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### sqrt1pm1

    #include <boost/math/special_functions/sqrt1pm1.hpp>

    namespace boost{ namespace math{

    template <class T>
    calculated-result-type sqrt1pm1(T x);

    template <class T, class Policy>
    calculated-result-type sqrt1pm1(T x, const Policy&);

    }} // namespaces

Returns `sqrt(1+x) - 1`.

The return type of this function is computed using the result type calculation rules: the return is `double` when x 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.

This function is useful when you need the difference between sqrt(x) and 1, when x is itself close to 1.

Implemented in terms of `log1p` and `expm1`.

The following graph illustrates the behaviour of sqrt1pm1:

##### Accuracy

For built in floating-point types `sqrt1pm1` should have approximately 3 epsilon accuracy.

Table 6.81. Error rates for sqrt1pm1

| Microsoft Visual C++ version 12.0 Win32 double | GNU C++ version 5.1.0 linux double | GNU C++ version 5.1.0 linux long double | Sun compiler version 0x5130 Sun Solaris long double
--- | --- | --- | --- | ---
sqrt1pm1 | Max = 1.36ε (Mean = 0.44ε) | Max = 1.3ε (Mean = 0.404ε) | Max = 1.33ε (Mean = 0.409ε) | Max = 1.54ε (Mean = 0.568ε)

##### Testing

A selection of random high precision test values calculated using NTL::RR at 1000-bit precision.