// <auto-generated />

//

// BigInteger.cs - Big Integer implementation

//

// Authors:

// Ben Maurer

// Chew Keong TAN

// Sebastien Pouliot (spouliot@motus.com)

//

// Copyright (c) 2003 Ben Maurer

// All rights reserved

//

// Copyright (c) 2002 Chew Keong TAN

// All rights reserved.

//

// Modified 2007 Andrew Arnott (http://blog.nerdbank.net)

// Rewrote unsafe code as safe code.

using System;

using System.Security.Cryptography;

using Mono.Math.Prime;

using Mono.Math.Prime.Generator;

namespace Mono.Math {

internal class BigInteger {

#region Data Storage

/// <summary>

/// The Length of this BigInteger

/// </summary>

uint length = 1;

/// <summary>

/// The data for this BigInteger

/// </summary>

uint [] data;

#endregion

#region Constants

/// <summary>

/// Default length of a BigInteger in bytes

/// </summary>

const uint DEFAULT_LEN = 20;

/// <summary>

/// Table of primes below 2000.

/// </summary>

/// <remarks>

/// <para>

/// This table was generated using Mathematica 4.1 using the following function:

/// </para>

/// <para>

/// <code>

/// PrimeTable [x_] := Prime [Range [1, PrimePi [x]]]

/// PrimeTable [6000]

/// </code>

/// </para>

/// </remarks>

public static readonly uint [] smallPrimes = {

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,

73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,

157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,

239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,

331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,

421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503,

509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,

613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,

709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,

821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,

919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,

1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,

1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181,

1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,

1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,

1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471,

1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,

1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,

1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,

1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867,

1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973,

1979, 1987, 1993, 1997, 1999,

2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089,

2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207,

2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,

2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389,

2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,

2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,

2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707,

2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797,

2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,

2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,

3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109,

3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,

3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329,

3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449,

3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,

3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631,

3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,

3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,

3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943,

3947, 3967, 3989,

4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091,

4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,

4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,

4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,

4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523,

4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649,

4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,

4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,

4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987,

4993, 4999,

5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101,

5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231,

5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351,

5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,

5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563,

5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669,

5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,

5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869,

5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987

};

public enum Sign : int {

Negative = -1,

Zero = 0,

Positive = 1

};

#region Exception Messages

const string WouldReturnNegVal = "Operation would return a negative value";

#endregion

#endregion

#region Constructors

public BigInteger ()

{

data = new uint [DEFAULT_LEN];

}

public BigInteger (Sign sign, uint len)

{

this.data = new uint [len];

this.length = len;

}

public BigInteger (BigInteger bi)

{

this.data = (uint [])bi.data.Clone ();

this.length = bi.length;

}

public BigInteger (BigInteger bi, uint len)

{

this.data = new uint [len];

for (uint i = 0; i < bi.length; i++)

this.data [i] = bi.data [i];

this.length = bi.length;

}

#endregion

public static BigInteger Parse(string number) {

if (number == null)

throw new ArgumentNullException(number);

int i = 0, len = number.Length;

char c;

bool digits_seen = false;

BigInteger val = new BigInteger(0);

if (number[i] == '+') {

i++;

} else if(number[i] == '-') {

throw new FormatException("Only positive integers are allowed.");

}

for(; i < len; i++) {

c = number[i];

if (c == '\0') {

i = len;

continue;

}

if (c >= '0' && c <= '9'){

val = val * 10 + (c - '0');

digits_seen = true;

} else {

if (Char.IsWhiteSpace(c)){

for (i++; i < len; i++){

if (!Char.IsWhiteSpace (number[i]))

throw new FormatException();

}

break;

} else

throw new FormatException();

}

}

if (!digits_seen)

throw new FormatException();

return val;

}

#region Conversions

public BigInteger (byte [] inData)

{

length = (uint)inData.Length >> 2;

int leftOver = inData.Length & 0x3;

// length not multiples of 4

if (leftOver != 0) length++;

data = new uint [length];

for (int i = inData.Length - 1, j = 0; i >= 3; i -= 4, j++) {

data [j] = (uint)(

(inData [i-3] << (3*8)) |

(inData [i-2] << (2*8)) |

(inData [i-1] << (1*8)) |

(inData [i-0] << (0*8))

);

}

switch (leftOver) {

case 1: data [length-1] = (uint)inData [0]; break;

case 2: data [length-1] = (uint)((inData [0] << 8) | inData [1]); break;

case 3: data [length-1] = (uint)((inData [0] << 16) | (inData [1] << 8) | inData [2]); break;

