Merge branch 'splitDlls'.

DNOA now builds and (in some cases) ships as many distinct assemblies.

1 files changed, 2241 insertions, 0 deletions

diff --git a/src/Mono.Math/BigInteger.cs b/src/Mono.Math/BigInteger.cs
new file mode 100644
index 0000000..33df8df
--- /dev/null
+++ b/src/Mono.Math/BigInteger.cs
@@ -0,0 +1,2241 @@
+// <auto-generated />
+
+//
+// BigInteger.cs - Big Integer implementation
+//
+// Authors:
+//	Ben Maurer
+//	Chew Keong TAN
+//	Sebastien Pouliot (spouliot@motus.com)
+//
+// Copyright (c) 2003 Ben Maurer
+// All rights reserved
+//
+// Copyright (c) 2002 Chew Keong TAN
+// All rights reserved.
+//
+// Modified 2007 Andrew Arnott (http://blog.nerdbank.net)
+// Rewrote unsafe code as safe code.
+
+using System;
+using System.Security.Cryptography;
+using Mono.Math.Prime;
+using Mono.Math.Prime.Generator;
+
+namespace Mono.Math {
+
+	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>
+		public 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
+		};
+
+		public 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];
+		}
+		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
+
+		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("Only positive integers are allowed.");
+			}
+			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;
+		}
+		
+		#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-0] << (0*8))
+					);
+			}
+
+			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));
+		}
+
+		#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 InvalidOperationException ();
+			}
+		}
+
+		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 Random
+		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>
+		/// <param name="rng">A random number generator to use to obtain the bits.</param>
+		/// <returns>A random number of the specified length.</returns>
+		public static BigInteger genRandom (int bits, RandomNumberGenerator rng)
+		{
+			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];
+
+			rng.GetBytes (random);
+			Buffer.BlockCopy (random, 0, ret.data, 0, (int)dwords << 2);
+
+			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>
+		/// Generates a new, random BigInteger of the specified length using the default RNG crypto service provider.
+		/// </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 genRandom (int bits)
+		{
+			return genRandom (bits, Rng);
+		}
+
+		/// <summary>
+		/// Randomizes the bits in "this" from the specified RNG.
+		/// </summary>
+		/// <param name="rng">A RNG.</param>
+		public void randomize (RandomNumberGenerator rng)
+		{
+			int bits = this.bitCount ();
+			int dwords = bits >> 5;
+			int remBits = bits & 0x1F;
+
+			if (remBits != 0)
+				dwords++;
+
+			byte [] random = new byte [dwords << 2];
+
+			rng.GetBytes (random);
+			Buffer.BlockCopy (random, 0, data, 0, (int)dwords << 2);
+
+			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 ();
+		}
+
+		/// <summary>
+		/// Randomizes the bits in "this" from the default RNG.
+		/// </summary>
+		public void randomize ()
+		{
+			randomize (Rng);
+		}
+
+		#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 ArgumentOutOfRangeException ("bitNum");
+
+			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 val)
+		{
+			uint bytePos = bitNum >> 5;             // divide by 32
+
+			if (bytePos < this.length) {
+				uint mask = (uint)1 << (int)(bitNum & 0x1F);
+				if (val)
+					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 charSet)
+		{
+			if (charSet.Length < radix)
+				throw new ArgumentException ("charSet length less than radix", "charSet");
+			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 = charSet [ (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 mod)
+		{
+			return Kernel.modInverse (this, mod);
+		}
+
+		public BigInteger modPow (BigInteger exp, BigInteger n)
+		{
+			ModulusRing mr = new ModulusRing (n);
+			return mr.Pow (this, exp);
+		}
+		
+		#endregion
+
+		#region Prime Testing
+
+		public bool isProbablePrime ()
+		{
+
+			for (int p = 0; p < smallPrimes.Length; p++) {
+				if (this == smallPrimes [p])
+					return true;
+				if (this % smallPrimes [p] == 0)
+					return false;
+			}
+
+			return PrimalityTests.RabinMillerTest (this, Prime.ConfidenceFactor.Medium);
