//[Fact]
public void Atan2Benchmark()
{
var deltas = new List <decimal>();
var swf = new Stopwatch();
var swd = new Stopwatch();
foreach (var y in m_testCases)
{
foreach (var x in m_testCases)
{
for (int k = 0; k < 1000; ++k)
{
var yf = (Fix64)y;
var xf = (Fix64)x;
swf.Start();
var actualF = MathFix.Atan2(yf, xf);
swf.Stop();
swd.Start();
var expected = Math.Atan2((double)yf, (double)xf);
swd.Stop();
deltas.Add(Math.Abs((decimal)actualF - (decimal)expected));
}
}
}
Console.WriteLine("Max error: {0} ({1} times precision)", deltas.Max(), deltas.Max() / Fix64.Precision);
Console.WriteLine("Average precision: {0} ({1} times precision)", deltas.Average(), deltas.Average() / Fix64.Precision);
Console.WriteLine("Fix64.Atan2 time = {0}ms, Math.Atan2 time = {1}ms", swf.ElapsedMilliseconds, swd.ElapsedMilliseconds);
}
public void Atan()
{
var maxDelta = 0.00000001m;
var deltas = new List <decimal>();
Assert.Equal(Fix64.Zero, MathFix.Atan(Fix64.Zero));
// Precision
for (var x = -1.0; x < 1.0; x += 0.0001)
{
var xf = (Fix64)x;
var actual = (decimal)MathFix.Atan(xf);
var expected = (decimal)Math.Atan((double)xf);
var delta = Math.Abs(actual - expected);
deltas.Add(delta);
Assert.True(delta <= maxDelta, string.Format("Precision: Atan({0}): expected {1} but got {2}", xf, expected, actual));
}
// Scalability and edge cases
foreach (var x in m_testCases)
{
var xf = (Fix64)x;
var actual = (decimal)MathFix.Atan(xf);
var expected = (decimal)Math.Atan((double)xf);
var delta = Math.Abs(actual - expected);
deltas.Add(delta);
Assert.True(delta <= maxDelta, string.Format("Scalability: Atan({0}): expected {1} but got {2}", xf, expected, actual));
}
Console.WriteLine("Max error: {0} ({1} times precision)", deltas.Max(), deltas.Max() / Fix64.Precision);
Console.WriteLine("Average precision: {0} ({1} times precision)", deltas.Average(), deltas.Average() / Fix64.Precision);
}
public void Pow()
{
for (int i = 0; i < m_testCases.Length; ++i)
{
var b = Fix64.FromRaw(m_testCases[i]);
for (int j = 0; j < m_testCases.Length; ++j)
{
var e = Fix64.FromRaw(m_testCases[j]);
if (b == Fix64.Zero && e < Fix64.Zero)
{
Assert.Throws <DivideByZeroException>(() => MathFix.Pow(b, e));
}
else if (b < Fix64.Zero && e != Fix64.Zero)
{
Assert.Throws <ArgumentOutOfRangeException>(() => MathFix.Pow(b, e));
}
else
{
var expected = e == Fix64.Zero ? 1 : b == Fix64.Zero ? 0 : Math.Min(Math.Pow((double)b, (double)e), (double)Fix64.MaxValue);
// Absolute precision deteriorates with large result values, take this into account
// Similarly, large exponents reduce precision, even if result is small.
double maxDelta = Math.Abs((double)e) > 100000000 ? 0.5 : expected > 100000000 ? 10 : expected > 1000 ? 0.5 : 0.00001;
var actual = (double)MathFix.Pow(b, e);
var delta = Math.Abs(expected - actual);
Assert.True(delta <= maxDelta, string.Format("Pow({0}, {1}) = expected {2} but got {3}", b, e, expected, actual));
}
}
}
}
public void Tan()
{
Assert.True(MathFix.Tan(Fix64.Zero) == Fix64.Zero);
Assert.True(MathFix.Tan(MathFix.PI) == Fix64.Zero);
Assert.True(MathFix.Tan(-MathFix.PI) == Fix64.Zero);
Assert.True(MathFix.Tan(MathFix.PIOver2 - (Fix64)0.001) > Fix64.Zero);
Assert.True(MathFix.Tan(MathFix.PIOver2 + (Fix64)0.001) < Fix64.Zero);
Assert.True(MathFix.Tan(-MathFix.PIOver2 - (Fix64)0.001) > Fix64.Zero);
Assert.True(MathFix.Tan(-MathFix.PIOver2 + (Fix64)0.001) < Fix64.Zero);
for (double angle = 0; /*-2 * Math.PI;*/ angle <= 2 * Math.PI; angle += 0.0001)
{
var f = (Fix64)angle;
var actualF = MathFix.Tan(f);
var expected = (decimal)Math.Tan(angle);
Assert.Equal(actualF > Fix64.Zero, expected > 0);
//TODO figure out a real way to test this function
}
//foreach (var val in m_testCases) {
// var f = (Fix64)val;
// var actualF = Fix64.Tan(f);
// var expected = (decimal)Math.Tan((double)f);
// var delta = Math.Abs(expected - (decimal)actualF);
// Assert.True(delta <= 0.01, string.Format("Tan({0}): expected {1} but got {2}", f, expected, actualF));
//}
}
public void Cos()
{
Assert.True(MathFix.Cos(Fix64.Zero) == Fix64.One);
Assert.True(MathFix.Cos(MathFix.PIOver2) == Fix64.Zero);
Assert.True(MathFix.Cos(MathFix.PI) == -Fix64.One);
Assert.True(MathFix.Cos(MathFix.PI + MathFix.PIOver2) == Fix64.Zero);
Assert.True(MathFix.Cos(MathFix.PITimes2) == Fix64.One);
Assert.True(MathFix.Cos(-MathFix.PIOver2) == -Fix64.Zero);
Assert.True(MathFix.Cos(-MathFix.PI) == -Fix64.One);
Assert.True(MathFix.Cos(-MathFix.PI - MathFix.PIOver2) == Fix64.Zero);
Assert.True(MathFix.Cos(-MathFix.PITimes2) == Fix64.One);
for (double angle = -2 * Math.PI; angle <= 2 * Math.PI; angle += 0.0001)
{
var f = (Fix64)angle;
var actualF = MathFix.Cos(f);
var expected = (decimal)Math.Cos(angle);
var delta = Math.Abs(expected - (decimal)actualF);
Assert.True(delta <= 3 * Fix64.Precision, string.Format("Cos({0}): expected {1} but got {2}", angle, expected, actualF));
}
foreach (var val in m_testCases)
{
var f = Fix64.FromRaw(val);
var actualF = MathFix.Cos(f);
var expected = (decimal)Math.Cos((double)f);
var delta = Math.Abs(expected - (decimal)actualF);
Assert.True(delta <= 0.0000001M, string.Format("Cos({0}): expected {1} but got {2}", f, expected, actualF));
}
}
public void Floor()
{
var sources = new[] { -5.1m, -1, 0, 1, 5.1m };
var expecteds = new[] { -6m, -1, 0, 1, 5m };
for (int i = 0; i < sources.Length; ++i)
{
var actual = (decimal)MathFix.Floor((Fix64)sources[i]);
var expected = expecteds[i];
Assert.Equal(expected, actual);
}
}
public void Sign()
{
var sources = new[] { Fix64.MinValue, (Fix64)(-1), Fix64.Zero, Fix64.One, Fix64.MaxValue };
var expecteds = new[] { -1, -1, 0, 1, 1 };
