context: //Modified by Nils Reimers for CryptoNet
  
  //
  // BigInteger.cs - Big Integer implementation
  //
  // Authors:
  //	Ben Maurer
  //	Chew Keong TAN
  //	Sebastien Pouliot <sebastien@ximian.com>
  //	Pieter Philippaerts <Pieter@mentalis.org>
  //
  // Copyright (c) 2003 Ben Maurer
  // All rights reserved
  //
  // Copyright (c) 2002 Chew Keong TAN
  // All rights reserved.
  //
  // Copyright (C) 2004 Novell, Inc (http://www.novell.com)
  //
  // Permission is hereby granted, free of charge, to any person obtaining
  // a copy of this software and associated documentation files (the
  // "Software"), to deal in the Software without restriction, including
  // without limitation the rights to use, copy, modify, merge, publish,
  // distribute, sublicense, and/or sell copies of the Software, and to
  // permit persons to whom the Software is furnished to do so, subject to
  // the following conditions:
  // 
  // The above copyright notice and this permission notice shall be
  // included in all copies or substantial portions of the Software.
  // 
  // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  // MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  // NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
  // LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
  // OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
  // WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  //
  
  using System;
  using System.Security.Cryptography;
  
  
  
  
  namespace CryptoNet
  {
  
  
  	internal class  BigInteger {
  
  		#region Data Storage
  
  		/// <summary>
  		/// The Length of this BigInteger
  		/// </summary>
  		uint length = 1;
  
  		/// <summary>
  		/// The data for this BigInteger
  		/// </summary>
  		uint [] data;
  
  		#endregion
  
  		#region Constants
  
  		/// <summary>
  		/// Default length of a BigInteger in bytes
  		/// </summary>
  		const uint DEFAULT_LEN = 20;
  
  		/// <summary>
  		///		Table of primes below 2000.
  		/// </summary>
  		/// <remarks>
  		///		<para>
  		///		This table was generated using Mathematica 4.1 using the following function:
  		///		</para>
  		///		<para>
  		///			<code>
  		///			PrimeTable [x_] := Prime [Range [1, PrimePi [x]]]
  		///			PrimeTable [6000]
  		///			</code>
  		///		</para>
  		/// </remarks>
  		internal static readonly uint [] smallPrimes = {
  			2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
  			73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
  			157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
  			239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
  			331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
  			421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
  			509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
  			613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
  			709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
  			821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
  			919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
  
  			1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
  			1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181,
  			1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
  			1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
  			1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471,
  			1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
  			1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
  			1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,
  			1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867,
  			1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973,
  			1979, 1987, 1993, 1997, 1999, 
  		
  			2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,
  			2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207,
  			2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
  			2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389,
  			2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,
  			2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
  			2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707,
  			2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797,
  			2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
  			2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
  			
  			3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109,
  			3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
  			3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329,
  			3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449,
  			3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
  			3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,
  			3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,
  			3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
  			3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943,
  			3947, 3967, 3989,
  			
  			4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091,
  			4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
  			4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
  			4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,
  			4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523,
  			4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,
  			4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,
  			4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
  			4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987,
  			4993, 4999,
  			
  			5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101,
  			5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 
  			5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,
  			5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
  			5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563,
  			5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669,
  			5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
  			5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869,
  			5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987
  		};
  
  		internal enum Sign : int {
  			Negative = -1,
  			Zero = 0,
  			Positive = 1
  		};
  
  		#region Exception Messages
  		const string WouldReturnNegVal = "Operation would return a negative value";
  		#endregion
  
  		#endregion
  
  		#region Constructors
  
  		public BigInteger ()
  		{
  			data = new uint [DEFAULT_LEN];
  			this.length = DEFAULT_LEN;
  		}
       
  		public BigInteger (Sign sign, uint len) 
  		{
  			this.data = new uint [len];
  			this.length = len;
  		}
  
  		public BigInteger (BigInteger bi)
  		{
  			this.data = (uint [])bi.data.Clone ();
  			this.length = bi.length;
  		}
  
  
  		public BigInteger (BigInteger bi, uint len)
  		{
  
  			this.data = new uint [len];
  
  			for (uint i = 0; i < bi.length; i++)
  				this.data [i] = bi.data [i];
  
  			this.length = bi.length;
  		}
  
  		#endregion
  
  		#region Conversions
  		
  		public BigInteger (byte [] inData)
  		{
  			length = (uint)inData.Length >> 2;
  			int leftOver = inData.Length & 0x3;
  
  			// length not multiples of 4
  			if (leftOver != 0) length++;
  
  			data = new uint [length];
  
  			for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++) {
  				data [j] = (uint)(
  					(inData [i-3] << (3*8)) |
  					(inData [i-2] << (2*8)) |
  					(inData [i-1] << (1*8)) |
  					(inData [i])
  					);
  			}
  
  			switch (leftOver) {
  			case 1: data [length-1] = (uint)inData [0]; break;
  			case 2: data [length-1] = (uint)((inData [0] << 8) | inData [1]); break;
  			case 3: data [length-1] = (uint)((inData [0] << 16) | (inData [1] << 8) | inData [2]); break;
  			}
  
  			this.Normalize ();
  		}
  
  
  		public BigInteger (uint [] inData)
  		{
  			length = (uint)inData.Length;
  
  			data = new uint [length];
  
  			for (int i = (int)length - 1, j = 0; i >= 0; i--, j++)
  				data [j] = inData [i];
  
  			this.Normalize ();
  		}
  
  
  		public BigInteger (uint ui)
  		{
  			data = new uint [] {ui};
  		}
  
  
  		public BigInteger (ulong ul)
  		{
  			data = new uint [2] { (uint)ul, (uint)(ul >> 32)};
  			length = 2;
  
  			this.Normalize ();
  		}
  
  
  		public static implicit operator BigInteger (uint value)
  		{
  			return (new BigInteger (value));
  		}
  
  		public static implicit operator BigInteger (int value)
  		{
  			if (value < 0) throw new ArgumentOutOfRangeException ("value");
  			return (new BigInteger ((uint)value));
  		}
  
  
  		public static implicit operator BigInteger (ulong value)
  		{
  			return (new BigInteger (value));
  		}
  
  		/* This is the BigInteger.Parse method I use. This method works
  		because BigInteger.ToString returns the input I gave to Parse. */
  		public static BigInteger Parse (string number) 
  		{
  			if (number == null)
  				throw new ArgumentNullException ("number");
  
  			int i = 0, len = number.Length;
  			char c;
  			bool digits_seen = false;
  			BigInteger val = new BigInteger (0);
  			if (number [i] == '+') {
  				i++;
  			} 
  			else if (number [i] == '-') {
  				throw new FormatException (WouldReturnNegVal);
  			}
  
  			for (; i < len; i++) {
  				c = number [i];
  				if (c == '\0') {
  					i = len;
  					continue;
  				}
  				if (c >= '0' && c <= '9') {
  					val = val * 10 + (c - '0');
  					digits_seen = true;
  				} 
  				else {
  					if (Char.IsWhiteSpace (c)) {
  						for (i++; i < len; i++) {
  							if (!Char.IsWhiteSpace (number [i]))
  								throw new FormatException ();
  						}
  						break;
  					} 
  					else
  						throw new FormatException ();
  				}
  			}
  			if (!digits_seen)
  				throw new FormatException ();
  			return val;
  		}
  
  		#endregion
  
  		#region Operators
  
  		public static BigInteger operator + (BigInteger bi1, BigInteger bi2)
  		{
  			if (bi1 == 0)
  				return new BigInteger (bi2);
  			else if (bi2 == 0)
  				return new BigInteger (bi1);
  			else
  				return Kernel.AddSameSign (bi1, bi2);
  		}
  
  		public static BigInteger operator - (BigInteger bi1, BigInteger bi2)
  		{
  			if (bi2 == 0)
  				return new BigInteger (bi1);
  
  			if (bi1 == 0)
  				throw new ArithmeticException (WouldReturnNegVal);
  
  			switch (Kernel.Compare (bi1, bi2)) {
  
  				case Sign.Zero:
  					return 0;
  
  				case Sign.Positive:
  					return Kernel.Subtract (bi1, bi2);
  
  				case Sign.Negative:
  					throw new ArithmeticException (WouldReturnNegVal);
  				default:
  					throw new Exception ();
  			}
  		}
  
  		public static int operator % (BigInteger bi, int i)
  		{
  			if (i > 0)
  				return (int)Kernel.DwordMod (bi, (uint)i);
  			else
  				return -(int)Kernel.DwordMod (bi, (uint)-i);
  		}
  
  		public static uint operator % (BigInteger bi, uint ui)
  		{
  			return Kernel.DwordMod (bi, (uint)ui);
  		}
  
  		public static BigInteger operator % (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.multiByteDivide (bi1, bi2)[1];
  		}
  
  		public static BigInteger operator / (BigInteger bi, int i)
  		{
  			if (i > 0)
  				return Kernel.DwordDiv (bi, (uint)i);
  
  			throw new ArithmeticException (WouldReturnNegVal);
  		}
  
  		public static BigInteger operator / (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.multiByteDivide (bi1, bi2)[0];
  		}
  
  		public static BigInteger operator * (BigInteger bi1, BigInteger bi2)
  		{
  			if (bi1 == 0 || bi2 == 0) return 0;
  
  			//
  			// Validate pointers
  			//
  			if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException ("bi1 out of range");
  			if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException ("bi2 out of range");
  
  			BigInteger ret = new BigInteger (Sign.Positive, bi1.length + bi2.length);
  
  			Kernel.Multiply (bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);
  
  			ret.Normalize ();
  			return ret;
  		}
  
  		public static BigInteger operator * (BigInteger bi, int i)
  		{
  			if (i < 0) throw new ArithmeticException (WouldReturnNegVal);
  			if (i == 0) return 0;
  			if (i == 1) return new BigInteger (bi);
  
  			return Kernel.MultiplyByDword (bi, (uint)i);
  		}
  
  		public static BigInteger operator << (BigInteger bi1, int shiftVal)
  		{
  			return Kernel.LeftShift (bi1, shiftVal);
  		}
  
  		public static BigInteger operator >> (BigInteger bi1, int shiftVal)
  		{
  			return Kernel.RightShift (bi1, shiftVal);
  		}
  
