/*
    Additional functions which can be used in Heta platforms
    can be added to index file by include ./qsp-functions.heta;
*/

// hyperbolic functions

#defineFunction sinh {
    arguments: [x],
    math: "0.5 * (exp(x) - exp(-x))"
};

#defineFunction cosh {
    arguments: [x],
    math: "0.5 * (exp(x) + exp(-x))"
};

#defineFunction tanh {
    arguments: [x],
    math: "(exp(2 * x) - 1) / (exp(2 * x) + 1)"
};

#defineFunction sech {
    arguments: [x],
    math: "1 / cosh(x)"
};

#defineFunction csch {
    arguments: [x],
    math: "1 / sinh(x)"
};

#defineFunction coth {
    arguments: [x],
    math: "1 / tanh(x)"
};


// inverse hyperbolic functions

#defineFunction arcsinh {
    arguments: [x],
    math: "ln(x + sqrt(x^2 + 1))"
};

#defineFunction arccosh {
    arguments: [x],
    math: "ln(x + sqrt(x^2 - 1))"
};

#defineFunction arctanh {
    arguments: [x],
    math: "0.5 * ln((1 + x) / (1 - x))"
};

#defineFunction arcsech {
    arguments: [x],
    math: "ln((1 + sqrt(1 - x^2)) / x)"
};

#defineFunction arccsch {
    arguments: [x],
    math: "ln(1 / x + sqrt(1 + 1 / x^2))"
};

#defineFunction arccoth {
    arguments: [x],
    math: "0.5 * ln((x + 1) / (x - 1))"
};