Data update

Task/Numeric-error-propagation/PascalABC.NET/numeric-error-propagation.pas

@@ -0,0 +1,64 @@
+type
+  Approx = record
+  private
+    value, sigma: real;
+  public
+    constructor(v, s: real);
+    begin
+      value := v;
+      sigma := s;
+    end;
+
+    class function operator-(a: Approx) := new Approx(-a.value, a.sigma);
+    class function operator+(a: Approx) := a;
+
+    class function operator+(a, b: Approx) := new Approx(a.value + b.value, (a.sigma.Sqr + b.sigma.Sqr).Sqrt);
+    class function operator+(a: Approx; b: real) := new Approx(a.value + b, a.sigma);
+    class function operator+(b: real; a: Approx) := a + b;
+
+    class function operator-(a, b: Approx) := a + (-b);
+    class function operator-(a: Approx; b: real) := a + (-b);
+    class function operator-(b: real; a: Approx) := (-a) + b;
+
+    class function operator*(a, b: Approx): Approx;
+    begin
+      var v := a.value * b.value;
+      Result := new Approx(v, v * ((a.sigma / a.value).Sqr + (b.sigma / b.value).Sqr).Sqrt)
+    end;
+
+    class function operator*(a: Approx; b: real) := new Approx(a.value * b, abs(a.sigma * b));
+    class function operator*(b: real; a: Approx) := a * b;
+
+    class function operator/(a, b: Approx): Approx;
+    begin
+      var v := a.value / b.value;
+      Result := new Approx(v, v * ((a.sigma / a.value).Sqr + (b.sigma / b.value).Sqr).Sqrt);
+    end;
+
+    class function operator/(a: Approx; b: real) := new Approx(a.value / b, abs(a.sigma * b));
+    class function operator/(b: real; a: Approx) := a / b;
+
+    class function operator**(a: Approx; b: real): Approx;
+    begin
+      var v := power(a.value, b);
+      Result := new Approx(v, abs(v * b * a.sigma / a.value));
+    end;
+
+    function ToString: string; override;
+    begin
+      Result := Format('{0} ± {1}', value, sigma);
+    end;
+  end;
+
+function Sqrt(Self: Approx): Approx; extensionmethod;
+begin
+  result := Self ** 0.5;
+end;
+
+begin
+  var x1 := new Approx(100, 1.1);
+  var y1 := new Approx(50, 1.2);
+  var x2 := new Approx(200, 2.2);
+  var y2 := new Approx(100, 2.3);
+  println(((x1 - x2) ** 2 + (y1 - y2) ** 2).Sqrt);
+end.