/*

 * // 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, dyad_fmla, f_fmla};

use crate::double_double::DoubleDouble;

use crate::exponents::exp2m1::{EXP_M1_2_TABLE1, EXP_M1_2_TABLE2};

use crate::rounding::CpuFloor;

use crate::rounding::CpuRoundTiesEven;

const LN10H: f64 = f64::from_bits(0x40026bb1bbb55516);

const LN10L: f64 = f64::from_bits(0xbcaf48ad494ea3e9);

struct Exp10m1 {

    exp: DoubleDouble,

    err: f64,

}

// Approximation for the fast path of exp(z) for z=zh+zl,

// with |z| < 0.000130273 < 2^-12.88 and |zl| < 2^-42.6

// (assuming x^y does not overflow or underflow)

#[inline]

fn q_1(dz: DoubleDouble) -> DoubleDouble {

    const Q_1: [u64; 5] = [

        0x3ff0000000000000,

        0x3ff0000000000000,

        0x3fe0000000000000,

        0x3fc5555555995d37,

        0x3fa55555558489dc,

    ];

    let z = dz.to_f64();

    let mut q = f_fmla(f64::from_bits(Q_1[4]), dz.hi, f64::from_bits(Q_1[3]));

    q = f_fmla(q, z, f64::from_bits(Q_1[2]));

    let mut p0 = DoubleDouble::from_exact_add(f64::from_bits(Q_1[1]), q * z);

    p0 = DoubleDouble::quick_mult(dz, p0);

    p0 = DoubleDouble::f64_add(f64::from_bits(Q_1[0]), p0);

    p0

}

#[inline]

fn exp1(x: DoubleDouble) -> DoubleDouble {

    const INVLOG2: f64 = f64::from_bits(0x40b71547652b82fe); /* |INVLOG2-2^12/log(2)| < 2^-43.4 */

    let k = (x.hi * INVLOG2).cpu_round_ties_even();

    const LOG2H: f64 = f64::from_bits(0x3f262e42fefa39ef);

    const LOG2L: f64 = f64::from_bits(0x3bbabc9e3b39803f);

    let mut zk = DoubleDouble::from_exact_mult(LOG2H, k);

    zk.lo = f_fmla(k, LOG2L, zk.lo);

    let mut yz = DoubleDouble::from_exact_add(x.hi - zk.hi, x.lo);

    yz.lo -= zk.lo;

    let ik: i64 = unsafe { k.to_int_unchecked::<i64>() }; /* Note: k is an integer, this is just a conversion. */

    let im: i64 = (ik >> 12).wrapping_add(0x3ff);

    let i2: i64 = (ik >> 6) & 0x3f;

    let i1: i64 = ik & 0x3f;

    let t1 = DoubleDouble::from_bit_pair(EXP_M1_2_TABLE1[i2 as usize]);

    let t2 = DoubleDouble::from_bit_pair(EXP_M1_2_TABLE2[i1 as usize]);

    let p0 = DoubleDouble::quick_mult(t2, t1);

    let mut q = q_1(yz);

    q = DoubleDouble::quick_mult(p0, q);

    /* Scale by 2^k. Warning: for x near 1024, we can have k=2^22, thus

    M = 2047, which encodes Inf */

    let mut du = (im as u64).wrapping_shl(52);

    if im == 0x7ff {

        q.hi *= 2.0;

        q.lo *= 2.0;

        du = (im.wrapping_sub(1) as u64).wrapping_shl(52);

    }

    q.hi *= f64::from_bits(du);

    q.lo *= f64::from_bits(du);

    q

}

#[inline]

fn exp10m1_fast(x: f64, tiny: bool) -> Exp10m1 {

    if tiny {

        return exp10m1_fast_tiny(x);

    }

    /* now -54 < x < -0.125 or 0.125 < x < 1024: we approximate exp(x*log(2))

    and subtract 1 */

    let v = DoubleDouble::quick_mult_f64(DoubleDouble::new(LN10L, LN10H), x);

    /*

    The a_mul() call is exact, and the error of the fma() is bounded by

     ulp(l).

