private static DD SlowPow(DD x, int exp)
{
if (exp == 0)
{
return(DD.ValueOf(1.0));
}
int 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 *= x;
}
if (exp < 0)
{
return(pow.Reciprocal());
}
return(pow);
}
/// <summary>
/// This routine simply tests for robustness of the toString function.
/// </summary>
static void WriteRepeatedSqr(DD xdd)
{
if (xdd.GreaterOrEqualThan(DD.ValueOf(1)))
{
throw new ArgumentException("Argument must be < 1");
}
int count = 0;
while (xdd.ToDoubleValue() > 1e-300)
{
count++;
double x = xdd.ToDoubleValue();
var xSqr = xdd.Sqr();
string s = xSqr.ToString();
// System.Console.WriteLine(count + ": " + s);
var xSqr2 = DD.Parse(s);
xdd = xSqr;
}
}
public void TestParse()
{
CheckParse("1.05e10", 1.05E10, 1e-32);
CheckParse("-1.05e10", -1.05E10, 1e-32);
CheckParse("1.05e-10", DD.ValueOf(105d).Divide(
DD.ValueOf(100d)).Divide(DD.ValueOf(1.0E10)), 1e-32);
CheckParse("-1.05e-10", DD.ValueOf(105d).Divide(
DD.ValueOf(100d)).Divide(DD.ValueOf(1.0E10))
.Negate(), 1e-32);
/**
* The Java double-precision constant 1.4 gives rise to a value which
* differs from the exact binary representation down around the 17th decimal
* place. Thus it will not compare exactly to the DoubleDouble
* representation of the same number. To avoid this, compute the expected
* value using full DD precision.
*/
CheckParse("1.4",
DD.ValueOf(14).Divide(DD.ValueOf(10)), 1e-30);
// 39.5D can be converted to an exact FP representation
CheckParse("39.5", 39.5, 1e-30);
CheckParse("-39.5", -39.5, 1e-30);
}
public void TestWriteStandardNotation()
{
// standard cases
CheckStandardNotation(1.0, "1.0");
CheckStandardNotation(0.0, "0.0");
// cases where hi is a power of 10 and lo is negative
CheckStandardNotation(DD.ValueOf(1e12) - DD.ValueOf(1), "999999999999.0");
CheckStandardNotation(DD.ValueOf(1e14) - DD.ValueOf(1), "99999999999999.0");
CheckStandardNotation(DD.ValueOf(1e16) - DD.ValueOf(1), "9999999999999999.0");
var num8Dec = DD.ValueOf(-379363639) / DD.ValueOf(100000000);
CheckStandardNotation(num8Dec, "-3.79363639");
CheckStandardNotation(new DD(-3.79363639, 8.039137357367426E-17),
"-3.7936363900000000000000000");
CheckStandardNotation(DD.ValueOf(34) / DD.ValueOf(1000), "0.034");
CheckStandardNotation(1.05e3, "1050.0");
CheckStandardNotation(0.34, "0.34000000000000002442490654175344");
CheckStandardNotation(DD.ValueOf(34) / DD.ValueOf(100), "0.34");
CheckStandardNotation(14, "14.0");
}
/// <summary>
///
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <param name="p"></param>
/// <returns></returns>
public static bool IsInCircleDDNormalized(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
var adx = DD.ValueOf(a.X) - p.X;
var ady = DD.ValueOf(a.Y) - p.Y;
var bdx = DD.ValueOf(b.X) - p.X;
var bdy = DD.ValueOf(b.Y) - p.Y;
var cdx = DD.ValueOf(c.X) - p.X;
var cdy = DD.ValueOf(c.Y) - p.Y;
var abdet = adx * bdy - bdx * ady;
var bcdet = bdx * cdy - cdx * bdy;
var cadet = cdx * ady - adx * cdy;
var alift = adx * adx + ady * ady;
var blift = bdx * bdx + bdy * bdy;
var clift = cdx * cdx + cdy * cdy;
var sum = alift * bcdet + blift * cadet + clift * abdet;
bool isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
/// <summary>
/// Tests if a point is inside the circle defined by the points a, b, c.
/// The computation uses <see cref="DD"/> arithmetic for robustness.
/// </summary>
/// <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><c>true</c> if this point is inside the circle defined by the points a, b, c</returns>
public static bool IsInCircleDD3(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
var adx = DD.ValueOf(a.X) - (p.X);
var ady = DD.ValueOf(a.Y) - (p.Y);
var bdx = DD.ValueOf(b.X) - (p.X);
var bdy = DD.ValueOf(b.Y) - (p.Y);
var cdx = DD.ValueOf(c.X) - (p.X);
var cdy = DD.ValueOf(c.Y) - (p.Y);
var abdet = adx * bdy - (bdx * ady);
var bcdet = bdx * cdy - (cdx * bdy);
var cadet = cdx * ady - (adx * cdy);
var alift = adx * adx - (ady * ady);
var blift = bdx * bdx - (bdy * bdy);
var clift = cdx * cdx - (cdy * cdy);
var sum = alift * bcdet + blift * cadet + clift * abdet;
bool isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
private static void CheckSciNotation(double x, string expectedStr)
{
CheckSciNotation(DD.ValueOf(x), expectedStr);
}
public void testRepeatedSqr()
{
WriteRepeatedSqr(DD.ValueOf(.9));
WriteRepeatedSqr(DD.PI.Divide(DD.ValueOf(10)));
}
public void TestRepeatedSqrt()
{
WriteRepeatedSqrt(DD.ValueOf(1.0));
WriteRepeatedSqrt(DD.ValueOf(.999999999999));
WriteRepeatedSqrt(DD.PI.Divide(DD.ValueOf(10)));
}
public void TestNaN()
{
Assert.IsTrue(DD.IsNaN(DD.ValueOf(1).Divide(DD.ValueOf(0))));
Assert.IsTrue(DD.IsNaN(DD.ValueOf(1).Multiply(DD.NaN)));
}
public void TestNaN()
{
Assert.IsTrue(DD.IsNaN(DD.ValueOf(1) / DD.ValueOf(0)));
Assert.IsTrue(DD.IsNaN(DD.ValueOf(1) * DD.NaN));
}
private void CheckDeterminant(double x1, double y1, double x2, double y2, double expected, double errBound)
{
var det = DD.Determinant(x1, y1, x2, y2);
CheckErrorBound("Determinant", det, DD.ValueOf(expected), errBound);
}
private static void CheckStandardNotation(double x, String expectedStr)
{
CheckStandardNotation(DD.ValueOf(x), expectedStr);
}
public void TestWriteRepeatedSqr()
{
WriteRepeatedSqr(DD.ValueOf(0.9));
WriteRepeatedSqr(DD.PI / DD.ValueOf(10));
}
private static DD ToDDAlt(double x)
{
// convert more accurately to DD from decimal representation
// very slow though - should be a better way
return(DD.ValueOf(x + ""));
}
