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primitive_float_acos_pi

malachite_float::float::arithmetic::acos

Function primitive_float_acos_pi 

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

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

This is primitive_float_acos_with_period with a period of 2: see primitive_float_acos_with_period for the error bounds, the special cases, and the complexity, with $u = 2$. A zero input gives $1/2$, an input of 1 gives $0.0$, and an input of $-1$ gives $1$; NaN, either infinity, and any $|x|>1$ give NaN. Overflow is not possible, since $0 \leq \arccos(x)/\pi \leq 1$.

§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::acos::primitive_float_acos_pi;

assert!(primitive_float_acos_pi(f32::NAN).is_nan());
// the arccosine is NaN outside [-1, 1]
assert!(primitive_float_acos_pi(2.0f32).is_nan());
assert_eq!(NiceFloat(primitive_float_acos_pi(0.0f32)), NiceFloat(0.5));
assert_eq!(NiceFloat(primitive_float_acos_pi(1.0f32)), NiceFloat(0.0));
assert_eq!(NiceFloat(primitive_float_acos_pi(-1.0f32)), NiceFloat(1.0));
assert_eq!(
    NiceFloat(primitive_float_acos_pi(0.25f32)),
    NiceFloat(0.41956937)
);
assert_eq!(
    NiceFloat(primitive_float_acos_pi(0.25f64)),
    NiceFloat(0.41956937674483374)
);