Function primitive_float_asin_pi 

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

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

This is primitive_float_asin_with_period with a period of 2: see primitive_float_asin_with_period for the error bounds, the special cases, and the complexity, with $u = 2$. An input of $\pm1$ gives $\pm1/2$ and a zero input gives $\pm0.0$; NaN, either infinity, and any $|x|>1$ give NaN. Overflow is not possible, since $|\arcsin(x)/\pi| \leq 1/2$.

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::float::NiceFloat;
use malachite_float::float::arithmetic::asin::primitive_float_asin_pi;

assert!(primitive_float_asin_pi(f32::NAN).is_nan());
// an input outside [-1, 1] is NaN
assert!(primitive_float_asin_pi(2.0f32).is_nan());
// an input of 1 is half a half-turn
assert_eq!(NiceFloat(primitive_float_asin_pi(1.0f32)), NiceFloat(0.5));
assert_eq!(
    NiceFloat(primitive_float_asin_pi(0.1f32)),
    NiceFloat(0.03188428)
);
assert_eq!(
    NiceFloat(primitive_float_asin_pi(0.1f64)),
    NiceFloat(0.03188428042925993)
);