use super::{log, log1p, sqrt};

const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42,  0xfefa39ef*/

/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */

/// Inverse hyperbolic sine (f64)

///

/// Calculates the inverse hyperbolic sine of `x`.

/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.

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

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

    let mut u = x.to_bits();

    let e = ((u >> 52) as usize) & 0x7ff;

    let sign = (u >> 63) != 0;

    /* |x| */

    u &= (!0) >> 1;

    x = f64::from_bits(u);

    if e >= 0x3ff + 26 {

        /* |x| >= 0x1p26 or inf or nan */

        x = log(x) + LN2;

    } else if e >= 0x3ff + 1 {

        /* |x| >= 2 */

        x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));

    } else if e >= 0x3ff - 26 {

        /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */

        x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));

    } else {

        /* |x| < 0x1p-26, raise inexact if x != 0 */

        let x1p120 = f64::from_bits(0x4770000000000000);

        force_eval!(x + x1p120);

    }

    if sign { -x } else { x }

}