+		}
+
+		[Obsolete]
+		public bool isProbablePrime (int notUsed)
+		{
+
+			for (int p = 0; p < smallPrimes.Length; p++) {
+				if (this % smallPrimes [p] == 0)
+					return false;
+			}
+
+			return
+				PrimalityTests.SmallPrimeSppTest (this, Prime.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 NextHightestPrime (BigInteger bi)
+		{
+			NextPrimeFinder npf = new NextPrimeFinder ();
+			return npf.GenerateNewPrime (0, bi);
+		}
+
+		public static BigInteger genPseudoPrime (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
+
+		public sealed class ModulusRing {
+
+			BigInteger mod, constant;
+
+			public ModulusRing (BigInteger mod)
+			{
+				this.mod = mod;
+
+				// 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 InvalidOperationException();
+				}
+
+				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);
+				} else {
+					if ((mod.data [0] & 1) == 1) return OddModTwoPow (exp);
+					else return EvenModTwoPow (exp);
+				}
+			}
+
+			private 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
+						//
+
+						uint u = 0;
+
+						uint i = 0;
+						ulong mc = 0;
+
+						do {
+							mc += (ulong)resultNum.data[u + i] * (ulong)b;
+							resultNum.data[u + i] = (uint)mc;
+							mc >>= 32;
+						} while (++i < resultNum.length);
+
+						if (resultNum.length < mod.length) {
+							if (mc != 0) {
+								resultNum.data[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)resultNum.data[u + i - 1]) /
+								(mod.data[mod.length - 1] + 1));
+
+							uint t;
+
+							i = 0;
+							mc = 0;
+							do {
+								mc += (ulong)mod.data[i] * (ulong)divEstimate;
+								t = resultNum.data[u + i];
+								resultNum.data[u + i] -= (uint)mc;
+								mc >>= 32;
+								if (resultNum.data[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) | ((resultNum.data[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 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
+						//
+
+						uint u = 0;
+
+						uint i = 0;
+						ulong mc = 0;
+
+						do {
+							mc += (ulong)resultNum.data[u + i] * (ulong)b;
+							resultNum.data[u + i] = (uint)mc;
+							mc >>= 32;
+						} while (++i < resultNum.length);
+
+						if (resultNum.length < mod.length) {
+							if (mc != 0) {
+								resultNum.data[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)resultNum.data[u + i - 1]) /
+								(mod.data[mod.length - 1] + 1));
+
+							uint t;
+
+							i = 0;
+							mc = 0;
+							do {
+								mc += (ulong)mod.data[i] * (ulong)divEstimate;
+								t = resultNum.data[u + i];
+								resultNum.data[u + i] -= (uint)mc;
+								mc >>= 32;
+								if (resultNum.data[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) | ((resultNum.data[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;
+			}
+
+			private 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
+							//
+
+							uint u = 0;
+							//
+							// Double
+							//
+							uint uu = u;
+							uint uuE = u + resultNum.length;
+							uint x, carry = 0;
+							while (uu < uuE) {
+								x = resultNum.data[uu];
+								resultNum.data[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) | ((resultNum.data[uu++] -= a) > ~a))
+										c = 1;
+									else
+										c = 0;
+									i++;
+								} while (uu < uuE);
+							}
+
+						}
+					} while ((mask >>= 1) > 0);
+					mask = 0x80000000;
+				} while (wPos-- > 0);
+
+				return resultNum;
+			}
+
+			private 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
+						//
+
+						uint u = 0;
+						//
+						// Double
+						//
+						uint uu = u;
+						uint uuE = u + resultNum.length;
+						uint x, carry = 0;
+						while (uu < uuE) {
+							x = resultNum.data[uu];
+							resultNum.data[uu] = (x << 1) | carry;
+							carry = x >> (32 - 1);
+							uu++;
+						}
+
+						// subtraction inlined because we know it is square
+						if (carry != 0 || resultNum >= mod) {
+							uint s = 0;
+							uu = u;
+							uint c = 0;
+							uint ss = s;
+							do {
+								uint a = mod.data[ss++];
+								if (((a += c) < c) | ((resultNum.data[uu++] -= a) > ~a))
+									c = 1;
+								else
+									c = 0;
+							} while (uu < uuE);
+						}
+					}