  		#endregion
  
  		#region Friendly names for operators
  
  		// with names suggested by FxCop 1.30
  
  		public static BigInteger Add (BigInteger bi1, BigInteger bi2) 
  		{
  			return (bi1 + bi2);
  		}
  
  		public static BigInteger Subtract (BigInteger bi1, BigInteger bi2) 
  		{
  			return (bi1 - bi2);
  		}
  
  		public static int Modulus (BigInteger bi, int i) 
  		{
  			return (bi % i);
  		}
  
  		public static uint Modulus (BigInteger bi, uint ui) 
  		{
  			return (bi % ui);
  		}
  
  		public static BigInteger Modulus (BigInteger bi1, BigInteger bi2) 
  		{
  			return (bi1 % bi2);
  		}
  
  		public static BigInteger Divid (BigInteger bi, int i) 
  		{
  			return (bi / i);
  		}
  
  		public static BigInteger Divid (BigInteger bi1, BigInteger bi2) 
  		{
  			return (bi1 / bi2);
  		}
  
  		public static BigInteger Multiply (BigInteger bi1, BigInteger bi2) 
  		{
  			return (bi1 * bi2);
  		}
  
  		public static BigInteger Multiply (BigInteger bi, int i) 
  		{
  			return (bi * i);
  		}
  
  		#endregion
  
  		#region Random
          private static CryptRand cryptRng = CryptRand.Instance;
  
  		/*private static RandomNumberGenerator rng;
  		private static RandomNumberGenerator Rng {
  			get {
  				if (rng == null)
  					rng = RandomNumberGenerator.Create ();
  				return rng;
  			}
  		}*/
  
  		/// <summary>
  		/// Generates a new, random BigInteger of the specified length.
  		/// </summary>
  		/// <param name="bits">The number of bits for the new number.</param>		
  		/// <returns>A random number of the specified length.</returns>
  		public static BigInteger GenerateRandom (int bits)
  		{
  			int dwords = bits >> 5;
  			int remBits = bits & 0x1F;
  
  			if (remBits != 0)
  				dwords++;
  
  			BigInteger ret = new BigInteger (Sign.Positive, (uint)dwords + 1);
  			//byte [] random = new byte [dwords << 2];
  
              for (int i = 0; i < dwords; ++i)
                  ret.data[i] = (uint)cryptRng.Next();
  			
  
  			if (remBits != 0) {
  				uint mask = (uint)(0x01 << (remBits-1));
  				ret.data [dwords-1] |= mask;
  
  				mask = (uint)(0xFFFFFFFF >> (32 - remBits));
  				ret.data [dwords-1] &= mask;
  			}
  			else
  				ret.data [dwords-1] |= 0x80000000;
  
  			ret.Normalize ();
  			return ret;
  		}
  
  		
  
  		/// <summary>
  		/// Randomizes the bits in "this" from the specified RNG.
  		/// </summary>
  		/// <param name="rng">A RNG.</param>
  		public void Randomize ()
  		{
  			if (this == 0)
  				return;
  
  			int bits = this.BitCount ();
  			int dwords = bits >> 5;
  			int remBits = bits & 0x1F;
  
  			if (remBits != 0)
  				dwords++;
  
  			byte [] random = new byte [dwords << 2];
  
              for (int i = 0; i < dwords; ++i)
                  data[i] = (uint)cryptRng.Next();
  
  			
  			if (remBits != 0) {
  				uint mask = (uint)(0x01 << (remBits-1));
  				data [dwords-1] |= mask;
  
  				mask = (uint)(0xFFFFFFFF >> (32 - remBits));
  				data [dwords-1] &= mask;
  			}
  
  			else
  				data [dwords-1] |= 0x80000000;
  
  			Normalize ();
  		}
  
  		
  
  		#endregion
  
  		#region Bitwise
  
  		public int BitCount ()
  		{
  			this.Normalize ();
  
  			uint value = data [length - 1];
  			uint mask = 0x80000000;
  			uint bits = 32;
  
  			while (bits > 0 && (value & mask) == 0) {
  				bits--;
  				mask >>= 1;
  			}
  			bits += ((length - 1) << 5);
  
  			return (int)bits;
  		}
  
  		/// <summary>
  		/// Tests if the specified bit is 1.
  		/// </summary>
  		/// <param name="bitNum">The bit to test. The least significant bit is 0.</param>
  		/// <returns>True if bitNum is set to 1, else false.</returns>
  		public bool TestBit (uint bitNum)
  		{
  			uint bytePos = bitNum >> 5;             // divide by 32
  			byte bitPos = (byte)(bitNum & 0x1F);    // get the lowest 5 bits
  
  			uint mask = (uint)1 << bitPos;
  			return ((this.data [bytePos] & mask) != 0);
  		}
  
  		public bool TestBit (int bitNum)
  		{
  			if (bitNum < 0) throw new IndexOutOfRangeException ("bitNum out of range");
  
  			uint bytePos = (uint)bitNum >> 5;             // divide by 32
  			byte bitPos = (byte)(bitNum & 0x1F);    // get the lowest 5 bits
  
  			uint mask = (uint)1 << bitPos;
  			return ((this.data [bytePos] | mask) == this.data [bytePos]);
  		}
  
  
  		public void SetBit (uint bitNum)
  		{
  			SetBit (bitNum, true);
  		}
  
  
  		public void ClearBit (uint bitNum)
  		{
  			SetBit (bitNum, false);
  		}
  
  
  		public void SetBit (uint bitNum, bool value)
  		{
  			uint bytePos = bitNum >> 5;             // divide by 32
  
  			if (bytePos < this.length) {
  				uint mask = (uint)1 << (int)(bitNum & 0x1F);
  				if (value)
  					this.data [bytePos] |= mask;
  				else
  					this.data [bytePos] &= ~mask;
  			}
  		}
  
  		public int LowestSetBit ()
  		{
  			if (this == 0) return -1;
  			int i = 0;
  			while (!TestBit (i)) i++;
  			return i;
  		}
  
