...one of the most highly
regarded and expertly designed C++ library projects in the
world. — Herb Sutter and Andrei
template<class T> calculated-result-type asinh(const T x); template<class T, class Policy> calculated-result-type asinh(const T x, const Policy&);
Computes the reciprocal of the hyperbolic sine function.
The return type of this function is computed using the result
type calculation rules: the return type is
double when T is an integer type, and T otherwise.
The final Policy argument is optional and can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the policy documentation for more details.
Generally accuracy is to within 1 or 2 machine epsilon across all supported platforms.
This function is tested using a combination of random test values designed to give full function coverage computed at high precision using the "naive" formula:
along with a selection of sanity check values computed using functions.wolfram.com to at least 50 decimal digits.
For sufficiently large x we can use the approximation:
While for very small x we can use the approximation:
For 0.5 > x > ε the following rearrangement of the primary definition is used:
Otherwise evalution is via the primary definition: