Function primitive_float_atanh 

pub fn primitive_float_atanh<T>(x: T) -> T
where
    Float: From<T> + PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float> + PrimitiveFloat,

Computes $\operatorname{atanh} x$, the inverse hyperbolic tangent of a primitive float. Using this function is more accurate than using the default atanh function or the one provided by libm.

$$ f(x) = \operatorname{atanh} x+\varepsilon. $$

• If $\operatorname{atanh} x$ is infinite, zero, or NaN, $\varepsilon$ may be ignored or assumed to be 0.
• If $\operatorname{atanh} x$ is finite and nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 |\operatorname{atanh} x|\rfloor-p}$, where $p$ is the precision of the output (24 if T is a f32 and 53 if T is a f64).

Special cases:

• $f(\text{NaN})=\text{NaN}$
• $f(\pm\infty)=\text{NaN}$
• $f(\pm0.0)=\pm0.0$
• $f(\pm1)=\pm\infty$
• $f(x)=\text{NaN}$ if $|x|>1$

Overflow is not possible. The result is subnormal only when $x$ is, and then it is $x$ itself, since $|\operatorname{atanh} x - x| < |x|^3/2$.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::basic::traits::NegativeInfinity;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::atanh::primitive_float_atanh;

assert!(primitive_float_atanh(f32::NAN).is_nan());
assert!(primitive_float_atanh(f32::INFINITY).is_nan());
assert!(primitive_float_atanh(f32::NEGATIVE_INFINITY).is_nan());
assert_eq!(NiceFloat(primitive_float_atanh(0.0f32)), NiceFloat(0.0));
assert_eq!(NiceFloat(primitive_float_atanh(-0.0f32)), NiceFloat(-0.0));
assert_eq!(
    NiceFloat(primitive_float_atanh(1.0f32)),
    NiceFloat(f32::INFINITY)
);
assert!(primitive_float_atanh(2.0f32).is_nan());
assert_eq!(
    NiceFloat(primitive_float_atanh(0.5f32)),
    NiceFloat(0.54930615)
);
assert_eq!(
    NiceFloat(primitive_float_atanh(0.5f64)),
    NiceFloat(0.5493061443340549)
);
assert_eq!(
    NiceFloat(primitive_float_atanh(-0.75f64)),
    NiceFloat(-0.9729550745276566)
);