(* ShortComplexMath.def provides access to the ShortComplex intrincics.

Copyright (C) 2010-2021 Free Software Foundation, Inc.
Contributed by Gaius Mulley <gaius.mulley@southwales.ac.uk>.

This file is part of GNU Modula-2.

GNU Modula-2 is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3, or (at your option)
any later version.

GNU Modula-2 is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  *)

DEFINITION MODULE ShortComplexMath;

  (* Mathematical functions for the type SHORTCOMPLEX *)

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

PROCEDURE abs (z: SHORTCOMPLEX): SHORTREAL;
  (* Returns the length of z *)

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

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

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

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

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

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

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

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

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

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

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

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

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

PROCEDURE scalarMult (scalar: SHORTREAL; z: SHORTCOMPLEX): SHORTCOMPLEX;
  (* 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 ShortComplexMath.