for (int i = 0; i < sources.Length; ++i)
{
var actual = MathFix.Sign(sources[i]);
var expected = expecteds[i];
Assert.Equal(expected, actual);
}
}
public void Round()
{
var sources = new[] { -5.5m, -5.1m, -4.5m, -4.4m, -1, 0, 1, 4.5m, 4.6m, 5.4m, 5.5m };
var expecteds = new[] { -6m, -5m, -4m, -4m, -1, 0, 1, 4m, 5m, 5m, 6m };
for (int i = 0; i < sources.Length; ++i)
{
var actual = (decimal)MathFix.Round((Fix64)sources[i]);
var expected = expecteds[i];
Assert.Equal(expected, actual);
}
Assert.Equal(Fix64.MaxValue, MathFix.Round(Fix64.MaxValue));
}
public void FastAbs()
{
Assert.Equal(Fix64.MinValue, MathFix.FastAbs(Fix64.MinValue));
var sources = new[] { -1, 0, 1, int.MaxValue };
var expecteds = new[] { 1, 0, 1, int.MaxValue };
for (int i = 0; i < sources.Length; ++i)
{
var actual = MathFix.FastAbs((Fix64)sources[i]);
var expected = (Fix64)expecteds[i];
Assert.Equal(expected, actual);
}
}
public void Ceiling()
{
var sources = new[] { -5.1m, -1, 0, 1, 5.1m };
var expecteds = new[] { -5m, -1, 0, 1, 6m };
for (int i = 0; i < sources.Length; ++i)
{
var actual = (decimal)MathFix.Ceiling((Fix64)sources[i]);
var expected = expecteds[i];
Assert.Equal(expected, actual);
}
Assert.Equal(Fix64.MaxValue, MathFix.Ceiling(Fix64.MaxValue));
}
public void Pow2()
{
double maxDelta = 0.0000001;
for (int i = 0; i < m_testCases.Length; ++i)
{
var e = Fix64.FromRaw(m_testCases[i]);
var expected = Math.Min(Math.Pow(2, (double)e), (double)Fix64.MaxValue);
var actual = (double)MathFix.Pow2(e);
var delta = Math.Abs(expected - actual);
Assert.True(delta <= maxDelta, string.Format("Pow2({0}) = expected {1} but got {2}", e, expected, actual));
}
}
public void Sqrt()
{
for (int i = 0; i < m_testCases.Length; ++i)
{
var f = Fix64.FromRaw(m_testCases[i]);
if (MathFix.Sign(f) < 0)
{
Assert.Throws <ArgumentOutOfRangeException>(() => MathFix.Sqrt(f));
}
else
{
var expected = Math.Sqrt((double)f);
var actual = (double)MathFix.Sqrt(f);
var delta = (decimal)Math.Abs(expected - actual);
Assert.True(delta <= Fix64.Precision);
}
}
}
public void Atan2()
{
var deltas = new List <decimal>();
// Identities
Assert.Equal(MathFix.Atan2(Fix64.Zero, -Fix64.One), MathFix.PI);
Assert.Equal(MathFix.Atan2(Fix64.Zero, Fix64.Zero), Fix64.Zero);
Assert.Equal(MathFix.Atan2(Fix64.Zero, Fix64.One), Fix64.Zero);
Assert.Equal(MathFix.Atan2(Fix64.One, Fix64.Zero), MathFix.PIOver2);
Assert.Equal(MathFix.Atan2(-Fix64.One, Fix64.Zero), -MathFix.PIOver2);
// Precision
for (var y = -1.0; y < 1.0; y += 0.01)
{
for (var x = -1.0; x < 1.0; x += 0.01)
{
var yf = (Fix64)y;
var xf = (Fix64)x;
var actual = MathFix.Atan2(yf, xf);
var expected = (decimal)Math.Atan2((double)yf, (double)xf);
var delta = Math.Abs((decimal)actual - expected);
deltas.Add(delta);
Assert.True(delta <= 0.005M, string.Format("Precision: Atan2({0}, {1}): expected {2} but got {3}", yf, xf, expected, actual));
}
}
// Scalability and edge cases
foreach (var y in m_testCases)
{
foreach (var x in m_testCases)
