/**
* 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;
}