public static FixedPoint Atan2(FixedPoint y, FixedPoint x)
{
if (y.Equals(FixedPoint.Zero) && x.Equals(FixedPoint.Zero))
{
return(FixedPoint.Zero);
}
var coefficient1 = FixedPoint.Pi / FixedPoint.Four;
var coefficient2 = FixedPoint.Three * coefficient1;
var absY = Abs(y) + FixedPoint.Kludge; // + 1e-10 // kludge to prevent 0/0 condition
FixedPoint angle;
if (x >= FixedPoint.Zero)
{
var r = (x - absY) / (x + absY);
angle = coefficient1 - coefficient1 * r;
}
else
{
var r = (x + absY) / (absY - x);
angle = coefficient2 - coefficient1 * r;
}
if (y < FixedPoint.Zero)
{
return(angle * FixedPoint.NegativeOne); // negate if in quad III or IV
}
return(angle);
}
public static FixedPoint Round(FixedPoint fp)
{
var integer = fp.Value >> FixedPoint.Q;
var remainder = fp.Value - (integer << FixedPoint.Q);
return(remainder >= FixedPoint.Half.Value
? FixedPoint.FromExplicit((integer + 1) << FixedPoint.Q)
: FixedPoint.FromExplicit(integer << FixedPoint.Q));
}
public static FixedPoint Ceiling(FixedPoint fp)
{
var integer = fp.Value >> FixedPoint.Q;
var remainder = fp.Value - (integer << FixedPoint.Q);
return(remainder > 0
? FixedPoint.FromExplicit((integer + 1) << FixedPoint.Q)
: FixedPoint.FromExplicit(integer << FixedPoint.Q));
}
public static FixedPoint Abs(FixedPoint fp)
{
if (fp >= FixedPoint.Zero)
{
return(fp);
}
return(fp * FixedPoint.NegativeOne);
}
public static FixedPoint Atan(FixedPoint fp)
{
if (!ProcessedTableService.Instance.AtanData.ContainsKey(fp.Value))
{
return(FixedPoint.NaN);
}
return(ProcessedTableService.Instance.AtanData[fp.Value]);
}
public static FixedPoint Sign(FixedPoint fp)
{
if (fp.Equals(FixedPoint.Zero))
{
return(FixedPoint.Zero);
}
return(fp > FixedPoint.Zero ? FixedPoint.One : FixedPoint.NegativeOne);
}
public static FixedPoint Acos(FixedPoint fp)
{
var data = ProcessedTableService.Instance.AcosData;
if (!data.ContainsKey(fp.Value))
{
return(FixedPoint.NaN);
}
return(data[fp.Value]);
}
public FixedPointVector2 NormalizeWithClampedMagnitude(FixedPoint clamp)
{
var magnitude = MathFixedPoint.ClampMagnitude(this, clamp);
if (magnitude > FixedPoint.Zero)
{
return(this / magnitude);
}
return(this);
}
public static FixedPoint Tanh(FixedPoint fp)
{
var sinh = Sinh(fp);
var cosh = Cosh(fp);
if (sinh.Equals(FixedPoint.Zero) || cosh.Equals(FixedPoint.Zero))
{
return(FixedPoint.Zero);
}
return(sinh / cosh);
}
static FixedPoint TrigonometricLookup(FixedPoint fp, IReadOnlyDictionary <FixedPoint, FixedPoint> data)
{
var value = Round(Abs(fp) / FixedPoint.Pi * TrigonometricSteps);
var flip = (Floor(value / TrigonometricSteps) % FixedPoint.Two).Equals(FixedPoint.Zero);
var result = flip
? data[value % TrigonometricSteps]
: data[value % TrigonometricSteps] * FixedPoint.NegativeOne;
return(result);
}
public static FixedPoint Tan(FixedPoint fp)
{
var sin = Sin(fp);
var cos = Cos(fp);
if (sin.Equals(FixedPoint.Zero) || cos.Equals(FixedPoint.Zero))
{
return(FixedPoint.Zero);
}
return(sin / cos);
}
public static FixedPoint Sqrt2(FixedPoint fp)
{
var estimate = fp / FixedPoint.Two + FixedPoint.One;
var n1 = (estimate + fp / estimate) / FixedPoint.Two;
while (n1 < estimate)
