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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 abs (z: COMPLEX): REAL;
  (* Returns the length of z *)
 
PROCEDURE arg (z: COMPLEX): REAL;
  (* Returns the angle that z subtends to the positive real axis, in the range [-pi, pi] *)
  
PROCEDURE conj (z: COMPLEX): COMPLEX;
  (* Returns the complex conjugate of z *)
  
PROCEDURE power (base: COMPLEX; exponent: REAL): COMPLEX;
  (* Returns the value of the number base raised to the power exponent *)
 
PROCEDURE sqrt (z: COMPLEX): COMPLEX;
  (* Returns the principal square root of z, with arg in the range [-pi/2, pi/2] *)
 
PROCEDURE exp (z: COMPLEX): COMPLEX;
  (* Returns the complex exponential of z *)
 
PROCEDURE ln (z: COMPLEX): COMPLEX;
  (* Returns the principal value of the natural logarithm of z *)
 
PROCEDURE sin (z: COMPLEX): COMPLEX;
  (* Returns the sine of z *)
 
PROCEDURE cos (z: COMPLEX): COMPLEX;
  (* Returns the cosine of z *)
 
PROCEDURE tan (z: COMPLEX): COMPLEX;
  (* Returns the tangent of z *)
 
PROCEDURE arcsin (z: COMPLEX): COMPLEX;
  (* Returns the arcsine of z *)
 
PROCEDURE arccos (z: COMPLEX): COMPLEX;
  (* Returns the arccosine of z *)
 
PROCEDURE 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 ComplexMath exception; otherwise returns FALSE.
  *)
 
END ComplexMath.