September 2017 Update

Task/Bernoulli-numbers/Pascal/bernoulli-numbers.pascal

@@ -0,0 +1,115 @@
+(* Taken from the 'Ada 99' project, https://marquisdegeek.com/code_ada99 *)
+
+program BernoulliForAda99;
+
+
+type
+  Fraction = object
+  private
+    numerator, denominator: Int64;
+
+  public
+    procedure assign(n, d: Int64);
+    procedure subtract(rhs: Fraction);
+    procedure multiply(value: Int64);
+    procedure reduce();
+    procedure writeOutput();
+end;
+
+
+function gcd(a, b: Int64):Int64;
+begin
+  if (b = 0) then
+    gcd := a
+  else
+    gcd := gcd(b, a mod b)
+end;
+
+
+procedure Fraction.writeOutput();
+begin
+  write(numerator);
+  if (numerator <> 0) then
+  begin
+    write('/');
+    write(denominator);
+  end;
+end;
+
+
+procedure Fraction.assign(n, d: Int64);
+begin
+  numerator := n;
+  denominator := d;
+end;
+
+
+procedure Fraction.subtract(rhs: Fraction);
+begin
+  numerator := numerator * rhs.denominator;
+  numerator := numerator - (rhs.numerator * denominator);
+  denominator := denominator * rhs.denominator;
+end;
+
+
+procedure Fraction.multiply(value: Int64);
+begin
+  numerator := numerator * value;
+end;
+
+
+procedure Fraction.reduce();
+var gcdResult: Int64;
+begin
+  gcdResult := gcd(numerator, denominator);
+
+  begin
+    numerator := numerator div gcdResult;     (* div is Int64 division *)
+    denominator := denominator div gcdResult; (* could also use round(d/r) *)
+  end;
+end;
+
+
+function calculateBernoulli(n: Int64) : Fraction;
+var
+  m, j: Int64;
+  results: array of Fraction;
+
+  begin
+    setlength(results, n);
+
+    for m:= 0 to n do
+    begin
+      results[m].assign(1, m+1);
+
+      for j:= m downto 1 do
+        begin
+          results[j-1].subtract(results[j]);
+          results[j-1].multiply(j);
+          results[j-1].reduce();
+        end;
+    end;
+
+    calculateBernoulli := results[0];
+end;
+
+
+(* Main program starts here *)
+
+var
+  b: Int64;
+  result: Fraction;
+
+begin
+  writeln('Calculating Bernoulli numbers...');
+
+  for b:= 1 to 25 do
+    begin
+      write(b);
+      write(' : ');
+      result := calculateBernoulli(b);
+      result.writeOutput();
+      writeln;
+  end;
+
+end.