-- GCEF spec
-- Question:  I like Jan Kok's rationale for the selection of which generic
--            formal parameters are needed: There are enough selectors
--            to decompose input parameters of functions into real values
--            and there are enough constructors to produce the required
--            outputs of type COMPLEX. Thus, persons having a complete set
--            of algorithms that compute the real and imaginary components
--            of the complex functions, using only real arithmetic, have
--            everything they need.
--            Short names, REAL, COMPLEX, IMAGINARY seem to be preferred.
--            Any suggested changes?  Jon

with ELEMENTARY_FUNCTIONS_EXCEPTIONS;
generic 
  type REAL is digits <>;
  type COMPLEX is private;
  type IMAGINARY is private;
  with function  RE (X : COMPLEX) return REAL is <>;
  with function  IM (X : COMPLEX) return REAL is <>;
  with function  IM (X : IMAGINARY) return REAL is <>;
  with function  COMPOSE_FROM_CARTESIAN (RE : REAL) return COMPLEX is <>;
  with function  COMPOSE_FROM_CARTESIAN (RE, IM : REAL) return COMPLEX is <>;
package GENERIC_COMPLEX_ELEMENTARY_FUNCTIONS is

    function SQRT (X : COMPLEX) return COMPLEX;
    function LOG (X : COMPLEX) return COMPLEX;
    function EXP (X : COMPLEX) return COMPLEX;
    function EXP (X : IMAGINARY) return COMPLEX;
    function "**" (LEFT, RIGHT : COMPLEX) return COMPLEX;
    function "**" (LEFT : COMPLEX; 
                   RIGHT : REAL) return COMPLEX;
    function "**" (LEFT : REAL; 
                   RIGHT : COMPLEX) return COMPLEX;

    function SIN (X : COMPLEX) return COMPLEX;
    function COS (X : COMPLEX) return COMPLEX;
    function TAN (X : COMPLEX) return COMPLEX;
    function COT (X : COMPLEX) return COMPLEX;

    function ARCSIN (X : COMPLEX) return COMPLEX;
    function ARCCOS (X : COMPLEX) return COMPLEX;
    function ARCTAN (X : COMPLEX) return COMPLEX;
    function ARCCOT (X : COMPLEX) return COMPLEX;

    function SINH (X : COMPLEX) return COMPLEX;
    function COSH (X : COMPLEX) return COMPLEX;
    function TANH (X : COMPLEX) return COMPLEX;
    function COTH (X : COMPLEX) return COMPLEX;

    function ARCSINH (X : COMPLEX) return COMPLEX;
    function ARCCOSH (X : COMPLEX) return COMPLEX;
    function ARCTANH (X : COMPLEX) return COMPLEX;
    function ARCCOTH (X : COMPLEX) return COMPLEX;

    -- EXCEPTIONS --

    ARGUMENT_ERROR : exception 
          renames ELEMENTARY_FUNCTIONS_EXCEPTIONS.ARGUMENT_ERROR;

end GENERIC_COMPLEX_ELEMENTARY_FUNCTIONS;