/// <summary>
/// Compute the square root of self to a given scale, Using Newton's
/// algorithm. x >= 0.
/// </summary>
/// <param name="scale">
/// the desired <c>scale</c> of the result. (where the <c>scale</c> is
/// the number of digits to the right of the decimal point.
/// </param>
/// <returns>
/// the result value
/// </returns>
/// <exception cref="ArgumentException">
/// if <c>scale</c> is <= 0.
/// </exception>
/// <exception cref="ArgumentException">
/// if <c>self</c> is < 0.
/// </exception>
public static DecimalX Sqrt(this DecimalX x, int scale)
{
// Check that scale > 0.
if (scale <= 0)
{
throw new ArgumentException(SqrtScaleInvalid);
}
// Check that x >= 0.
if (x.Signum() < 0)
{
throw new ArgumentException(NegativeSquareRoot);
}
if (x.Signum() == 0)
{
return(new DecimalX(x.ToIntegerX(), -scale));
}
// n = x*(10^(2*scale))
var n = x.MovePointRight(scale << 1).ToIntegerX();
// The first approximation is the upper half of n.
var bits = (int)(n.BitLength() + 1) >> 1;
var ix = n.RightShift(bits);
IntegerX ixPrev = 0;
// Loop until the approximations converge
// (two successive approximations are equal after rounding).
while (ix.CompareTo(ixPrev) != 0)
{
ixPrev = ix;
// x = (x + n/x)/2
ix = ix.Add(n.Divide(ix)).RightShift(1);
}
return(new DecimalX(ix, -scale));
}
public bool RoundingNeeded(IntegerX bi) => true;