     We have |t| <= ulp(h) <= ulp(LN2H*1024) = 2^-43,

     |t+x*LN2L| <= 2^-43 * 1024*LN2L < 2^-42.7,

     thus |l| <= |t| + |x*LN2L| + ulp(t+x*LN2L)

              <= 2^-42.7 + 2^-95 <= 2^-42.6, and ulp(l) <= 2^-95.

     Thus:

     |h + l - x*log(2)| <= |h + l - x*(LN2H+LN2L)| + |x|*|LN2H+LN2L-log(2)|

                        <= 2^-95 + 1024*2^-110.4 < 2^-94.9 */

    let mut p = exp1(v);

    let zf: DoubleDouble = if x >= 0. {

        // implies h >= 1 and the fast_two_sum pre-condition holds

        DoubleDouble::from_exact_add(p.hi, -1.0)

    } else {

        DoubleDouble::from_exact_add(-1.0, p.hi)

    };

    p.lo += zf.lo;

    p.hi = zf.hi;

    /* The error in the above fast_two_sum is bounded by 2^-105*|h|,

    with the new value of h, thus the total absolute error is bounded

    by eps1*|h_in|+2^-105*|h|.

    Relatively to h this yields eps1*|h_in/h| + 2^-105, where the maximum

    of |h_in/h| is obtained for x near -0.125, with |2^x/(2^x-1)| < 11.05.

    We get a relative error bound of 2^-74.138*11.05 + 2^-105 < 2^-70.67. */

    Exp10m1 {

        exp: p,

        err: f64::from_bits(0x3b77a00000000000) * p.hi, /* 2^-70.67 < 0x1.42p-71 */

    }

}

// Approximation for the accurate path of exp(z) for z=zh+zl,

// with |z| < 0.000130273 < 2^-12.88 and |zl| < 2^-42.6

// (assuming x^y does not overflow or underflow)

#[inline]

fn q_2(dz: DoubleDouble) -> DoubleDouble {

    /* Let q[0]..q[7] be the coefficients of degree 0..7 of Q_2.

    The ulp of q[7]*z^7 is at most 2^-155, thus we can compute q[7]*z^7

    in double precision only.

    The ulp of q[6]*z^6 is at most 2^-139, thus we can compute q[6]*z^6

    in double precision only.

    The ulp of q[5]*z^5 is at most 2^-124, thus we can compute q[5]*z^5

    in double precision only. */

    /* The following is a degree-7 polynomial generated by Sollya for exp(z)

    over [-0.000130273,0.000130273] with absolute error < 2^-113.218

    (see file exp_accurate.sollya). Since we use this code only for

    |x| > 0.125 in exp2m1(x), the corresponding relative error for exp2m1

    is about 2^-113.218/|exp2m1(-0.125)| which is about 2^-110. */

    const Q_2: [u64; 9] = [

        0x3ff0000000000000,

        0x3ff0000000000000,

        0x3fe0000000000000,

        0x3fc5555555555555,

        0x3c655555555c4d26,

        0x3fa5555555555555,

        0x3f81111111111111,

        0x3f56c16c3fbb4213,

        0x3f2a01a023ede0d7,

    ];

    let z = dz.to_f64();

    let mut q = dd_fmla(f64::from_bits(Q_2[8]), dz.hi, f64::from_bits(Q_2[7]));

    q = dd_fmla(q, z, f64::from_bits(Q_2[6]));

    q = dd_fmla(q, z, f64::from_bits(Q_2[5]));

    // multiply q by z and add Q_2[3] + Q_2[4]

    let mut p = DoubleDouble::from_exact_mult(q, z);

    let r0 = DoubleDouble::from_exact_add(f64::from_bits(Q_2[3]), p.hi);

    p.hi = r0.hi;

    p.lo += r0.lo + f64::from_bits(Q_2[4]);

