Function primitive_float_atan_pi 

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

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

This is primitive_float_atan_with_period with a period of 2: see primitive_float_atan_with_period for the error bound and the special cases, with $u = 2$. An infinite input gives exactly $\pm1/2$, an input of $\pm1$ exactly $\pm1/4$, and a zero input exactly $\pm0.0$; those are the only exact cases. Overflow is not possible, since $|\arctan(x)/\pi| < 1/2$, and the result is subnormal, or zero, only for a subnormal input.

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::atan::primitive_float_atan_pi;

assert!(primitive_float_atan_pi(f32::NAN).is_nan());
// an infinite input is half a turn
assert_eq!(
    NiceFloat(primitive_float_atan_pi(f32::INFINITY)),
    NiceFloat(0.5)
);
assert_eq!(
    NiceFloat(primitive_float_atan_pi(f32::NEGATIVE_INFINITY)),
    NiceFloat(-0.5)
);
// an input of 1 is a quarter of a half-turn
assert_eq!(NiceFloat(primitive_float_atan_pi(1.0f32)), NiceFloat(0.25));
assert_eq!(
    NiceFloat(primitive_float_atan_pi(0.1f32)),
    NiceFloat(0.03172552)
);
assert_eq!(
    NiceFloat(primitive_float_atan_pi(0.1f64)),
    NiceFloat(0.031725517430553574)
);