September Morn Update

Task/Arithmetic-geometric-mean/C-sharp/arithmetic-geometric-mean-2.cs

@@ -0,0 +1,47 @@
+using System;
+using System.Numerics;
+
+namespace agm
+{
+    class Program
+    {
+        static BigInteger BIP(char leadDig, int numDigs)
+        {
+            return BigInteger.Parse(leadDig + new string('0', numDigs));
+        }
+
+        static BigInteger IntSqRoot(BigInteger v)
+        {
+            int digs = Math.Max(0, v.ToString().Length / 2);
+            BigInteger res = BIP('3', digs), term;
+            while (true) {
+                term = v / res; if (Math.Abs((double)(term - res)) < 2) break;
+                res = (res + term) / 2; } return res;
+        }
+
+        static BigInteger CalcByAGM(int digits)
+        {
+            int digs = digits + (int)(Math.Log(digits) / 2), d2 = digs * 2;
+            BigInteger a = BIP('1', digs),              // initial value = 1
+                       b = IntSqRoot(BIP('5', d2 - 1)), // initial value = square root of 0.5
+                       c;
+            while (true) {
+                c = a; a = ((a + b) / 2); b = IntSqRoot(c * b);
+                if (Math.Abs((double)(a - b)) <= 1) break;
+            }
+            return b;
+        }
+
+        static void Main(string[] args)
+        {
+            int digits = 25000;
+            if (args.Length > 0)
+            {
+                int.TryParse(args[0], out digits);
+                if (digits < 1 || digits > 999999) digits = 25000;
+            }
+            Console.WriteLine("0.{0}", CalcByAGM(digits).ToString());
+            if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
+        }
+    }
+}