/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

/* double log1p(double x)

 * Return the natural logarithm of 1+x.

 *

 * Method :

 *   1. Argument Reduction: find k and f such that

 *                      1+x = 2^k * (1+f),

 *         where  sqrt(2)/2 < 1+f < sqrt(2) .

 *

 *      Note. If k=0, then f=x is exact. However, if k!=0, then f

 *      may not be representable exactly. In that case, a correction

 *      term is need. Let u=1+x rounded. Let c = (1+x)-u, then

 *      log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),

 *      and add back the correction term c/u.

 *      (Note: when x > 2**53, one can simply return log(x))

 *

 *   2. Approximation of log(1+f): See log.c

 *

 *   3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c

 *

 * Special cases:

 *      log1p(x) is NaN with signal if x < -1 (including -INF) ;

 *      log1p(+INF) is +INF; log1p(-1) is -INF with signal;

 *      log1p(NaN) is that NaN with no signal.

 *

 * Accuracy:

 *      according to an error analysis, the error is always less than

 *      1 ulp (unit in the last place).

 *

 * Constants:

 * The hexadecimal values are the intended ones for the following

 * constants. The decimal values may be used, provided that the

 * compiler will convert from decimal to binary accurately enough

 * to produce the hexadecimal values shown.

 *

 * Note: Assuming log() return accurate answer, the following

 *       algorithm can be used to compute log1p(x) to within a few ULP:

 *

 *              u = 1+x;

 *              if(u==1.0) return x ; else

 *                         return log(u)*(x/(u-1.0));

 *

 *       See HP-15C Advanced Functions Handbook, p.193.

 */

use core::f64;

const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */

const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */

const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */

const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */

const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */

const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */

const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */

const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */

const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */

/// The natural logarithm of 1+`x` (f64).

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

pub fn log1p(x: f64) -> f64 {

    let mut ui: u64 = x.to_bits();

    let hfsq: f64;

    let mut f: f64 = 0.;

    let mut c: f64 = 0.;

    let s: f64;

    let z: f64;

    let r: f64;

    let w: f64;

    let t1: f64;

    let t2: f64;

    let dk: f64;

    let hx: u32;

    let mut hu: u32;

    let mut k: i32;

    hx = (ui >> 32) as u32;

    k = 1;

    if hx < 0x3fda827a || (hx >> 31) > 0 {

        /* 1+x < sqrt(2)+ */

        if hx >= 0xbff00000 {

            /* x <= -1.0 */

            if x == -1. {

                return x / 0.0; /* log1p(-1) = -inf */

            }

            return (x - x) / 0.0; /* log1p(x<-1) = NaN */

        }

        if hx << 1 < 0x3ca00000 << 1 {

            /* |x| < 2**-53 */

            /* underflow if subnormal */

            if (hx & 0x7ff00000) == 0 {

                force_eval!(x as f32);

            }

            return x;

        }

        if hx <= 0xbfd2bec4 {

            /* sqrt(2)/2- <= 1+x < sqrt(2)+ */

            k = 0;

            c = 0.;

            f = x;

        }

    } else if hx >= 0x7ff00000 {

        return x;

    }

    if k > 0 {

        ui = (1. + x).to_bits();

        hu = (ui >> 32) as u32;

        hu += 0x3ff00000 - 0x3fe6a09e;

        k = (hu >> 20) as i32 - 0x3ff;

        /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */

        if k < 54 {

            c = if k >= 2 { 1. - (f64::from_bits(ui) - x) } else { x - (f64::from_bits(ui) - 1.) };

            c /= f64::from_bits(ui);

        } else {

            c = 0.;

        }

        /* reduce u into [sqrt(2)/2, sqrt(2)] */

        hu = (hu & 0x000fffff) + 0x3fe6a09e;

        ui = (hu as u64) << 32 | (ui & 0xffffffff);

        f = f64::from_bits(ui) - 1.;

    }

    hfsq = 0.5 * f * f;

    s = f / (2.0 + f);

    z = s * s;

    w = z * z;

    t1 = w * (LG2 + w * (LG4 + w * LG6));

    t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));

    r = t2 + t1;

    dk = k as f64;

    s * (hfsq + r) + (dk * LN2_LO + c) - hfsq + f + dk * LN2_HI

}