DEFINITION MODULE LongComplexMath;

IMPORT LONGCOMPLEX;

(* Mathematical Constants and Functions for Type LONGCOMPLEX *)

CONST
  i =    { 0.0, 1.0 };
  one =  { 1.0, 0.0 };
  zero = { 0.0, 0.0 };

PROCEDURE arg ( z : LONGCOMPLEX ) : LONGREAL;
(* Returns the argument of z. *)

PROCEDURE conj ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the complex conjugate of z. *)

PROCEDURE power ( base : LONGCOMPLEX; exponent : LONGREAL ) : LONGCOMPLEX;
(* Returns the value of base raised to the power exponent. *)

PROCEDURE sqrt ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the square root of z. *)

PROCEDURE ln ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the natural logarithm of z. *)

PROCEDURE log ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the decimal logarithm of z. *)

PROCEDURE sin ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the sine of z. *)

PROCEDURE cos ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the cosine of z. *)

PROCEDURE tan ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the tangent of z. *)

PROCEDURE arcsin ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the arcsine of z. *)

PROCEDURE arccos ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the arccosine of z. *)

PROCEDURE arctan ( z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the arctangent of z. *)

PROCEDURE polarToComplex ( abs, arg : LONGREAL ) : LONGCOMPLEX;
(* Returns the complex value with the specified polar coordinates. *)

PROCEDURE scalarMult ( scalar : LONGREAL; z : LONGCOMPLEX ) : LONGCOMPLEX;
(* Returns the scalar product of scalar and z. *)

END LongComplexMath.