f64 = 1.0 / z;

    let rr: f64 = r * rsc[((it as usize) << 1) | sign as usize];

    let z2: f64 = z * z;

    let c0: f64 = C[0] + z * C[1];

    let c2: f64 = C[2] + z * C[3];

    let mut y: f64 = c0 + z2 * c2;

    let mut y2: f64 = y * y;

    /* y is an approximation of z^(1/3) */

    let mut h: f64 = y2 * (y * r) - 1.0;

    /* h determines the error between y and z^(1/3) */

    y -= (h * y) * (u0 - u1 * h);

    /* The correction y -= (h*y)*(u0 - u1*h) corresponds to a cubic variant

    of Newton's method, with the function f(y) = 1-z/y^3. */

    y *= f64::from_bits(cvt2);

    /* Now y is an approximation of zz^(1/3),

     * and rr an approximation of 1/zz. We now perform another iteration of

     * Newton-Raphson, this time with a linear approximation only. */

    y2 = y * y;

    let mut y2l: f64 = y.fma(y, -y2);

    /* y2 + y2l = y^2 exactly */

    let mut y3: f64 = y2 * y;

    let mut y3l: f64 = y.fma(y2, -y3) + y * y2l;

    /* y3 + y3l approximates y^3 with about 106 bits of accuracy */

    h = ((y3 - zz) + y3l) * rr;

    let mut dy: f64 = h * (y * u0);

    /* the approximation of zz^(1/3) is y - dy */

    let mut y1: f64 = y - dy;

    dy = (y - y1) - dy;

    /* the approximation of zz^(1/3) is now y1 + dy, where |dy| < 1/2 ulp(y)

     * (for rounding to nearest) */

    let mut ady: f64 = dy.abs();

    /* For directed roundings, ady0 is tiny when dy is tiny, or ady0 is near

     * from ulp(1);

     * for rounding to nearest, ady0 is tiny when dy is near from 1/2 ulp(1),

     * or from 3/2 ulp(1). */

    let mut ady0: f64 = (ady - off[round as usize]).abs();

    let mut ady1: f64 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();

    if ady0 < hf64!("0x1p-75") || ady1 < hf64!("0x1p-75") {

        cold_path();

        y2 = y1 * y1;

        y2l = y1.fma(y1, -y2);

        y3 = y2 * y1;

        y3l = y1.fma(y2, -y3) + y1 * y2l;

        h = ((y3 - zz) + y3l) * rr;

        dy = h * (y1 * u0);

        y = y1 - dy;

        dy = (y1 - y) - dy;

        y1 = y;

        ady = dy.abs();

        ady0 = (ady - off[round as usize]).abs();

        ady1 = (ady - (hf64!("0x1p-52") + off[round as usize])).abs();

        if ady0 < hf64!("0x1p-98") || ady1 < hf64!("0x1p-98") {

            cold_path();

            let azz: f64 = zz.abs();

            // ~ 0x1.79d15d0e8d59b80000000000000ffc3dp+0

            if azz == hf64!("0x1.9b78223aa307cp+1") {

                y1 = hf64!("0x1.79d15d0e8d59cp+0").copysign(zz);

            }

            // ~ 0x1.de87aa837820e80000000000001c0f08p+0

            if azz == hf64!("0x1.a202bfc89ddffp+2") {

                y1 = hf64!("0x1.de87aa837820fp+0").copysign(zz);

            }

            if round != Round::Nearest {

                let wlist = [

                    (hf64!("0x1.3a9ccd7f022dbp+0"), hf64!("0x1.1236160ba9b93p+0")), // ~ 0x1.1236160ba9b930000000000001e7e8fap+0

                    (hf64!("0x1.7845d2faac6fep+0"), hf64!("0x1.23115e657e49cp+0")), // ~ 0x1.23115e657e49c0000000000001d7a799p+0

                    (hf64!("0x1.d1ef81cbbbe71p+0"), hf64!("0x1.388fb44cdcf5ap+0")), // ~ 0x1.388fb44cdcf5a0000000000002202c55p+0

                    (hf64!("0x1.0a2014f62987cp+1"), hf64!("0x1.46bcbf47dc1e8p+0")), // ~ 0x1.46bcbf47dc1e8000000000000303aa2dp+0

                    (hf64!("0x1.fe18a044a5501p+1"), hf64!("0x1.95decfec9c904p+0")), // ~ 0x1.95decfec9c9040000000000000159e8ep+0

                    (hf64!("0x1.a6bb8c803147bp+2"), hf64!("0x1.e05335a6401dep+0")), // ~ 0x1.e05335a6401de00000000000027ca017p+0

                    (hf64!("0x1.ac8538a031cbdp+2"), hf64!("0x1.e281d87098de8p+0")), // ~ 0x1.e281d87098de80000000000000ee9314p+0

                ];

                for (a, b) in wlist {

                    if azz == a {

                        let tmp = if round as u64 + sign == 2 {

                            hf64!("0x1p-52")

                        } else {

                            0.0

                        };

                        y1 = (b + tmp).copysign(zz);

                    }

                }

            }

        }

    }

    let mut cvt3: u64 = y1.to_bits();

    cvt3 = cvt3.wrapping_add(((et.wrapping_sub(342).wrapping_sub(1023)) as u64) << 52);

    let m0: u64 = cvt3 << 30;

    let m1 = m0 >> 63;

    if (m0 ^ m1) <= (1u64 << 30) {

        cold_path();

        let mut cvt4: u64 = y1.to_bits();

        cvt4 = (cvt4 + (164 << 15)) & 0xffffffffffff0000u64;

        if ((f64::from_bits(cvt4) - y1) - dy).abs() < hf64!("0x1p-60") || (zz).abs() == 1.0 {

            cvt3 = (cvt3 + (1u64 << 15)) & 0xffffffffffff0000u64;

        }

    }

    FpResult::ok(f64::from_bits(cvt3))

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn spot_checks() {

        if !cfg!(x86_no_sse) {

            // Exposes a rounding mode problem. Ignored on i586 because of inaccurate FMA.

            assert_biteq!(

                cbrt(f64::from_bits(0xf7f792b28f600000)),

                f64::from_bits(0xd29ce68655d962f3)

            );

        }

    }

}