public void FloatPriorTest()
{
// edges
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatPrior(double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatPrior(double.PositiveInfinity));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatPrior(double.NegativeInfinity));
Assert.AreEqual(double.NegativeInfinity, Math2.FloatPrior(double.MinValue));
Assert.AreEqual(-double.Epsilon, Math2.FloatPrior(-0.0), 1); // -0.0, double.Epsilon
foreach (var item in _FloatData)
{
// swap result and x
if (item.Distance != 1)
{
continue;
}
double x = item.Result;
double expected = item.X;
double actual = Math2.FloatPrior(x);
Assert2.AreNear(expected, actual, 0,
() => { return(string.Format("FloatPrior({0:E16}) = {1:E16}; got {2:E16}; ulps = {3}", x, expected, actual, 0)); });
}
}
public void EvalTestOneArray()
{
double[] b0Values = { 0.0, 1.0 };
double[][] bValues =
{
new double[] { },
new double[] { 2.0 },
new double[] {2.0, 2.0 },
new double[] {2.0, 2.0, 2.0 },
new double[] {2.0, 2.0, 2.0, 2.0 }
};
foreach (double b0 in b0Values)
{
for (int i = 0; i < b0Values.Length; i++)
{
double[] b = bValues[i];
TestFraction1 f = _Fractions1[i];
double result = ContinuedFraction.Eval(b0, 1.0, b);
double expected = f.EquivalentFunction(b0, b);
Assert2.AreNear(expected, result, 2);
}
}
}
public void EvaluatePolynomial2Test()
{
double[][] c = new double[][] {
new double[] { 1.0 },
new double[] { 0.0, 1.0 },
new double[] { 0.0, 0.0, 1.0 },
new double[] { 0.0, 0.0, 0.0, 1.0 },
new double[] { 0.0, 0.0, 0.0, 0.0, 1.0 },
new double[] { 1.0, 1.0, 1.0, 1.0, 1.0 },
};
Random rnd = new Random();
for (int i = 0; i < 100; i++)
{
double x = rnd.NextDouble();
double y = rnd.NextDouble();
double a0 = 1;
double a1 = x;
double a2 = x * x;
double a3 = x * x * x;
double a4 = x * x * x * x;
double a5 = 1.0 + x + x * x + x * x * x + x * x * x * x;
double expected = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5))));
double result = Polynomial.Eval(c, x, y);
Assert2.AreNear(expected, result, 2,
() => $"Polynomial.Eval(c, x, y) = {result}; Expected: {expected}");
}
}
public void EvalTestInfinite()
{
double expected, actual;
expected = 1.0 / (Math.Sqrt(Math.E) - 1.0);
// actual = ContinuedFraction.Eval(1.0, Series1(),tolerance,100);
actual = ContinuedFraction.Eval(1.0, Series1());
Assert2.AreNear(expected, actual, 10);
expected = 1.0 / (Math.E - 1.0);
// actual = ContinuedFraction.Eval(0.0, Series2(),tolerance,100);
actual = ContinuedFraction.Eval(0.0, Series2());
Assert2.AreNear(expected, actual, 10);
}
public void EvalTestInfiniteF()
{
double expected, actual;
Series1Function f1 = new Series1Function();
expected = 1.0 / (Math.Sqrt(Math.E) - 1.0);
// actual = ContinuedFraction.Eval(1.0, Series1(),tolerance,100);
actual = ContinuedFraction.Eval(1.0, f1.Next);
Assert2.AreNear(expected, actual, 10);
Series2Function f2 = new Series2Function();
expected = 1.0 / (Math.E - 1.0);
// actual = ContinuedFraction.Eval(0.0, Series2(),tolerance,100);
actual = ContinuedFraction.Eval(0.0, f2.Next);
Assert2.AreNear(expected, actual, 10);
}
public void EvalTestTwoArray()
{
double[] b0Values = { 0.0, 1.0 };
Tuple <double[], double[]>[] abValues =
{
new Tuple <double[], double[]>(new double[] { },
new double[] { }),
new Tuple <double[], double[]>(new double[] { 1.0 },
new double[] { 2.0 }),
