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### sinh_sinh

    template<class Real>
    class sinh_sinh
    {
    public:
        sinh_sinh(size_t max_refinements = 9);

        template<class F>
        auto integrate(const F f,
                       Real tol = sqrt(std::numeric_limits<Real>::epsilon()),
                       Real* error = nullptr,
                       Real* L1 = nullptr,
                       size_t* levels = nullptr)->decltype(std::declval<F>()(std::declval<Real>())) const;;
    };

The sinh-sinh quadrature allows computation over the entire real line, and is called as follows:

    sinh_sinh<double> integrator;
    auto f = [](double x) { return exp(-x*x); };
    double error;
    double L1;
    double Q = integrator.integrate(f, &error, &L1);

Note that the limits of integration are understood to be (-∞, +∞).

Complex valued integrands are supported as well, for example the Dirichlet Eta function can be represented via:

which we can directly code up as:

    template <class Complex>
    Complex eta(Complex s)
    {
       typedef typename Complex::value_type value_type;
       using std::pow;  using std::exp;
       Complex i(0, 1);
       value_type pi = boost::math::constants::pi<value_type>();
       auto f = [&, s, i](value_type t) { return pow(0.5 + i * t, -s) / (exp(pi * t) + exp(-pi * t)); };
       boost::math::quadrature::sinh_sinh<value_type> integrator;
       return integrator.integrate(f);
    }