    // multiply hi+lo by zh+zl and add Q_2[2]

    p = DoubleDouble::quick_mult(p, dz);

    let r1 = DoubleDouble::from_exact_add(f64::from_bits(Q_2[2]), p.hi);

    p.hi = r1.hi;

    p.lo += r1.lo;

    // multiply hi+lo by zh+zl and add Q_2[1]

    p = DoubleDouble::quick_mult(p, dz);

    let r1 = DoubleDouble::from_exact_add(f64::from_bits(Q_2[1]), p.hi);

    p.hi = r1.hi;

    p.lo += r1.lo;

    // multiply hi+lo by zh+zl and add Q_2[0]

    p = DoubleDouble::quick_mult(p, dz);

    let r1 = DoubleDouble::from_exact_add(f64::from_bits(Q_2[0]), p.hi);

    p.hi = r1.hi;

    p.lo += r1.lo;

    p

}

// returns a double-double approximation hi+lo of exp(x*log(10))

// assumes -0x1.041704c068efp+4 < x <= 0x1.34413509f79fep+8

#[inline]

fn exp_2(x: f64) -> DoubleDouble {

    let mut k = (x * f64::from_bits(0x40ca934f0979a371)).cpu_round_ties_even();

    if k == 4194304. {

        k = 4194303.; // ensures M < 2047 below

    }

    // since |x| <= 745 we have k <= 3051520

    const LOG2_10H: f64 = f64::from_bits(0x3f134413509f79ff);

    const LOG2_10M: f64 = f64::from_bits(0xbb89dc1da9800000);

    const LOG2_10L: f64 = f64::from_bits(0xb984fd20dba1f655);

    let yhh = dd_fmla(-k, LOG2_10H, x); // exact, |yh| <= 2^-13

    let mut ky0 = DoubleDouble::from_exact_add(yhh, -k * LOG2_10M);

    ky0.lo = dd_fmla(-k, LOG2_10L, ky0.lo);

    /* now x = k + yh, thus 2^x = 2^k * 2^yh, and we multiply yh by log(10)

    to use the accurate path of exp() */

    let ky = DoubleDouble::quick_mult(ky0, DoubleDouble::new(LN10L, LN10H));

    let ik = unsafe {

        k.to_int_unchecked::<i64>() // k is already integer, this is just a conversion

    };

    let im = (ik >> 12).wrapping_add(0x3ff);

    let i2 = (ik >> 6) & 0x3f;

    let i1 = ik & 0x3f;

    let t1 = DoubleDouble::from_bit_pair(EXP_M1_2_TABLE1[i2 as usize]);

    let t2 = DoubleDouble::from_bit_pair(EXP_M1_2_TABLE2[i1 as usize]);

    let p = DoubleDouble::quick_mult(t2, t1);

    let mut q = q_2(ky);

    q = DoubleDouble::quick_mult(p, q);

    let mut ud: u64 = (im as u64).wrapping_shl(52);

    if im == 0x7ff {

        q.hi *= 2.0;

        q.lo *= 2.0;

        ud = (im.wrapping_sub(1) as u64).wrapping_shl(52);

    }

    q.hi *= f64::from_bits(ud);

    q.lo *= f64::from_bits(ud);

    q

}

#[cold]

fn exp10m1_accurate_tiny(x: f64) -> f64 {

    let x2 = x * x;

    let x4 = x2 * x2;