new Tuple <double[], double[]>(new double[] {1.0, 1.0 },
new double[] { 2.0, 2.0 }),
new Tuple <double[], double[]>(new double[] {1.0, 1.0, 1.0 },
new double[] { 2.0, 2.0, 2.0 }),
new Tuple <double[], double[]>(new double[] {1.0, 1.0, 1.0 },
new double[] { 2.0, 2.0, 2.0 }),
// infinite series would =1/(Sqrt(e)-1)
// Source:http://mathworld.wolfram.com/ContinuedFraction.html
new Tuple <double[], double[]>(new double[] {2.0, 4.0, 6.0, 8.0 },
new double[] { 3.0, 5.0, 7.0, 9.0 }),
// infinite series would =1/(e-1)
// Source: http://mathworld.wolfram.com/ContinuedFraction.html
new Tuple <double[], double[]>(new double[] {1.0, 2.0, 3.0, 4.0 },
new double[] { 1.0, 2.0, 3.0, 4.0 })
};
foreach (double b0 in b0Values)
{
foreach (var abValue in abValues)
{
double[] a = abValue.Item1;
double[] b = abValue.Item2;
Debug.Assert(a.Length == b.Length);
TestFraction2 f = _Fractions2[a.Length];
double result = ContinuedFraction.Eval(b0, a, b);
double expected = f.EquivalentFunction(b0, a, b);
Assert2.AreNear(expected, result, 2);
}
}
}
public void FloatAdvanceTest()
{
// test non-symettrical behaviors - NaN, -0.0, Infinity
for (int i = 1; i < 255; i++)
{
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.NaN, i));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.NaN, -i));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.PositiveInfinity, i));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.PositiveInfinity, -i));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.NegativeInfinity, i));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatAdvance(double.NegativeInfinity, -i));
Assert.AreEqual(double.PositiveInfinity, Math2.FloatAdvance(double.MaxValue, i));
Assert.AreEqual(double.NegativeInfinity, Math2.FloatAdvance(double.MinValue, -i));
Assert.AreEqual(double.Epsilon * (double)i, Math2.FloatAdvance(-0.0, i)); // -0.0, double.Epsilon
Assert.AreEqual(-double.Epsilon * (double)i, Math2.FloatAdvance(-0.0, -i)); // -0.0, -double.Epsilon
}
foreach (var item in _FloatData)
{
double x = item.X;
int distance = item.Distance;
double expected = item.Result;
double actual = Math2.FloatAdvance(x, distance);
Assert2.AreNear(expected, actual, 0,
() => { return(string.Format("FloatAdvance({0:E16},{1}) = {2:E16}; got = {3:E16}; ulps = {4}", x, distance, expected, actual, 0)); });
// check to see that the reverse is true
x = item.Result;
distance = -item.Distance;
expected = item.X;
actual = Math2.FloatAdvance(x, distance);
Assert2.AreNear(expected, actual, 0,
() => { return(string.Format("FloatAdvance({0:E16},{1}) = {2:E16}; got = {3:E16}; ulps = {4}", x, distance, expected, actual, 0)); });
}
}
public void FloatDistanceTest()
{
// test non-symettrical behaviors - NaN, -0.0, Infinity
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.PositiveInfinity, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NegativeInfinity, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.MaxValue, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.MinValue, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(0.0, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(-0.0, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.NaN));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.PositiveInfinity));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.NegativeInfinity));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.MaxValue));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, double.MinValue));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, 