Function primitive_float_asec_pi 

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

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

This is primitive_float_asec_with_period with a period of 2: see primitive_float_asec_with_period for the error bounds, the special cases, and the complexity, with $u = 2$. Either infinity gives $1/2$, an input of 1 gives $0.0$, and an input of $-1$ gives $1$; NaN and any $|x|<1$, including the zeros, give NaN. Overflow is not possible, since $0 \leq \operatorname{asec}(x)/\pi \leq 1$.

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::asec::primitive_float_asec_pi;

assert!(primitive_float_asec_pi(f32::NAN).is_nan());
// the arcsecant is NaN inside (-1, 1)
assert!(primitive_float_asec_pi(0.5f32).is_nan());
assert_eq!(
    NiceFloat(primitive_float_asec_pi(f32::INFINITY)),
    NiceFloat(0.5)
);
assert_eq!(NiceFloat(primitive_float_asec_pi(1.0f32)), NiceFloat(0.0));
assert_eq!(NiceFloat(primitive_float_asec_pi(-1.0f32)), NiceFloat(1.0));
assert_eq!(
    NiceFloat(primitive_float_asec_pi(2.5f32)),
    NiceFloat(0.36901012)
);
assert_eq!(
    NiceFloat(primitive_float_asec_pi(2.5f64)),
    NiceFloat(0.36901011956554536)
);