// The relative error is less than 1E-10 for x in [-2PI, 2PI], and less than 1E-7 in the worst case.
/// <summary>
/// Returns the sine of the specified angle.
/// </summary>
/// <param name="x">An angle, measured in radians.</param>
/// <returns></returns>
public static Fix64 Sin(Fix64 x)
{
var clampedL = ClampSinValue(x.RawValue, out var flipHorizontal, out var flipVertical);
var clamped = new Fix64(clampedL);
// Find the two closest values in the LUT and perform linear interpolation
// This is what kills the performance of this function on x86 - x64 is fine though
var rawIndex = Fix64.FastMultiply(clamped, LutInterval);
var roundedIndex = Round(rawIndex);
var indexError = Fix64.FastSubtract(rawIndex, roundedIndex);
var nearestValue = new Fix64(SinLut[flipHorizontal ?
SinLut.Length - 1 - (int)roundedIndex :
(int)roundedIndex]);
var secondNearestValue = new Fix64(SinLut[flipHorizontal ?
SinLut.Length - 1 - (int)roundedIndex - Sign(indexError) :
(int)roundedIndex + Sign(indexError)]);
var delta = Fix64.FastMultiply(indexError, FastAbs(Fix64.FastSubtract(nearestValue, secondNearestValue))).RawValue;
var interpolatedValue = nearestValue.RawValue + (flipHorizontal ? -delta : delta);
var finalValue = flipVertical ? -interpolatedValue : interpolatedValue;
return(new Fix64(finalValue));
}
// Returns the arctan of of the specified number, calculated using Euler series
// This function has at least 7 decimals of accuracy.
/// <summary>
/// Returns the angle whose tangent is the specified number.
/// </summary>
/// <param name="x">A number representing a tangent.</param>
/// <returns></returns>
public static Fix64 Atan(Fix64 x)
{
if (x.RawValue == 0)
{
return(Fix64.Zero);
}
// Force positive values for argument
// Atan(-z) = -Atan(z).
var neg = x.RawValue < 0;
if (neg)
{
x = -x;
}
Fix64 result;
var two = (Fix64)2;
var three = (Fix64)3;
bool invert = x > Fix64.One;
if (invert)
{
x = Fix64.One / x;
}
result = Fix64.One;
var term = Fix64.One;
var zSq = x * x;
var zSq2 = zSq * two;
var zSqPlusOne = zSq + Fix64.One;
var zSq12 = zSqPlusOne * two;
var dividend = zSq2;
var divisor = zSqPlusOne * three;
for (var i = 2; i < 30; ++i)
{
term *= dividend / divisor;
result += term;
dividend += zSq2;
divisor += zSq12;
if (term.RawValue == 0)
{
break;
}
}
result = result * x / zSqPlusOne;
if (invert)
{
result = PIOver2 - result;
}
if (neg)
{
result = -result;
}
return(result);
}
public static Fix64 Asinh(Fix64 x)
{
throw new NotImplementedException();
}
/// <summary>
/// Returns the hyperbolic tangent of the specified angle.
/// </summary>
/// <param name="value">An angle, measured in radians.</param>
/// <returns></returns>
public static Fix64 Tanh(Fix64 value)
{
throw new NotImplementedException();
}