public static void Main(string[] args)
{
// BigInteger a = 1432604672;
// BigInteger b = 245760;
// BigInteger a = 935;
// BigInteger b = 714;
BigInteger a = 1889826700059L;
BigInteger b = 421872857844L;
Console.WriteLine("{0} / {1} = {2}", a, b, BinaryDivide(a, b));
Console.WriteLine("GCD({0}, {1}) = {2}", a, b, ModuloArithmetic.SlowGcd((long)a, (long)b));
Console.WriteLine("GCD({0}, {1}) = {2}", a, b, HalfBinaryGcd(a, b, 20));
}
public static (BigInteger, BigInteger[, ]) HalfBinaryGcd(BigInteger a, BigInteger b, int k)
{
if (Nu(b) > k)
{
return(0, new BigInteger[, ] {
{ 1, 0 }, { 0, 1 }
});
}
var k1 = k >> 1;
var a1 = a % BigInteger.Pow(Two, 2 * k1 + 1); // TODO refact
var b1 = b % BigInteger.Pow(Two, 2 * k1 + 1);
var(j1, R) = HalfBinaryGcd(a1, b1, k1);
var at = BigInteger.Pow(Two, -2 * (int)j1) * (R[0, 0] * a + R[0, 1] * b);
var bt = BigInteger.Pow(Two, -2 * (int)j1) * (R[1, 0] * a + R[1, 1] * b);
var j0 = Nu(bt);
if (j0 + j1 > k)
{
return(j1, R);
}
var(q, r) = BinaryDivide(at, bt);
var k2 = k - (j0 + j1);
var a2 = ModuloArithmetic.Divide(bt, BigInteger.One << j0, BigInteger.One << 2 * (int)k2 + 1);
var b2 = ModuloArithmetic.Divide(r, BigInteger.One << j0, BigInteger.One << 2 * (int)k2 + 1);
var(j2, S) = HalfBinaryGcd(a2, b2, (int)k2);
return(j1 + j0 + j2,
MatrixArithmetic.Product(
MatrixArithmetic.Product(S,
new BigInteger[, ] {
{ 0, BigInteger.One << j0 }, { BigInteger.One << j0, q }
}),
R)
);
}
public static (BigInteger, BigInteger) BinaryDivide(BigInteger a, BigInteger b)
{
int j = Nu(b) - Nu(a);
if (j <= 0)
{
throw new ArgumentException("ν(b) > ν(a) is not true");
}
var bt = b >> j; // Math.Pow(2, -j) * b
var twoToTheJPlusOne = BigInteger.One << (j + 1);
var q = BigInteger.Remainder(ModuloArithmetic.Negate(a, twoToTheJPlusOne) * ModuloArithmetic.Invert(bt, twoToTheJPlusOne), twoToTheJPlusOne);
if (q >= twoToTheJPlusOne >> 1)
{
q -= twoToTheJPlusOne;
}
var r = a + q * (b >> j);
return(q, r);
}