public BigComplex Sqrt(MathContext mc)
{
BigDecimal half = new BigDecimal(2);
/* compute l=sqrt(re^2+im^2), then u=sqrt((l+re)/2)
* and v= +- sqrt((l-re)/2 as the new real and imaginary parts.
*/
BigDecimal l = Abs(mc);
if (l.CompareTo(BigDecimal.Zero) == 0)
{
return(new BigComplex(BigMath.ScalePrecision(BigDecimal.Zero, mc),
BigMath.ScalePrecision(BigDecimal.Zero, mc)));
}
BigDecimal u = BigMath.Sqrt(l.Add(Real).Divide(half, mc), mc);
BigDecimal v = BigMath.Sqrt(l.Subtract(Real).Divide(half, mc), mc);
if (Imaginary.CompareTo(BigDecimal.Zero) >= 0)
{
return(new BigComplex(u, v));
}
else
{
return(new BigComplex(u, v.Negate()));
}
}
public BigDecimal ToBigDecimal(MathContext mc)
{
/* numerator and denominator individually rephrased
*/
var n = new BigDecimal(Numerator);
var d = new BigDecimal(Denominator);
/* the problem with n.divide(d,mc) is that the apparent precision might be
* smaller than what is set by mc if the value has a precise truncated representation.
* 1/4 will appear as 0.25, independent of mc
*/
return(BigMath.ScalePrecision(n.Divide(d, mc), mc));
}