}

this.Normalize ();

}

public BigInteger (uint [] inData)

{

length = (uint)inData.Length;

data = new uint [length];

for (int i = (int)length - 1, j = 0; i >= 0; i--, j++)

data [j] = inData [i];

this.Normalize ();

}

public BigInteger (uint ui)

{

data = new uint [] {ui};

}

public BigInteger (ulong ul)

{

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

length = 2;

this.Normalize ();

}

public static implicit operator BigInteger (uint value)

{

return (new BigInteger (value));

}

public static implicit operator BigInteger (int value)

{

if (value < 0) throw new ArgumentOutOfRangeException ("value");

return (new BigInteger ((uint)value));

}

public static implicit operator BigInteger (ulong value)

{

return (new BigInteger (value));

}

#endregion

#region Operators

public static BigInteger operator + (BigInteger bi1, BigInteger bi2)

{

if (bi1 == 0)

return new BigInteger (bi2);

else if (bi2 == 0)

return new BigInteger (bi1);

else

return Kernel.AddSameSign (bi1, bi2);

}

public static BigInteger operator - (BigInteger bi1, BigInteger bi2)

{

if (bi2 == 0)

return new BigInteger (bi1);

if (bi1 == 0)

throw new ArithmeticException (WouldReturnNegVal);

switch (Kernel.Compare (bi1, bi2)) {

case Sign.Zero:

return 0;

case Sign.Positive:

return Kernel.Subtract (bi1, bi2);

case Sign.Negative:

throw new ArithmeticException (WouldReturnNegVal);

default:

throw new InvalidOperationException ();

}

}

public static int operator % (BigInteger bi, int i)

{

if (i > 0)

return (int)Kernel.DwordMod (bi, (uint)i);

else

return -(int)Kernel.DwordMod (bi, (uint)-i);

}

public static uint operator % (BigInteger bi, uint ui)

{

return Kernel.DwordMod (bi, (uint)ui);

}

public static BigInteger operator % (BigInteger bi1, BigInteger bi2)

{

return Kernel.multiByteDivide (bi1, bi2)[1];

}

public static BigInteger operator / (BigInteger bi, int i)

{

if (i > 0)

return Kernel.DwordDiv (bi, (uint)i);

throw new ArithmeticException (WouldReturnNegVal);

}

public static BigInteger operator / (BigInteger bi1, BigInteger bi2)

{

return Kernel.multiByteDivide (bi1, bi2)[0];

}

public static BigInteger operator * (BigInteger bi1, BigInteger bi2)

{

if (bi1 == 0 || bi2 == 0) return 0;

//

// Validate pointers

//

if (bi1.data.Length < bi1.length) throw new IndexOutOfRangeException ("bi1 out of range");

if (bi2.data.Length < bi2.length) throw new IndexOutOfRangeException ("bi2 out of range");

BigInteger ret = new BigInteger (Sign.Positive, bi1.length + bi2.length);

Kernel.Multiply (bi1.data, 0, bi1.length, bi2.data, 0, bi2.length, ret.data, 0);

ret.Normalize ();

return ret;

}

public static BigInteger operator * (BigInteger bi, int i)

{

if (i < 0) throw new ArithmeticException (WouldReturnNegVal);

if (i == 0) return 0;

if (i == 1) return new BigInteger (bi);

return Kernel.MultiplyByDword (bi, (uint)i);

}

public static BigInteger operator << (BigInteger bi1, int shiftVal)

{

return Kernel.LeftShift (bi1, shiftVal);

}

public static BigInteger operator >> (BigInteger bi1, int shiftVal)

{

return Kernel.RightShift (bi1, shiftVal);

}

#endregion

#region Random

private static RandomNumberGenerator rng;

private static RandomNumberGenerator Rng {

get {

if (rng == null)

rng = RandomNumberGenerator.Create ();

return rng;

}

}

/// <summary>

/// Generates a new, random BigInteger of the specified length.

/// </summary>

/// <param name="bits">The number of bits for the new number.</param>

/// <param name="rng">A random number generator to use to obtain the bits.</param>

/// <returns>A random number of the specified length.</returns>

public static BigInteger genRandom (int bits, RandomNumberGenerator rng)

{

int dwords = bits >> 5;

int remBits = bits & 0x1F;

if (remBits != 0)

dwords++;

BigInteger ret = new BigInteger (Sign.Positive, (uint)dwords + 1);

byte [] random = new byte [dwords << 2];

rng.GetBytes (random);

Buffer.BlockCopy (random, 0, ret.data, 0, (int)dwords << 2);

if (remBits != 0) {

uint mask = (uint)(0x01 << (remBits-1));

ret.data [dwords-1] |= mask;

mask = (uint)(0xFFFFFFFF >> (32 - remBits));

ret.data [dwords-1] &= mask;

}

else

ret.data [dwords-1] |= 0x80000000;

ret.Normalize ();

return ret;

}

/// <summary>

/// Generates a new, random BigInteger of the specified length using the default RNG crypto service provider.