+				} while (pos-- > 0);
+
+				resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
+				return resultNum;
+			}
+			
+			#endregion
+		}
+
+		public sealed class 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 BigInteger Reduce(BigInteger n, BigInteger m, uint mPrime)
+			{
+				BigInteger A = n;
+				uint a = 0, mm = 0;
+				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.data[a] * 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)m.data[mP++] + A.data[aSP++];
+					c >>= 32;
+					uint j = 1;
+
+					// Multiply and add
+					for (; j < m.length; j++) {
+						c += (ulong)u_i * (ulong)m.data[mP++] + A.data[aSP++];
+						A.data[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 += A.data[aSP++];
+						A.data[aDP++] = (uint)c;
+						c >>= 32;
+						if (c == 0) { j++; break; }
+					}
+					// Copy the rest
+					for (; j < A.length; j++) {
+						A.data[aDP++] = A.data[aSP++];
+					}
+
+					A.data[aDP++] = (uint)c;
+				}
+
+				while (A.length > 1 && A.data[a + A.length - 1] == 0) A.length--;
+
+				if (A >= m) Kernel.MinusEq(A, m);
+
+				return A;
+			}
+
+			public static BigInteger Reduce (BigInteger n, BigInteger m)
+			{
+				return Reduce (n, m, Inverse (m.data [0]));
+			}
+		}
+
+		/// <summary>
+		/// Low level functions for the BigInteger
+		/// </summary>
+		private sealed class Kernel {
+			private 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
+							carry = ((r [i] = x [i] + 1) == 0);
+						while (++i < xMax && carry);
+					}
+
+					if (carry) {
+						r [i] = 1;
+						result.length = ++i;
+						return result;
+					}
+				}
+
+				// Copy the rest
+				if (i < xMax) {
+					do
+						r [i] = x [i];
+					while (++i < xMax);
+				}
+
+				result.Normalize ();
+				return result;
+			}
+
+			public static BigInteger Subtract (BigInteger big, BigInteger small)
+			{
+				BigInteger result = new BigInteger (Sign.Positive, big.length);
+
+				uint [] r = result.data, b = big.data, s = small.data;
+				uint i = 0, c = 0;
+
+				do {
+
+					uint x = s [i];
+					if (((x += c) < c) | ((r [i] = b [i] - x) > ~x))
+						c = 1;
+					else
+						c = 0;
+
+				} while (++i < small.length);
+
+				if (i == big.length) goto fixup;
+
+				if (c == 1) {
+					do
+						r [i] = b [i] - 1;
+					while (b [i++] == 0 && i < big.length);
+
+					if (i == big.length) goto fixup;
+				}
+
+				do
+					r [i] = b [i];
+				while (++i < big.length);
+
+				fixup:
+
+					result.Normalize ();
+				return result;
+			}
+
+			public static void MinusEq (BigInteger big, BigInteger small)
+			{
+				uint [] b = big.data, s = small.data;
+				uint i = 0, c = 0;
+
+				do {
+					uint x = s [i];
+					if (((x += c) < c) | ((b [i] -= x) > ~x))
+						c = 1;
+					else
+						c = 0;
+				} while (++i < small.length);
+
+				if (i == big.length) goto fixup;
+
+				if (c == 1) {
+					do
+						b [i]--;
+					while (b [i++] == 0 && i < big.length);
+				}
+
+				fixup:
+
+					// Normalize length
+					while (big.length > 0 && big.data [big.length-1] == 0) big.length--;
+
+				// Check for zero
+				if (big.length == 0)
+					big.length++;
+
+			}
+
+			public static void PlusEq (BigInteger bi1, BigInteger bi2)
+			{
+				uint [] x, y;
+				uint yMax, xMax, i = 0;
+				bool flag = false;
+
+				// x should be bigger
+				if (bi1.length < bi2.length){
+					flag = true;
+					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;
+				}
+
+				uint [] r = bi1.data;
+
+				ulong sum = 0;
+
+				// Add common parts of both numbers
+				do {
+					sum += ((ulong)x [i]) + ((ulong)y [i]);
+					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
+							carry = ((r [i] = x [i] + 1) == 0);
+						while (++i < xMax && carry);
+					}
+
+					if (carry) {
+						r [i] = 1;
+						bi1.length = ++i;
+						return;
+					}
+				}
+
+				// Copy the rest
+				if (flag && i < xMax - 1) {
+					do
+						r [i] = x [i];
+					while (++i < xMax);
+				}
+
+				bi1.length = xMax + 1;
+				bi1.Normalize ();
+			}
+
+			#endregion
+
+			#region Compare
+
+			/// <summary>
+			/// Compares two BigInteger
+			/// </summary>
+			/// <param name="bi1">A BigInteger</param>
+			/// <param name="bi2">A BigInteger</param>
