(* Library module defined by the International Standard
   Information technology - programming languages
   BS ISO/IEC 10514-1:1996E Part 1: Modula-2, Base Language.

   Copyright ISO/IEC (International Organization for Standardization
   and International Electrotechnical Commission) 1996-2021.

   It may be freely copied for the purpose of implementation (see page
   707 of the Information technology - Programming languages Part 1:
   Modula-2, Base Language.  BS ISO/IEC 10514-1:1996).  *)

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.