    /* The following is a degree-17 polynomial generated by Sollya

    (file exp10m1_accurate.sollya),

    which approximates exp10m1(x) with relative error bounded by 2^-107.506

    for |x| <= 0.0625. */

    const Q: [u64; 25] = [

        0x40026bb1bbb55516,

        0xbcaf48ad494ea3e9,

        0x40053524c73cea69,

        0xbcae2bfab318d696,

        0x4000470591de2ca4,

        0x3ca823527cebf918,

        0x3ff2bd7609fd98c4,

        0x3c931ea51f6641df,

        0x3fe1429ffd1d4d76,

        0x3c7117195be7f232,

        0x3fca7ed70847c8b6,

        0xbc54260c5e23d0c8,

        0x3fb16e4dfc333a87,

        0xbc533fd284110905,

        0x3f94116b05fdaa5d,

        0xbc20721de44d79a8,

        0x3f74897c45d93d43,

        0x3f52ea52b2d182ac,

        0x3f2facfd5d905b22,

        0x3f084fe12df8bde3,

        0x3ee1398ad75d01bf,

        0x3eb6a9e96fbf6be7,

        0x3e8bd456a29007c2,

        0x3e6006cf8378cf9b,

        0x3e368862b132b6e2,

    ];

    let mut c13 = dd_fmla(f64::from_bits(Q[23]), x, f64::from_bits(Q[22])); // degree 15

    let c11 = dd_fmla(f64::from_bits(Q[21]), x, f64::from_bits(Q[20])); // degree 14

    c13 = dd_fmla(f64::from_bits(Q[24]), x2, c13); // degree 15

    // add Q[19]*x+c13*x2+c15*x4 to Q[18] (degree 11)

    let mut p = DoubleDouble::from_exact_add(

        f64::from_bits(Q[18]),

        f_fmla(f64::from_bits(Q[19]), x, f_fmla(c11, x2, c13 * x4)),

    );

    // multiply h+l by x and add Q[17] (degree 10)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[17]), p.hi);

    p.lo += p0.lo;

    p.hi = p0.hi;

    // multiply h+l by x and add Q[16] (degree 9)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[16]), p.hi);

    p.lo += p0.lo;

    p.hi = p0.hi;

    // multiply h+l by x and add Q[14]+Q[15] (degree 8)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[14]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[15]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[12]+Q[13] (degree 7)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[12]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[13]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[10]+Q[11] (degree 6)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[10]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[11]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[8]+Q[9] (degree 5)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[8]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[9]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[6]+Q[7] (degree 4)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[6]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[7]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[4]+Q[5] (degree 3)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[4]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[5]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[2]+Q[3] (degree 2)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[2]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[3]);

    p.hi = p0.hi;

    // multiply h+l by x and add Q[0]+Q[1] (degree 2)

    p = DoubleDouble::quick_f64_mult(x, p);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(Q[0]), p.hi);

    p.lo += p0.lo + f64::from_bits(Q[1]);

    p.hi = p0.hi;

    // multiply h+l by x

    p = DoubleDouble::quick_f64_mult(x, p);

    p.to_f64()

}

#[cold]

fn exp10m1_accurate(x: f64) -> f64 {

    let t = x.to_bits();

    let ux = t;

    let ax = ux & 0x7fffffffffffffffu64;

    if ax <= 0x3fc0000000000000u64 {

        // |x| <= 0.125

        return exp10m1_accurate_tiny(x);

    }

    let mut p = exp_2(x);

    let zf: DoubleDouble = DoubleDouble::from_full_exact_add(p.hi, -1.0);

    p.lo += zf.lo;

    p.hi = zf.hi;

    p.to_f64()

}

/* |x| <= 0.125, put in h + l a double-double approximation of exp2m1(x),

and return the maximal corresponding absolute error.

We also have |x| > 0x1.0527dbd87e24dp-51.

With xmin=RR("0x1.0527dbd87e24dp-51",16), the routine

exp2m1_fast_tiny_all(xmin,0.125,2^-65.73) in exp2m1.sage returns

1.63414352331297e-20 < 2^-65.73, and

exp2m1_fast_tiny_all(-0.125,-xmin,2^-65.62) returns

1.76283772822891e-20 < 2^-65.62, which proves the relative

error is bounded by 2^-65.62. */

#[inline]

