Function primitive_float_csc_pi 

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

Computes $\csc(\pi x)$, the cosecant of a primitive float measured in half-turns.

This is primitive_float_csc_with_period with a period of 2: see primitive_float_csc_with_period for the error bound and the special cases, with $u = 2$. Integers are poles and give exactly $\pm\infty$ with the sign of $x$; half-integers give exactly $\pm1$; odd multiples of $1/6$ give exactly $\pm2$; odd multiples of $1/4$ give $\pm\sqrt2$; and multiples of $1/3$ that are not integers give $\pm2\sqrt3/3$.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::csc::primitive_float_csc_pi;

assert!(primitive_float_csc_pi(f32::NAN).is_nan());
// a half-integer is exactly 1
assert_eq!(NiceFloat(primitive_float_csc_pi(0.5f32)), NiceFloat(1.0));
// an integer is a pole
assert_eq!(
    NiceFloat(primitive_float_csc_pi(1.0f64)),
    NiceFloat(f64::INFINITY)
);
// an odd multiple of a quarter: sqrt(2)
assert_eq!(
    NiceFloat(primitive_float_csc_pi(0.25f32)),
    NiceFloat(core::f32::consts::SQRT_2)
);
assert_eq!(
    NiceFloat(primitive_float_csc_pi(0.1f32)),
    NiceFloat(3.236068)
);
assert_eq!(
    NiceFloat(primitive_float_csc_pi(0.1f64)),
    NiceFloat(3.2360679774997894)
);