  		public byte[] GetBytes ()
  		{
  			if (this == 0) return new byte [1];
  
  			int numBits = BitCount ();
  			int numBytes = numBits >> 3;
  			if ((numBits & 0x7) != 0)
  				numBytes++;
  
  			byte [] result = new byte [numBytes];
  
  			int numBytesInWord = numBytes & 0x3;
  			if (numBytesInWord == 0) numBytesInWord = 4;
  
  			int pos = 0;
  			for (int i = (int)length - 1; i >= 0; i--) {
  				uint val = data [i];
  				for (int j = numBytesInWord - 1; j >= 0; j--) {
  					result [pos+j] = (byte)(val & 0xFF);
  					val >>= 8;
  				}
  				pos += numBytesInWord;
  				numBytesInWord = 4;
  			}
  			return result;
  		}
  
  		#endregion
  
  		#region Compare
  
  
  		public static bool operator == (BigInteger bi1, uint ui)
  		{
  			if (bi1.length != 1) bi1.Normalize ();
  			return bi1.length == 1 && bi1.data [0] == ui;
  		}
  
  
  		public static bool operator != (BigInteger bi1, uint ui)
  		{
  			if (bi1.length != 1) bi1.Normalize ();
  			return !(bi1.length == 1 && bi1.data [0] == ui);
  		}
  
  		public static bool operator == (BigInteger bi1, BigInteger bi2)
  		{
  			// we need to compare with null
  			if ((bi1 as object) == (bi2 as object))
  				return true;
  			if (null == bi1 || null == bi2)
  				return false;
  			return Kernel.Compare (bi1, bi2) == 0;
  		}
  
  		public static bool operator != (BigInteger bi1, BigInteger bi2)
  		{
  			// we need to compare with null
  			if ((bi1 as object) == (bi2 as object))
  				return false;
  			if (null == bi1 || null == bi2)
  				return true;
  			return Kernel.Compare (bi1, bi2) != 0;
  		}
  
  		public static bool operator > (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.Compare (bi1, bi2) > 0;
  		}
  
  		public static bool operator < (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.Compare (bi1, bi2) < 0;
  		}
  
  		public static bool operator >= (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.Compare (bi1, bi2) >= 0;
  		}
  
  		public static bool operator <= (BigInteger bi1, BigInteger bi2)
  		{
  			return Kernel.Compare (bi1, bi2) <= 0;
  		}
  
  		public Sign Compare (BigInteger bi)
  		{
  			return Kernel.Compare (this, bi);
  		}
  
  		#endregion
  
  		#region Formatting
  
   
  		public string ToString (uint radix)
  		{
  			return ToString (radix, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");
  		}
  
  		public string ToString (uint radix, string characterSet)
  		{
  			if (characterSet.Length < radix)
  				throw new ArgumentException ("charSet length less than radix", "characterSet");
  			if (radix == 1)
  				throw new ArgumentException ("There is no such thing as radix one notation", "radix");
  
  			if (this == 0) return "0";
  			if (this == 1) return "1";
  
  			string result = "";
  
  			BigInteger a = new BigInteger (this);
  
  			while (a != 0) {
  				uint rem = Kernel.SingleByteDivideInPlace (a, radix);
  				result = characterSet [(int) rem] + result;
  			}
  
  			return result;
  		}
  
  		#endregion
  
  		#region Misc
  
  		/// <summary>
  		///     Normalizes this by setting the length to the actual number of
  		///     uints used in data and by setting the sign to Sign.Zero if the
  		///     value of this is 0.
  		/// </summary>
  		private void Normalize ()
  		{
  			// Normalize length
  			while (length > 0 && data [length-1] == 0) length--;
  
  			// Check for zero
  			if (length == 0)
  				length++;
  		}
  
  		public void Clear () 
  		{
  			for (int i=0; i < length; i++)
  				data [i] = 0x00;
  		}
  
  		#endregion
  
  		#region Object Impl
  
  		public override int GetHashCode ()
  		{
  			uint val = 0;
  
  			for (uint i = 0; i < this.length; i++)
  				val ^= this.data [i];
  
  			return (int)val;
  		}
  
  		public override string ToString ()
  		{
  			return ToString (10);
  		}
  
  		public override bool Equals (object o)
  		{
  			if (o == null) return false;
  			if (o is int) return (int)o >= 0 && this == (uint)o;
  
  			return Kernel.Compare (this, (BigInteger)o) == 0;
  		}
  
  		#endregion
  
  		#region Number Theory
  
  		public BigInteger GCD (BigInteger bi)
  		{
  			return Kernel.gcd (this, bi);
  		}
  
  		public BigInteger ModInverse (BigInteger modulus)
  		{
  			return Kernel.modInverse (this, modulus);
  		}
  
  		public BigInteger ModPow (BigInteger exp, BigInteger n)
  		{
  			ModulusRing mr = new ModulusRing (n);
  			return mr.Pow (this, exp);
  		}
  		
  		#endregion
  
  		#region Prime Testing
  
  		public bool IsProbablePrime ()
  		{
  			if (this < smallPrimes [smallPrimes.Length - 1]) {
  				for (int p = 0; p < smallPrimes.Length; p++) {
  					if (this == smallPrimes [p])
  						return true;
  				}
  			}
  			else {
  				for (int p = 0; p < smallPrimes.Length; p++) {
  					if (this % smallPrimes [p] == 0)
  						return false;
  				}
  			}
  			return PrimalityTests.RabinMillerTest (this, ConfidenceFactor.Medium);
  		}
  