/// </summary>

/// <param name="bits">The number of bits for the new number.</param>

/// <returns>A random number of the specified length.</returns>

public static BigInteger genRandom (int bits)

{

return genRandom (bits, Rng);

}

/// <summary>

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

/// </summary>

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

public void randomize (RandomNumberGenerator rng)

{

int bits = this.bitCount ();

int dwords = bits >> 5;

int remBits = bits & 0x1F;

if (remBits != 0)

dwords++;

byte [] random = new byte [dwords << 2];

rng.GetBytes (random);

Buffer.BlockCopy (random, 0, data, 0, (int)dwords << 2);

if (remBits != 0) {

uint mask = (uint)(0x01 << (remBits-1));

data [dwords-1] |= mask;

mask = (uint)(0xFFFFFFFF >> (32 - remBits));

data [dwords-1] &= mask;

}

else

data [dwords-1] |= 0x80000000;

Normalize ();

}

/// <summary>

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

/// </summary>

public void randomize ()

{

randomize (Rng);

}

#endregion

#region Bitwise

public int bitCount ()

{

this.Normalize ();

uint value = data [length - 1];

uint mask = 0x80000000;

uint bits = 32;

while (bits > 0 && (value & mask) == 0) {

bits--;

mask >>= 1;

}

bits += ((length - 1) << 5);

return (int)bits;

}

/// <summary>

/// Tests if the specified bit is 1.

/// </summary>

/// <param name="bitNum">The bit to test. The least significant bit is 0.</param>

/// <returns>True if bitNum is set to 1, else false.</returns>

public bool testBit (uint bitNum)

{

uint bytePos = bitNum >> 5; // divide by 32

byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits

uint mask = (uint)1 << bitPos;

return ((this.data [bytePos] & mask) != 0);

}

public bool testBit (int bitNum)

{

if (bitNum < 0) throw new ArgumentOutOfRangeException ("bitNum");

uint bytePos = (uint)bitNum >> 5; // divide by 32

byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits

uint mask = (uint)1 << bitPos;

return ((this.data [bytePos] | mask) == this.data [bytePos]);

}

public void setBit (uint bitNum)

{

setBit (bitNum, true);

}

public void clearBit (uint bitNum)

{

setBit (bitNum, false);

}

public void setBit (uint bitNum, bool val)

{

uint bytePos = bitNum >> 5; // divide by 32

if (bytePos < this.length) {

uint mask = (uint)1 << (int)(bitNum & 0x1F);

if (val)

this.data [bytePos] |= mask;

else

this.data [bytePos] &= ~mask;

}

}

public int LowestSetBit ()

{

if (this == 0) return -1;

int i = 0;

while (!testBit (i)) i++;

return i;

}

public byte [] getBytes ()

{

if (this == 0) return new byte [1];

int numBits = bitCount ();

int numBytes = numBits >> 3;

if ((numBits & 0x7) != 0)

numBytes++;

byte [] result = new byte [numBytes];

int numBytesInWord = numBytes & 0x3;

if (numBytesInWord == 0) numBytesInWord = 4;

int pos = 0;

for (int i = (int)length - 1; i >= 0; i--) {

uint val = data [i];

for (int j = numBytesInWord - 1; j >= 0; j--) {

result [pos+j] = (byte)(val & 0xFF);

val >>= 8;

}

pos += numBytesInWord;

numBytesInWord = 4;

}

return result;

}

#endregion

#region Compare

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

{

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

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

}

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

{

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

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

}

public static bool operator == (BigInteger bi1, BigInteger bi2)

{

// we need to compare with null

if ((bi1 as object) == (bi2 as object))

return true;

if (null == bi1 || null == bi2)

return false;

return Kernel.Compare (bi1, bi2) == 0;

}

public static bool operator != (BigInteger bi1, BigInteger bi2)

{

// we need to compare with null

if ((bi1 as object) == (bi2 as object))

return false;

if (null == bi1 || null == bi2)

return true;

return Kernel.Compare (bi1, bi2) != 0;

