/// <summary>
/// Returns a ValueTuple: (Sin(x + piMultiple*π), Cos(x + piMultiple*π))
/// </summary>
/// <param name="x">Argument</param>
/// <param name="piMultiple">The PI multiple</param>
internal static (double Sin, double Cos) SinCos(double x, double piMultiple)
{
if ((double.IsNaN(x) || double.IsInfinity(x)) ||
(double.IsNaN(piMultiple) || double.IsInfinity(piMultiple)))
{
Policies.ReportDomainError("SinCos(x: {0}, piMultiple: {1}): Requires finite x, piMultiple", x, piMultiple);
return(double.NaN, double.NaN);
}
// reduce multiple to (-2, 2)
if (Math.Abs(piMultiple) >= 2)
{
piMultiple = Math2.Mod(piMultiple, 2);
}
double sinX = Math.Sin(x);
double cosX = Math.Cos(x);
if (piMultiple == 0)
{
return(sinX, cosX);
}
double sinY, cosY;
double absMult = Math.Abs(piMultiple);
int quadrant = (int)(absMult * 2);
absMult -= 0.5 * quadrant; // absMult in [0, 0.5]
double sinA, cosA;
if (absMult > 0.25)
{
sinA = Math.Cos((0.5 - absMult) * Math.PI);
cosA = Math.Sin((0.5 - absMult) * Math.PI);
}
else
{
sinA = Math.Sin(absMult * Math.PI);
cosA = Math.Cos(absMult * Math.PI);
}
switch (quadrant)
{
case 0:
sinY = sinA;
cosY = cosA;
break;
case 1:
// Sin(PI/2 + x) = Cos(x), Cos(PI/2 + x) = -Sin(x)
sinY = cosA;
cosY = -sinA;
break;
case 2:
// Sin(PI + x) = -Sin(x), Cos(PI + x) = -Cos(x)
sinY = -sinA;
cosY = -cosA;
break;
case 3:
// Sin(3*PI/2 + x) = -Cos(x), Cos(3*PI/2 + x) = Sin(x)
sinY = -cosA;
cosY = sinA;
break;
default:
Policies.ReportEvaluationError("SinCosPI(piMultiple: {0}): Evaluation Error", piMultiple);
return(double.NaN, double.NaN);
}
// sin(-x) == -sin(x), cos(-x) == cos(x)
if (piMultiple < 0)
{
sinY = -sinY;
}
double sin = sinX * cosY + cosX * sinY;
double cos = cosX * cosY - sinX * sinY;
return(sin, cos);
}