Function primitive_float_atan_rational 

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

Computes $\arctan x$, the arctangent of a Rational, returning the result as a primitive float.

$$ f(x) = \arctan x+\varepsilon, $$ where $|\varepsilon| < 2^{\lfloor\log_2 |\arctan x|\rfloor-p}$, and $p$ is the precision of the output (24 if T is a f32 and 53 if T is a f64).

Special cases:

• $f(0)=0$

Overflow is not possible, since the result lies in $(-\pi/2, \pi/2)$. The result underflows, to a subnormal or to zero, only when $x$ is tiny, since $|\arctan x| < |x|$ and $\arctan x$ is very close to $x$ there.

Worst-case complexity

$T(m) = O(m (\log m)^2 \log\log m)$

$M(m) = O(m \log m)$

where $T$ is time, $M$ is additional memory, and $m$ is x.significant_bits().

Examples

use malachite_base::num::basic::traits::Zero;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::atan::primitive_float_atan_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_atan_rational::<f64>(&Rational::ZERO)),
    NiceFloat(0.0)
);
assert_eq!(
    NiceFloat(primitive_float_atan_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.3217505543966422)
);
assert_eq!(
    NiceFloat(primitive_float_atan_rational::<f32>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.32175055)
);
assert_eq!(
    NiceFloat(primitive_float_atan_rational::<f64>(&Rational::from(10000))),
    NiceFloat(1.5706963267952299)
);