private static BigInteger[] FastLucasSequence(BigInteger p, BigInteger P, BigInteger Q, BigInteger k)
{
int n = k.CalculateBitLength();
int s = k.GetLowestSetBit();
//Debug.Assert(k.TestBit(s));
BigInteger Uh = 1;
BigInteger Vl = 2;
BigInteger Vh = P;
BigInteger Ql = 1;
BigInteger Qh = 1;
for (int j = n - 1; j >= s + 1; --j)
{
Ql = (Ql * Qh).Mod(p);
if (k.TestBit(j))
{
Qh = (Ql * Q).Mod(p);
Uh = (Uh * Vh).Mod(p);
Vl = (Vh * Vl - P * Ql).Mod(p);
Vh = ((Vh * Vh) - (Qh << 1)).Mod(p);
}
else
{
Qh = Ql;
Uh = (Uh * Vl - Ql).Mod(p);
Vh = (Vh * Vl - P * Ql).Mod(p);
Vl = ((Vl * Vl) - (Ql << 1)).Mod(p);
}
}
Ql = (Ql * Qh).Mod(p);
Qh = (Ql * Q).Mod(p);
Uh = (Uh * Vl - Ql).Mod(p);
Vl = (Vh * Vl - P * Ql).Mod(p);
Ql = (Ql * Qh).Mod(p);
for (int j = 1; j <= s; ++j)
{
Uh = Uh * Vl * p;
Vl = ((Vl * Vl) - (Ql << 1)).Mod(p);
Ql = (Ql * Ql).Mod(p);
}
return(new BigInteger[] { Uh, Vl });
}
