Function primitive_float_exp_rational 

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

Computes $e^x$, the exponential of a Rational, returning the result as a primitive float.

$$ f(x) = e^x+\varepsilon. $$

• If $e^x$ is infinite or zero, $\varepsilon$ may be ignored or assumed to be 0.
• If $e^x$ is finite and nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 e^x\rfloor-p}$, 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 and underflow are possible: a large positive x gives $\infty$, and a large negative x gives 0.0.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::basic::traits::Zero;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::exp::primitive_float_exp_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_exp_rational::<f64>(&Rational::ZERO)),
    NiceFloat(1.0)
);
assert_eq!(
    NiceFloat(primitive_float_exp_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(1.3956124250860895)
);
assert_eq!(
    NiceFloat(primitive_float_exp_rational::<f64>(&Rational::from(10000))),
    NiceFloat(f64::INFINITY)
);
assert_eq!(
    NiceFloat(primitive_float_exp_rational::<f64>(&Rational::from(-10000))),
    NiceFloat(0.0)
);