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use super::log1p;
/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
/// Inverse hyperbolic tangent (f64)
///
/// Calculates the inverse hyperbolic tangent of `x`.
/// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`.
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn atanh(x: f64) -> f64 {
let u = x.to_bits();
let e = ((u >> 52) as usize) & 0x7ff;
let sign = (u >> 63) != 0;
/* |x| */
let mut y = f64::from_bits(u & 0x7fff_ffff_ffff_ffff);
if e < 0x3ff - 1 {
if e < 0x3ff - 32 {
/* handle underflow */
if e == 0 {
force_eval!(y as f32);
}
} else {
/* |x| < 0.5, up to 1.7ulp error */
y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y));
}
} else {
/* avoid overflow */
y = 0.5 * log1p(2.0 * (y / (1.0 - y)));
}
if sign {
-y
} else {
y
}
}
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