/** * Computes (a+b)^2 in two different ways and compares the result. * For correct results, a and b should be integers. * * @param a * @param b */ private static void CheckBinomialSquare(double a, double b) { // binomial square var add = new DD(a); var bdd = new DD(b); var aPlusb = add.Add(bdd); var abSq = aPlusb.Multiply(aPlusb); // System.out.println("(a+b)^2 = " + abSq); // expansion var a2DD = add.Multiply(add); var b2DD = bdd.Multiply(bdd); var ab = add.Multiply(bdd); var sum = b2DD.Add(ab).Add(ab); // System.out.println("2ab+b^2 = " + sum); var diff = abSq.Subtract(a2DD); // System.out.println("(a+b)^2 - a^2 = " + diff); var delta = diff.Subtract(sum); Console.WriteLine("\nA = " + a + ", B = " + b); Console.WriteLine("[DD] 2ab+b^2 = " + sum + " (a+b)^2 - a^2 = " + diff + " delta = " + delta); PrintBinomialSquareDouble(a, b); var isSame = diff.Equals(sum); Assert.IsTrue(isSame); var isDeltaZero = delta.IsZero; Assert.IsTrue(isDeltaZero); }
/** * This routine simply tests for robustness of the toString function. * * @param xdd */ private static void WriteRepeatedSqrt(DD xdd) { int count = 0; while (xdd.ToDoubleValue() > 1e-300) { count++; //if (count == 100) // count = count; double x = xdd.ToDoubleValue(); DD xSqrt = xdd.Sqrt(); String s = xSqrt.ToString(); // System.out.println(count + ": " + s); DD xSqrt2 = DD.Parse(s); DD xx = xSqrt2.Multiply(xSqrt2); double err = Math.Abs(xx.ToDoubleValue() - x); //assertTrue(err < 1e-10); xdd = xSqrt; // square roots converge on 1 - stop when very close DD distFrom1DD = xSqrt.Subtract(DD.ValueOf(1.0)); double distFrom1 = distFrom1DD.ToDoubleValue(); if (Math.Abs(distFrom1) < 1.0e-40) { break; } } }
private static void CheckAddMult2(DD dd) { DD sum = dd.Add(dd); DD prod = dd.Multiply(new DD(2.0)); CheckErrorBound("AddMult2", sum, prod, 0.0); }
private static void CheckBinomial2(double a, double b) { // binomial product var add = new DD(a); var bdd = new DD(b); var aPlusb = add.Add(bdd); var aSubb = add.Subtract(bdd); var abProd = aPlusb.Multiply(aSubb); // System.out.println("(a+b)^2 = " + abSq); // expansion var a2DD = add.Multiply(add); var b2DD = bdd.Multiply(bdd); // System.out.println("2ab+b^2 = " + sum); // this should equal b^2 var diff = abProd.Subtract(a2DD).Negate(); // System.out.println("(a+b)^2 - a^2 = " + diff); var delta = diff.Subtract(b2DD); Console.WriteLine("\nA = " + a + ", B = " + b); Console.WriteLine("[DD] (a+b)(a-b) = " + abProd + " -((a^2 - b^2) - a^2) = " + diff + " delta = " + delta); // printBinomialSquareDouble(a,b); var isSame = diff.Equals(b2DD); Assert.IsTrue(isSame); var isDeltaZero = delta.IsZero; Assert.IsTrue(isDeltaZero); }
public static bool IsInCircleDD( Coordinate a, Coordinate b, Coordinate c, Coordinate p) { var px = new DD(p.X); var py = new DD(p.Y); var ax = new DD(a.X); var ay = new DD(a.Y); var bx = new DD(b.X); var by = new DD(b.Y); var cx = new DD(c.X); var cy = new DD(c.Y); var aTerm = (ax.Multiply(ax).Add(ay.Multiply(ay))) .Multiply(TriAreaDD(bx, by, cx, cy, px, py)); var bTerm = (bx.Multiply(bx).Add(by.Multiply(by))) .Multiply(TriAreaDD(ax, ay, cx, cy, px, py)); var cTerm = (cx.Multiply(cx).Add(cy.Multiply(cy))) .Multiply(TriAreaDD(ax, ay, bx, by, px, py)); var pTerm = (px.Multiply(px).Add(py.Multiply(py))) .Multiply(TriAreaDD(ax, ay, bx, by, cx, cy)); var sum = aTerm.Subtract(bTerm).Add(cTerm).Subtract(pTerm); bool isInCircle = sum.ToDoubleValue() > 0; return(isInCircle); }