}

public static bool operator > (BigInteger bi1, BigInteger bi2)

{

return Kernel.Compare (bi1, bi2) > 0;

}

public static bool operator < (BigInteger bi1, BigInteger bi2)

{

return Kernel.Compare (bi1, bi2) < 0;

}

public static bool operator >= (BigInteger bi1, BigInteger bi2)

{

return Kernel.Compare (bi1, bi2) >= 0;

}

public static bool operator <= (BigInteger bi1, BigInteger bi2)

{

return Kernel.Compare (bi1, bi2) <= 0;

}

public Sign Compare (BigInteger bi)

{

return Kernel.Compare (this, bi);

}

#endregion

#region Formatting

public string ToString (uint radix)

{

return ToString (radix, "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ");

}

public string ToString (uint radix, string charSet)

{

if (charSet.Length < radix)

throw new ArgumentException ("charSet length less than radix", "charSet");

if (radix == 1)

throw new ArgumentException ("There is no such thing as radix one notation", "radix");

if (this == 0) return "0";

if (this == 1) return "1";

string result = "";

BigInteger a = new BigInteger (this);

while (a != 0) {

uint rem = Kernel.SingleByteDivideInPlace (a, radix);

result = charSet [ (int)rem] + result;

}

return result;

}

#endregion

#region Misc

/// <summary>

/// Normalizes this by setting the length to the actual number of

/// uints used in data and by setting the sign to Sign.Zero if the

/// value of this is 0.

/// </summary>

private void Normalize ()

{

// Normalize length

while (length > 0 && data [length-1] == 0) length--;

// Check for zero

if (length == 0)

length++;

}

public void Clear ()

{

for (int i=0; i < length; i++)

data [i] = 0x00;

}

#endregion

#region Object Impl

public override int GetHashCode ()

{

uint val = 0;

for (uint i = 0; i < this.length; i++)

val ^= this.data [i];

return (int)val;

}

public override string ToString ()

{

return ToString (10);

}

public override bool Equals (object o)

{

if (o == null) return false;

if (o is int) return (int)o >= 0 && this == (uint)o;

return Kernel.Compare (this, (BigInteger)o) == 0;

}

#endregion

#region Number Theory

public BigInteger gcd (BigInteger bi)

{

return Kernel.gcd (this, bi);

}

public BigInteger modInverse (BigInteger mod)

{

return Kernel.modInverse (this, mod);

}

public BigInteger modPow (BigInteger exp, BigInteger n)

{

ModulusRing mr = new ModulusRing (n);

return mr.Pow (this, exp);

}

#endregion

#region Prime Testing

public bool isProbablePrime ()

{

for (int p = 0; p < smallPrimes.Length; p++) {

if (this == smallPrimes [p])

return true;

if (this % smallPrimes [p] == 0)

return false;

}

return PrimalityTests.RabinMillerTest (this, Prime.ConfidenceFactor.Medium);

}

[Obsolete]

public bool isProbablePrime (int notUsed)

{

for (int p = 0; p < smallPrimes.Length; p++) {

if (this % smallPrimes [p] == 0)

return false;

}

return

PrimalityTests.SmallPrimeSppTest (this, Prime.ConfidenceFactor.Medium);

}

#endregion

#region Prime Number Generation

/// <summary>

/// Generates the smallest prime >= bi

/// </summary>

/// <param name="bi">A BigInteger</param>

/// <returns>The smallest prime >= bi. More mathematically, if bi is prime: bi, else Prime [PrimePi [bi] + 1].</returns>

public static BigInteger NextHightestPrime (BigInteger bi)

{

NextPrimeFinder npf = new NextPrimeFinder ();

return npf.GenerateNewPrime (0, bi);

}

public static BigInteger genPseudoPrime (int bits)

{

SequentialSearchPrimeGeneratorBase sspg = new SequentialSearchPrimeGeneratorBase ();

return sspg.GenerateNewPrime (bits);

}

/// <summary>

/// Increments this by two

/// </summary>

public void Incr2 ()

{

int i = 0;

data [0] += 2;

// If there was no carry, nothing to do

if (data [0] < 2) {

// Account for the first carry

data [++i]++;

// Keep adding until no carry

while (data [i++] == 0x0)

data [i]++;

// See if we increased the data length

if (length == (uint)i)

length++;

}

}

#endregion

public sealed class ModulusRing {

BigInteger mod, constant;

public ModulusRing (BigInteger mod)

{

this.mod = mod;

// calculate constant = b^ (2k) / m

uint i = mod.length << 1;

constant = new BigInteger (Sign.Positive, i + 1);

constant.data [i] = 0x00000001;

constant = constant / mod;

