/*

 * // 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.

 */

use crate::common::{dd_fmla, f_fmla};

use crate::double_double::DoubleDouble;

use crate::exponents::{EXP_REDUCE_T0, EXP_REDUCE_T1};

use crate::hyperbolic::acosh::lpoly_xd_generic;

#[cold]

pub(crate) fn hyperbolic_exp_accurate(x: f64, t: f64, zt: DoubleDouble) -> DoubleDouble {

    static CH: [(u64, u64); 3] = [

        (0x3a16c16bd194535d, 0x3ff0000000000000),

        (0xba28259d904fd34f, 0x3fe0000000000000),

        (0x3c653e93e9f26e62, 0x3fc5555555555555),

    ];

    const L2H: f64 = f64::from_bits(0x3f262e42ff000000);

    const L2L: f64 = f64::from_bits(0x3d0718432a1b0e26);

    const L2LL: f64 = f64::from_bits(0x3999ff0342542fc3);

    let dx = x - L2H * t;

    let mut dxl = L2L * t;

    let dxll = f_fmla(L2LL, t, dd_fmla(L2L, t, -dxl));

    let dxh = dx + dxl;

    dxl = ((dx - dxh) + dxl) + dxll;

    let fl0 = f_fmla(

        dxh,

        f64::from_bits(0x3f56c16c169400a7),

        f64::from_bits(0x3f811111113e93e9),

    );

    let fl = dxh * f_fmla(dxh, fl0, f64::from_bits(0x3fa5555555555555));

    let mut f = lpoly_xd_generic(DoubleDouble::new(dxl, dxh), CH, fl);

    f = DoubleDouble::quick_mult(DoubleDouble::new(dxl, dxh), f);

    f = DoubleDouble::quick_mult(zt, f);

    let zh = zt.hi + f.hi;

    let zl = (zt.hi - zh) + f.hi;

    let uh = zh + zt.lo;

    let ul = ((zh - uh) + zt.lo) + zl;

    let vh = uh + f.lo;

    let vl = ((uh - vh) + f.lo) + ul;

    DoubleDouble::new(vl, vh)

}

#[cold]

fn as_sinh_zero(x: f64) -> f64 {

    static CH: [(u64, u64); 5] = [

        (0x3c6555555555552f, 0x3fc5555555555555),

        (0x3c011111115cf00d, 0x3f81111111111111),

        (0x3b6a0011c925b85c, 0x3f2a01a01a01a01a),

        (0xbb6b4e2835532bcd, 0x3ec71de3a556c734),

        (0xbaedefcf17a6ab79, 0x3e5ae64567f54482),

    ];

    let d2x = DoubleDouble::from_exact_mult(x, x);

    let yw0 = f_fmla(

        d2x.hi,

        f64::from_bits(0x3ce95785063cd974),

        f64::from_bits(0x3d6ae7f36beea815),

    );

    let y2 = d2x.hi * f_fmla(d2x.hi, yw0, f64::from_bits(0x3de6124613aef206));

    let mut y1 = lpoly_xd_generic(d2x, CH, y2);

    y1 = DoubleDouble::quick_mult_f64(y1, x);

    y1 = DoubleDouble::quick_mult(y1, d2x); // y2 = y1.l

    let y0 = DoubleDouble::from_exact_add(x, y1.hi); // y0 = y0.hi

    let mut p = DoubleDouble::from_exact_add(y0.lo, y1.lo);

    let mut t = p.hi.to_bits();

    if (t & 0x000fffffffffffff) == 0 {

        let w = p.lo.to_bits();

        if ((w ^ t) >> 63) != 0 {

            t = t.wrapping_sub(1);

        } else {

            t = t.wrapping_add(1);

        }

        p.hi = f64::from_bits(t);

    }

    y0.hi + p.hi

}

/// Hyperbolic sine function

///

/// Max ULP 0.5

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

    /*

     The function sinh(x) is approximated by a minimax polynomial for

     |x|<0.25. For other arguments the identity

     sinh(x)=(exp(|x|)-exp(-|x|))/2*copysign(1,x) is used. For |x|<5

     both exponents are calculated with slightly higher precision than

     double. For 5<|x|<36.736801 the exp(-|x|) is small and is

     calculated with double precision but exp(|x|) is calculated with

     higher than double precision. For 36.736801<|x|<710.47586

     exp(-|x|) becomes too small and only exp(|x|) is calculated.

