HOMEWORK PROBLEM 5         INTRODUCTION TO Ada I   586.1
     
     PURPOSE:      To learn about matrices and overloaded
                   operators.
                   To specify types and exceptions in a
                   utility library package
     
     END RESULT:   A complete Ada program that is a main procedure
                   that WITH's a package you modify.
     
     PROBLEM:      Modify the attached package 
                   Real_Matrix_Arithmetic , a skeleton
                   for a complete real matrix arithmetic package.
                   Use the matrix multiply "*" as a guide to write
                   matrix add "+". Keep the matrix multiply
                   and use both in the main procedure.
                   The only requirement for matrix add is that
                   A'Length(1) = B'Length(1) and
                   A'Length(2) = B'Length(2).
     
     TURN IN:      Printout of main procedure and package.
                   Printout of execution for test data. ( modify to
                   suit your needs. Matrices as small as 3 by 2 
                   are acceptable , not square matrices)
     
     OBSERVE:      The type Real_Matrix is defined in the package
                   and is visible in the main procedure because
                   of the "with" and "use" on Real_Matrix_Arithmetic.
                   The objects MAT_1 etc. are declared and assigned
                   storage in the main procedure. The object C is
                   dynamically assigned storage with a size that
                   depends on the formal parameter A when "*" is
                   called.
                   The user defined exception Matrix_Error is defined
                   and may be raised in the package. This exception
                   may then be handled as the user desires in the
                   main procedure. This avoids the need for math
                   routines to print out errors and allows the
                   calling procedure to take corrective action
                   for some types of errors.
     
                   Be sure to handle first and second subscript ranges
                   having different first subscripts. Only the length
                   of the side of the matrix is important.
     
     EXTRA         Add tests to make sure all cases work.
     
     READING:      BARNES  9.1  9.2  9.3  A1.2
                   ISO 8652:1995  6.1  6.2  6.3  6.4  Annex K
     
     LECTURE:      will also cover attributes in Annex K
     
            QUIZ  NEXT  SESSION

     The following are some convenient packages to have compiled.
     
     
     Int_IO.ads
     
     with Ada.Text_IO ;
     package Int_IO is new Ada.Text_IO.Integer_IO ( Integer ) ;
     
     NOTE: compiling the above package may allow faster compilation
           of later units.
     
        Replace "package Int_IO is new Integer_IO ( Integer ) ; use Int_IO ;"
     
        with    "with Int_IO ; use Int_IO ;"  before the package or procedure
     
     
     Define_Real.ads
     
     -- This package provides the definition of the type Real and Long_Real.
     -- For computers with only one floating point hardware both subtypes
     -- become the same.
     
     package Define_Real is
       subtype Real is Float ;             -- may be Short_Float
       subtype Long_Real is Long_Float ;   -- may be Float
     end Define_Real ;
     
     Real_IO.ads
     
     with Define_Real ;
     with Ada.Text_IO ;
     package Real_IO is new Ada.Text_IO.Float_IO ( Define_Real.Real ) ;
     
     
     Note: As projects get larger, there is more importance on not changing
           package specifications. This has two ramifications.
              First put the package specification in one file and the
           package body in another. (.ads  and  .ads  for  gnat)
              Second, only put "with" statements on the specification
           that are needed by the specification. The body typically needs
           more "with" statements. This speeds up compilations and
           reduces dependencies.
     
     
     More stray information :

          The VAX VMS naming convention for files containing package
          specifications is to add an underscore to the package name
          in order to get the file name. The package body file name
          is the same as the package name.
          The gnat naming convention is to use the package name with
          extensions  .ads  for specifications and  .adb  for bodies.