}

public void BarrettReduction (BigInteger x)

{

BigInteger n = mod;

uint k = n.length,

kPlusOne = k+1,

kMinusOne = k-1;

// x < mod, so nothing to do.

if (x.length < k) return;

BigInteger q3;

//

// Validate pointers

//

if (x.data.Length < x.length) throw new IndexOutOfRangeException ("x out of range");

// q1 = x / b^ (k-1)

// q2 = q1 * constant

// q3 = q2 / b^ (k+1), Needs to be accessed with an offset of kPlusOne

// TODO: We should the method in HAC p 604 to do this (14.45)

q3 = new BigInteger (Sign.Positive, x.length - kMinusOne + constant.length);

Kernel.Multiply (x.data, kMinusOne, x.length - kMinusOne, constant.data, 0, constant.length, q3.data, 0);

// r1 = x mod b^ (k+1)

// i.e. keep the lowest (k+1) words

uint lengthToCopy = (x.length > kPlusOne) ? kPlusOne : x.length;

x.length = lengthToCopy;

x.Normalize ();

// r2 = (q3 * n) mod b^ (k+1)

// partial multiplication of q3 and n

BigInteger r2 = new BigInteger (Sign.Positive, kPlusOne);

Kernel.MultiplyMod2p32pmod (q3.data, (int)kPlusOne, (int)q3.length - (int)kPlusOne, n.data, 0, (int)n.length, r2.data, 0, (int)kPlusOne);

r2.Normalize ();

if (r2 < x) {

Kernel.MinusEq (x, r2);

} else {

BigInteger val = new BigInteger (Sign.Positive, kPlusOne + 1);

val.data [kPlusOne] = 0x00000001;

Kernel.MinusEq (val, r2);

Kernel.PlusEq (x, val);

}

while (x >= n)

Kernel.MinusEq (x, n);

}

public BigInteger Multiply (BigInteger a, BigInteger b)

{

if (a == 0 || b == 0) return 0;

if (a.length >= mod.length << 1)

a %= mod;

if (b.length >= mod.length << 1)

b %= mod;

if (a.length >= mod.length)

BarrettReduction (a);

if (b.length >= mod.length)

BarrettReduction (b);

BigInteger ret = new BigInteger (a * b);

BarrettReduction (ret);

return ret;

}

public BigInteger Difference (BigInteger a, BigInteger b)

{

Sign cmp = Kernel.Compare (a, b);

BigInteger diff;

switch (cmp) {

case Sign.Zero:

return 0;

case Sign.Positive:

diff = a - b; break;

case Sign.Negative:

diff = b - a; break;

default:

throw new InvalidOperationException();

}

if (diff >= mod) {

if (diff.length >= mod.length << 1)

diff %= mod;

else

BarrettReduction (diff);

}

if (cmp == Sign.Negative)

diff = mod - diff;

return diff;

}

public BigInteger Pow (BigInteger b, BigInteger exp)

{

if ((mod.data [0] & 1) == 1) return OddPow (b, exp);

else return EvenPow (b, exp);

}

public BigInteger EvenPow (BigInteger b, BigInteger exp)

{

BigInteger resultNum = new BigInteger ((BigInteger)1, mod.length << 1);

BigInteger tempNum = new BigInteger (b % mod, mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)

uint totalBits = (uint)exp.bitCount ();

uint [] wkspace = new uint [mod.length << 1];

// perform squaring and multiply exponentiation

for (uint pos = 0; pos < totalBits; pos++) {

if (exp.testBit (pos)) {

Array.Clear (wkspace, 0, wkspace.Length);

Kernel.Multiply (resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);

resultNum.length += tempNum.length;

uint [] t = wkspace;

wkspace = resultNum.data;

resultNum.data = t;

BarrettReduction (resultNum);

}

Kernel.SquarePositive (tempNum, ref wkspace);

BarrettReduction (tempNum);

if (tempNum == 1) {

return resultNum;

}

}

return resultNum;

}

private BigInteger OddPow (BigInteger b, BigInteger exp)

{

BigInteger resultNum = new BigInteger (Montgomery.ToMont (1, mod), mod.length << 1);

BigInteger tempNum = new BigInteger (Montgomery.ToMont (b, mod), mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)

uint mPrime = Montgomery.Inverse (mod.data [0]);

uint totalBits = (uint)exp.bitCount ();

uint [] wkspace = new uint [mod.length << 1];

// perform squaring and multiply exponentiation