/DiffieHellman/mono/BigInteger.cs
C# | 2257 lines | 1532 code | 477 blank | 248 comment | 421 complexity | 2960cb33f32a806a2ac62e97d6c2dbce MD5 | raw file
Large files files are truncated, but you can click here to view the full file
- //
- // 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.
-
- using System;
- using System.Security.Cryptography;
- using Mono.Math.Prime;
- using Mono.Math.Prime.Generator;
-
- namespace Mono.Math {
-
- [CLSCompliant(false)]
- 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 Exception ();
- }
- }
-
- public static int operator % (BigInteger bi, int i)
- {
- if (i > 0)
- return (int)Kernel.DwordMod (bi, (uint)i);
- else
- return -(int)Kernel.DwordMod (bi, (uint)-i);
- }
-
- public static uint operator % (BigInteger bi, uint ui)
- {
- return Kernel.DwordMod (bi, (uint)ui);
- }
-
- public static BigInteger operator % (BigInteger bi1, BigInteger bi2)
- {
- return Kernel.multiByteDivide (bi1, bi2)[1];
- }
-
- public static BigInteger operator / (BigInteger bi, int i)
- {
- if (i > 0)
- return Kernel.DwordDiv (bi, (uint)i);
-
- throw new ArithmeticException (WouldReturnNegVal);
- }
-
- public static BigInteger operator / (BigInteger bi1, BigInteger bi2)
- {
- return Kernel.multiByteDivide (bi1, bi2)[0];
- }
-
- public static BigInteger operator * (BigInteger bi1, BigInteger bi2)
- {
- if (bi1 == 0 || bi2 == 0) return 0;
-
- //
- // Validate pointers
- //
- if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException ("bi1 out of range");
- if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException ("bi2 out of range");
-
- BigInteger ret = new BigInteger (Sign.Positive, bi1.length + bi2.length);
-
- Kernel.Multiply (bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);
-
- ret.Normalize ();
- return ret;
- }
-
- public static BigInteger operator * (BigInteger bi, int i)
- {
- if (i < 0) throw new ArithmeticException (WouldReturnNegVal);
- if (i == 0) return 0;
- if (i == 1) return new BigInteger (bi);
-
- return Kernel.MultiplyByDword (bi, (uint)i);
- }
-
- public static BigInteger operator << (BigInteger bi1, int shiftVal)
- {
- return Kernel.LeftShift (bi1, shiftVal);
- }
-
- public static BigInteger operator >> (BigInteger bi1, int shiftVal)
- {
- return Kernel.RightShift (bi1, shiftVal);
- }
-
- #endregion
-
- #region 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 IndexOutOfRangeException ("bitNum out of range");
-
- uint bytePos = (uint)bitNum >> 5; // divide by 32
- byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits
-
- uint mask = (uint)1 << bitPos;
- return ((this.data [bytePos] | mask) == this.data [bytePos]);
- }
-
- public void setBit (uint bitNum)
- {
- setBit (bitNum, true);
- }
- public void clearBit (uint bitNum)
- {
- setBit (bitNum, false);
- }
-
- public void setBit (uint bitNum, bool 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, 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, 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 Exception ();
- }
-
- if (diff >= mod) {
- if (diff.length >= mod.length << 1)
- diff %= mod;
- else
- BarrettReduction (diff);
- }
- if (cmp == Sign.Negative)
- diff = mod - diff;
- return diff;
- }
-
- public BigInteger Pow (BigInteger b, BigInteger exp)
- {
- if ((mod.data [0] & 1) == 1) return OddPow (b, exp);
- else return EvenPow (b, exp);
- }
-
- public BigInteger EvenPow (BigInteger b, BigInteger exp)
- {
- BigInteger resultNum = new BigInteger ((BigInteger)1, mod.length << 1);
- BigInteger tempNum = new BigInteger (b % mod, mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
-
- uint totalBits = (uint)exp.bitCount ();
-
- uint [] wkspace = new uint [mod.length << 1];
-
- // perform squaring and multiply exponentiation
- for (uint pos = 0; pos < totalBits; pos++) {
- if (exp.testBit (pos)) {
-
- Array.Clear (wkspace, 0, wkspace.Length);
- Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
- resultNum.length += tempNum.length;
- uint [] t = wkspace;
- wkspace = resultNum.data;
- resultNum.data = t;
-
- BarrettReduction (resultNum);
- }
-
- Kernel.SquarePositive (tempNum, ref wkspace);
- BarrettReduction (tempNum);
-
- if (tempNum == 1) {
- return resultNum;
- }
- }
-
- return resultNum;
- }
-
- private BigInteger OddPow (BigInteger b, BigInteger exp)
- {
- BigInteger resultNum = new BigInteger (Montgomery.ToMont (1, mod), mod.length << 1);
- BigInteger tempNum = new BigInteger (Montgomery.ToMont (b, mod), mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
- uint mPrime = Montgomery.Inverse (mod.data [0]);
- uint totalBits = (uint)exp.bitCount ();
-
- uint [] wkspace = new uint [mod.length << 1];
-
- // perform squaring and multiply exponentiation
- for (uint pos = 0; pos < totalBits; pos++) {
- if (exp.testBit (pos)) {
-
- Array.Clear (wkspace, 0, wkspace.Length);
- Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
- resultNum.length += tempNum.length;
- uint [] t = wkspace;
- wkspace = resultNum.data;
- resultNum.data = t;
-
- Montgomery.Reduce (resultNum, mod, mPrime);
- }
-
- Kernel.SquarePositive (tempNum, ref wkspace);
- Montgomery.Reduce (tempNum, mod, mPrime);
- }
-
- Montgomery.Reduce (resultNum, mod, mPrime);
- return resultNum;
- }
-
- #region Pow Small Base
-
- // TODO: Make tests for this, not really needed b/c prime stuff
- // checks it, but still would be nice
- public BigInteger Pow (uint b, BigInteger exp)
- {
- if (b != 2) {
- if ((mod.data [0] & 1) == 1) return OddPow (b, exp);
- else return EvenPow (b, exp);
- } 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 = (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);
-
- 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;
- }
-
- 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
- }
-
- 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 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;
- }
-
- 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 {
-
- #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 (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 =…
Large files files are truncated, but you can click here to view the full file