/// <summary> /// Tests if a point is inside the circle defined by /// the triangle with vertices a, b, c (oriented counter-clockwise). /// </summary> /// <remarks> /// The computation uses <see cref="DD"/> arithmetic for robustness. /// </remarks> /// <param name="a">A vertex of the triangle</param> /// <param name="b">A vertex of the triangle</param> /// <param name="c">A vertex of the triangle</param> /// <param name="p">The point to test</param> /// <returns>true if this point is inside the circle defined by the points a, b, c</returns> public static bool IsInCircleDDSlow( Coordinate a, Coordinate b, Coordinate c, Coordinate p) { DD px = DD.ValueOf(p.X); DD py = DD.ValueOf(p.Y); DD ax = DD.ValueOf(a.X); DD ay = DD.ValueOf(a.Y); DD bx = DD.ValueOf(b.X); DD by = DD.ValueOf(b.Y); DD cx = DD.ValueOf(c.X); DD cy = DD.ValueOf(c.Y); DD aTerm = (ax.Multiply(ax).Add(ay.Multiply(ay))) .Multiply(TriAreaDDSlow(bx, by, cx, cy, px, py)); DD bTerm = (bx.Multiply(bx).Add(by.Multiply(by))) .Multiply(TriAreaDDSlow(ax, ay, cx, cy, px, py)); DD cTerm = (cx.Multiply(cx).Add(cy.Multiply(cy))) .Multiply(TriAreaDDSlow(ax, ay, bx, by, px, py)); DD pTerm = (px.Multiply(px).Add(py.Multiply(py))) .Multiply(TriAreaDDSlow(ax, ay, bx, by, cx, cy)); DD sum = aTerm.Subtract(bTerm).Add(cTerm).Subtract(pTerm); bool isInCircle = sum.ToDoubleValue() > 0; return(isInCircle); }
private void CheckSqrt(DD x, double errBound) { DD sqrt = x.Sqrt(); DD x2 = sqrt.Multiply(sqrt); CheckErrorBound("Sqrt", x, x2, errBound); }
/// <summary> /// Computes the sign of the determinant of the 2x2 matrix /// with the given entries. /// </summary> /// <param name="x1"></param> /// <param name="y1"></param> /// <param name="x2"></param> /// <param name="y2"></param> /// <returns> /// <list type="Bullet"> /// <item>-1 if the determinant is negative,</item> /// <item>1 if the determinant is positive,</item> /// <item>0 if the determinant is 0.</item> /// </list> /// </returns> public static int SignOfDet2x2(DD x1, DD y1, DD x2, DD y2) { DD det = x1.Multiply(y2).Subtract(y1.Multiply(x2)); if (det.IsZero) return 0; if (det.IsNegative) return -1; return 1; }
/// <summary> /// Computes the sign of the determinant of the 2x2 matrix /// with the given entries. /// </summary> /// <param name="x1"></param> /// <param name="y1"></param> /// <param name="x2"></param> /// <param name="y2"></param> /// <returns> /// <list type="Bullet"> /// <item>-1 if the determinant is negative,</item> /// <item>1 if the determinant is positive,</item> /// <item>0 if the determinant is 0.</item> /// </list> /// </returns> public static int SignOfDet2x2(DD x1, DD y1, DD x2, DD y2) { DD det = x1.Multiply(y2).Subtract(y1.Multiply(x2)); if (det.IsZero) { return(0); } if (det.IsNegative) { return(-1); } return(1); }
private static DD SlowPow(DD x, int exp) { if (exp == 0) { return(DD.ValueOf(1.0)); } var n = Math.Abs(exp); // MD - could use binary exponentiation for better precision & speed var pow = new DD(x); for (int i = 1; i < n; i++) { pow = pow.Multiply(x); } if (exp < 0) { return(pow.Reciprocal()); } return(pow); }
public double RunDoubleDouble(int nIter) { var sw = new Stopwatch(); sw.Start(); for (int i = 0; i < nIter; i++) { var a = new DD(9.0); var factor = new DD(10.0); var aMul = factor.Multiply(a); var aDiv = a.Divide(factor); var det = a.Multiply(a) .Subtract(aMul.Multiply(aDiv)); // Console.WriteLine(aDiv); // Console.WriteLine(det); } sw.Stop(); Console.WriteLine("DD: nIter = " + nIter + " time = " + sw.ElapsedMilliseconds); return(sw.ElapsedMilliseconds / (double)nIter); }
