/*

 * // Copyright (c) Radzivon Bartoshyk 8/2025. 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::bits::{EXP_MASK, get_exponent_f64};

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::logs::log1p::{LOG_R1_DD, R1};

use crate::logs::log1p_dd;

use crate::polyeval::{f_estrin_polyeval8, f_polyeval4, f_polyeval5};

#[cold]

fn tiny_hard(x: f64) -> f64 {

    // d = [-2^-10; 2^-10];

    // f_log1pf = (log(1+x) - x)/x^2;

    // Q = fpminimax(f_log1pf, 7, [|0, 107...|], d);

    // See ./notes/log1pmx_at_zero_hard.sollya

    let x2 = DoubleDouble::from_exact_mult(x, x);

    const C: [(u64, u64); 7] = [

        (0x3c755555555129de, 0x3fd5555555555555),

        (0xbbd333352fe28400, 0xbfd0000000000000),

        (0xbc698cb3ef1ea2dd, 0x3fc999999999999a),

        (0x3c4269700b3f95d0, 0xbfc55555555546ef),

        (0x3c61290e9261823e, 0x3fc2492492491565),

        (0x3c6fb0a243c2a59c, 0xbfc000018af8cb7e),

        (0x3c3b271ceb5c60a0, 0x3fbc71ca10b30518),

    ];

    let mut r = DoubleDouble::mul_f64_add(

        DoubleDouble::from_bit_pair(C[6]),

        x,

        DoubleDouble::from_bit_pair(C[5]),

    );

    r = DoubleDouble::mul_f64_add(r, x, DoubleDouble::from_bit_pair(C[4]));

    r = DoubleDouble::mul_f64_add(r, x, DoubleDouble::from_bit_pair(C[3]));

    r = DoubleDouble::mul_f64_add(r, x, DoubleDouble::from_bit_pair(C[2]));

    r = DoubleDouble::mul_f64_add(r, x, DoubleDouble::from_bit_pair(C[1]));

    r = DoubleDouble::mul_f64_add(r, x, DoubleDouble::from_bit_pair(C[0]));

    r = DoubleDouble::mul_f64_add_f64(r, x, f64::from_bits(0xbfe0000000000000));

    r = DoubleDouble::quick_mult(r, x2);

    r.to_f64()

}

fn log1pmx_big(x: f64) -> f64 {

    let mut x_u = x.to_bits();

    let mut x_dd = DoubleDouble::default();

    let x_exp: u16 = ((x_u >> 52) & 0x7ff) as u16;

    const EXP_BIAS: u16 = (1u16 << (11 - 1u16)) - 1u16;

    if x_exp >= EXP_BIAS {

        // |x| >= 1

        if x_u >= 0x4650_0000_0000_0000u64 {

            x_dd.hi = x;

        } else {

            x_dd = DoubleDouble::from_exact_add(x, 1.0);

        }

    } else {

        // |x| < 1

        x_dd = DoubleDouble::from_exact_add(1.0, x);

    }

    // At this point, x_dd is the exact sum of 1 + x:

    //   x_dd.hi + x_dd.lo = x + 1.0 exactly.

    //   |x_dd.hi| >= 2^-54

    //   |x_dd.lo| < ulp(x_dd.hi)

    let xhi_bits = x_dd.hi.to_bits();

    let xhi_frac = xhi_bits & ((1u64 << 52) - 1);

    x_u = xhi_bits;

    // Range reduction:

    // Find k such that |x_hi - k * 2^-7| <= 2^-8.

    let idx: i32 = ((xhi_frac.wrapping_add(1u64 << (52 - 8))) >> (52 - 7)) as i32;

    let x_e = (get_exponent_f64(f64::from_bits(xhi_bits)) as i32).wrapping_add(idx >> 7);

    let e_x = x_e as f64;

    const LOG_2: DoubleDouble = DoubleDouble::new(

        f64::from_bits(0x3d2ef35793c76730),

        f64::from_bits(0x3fe62e42fefa3800),

    );

    // hi is exact

    // ulp(hi) = ulp(LOG_2_HI) = ulp(LOG_R1_DD[idx].hi) = 2^-43

    let r_dd = LOG_R1_DD[idx as usize];

    let hi = f_fmla(e_x, LOG_2.hi, f64::from_bits(r_dd.1));

    // lo errors < |e_x| * ulp(LOG_2_LO) + ulp(LOG_R1[idx].lo)

    //           <= 2^11 * 2^(-43-53) = 2^-85

    let lo = f_fmla(e_x, LOG_2.lo, f64::from_bits(r_dd.0));

    // Scale x_dd by 2^(-xh_bits.get_exponent()).

    let s_u: i64 = (x_u & EXP_MASK) as i64 - (EXP_BIAS as i64).wrapping_shl(52);

    // Normalize arguments:

    //   1 <= m_dd.hi < 2

    //   |m_dd.lo| < 2^-52.