+			/// <returns>The sign of bi1 - bi2</returns>
+			public static Sign Compare (BigInteger bi1, BigInteger bi2)
+			{
+				//
+				// Step 1. Compare the lengths
+				//
+				uint l1 = bi1.length, l2 = bi2.length;
+
+				while (l1 > 0 && bi1.data [l1-1] == 0) l1--;
+				while (l2 > 0 && bi2.data [l2-1] == 0) l2--;
+
+				if (l1 == 0 && l2 == 0) return Sign.Zero;
+
+				// bi1 len < bi2 len
+				if (l1 < l2) return Sign.Negative;
+				// bi1 len > bi2 len
+				else if (l1 > l2) return Sign.Positive;
+
+				//
+				// Step 2. Compare the bits
+				//
+
+				uint pos = l1 - 1;
+
+				while (pos != 0 && bi1.data [pos] == bi2.data [pos]) pos--;
+				
+				if (bi1.data [pos] < bi2.data [pos])
+					return Sign.Negative;
+				else if (bi1.data [pos] > bi2.data [pos])
+					return Sign.Positive;
+				else
+					return Sign.Zero;
+			}
+
+			#endregion
+
+			#region Division
+
+			#region Dword
+
+			/// <summary>
+			/// Performs n / d and n % d in one operation.
+			/// </summary>
+			/// <param name="n">A BigInteger, upon exit this will hold n / d</param>
+			/// <param name="d">The divisor</param>
+			/// <returns>n % d</returns>
+			public static uint SingleByteDivideInPlace (BigInteger n, uint d)
+			{
+				ulong r = 0;
+				uint i = n.length;
+
+				while (i-- > 0) {
+					r <<= 32;
+					r |= n.data [i];
+					n.data [i] = (uint)(r / d);
+					r %= d;
+				}
+				n.Normalize ();
+
+				return (uint)r;
+			}
+
+			public static uint DwordMod (BigInteger n, uint d)
+			{
+				ulong r = 0;
+				uint i = n.length;
+
+				while (i-- > 0) {
+					r <<= 32;
+					r |= n.data [i];
+					r %= d;
+				}
+
+				return (uint)r;
+			}
+
+			public static BigInteger DwordDiv (BigInteger n, uint d)
+			{
+				BigInteger ret = new BigInteger (Sign.Positive, n.length);
+
+				ulong r = 0;
+				uint i = n.length;
+
+				while (i-- > 0) {
+					r <<= 32;
+					r |= n.data [i];
+					ret.data [i] = (uint)(r / d);
+					r %= d;
+				}
+				ret.Normalize ();
+
+				return ret;
+			}
+
+			public static BigInteger [] DwordDivMod (BigInteger n, uint d)
+			{
+				BigInteger ret = new BigInteger (Sign.Positive , n.length);
+
+				ulong r = 0;
+				uint i = n.length;
+
+				while (i-- > 0) {
+					r <<= 32;
+					r |= n.data [i];
+					ret.data [i] = (uint)(r / d);
+					r %= d;
+				}
+				ret.Normalize ();
+
+				BigInteger rem = (uint)r;
+
+				return new BigInteger [] {ret, rem};
+			}
+
+				#endregion
+
+			#region BigNum
+
+			public static BigInteger [] multiByteDivide (BigInteger bi1, BigInteger bi2)
+			{
+				if (Kernel.Compare (bi1, bi2) == Sign.Negative)
+					return new BigInteger [2] { 0, new BigInteger (bi1) };
+
+				bi1.Normalize (); bi2.Normalize ();
+
+				if (bi2.length == 1)
+					return DwordDivMod (bi1, bi2.data [0]);
+
+				uint remainderLen = bi1.length + 1;
+				int divisorLen = (int)bi2.length + 1;
+
+				uint mask = 0x80000000;
+				uint val = bi2.data [bi2.length - 1];
+				int shift = 0;
+				int resultPos = (int)bi1.length - (int)bi2.length;
+
+				while (mask != 0 && (val & mask) == 0) {
+					shift++; mask >>= 1;
+				}
+
+				BigInteger quot = new BigInteger (Sign.Positive, bi1.length - bi2.length + 1);
+				BigInteger rem = (bi1 << shift);
+
+				uint [] remainder = rem.data;
+
+				bi2 = bi2 << shift;
+
+				int j = (int)(remainderLen - bi2.length);
+				int pos = (int)remainderLen - 1;
+
+				uint firstDivisorByte = bi2.data [bi2.length-1];
+				ulong secondDivisorByte = bi2.data [bi2.length-2];
+
+				while (j > 0) {
+					ulong dividend = ((ulong)remainder [pos] << 32) + (ulong)remainder [pos-1];
+
+					ulong q_hat = dividend / (ulong)firstDivisorByte;
+					ulong r_hat = dividend % (ulong)firstDivisorByte;
+
+					do {
+
+						if (q_hat == 0x100000000 ||
+							(q_hat * secondDivisorByte) > ((r_hat << 32) + remainder [pos-2])) {
+							q_hat--;
+							r_hat += (ulong)firstDivisorByte;
+
+							if (r_hat < 0x100000000)
+								continue;
+						}
+						break;
+					} while (true);
+
+					//
+					// At this point, q_hat is either exact, or one too large
+					// (more likely to be exact) so, we attempt to multiply the
+					// divisor by q_hat, if we get a borrow, we just subtract
+					// one from q_hat and add the divisor back.
