/* sqrt(a+ib) = sqrt(a+sqrt(a*a-n*b*b)/2)+ib/(2*sqrt(a+sqrt(a*a-n*b*b)/2)) */
/* returns true if this is QR */
public bool Sqrt()
{
if (IsZilch())
{
return(true);
}
FP2 wa = new FP2(a);
FP2 ws = new FP2(b);
FP2 wt = new FP2(a);
if (ws.IsZilch())
{
if (wt.Sqrt())
{
a.Copy(wt);
b.Zero();
}
else
{
wt.Div_Ip();
wt.Sqrt();
b.Copy(wt);
a.Zero();
}
return(true);
}
ws.Sqr();
wa.Sqr();
ws.Mul_Ip();
ws.Norm();
wa.Sub(ws);
ws.Copy(wa);
if (!ws.Sqrt())
{
return(false);
}
wa.Copy(wt);
wa.Add(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
wa.Copy(wt);
wa.Sub(ws);
wa.Norm();
wa.Div2();
if (!wa.Sqrt())
{
return(false);
}
}
wt.Copy(b);
ws.Copy(wa);
ws.Add(wa);
ws.Inverse();
wt.Mul(ws);
a.Copy(wa);
b.Copy(wt);
return(true);
}
/* test this==0 ? */
public bool IsZilch()
{
//reduce();
return(a.IsZilch() && b.IsZilch());
}