  		#endregion
  
  		#region Prime Number Generation
  
  		/// <summary>
  		/// Generates the smallest prime >= bi
  		/// </summary>
  		/// <param name="bi">A BigInteger</param>
  		/// <returns>The smallest prime >= bi. More mathematically, if bi is prime: bi, else Prime [PrimePi [bi] + 1].</returns>
  		public static BigInteger NextHighestPrime (BigInteger bi)
  		{
  			NextPrimeFinder npf = new NextPrimeFinder ();
  			return npf.GenerateNewPrime (0, bi);
  		}
  
  		public static BigInteger GeneratePseudoPrime (int bits)
  		{
  			SequentialSearchPrimeGeneratorBase sspg = new SequentialSearchPrimeGeneratorBase ();
  			return sspg.GenerateNewPrime (bits);
  		}
  
  		/// <summary>
  		/// Increments this by two
  		/// </summary>
  		public void Incr2 ()
  		{
  			int i = 0;
  
  			data [0] += 2;
  
  			// If there was no carry, nothing to do
  			if (data [0] < 2) {
  
  				// Account for the first carry
  				data [++i]++;
  
  				// Keep adding until no carry
  				while (data [i++] == 0x0)
  					data [i]++;
  
  				// See if we increased the data length
  				if (length == (uint)i)
  					length++;
  			}
  		}
  
  		#endregion
  
  
  		internal sealed class ModulusRing {
  
  			BigInteger mod, constant;
  
  			public ModulusRing (BigInteger modulus)
  			{
  				this.mod = modulus;
  
  				// calculate constant = b^ (2k) / m
  				uint i = mod.length << 1;
  
  				constant = new BigInteger (Sign.Positive, i + 1);
  				constant.data [i] = 0x00000001;
  
  				constant = constant / mod;
  			}
  
  			public void BarrettReduction (BigInteger x)
  			{
  				BigInteger n = mod;
  				uint k = n.length,
  					kPlusOne = k+1,
  					kMinusOne = k-1;
  
  				// x < mod, so nothing to do.
  				if (x.length < k) return;
  
  				BigInteger q3;
  
  				//
  				// Validate pointers
  				//
  				if (x.data.Length < x.length) throw new IndexOutOfRangeException ("x out of range");
  
  				// q1 = x / b^ (k-1)
  				// q2 = q1 * constant
  				// q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne
  
  				// TODO: We should the method in HAC p 604 to do this (14.45)
  				q3 = new BigInteger (Sign.Positive, x.length - kMinusOne + constant.length);
  				Kernel.Multiply (x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);
  
  				// r1 = x mod b^ (k+1)
  				// i.e. keep the lowest (k+1) words
  
  				uint lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;
  
  				x.length = lengthToCopy;
  				x.Normalize ();
  
  				// r2 = (q3 * n) mod b^ (k+1)
  				// partial multiplication of q3 and n
  
  				BigInteger r2 = new BigInteger (Sign.Positive, kPlusOne);
  				Kernel.MultiplyMod2p32pmod (q3.data, (int)kPlusOne, (int)q3.length - (int)kPlusOne, n.data, 0, (int)n.length, r2.data, 0, (int)kPlusOne);
  
  				r2.Normalize ();
  
  				if (r2 <= x) {
  					Kernel.MinusEq (x, r2);
  				} else {
  					BigInteger val = new BigInteger (Sign.Positive, kPlusOne + 1);
  					val.data [kPlusOne] = 0x00000001;
  
  					Kernel.MinusEq (val, r2);
  					Kernel.PlusEq (x, val);
  				}
  
  				while (x >= n)
  					Kernel.MinusEq (x, n);
  			}
  
  			public BigInteger Multiply (BigInteger a, BigInteger b)
  			{
  				if (a == 0 || b == 0) return 0;
  
  				if (a.length >= mod.length << 1)
  					a %= mod;
  
  				if (b.length >= mod.length << 1)
  					b %= mod;
  
  				if (a.length >= mod.length)
  					BarrettReduction (a);
  
  				if (b.length >= mod.length)
  					BarrettReduction (b);
  
  				BigInteger ret = new BigInteger (a * b);
  				BarrettReduction (ret);
  
  				return ret;
  			}
  
  			public BigInteger Difference (BigInteger a, BigInteger b)
  			{
  				Sign cmp = Kernel.Compare (a, b);
  				BigInteger diff;
  
  				switch (cmp) {
  					case Sign.Zero:
  						return 0;
  					case Sign.Positive:
  						diff = a - b; break;
  					case Sign.Negative:
  						diff = b - a; break;
  					default:
  						throw new Exception ();
  				}
  
  				if (diff >= mod) {
  					if (diff.length >= mod.length << 1)
  						diff %= mod;
  					else
  						BarrettReduction (diff);
  				}
  				if (cmp == Sign.Negative)
  					diff = mod - diff;
  				return diff;
  			}
  
  			public BigInteger Pow (BigInteger b, BigInteger exp)
  			{
  				if ((mod.data [0] & 1) == 1) return OddPow (b, exp);
  				else return EvenPow (b, exp);
  			}
  			
  			public BigInteger EvenPow (BigInteger b, BigInteger exp)
  			{
  				BigInteger resultNum = new BigInteger ((BigInteger)1, mod.length << 1);
  				BigInteger tempNum = new BigInteger (b % mod, mod.length << 1);  // ensures (tempNum * tempNum) < b^ (2k)
  
  				uint totalBits = (uint)exp.BitCount ();
  
  				uint [] wkspace = new uint [mod.length << 1];
  