{
estimate = n1;
n1 = (estimate + fp / estimate) / FixedPoint.Two;
}
return(estimate);
}
static FixedPoint HyperbolicLookup
(FixedPoint fp, IReadOnlyDictionary <FixedPoint, FixedPoint> data, FixedPoint nanIfLessThan)
{
if (fp < nanIfLessThan)
{
return(FixedPoint.NaN);
}
if (fp > FixedPoint.Zero && fp < HyperbolicMediumResolution)
{
return(data[RoundToNearestStep(fp, HyperbolicHighResolutionStep)]);
}
if (fp >= HyperbolicMediumResolution && fp < HyperbolicLowResolution)
{
return(data[RoundToNearestStep(fp, HyperbolicMediumResolutionStep)]);
}
return(data[RoundToNearestStep(fp, HyperbolicLowResolutionStep)]);
}
public static FixedPoint Sqrt(FixedPoint fp)
{
var data = ProcessedTableService.Instance.SqrtData;
if (fp < FixedPoint.Zero)
{
return(FixedPoint.NaN);
}
if (fp > FixedPoint.Zero && fp < SqrtMediumResolution)
{
return(data[RoundToNearestStep(fp, SqrtHighResolutionStep)]);
}
if (fp >= SqrtMediumResolution && fp < SqrtLowResolution)
{
return(data[RoundToNearestStep(fp, SqrtMediumResolutionStep)]);
}
return(data[RoundToNearestStep(fp, SqrtLowResolutionStep)]);
}
public FixedPointVector2 CloneWithReplacedX(FixedPoint x)
{
return(new FixedPointVector2(x, Y));
}
public static FixedPoint Cos(FixedPoint fp)
{
return(TrigonometricLookup(fp, ProcessedTableService.Instance.CosData));
}
public static FixedPoint Cosh(FixedPoint fp)
{
return(HyperbolicLookup(Abs(fp), ProcessedTableService.Instance.CoshData, FixedPoint.Zero));
}
public static FixedPoint Asinh(FixedPoint fp)
{
return(HyperbolicLookup(fp, ProcessedTableService.Instance.AsinhData, FixedPoint.One));
}
public static FixedPoint Sin(FixedPoint fp)
{
return(TrigonometricLookup(fp, ProcessedTableService.Instance.SinData) * Sign(fp));
}
public static FixedPointVector2 From(int x, int y)
{
return(new FixedPointVector2(FixedPoint.From(x), FixedPoint.From(y)));
}
public static FixedPointVector2 Interpolate(FixedPointVector2 v1, FixedPointVector2 v2, FixedPoint time)
{
return(new FixedPointVector2(v1.X * (FixedPoint.One - time) + v2.X * time
, v1.Y * (FixedPoint.One - time) + v2.Y * time));
}
public static FixedPoint Min(FixedPoint a, FixedPoint b)
{
return(a < b ? a : b);
}
public static FixedPoint Sinh(FixedPoint fp)
{
return(HyperbolicLookup(Abs(fp), ProcessedTableService.Instance.SinhData, FixedPoint.Zero) * Sign(fp));
}
public FixedPointVector2 CloneWithReplacedY(FixedPoint y)
{
return(new FixedPointVector2(X, y));
}
public void Deconstruct(out float x, out float y)
{
x = FixedPoint.ConvertToFloat(X);
y = FixedPoint.ConvertToFloat(Y);
}
public static FixedPoint Max(FixedPoint a, FixedPoint b)
{
return(a >= b ? a : b);
}
public static FixedPointVector2 From(FixedPoint x, FixedPoint y)
{
return(new FixedPointVector2(x, y));
}
public static FixedPoint Floor(FixedPoint fp)
{
return(FixedPoint.FromExplicit((fp.Value >> FixedPoint.Q) << FixedPoint.Q));
}
FixedPointVector2(FixedPoint x, FixedPoint y)
{
X = x;
Y = y;
}
public static FixedPoint RoundToNearestStep(FixedPoint fp, FixedPoint step)
{
var floored = Floor(fp / step) * step;
return(fp - floored > step / FixedPoint.Half ? floored + step : floored);
}