Function primitive_float_acot_pi_rational 

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

Computes $\operatorname{acot}(x)/\pi$, the arccotangent of a Rational measured in half-turns, returning the result as a primitive float.

This is primitive_float_acot_with_period_rational with a period of 2: see primitive_float_acot_with_period_rational for the error bounds, the special cases, and the complexity, with $u = 2$. A zero gives $1/2$ and $\pm1$ give $\pm1/4$. Overflow is not possible, since $|\operatorname{acot}(x)/\pi| \leq 1/2$.

Worst-case complexity

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

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

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

Examples

use malachite_base::num::basic::traits::{NegativeOne, One, OneHalf, Zero};
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::acot::primitive_float_acot_pi_rational;
use malachite_q::Rational;

// a zero is half a half-turn, and the arccotangent is defined inside (-1, 1) too
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f64>(&Rational::ZERO)),
    NiceFloat(0.5)
);
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f64>(&Rational::ONE_HALF)),
    NiceFloat(0.35241638234956674)
);
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f64>(&Rational::ONE)),
    NiceFloat(0.25)
);
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f64>(
        &Rational::NEGATIVE_ONE
    )),
    NiceFloat(-0.25)
);
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f64>(
        &Rational::from_unsigneds(5u8, 3)
    )),
    NiceFloat(0.17202086962263066)
);
assert_eq!(
    NiceFloat(primitive_float_acot_pi_rational::<f32>(
        &Rational::from_unsigneds(5u8, 3)
    )),
    NiceFloat(0.17202087)
);