    */

    const S: f64 = f64::from_bits(0x40b71547652b82fe);

    let ax = x.abs();

    let v0 = dd_fmla(ax, S, f64::from_bits(0x4198000002000000));

    let jt = v0.to_bits();

    let v = v0.to_bits() & 0xfffffffffc000000;

    let t = f64::from_bits(v) - f64::from_bits(0x4198000000000000);

    let ix = ax.to_bits();

    let aix = ix;

    if aix < 0x3fd0000000000000u64 {

        // |x| < 0x1p-2

        if aix < 0x3e57137449123ef7u64 {

            // |x| < 0x1.7137449123ef7p-26

            /* We have underflow exactly when 0 < |x| < 2^-1022:

            for RNDU, sinh(2^-1022-2^-1074) would round to 2^-1022-2^-1075

            with unbounded exponent range */

            return dd_fmla(x, f64::from_bits(0x3c80000000000000), x);

        }

        const C: [u64; 5] = [

            0x3fc5555555555555,

            0x3f81111111111087,

            0x3f2a01a01a12e1c3,

            0x3ec71de2e415aa36,

            0x3e5aed2bff4269e6,

        ];

        let x2 = x * x;

        let x3 = x2 * x;

        let x4 = x2 * x2;

        let pw0 = f_fmla(x2, f64::from_bits(C[3]), f64::from_bits(C[2]));

        let pw1 = f_fmla(x2, f64::from_bits(C[1]), f64::from_bits(C[0]));

        let pw2 = f_fmla(x4, f64::from_bits(C[4]), pw0);

        let p = x3 * f_fmla(x4, pw2, pw1);

        let e = x3 * f64::from_bits(0x3ca9000000000000);

        let lb = x + (p - e);

        let ub = x + (p + e);

        if lb == ub {

            return lb;

        }

        return as_sinh_zero(x);

    }

    if aix > 0x408633ce8fb9f87du64 {

        // |x| >~ 710.47586

        if aix >= 0x7ff0000000000000u64 {

            return x + x;

        } // nan Inf

        return f64::copysign(f64::from_bits(0x7fe0000000000000), x) * 2.0;

    }

    let il: i64 = ((jt.wrapping_shl(14)) >> 40) as i64;

    let jl = -il;

    let i1 = il & 0x3f;

    let i0 = (il >> 6) & 0x3f;

    let ie = il >> 12;

    let j1 = jl & 0x3f;

    let j0 = (jl >> 6) & 0x3f;

    let je = jl >> 12;

    let mut sp = (1022i64.wrapping_add(ie) as u64).wrapping_shl(52);

    let sm = (1022i64.wrapping_add(je) as u64).wrapping_shl(52);

    let sn0 = EXP_REDUCE_T0[i0 as usize];

    let sn1 = EXP_REDUCE_T1[i1 as usize];

    let t0h = f64::from_bits(sn0.1);

    let t0l = f64::from_bits(sn0.0);

    let t1h = f64::from_bits(sn1.1);

    let t1l = f64::from_bits(sn1.0);

    let mut th = t0h * t1h;

    let mut tl = f_fmla(t0h, t1l, t1h * t0l) + dd_fmla(t0h, t1h, -th);

    const L2H: f64 = f64::from_bits(0x3f262e42ff000000);

    const L2L: f64 = f64::from_bits(0x3d0718432a1b0e26);

    let dx = f_fmla(L2L, t, f_fmla(-L2H, t, ax));

    let dx2 = dx * dx;

    let mx = -dx;

    const CH: [u64; 4] = [

        0x3ff0000000000000,

        0x3fe0000000000000,

        0x3fc5555555aaaaae,

        0x3fa55555551c98c0,

    ];

    let (mut rl, mut rh);

    let pp0 = f_fmla(dx, f64::from_bits(CH[3]), f64::from_bits(CH[2]));

    let pp1 = f_fmla(dx, f64::from_bits(CH[1]), f64::from_bits(CH[0]));

    let pp = dx * f_fmla(dx2, pp0, pp1);

    if aix > 0x4014000000000000u64 {

        // |x| > 5

        if aix > 0x40425e4f7b2737fau64 {

            // |x| >~ 36.736801

            sp = (1021i64.wrapping_add(ie) as u64).wrapping_shl(52);

            let mut rh = th;

            let mut rl = tl + th * pp;

            rh *= f64::copysign(1., x);

            rl *= f64::copysign(1., x);

            let e = 0.11e-18 * th;

            let lb = rh + (rl - e);

            let ub = rh + (rl + e);

            if lb == ub {

                return (lb * f64::from_bits(sp)) * 2.;