0.0));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NaN, -0.0));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.PositiveInfinity, double.MaxValue));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.MaxValue, double.PositiveInfinity));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.NegativeInfinity, double.MinValue));
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.FloatDistance(double.MinValue, double.NegativeInfinity));
Assert.AreEqual(1.0, Math2.FloatDistance(double.Epsilon, -0.0));
Assert.AreEqual(-1.0, Math2.FloatDistance(-double.Epsilon, -0.0));
Assert.AreEqual(-1.0, Math2.FloatDistance(-0.0, double.Epsilon));
Assert.AreEqual(1.0, Math2.FloatDistance(-0.0, -double.Epsilon));
// large distance
double ZeroToMax = (double)BitConverter.DoubleToInt64Bits(double.MaxValue);
double ZeroToMin = ZeroToMax + 1.0;
double MaxToMin = ZeroToMax + ZeroToMin;
Assert.AreEqual(ZeroToMax, Math2.FloatDistance(double.MaxValue, 0));
Assert.AreEqual(-ZeroToMax, Math2.FloatDistance(0, double.MaxValue));
Assert.AreEqual(-ZeroToMin, Math2.FloatDistance(double.MinValue, 0));
Assert.AreEqual(ZeroToMin, Math2.FloatDistance(0, double.MinValue));
Assert.AreEqual(MaxToMin, Math2.FloatDistance(double.MaxValue, double.MinValue));
Assert.AreEqual(-MaxToMin, Math2.FloatDistance(double.MinValue, double.MaxValue));
// now test symmetrical behavior
foreach (var item in _FloatData)
{
double x = item.X;
double y = item.Result;
double expected = item.Distance;
double actual = Math2.FloatDistance(y, x);
Assert2.AreNear(expected, actual, 0,
() => { return(string.Format("FloatDistance({0:E16},{1:E16}) = {2:E16}; got = {3:E16}; ulps = {4}", y, x, expected, actual, 0)); });
// Reverse parameters should yield negative answer
expected = -item.Distance;
actual = Math2.FloatDistance(x, y);
Assert2.AreNear(expected, actual, 0,
() => { return(string.Format("FloatDistance({0:E16},{1:E16}) = {2:E16}; got = {3:E16}; ulps = {4}", x, y, expected, actual, 0)); });
}
}
public void LdexpTest()
{
Assert.AreEqual(0.75 * Math.Pow(2, -1073), Math2.Ldexp(0.75, -1073));
const int MaxNormalExponent = 1023;
const int MinNormalExponent = -1022;
const int MinDenormExponent = -1074;
// NaN
int[] nValues = { -1, 0, 1, 2 };
foreach (int n in nValues)
{
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.Ldexp(double.NaN, n));
}
// edge values
double[] xValues = { double.PositiveInfinity, double.NegativeInfinity, 0 };
nValues = new int[] { -1, 0, 1, 2 };
foreach (double x in xValues)
{
foreach (int n in nValues)
{
Assert.AreEqual(Math2.Ldexp(x, n), x);
}
}
// overflow and underflow
Assert.AreEqual(0.0, Math2.Ldexp(1, MinDenormExponent - 1));
Assert.AreEqual(-0.0, Math2.Ldexp(-1, MinDenormExponent - 1));
Assert.AreEqual(double.PositiveInfinity, Math2.Ldexp(1, MaxNormalExponent + 1));
Assert.AreEqual(double.NegativeInfinity, Math2.Ldexp(-1, MaxNormalExponent + 1));
// normal powers of 2
for (int i = MinNormalExponent; i < MaxNormalExponent; i++)
{
double expected = Math.Pow(2, i);
double calculated = Math2.Ldexp(1, i);
Assert2.AreNear(expected, calculated, 2,
() => string.Format("Ldexp(1, {0}) = {1:E16}; got {2:E16}", i, expected, calculated));
