(* 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 LongComplexMath;

  (* Mathematical functions for the type LONGCOMPLEX *)

CONST
  i =    CMPLX (0.0, 1.0);
  one =  CMPLX (1.0, 0.0);
  zero = CMPLX (0.0, 0.0);

PROCEDURE abs (z: LONGCOMPLEX): LONGREAL;
  (* Returns the length of z *)

PROCEDURE arg (z: LONGCOMPLEX): LONGREAL;
  (* Returns the angle that z subtends to the positive real axis *)

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

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

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

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

PROCEDURE ln (z: LONGCOMPLEX): LONGCOMPLEX;
  (* Returns the principal value of the natural 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 number with the specified polar coordinates *)

PROCEDURE scalarMult (scalar: LONGREAL; z: LONGCOMPLEX): LONGCOMPLEX;
  (* 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 LongComplexMath.