fn exp10m1_fast_tiny(x: f64) -> Exp10m1 {

    /* The following is a degree-11 polynomial generated by Sollya

    (file exp10m1_fast.sollya),

    which approximates exp10m1(x) with relative error bounded by 2^-69.58

    for |x| <= 0.0625. */

    const P: [u64; 14] = [

        0x40026bb1bbb55516,

        0xbcaf48abcf79e094,

        0x40053524c73cea69,

        0xbcae1badf796d704,

        0x4000470591de2ca4,

        0x3ca7db8caacb2cea,

        0x3ff2bd7609fd98ba,

        0x3fe1429ffd1d4d98,

        0x3fca7ed7084998e1,

        0x3fb16e4dfc30944b,

        0x3f94116ae4b57526,

        0x3f74897c6a90f61c,

        0x3f52ec689c32b3a0,

        0x3f2faced20d698fe,

    ];

    let x2 = x * x;

    let x4 = x2 * x2;

    let mut c9 = dd_fmla(f64::from_bits(P[12]), x, f64::from_bits(P[11])); // degree 9

    let c7 = dd_fmla(f64::from_bits(P[10]), x, f64::from_bits(P[9])); // degree 7

    let mut c5 = dd_fmla(f64::from_bits(P[8]), x, f64::from_bits(P[7])); // degree 5

    c9 = dd_fmla(f64::from_bits(P[13]), x2, c9); // degree 9

    c5 = dd_fmla(c7, x2, c5); // degree 5

    c5 = dd_fmla(c9, x4, c5); // degree 5

    let mut p = DoubleDouble::from_exact_mult(c5, x);

    let p0 = DoubleDouble::from_exact_add(f64::from_bits(P[6]), p.hi);

    p.lo += p0.lo;

    p.hi = p0.hi;

    p = DoubleDouble::quick_f64_mult(x, p);

    let p1 = DoubleDouble::from_exact_add(f64::from_bits(P[4]), p.hi);

    p.lo += p1.lo + f64::from_bits(P[5]);

    p.hi = p1.hi;

    p = DoubleDouble::quick_f64_mult(x, p);

    let p2 = DoubleDouble::from_exact_add(f64::from_bits(P[2]), p.hi);

    p.lo += p2.lo + f64::from_bits(P[3]);

    p.hi = p2.hi;

    p = DoubleDouble::quick_f64_mult(x, p);

    let p2 = DoubleDouble::from_exact_add(f64::from_bits(P[0]), p.hi);

    p.lo += p2.lo + f64::from_bits(P[1]);

    p.hi = p2.hi;

    p = DoubleDouble::quick_f64_mult(x, p);

    Exp10m1 {

        exp: p,

        err: f64::from_bits(0x3bb0a00000000000) * p.hi, // 2^-65.62 < 0x1.4ep-66

    }

}

/// Computes 10^x - 1

///

/// Max found ULP 0.5

pub fn f_exp10m1(d: f64) -> f64 {

    let mut x = d;

    let t = x.to_bits();

    let ux = t;

    let ax = ux & 0x7fffffffffffffffu64;

    if ux >= 0xc03041704c068ef0u64 {

        // x = -NaN or x <= -0x1.041704c068efp+4

        if (ux >> 52) == 0xfff {

            // -NaN or -Inf

            return if ux > 0xfff0000000000000u64 {

                x + x

            } else {

                -1.0

            };

        }

        // for x <= -0x1.041704c068efp+4, exp10m1(x) rounds to -1 to nearest

        return -1.0 + f64::from_bits(0x3c90000000000000);

    } else if ax > 0x40734413509f79feu64 {

        // x = +NaN or x >= 1024

        if (ux >> 52) == 0x7ff {

            // +NaN

            return x + x;

        }

        return f64::from_bits(0x7fefffffffffffff) * x;

    } else if ax <= 0x3c90000000000000u64

    // |x| <= 0x1.0527dbd87e24dp-51

    /* then the second term of the Taylor expansion of 2^x-1 at x=0 is

    smaller in absolute value than 1/2 ulp(first term):

    log(2)*x + log(2)^2*x^2/2 + ... */

    {

        /* we use special code when log(2)*|x| is very small, in which case

        the double-double approximation h+l has its lower part l

        "truncated" */

        return if ax <= 0x3970000000000000u64

        // |x| <= 2^-104

        {

            // special case for 0

            if x == 0. {

                return x;