public static bool IsInCircleDD( Coordinate a, Coordinate b, Coordinate c, Coordinate p) { DD px = new DD(p.X); DD py = new DD(p.Y); DD ax = new DD(a.X); DD ay = new DD(a.Y); DD bx = new DD(b.X); DD by = new DD(b.Y); DD cx = new DD(c.X); DD cy = new DD(c.Y); DD aTerm = (ax.Multiply(ax).Add(ay.Multiply(ay))) .Multiply(TriAreaDD(bx, by, cx, cy, px, py)); DD bTerm = (bx.Multiply(bx).Add(by.Multiply(by))) .Multiply(TriAreaDD(ax, ay, cx, cy, px, py)); DD cTerm = (cx.Multiply(cx).Add(cy.Multiply(cy))) .Multiply(TriAreaDD(ax, ay, bx, by, px, py)); DD pTerm = (px.Multiply(px).Add(py.Multiply(py))) .Multiply(TriAreaDD(ax, ay, bx, by, cx, cy)); DD sum = aTerm.Subtract(bTerm).Add(cTerm).Subtract(pTerm); var isInCircle = sum.ToDoubleValue() > 0; return isInCircle; }
private static void CheckAddMult2(DD dd) { DD sum = dd.Add(dd); DD prod = dd.Multiply(new DD(2.0)); CheckErrorBound("AddMult2", sum, prod, 0.0); }
private static void CheckMultiplyDivide(DD a, DD b, double errBound) { DD a2 = a.Multiply(b).Divide(b); CheckErrorBound("MultiplyDivide", a, a2, errBound); }
private static void CheckMultiplyDivide(DD a, DD b, double errBound) { DD a2 = a.Multiply(b).Divide(b); CheckErrorBound("MultiplyDivide", a, a2, errBound); }
/** * Computes (a+b)^2 in two different ways and compares the result. * For correct results, a and b should be integers. * * @param a * @param b */ private static void CheckBinomialSquare(double a, double b) { // binomial square var add = new DD(a); var bdd = new DD(b); var aPlusb = add.Add(bdd); var abSq = aPlusb.Multiply(aPlusb); // System.out.println("(a+b)^2 = " + abSq); // expansion var a2DD = add.Multiply(add); var b2DD = bdd.Multiply(bdd); var ab = add.Multiply(bdd); var sum = b2DD.Add(ab).Add(ab); // System.out.println("2ab+b^2 = " + sum); var diff = abSq.Subtract(a2DD); // System.out.println("(a+b)^2 - a^2 = " + diff); var delta = diff.Subtract(sum); Console.WriteLine("\nA = " + a + ", B = " + b); Console.WriteLine("[DD] 2ab+b^2 = " + sum + " (a+b)^2 - a^2 = " + diff + " delta = " + delta); PrintBinomialSquareDouble(a, b); var isSame = diff.Equals(sum); Assert.IsTrue(isSame); var isDeltaZero = delta.IsZero; Assert.IsTrue(isDeltaZero); }
private static void CheckBinomial2(double a, double b) { // binomial product var add = new DD(a); var bdd = new DD(b); var aPlusb = add.Add(bdd); var aSubb = add.Subtract(bdd); var abProd = aPlusb.Multiply(aSubb); // System.out.println("(a+b)^2 = " + abSq); // expansion var a2DD = add.Multiply(add); var b2DD = bdd.Multiply(bdd); // System.out.println("2ab+b^2 = " + sum); // this should equal b^2 var diff = abProd.Subtract(a2DD).Negate(); // System.out.println("(a+b)^2 - a^2 = " + diff); var delta = diff.Subtract(b2DD); Console.WriteLine("\nA = " + a + ", B = " + b); Console.WriteLine("[DD] (a+b)(a-b) = " + abProd + " -((a^2 - b^2) - a^2) = " + diff + " delta = " + delta); // printBinomialSquareDouble(a,b); var isSame = diff.Equals(b2DD); Assert.IsTrue(isSame); var isDeltaZero = delta.IsZero; Assert.IsTrue(isDeltaZero); }
public double RunDoubleDouble(int nIter) { Stopwatch sw = new Stopwatch(); sw.Start(); for (int i = 0; i < nIter; i++) { DD a = new DD(9.0); DD factor = new DD(10.0); DD aMul = factor.Multiply(a); DD aDiv = a.Divide(factor); DD det = a.Multiply(a) .Subtract(aMul.Multiply(aDiv)); // Console.WriteLine(aDiv); // Console.WriteLine(det); } sw.Stop(); Console.WriteLine("DD: nIter = " + nIter + " time = " + sw.ElapsedMilliseconds); return sw.ElapsedMilliseconds/(double) nIter; }
private static DD SlowPow(DD x, int exp) { if (exp == 0) return DD.ValueOf(1.0); var n = Math.Abs(exp); // MD - could use binary exponentiation for better precision & speed var pow = new DD(x); for (int i = 1; i < n; i++) { pow = pow.Multiply(x); } if (exp < 0) { return pow.Reciprocal(); } return pow; }