# The GNU Modula-2 front end to GCC

#### gm2-libs-iso/ComplexMath

```DEFINITION MODULE ComplexMath;

(* Mathematical functions for the type COMPLEX *)

CONST

i =    CMPLX (0.0, 1.0);

one =  CMPLX (1.0, 0.0);

zero = CMPLX (0.0, 0.0);

PROCEDURE __BUILTIN__ abs (z: COMPLEX): REAL;
(* Returns the length of z *)

PROCEDURE __BUILTIN__ arg (z: COMPLEX): REAL;
(* Returns the angle that z subtends to the positive real axis *)

PROCEDURE __BUILTIN__ conj (z: COMPLEX): COMPLEX;
(* Returns the complex conjugate of z *)

PROCEDURE __BUILTIN__ power (base: COMPLEX; exponent: REAL): COMPLEX;
(* Returns the value of the number base raised to the power exponent *)

PROCEDURE __BUILTIN__ sqrt (z: COMPLEX): COMPLEX;
(* Returns the principal square root of z *)

PROCEDURE __BUILTIN__ exp (z: COMPLEX): COMPLEX;
(* Returns the complex exponential of z *)

PROCEDURE __BUILTIN__ ln (z: COMPLEX): COMPLEX;
(* Returns the principal value of the natural logarithm of z *)

PROCEDURE __BUILTIN__ sin (z: COMPLEX): COMPLEX;
(* Returns the sine of z *)

PROCEDURE __BUILTIN__ cos (z: COMPLEX): COMPLEX;
(* Returns the cosine of z *)

PROCEDURE __BUILTIN__ tan (z: COMPLEX): COMPLEX;
(* Returns the tangent of z *)

PROCEDURE __BUILTIN__ arcsin (z: COMPLEX): COMPLEX;
(* Returns the arcsine of z *)

PROCEDURE __BUILTIN__ arccos (z: COMPLEX): COMPLEX;
(* Returns the arccosine of z *)

PROCEDURE __BUILTIN__ arctan (z: COMPLEX): COMPLEX;
(* Returns the arctangent of z *)

PROCEDURE polarToComplex (abs, arg: REAL): COMPLEX;
(* Returns the complex number with the specified polar coordinates *)

PROCEDURE scalarMult (scalar: REAL; z: COMPLEX): COMPLEX;
(* Returns the scalar product of scalar with z *)

PROCEDURE IsCMathException (): BOOLEAN;
(* Returns TRUE if the current coroutine is in the exceptional
execution state because of the raising of an exception in a
routine from this module; otherwise returns FALSE.
*)

END ComplexMath.

```