// Install NuGet package: Sdcb.Arithmetic.Gmp
// Install NuGet package: Sdcb.Arithmetic.Gmp.runtime.win-x64(for windows)
Console.WriteLine(CalcPI().ToString());

GmpFloat CalcPI(int inputDigits = 1_000_000)
{
    const double DIGITS_PER_TERM = 14.1816474627254776555; // = log(53360^3) / log(10)
    int DIGITS = (int)Math.Max(inputDigits, Math.Ceiling(DIGITS_PER_TERM));
    uint PREC = (uint)(DIGITS * Math.Log2(10));
    int N = (int)(DIGITS / DIGITS_PER_TERM);
    GmpInteger A = GmpInteger.From(13591409);
    GmpInteger B = GmpInteger.From(545140134);
    GmpInteger C = GmpInteger.From(640320);
    GmpInteger D = GmpInteger.From(426880);
    GmpInteger E = GmpInteger.From(10005);
    GmpInteger E3_24 = C * C * C / 24;

    using PQT pqt = ComputePQT(0, N);

    GmpFloat pi = new GmpFloat(precision: PREC);
    // pi = D * sqrt((mpf_class)E) * PQT.Q;
    pi.Assign(GmpFloat.From(D, PREC) * GmpFloat.Sqrt((GmpFloat)E, PREC) * (GmpFloat)pqt.Q);
    // pi /= (A * PQT.Q + PQT.T);
    GmpFloat.DivideInplace(pi, pi, GmpFloat.From(A * pqt.Q + pqt.T, PREC));
    return pi;

    PQT ComputePQT(int n1, int n2)
    {
        int m;

        if (n1 + 1 == n2)
        {
            PQT res = new PQT();
            res.P = GmpInteger.From(2 * n2 - 1);
            GmpInteger.MultiplyInplace(res.P, res.P, 6 * n2 - 1);
            GmpInteger.MultiplyInplace(res.P, res.P, 6 * n2 - 5);

            GmpInteger q = GmpInteger.From(E3_24);
            GmpInteger.MultiplyInplace(q, q, n2);
            GmpInteger.MultiplyInplace(q, q, n2);
            GmpInteger.MultiplyInplace(q, q, n2);
            res.Q = q;

            GmpInteger t = GmpInteger.From(B);
            GmpInteger.MultiplyInplace(t, t, n2);
            GmpInteger.AddInplace(t, t, A);
            GmpInteger.MultiplyInplace(t, t, res.P);
            // res.T = (A + B * n2) * res.P;            
            if ((n2 & 1) == 1) GmpInteger.NegateInplace(t, t);
            res.T = t;

            return res;
        }
        else
        {
            m = (n1 + n2) / 2;
            PQT res1 = ComputePQT(n1, m);
            using PQT res2 = ComputePQT(m, n2);
            GmpInteger p = res1.P * res2.P;
            GmpInteger q = res1.Q * res2.Q;

            // t = res1.T * res2.Q + res1.P * res2.T
            GmpInteger.MultiplyInplace(res1.T, res1.T, res2.Q);
            GmpInteger.MultiplyInplace(res1.P, res1.P, res2.T);
            GmpInteger.AddInplace(res1.T, res1.T, res1.P);
            res1.P.Dispose();
            res1.Q.Dispose();
            return new PQT
            {
                P = p,
                Q = q,
                T = res1.T,
            };
        }
    }
}

public ref struct PQT
{
    public GmpInteger P;
    public GmpInteger Q;
    public GmpInteger T;

    public void Dispose()
    {
        P?.Dispose();
        Q?.Dispose();
        T?.Dispose();
    }
}