    // This is exact.

    let m_hi = 1f64.to_bits() | xhi_frac;

    let m_lo = if x_dd.lo.abs() > x_dd.hi * f64::from_bits(0x3800000000000000) {

        (x_dd.lo.to_bits() as i64).wrapping_sub(s_u)

    } else {

        0

    };

    let m_dd = DoubleDouble::new(f64::from_bits(m_lo as u64), f64::from_bits(m_hi));

    // Perform range reduction:

    //   r * m - 1 = r * (m_dd.hi + m_dd.lo) - 1

    //             = (r * m_dd.hi - 1) + r * m_dd.lo

    //             = v_hi + (v_lo.hi + v_lo.lo)

    // where:

    //   v_hi = r * m_dd.hi - 1          (exact)

    //   v_lo.hi + v_lo.lo = r * m_dd.lo (exact)

    // Bounds on the values:

    //   -0x1.69000000000edp-8 < r * m - 1 < 0x1.7f00000000081p-8

    //   |v_lo.hi| <= |r| * |m_dd.lo| < 2^-52

    //   |v_lo.lo| < ulp(v_lo.hi) <= 2^(-52 - 53) = 2^(-105)

    let r = R1[idx as usize];

    let v_hi;

    let v_lo = DoubleDouble::from_exact_mult(m_dd.lo, f64::from_bits(r));

    #[cfg(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    ))]

    {

        v_hi = f_fmla(f64::from_bits(r), m_dd.hi, -1.0); // Exact.

    }

    #[cfg(not(any(

        all(

            any(target_arch = "x86", target_arch = "x86_64"),

            target_feature = "fma"

        ),

        target_arch = "aarch64"

    )))]

    {

        use crate::logs::log1p::RCM1;

        let c = f64::from_bits(

            (idx as u64)

                .wrapping_shl(52 - 7)

                .wrapping_add(0x3FF0_0000_0000_0000u64),

        );

        v_hi = f_fmla(

            f64::from_bits(r),

            m_dd.hi - c,

            f64::from_bits(RCM1[idx as usize]),

        ); // Exact

    }

    // Range reduction output:

    //   -0x1.69000000000edp-8 < v_hi + v_lo < 0x1.7f00000000081p-8

    //   |v_dd.lo| < ulp(v_dd.hi) <= 2^(-7 - 53) = 2^-60

    let mut v_dd = DoubleDouble::from_exact_add(v_hi, v_lo.hi);

    v_dd.lo += v_lo.lo;

    // Exact sum:

    //   r1.hi + r1.lo = e_x * log(2)_hi - log(r)_hi + u

    let mut r1 = DoubleDouble::from_exact_add(hi, v_dd.hi);

    // Degree-7 minimax polynomial log(1 + v) ~ v - v^2 / 2 + ...

    // generated by Sollya with:

    // > P = fpminimax(log(1 + x)/x, 6, [|1, 1, D...|],

    //                 [-0x1.69000000000edp-8, 0x1.7f00000000081p-8]);

    const P_COEFFS: [u64; 6] = [

        0xbfe0000000000000,

        0x3fd5555555555166,

        0xbfcfffffffdb7746,

        0x3fc99999a8718a60,

        0xbfc555874ce8ce22,

        0x3fc24335555ddbe5,

    ];

    //   C * ulp(v_sq) + err_hi

    let v_sq = v_dd.hi * v_dd.hi;

    let p0 = f_fmla(

        v_dd.hi,

        f64::from_bits(P_COEFFS[1]),

        f64::from_bits(P_COEFFS[0]),

    );

    let p1 = f_fmla(

        v_dd.hi,

        f64::from_bits(P_COEFFS[3]),

        f64::from_bits(P_COEFFS[2]),

    );

    let p2 = f_fmla(

        v_dd.hi,

        f64::from_bits(P_COEFFS[5]),

        f64::from_bits(P_COEFFS[4]),

    );

    let p = f_polyeval4(v_sq, (v_dd.lo + r1.lo) + lo, p0, p1, p2);

    const ERR_HI: [f64; 2] = [f64::from_bits(0x3aa0000000000000), 0.0];

    let err_hi = ERR_HI[if hi == 0.0 { 1 } else { 0 }];

    let err = f_fmla(v_sq, f64::from_bits(0x3ce0000000000000), err_hi);

    r1.lo = p;

    r1 = DoubleDouble::from_exact_add(r1.hi, r1.lo);

    r1 = DoubleDouble::full_add_f64(r1, -x);

    let left = r1.hi + (r1.lo - err);

    let right = r1.hi + (r1.lo + err);

    // Ziv's test to see if fast pass is accurate enough.

    if left == right {

        return left;

    }

    log1pmx_accurate_dd(x)

}

#[cold]

fn log1pmx_accurate_dd(x: f64) -> f64 {

    let r = log1p_dd(x);

    DoubleDouble::full_add_f64(r, -x).to_f64()

