private static IBigInteger[] FastLucasSequence(IBigInteger p, IBigInteger P, IBigInteger Q, IBigInteger k)
{
// TODO Research and apply "common-multiplicand multiplication here"
var n = k.BitLength;
var s = k.GetLowestSetBit();
Debug.Assert(k.TestBit(s));
var uh = BigInteger.One;
var vl = BigInteger.Two;
var vh = P;
var ql = BigInteger.One;
var qh = BigInteger.One;
for (var j = n - 1; j >= s + 1; --j)
{
ql = ql.Multiply(qh).Mod(p);
if (k.TestBit(j))
{
qh = ql.Multiply(Q).Mod(p);
uh = uh.Multiply(vh).Mod(p);
vl = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
vh = vh.Multiply(vh).Subtract(qh.ShiftLeft(1)).Mod(p);
}
else
{
qh = ql;
uh = uh.Multiply(vl).Subtract(ql).Mod(p);
vh = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
vl = vl.Multiply(vl).Subtract(ql.ShiftLeft(1)).Mod(p);
}
}
ql = ql.Multiply(qh).Mod(p);
qh = ql.Multiply(Q).Mod(p);
uh = uh.Multiply(vl).Subtract(ql).Mod(p);
vl = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
ql = ql.Multiply(qh).Mod(p);
for (var j = 1; j <= s; ++j)
{
uh = uh.Multiply(vl).Mod(p);
vl = vl.Multiply(vl).Subtract(ql.ShiftLeft(1)).Mod(p);
ql = ql.Multiply(ql).Mod(p);
}
return(new[] { uh, vl });
}
private static IBigInteger[] FastLucasSequence(IBigInteger p, IBigInteger P, IBigInteger Q, IBigInteger k)
{
// TODO Research and apply "common-multiplicand multiplication here"
var n = k.BitLength;
var s = k.GetLowestSetBit();
Debug.Assert(k.TestBit(s));
var uh = BigInteger.One;
var vl = BigInteger.Two;
var vh = P;
var ql = BigInteger.One;
var qh = BigInteger.One;
for (var j = n - 1; j >= s + 1; --j)
{
ql = ql.Multiply(qh).Mod(p);
if (k.TestBit(j))
{
qh = ql.Multiply(Q).Mod(p);
uh = uh.Multiply(vh).Mod(p);
vl = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
vh = vh.Multiply(vh).Subtract(qh.ShiftLeft(1)).Mod(p);
}
else
{
qh = ql;
uh = uh.Multiply(vl).Subtract(ql).Mod(p);
vh = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
vl = vl.Multiply(vl).Subtract(ql.ShiftLeft(1)).Mod(p);
}
}
ql = ql.Multiply(qh).Mod(p);
qh = ql.Multiply(Q).Mod(p);
uh = uh.Multiply(vl).Subtract(ql).Mod(p);
vl = vh.Multiply(vl).Subtract(P.Multiply(ql)).Mod(p);
ql = ql.Multiply(qh).Mod(p);
for (var j = 1; j <= s; ++j)
{
uh = uh.Multiply(vl).Mod(p);
vl = vl.Multiply(vl).Subtract(ql.ShiftLeft(1)).Mod(p);
ql = ql.Multiply(ql).Mod(p);
}
return new[] { uh, vl };
}