            }

            if x.abs() == f64::from_bits(0x000086c73059343c) {

                return dd_fmla(

                    -f64::copysign(f64::from_bits(0x1e60010000000000), x),

                    f64::from_bits(0x1e50000000000000),

                    f64::copysign(f64::from_bits(0x000136568740cb56), x),

                );

            }

            if x.abs() == f64::from_bits(0x00013a7b70d0248c) {

                return dd_fmla(

                    f64::copysign(f64::from_bits(0x1e5ffe0000000000), x),

                    f64::from_bits(0x1e50000000000000),

                    f64::copysign(f64::from_bits(0x0002d41f3b972fc7), x),

                );

            }

            // scale x by 2^106

            x *= f64::from_bits(0x4690000000000000);

            let mut z = DoubleDouble::from_exact_mult(LN10H, x);

            z.lo = dd_fmla(LN10L, x, z.lo);

            let mut h2 = z.to_f64(); // round to 53-bit precision

            // scale back, hoping to avoid double rounding

            h2 *= f64::from_bits(0x3950000000000000);

            // now subtract back h2 * 2^106 from h to get the correction term

            let mut h = dd_fmla(-h2, f64::from_bits(0x4690000000000000), z.hi);

            // add l

            h += z.lo;

            /* add h2 + h * 2^-106. Warning: when h=0, 2^-106*h2 might be exact,

            thus no underflow will be raised. We have underflow for

            0 < x <= 0x1.71547652b82fep-1022 for RNDZ, and for

            0 < x <= 0x1.71547652b82fdp-1022 for RNDN/RNDU. */

            dyad_fmla(h, f64::from_bits(0x3950000000000000), h2)

        } else {

            const C2: f64 = f64::from_bits(0x40053524c73cea69); // log(2)^2/2

            let mut z = DoubleDouble::quick_mult_f64(DoubleDouble::new(LN10L, LN10H), x);

            /* h+l approximates the first term x*log(2) */

            /* we add C2*x^2 last, so that in case there is a cancellation in

            LN10L*x+l, it will contribute more bits */

            z.lo = dd_fmla(C2 * x, x, z.lo);

            z.to_f64()

        };

    }

    /* now -0x1.041704c068efp+4 < x < -2^-54

    or 2^-54 < x <= 0x1.34413509f79fep+8 */

    /* 10^x-1 is exact for x integer, 1 <= x <= 15 */

    if ux << 15 == 0 {

        let i = unsafe { x.cpu_floor().to_int_unchecked::<i32>() };

        if x == i as f64 && 1 <= i && i <= 15 {

            static EXP10_1_15: [u64; 16] = [

                0x0000000000000000,

                0x4022000000000000,

                0x4058c00000000000,

                0x408f380000000000,

                0x40c3878000000000,

                0x40f869f000000000,

                0x412e847e00000000,

                0x416312cfe0000000,

                0x4197d783fc000000,

                0x41cdcd64ff800000,

                0x4202a05f1ff80000,

                0x42374876e7ff0000,

                0x426d1a94a1ffe000,

                0x42a2309ce53ffe00,

                0x42d6bcc41e8fffc0,

                0x430c6bf52633fff8,

            ];

            return f64::from_bits(EXP10_1_15[i as usize]);

        }

    }

    let result = exp10m1_fast(x, ax <= 0x3fb0000000000000u64);

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

    let right = result.exp.hi + (result.exp.lo + result.err);

    if left != right {

        return exp10m1_accurate(x);

    }

    left

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_exp10m1() {

        assert_eq!(f_exp10m1(0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002364140972981833),

                   0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005443635762124408);

        assert_eq!(99., f_exp10m1(2.0));

        assert_eq!(315.22776601683796, f_exp10m1(2.5));

        assert_eq!(-0.7056827241416722, f_exp10m1(-0.5311842449009418));

    }

}