public void ComparePowIntAndMathSqrtInAccuracy()
{
var pi6PowInt = DoubleArithmetic.PowInt(Math.PI, 6);
var oneHalfTo4PowInt = DoubleArithmetic.PowInt(0.5, 4);
var piSquaredPowInt = DoubleArithmetic.PowInt(Math.PI, 2);
var pi6 = DoubleArithmetic.Pow6(Math.PI);
var pi6Math = Math.Pow(Math.PI, 6.0);
var oneHalfTo4Math = Math.Pow(0.5, 4.0);
var piSquaredMath = Math.Pow(Math.PI, 2.0);
const double oneHalfTo4 = 1.0 / 16.0;
const double piSquared = Constants.PISquared;
double[] powIntErrors =
{
DoubleArithmetic.RelativeError(pi6, pi6PowInt),
DoubleArithmetic.RelativeError(oneHalfTo4, oneHalfTo4PowInt),
DoubleArithmetic.RelativeError(piSquared, piSquaredPowInt)
};
double[] mathErrors =
{
DoubleArithmetic.RelativeError(pi6, pi6Math),
DoubleArithmetic.RelativeError(oneHalfTo4, oneHalfTo4Math),
DoubleArithmetic.RelativeError(piSquared, piSquaredMath)
};
for (var i = 0; i < powIntErrors.Length; i++)
{
Assert.IsTrue(mathErrors[i] >= powIntErrors[i]);
}
}
public void ComparePowIntAndMathSqrtInSpeed()
{
Math.PI.Pow(6);
var sw = Stopwatch.StartNew();
for (var i = 0; i < 250000; i++)
{
DoubleArithmetic.PowInt(Math.PI, 6);
}
sw.Stop();
var arth = sw.ElapsedMilliseconds;
sw.Restart();
for (var i = 0; i < 250000; i++)
{
Math.Pow(Math.PI, 6.0);
}
sw.Stop();
var math = sw.ElapsedMilliseconds;
Assert.IsTrue(math > arth);
}
public void ComparePowIntAndNaiveInSpeed()
{
DoubleArithmetic.Pow(Math.PI, 6);
var sw = Stopwatch.StartNew();
for (var i = 0; i < 250000; i++)
{
DoubleArithmetic.PowInt(Math.PI, 6);
}
sw.Stop();
var arth = sw.ElapsedMilliseconds;
sw.Restart();
for (var i = 0; i < 250000; i++)
{
NaivePower(Math.PI, 6);
}
sw.Stop();
var naive = sw.ElapsedMilliseconds;
Assert.IsTrue(naive > arth);
}
public void TestPowIntCorrectnessAndConsistency()
{
var pi6 = DoubleArithmetic.PowInt(Math.PI, 6);
var pi18 = DoubleArithmetic.PowInt(Math.PI, 18);
var pi17 = DoubleArithmetic.PowInt(Math.PI, 17);
var oneHalfTo4 = DoubleArithmetic.PowInt(0.5, 4);
var e218 = DoubleArithmetic.PowInt(Math.E, 218);
var piToMinus2 = DoubleArithmetic.PowInt(Math.PI, -2);
var pi6Expected = DoubleArithmetic.Pow6(Math.PI);
Assert.AreEqual(32.0, DoubleArithmetic.PowInt(2.0, 5));
Assert.AreEqual(81.0, DoubleArithmetic.PowInt(3.0, 4));
Assert.AreEqual(pi6Expected, pi6, 1e-12, "on pi ^ 6, delta = {0}", Math.Abs(pi6 - pi6Expected));
Assert.AreEqual(pi18, pi17 * Math.PI, 1e-6, "on pi^18=p^17/pi, delta = {0}", Math.Abs(pi18 - pi17 * Math.PI));
Assert.AreEqual(1.0 / 16.0, oneHalfTo4, 0, "on 0.5^4=1/16, delta = {0}", Math.Abs(1.0 / 16.0 - oneHalfTo4));
Assert.AreEqual(218.0, Math.Log(e218), 0, "on ln(e^218)=218, delta = {0}", Math.Abs(218.0 - Math.Log(e218)));
Assert.AreEqual(1.0 / Constants.PISquared, piToMinus2, 1e-16, "on 1/(pi^2), delta = {0}",
Math.Abs(1.0 / Constants.PISquared - piToMinus2));
}
/// <summary>
/// x * 2 ^ n
/// </summary>
/// <param name="x"></param>
/// <param name="n"></param>
/// <returns></returns>
public static double TimesTwoTo(double x, int n)
{
return(x * DoubleArithmetic.PowInt(2.0, n));
}