Function primitive_float_atan2_pi_rational 

pub fn primitive_float_atan2_pi_rational<T>(y: &Rational, x: &Rational) -> T
where
    Float: PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + PrimitiveFloat,

Computes $\operatorname{atan2}(y,x)/\pi$, the angle of the point $(x,y)$ measured from the positive $x$-axis in half-turns, for Rationals, returning the result as a primitive float.

This is primitive_float_atan2_with_period_rational with a period of 2: see primitive_float_atan2_with_period_rational for the error bound and the special cases, with $u = 2$.

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 max(y.significant_bits(), x.significant_bits()).

Examples

use malachite_base::num::basic::traits::{NegativeOne, Zero};
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::atan2::primitive_float_atan2_pi_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_atan2_pi_rational::<f64>(
        &Rational::from(3),
        &Rational::from(4)
    )),
    NiceFloat(0.20483276469913345)
);
// a negative x with a zero y is half a turn
assert_eq!(
    NiceFloat(primitive_float_atan2_pi_rational::<f64>(
        &Rational::ZERO,
        &Rational::NEGATIVE_ONE
    )),
    NiceFloat(1.0)
);