Function primitive_float_sec_pi 

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

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

This is primitive_float_sec_with_period with a period of 2: see primitive_float_sec_with_period for the error bound and the special cases, with $u = 2$. Half-integers are poles and give exactly $\infty$; even integers give exactly $1$ and odd ones $-1$; odd multiples of $1/4$ give $\pm\sqrt2$; and multiples of $1/3$ give exactly $\pm2$.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::sec::primitive_float_sec_pi;

assert!(primitive_float_sec_pi(f32::NAN).is_nan());
// a half-integer is a pole
assert_eq!(
    NiceFloat(primitive_float_sec_pi(0.5f32)),
    NiceFloat(f32::INFINITY)
);
// an odd integer is exactly -1
assert_eq!(NiceFloat(primitive_float_sec_pi(1.0f64)), NiceFloat(-1.0));
// an odd multiple of a quarter: sqrt(2)
assert_eq!(
    NiceFloat(primitive_float_sec_pi(0.25f32)),
    NiceFloat(core::f32::consts::SQRT_2)
);
assert_eq!(
    NiceFloat(primitive_float_sec_pi(0.1f32)),
    NiceFloat(1.0514622)
);
assert_eq!(
    NiceFloat(primitive_float_sec_pi(0.1f64)),
    NiceFloat(1.0514622242382672)
);