/* return this^e mod Modulus
* public FP pow(BIG e)
* {
* int bt;
* FP r=new FP(1);
* e.norm();
* x.norm();
* FP m=new FP(this);
* while (true)
* {
* bt=e.parity();
* e.fshr(1);
* if (bt==1) r.mul(m);
* if (e.iszilch()) break;
* m.sqr();
* }
* r.x.mod(p);
* return r;
* } */
/* return sqrt(this) mod Modulus */
public FP Sqrt()
{
Reduce();
BIG b = new BIG(ROM.Modulus);
if (MOD8 == 5)
{
b.Dec(5);
b.Norm();
b.Shr(3);
FP i = new FP(this);
i.x.Shl(1);
FP v = i.Pow(b);
i.Mul(v);
i.Mul(v);
i.x.Dec(1);
FP r = new FP(this);
r.Mul(v);
r.Mul(i);
r.Reduce();
return(r);
}
else
{
b.Inc(1);
b.Norm();
b.Shr(2);
return(Pow(b));
}
}
/* return this/c */
public virtual BIG Div(BIG c)
{
int d, k = 0;
DBIG m = new DBIG(c);
DBIG dr = new DBIG(0);
BIG r = new BIG(0);
BIG a = new BIG(0);
BIG e = new BIG(1);
Norm();
while (Comp(this, m) >= 0)
{
e.FShl(1);
m.Shl(1);
k++;
}
while (k > 0)
{
m.Shr(1);
e.Shr(1);
dr.Copy(this);
dr.Sub(m);
dr.Norm();
d = (int)(1 - ((dr.w[BIG.DNLEN - 1] >> (BIG.CHUNK - 1)) & 1));
CMove(dr, d);
r.Copy(a);
r.Add(e);
r.Norm();
a.CMove(r, d);
k--;
}
return(a);
}