Function primitive_float_atan_pi_rational 

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

Computes $\arctan(x)/\pi$, the arctangent of a Rational measured in half-turns, returning the result as a primitive float.

This is primitive_float_atan_with_period_rational with a period of 2: see primitive_float_atan_with_period_rational for the error bound and the special cases, with $u = 2$. An input of $\pm1$ gives exactly $\pm1/4$ and a zero input exactly $0.0$; those are the only exact cases. Overflow is not possible, since $|\arctan(x)/\pi| < 1/2$.

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::{One, Zero};
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::atan::primitive_float_atan_pi_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_atan_pi_rational::<f64>(&Rational::ZERO)),
    NiceFloat(0.0)
);
// an input of 1 is a quarter of a half-turn
assert_eq!(
    NiceFloat(primitive_float_atan_pi_rational::<f64>(&Rational::ONE)),
    NiceFloat(0.25)
);
assert_eq!(
    NiceFloat(primitive_float_atan_pi_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.10241638234956672)
);
assert_eq!(
    NiceFloat(primitive_float_atan_pi_rational::<f32>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.10241638)
);