Task: Metallic ratios



C#: using static System.Math;
using static System.Console;
using BI = System.Numerics.BigInteger;
 
class Program {
 
    static BI IntSqRoot(BI v, BI res) { 
        BI term = 0, d = 0, dl = 1; while (dl != d) { term = v / res; res = (res + term) >> 1;
            dl = d; d = term - res; } return term; }
 
    static string doOne(int b, int digs) { 
        int s = b * b + 4; BI g = (BI)(Sqrt((double)s) * Pow(10, ++digs)),
            bs = IntSqRoot(s * BI.Parse('1' + new string('0', digs << 1)), g);
        bs += b * BI.Parse('1' + new string('0', digs));
        bs >>= 1; bs += 4; string st = bs.ToString();
        return string.Format("{0}.{1}", st[0], st.Substring(1, --digs)); }
 
    static string divIt(BI a, BI b, int digs) { 
        int al = a.ToString().Length, bl = b.ToString().Length;
        a *= BI.Pow(10, ++digs << 1); b *= BI.Pow(10, digs);
        string s = (a / b + 5).ToString(); return s[0] + "." + s.Substring(1, --digs); }
 
    
    static string joined(BI[] x) { int[] wids = {1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13};
        string res = ""; for (int i = 0; i < x.Length; i++) res += 
            string.Format("{0," + (-wids[i]).ToString() + "} ", x[i]); return res; }
 
    static void Main(string[] args) { 
        WriteLine("Metal B Sq.Rt Iters /---- 32 decimal place value ----\\  Matches Sq.Rt Calc");
        int k; string lt, t = ""; BI n, nm1, on; for (int b = 0; b < 10; b++) {
            BI[] lst = new BI[15]; lst[0] = lst[1] = 1;
            for (int i = 2; i < 15; i++) lst[i] = b * lst[i - 1] + lst[i - 2];
            
            n = lst[14]; nm1 = lst[13]; k = 0; for (int j = 13; k == 0; j++) {
                lt = t; if (lt == (t = divIt(n, nm1, 32))) k = b == 0 ? 1 : j;
                on = n; n = b * n + nm1; nm1 = on; }
            WriteLine("{0,4}  {1}   {2,2}    {3, 2}  {4}  {5}\n{6,19} {7}", "Pt Au Ag CuSn Cu Ni Al Fe Sn Pb"
                .Split(' ')[b], b, b * b + 4, k, t, t == doOne(b, 32), "", joined(lst)); }
        
        n = nm1 =1; k = 0; for (int j = 1; k == 0; j++) {
            lt = t; if (lt == (t = divIt(n, nm1, 256))) k = j;
                on = n; n += nm1; nm1 = on; }
        WriteLine("\nAu to 256 digits:"); WriteLine(t);
        WriteLine("Iteration count: {0}  Matched Sq.Rt Calc: {1}", k, t == doOne(1, 256)); }
}






VB: Imports BI = System.Numerics.BigInteger

Module Module1

    Function IntSqRoot(v As BI, res As BI) As BI
        REM res is the initial guess
        Dim term As BI = 0
        Dim d As BI = 0
        Dim dl As BI = 1
        While dl <> d
            term = v / res
            res = (res + term) >> 1
            dl = d
            d = term - res
        End While
        Return term
    End Function

    Function DoOne(b As Integer, digs As Integer) As String
        REM calculates result via square root, not iterations
        Dim s = b * b + 4
        digs += 1
        Dim g As BI = Math.Sqrt(s * Math.Pow(10, digs))
        Dim bs = IntSqRoot(s * BI.Parse("1" + New String("0", digs << 1)), g)
        bs += b * BI.Parse("1" + New String("0", digs))
        bs >>= 1
        bs += 4
        Dim st = bs.ToString
        digs -= 1
        Return String.Format("{0}.{1}", st(0), st.Substring(1, digs))
    End Function

    Function DivIt(a As BI, b As BI, digs As Integer) As String
        REM performs division
        Dim al = a.ToString.Length
        Dim bl = b.ToString.Length
        digs += 1
        a *= BI.Pow(10, digs << 1)
        b *= BI.Pow(10, digs)
        Dim s = (a / b + 5).ToString
        digs -= 1
        Return s(0) + "." + s.Substring(1, digs)
    End Function

    REM custom formatting
    Function Joined(x() As BI) As String
        Dim wids() = {1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
        Dim res = ""
        For i = 0 To x.Length - 1
            res += String.Format("{0," + (-wids(i)).ToString + "} ", x(i))
        Next
        Return res
    End Function

    Sub Main()
        REM calculates and checks each "metal"
        Console.WriteLine("Metal B Sq.Rt Iters /---- 32 decimal place value ----\\  Matches Sq.Rt Calc")
        Dim t = ""
        Dim n As BI
        Dim nm1 As BI
        Dim k As Integer
        Dim j As Integer
        For b = 0 To 9
            Dim lst(14) As BI
            lst(0) = 1
            lst(1) = 1
            For i = 2 To 14
                lst(i) = b * lst(i - 1) + lst(i - 2)
            Next
            REM since all the iterations (except Pt) are > 15, continue iterating from the end of the list of 15
            n = lst(14)
            nm1 = lst(13)
            k = 0
            j = 13
            While k = 0
                Dim lt = t
                t = DivIt(n, nm1, 32)
                If lt = t Then
                    k = If(b = 0, 1, j)
                End If
                Dim onn = n
                n = b * n + nm1
                nm1 = onn

                j += 1
            End While
            Console.WriteLine("{0,4}  {1}   {2,2}    {3, 2}  {4}  {5}" + vbNewLine + "{6,19} {7}", "Pt Au Ag CuSn Cu Ni Al Fe Sn Pb".Split(" ")(b), b, b * b + 4, k, t, t = DoOne(b, 32), "", Joined(lst))
        Next
        REM now calculate and check big one
        n = 1
        nm1 = 1
        k = 0
        j = 1
        While k = 0
            Dim lt = t
            t = DivIt(n, nm1, 256)
            If lt = t Then
                k = j
            End If
            Dim onn = n
            n += nm1
            nm1 = onn

            j += 1
        End While
        Console.WriteLine()
        Console.WriteLine("Au to 256 digits:")
        Console.WriteLine(t)
        Console.WriteLine("Iteration count: {0}  Matched Sq.Rt Calc: {1}", k, t = DoOne(1, 256))
    End Sub

End Module