{
var yf = (Fix64)y;
var xf = (Fix64)x;
var actual = (decimal)MathFix.Atan2(yf, xf);
var expected = (decimal)Math.Atan2((double)yf, (double)xf);
var delta = Math.Abs(actual - expected);
deltas.Add(delta);
Assert.True(delta <= 0.005M, string.Format("Scalability: Atan2({0}, {1}): expected {2} but got {3}", yf, xf, expected, actual));
}
}
Console.WriteLine("Max error: {0} ({1} times precision)", deltas.Max(), deltas.Max() / Fix64.Precision);
Console.WriteLine("Average precision: {0} ({1} times precision)", deltas.Average(), deltas.Average() / Fix64.Precision);
}
public void FastCos()
{
for (double angle = -2 * Math.PI; angle <= 2 * Math.PI; angle += 0.0001)
{
var f = (Fix64)angle;
var actualF = MathFix.FastCos(f);
var expected = (decimal)Math.Cos(angle);
var delta = Math.Abs(expected - (decimal)actualF);
Assert.True(delta <= 50000 * Fix64.Precision, string.Format("Cos({0}): expected {1} but got {2}", angle, expected, actualF));
}
foreach (var val in m_testCases)
{
var f = Fix64.FromRaw(val);
var actualF = MathFix.FastCos(f);
var expected = (decimal)Math.Cos((double)f);
var delta = Math.Abs(expected - (decimal)actualF);
Assert.True(delta <= 0.01M, string.Format("Cos({0}): expected {1} but got {2}", f, expected, actualF));
}
}
public void Acos()
{
var maxDelta = 0.00000001m;
var deltas = new List <decimal>();
Assert.Equal(Fix64.Zero, MathFix.Acos(Fix64.One));
Assert.Equal(MathFix.PIOver2, MathFix.Acos(Fix64.Zero));
Assert.Equal(MathFix.PI, MathFix.Acos(-Fix64.One));
// Precision
for (var x = -1.0; x < 1.0; x += 0.001)
{
var xf = (Fix64)x;
var actual = (decimal)MathFix.Acos(xf);
var expected = (decimal)Math.Acos((double)xf);
var delta = Math.Abs(actual - expected);
deltas.Add(delta);
Assert.True(delta <= maxDelta, string.Format("Precision: Acos({0}): expected {1} but got {2}", xf, expected, actual));
}
for (int i = 0; i < m_testCases.Length; ++i)
{
var b = Fix64.FromRaw(m_testCases[i]);
if (b < -Fix64.One || b > Fix64.One)
{
Assert.Throws <ArgumentOutOfRangeException>(() => MathFix.Acos(b));
}
else
{
var expected = (decimal)Math.Acos((double)b);
var actual = (decimal)MathFix.Acos(b);
var delta = Math.Abs(expected - actual);
deltas.Add(delta);
Assert.True(delta <= maxDelta, string.Format("Acos({0}) = expected {1} but got {2}", b, expected, actual));
}
}
Console.WriteLine("Max error: {0} ({1} times precision)", deltas.Max(), deltas.Max() / Fix64.Precision);
Console.WriteLine("Average precision: {0} ({1} times precision)", deltas.Average(), deltas.Average() / Fix64.Precision);
}
public void Ln()
{
double maxDelta = 0.00000001;
for (int j = 0; j < m_testCases.Length; ++j)
{
var b = Fix64.FromRaw(m_testCases[j]);
if (b <= Fix64.Zero)
{
Assert.Throws <ArgumentOutOfRangeException>(() => MathFix.Log(b));
}
else
{
var expected = Math.Log((double)b);
var actual = (double)MathFix.Log(b);
var delta = Math.Abs(expected - actual);
Assert.True(delta <= maxDelta, string.Format("Ln({0}) = expected {1} but got {2}", b, expected, actual));
}
}
}