Function primitive_float_acot_rational 

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

Computes $\operatorname{acot} x$, the arccotangent of a Rational, returning the result as a primitive float.

This is the correctly rounded arccotangent: the exact $\operatorname{acot}(x)$ is rounded once, to the nearest value of the output type.

Special cases:

• $f(0)=\pi/2$
• $f(\pm1)=\pm\pi/4$

This is the odd arccotangent, the arctangent of the reciprocal, with range $(-\pi/2,\pi/2]$. Overflow is not possible, since $|\operatorname{acot}(x)| \leq \pi/2$. The result is subnormal, or zero, only when $|x|$ is large enough to put $1/|x|$ below the bottom of the output type’s normal range.

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::basic::traits::{NegativeOne, One, Two, Zero};
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::acot::primitive_float_acot_rational;
use malachite_q::Rational;

// an input of zero gives pi/2
assert_eq!(
    NiceFloat(primitive_float_acot_rational::<f64>(&Rational::ZERO)),
    NiceFloat(core::f64::consts::FRAC_PI_2)
);
assert_eq!(
    NiceFloat(primitive_float_acot_rational::<f64>(&Rational::ONE)),
    NiceFloat(0.7853981633974483)
);
assert_eq!(
    NiceFloat(primitive_float_acot_rational::<f64>(
        &Rational::NEGATIVE_ONE
    )),
    NiceFloat(-0.7853981633974483)
);
assert_eq!(
    NiceFloat(primitive_float_acot_rational::<f64>(&Rational::TWO)),
    NiceFloat(0.4636476090008061)
);
assert_eq!(
    NiceFloat(primitive_float_acot_rational::<f32>(
        &Rational::from_unsigneds(5u8, 3)
    )),
    NiceFloat(0.5404195)
);