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Complex Math

Spec.ComplexMath History

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2010-05-24 13:19 by benjk -
Deleted lines 2-8:
(* =========================================
    Original COMPLEX specification and
          design of ComplexMath
    Copyright © 1990-1991 by R. Sutcliffe
    Assigned to the BSI for standards work
===========================================*)
Changed lines 5-6 from:
  (* Mathematical functions for the type COMPLEX *)
 
to:
(* Mathematical Constants and Functions for Type COMPLEX *)
Changed lines 8-52 from:
  i =    CMPLX (0.0, 1.0);
  one =  CMPLX (1.0, 0.0);
  zero = CMPLX (0.0, 0.0);

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

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 *)

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 *)
to:
  i =    { 0.0, 1.0 };
  one =  { 1.0, 0.0 };
  zero = { 0.0, 0.0 };

PROCEDURE arg ( z : COMPLEX ) : REAL;
(* Returns the argument of z. *)

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

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

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

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

PROCEDURE log ( z : COMPLEX ) : COMPLEX;
(* Returns the decimal 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 value with the specified polar coordinates. *)

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