// This function is not well-tested. It may be wildly inaccurate.
/// <summary>
/// Returns the tangent of the specified angle.
/// </summary>
/// <param name="x">An angle, measured in radians.</param>
/// <returns></returns>
public static Fix64 Tan(Fix64 x)
{
var clampedPi = x.RawValue % _PI;
var flip = false;
if (clampedPi < 0)
{
clampedPi = -clampedPi;
flip = true;
}
if (clampedPi > PI_OVER_2)
{
flip = !flip;
clampedPi = PI_OVER_2 - (clampedPi - PI_OVER_2);
}
var clamped = new Fix64(clampedPi);
// Find the two closest values in the LUT and perform linear interpolation
var rawIndex = Fix64.FastMultiply(clamped, LutInterval);
var roundedIndex = Round(rawIndex);
var indexError = Fix64.FastSubtract(rawIndex, roundedIndex);
var nearestValue = new Fix64(TanLut[(int)roundedIndex]);
var secondNearestValue = new Fix64(TanLut[(int)roundedIndex + Sign(indexError)]);
var delta = Fix64.FastMultiply(indexError, FastAbs(Fix64.FastSubtract(nearestValue, secondNearestValue))).RawValue;
var interpolatedValue = nearestValue.RawValue + delta;
var finalValue = flip ? -interpolatedValue : interpolatedValue;
return(new Fix64(finalValue));
}
// 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));
}