+					//
+
+					uint t;
+					uint dPos = 0;
+					int nPos = pos - divisorLen + 1;
+					ulong mc = 0;
+					uint uint_q_hat = (uint)q_hat;
+					do {
+						mc += (ulong)bi2.data [dPos] * (ulong)uint_q_hat;
+						t = remainder [nPos];
+						remainder [nPos] -= (uint)mc;
+						mc >>= 32;
+						if (remainder [nPos] > t) mc++;
+						dPos++; nPos++;
+					} while (dPos < divisorLen);
+
+					nPos = pos - divisorLen + 1;
+					dPos = 0;
+
+					// Overestimate
+					if (mc != 0) {
+						uint_q_hat--;
+						ulong sum = 0;
+
+						do {
+							sum = ((ulong)remainder [nPos]) + ((ulong)bi2.data [dPos]) + sum;
+							remainder [nPos] = (uint)sum;
+							sum >>= 32;
+							dPos++; nPos++;
+						} while (dPos < divisorLen);
+
+					}
+
+					quot.data [resultPos--] = (uint)uint_q_hat;
+
+					pos--;
+					j--;
+				}
+
+				quot.Normalize ();
+				rem.Normalize ();
+				BigInteger [] ret = new BigInteger [2] { quot, rem };
+
+				if (shift != 0)
+					ret [1] >>= shift;
+
+				return ret;
+			}
+
+			#endregion
+
+			#endregion
+
+			#region Shift
+			public static BigInteger LeftShift (BigInteger bi, int n)
+			{
+				if (n == 0) return new BigInteger (bi, bi.length + 1);
+
+				int w = n >> 5;
+				n &= ((1 << 5) - 1);
+
+				BigInteger ret = new BigInteger (Sign.Positive, bi.length + 1 + (uint)w);
+
+				uint i = 0, l = bi.length;
+				if (n != 0) {
+					uint x, carry = 0;
+					while (i < l) {
+						x = bi.data [i];
+						ret.data [i + w] = (x << n) | carry;
+						carry = x >> (32 - n);
+						i++;
+					}
+					ret.data [i + w] = carry;
+				} else {
+					while (i < l) {
+						ret.data [i + w] = bi.data [i];
+						i++;
+					}
+				}
+
+				ret.Normalize ();
+				return ret;
+			}
+
+			public static BigInteger RightShift (BigInteger bi, int n)
+			{
+				if (n == 0) return new BigInteger (bi);
+
+				int w = n >> 5;
+				int s = n & ((1 << 5) - 1);
+
+				BigInteger ret = new BigInteger (Sign.Positive, bi.length - (uint)w + 1);
+				uint l = (uint)ret.data.Length - 1;
+
+				if (s != 0) {
+
+					uint x, carry = 0;
+
+					while (l-- > 0) {
+						x = bi.data [l + w];
+						ret.data [l] = (x >> n) | carry;
+						carry = x << (32 - n);
+					}
+				} else {
+					while (l-- > 0)
+						ret.data [l] = bi.data [l + w];
+
+				}
+				ret.Normalize ();
+				return ret;
+			}
+
+			#endregion
+
+			#region Multiply
+
+			public static BigInteger MultiplyByDword (BigInteger n, uint f)
+			{
+				BigInteger ret = new BigInteger (Sign.Positive, n.length + 1);
+
+				uint i = 0;
+				ulong c = 0;
+
+				do {
+					c += (ulong)n.data [i] * (ulong)f;
+					ret.data [i] = (uint)c;
+					c >>= 32;
+				} while (++i < n.length);
+				ret.data [i] = (uint)c;
+				ret.Normalize ();
+				return ret;
+
+			}
+
+			/// <summary>
+			/// Multiplies the data in x [xOffset:xOffset+xLen] by
+			/// y [yOffset:yOffset+yLen] and puts it into
+			/// d [dOffset:dOffset+xLen+yLen].