expected = -expected;
calculated = Math2.Ldexp(-1, i);
Assert2.AreNear(expected, calculated, 2,
() => string.Format("Ldexp(-1, {0}) = {1:E16}; got {2:E16}", i, expected, calculated));
}
// denorm
for (int i = 0; i < 52; i++)
{
double expected = double.Epsilon * (1UL << i);
Assert.IsTrue(expected > 0);
int n = MinDenormExponent + i;
double calculated = Math2.Ldexp(1, n);
Assert2.AreNear(expected, calculated, 0,
() => string.Format("Ldexp(1, {0}) = {1:E16}; got {2:E16}", n, expected, calculated));
expected = -expected;
calculated = Math2.Ldexp(-1, n);
Assert2.AreNear(expected, calculated, 0,
() => string.Format("Ldexp(-1, {0}) = {1:E16}; got {2:E16}", n, expected, calculated));
}
// denorm
for (int i = 0; i < 52; i++)
{
double expected = double.Epsilon * (1UL << i);
Assert.IsTrue(expected > 0);
double calculated = Math2.Ldexp(double.Epsilon, i);
Assert2.AreNear(expected, calculated, 0,
() => string.Format("Ldexp(double.Epsilon, {0}) = {1:E16}; got {2:E16}", i, expected, calculated));
expected = -expected;
calculated = Math2.Ldexp(-double.Epsilon, i);
Assert2.AreNear(expected, calculated, 0,
() => string.Format("Ldexp(-double.Epsilon, {0}) = {1:E16}; got {2:E16}", i, expected, calculated));
}
foreach (var item in _LdexpData)
{
double x = item.X;
int n = item.N;
double expected = item.Result;
double computed = Math2.Ldexp(x, n);
Assert2.AreNear(expected, computed, 1);
}
}
public void FrexpTest()
{
const int MaxNormalExponent = 1023;
const int MinNormalExponent = -1022;
const int MinDenormExponent = -1074;
int exponent;
double mantissa;
// Zero
mantissa = Math2.Frexp(0.0, out exponent);
Assert.AreEqual(0, mantissa);
Assert.AreEqual(0, exponent);
// NaN
Assert2.AreEqual <Exceptions.DomainException>(double.NaN, () => Math2.Frexp(double.NaN, out exponent));
mantissa = Math2.Frexp(double.PositiveInfinity, out exponent);
Assert.AreEqual(double.PositiveInfinity, mantissa);
mantissa = Math2.Frexp(double.NegativeInfinity, out exponent);
Assert.AreEqual(double.NegativeInfinity, mantissa);
mantissa = Math2.Frexp(double.Epsilon, out exponent);
Assert.AreEqual(0.5, mantissa);
Assert.AreEqual(MinDenormExponent + 1, exponent);
mantissa = Math2.Frexp(double.MaxValue, out exponent);
// Assert.AreEqual(0.5, mantissa);
Assert.AreEqual(1024, exponent);
// check normal numbers -- powers of 2
for (int i = MinNormalExponent; i < MaxNormalExponent; i++)
{
double x = Math.Pow(2, i);
mantissa = Math2.Frexp(x, out exponent);
Assert2.AreNear(0.5, mantissa, 1);
Assert.AreEqual(i + 1, exponent);
x = -x;
mantissa = Math2.Frexp(x, out exponent);
Assert2.AreNear(-0.5, mantissa, 1);
Assert.AreEqual(i + 1, exponent);
}
// denorm
for (int i = 0; i < 52; i++)
{
double x = double.Epsilon * (double)(1UL << i);
Assert.IsTrue(x > 0);
mantissa = Math2.Frexp(x, out exponent);
Assert2.AreNear(0.5, mantissa, 0);
Assert.AreEqual(MinDenormExponent + 1 + i, exponent);
x = -x;
mantissa = Math2.Frexp(x, out exponent);
Assert2.AreNear(-0.5, mantissa, 0);
Assert.AreEqual(MinDenormExponent + 1 + i, exponent);
}
foreach (var item in _FrexpData)
{
double x = item.X;
double fraction = item.Fraction;
int exp = item.Exponent;
int computed_exponent;
double computed_fraction = Math2.Frexp(x, out computed_exponent);
Assert2.AreNear(fraction, computed_fraction, 1);
Assert.AreEqual(exp, computed_exponent);
}
}