/SSISSSHFTP/SSISSharpSSHFTP/SharpSSH/BigInteger.cs

using System;

using System.Collections.Generic;

using System.Text;



namespace Tamir.SharpSsh

{

    //

    // 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;



    public 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

		};



        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];

            this.length = DEFAULT_LEN;

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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;

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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();

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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();

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public BigInteger(uint ui)

        {

            data = new uint[] { ui };

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public BigInteger(ulong ul)

        {

            data = new uint[2] { (uint)ul, (uint)(ul >> 32) };

            length = 2;



            this.Normalize();

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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));

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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);

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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);

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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 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 GenerateRandom(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 GenerateRandom(int bits)

        {

            return GenerateRandom(bits, Rng);

        }



        /// <summary>

        /// Randomizes the bits in "this" from the specified RNG.

        /// </summary>

        /// <param name="rng">A RNG.</param>

        public void Randomize(RandomNumberGenerator rng)

        {

            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];



            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>

#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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]);

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public void SetBit(uint bitNum)

        {

            SetBit(bitNum, true);

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public void ClearBit(uint bitNum)

        {

            SetBit(bitNum, false);

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public static bool operator ==(BigInteger bi1, uint ui)

        {

            if (bi1.length != 1) bi1.Normalize();

            return bi1.length == 1 && bi1.data[0] == ui;

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        public string ToString(uint radix)

        {

            return ToString(radix, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");

        }



#if !INSIDE_CORLIB

        [CLSCompliant(false)]

#endif

        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, Prime.ConfidenceFactor.Medium);

        }

        */



        #endregion



        #region Prime Number Generation





        /// <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



#if INSIDE_CORLIB

		internal

#else

        public

#endif

 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

#if !INSIDE_CORLIB

            [CLSCompliant(false)]

#endif

            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

                            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>

            /// <remarks>

            /// This code is unsafe! It is the caller's responsibility to make

            /// sure that it is safe to access x [xOffset:xOffset+xLen],

            /// y [yOffset:yOffset+yLen], and d [dOffset:dOffset+xLen+yLen].

            /// </remarks>

            public static unsafe void Multiply(uint[] x, uint xOffset, uint xLen, uint[] y, uint yOffset, uint yLen, uint[] d, uint dOffset)

            {

                fixed (uint* xx = x, yy = y, dd = d)

                {

                    uint* xP = xx + xOffset,

                        xE = xP + xLen,

                        yB = yy + yOffset,

                        yE = yB + yLen,

                        dB = dd + dOffset;



                    for (; xP < xE; xP++, dB++)

                    {



                        if (*xP == 0) continue;



                        ulong mcarry = 0;



                        uint* dP = dB;

                        for (uint* yP = yB; yP < yE; yP++, dP++)

                        {

                            mcarry += ((ulong)*xP * (ulong)*yP) + (ulong)*dP;



                            *dP = (uint)mcarry;

                            mcarry >>= 32;

                        }



                        if (mcarry != 0)

                            *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>

            /// <remarks>

            /// This code is unsafe! It is the caller's responsibility to make

            /// sure that it is safe to access x [xOffset:xOffset+xLen],

            /// y [yOffset:yOffset+yLen], and d [dOffset:dOffset+mod].

            /// </remarks>

            public static unsafe void MultiplyMod2p32pmod(uint[] x, int xOffset, int xLen, uint[] y, int yOffest, int yLen, uint[] d, int dOffset, int mod)

            {

                fixed (uint* xx = x, yy = y, dd = d)

                {

                    uint* xP = xx + xOffset,

                        xE = xP + xLen,

                        yB = yy + yOffest,

                        yE = yB + yLen,

                        dB = dd + dOffset,

                        dE = dB + mod;



                    for (; xP < xE; xP++, dB++)

                    {



                        if (*xP == 0) continue;



                        ulong mcarry = 0;

                        uint* dP = dB;

                        for (uint* yP = yB; yP < yE && dP < dE; yP++, dP++)

                        {

                            mcarry += ((ulong)*xP * (ulong)*yP) + (ulong)*dP;



                            *dP = (uint)mcarry;

                            mcarry >>= 32;

                        }



                        if (mcarry != 0 && dP < dE)

                            *dP = (uint)mcarry;

                    }

                }

            }



            public static unsafe void SquarePositive(BigInteger bi, ref uint[] wkSpace)

            {

                uint[] t = wkSpace;

                wkSpace = bi.data;

                uint[] d = bi.data;

                uint dl = bi.length;

                bi.data = t;



                fixed (uint* dd = d, tt = t)

                {



                    uint* ttE = tt + t.Length;

                    // Clear the dest

                    for (uint* ttt = tt; ttt < ttE; ttt++)

                        *ttt = 0;



                    uint* dP = dd, tP = tt;



                    for (uint i = 0; i < dl; i++, dP++)

                    {

                        if (*dP == 0)

                            continue;



                        ulong mcarry = 0;

                        uint bi1val = *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)*dP2) + *tP2;



                            *tP2 = (uint)mcarry;

                            mcarry >>= 32;

                        }



                        if (mcarry != 0)

                            *tP2 = (uint)mcarry;

                    }



                    // Double t. Inlined for speed.



                    tP = tt;



                    uint x, carry = 0;

                    while (tP < ttE)

                    {

                        x = *tP;

                        *tP = (x << 1) | carry;

                        carry = x >> (32 - 1);

                        tP++;

                    }

                    if (carry != 0) *tP = carry;



                    // Add in the diagnals



                    dP = dd;

                    tP = tt;

                    for (uint* dE = dP + dl; (dP < dE); dP++, tP++)

                    {

                        ulong val = (ulong)*dP * (ulong)*dP + *tP;

                        *tP = (uint)val;

                        val >>= 32;

                        *(++tP) += (uint)val;

                        if (*tP < (uint)val)

                        {

                            uint* tP3 = tP;

                            // Account for the first carry

                            (*++tP3)++;



                            // Keep adding until no carry

                            while ((*tP3++) == 0)

                                (*tP3)++;

                        }



                    }



                    bi.length <<= 1;



                    // Normalize length

                    while (tt[bi.length - 1] == 0 && bi.length > 1) bi.length--;



                }

            }



            /* 

             * Never called in BigInteger (and part of a private class)

             * 			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;

                        }*/



            #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

        }

    }

}