PASCAL-XSC: PASCAL for Extended Scientific Computing

Institut für Angewandte Mathematik, Forschungsschwerpunkt CAVN, Universität Karlsruhe
Wissenschaftliches Rechnen/Softwaretechnologie, Universität Wuppertal

• Linear systems of equations
• Matrix inversion
• Nonlinear systems of equations
• Eigenvalues and eigenvectors
• Evaluation of arithmetic expressions
• Evaluation of polynomials and zeros of polynomials
• Numerical quadrature
• Initial and boundary value problems in ordinary differential equations
• Integral equations
• Automatic differentiation
• Optimization problems

In the subsequent paragraphs, the most important new concepts are considered briefly.

Universal Operator Concept and Arbitrary Result Type

const maximum_degree = 20;

type  polynomial = array [0..maximum_degree] of real;

procedure add (a, b: polynomial; var c: polynomial);
  { Computes c = a + b for polynomials }
  var i: integer;
  begin
    for i:= 0 to maximum_degree do
      c[i]:= a[i] + b[i];
  end;

add (a,b,z);
add (z,c,z);
add (z,d,z);

function add (a, b: polynomial): polynomial;
  { Delivers the sum a + b for polynomials }
  var i: integer;
  begin
    for i:= 0 to maximum_degree do
      add[i]:= a[i] + b[i];
  end;

z:= add(a,add(b,add(c,d)))

operator + (a, b: polynomial) result_polynomial : polynomial;
  { Delivers the sum a + b for polynomials }
  var i: integer;
  begin
    for i:= 0 to maximum_degree do
      result_polynomial[i]:= a[i] + b[i];
  end;

z:= a+b+c+d

Overloading of Procedures, Functions, and Operators

As illustrated above, operators may also be overloaded. Even the assignment operator := may be overloaded so that the mathematical notation may be used for assignments:

var
  c: complex;
  r: real;

operator := (var c : complex; r: real);
  begin
    c.re := r;
    c.im := 0;
  end;

...

  r:= 1.5;
  c:= r;  {complex number with real part 1.5 and imaginary part 0}

Module Concept

module poly;
  use {other modules}
  ...
  {local declarations}
  ...
  {global declarations}
  global type  polynomial = ...
  ...
  global procedure read (...
  ...
  global procedure write (...
  ...
  global operator + (...
  ...
  global operator * (...
  ...
begin
  {initialization part of the module}
  ...
end. {module poly}

Dynamic Arrays and Subarrays

type  polynomial = dynamic array [*] of real;

var  p, q : polynomial [0..2*n];

operator * (a, b: polynomial)
           product: polynomial[0..ubound(a)+ubound(b)];
  { Delivers the product a * b of two polynomials a, b }
  var i, j   : integer;
      result : polynomial[0..ubound(a)+ubound(b)];
  begin
    for i:= 0 to ubound(a)+ubound(b) do
      result[i]:= 0;
    for i:= 0 to ubound(a) do
      for j:= 0 to ubound(b) do
        result[i+j]:= result[i+j] + a[i] * b[j];
    product:= result;
  end;

program dynatest (input, output);
...
type polynomial = dynamic array [*] of real;
...
var  maximum_degree : integer;
...
operator * (a, b:polynomial)...
...
procedure write (var f : text; p: polynomial);
...
procedure main (degree : integer);
  var
    p,q : polynomial[0..degree];
    r   : polynomial[0..2*degree];
  begin
    ...
    r:= p * q;
    writeln ('p*q = ', r);
    ...
  end;

begin {main program}
  read (maximum_degree);
  main (maximum_degree);
end. {main program}

type vector =  dynamic array [*] of real;
type matrix =  dynamic array [*] of vector;
var  v : vector[1..n];
     m : matrix[1..n,1..n];
...
  v      := m[i];   { i-th row of m    }
  m[*,j] := v;      { j-th column of m }

type vector = dynamic array [*] of real;

procedure high_accuracy (basic_length: integer; result: real);
var
  accurate : boolean;
  rvec     : vector;
  k        : integer;
begin
  accurate := false;   k := 0;

  repeat
    k:= k+1;
    allocate (rvec, 1..k*basic_length);

    ...  { computations }

    accurate := ...

    free (rvec);   { might be omitted }
  until accurate;

  result := ...
end;

String Concept

Arithmetic and Rounding

Accurate Expressions

How can I get the Pascal-XSC compiler?

http://www2.math.uni-wuppertal.de/wrswt/xsc/pxsc_download.html
or
http://www.xsc.de