Function primitive_float_coth_rational 

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

Computes $\coth x$, the hyperbolic cotangent of a Rational, returning the result as a primitive float. The result is correctly rounded.

$$ f(x) = \coth x+\varepsilon. $$

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

Special cases:

• $f(0)=\infty$

An x of magnitude below the reciprocal of the largest finite value gives a result that overflows to $\pm\infty$. Underflow is not possible, since $|\coth x| > 1$.

Worst-case complexity

$T(m) = O(m (\log m)^2 \log\log m)$

$M(m) = O(m \log m)$

where $T$ is time, $M$ is additional memory, and $m$ is x.significant_bits().

Examples

use malachite_base::num::basic::traits::Zero;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::coth::primitive_float_coth_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_coth_rational::<f64>(&Rational::ZERO)),
    NiceFloat(f64::INFINITY)
);
assert_eq!(
    NiceFloat(primitive_float_coth_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(3.110296679619444)
);
assert_eq!(
    NiceFloat(primitive_float_coth_rational::<f64>(
        &Rational::from_signeds(-1i8, 3)
    )),
    NiceFloat(-3.110296679619444)
);
assert_eq!(
    NiceFloat(primitive_float_coth_rational::<f64>(&Rational::from(10000))),
    NiceFloat(1.0)
);