            }

            let mut tt = hyperbolic_exp_accurate(ax, t, DoubleDouble::new(tl, th));

            tt = DoubleDouble::from_exact_add(tt.hi, tt.lo);

            th = tt.hi;

            tl = tt.lo;

            th *= f64::copysign(1., x);

            tl *= f64::copysign(1., x);

            th += tl;

            th *= 2.;

            th *= f64::from_bits(sp);

            return th;

        }

        let q0h = f64::from_bits(EXP_REDUCE_T0[j0 as usize].1);

        let q1h = f64::from_bits(EXP_REDUCE_T1[j1 as usize].1);

        let mut qh = q0h * q1h;

        th *= f64::from_bits(sp);

        tl *= f64::from_bits(sp);

        qh *= f64::from_bits(sm);

        let pm0 = f_fmla(mx, f64::from_bits(CH[3]), f64::from_bits(CH[2]));

        let pm1 = f_fmla(mx, f64::from_bits(CH[1]), f64::from_bits(CH[0]));

        let pm = mx * f_fmla(dx2, pm0, pm1);

        let em = f_fmla(qh, pm, qh);

        rh = th;

        rl = f_fmla(th, pp, tl - em);

        rh *= f64::copysign(1., x);

        rl *= f64::copysign(1., x);

        let e = 0.09e-18 * rh;

        let lb = rh + (rl - e);

        let ub = rh + (rl + e);

        if lb == ub {

            return lb;

        }

        let tt = hyperbolic_exp_accurate(ax, t, DoubleDouble::new(tl, th));

        th = tt.hi;

        tl = tt.lo;

        if aix > 0x403f666666666666u64 {

            rh = th - qh;

            rl = ((th - rh) - qh) + tl;

        } else {

            qh = q0h * q1h;

            let q0l = f64::from_bits(EXP_REDUCE_T0[j0 as usize].0);

            let q1l = f64::from_bits(EXP_REDUCE_T1[j1 as usize].0);

            let mut ql = f_fmla(q0h, q1l, q1h * q0l) + dd_fmla(q0h, q1h, -qh);

            qh *= f64::from_bits(sm);

            ql *= f64::from_bits(sm);

            let qq = hyperbolic_exp_accurate(-ax, -t, DoubleDouble::new(ql, qh));

            rh = th - qq.hi;

            rl = (((th - rh) - qq.hi) - qq.lo) + tl;

        }

    } else {

        let tq0 = EXP_REDUCE_T0[j0 as usize];

        let tq1 = EXP_REDUCE_T1[j1 as usize];

        let q0h = f64::from_bits(tq0.1);

        let q0l = f64::from_bits(tq0.0);

        let q1h = f64::from_bits(tq1.1);

        let q1l = f64::from_bits(tq1.0);

        let mut qh = q0h * q1h;

        let mut ql = f_fmla(q0h, q1l, q1h * q0l) + dd_fmla(q0h, q1h, -qh);

        th *= f64::from_bits(sp);

        tl *= f64::from_bits(sp);

        qh *= f64::from_bits(sm);

        ql *= f64::from_bits(sm);

        let pm0 = f_fmla(mx, f64::from_bits(CH[3]), f64::from_bits(CH[2]));

        let pm1 = f_fmla(mx, f64::from_bits(CH[1]), f64::from_bits(CH[0]));

        let pm = mx * f_fmla(dx2, pm0, pm1);

        let fph = th;

        let fpl = f_fmla(th, pp, tl);

        let fmh = qh;

        let fml = f_fmla(qh, pm, ql);

        rh = fph - fmh;

        rl = ((fph - rh) - fmh) - fml + fpl;

        rh *= f64::copysign(1., x);

        rl *= f64::copysign(1., x);

        let e = 0.28e-18 * rh;

        let lb = rh + (rl - e);

        let ub = rh + (rl + e);

        if lb == ub {

            return lb;

        }

        let tt = hyperbolic_exp_accurate(ax, t, DoubleDouble::new(tl, th));

        let qq = hyperbolic_exp_accurate(-ax, -t, DoubleDouble::new(ql, qh));

        rh = tt.hi - qq.hi;

        rl = ((tt.hi - rh) - qq.hi) - qq.lo + tt.lo;

    }

    let r = DoubleDouble::from_exact_add(rh, rl);

    rh = r.hi;

    rl = r.lo;

    rh *= f64::copysign(1., x);

    rl *= f64::copysign(1., x);

    rh += rl;

    rh

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_f_sinh() {

        assert_eq!(f_sinh(1.), 1.1752011936438014);

    }

}