Function primitive_float_sinh 

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

Computes $\sinh x$, the hyperbolic sine of a primitive float. The result is correctly rounded.

$$ f(x) = \sinh x+\varepsilon. $$

• If $\sinh x$ is infinite, zero, or NaN, $\varepsilon$ may be ignored or assumed to be 0.
• If $\sinh x$ is finite and nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 |\sinh x|\rfloor-p}$, 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:

• $f(\text{NaN})=\text{NaN}$
• $f(\infty)=\infty$
• $f(-\infty)=-\infty$
• $f(0.0)=0.0$
• $f(-0.0)=-0.0$

Overflow is possible: a large positive x gives $\infty$, and a large negative x gives $-\infty$. Since $|\sinh x|\geq|x|$, the result never underflows.

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::basic::traits::NegativeInfinity;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::sinh::primitive_float_sinh;

assert!(primitive_float_sinh(f32::NAN).is_nan());
assert_eq!(
    NiceFloat(primitive_float_sinh(f32::INFINITY)),
    NiceFloat(f32::INFINITY)
);
assert_eq!(
    NiceFloat(primitive_float_sinh(f32::NEGATIVE_INFINITY)),
    NiceFloat(f32::NEGATIVE_INFINITY)
);
assert_eq!(NiceFloat(primitive_float_sinh(-0.0f32)), NiceFloat(-0.0));
assert_eq!(
    NiceFloat(primitive_float_sinh(1.0f32)),
    NiceFloat(1.1752012)
);
assert_eq!(
    NiceFloat(primitive_float_sinh(-1.0f32)),
    NiceFloat(-1.1752012)
);
assert_eq!(
    NiceFloat(primitive_float_sinh(-100.0f32)),
    NiceFloat(f32::NEGATIVE_INFINITY)
);