use super::{log1pf, logf, sqrtf};

const LN2: f32 = 0.693147180559945309417232121458176568;

/// Inverse hyperbolic cosine (f32)

///

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

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

/// `x` must be a number greater than or equal to 1.

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

pub fn acoshf(x: f32) -> f32 {

    let u = x.to_bits();

    let a = u & 0x7fffffff;

    if a < 0x3f800000 + (1 << 23) {

        /* |x| < 2, invalid if x < 1 or nan */

        /* up to 2ulp error in [1,1.125] */

        return log1pf(x - 1.0 + sqrtf((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));

    }

    if a < 0x3f800000 + (12 << 23) {

        /* |x| < 0x1p12 */

        return logf(2.0 * x - 1.0 / (x + sqrtf(x * x - 1.0)));

    }

    /* x >= 0x1p12 */

    return logf(x) + LN2;

}