  				// perform squaring and multiply exponentiation
  				for (uint pos = 0; pos < totalBits; pos++) {
  					if (exp.TestBit (pos)) {
  
  						Array.Clear (wkspace, 0, wkspace.Length);
  						Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
  						resultNum.length += tempNum.length;
  						uint [] t = wkspace;
  						wkspace = resultNum.data;
  						resultNum.data = t;
  
  						BarrettReduction (resultNum);
  					}
  
  					Kernel.SquarePositive (tempNum, ref wkspace);
  					BarrettReduction (tempNum);
  
  					if (tempNum == 1) {
  						return resultNum;
  					}
  				}
  
  				return resultNum;
  			}
  
  			private BigInteger OddPow (BigInteger b, BigInteger exp)
  			{
  				BigInteger resultNum = new BigInteger (Montgomery.ToMont (1, mod), mod.length << 1);
  				BigInteger tempNum = new BigInteger (Montgomery.ToMont (b, mod), mod.length << 1);  // ensures (tempNum * tempNum) < b^ (2k)
  				uint mPrime = Montgomery.Inverse (mod.data [0]);
  				uint totalBits = (uint)exp.BitCount ();
  
  				uint [] wkspace = new uint [mod.length << 1];
  
  				// perform squaring and multiply exponentiation
  				for (uint pos = 0; pos < totalBits; pos++) {
  					if (exp.TestBit (pos)) {
  
  						Array.Clear (wkspace, 0, wkspace.Length);
  						Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
  						resultNum.length += tempNum.length;
  						uint [] t = wkspace;
  						wkspace = resultNum.data;
  						resultNum.data = t;
  
  						Montgomery.Reduce (resultNum, mod, mPrime);
  					}
  
  					Kernel.SquarePositive (tempNum, ref wkspace);
  					Montgomery.Reduce (tempNum, mod, mPrime);
  				}
  
  				Montgomery.Reduce (resultNum, mod, mPrime);
  				return resultNum;
  			}
  
  			#region Pow Small Base
  
  			// TODO: Make tests for this, not really needed b/c prime stuff
  			// checks it, but still would be nice
  
  			public BigInteger Pow (uint b, BigInteger exp)
  			{
  //				if (b != 2) {
  					if ((mod.data [0] & 1) == 1)
  						return OddPow (b, exp);
  					else
  						return EvenPow (b, exp);
  /* buggy in some cases (like the well tested primes)
  				} else {
  					if ((mod.data [0] & 1) == 1)
  						return OddModTwoPow (exp);
  					else 
  						return EvenModTwoPow (exp);
  				}*/
  			}
  
  			private unsafe BigInteger OddPow (uint b, BigInteger exp)
  			{
  				exp.Normalize ();
  				uint [] wkspace = new uint [mod.length << 1 + 1];
  
  				BigInteger resultNum = Montgomery.ToMont ((BigInteger)b, this.mod);
  				resultNum = new BigInteger (resultNum, mod.length << 1 +1);
  
  				uint mPrime = Montgomery.Inverse (mod.data [0]);
  
  				uint pos = (uint)exp.BitCount () - 2;
  
  				//
  				// We know that the first itr will make the val b
  				//
  
  				do {
  					//
  					// r = r ^ 2 % m
  					//
  					Kernel.SquarePositive (resultNum, ref wkspace);
  					resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
  
  					if (exp.TestBit (pos)) {
  
  						//
  						// r = r * b % m
  						//
  
  						// TODO: Is Unsafe really speeding things up?
  						fixed (uint* u = resultNum.data) {
  
  							uint i = 0;
  							ulong mc = 0;
  
  							do {
  								mc += (ulong)u [i] * (ulong)b;
  								u [i] = (uint)mc;
  								mc >>= 32;
  							} while (++i < resultNum.length);
  
  							if (resultNum.length < mod.length) {
  								if (mc != 0) {
  									u [i] = (uint)mc;
  									resultNum.length++;
  									while (resultNum >= mod)
  										Kernel.MinusEq (resultNum, mod);
  								}
  							} else if (mc != 0) {
  
  								//
  								// First, we estimate the quotient by dividing
  								// the first part of each of the numbers. Then
  								// we correct this, if necessary, with a subtraction.
  								//
  
  								uint cc = (uint)mc;
  
  								// We would rather have this estimate overshoot,
  								// so we add one to the divisor
  								uint divEstimate;
  								if (mod.data [mod.length - 1] < UInt32.MaxValue) {
  									divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
  										(mod.data [mod.length-1] + 1));
  								}
  								else {
  									// guess but don't divide by 0
  									divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
  										(mod.data [mod.length-1]));
  								}
  
  								uint t;
  
  								i = 0;
  								mc = 0;
  								do {
  									mc += (ulong)mod.data [i] * (ulong)divEstimate;
  									t = u [i];
  									u [i] -= (uint)mc;
  									mc >>= 32;
  									if (u [i] > t) mc++;
  									i++;
  								} while (i < resultNum.length);
  								cc -= (uint)mc;
  
  								if (cc != 0) {
  
  									uint sc = 0, j = 0;
  									uint [] s = mod.data;
  									do {
  										uint a = s [j];
  										if (((a += sc) < sc) | ((u [j] -= a) > ~a)) sc = 1;
  										else sc = 0;
  										j++;
  									} while (j < resultNum.length);
  									cc -= sc;
  								}
  								while (resultNum >= mod)
  									Kernel.MinusEq (resultNum, mod);
  							} else {
  								while (resultNum >= mod)
  									Kernel.MinusEq (resultNum, mod);
  							}
  						}
  					}
  				} while (pos-- > 0);
  
  				resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
  				return resultNum;
  