+			/// </summary>
+			public static void Multiply(uint[] x, uint xOffset, uint xLen, uint[] y, uint yOffset, uint yLen, uint[] d, uint dOffset)
+			{
+				uint xx = 0, yy = 0, dd = 0;
+				uint xP = xx + xOffset,
+					xE = xP + xLen,
+					yB = yy + yOffset,
+					yE = yB + yLen,
+					dB = dd + dOffset;
+
+				for (; xP < xE; xP++, dB++) {
+
+					if (x[xP] == 0) continue;
+
+					ulong mcarry = 0;
+
+					uint dP = dB;
+					for (uint yP = yB; yP < yE; yP++, dP++) {
+						mcarry += ((ulong)x[xP] * (ulong)y[yP]) + (ulong)d[dP];
+
+						d[dP] = (uint)mcarry;
+						mcarry >>= 32;
+					}
+
+					if (mcarry != 0)
+						d[dP] = (uint)mcarry;
+				}
+			}
+
+			/// <summary>
+			/// Multiplies the data in x [xOffset:xOffset+xLen] by
+			/// y [yOffset:yOffset+yLen] and puts the low mod words into
+			/// d [dOffset:dOffset+mod].
+			/// </summary>
+			public static void MultiplyMod2p32pmod(uint[] x, int xOffset, int xLen, uint[] y, int yOffest, int yLen, uint[] d, int dOffset, int mod)
+			{
+				uint xx = 0, yy = 0, dd = 0;
+				uint xP = (uint)(xx + xOffset),
+					xE = (uint)(xP + xLen),
+					yB = (uint)(yy + yOffest),
+					yE = (uint)(yB + yLen),
+					dB = (uint)(dd + dOffset),
+					dE = (uint)(dB + mod);
+
+				for (; xP < xE; xP++, dB++)
+				{
+
+					if (x[xP] == 0) continue;
+
+					ulong mcarry = 0;
+					uint dP = dB;
+					for (uint yP = yB; yP < yE && dP < dE; yP++, dP++)
+					{
+						mcarry += ((ulong)x[xP] * (ulong)y[yP]) + (ulong)d[dP];
+
+						d[dP] = (uint)mcarry;
+						mcarry >>= 32;
+					}
+
+					if (mcarry != 0 && dP < dE)
+						d[dP] = (uint)mcarry;
+				}
+			}
+
+			public static void SquarePositive(BigInteger bi, ref uint[] wkSpace) {
+				uint[] t = wkSpace;
+				wkSpace = bi.data;
+				uint[] d = bi.data;
+				uint dl = bi.length;
+				bi.data = t;
+
+				uint dd = 0, tt = 0;
+
+				uint ttE = (uint)t.Length;
+				// Clear the dest
+				for (uint ttt = tt; ttt < ttE; ttt++)
+					t[ttt] = 0;
+
+				uint dP = dd, tP = tt;
+
+				for (uint i = 0; i < dl; i++, dP++) {
+					if (d[dP] == 0)
+						continue;
+
+					ulong mcarry = 0;
+					uint bi1val = d[dP];
+
+					uint dP2 = dP + 1, tP2 = tP + 2 * i + 1;
+
+					for (uint j = i + 1; j < dl; j++, tP2++, dP2++) {
+						// k = i + j
+						mcarry += ((ulong)bi1val * (ulong)d[dP2]) + t[tP2];
+
+						t[tP2] = (uint)mcarry;
+						mcarry >>= 32;
+					}
+
+					if (mcarry != 0)
+						t[tP2] = (uint)mcarry;
+				}
+
+				// Double t. Inlined for speed.
