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RobustToolbox/Lidgren.Network/NetBigInteger.cs
spoogemonster b59a2b6be3 moving main source tree into trunk
2011-05-11 03:58:10 +00:00

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//
// 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;
//using Mono.Math.Prime.Generator;
//using Mono.Math.Prime;
namespace Lidgren.Network
{
#if INSIDE_CORLIB
internal
#else
public
#endif
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 BigInteger Modulus(BigInteger mod)
{
return BigInteger.Modulus(this, mod);
}
public BigInteger Multiply(BigInteger mult)
{
return BigInteger.Multiply(this, mult);
}
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
#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
}
}
}
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