/// <summary>
/// Computes the cosine of the given value to full significance over the full range of arguments.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of sin(x).</returns>
/// <remarks>
/// <para>For an explanaition of this method, see the remarks for the <see cref="MoreMath.Sin"/> method.</para>
/// </remarks>
public static double Cos(double x)
{
// Ensure x is non-negative; this is easy because cosine is an even function.
if (x < 0.0)
{
x = -x;
}
if (x < 1.0)
{
// If x is small enough not to cross a zero, use the built-in function
return(Math.Cos(x));
}
else if (x < RangeReduction.xLimit)
{
// If x is in the intermediate region, try the built-in function but switch to our range-reduction
// algorithm if the result is too small.
double y = Math.Cos(x);
double ym = x / RangeReduction.xLimit;
if (Math.Abs(y) < ym)
{
return(RangeReduction.Cos(x));
}
else
{
return(y);
}
}
else
{
// If x is beyond the range of the built-in function eintirely, use our range-reduction algorithm
return(RangeReduction.Cos(x));
}
}
internal static double CosPi(double x)
{
long y0;
double y1;
RangeReduction.ReduceByOnes(2.0 * x, out y0, out y1);
return(RangeReduction.Cos(y0, y1));
}
/// <summary>
/// Computes the cosine of the given multiple of π.
/// </summary>
/// <param name="x">The argument.</param>
/// <returns>The value of cos(<paramref name="x"/>π).</returns>
/// <remarks>
/// <para>For an explanation of why and when to use this function,
/// see <see cref="SinPi(double)"/>.</para>
/// </remarks>
/// <seealso cref="SinPi(double)"/>
public static double CosPi(double x)
{
RangeReduction.ReduceByOnes(2.0 * x, out long y0, out double y1);
return(RangeReduction.Cos(y0, y1));
}