  			}
  			
  			private unsafe BigInteger EvenPow (uint b, BigInteger exp)
  			{
  				exp.Normalize ();
  				uint [] wkspace = new uint [mod.length << 1 + 1];
  				BigInteger resultNum = new BigInteger ((BigInteger)b, mod.length << 1 + 1);
  
  				uint pos = (uint)exp.BitCount () - 2;
  
  				//
  				// We know that the first itr will make the val b
  				//
  
  				do {
  					//
  					// r = r ^ 2 % m
  					//
  					Kernel.SquarePositive (resultNum, ref wkspace);
  					if (!(resultNum.length < mod.length))
  						BarrettReduction (resultNum);
  
  					if (exp.TestBit (pos)) {
  
  						//
  						// r = r * b % m
  						//
  
  						// TODO: Is Unsafe really speeding things up?
  						fixed (uint* u = resultNum.data) {
  
  							uint i = 0;
  							ulong mc = 0;
  
  							do {
  								mc += (ulong)u [i] * (ulong)b;
  								u [i] = (uint)mc;
  								mc >>= 32;
  							} while (++i < resultNum.length);
  
  							if (resultNum.length < mod.length) {
  								if (mc != 0) {
  									u [i] = (uint)mc;
  									resultNum.length++;
  									while (resultNum >= mod)
  										Kernel.MinusEq (resultNum, mod);
  								}
  							} else if (mc != 0) {
  
  								//
  								// First, we estimate the quotient by dividing
  								// the first part of each of the numbers. Then
  								// we correct this, if necessary, with a subtraction.
  								//
  
  								uint cc = (uint)mc;
  
  								// We would rather have this estimate overshoot,
  								// so we add one to the divisor
  								uint divEstimate = (uint) ((((ulong)cc << 32) | (ulong) u [i -1]) /
  									(mod.data [mod.length-1] + 1));
  
  								uint t;
  
  								i = 0;
  								mc = 0;
  								do {
  									mc += (ulong)mod.data [i] * (ulong)divEstimate;
  									t = u [i];
  									u [i] -= (uint)mc;
  									mc >>= 32;
  									if (u [i] > t) mc++;
  									i++;
  								} while (i < resultNum.length);
  								cc -= (uint)mc;
  
  								if (cc != 0) {
  
  									uint sc = 0, j = 0;
  									uint [] s = mod.data;
  									do {
  										uint a = s [j];
  										if (((a += sc) < sc) | ((u [j] -= a) > ~a)) sc = 1;
  										else sc = 0;
  										j++;
  									} while (j < resultNum.length);
  									cc -= sc;
  								}
  								while (resultNum >= mod)
  									Kernel.MinusEq (resultNum, mod);
  							} else {
  								while (resultNum >= mod)
  									Kernel.MinusEq (resultNum, mod);
  							}
  						}
  					}
  				} while (pos-- > 0);
  
  				return resultNum;
  			}
  
  /* known to be buggy in some cases
  			private unsafe BigInteger EvenModTwoPow (BigInteger exp)
  			{
  				exp.Normalize ();
  				uint [] wkspace = new uint [mod.length << 1 + 1];
  
  				BigInteger resultNum = new BigInteger (2, mod.length << 1 +1);
  
  				uint value = exp.data [exp.length - 1];
  				uint mask = 0x80000000;
  
  				// Find the first bit of the exponent
  				while ((value & mask) == 0)
  					mask >>= 1;
  
  				//
  				// We know that the first itr will make the val 2,
  				// so eat one bit of the exponent
  				//
  				mask >>= 1;
  
  				uint wPos = exp.length - 1;
  
  				do {
  					value = exp.data [wPos];
  					do {
  						Kernel.SquarePositive (resultNum, ref wkspace);
  						if (resultNum.length >= mod.length)
  							BarrettReduction (resultNum);
  
  						if ((value & mask) != 0) {
  							//
  							// resultNum = (resultNum * 2) % mod
  							//
  
  							fixed (uint* u = resultNum.data) {
  								//
  								// Double
  								//
  								uint* uu = u;
  								uint* uuE = u + resultNum.length;
  								uint x, carry = 0;
  								while (uu < uuE) {
  									x = *uu;
  									*uu = (x << 1) | carry;
  									carry = x >> (32 - 1);
  									uu++;
  								}
  
  								// subtraction inlined because we know it is square
  								if (carry != 0 || resultNum >= mod) {
  									uu = u;
  									uint c = 0;
  									uint [] s = mod.data;
  									uint i = 0;
  									do {
  										uint a = s [i];
  										if (((a += c) < c) | ((* (uu++) -= a) > ~a))
  											c = 1;
  										else
  											c = 0;
  										i++;
  									} while (uu < uuE);
  								}
  							}
  						}
  					} while ((mask >>= 1) > 0);
  					mask = 0x80000000;
  				} while (wPos-- > 0);
  
  				return resultNum;
  			}
  
  			private unsafe BigInteger OddModTwoPow (BigInteger exp)
  			{
  
  				uint [] wkspace = new uint [mod.length << 1 + 1];
  
