Function primitive_float_sech_rational 

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

Computes $\operatorname{sech} x$, the hyperbolic secant of a Rational, returning the result as a primitive float. The result is correctly rounded.

$$ f(x) = \operatorname{sech} x+\varepsilon. $$

• If $\operatorname{sech} x$ is zero, $\varepsilon$ may be ignored or assumed to be 0.
• If $\operatorname{sech} x$ is nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 \operatorname{sech} x\rfloor-p}$, where $p$ is the precision of the output (typically 24 if T is a f32 and 53 if T is a f64, but less if the output is subnormal).

Special cases:

• $f(0)=1$

Overflow is not possible, since the result lies in $(0, 1]$. An x of large magnitude gives a subnormal result, or underflows to 0.0.

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::sech::primitive_float_sech_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_sech_rational::<f64>(&Rational::ZERO)),
    NiceFloat(1.0)
);
assert_eq!(
    NiceFloat(primitive_float_sech_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.9469052537634979)
);
assert_eq!(
    NiceFloat(primitive_float_sech_rational::<f64>(
        &Rational::from_signeds(-1i8, 3)
    )),
    NiceFloat(0.9469052537634979)
);
assert_eq!(
    NiceFloat(primitive_float_sech_rational::<f64>(&Rational::from(10000))),
    NiceFloat(0.0)
);