+
+				tP = tt;
+
+				uint x, carry = 0;
+				while (tP < ttE) {
+					x = t[tP];
+					t[tP] = (x << 1) | carry;
+					carry = x >> (32 - 1);
+					tP++;
+				}
+				if (carry != 0) t[tP] = carry;
+
+				// Add in the diagnals
+
+				dP = dd;
+				tP = tt;
+				for (uint dE = dP + dl; (dP < dE); dP++, tP++) {
+					ulong val = (ulong)d[dP] * (ulong)d[dP] + t[tP];
+					t[tP] = (uint)val;
+					val >>= 32;
+					t[(++tP)] += (uint)val;
+					if (t[tP] < (uint)val) {
+						uint tP3 = tP;
+						// Account for the first carry
+						(t[++tP3])++;
+
+						// Keep adding until no carry
+						while ((t[tP3++]) == 0x0)
+							(t[tP3])++;
+					}
+
+				}
+
+				bi.length <<= 1;
+
+				// Normalize length
+				while (t[tt + bi.length - 1] == 0 && bi.length > 1) bi.length--;
+
+			}
+#if UNUSED
+			public static bool Double (uint [] u, int l)
+			{
+				uint x, carry = 0;
+				uint i = 0;
+				while (i < l) {
+					x = u [i];
+					u [i] = (x << 1) | carry;
+					carry = x >> (32 - 1);
+					i++;
+				}
+				if (carry != 0) u [l] = carry;
+				return carry != 0;
+			}
+#endif
+			#endregion
+
+			#region Number Theory
+
+			public static BigInteger gcd (BigInteger a, BigInteger b)
+			{
+				BigInteger x = a;
+				BigInteger y = b;
+
+				BigInteger g = y;
+
+				while (x.length > 1) {
+					g = x;
+					x = y % x;
+					y = g;
+
+				}
+				if (x == 0) return g;
+
+				// TODO: should we have something here if we can convert to long?
+
+				//
+				// Now we can just do it with single precision. I am using the binary gcd method,
+				// as it should be faster.
+				//
+
+				uint yy = x.data [0];
+				uint xx = y % yy;
+
+				int t = 0;
+
+				while (((xx | yy) & 1) == 0) {
+					xx >>= 1; yy >>= 1; t++;
+				}
+				while (xx != 0) {
+					while ((xx & 1) == 0) xx >>= 1;
+					while ((yy & 1) == 0) yy >>= 1;
+					if (xx >= yy)
+						xx = (xx - yy) >> 1;
+					else
+						yy = (yy - xx) >> 1;
+				}
+
+				return yy << t;
+			}
+
+			public static uint modInverse (BigInteger bi, uint modulus)
+			{
+				uint a = modulus, b = bi % modulus;
+				uint p0 = 0, p1 = 1;
+
+				while (b != 0) {
+					if (b == 1)
+						return p1;
+					p0 += (a / b) * p1;
+					a %= b;
+
+					if (a == 0)
+						break;
+					if (a == 1)
+						return modulus-p0;
+
+					p1 += (b / a) * p0;
+					b %= a;
+
+				}
+				return 0;
+			}
+			
+			public static BigInteger modInverse (BigInteger bi, BigInteger modulus)
+			{
+				if (modulus.length == 1) return modInverse (bi, modulus.data [0]);
+
+				BigInteger [] p = { 0, 1 };
+				BigInteger [] q = new BigInteger [2];    // quotients
+				BigInteger [] r = { 0, 0 };             // remainders
+
+				int step = 0;
+
+				BigInteger a = modulus;
+				BigInteger b = bi;
+
+				ModulusRing mr = new ModulusRing (modulus);
+
+				while (b != 0) {
+
+					if (step > 1) {
+
+						BigInteger pval = mr.Difference (p [0], p [1] * q [0]);
+						p [0] = p [1]; p [1] = pval;
+					}
+
+					BigInteger [] divret = multiByteDivide (a, b);
+
+					q [0] = q [1]; q [1] = divret [0];
+					r [0] = r [1]; r [1] = divret [1];
+					a = b;
+					b = divret [1];
+
+					step++;
+				}
+
+				if (r [0] != 1)
+					throw (new ArithmeticException ("No inverse!"));
+
+				return mr.Difference (p [0], p [1] * q [0]);
+
+			}
+			#endregion
+		}
+	}
+}