  				BigInteger resultNum = Montgomery.ToMont ((BigInteger)2, this.mod);
  				resultNum = new BigInteger (resultNum, mod.length << 1 +1);
  
  				uint mPrime = Montgomery.Inverse (mod.data [0]);
  
  				//
  				// TODO: eat small bits, the ones we can do with no modular reduction
  				//
  				uint pos = (uint)exp.BitCount () - 2;
  
  				do {
  					Kernel.SquarePositive (resultNum, ref wkspace);
  					resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
  
  					if (exp.TestBit (pos)) {
  						//
  						// resultNum = (resultNum * 2) % mod
  						//
  
  						fixed (uint* u = resultNum.data) {
  							//
  							// Double
  							//
  							uint* uu = u;
  							uint* uuE = u + resultNum.length;
  							uint x, carry = 0;
  							while (uu < uuE) {
  								x = *uu;
  								*uu = (x << 1) | carry;
  								carry = x >> (32 - 1);
  								uu++;
  							}
  
  							// subtraction inlined because we know it is square
  							if (carry != 0 || resultNum >= mod) {
  								fixed (uint* s = mod.data) {
  									uu = u;
  									uint c = 0;
  									uint* ss = s;
  									do {
  										uint a = *ss++;
  										if (((a += c) < c) | ((* (uu++) -= a) > ~a))
  											c = 1;
  										else
  											c = 0;
  									} while (uu < uuE);
  								}
  							}
  						}
  					}
  				} while (pos-- > 0);
  
  				resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
  				return resultNum;
  			}
  */			
  			#endregion
  		}
  
  		internal sealed class Montgomery {
  
  			private Montgomery () 
  			{
  			}
  
  			public static uint Inverse (uint n)
  			{
  				uint y = n, z;
  
  				while ((z = n * y) != 1)
  					y *= 2 - z;
  
  				return (uint)-y;
  			}
  
  			public static BigInteger ToMont (BigInteger n, BigInteger m)
  			{
  				n.Normalize (); m.Normalize ();
  
  				n <<= (int)m.length * 32;
  				n %= m;
  				return n;
  			}
  
  			public static unsafe BigInteger Reduce (BigInteger n, BigInteger m, uint mPrime)
  			{
  				BigInteger A = n;
  				fixed (uint* a = A.data, mm = m.data) {
  					for (uint i = 0; i < m.length; i++) {
  						// The mod here is taken care of by the CPU,
  						// since the multiply will overflow.
  						uint u_i = a [0] * mPrime /* % 2^32 */;
  
  						//
  						// A += u_i * m;
  						// A >>= 32
  						//
  
  						// mP = Position in mod
  						// aSP = the source of bits from a
  						// aDP = destination for bits
  						uint* mP = mm, aSP = a, aDP = a;
  
  						ulong c = (ulong)u_i * ((ulong)*(mP++)) + *(aSP++);
  						c >>= 32;
  						uint j = 1;
  
  						// Multiply and add
  						for (; j < m.length; j++) {
  							c += (ulong)u_i * (ulong)*(mP++) + *(aSP++);
  							*(aDP++) = (uint)c;
  							c >>= 32;
  						}
  
  						// Account for carry
  						// TODO: use a better loop here, we dont need the ulong stuff
  						for (; j < A.length; j++) {
  							c += *(aSP++);
  							*(aDP++) = (uint)c;
  							c >>= 32;
  							if (c == 0) {j++; break;}
  						}
  						// Copy the rest
  						for (; j < A.length; j++) {
  							*(aDP++) = *(aSP++);
  						}
  
  						*(aDP++) = (uint)c;
  					}
  
  					while (A.length > 1 && a [A.length-1] == 0) A.length--;
  
  				}
  				if (A >= m) Kernel.MinusEq (A, m);
  
  				return A;
  			}
  #if _NOT_USED_
  			public static BigInteger Reduce (BigInteger n, BigInteger m)
  			{
  				return Reduce (n, m, Inverse (m.data [0]));
  			}
  #endif
  		}
  
  		/// <summary>
  		/// Low level functions for the BigInteger
  		/// </summary>
  		private sealed class Kernel {
  
  			#region Addition/Subtraction
  
  			/// <summary>
  			/// Adds two numbers with the same sign.
  			/// </summary>
  			/// <param name="bi1">A BigInteger</param>
  			/// <param name="bi2">A BigInteger</param>
  			/// <returns>bi1 + bi2</returns>
  			public static BigInteger AddSameSign (BigInteger bi1, BigInteger bi2)
  			{
  				uint [] x, y;
  				uint yMax, xMax, i = 0;
  
  				// x should be bigger
  				if (bi1.length < bi2.length) {
  					x = bi2.data;
  					xMax = bi2.length;
  					y = bi1.data;
  					yMax = bi1.length;
  				} else {
  					x = bi1.data;
  					xMax = bi1.length;
  					y = bi2.data;
  					yMax = bi2.length;
  				}
  				
  				BigInteger result = new BigInteger (Sign.Positive, xMax + 1);
  
  				uint [] r = result.data;
  
  				ulong sum = 0;
  
  				// Add common parts of both numbers
  				do {
  					sum = ((ulong)x [i]) + ((ulong)y [i]) + sum;
  					r [i] = (uint)sum;
  					sum >>= 32;
  				} while (++i < yMax);
  
  				// Copy remainder of longer number while carry propagation is required
  				bool carry = (sum != 0);
  
  				if (carry) {
  
  					if (i < xMax) {
  						do
  
gt: 							carry = ((r [i] = x [i] + 1) == 0);