/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.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.

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

 */

use core::f64;

const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */

const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */

const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */

const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */

/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */

const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */

const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */

const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */

const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */

const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */

/// Exponential, base *e*, of x-1 (f64)

///

/// Calculates the exponential of `x` and subtract 1, that is, *e* raised

/// to the power `x` minus 1 (where *e* is the base of the natural

/// system of logarithms, approximately 2.71828).

/// The result is accurate even for small values of `x`,

/// where using `exp(x)-1` would lose many significant digits.

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

pub fn expm1(mut x: f64) -> f64 {

    let hi: f64;

    let lo: f64;

    let k: i32;

    let c: f64;

    let mut t: f64;

    let mut y: f64;

    let mut ui = x.to_bits();

    let hx = ((ui >> 32) & 0x7fffffff) as u32;

    let sign = (ui >> 63) as i32;

    /* filter out huge and non-finite argument */

    if hx >= 0x4043687A {

        /* if |x|>=56*ln2 */

        if x.is_nan() {

            return x;

        }

        if sign != 0 {

            return -1.0;

        }

        if x > O_THRESHOLD {

            x *= f64::from_bits(0x7fe0000000000000);

            return x;

        }

    }

    /* argument reduction */

    if hx > 0x3fd62e42 {

        /* if  |x| > 0.5 ln2 */

        if hx < 0x3FF0A2B2 {

            /* and |x| < 1.5 ln2 */

            if sign == 0 {

                hi = x - LN2_HI;

                lo = LN2_LO;

                k = 1;

            } else {

                hi = x + LN2_HI;

                lo = -LN2_LO;

                k = -1;

            }

        } else {

            k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;

            t = k as f64;

            hi = x - t * LN2_HI; /* t*ln2_hi is exact here */

            lo = t * LN2_LO;

        }

        x = hi - lo;

        c = (hi - x) - lo;

    } else if hx < 0x3c900000 {

        /* |x| < 2**-54, return x */

        if hx < 0x00100000 {

            force_eval!(x);

        }

        return x;

    } else {

        c = 0.0;

        k = 0;

    }

    /* x is now in primary range */

    let hfx = 0.5 * x;

    let hxs = x * hfx;

    let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));

    t = 3.0 - r1 * hfx;

    let mut e = hxs * ((r1 - t) / (6.0 - x * t));

    if k == 0 {

        /* c is 0 */

        return x - (x * e - hxs);

    }

    e = x * (e - c) - c;

    e -= hxs;

    /* exp(x) ~ 2^k (x_reduced - e + 1) */

    if k == -1 {

        return 0.5 * (x - e) - 0.5;

    }

    if k == 1 {

        if x < -0.25 {

            return -2.0 * (e - (x + 0.5));

        }

        return 1.0 + 2.0 * (x - e);

    }

    ui = ((0x3ff + k) as u64) << 52; /* 2^k */

    let twopk = f64::from_bits(ui);

    if k < 0 || k > 56 {

        /* suffice to return exp(x)-1 */

        y = x - e + 1.0;

        if k == 1024 {

            y = y * 2.0 * f64::from_bits(0x7fe0000000000000);

        } else {

            y = y * twopk;

        }

        return y - 1.0;

    }

    ui = ((0x3ff - k) as u64) << 52; /* 2^-k */

    let uf = f64::from_bits(ui);

    if k < 20 {

        y = (x - e + (1.0 - uf)) * twopk;

    } else {

        y = (x - (e + uf) + 1.0) * twopk;

    }

    y

}

#[cfg(test)]

mod tests {

    #[test]

    fn sanity_check() {

        assert_eq!(super::expm1(1.1), 2.0041660239464334);

    }

}