}

/// Computes log(1+x) - x

///

/// ulp 0.5

pub fn f_log1pmx(x: f64) -> f64 {

    let ax = x.to_bits() & 0x7fff_ffff_ffff_ffffu64;

    let x_e = (x.to_bits() >> 52) & 0x7ff;

    if !x.is_normal() {

        if x.is_nan() {

            return x + x;

        }

        if x.is_infinite() {

            return f64::NAN;

        }

        if x == 0. {

            return x;

        }

    }

    if ax > 0x3f90000000000000u64 {

        // |x| > 2^-6

        if x <= -1. {

            if x == -1. {

                return f64::NEG_INFINITY;

            }

            return f64::NAN;

        }

        return log1pmx_big(x);

    }

    const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;

    // log(1+x) is expected to be used near zero

    if x_e < E_BIAS - 10 {

        if x_e < E_BIAS - 100 {

            // |x| < 2^-100

            // taylor series log(1+x) - x ~ -x^2/2 + x^3/3

            let x2 = x * x;

            let dx2 = f_fmla(x, x, -x2);

            let rl = dx2 * -0.5;

            return f_fmla(x2, -0.5, rl);

        }

        // Polynomial generated by Sollya in form log(1+x) - x = x^2 * R(x):

        // d = [-2^-10; 2^-10];

        // f_log1pf = (log(1+x) - x)/x^2;

        // Q = fpminimax(f_log1pf, 7, [|0, 107, 107, D...|], d);

        // See ./notes/log1pmx_at_zero.sollya

        let p = f_polyeval5(

            x,

            f64::from_bits(0x3fc999999999999a),

            f64::from_bits(0xbfc55555555546ef),

            f64::from_bits(0x3fc24924923d3abf),

            f64::from_bits(0xbfc000018af7f637),

            f64::from_bits(0x3fbc72984db24b6a),

        );

        let x2 = DoubleDouble::from_exact_mult(x, x);

        let mut r = DoubleDouble::f64_mul_f64_add(

            x,

            p,

            DoubleDouble::from_bit_pair((0xbbd3330899095800, 0xbfd0000000000000)),

        );

        r = DoubleDouble::mul_f64_add(

            r,

            x,

            DoubleDouble::from_bit_pair((0x3c75555538509407, 0x3fd5555555555555)),

        );

        r = DoubleDouble::mul_f64_add_f64(r, x, f64::from_bits(0xbfe0000000000000));

        r = DoubleDouble::quick_mult(r, x2);

        const ERR: f64 = f64::from_bits(0x3af0000000000000); // 2^-80

        let ub = r.hi + (r.lo + ERR);

        let lb = r.hi + (r.lo - ERR);

        if lb == ub {

            return r.to_f64();

        }

        return tiny_hard(x);

    }

    // Polynomial generated by Sollya in form log(1+x) - x = x^2 * R(x):

    // d = [-2^-6; 2^-6];

    // f_log1pf = (log(1+x) - x)/x^2;

    // Q = fpminimax(f_log1pf, 10, [|0, 107, 107, D...|], d);

    // See ./notes/log1pmx.sollya

    let p = f_estrin_polyeval8(

        x,

        f64::from_bits(0x3fc9999999999997),

        f64::from_bits(0xbfc5555555555552),

        f64::from_bits(0x3fc249249249fb64),

        f64::from_bits(0xbfc000000000f450),

        f64::from_bits(0x3fbc71c6e2591149),

        f64::from_bits(0xbfb999995cf14d86),

        f64::from_bits(0x3fb7494eb6c2c544),

        f64::from_bits(0xbfb558bf05690e85),

    );

    let x2 = DoubleDouble::from_exact_mult(x, x);

    let mut r = DoubleDouble::f64_mul_f64_add(

        x,

        p,

        DoubleDouble::from_bit_pair((0xbb9d89dc15a38000, 0xbfd0000000000000)),

    );

    r = DoubleDouble::mul_f64_add(

        r,

        x,

        DoubleDouble::from_bit_pair((0x3c7555a15a94e505, 0x3fd5555555555555)),

    );

    r = DoubleDouble::mul_f64_add_f64(r, x, f64::from_bits(0xbfe0000000000000));

    r = DoubleDouble::quick_mult(r, x2);

    r.to_f64()

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_log1pmx() {

        assert_eq!(

            f_log1pmx(0.00000000000000005076835735015165),

            -0.0000000000000000000000000000000012887130540163486

        );

        assert_eq!(f_log1pmx(5.), -3.208240530771945);

        assert_eq!(f_log1pmx(-0.99), -3.6151701859880907);

        assert_eq!(f_log1pmx(-1.), f64::NEG_INFINITY);

        assert_eq!(

            f_log1pmx(1.0000000000008708e-13),

            -0.0000000000000000000000000050000000000083744

        );

        assert_eq!(

            f_log1pmx(1.0000000000008708e-26),

            -0.00000000000000000000000000000000000000000000000000005000000000008707

        );

        assert_eq!(f_log1pmx(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012890176556069385),

                   -0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000830783258233204);

    }

}