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#include <boost/math/special_functions/acosh.hpp>
template<class T> calculated-result-type acosh(const T x); template<class T, class Policy> calculated-result-type acosh(const T x, const Policy&);
        Computes the reciprocal of (the restriction to the range of [0;+∞[)
        the hyperbolic cosine
        function, at x. Values returned are positive.
      
        If x is in the range ]-∞;+1[ then returns the result of
        domain_error.
      
        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:
For x sufficiently close to 1 we can use the approximation:
Otherwise for x close to 1 we can use the following rearrangement of the primary definition to preserve accuracy:
Otherwise the primary definition is used: