using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.Text;
namespace TLSharp.Core.MTProto.Crypto
{
#if !(NETCF_1_0 || NETCF_2_0 || SILVERLIGHT)
[Serializable]
#endif
public class BigInteger
{
private const long IMASK = 0xffffffffL;
private const int BitsPerByte = 8;
private const int BitsPerInt = 32;
private const int BytesPerInt = 4;
// The primes b/w 2 and ~2^10
/*
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
*/
// Each list has a product < 2^31
private static readonly int[][] primeLists =
{
new[] {3, 5, 7, 11, 13, 17, 19, 23},
new[] {29, 31, 37, 41, 43},
new[] {47, 53, 59, 61, 67},
new[] {71, 73, 79, 83},
new[] {89, 97, 101, 103},
new[] {107, 109, 113, 127},
new[] {131, 137, 139, 149},
new[] {151, 157, 163, 167},
new[] {173, 179, 181, 191},
new[] {193, 197, 199, 211},
new[] {223, 227, 229},
new[] {233, 239, 241},
new[] {251, 257, 263},
new[] {269, 271, 277},
new[] {281, 283, 293},
new[] {307, 311, 313},
new[] {317, 331, 337},
new[] {347, 349, 353},
new[] {359, 367, 373},
new[] {379, 383, 389},
new[] {397, 401, 409},
new[] {419, 421, 431},
new[] {433, 439, 443},
new[] {449, 457, 461},
new[] {463, 467, 479},
new[] {487, 491, 499},
new[] {503, 509, 521},
new[] {523, 541, 547},
new[] {557, 563, 569},
new[] {571, 577, 587},
new[] {593, 599, 601},
new[] {607, 613, 617},
new[] {619, 631, 641},
new[] {643, 647, 653},
new[] {659, 661, 673},
new[] {677, 683, 691},
new[] {701, 709, 719},
new[] {727, 733, 739},
new[] {743, 751, 757},
new[] {761, 769, 773},
new[] {787, 797, 809},
new[] {811, 821, 823},
new[] {827, 829, 839},
new[] {853, 857, 859},
new[] {863, 877, 881},
new[] {883, 887, 907},
new[] {911, 919, 929},
new[] {937, 941, 947},
new[] {953, 967, 971},
new[] {977, 983, 991},
new[] {997, 1009, 1013},
new[] {1019, 1021, 1031}
};
private static readonly int[] primeProducts;
private static readonly ulong UIMASK = IMASK;
private static readonly int[] ZeroMagnitude = new int[0];
private static readonly byte[] ZeroEncoding = new byte[0];
public static readonly BigInteger Zero = new BigInteger(0, ZeroMagnitude, false);
public static readonly BigInteger One = createUValueOf(1);
public static readonly BigInteger Two = createUValueOf(2);
public static readonly BigInteger Three = createUValueOf(3);
public static readonly BigInteger Ten = createUValueOf(10);
private static readonly int chunk2 = 1; // TODO Parse 64 bits at a time
private static readonly BigInteger radix2 = ValueOf(2);
private static readonly BigInteger radix2E = radix2.Pow(chunk2);
private static readonly int chunk10 = 19;
private static readonly BigInteger radix10 = ValueOf(10);
private static readonly BigInteger radix10E = radix10.Pow(chunk10);
private static readonly int chunk16 = 16;
private static readonly BigInteger radix16 = ValueOf(16);
private static readonly BigInteger radix16E = radix16.Pow(chunk16);
private static readonly Random RandomSource = new Random();
private static readonly byte[] rndMask = {255, 127, 63, 31, 15, 7, 3, 1};
private static readonly byte[] bitCounts =
{
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1,
2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4,
4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3,
4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5,
3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2,
3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3,
3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6,
7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6,
5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5,
6, 6, 7, 6, 7, 7, 8
};
private int[] magnitude; // array of ints with [0] being the most significant
private long mQuote = -1L; // -m^(-1) mod b, b = 2^32 (see Montgomery mult.)
private int nBitLength = -1; // cache calcBitLength() value
private int nBits = -1; // cache BitCount() value
static BigInteger()
{
primeProducts = new int[primeLists.Length];
for (var i = 0; i < primeLists.Length; ++i)
{
var primeList = primeLists[i];
var product = 1;
for (var j = 0; j < primeList.Length; ++j)
product *= primeList[j];
primeProducts[i] = product;
}
}
private BigInteger()
{
}
private BigInteger(
int signum,
int[] mag,
bool checkMag)
{
if (checkMag)
{
var i = 0;
while (i < mag.Length && mag[i] == 0)
++i;
if (i == mag.Length)
{
// this.sign = 0;
magnitude = ZeroMagnitude;
}
else
{
SignValue = signum;
if (i == 0)
{
magnitude = mag;
}
else
{
// strip leading 0 words
magnitude = new int[mag.Length - i];
Array.Copy(mag, i, magnitude, 0, magnitude.Length);
}
}
}
else
{
SignValue = signum;
magnitude = mag;
}
}
public BigInteger(
string value)
: this(value, 10)
{
}
public BigInteger(
string str,
int radix)
{
if (str.Length == 0)
throw new FormatException("Zero length BigInteger");
NumberStyles style;
int chunk;
BigInteger r;
BigInteger rE;
switch (radix)
{
case 2:
// Is there anyway to restrict to binary digits?
style = NumberStyles.Integer;
chunk = chunk2;
r = radix2;
rE = radix2E;
break;
case 10:
// This style seems to handle spaces and minus sign already (our processing redundant?)
style = NumberStyles.Integer;
chunk = chunk10;
r = radix10;
rE = radix10E;
break;
case 16:
// TODO Should this be HexNumber?
style = NumberStyles.AllowHexSpecifier;
chunk = chunk16;
r = radix16;
rE = radix16E;
break;
default:
throw new FormatException("Only bases 2, 10, or 16 allowed");
}
var index = 0;
SignValue = 1;
if (str[0] == '-')
{
if (str.Length == 1)
throw new FormatException("Zero length BigInteger");
SignValue = -1;
index = 1;
}
// strip leading zeros from the string str
while (index < str.Length && int.Parse(str[index].ToString(), style) == 0)
index++;
if (index >= str.Length)
{
// zero value - we're done
SignValue = 0;
magnitude = ZeroMagnitude;
return;
}
//////
// could we work out the max number of ints required to store
// str.Length digits in the given base, then allocate that
// storage in one hit?, then Generate the magnitude in one hit too?
//////
var b = Zero;
var next = index + chunk;
if (next <= str.Length)
do
{
var s = str.Substring(index, chunk);
var i = ulong.Parse(s, style);
var bi = createUValueOf(i);
switch (radix)
{
case 2:
// TODO Need this because we are parsing in radix 10 above
if (i > 1)
throw new FormatException("Bad character in radix 2 string: " + s);
// TODO Parse 64 bits at a time
b = b.ShiftLeft(1);
break;
case 16:
b = b.ShiftLeft(64);
break;
default:
b = b.Multiply(rE);
break;
}
b = b.Add(bi);
index = next;
next += chunk;
} while (next <= str.Length);
if (index < str.Length)
{
var s = str.Substring(index);
var i = ulong.Parse(s, style);
var bi = createUValueOf(i);
if (b.SignValue > 0)
{
if (radix == 2)
Debug.Assert(false);
else if (radix == 16)
b = b.ShiftLeft(s.Length << 2);
else b = b.Multiply(r.Pow(s.Length));
b = b.Add(bi);
}
else
{
b = bi;
}
}
// Note: This is the previous (slower) algorithm
// while (index < value.Length)
// {
// char c = value[index];
// string s = c.ToString();
// int i = Int32.Parse(s, style);
//
// b = b.Multiply(r).Add(ValueOf(i));
// index++;
// }
magnitude = b.magnitude;
}
public BigInteger(
byte[] bytes)
: this(bytes, 0, bytes.Length)
{
}
public BigInteger(
byte[] bytes,
int offset,
int length)
{
if (length == 0)
throw new FormatException("Zero length BigInteger");
// TODO Move this processing into MakeMagnitude (provide sign argument)
if ((sbyte) bytes[offset] < 0)
{
SignValue = -1;
var end = offset + length;
int iBval;
// strip leading sign bytes
for (iBval = offset; iBval < end && (sbyte) bytes[iBval] == -1; iBval++)
{
}
if (iBval >= end)
{
magnitude = One.magnitude;
}
else
{
var numBytes = end - iBval;
var inverse = new byte[numBytes];
var index = 0;
while (index < numBytes)
inverse[index++] = (byte) ~bytes[iBval++];
Debug.Assert(iBval == end);
while (inverse[--index] == byte.MaxValue)
inverse[index] = byte.MinValue;
inverse[index]++;
magnitude = MakeMagnitude(inverse, 0, inverse.Length);
}
}
else
{
// strip leading zero bytes and return magnitude bytes
magnitude = MakeMagnitude(bytes, offset, length);
SignValue = magnitude.Length > 0 ? 1 : 0;
}
}
public BigInteger(
int sign,
byte[] bytes)
: this(sign, bytes, 0, bytes.Length)
{
}
public BigInteger(
int sign,
byte[] bytes,
int offset,
int length)
{
if (sign < -1 || sign > 1)
throw new FormatException("Invalid sign value");
if (sign == 0)
{
//this.sign = 0;
magnitude = ZeroMagnitude;
}
else
{
// copy bytes
magnitude = MakeMagnitude(bytes, offset, length);
SignValue = magnitude.Length < 1 ? 0 : sign;
}
}
public BigInteger(
int sizeInBits,
Random random)
{
if (sizeInBits < 0)
throw new ArgumentException("sizeInBits must be non-negative");
nBits = -1;
nBitLength = -1;
if (sizeInBits == 0)
{
// this.sign = 0;
magnitude = ZeroMagnitude;
return;
}
var nBytes = GetByteLength(sizeInBits);
var b = new byte[nBytes];
random.NextBytes(b);
// strip off any excess bits in the MSB
b[0] &= rndMask[BitsPerByte * nBytes - sizeInBits];
magnitude = MakeMagnitude(b, 0, b.Length);
SignValue = magnitude.Length < 1 ? 0 : 1;
}
public BigInteger(
int bitLength,
int certainty,
Random random)
{
if (bitLength < 2)
throw new ArithmeticException("bitLength < 2");
SignValue = 1;
nBitLength = bitLength;
if (bitLength == 2)
{
magnitude = random.Next(2) == 0
? Two.magnitude
: Three.magnitude;
return;
}
var nBytes = GetByteLength(bitLength);
var b = new byte[nBytes];
var xBits = BitsPerByte * nBytes - bitLength;
var mask = rndMask[xBits];
for (;;)
{
random.NextBytes(b);
// strip off any excess bits in the MSB
b[0] &= mask;
// ensure the leading bit is 1 (to meet the strength requirement)
b[0] |= (byte) (1 << (7 - xBits));
// ensure the trailing bit is 1 (i.e. must be odd)
b[nBytes - 1] |= 1;
magnitude = MakeMagnitude(b, 0, b.Length);
nBits = -1;
mQuote = -1L;
if (certainty < 1)
break;
if (CheckProbablePrime(certainty, random))
break;
if (bitLength > 32)
for (var rep = 0; rep < 10000; ++rep)
{
var n = 33 + random.Next(bitLength - 2);
magnitude[magnitude.Length - (n >> 5)] ^= 1 << (n & 31);
magnitude[magnitude.Length - 1] ^= (random.Next() + 1) << 1;
mQuote = -1L;
if (CheckProbablePrime(certainty, random))
return;
}
}
}
public int BitCount
{
get
{
if (nBits == -1)
if (SignValue < 0)
{
// TODO Optimise this case
nBits = Not().BitCount;
}
else
{
var sum = 0;
for (var i = 0; i < magnitude.Length; i++)
{
sum += bitCounts[(byte) magnitude[i]];
sum += bitCounts[(byte) (magnitude[i] >> 8)];
sum += bitCounts[(byte) (magnitude[i] >> 16)];
sum += bitCounts[(byte) (magnitude[i] >> 24)];
}
nBits = sum;
}
return nBits;
}
}
public int BitLength
{
get
{
if (nBitLength == -1)
nBitLength = SignValue == 0
? 0
: calcBitLength(0, magnitude);
return nBitLength;
}
}
public int IntValue => SignValue == 0
? 0
: SignValue > 0
? magnitude[magnitude.Length - 1]
: -magnitude[magnitude.Length - 1];
// private bool SolovayStrassenTest(
// int certainty,
// Random random)
// {
// Debug.Assert(certainty > 0);
// Debug.Assert(CompareTo(Two) > 0);
// Debug.Assert(TestBit(0));
//
// BigInteger n = this;
// BigInteger nMinusOne = n.Subtract(One);
// BigInteger e = nMinusOne.ShiftRight(1);
//
// do
// {
// BigInteger a;
// do
// {
// a = new BigInteger(nBitLength, random);
// }
// // NB: Spec says 0 < x < n, but 1 is trivial
// while (a.CompareTo(One) <= 0 || a.CompareTo(n) >= 0);
//
//
// // TODO Check this is redundant given the way Jacobi() works?
//// if (!a.Gcd(n).Equals(One))
//// return false;
//
// int x = Jacobi(a, n);
//
// if (x == 0)
// return false;
//
// BigInteger check = a.ModPow(e, n);
//
// if (x == 1 && !check.Equals(One))
// return false;
//
// if (x == -1 && !check.Equals(nMinusOne))
// return false;
//
// --certainty;
// }
// while (certainty > 0);
//
// return true;
// }
//
// private static int Jacobi(
// BigInteger a,
// BigInteger b)
// {
// Debug.Assert(a.sign >= 0);
// Debug.Assert(b.sign > 0);
// Debug.Assert(b.TestBit(0));
// Debug.Assert(a.CompareTo(b) < 0);
//
// int totalS = 1;
// for (;;)
// {
// if (a.sign == 0)
// return 0;
//
// if (a.Equals(One))
// break;
//
// int e = a.GetLowestSetBit();
//
// int bLsw = b.magnitude[b.magnitude.Length - 1];
// if ((e & 1) != 0 && ((bLsw & 7) == 3 || (bLsw & 7) == 5))
// totalS = -totalS;
//
// // TODO Confirm this is faster than later a1.Equals(One) test
// if (a.BitLength == e + 1)
// break;
// BigInteger a1 = a.ShiftRight(e);
//// if (a1.Equals(One))
//// break;
//
// int a1Lsw = a1.magnitude[a1.magnitude.Length - 1];
// if ((bLsw & 3) == 3 && (a1Lsw & 3) == 3)
// totalS = -totalS;
//
//// a = b.Mod(a1);
// a = b.Remainder(a1);
// b = a1;
// }
// return totalS;
// }
public long LongValue
{
get
{
if (SignValue == 0)
return 0;
long v;
if (magnitude.Length > 1)
v = ((long) magnitude[magnitude.Length - 2] << 32)
| (magnitude[magnitude.Length - 1] & IMASK);
else v = magnitude[magnitude.Length - 1] & IMASK;
return SignValue < 0 ? -v : v;
}
}
public int SignValue { get; private set; }
private static int GetByteLength(
int nBits)
{
return (nBits + BitsPerByte - 1) / BitsPerByte;
}
private static int[] MakeMagnitude(
byte[] bytes,
int offset,
int length)
{
var end = offset + length;
// strip leading zeros
int firstSignificant;
for (firstSignificant = offset;
firstSignificant < end
&& bytes[firstSignificant] == 0;
firstSignificant++)
{
}
if (firstSignificant >= end)
return ZeroMagnitude;
var nInts = (end - firstSignificant + 3) / BytesPerInt;
var bCount = (end - firstSignificant) % BytesPerInt;
if (bCount == 0)
bCount = BytesPerInt;
if (nInts < 1)
return ZeroMagnitude;
var mag = new int[nInts];
var v = 0;
var magnitudeIndex = 0;
for (var i = firstSignificant; i < end; ++i)
{
v <<= 8;
v |= bytes[i] & 0xff;
bCount--;
if (bCount <= 0)
{
mag[magnitudeIndex] = v;
magnitudeIndex++;
bCount = BytesPerInt;
v = 0;
}
}
if (magnitudeIndex < mag.Length)
mag[magnitudeIndex] = v;
return mag;
}
public BigInteger Abs()
{
return SignValue >= 0 ? this : Negate();
}
/**
* return a = a + b - b preserved.
*/
private static int[] AddMagnitudes(
int[] a,
int[] b)
{
var tI = a.Length - 1;
var vI = b.Length - 1;
long m = 0;
while (vI >= 0)
{
m += (uint) a[tI] + (long) (uint) b[vI--];
a[tI--] = (int) m;
m = (long) ((ulong) m >> 32);
}
if (m != 0)
while (tI >= 0 && ++a[tI--] == 0)
{
}
return a;
}
public BigInteger Add(
BigInteger value)
{
if (SignValue == 0)
return value;
if (SignValue != value.SignValue)
{
if (value.SignValue == 0)
return this;
if (value.SignValue < 0)
return Subtract(value.Negate());
return value.Subtract(Negate());
}
return AddToMagnitude(value.magnitude);
}
private BigInteger AddToMagnitude(
int[] magToAdd)
{
int[] big, small;
if (magnitude.Length < magToAdd.Length)
{
big = magToAdd;
small = magnitude;
}
else
{
big = magnitude;
small = magToAdd;
}
// Conservatively avoid over-allocation when no overflow possible
var limit = uint.MaxValue;
if (big.Length == small.Length)
limit -= (uint) small[0];
var possibleOverflow = (uint) big[0] >= limit;
int[] bigCopy;
if (possibleOverflow)
{
bigCopy = new int[big.Length + 1];
big.CopyTo(bigCopy, 1);
}
else
{
bigCopy = (int[]) big.Clone();
}
bigCopy = AddMagnitudes(bigCopy, small);
return new BigInteger(SignValue, bigCopy, possibleOverflow);
}
public BigInteger And(
BigInteger value)
{
if (SignValue == 0 || value.SignValue == 0)
return Zero;
var aMag = SignValue > 0
? magnitude
: Add(One).magnitude;
var bMag = value.SignValue > 0
? value.magnitude
: value.Add(One).magnitude;
var resultNeg = SignValue < 0 && value.SignValue < 0;
var resultLength = Math.Max(aMag.Length, bMag.Length);
var resultMag = new int[resultLength];
var aStart = resultMag.Length - aMag.Length;
var bStart = resultMag.Length - bMag.Length;
for (var i = 0; i < resultMag.Length; ++i)
{
var aWord = i >= aStart ? aMag[i - aStart] : 0;
var bWord = i >= bStart ? bMag[i - bStart] : 0;
if (SignValue < 0)
aWord = ~aWord;
if (value.SignValue < 0)
bWord = ~bWord;
resultMag[i] = aWord & bWord;
if (resultNeg)
resultMag[i] = ~resultMag[i];
}
var result = new BigInteger(1, resultMag, true);
// TODO Optimise this case
if (resultNeg)
result = result.Not();
return result;
}
public BigInteger AndNot(
BigInteger val)
{
return And(val.Not());
}
private int calcBitLength(
int indx,
int[] mag)
{
for (;;)
{
if (indx >= mag.Length)
return 0;
if (mag[indx] != 0)
break;
++indx;
}
// bit length for everything after the first int
var bitLength = 32 * (mag.Length - indx - 1);
// and determine bitlength of first int
var firstMag = mag[indx];
bitLength += BitLen(firstMag);
// Check for negative powers of two
if (SignValue < 0 && (firstMag & -firstMag) == firstMag)
do
{
if (++indx >= mag.Length)
{
--bitLength;
break;
}
} while (mag[indx] == 0);
return bitLength;
}
//
// BitLen(value) is the number of bits in value.
//
private static int BitLen(
int w)
{
// Binary search - decision tree (5 tests, rarely 6)
return w < 1 << 15
? (w < 1 << 7
? (w < 1 << 3
? (w < 1 << 1
? (w < 1 << 0 ? (w < 0 ? 32 : 0) : 1)
: (w < 1 << 2 ? 2 : 3))
: (w < 1 << 5
? (w < 1 << 4 ? 4 : 5)
: (w < 1 << 6 ? 6 : 7)))
: (w < 1 << 11
? (w < 1 << 9 ? (w < 1 << 8 ? 8 : 9) : (w < 1 << 10 ? 10 : 11))
: (w < 1 << 13 ? (w < 1 << 12 ? 12 : 13) : (w < 1 << 14 ? 14 : 15))))
: (w < 1 << 23
? (w < 1 << 19
? (w < 1 << 17 ? (w < 1 << 16 ? 16 : 17) : (w < 1 << 18 ? 18 : 19))
: (w < 1 << 21 ? (w < 1 << 20 ? 20 : 21) : (w < 1 << 22 ? 22 : 23)))
: (w < 1 << 27
? (w < 1 << 25 ? (w < 1 << 24 ? 24 : 25) : (w < 1 << 26 ? 26 : 27))
: (w < 1 << 29 ? (w < 1 << 28 ? 28 : 29) : (w < 1 << 30 ? 30 : 31))));
}
// private readonly static byte[] bitLengths =
// {
// 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
// 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
// 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
// 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
// 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8,
// 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
// 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
// 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
// 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
// 8, 8, 8, 8, 8, 8, 8, 8
// };
private bool QuickPow2Check()
{
return SignValue > 0 && nBits == 1;
}
public int CompareTo(
object obj)
{
return CompareTo((BigInteger) obj);
}
/**
* unsigned comparison on two arrays - note the arrays may
* start with leading zeros.
*/
private static int CompareTo(
int xIndx,
int[] x,
int yIndx,
int[] y)
{
while (xIndx != x.Length && x[xIndx] == 0)
xIndx++;
while (yIndx != y.Length && y[yIndx] == 0)
yIndx++;
return CompareNoLeadingZeroes(xIndx, x, yIndx, y);
}
private static int CompareNoLeadingZeroes(
int xIndx,
int[] x,
int yIndx,
int[] y)
{
var diff = x.Length - y.Length - (xIndx - yIndx);
if (diff != 0)
return diff < 0 ? -1 : 1;
// lengths of magnitudes the same, test the magnitude values
while (xIndx < x.Length)
{
var v1 = (uint) x[xIndx++];
var v2 = (uint) y[yIndx++];
if (v1 != v2)
return v1 < v2 ? -1 : 1;
}
return 0;
}
public int CompareTo(
BigInteger value)
{
return SignValue < value.SignValue
? -1
: SignValue > value.SignValue
? 1
: SignValue == 0
? 0
: SignValue * CompareNoLeadingZeroes(0, magnitude, 0, value.magnitude);
}
/**
* return z = x / y - done in place (z value preserved, x contains the
* remainder)
*/
private int[] Divide(
int[] x,
int[] y)
{
var xStart = 0;
while (xStart < x.Length && x[xStart] == 0)
++xStart;
var yStart = 0;
while (yStart < y.Length && y[yStart] == 0)
++yStart;
Debug.Assert(yStart < y.Length);
var xyCmp = CompareNoLeadingZeroes(xStart, x, yStart, y);
int[] count;
if (xyCmp > 0)
{
var yBitLength = calcBitLength(yStart, y);
var xBitLength = calcBitLength(xStart, x);
var shift = xBitLength - yBitLength;
int[] iCount;
var iCountStart = 0;
int[] c;
var cStart = 0;
var cBitLength = yBitLength;
if (shift > 0)
{
// iCount = ShiftLeft(One.magnitude, shift);
iCount = new int[(shift >> 5) + 1];
iCount[0] = 1 << (shift % 32);
c = ShiftLeft(y, shift);
cBitLength += shift;
}
else
{
iCount = new[] {1};
var len = y.Length - yStart;
c = new int[len];
Array.Copy(y, yStart, c, 0, len);
}
count = new int[iCount.Length];
for (;;)
{
if (cBitLength < xBitLength
|| CompareNoLeadingZeroes(xStart, x, cStart, c) >= 0)
{
Subtract(xStart, x, cStart, c);
AddMagnitudes(count, iCount);
while (x[xStart] == 0)
if (++xStart == x.Length)
return count;
//xBitLength = calcBitLength(xStart, x);
xBitLength = 32 * (x.Length - xStart - 1) + BitLen(x[xStart]);
if (xBitLength <= yBitLength)
{
if (xBitLength < yBitLength)
return count;
xyCmp = CompareNoLeadingZeroes(xStart, x, yStart, y);
if (xyCmp <= 0)
break;
}
}
shift = cBitLength - xBitLength;
// NB: The case where c[cStart] is 1-bit is harmless
if (shift == 1)
{
var firstC = (uint) c[cStart] >> 1;
var firstX = (uint) x[xStart];
if (firstC > firstX)
++shift;
}
if (shift < 2)
{
ShiftRightOneInPlace(cStart, c);
--cBitLength;
ShiftRightOneInPlace(iCountStart, iCount);
}
else
{
ShiftRightInPlace(cStart, c, shift);
cBitLength -= shift;
ShiftRightInPlace(iCountStart, iCount, shift);
}
//cStart = c.Length - ((cBitLength + 31) / 32);
while (c[cStart] == 0)
++cStart;
while (iCount[iCountStart] == 0)
++iCountStart;
}
}
else
{
count = new int[1];
}
if (xyCmp == 0)
{
AddMagnitudes(count, One.magnitude);
Array.Clear(x, xStart, x.Length - xStart);
}
return count;
}
public BigInteger Divide(
BigInteger val)
{
if (val.SignValue == 0)
throw new ArithmeticException("Division by zero error");
if (SignValue == 0)
return Zero;
if (val.QuickPow2Check()) // val is power of two
{
var result = Abs().ShiftRight(val.Abs().BitLength - 1);
return val.SignValue == SignValue ? result : result.Negate();
}
var mag = (int[]) magnitude.Clone();
return new BigInteger(SignValue * val.SignValue, Divide(mag, val.magnitude), true);
}
public BigInteger[] DivideAndRemainder(
BigInteger val)
{
if (val.SignValue == 0)
throw new ArithmeticException("Division by zero error");
var biggies = new BigInteger[2];
if (SignValue == 0)
{
biggies[0] = Zero;
biggies[1] = Zero;
}
else if (val.QuickPow2Check()) // val is power of two
{
var e = val.Abs().BitLength - 1;
var quotient = Abs().ShiftRight(e);
var remainder = LastNBits(e);
biggies[0] = val.SignValue == SignValue ? quotient : quotient.Negate();
biggies[1] = new BigInteger(SignValue, remainder, true);
}
else
{
var remainder = (int[]) magnitude.Clone();
var quotient = Divide(remainder, val.magnitude);
biggies[0] = new BigInteger(SignValue * val.SignValue, quotient, true);
biggies[1] = new BigInteger(SignValue, remainder, true);
}
return biggies;
}
public override bool Equals(
object obj)
{
if (obj == this)
return true;
var biggie = obj as BigInteger;
if (biggie == null)
return false;
if (biggie.SignValue != SignValue || biggie.magnitude.Length != magnitude.Length)
return false;
for (var i = 0; i < magnitude.Length; i++)
if (biggie.magnitude[i] != magnitude[i])
return false;
return true;
}
public BigInteger Gcd(
BigInteger value)
{
if (value.SignValue == 0)
return Abs();
if (SignValue == 0)
return value.Abs();
BigInteger r;
var u = this;
var v = value;
while (v.SignValue != 0)
{
r = u.Mod(v);
u = v;
v = r;
}
return u;
}
public override int GetHashCode()
{
var hc = magnitude.Length;
if (magnitude.Length > 0)
{
hc ^= magnitude[0];
if (magnitude.Length > 1)
hc ^= magnitude[magnitude.Length - 1];
}
return SignValue < 0 ? ~hc : hc;
}
// TODO Make public?
private BigInteger Inc()
{
if (SignValue == 0)
return One;
if (SignValue < 0)
return new BigInteger(-1, doSubBigLil(magnitude, One.magnitude), true);
return AddToMagnitude(One.magnitude);
}
/**
* return whether or not a BigInteger is probably prime with a
* probability of 1 - (1/2)**certainty.
*
From Knuth Vol 2, pg 395.
*/
public bool IsProbablePrime(
int certainty)
{
if (certainty <= 0)
return true;
var n = Abs();
if (!n.TestBit(0))
return n.Equals(Two);
if (n.Equals(One))
return false;
return n.CheckProbablePrime(certainty, RandomSource);
}
private bool CheckProbablePrime(
int certainty,
Random random)
{
Debug.Assert(certainty > 0);
Debug.Assert(CompareTo(Two) > 0);
Debug.Assert(TestBit(0));
// Try to reduce the penalty for really small numbers
var numLists = Math.Min(BitLength - 1, primeLists.Length);
for (var i = 0; i < numLists; ++i)
{
var test = Remainder(primeProducts[i]);
var primeList = primeLists[i];
for (var j = 0; j < primeList.Length; ++j)
{
var prime = primeList[j];
var qRem = test % prime;
if (qRem == 0)
return BitLength < 16 && IntValue == prime;
}
}
// TODO Special case for < 10^16 (RabinMiller fixed list)
// if (BitLength < 30)
// {
// RabinMiller against 2, 3, 5, 7, 11, 13, 23 is sufficient
// }
// TODO Is it worth trying to create a hybrid of these two?
return RabinMillerTest(certainty, random);
// return SolovayStrassenTest(certainty, random);
// bool rbTest = RabinMillerTest(certainty, random);
// bool ssTest = SolovayStrassenTest(certainty, random);
//
// Debug.Assert(rbTest == ssTest);
//
// return rbTest;
}
internal bool RabinMillerTest(
int certainty,
Random random)
{
Debug.Assert(certainty > 0);
Debug.Assert(BitLength > 2);
Debug.Assert(TestBit(0));
// let n = 1 + d . 2^s
var n = this;
var nMinusOne = n.Subtract(One);
var s = nMinusOne.GetLowestSetBit();
var r = nMinusOne.ShiftRight(s);
Debug.Assert(s >= 1);
do
{
// TODO Make a method for random BigIntegers in range 0 < x < n)
// - Method can be optimized by only replacing examined bits at each trial
BigInteger a;
do
{
a = new BigInteger(n.BitLength, random);
} while (a.CompareTo(One) <= 0 || a.CompareTo(nMinusOne) >= 0);
var y = a.ModPow(r, n);
if (!y.Equals(One))
{
var j = 0;
while (!y.Equals(nMinusOne))
{
if (++j == s)
return false;
y = y.ModPow(Two, n);
if (y.Equals(One))
return false;
}
}
certainty -= 2; // composites pass for only 1/4 possible 'a'
} while (certainty > 0);
return true;
}
public BigInteger Max(
BigInteger value)
{
return CompareTo(value) > 0 ? this : value;
}
public BigInteger Min(
BigInteger value)
{
return CompareTo(value) < 0 ? this : value;
}
public BigInteger Mod(
BigInteger m)
{
if (m.SignValue < 1)
throw new ArithmeticException("Modulus must be positive");
var biggie = Remainder(m);
return biggie.SignValue >= 0 ? biggie : biggie.Add(m);
}
public BigInteger ModInverse(
BigInteger m)
{
if (m.SignValue < 1)
throw new ArithmeticException("Modulus must be positive");
// TODO Too slow at the moment
// // "Fast Key Exchange with Elliptic Curve Systems" R.Schoeppel
// if (m.TestBit(0))
// {
// //The Almost Inverse Algorithm
// int k = 0;
// BigInteger B = One, C = Zero, F = this, G = m, tmp;
//
// for (;;)
// {
// // While F is even, do F=F/u, C=C*u, k=k+1.
// int zeroes = F.GetLowestSetBit();
// if (zeroes > 0)
// {
// F = F.ShiftRight(zeroes);
// C = C.ShiftLeft(zeroes);
// k += zeroes;
// }
//
// // If F = 1, then return B,k.
// if (F.Equals(One))
// {
// BigInteger half = m.Add(One).ShiftRight(1);
// BigInteger halfK = half.ModPow(BigInteger.ValueOf(k), m);
// return B.Multiply(halfK).Mod(m);
// }
//
// if (F.CompareTo(G) < 0)
// {
// tmp = G; G = F; F = tmp;
// tmp = B; B = C; C = tmp;
// }
//
// F = F.Add(G);
// B = B.Add(C);
// }
// }
var x = new BigInteger();
var gcd = ExtEuclid(Mod(m), m, x, null);
if (!gcd.Equals(One))
throw new ArithmeticException("Numbers not relatively prime.");
if (x.SignValue < 0)
{
x.SignValue = 1;
//x = m.Subtract(x);
x.magnitude = doSubBigLil(m.magnitude, x.magnitude);
}
return x;
}
/**
* Calculate the numbers u1, u2, and u3 such that:
*
* u1 * a + u2 * b = u3
*
* where u3 is the greatest common divider of a and b.
* a and b using the extended Euclid algorithm (refer p. 323
* of The Art of Computer Programming vol 2, 2nd ed).
* This also seems to have the side effect of calculating
* some form of multiplicative inverse.
*
* @param a First number to calculate gcd for
* @param b Second number to calculate gcd for
* @param u1Out the return object for the u1 value
* @param u2Out the return object for the u2 value
* @return The greatest common divisor of a and b
*/
private static BigInteger ExtEuclid(
BigInteger a,
BigInteger b,
BigInteger u1Out,
BigInteger u2Out)
{
var u1 = One;
var u3 = a;
var v1 = Zero;
var v3 = b;
while (v3.SignValue > 0)
{
var q = u3.DivideAndRemainder(v3);
var tmp = v1.Multiply(q[0]);
var tn = u1.Subtract(tmp);
u1 = v1;
v1 = tn;
u3 = v3;
v3 = q[1];
}
if (u1Out != null)
{
u1Out.SignValue = u1.SignValue;
u1Out.magnitude = u1.magnitude;
}
if (u2Out != null)
{
var tmp = u1.Multiply(a);
tmp = u3.Subtract(tmp);
var res = tmp.Divide(b);
u2Out.SignValue = res.SignValue;
u2Out.magnitude = res.magnitude;
}
return u3;
}
private static void ZeroOut(
int[] x)
{
Array.Clear(x, 0, x.Length);
}
public BigInteger ModPow(
BigInteger exponent,
BigInteger m)
{
if (m.SignValue < 1)
throw new ArithmeticException("Modulus must be positive");
if (m.Equals(One))
return Zero;
if (exponent.SignValue == 0)
return One;
if (SignValue == 0)
return Zero;
int[] zVal = null;
int[] yAccum = null;
int[] yVal;
// Montgomery exponentiation is only possible if the modulus is odd,
// but AFAIK, this is always the case for crypto algo's
var useMonty = (m.magnitude[m.magnitude.Length - 1] & 1) == 1;
long mQ = 0;
if (useMonty)
{
mQ = m.GetMQuote();
// tmp = this * R mod m
var tmp = ShiftLeft(32 * m.magnitude.Length).Mod(m);
zVal = tmp.magnitude;
useMonty = zVal.Length <= m.magnitude.Length;
if (useMonty)
{
yAccum = new int[m.magnitude.Length + 1];
if (zVal.Length < m.magnitude.Length)
{
var longZ = new int[m.magnitude.Length];
zVal.CopyTo(longZ, longZ.Length - zVal.Length);
zVal = longZ;
}
}
}
if (!useMonty)
{
if (magnitude.Length <= m.magnitude.Length)
{
//zAccum = new int[m.magnitude.Length * 2];
zVal = new int[m.magnitude.Length];
magnitude.CopyTo(zVal, zVal.Length - magnitude.Length);
}
else
{
//
// in normal practice we'll never see this...
//
var tmp = Remainder(m);
//zAccum = new int[m.magnitude.Length * 2];
zVal = new int[m.magnitude.Length];
tmp.magnitude.CopyTo(zVal, zVal.Length - tmp.magnitude.Length);
}
yAccum = new int[m.magnitude.Length * 2];
}
yVal = new int[m.magnitude.Length];
//
// from LSW to MSW
//
for (var i = 0; i < exponent.magnitude.Length; i++)
{
var v = exponent.magnitude[i];
var bits = 0;
if (i == 0)
{
while (v > 0)
{
v <<= 1;
bits++;
}
//
// first time in initialise y
//
zVal.CopyTo(yVal, 0);
v <<= 1;
bits++;
}
while (v != 0)
{
if (useMonty)
{
// Montgomery square algo doesn't exist, and a normal
// square followed by a Montgomery reduction proved to
// be almost as heavy as a Montgomery mulitply.
MultiplyMonty(yAccum, yVal, yVal, m.magnitude, mQ);
}
else
{
Square(yAccum, yVal);
Remainder(yAccum, m.magnitude);
Array.Copy(yAccum, yAccum.Length - yVal.Length, yVal, 0, yVal.Length);
ZeroOut(yAccum);
}
bits++;
if (v < 0)
if (useMonty)
{
MultiplyMonty(yAccum, yVal, zVal, m.magnitude, mQ);
}
else
{
Multiply(yAccum, yVal, zVal);
Remainder(yAccum, m.magnitude);
Array.Copy(yAccum, yAccum.Length - yVal.Length, yVal, 0,
yVal.Length);
ZeroOut(yAccum);
}
v <<= 1;
}
while (bits < 32)
{
if (useMonty)
{
MultiplyMonty(yAccum, yVal, yVal, m.magnitude, mQ);
}
else
{
Square(yAccum, yVal);
Remainder(yAccum, m.magnitude);
Array.Copy(yAccum, yAccum.Length - yVal.Length, yVal, 0, yVal.Length);
ZeroOut(yAccum);
}
bits++;
}
}
if (useMonty)
{
// Return y * R^(-1) mod m by doing y * 1 * R^(-1) mod m
ZeroOut(zVal);
zVal[zVal.Length - 1] = 1;
MultiplyMonty(yAccum, yVal, zVal, m.magnitude, mQ);
}
var result = new BigInteger(1, yVal, true);
return exponent.SignValue > 0
? result
: result.ModInverse(m);
}
/**
* return w with w = x * x - w is assumed to have enough space.
*/
private static int[] Square(
int[] w,
int[] x)
{
// Note: this method allows w to be only (2 * x.Length - 1) words if result will fit
// if (w.Length != 2 * x.Length)
// throw new ArgumentException("no I don't think so...");
ulong u1, u2, c;
var wBase = w.Length - 1;
for (var i = x.Length - 1; i != 0; i--)
{
ulong v = (uint) x[i];
u1 = v * v;
u2 = u1 >> 32;
u1 = (uint) u1;
u1 += (uint) w[wBase];
w[wBase] = (int) (uint) u1;
c = u2 + (u1 >> 32);
for (var j = i - 1; j >= 0; j--)
{
--wBase;
u1 = v * (uint) x[j];
u2 = u1 >> 31; // multiply by 2!
u1 = (uint) (u1 << 1); // multiply by 2!
u1 += c + (uint) w[wBase];
w[wBase] = (int) (uint) u1;
c = u2 + (u1 >> 32);
}
c += (uint) w[--wBase];
w[wBase] = (int) (uint) c;
if (--wBase >= 0)
w[wBase] = (int) (uint) (c >> 32);
else Debug.Assert((uint) (c >> 32) == 0);
wBase += i;
}
u1 = (uint) x[0];
u1 = u1 * u1;
u2 = u1 >> 32;
u1 = u1 & IMASK;
u1 += (uint) w[wBase];
w[wBase] = (int) (uint) u1;
if (--wBase >= 0)
w[wBase] = (int) (uint) (u2 + (u1 >> 32) + (uint) w[wBase]);
else Debug.Assert((uint) (u2 + (u1 >> 32)) == 0);
return w;
}
/**
* return x with x = y * z - x is assumed to have enough space.
*/
private static int[] Multiply(
int[] x,
int[] y,
int[] z)
{
var i = z.Length;
if (i < 1)
return x;
var xBase = x.Length - y.Length;
for (;;)
{
var a = z[--i] & IMASK;
long val = 0;
for (var j = y.Length - 1; j >= 0; j--)
{
val += a * (y[j] & IMASK) + (x[xBase + j] & IMASK);
x[xBase + j] = (int) val;
val = (long) ((ulong) val >> 32);
}
--xBase;
if (i < 1)
{
if (xBase >= 0)
x[xBase] = (int) val;
else Debug.Assert(val == 0);
break;
}
x[xBase] = (int) val;
}
return x;
}
private static long FastExtEuclid(
long a,
long b,
long[] uOut)
{
long u1 = 1;
var u3 = a;
long v1 = 0;
var v3 = b;
while (v3 > 0)
{
long q, tn;
q = u3 / v3;
tn = u1 - v1 * q;
u1 = v1;
v1 = tn;
tn = u3 - v3 * q;
u3 = v3;
v3 = tn;
}
uOut[0] = u1;
uOut[1] = (u3 - u1 * a) / b;
return u3;
}
private static long FastModInverse(
long v,
long m)
{
if (m < 1)
throw new ArithmeticException("Modulus must be positive");
var x = new long[2];
var gcd = FastExtEuclid(v, m, x);
if (gcd != 1)
throw new ArithmeticException("Numbers not relatively prime.");
if (x[0] < 0)
x[0] += m;
return x[0];
}
// private static BigInteger MQuoteB = One.ShiftLeft(32);
// private static BigInteger MQuoteBSub1 = MQuoteB.Subtract(One);
/**
* Calculate mQuote = -m^(-1) mod b with b = 2^32 (32 = word size)
*/
private long GetMQuote()
{
Debug.Assert(SignValue > 0);
if (mQuote != -1)
return mQuote; // already calculated
if (magnitude.Length == 0 || (magnitude[magnitude.Length - 1] & 1) == 0)
return -1; // not for even numbers
var v = (~magnitude[magnitude.Length - 1] | 1) & 0xffffffffL;
mQuote = FastModInverse(v, 0x100000000L);
return mQuote;
}
/**
* Montgomery multiplication: a = x * y * R^(-1) mod m
*
* Based algorithm 14.36 of Handbook of Applied Cryptography.
*
*
m, x, y should have length n
*
a should have length (n + 1)
*
b = 2^32, R = b^n
*
* The result is put in x
*
* NOTE: the indices of x, y, m, a different in HAC and in Java
*/
private static void MultiplyMonty(
int[] a,
int[] x,
int[] y,
int[] m,
long mQuote)
// mQuote = -m^(-1) mod b
{
if (m.Length == 1)
{
x[0] = (int) MultiplyMontyNIsOne((uint) x[0], (uint) y[0], (uint) m[0], (ulong) mQuote);
return;
}
var n = m.Length;
var nMinus1 = n - 1;
var y_0 = y[nMinus1] & IMASK;
// 1. a = 0 (Notation: a = (a_{n} a_{n-1} ... a_{0})_{b} )
Array.Clear(a, 0, n + 1);
// 2. for i from 0 to (n - 1) do the following:
for (var i = n; i > 0; i--)
{
var x_i = x[i - 1] & IMASK;
// 2.1 u = ((a[0] + (x[i] * y[0]) * mQuote) mod b
var u = ((((a[n] & IMASK) + ((x_i * y_0) & IMASK)) & IMASK) * mQuote) & IMASK;
// 2.2 a = (a + x_i * y + u * m) / b
var prod1 = x_i * y_0;
var prod2 = u * (m[nMinus1] & IMASK);
var tmp = (a[n] & IMASK) + (prod1 & IMASK) + (prod2 & IMASK);
var carry = (long) ((ulong) prod1 >> 32) + (long) ((ulong) prod2 >> 32) + (long) ((ulong) tmp >> 32);
for (var j = nMinus1; j > 0; j--)
{
prod1 = x_i * (y[j - 1] & IMASK);
prod2 = u * (m[j - 1] & IMASK);
tmp = (a[j] & IMASK) + (prod1 & IMASK) + (prod2 & IMASK) + (carry & IMASK);
carry = (long) ((ulong) carry >> 32) + (long) ((ulong) prod1 >> 32) +
(long) ((ulong) prod2 >> 32) + (long) ((ulong) tmp >> 32);
a[j + 1] = (int) tmp; // division by b
}
carry += a[0] & IMASK;
a[1] = (int) carry;
a[0] = (int) ((ulong) carry >> 32); // OJO!!!!!
}
// 3. if x >= m the x = x - m
if (CompareTo(0, a, 0, m) >= 0)
Subtract(0, a, 0, m);
// put the result in x
Array.Copy(a, 1, x, 0, n);
}
private static uint MultiplyMontyNIsOne(
uint x,
uint y,
uint m,
ulong mQuote)
{
ulong um = m;
var prod1 = x * (ulong) y;
var u = (prod1 * mQuote) & UIMASK;
var prod2 = u * um;
var tmp = (prod1 & UIMASK) + (prod2 & UIMASK);
var carry = (prod1 >> 32) + (prod2 >> 32) + (tmp >> 32);
if (carry > um)
carry -= um;
return (uint) (carry & UIMASK);
}
public BigInteger Multiply(
BigInteger val)
{
if (SignValue == 0 || val.SignValue == 0)
return Zero;
if (val.QuickPow2Check()) // val is power of two
{
var result = ShiftLeft(val.Abs().BitLength - 1);
return val.SignValue > 0 ? result : result.Negate();
}
if (QuickPow2Check()) // this is power of two
{
var result = val.ShiftLeft(Abs().BitLength - 1);
return SignValue > 0 ? result : result.Negate();
}
var resLength = (BitLength + val.BitLength) / BitsPerInt + 1;
var res = new int[resLength];
if (val == this)
Square(res, magnitude);
else Multiply(res, magnitude, val.magnitude);
return new BigInteger(SignValue * val.SignValue, res, true);
}
public BigInteger Negate()
{
if (SignValue == 0)
return this;
return new BigInteger(-SignValue, magnitude, false);
}
public BigInteger NextProbablePrime()
{
if (SignValue < 0)
throw new ArithmeticException("Cannot be called on value < 0");
if (CompareTo(Two) < 0)
return Two;
var n = Inc().SetBit(0);
while (!n.CheckProbablePrime(100, RandomSource))
n = n.Add(Two);
return n;
}
public BigInteger Not()
{
return Inc().Negate();
}
public BigInteger Pow(int exp)
{
if (exp < 0)
throw new ArithmeticException("Negative exponent");
if (exp == 0)
return One;
if (SignValue == 0 || Equals(One))
return this;
var y = One;
var z = this;
for (;;)
{
if ((exp & 0x1) == 1)
y = y.Multiply(z);
exp >>= 1;
if (exp == 0) break;
z = z.Multiply(z);
}
return y;
}
public static BigInteger ProbablePrime(
int bitLength,
Random random)
{
return new BigInteger(bitLength, 100, random);
}
private int Remainder(
int m)
{
Debug.Assert(m > 0);
long acc = 0;
for (var pos = 0; pos < magnitude.Length; ++pos)
{
long posVal = (uint) magnitude[pos];
acc = ((acc << 32) | posVal) % m;
}
return (int) acc;
}
/**
* return x = x % y - done in place (y value preserved)
*/
private int[] Remainder(
int[] x,
int[] y)
{
var xStart = 0;
while (xStart < x.Length && x[xStart] == 0)
++xStart;
var yStart = 0;
while (yStart < y.Length && y[yStart] == 0)
++yStart;
Debug.Assert(yStart < y.Length);
var xyCmp = CompareNoLeadingZeroes(xStart, x, yStart, y);
if (xyCmp > 0)
{
var yBitLength = calcBitLength(yStart, y);
var xBitLength = calcBitLength(xStart, x);
var shift = xBitLength - yBitLength;
int[] c;
var cStart = 0;
var cBitLength = yBitLength;
if (shift > 0)
{
c = ShiftLeft(y, shift);
cBitLength += shift;
Debug.Assert(c[0] != 0);
}
else
{
var len = y.Length - yStart;
c = new int[len];
Array.Copy(y, yStart, c, 0, len);
}
for (;;)
{
if (cBitLength < xBitLength
|| CompareNoLeadingZeroes(xStart, x, cStart, c) >= 0)
{
Subtract(xStart, x, cStart, c);
while (x[xStart] == 0)
if (++xStart == x.Length)
return x;
//xBitLength = calcBitLength(xStart, x);
xBitLength = 32 * (x.Length - xStart - 1) + BitLen(x[xStart]);
if (xBitLength <= yBitLength)
{
if (xBitLength < yBitLength)
return x;
xyCmp = CompareNoLeadingZeroes(xStart, x, yStart, y);
if (xyCmp <= 0)
break;
}
}
shift = cBitLength - xBitLength;
// NB: The case where c[cStart] is 1-bit is harmless
if (shift == 1)
{
var firstC = (uint) c[cStart] >> 1;
var firstX = (uint) x[xStart];
if (firstC > firstX)
++shift;
}
if (shift < 2)
{
ShiftRightOneInPlace(cStart, c);
--cBitLength;
}
else
{
ShiftRightInPlace(cStart, c, shift);
cBitLength -= shift;
}
//cStart = c.Length - ((cBitLength + 31) / 32);
while (c[cStart] == 0)
++cStart;
}
}
if (xyCmp == 0)
Array.Clear(x, xStart, x.Length - xStart);
return x;
}
public BigInteger Remainder(
BigInteger n)
{
if (n.SignValue == 0)
throw new ArithmeticException("Division by zero error");
if (SignValue == 0)
return Zero;
// For small values, use fast remainder method
if (n.magnitude.Length == 1)
{
var val = n.magnitude[0];
if (val > 0)
{
if (val == 1)
return Zero;
// TODO Make this func work on uint, and handle val == 1?
var rem = Remainder(val);
return rem == 0
? Zero
: new BigInteger(SignValue, new[] {rem}, false);
}
}
if (CompareNoLeadingZeroes(0, magnitude, 0, n.magnitude) < 0)
return this;
int[] result;
if (n.QuickPow2Check()) // n is power of two
{
// TODO Move before small values branch above?
result = LastNBits(n.Abs().BitLength - 1);
}
else
{
result = (int[]) magnitude.Clone();
result = Remainder(result, n.magnitude);
}
return new BigInteger(SignValue, result, true);
}
private int[] LastNBits(
int n)
{
if (n < 1)
return ZeroMagnitude;
var numWords = (n + BitsPerInt - 1) / BitsPerInt;
numWords = Math.Min(numWords, magnitude.Length);
var result = new int[numWords];
Array.Copy(magnitude, magnitude.Length - numWords, result, 0, numWords);
var hiBits = n % 32;
if (hiBits != 0)
result[0] &= ~(-1 << hiBits);
return result;
}
/**
* do a left shift - this returns a new array.
*/
private static int[] ShiftLeft(
int[] mag,
int n)
{
var nInts = (int) ((uint) n >> 5);
var nBits = n & 0x1f;
var magLen = mag.Length;
int[] newMag;
if (nBits == 0)
{
newMag = new int[magLen + nInts];
mag.CopyTo(newMag, 0);
}
else
{
var i = 0;
var nBits2 = 32 - nBits;
var highBits = (int) ((uint) mag[0] >> nBits2);
if (highBits != 0)
{
newMag = new int[magLen + nInts + 1];
newMag[i++] = highBits;
}
else
{
newMag = new int[magLen + nInts];
}
var m = mag[0];
for (var j = 0; j < magLen - 1; j++)
{
var next = mag[j + 1];
newMag[i++] = (m << nBits) | (int) ((uint) next >> nBits2);
m = next;
}
newMag[i] = mag[magLen - 1] << nBits;
}
return newMag;
}
public BigInteger ShiftLeft(
int n)
{
if (SignValue == 0 || magnitude.Length == 0)
return Zero;
if (n == 0)
return this;
if (n < 0)
return ShiftRight(-n);
var result = new BigInteger(SignValue, ShiftLeft(magnitude, n), true);
if (nBits != -1)
result.nBits = SignValue > 0
? nBits
: nBits + n;
if (nBitLength != -1)
result.nBitLength = nBitLength + n;
return result;
}
/**
* do a right shift - this does it in place.
*/
private static void ShiftRightInPlace(
int start,
int[] mag,
int n)
{
var nInts = (int) ((uint) n >> 5) + start;
var nBits = n & 0x1f;
var magEnd = mag.Length - 1;
if (nInts != start)
{
var delta = nInts - start;
for (var i = magEnd; i >= nInts; i--)
mag[i] = mag[i - delta];
for (var i = nInts - 1; i >= start; i--)
mag[i] = 0;
}
if (nBits != 0)
{
var nBits2 = 32 - nBits;
var m = mag[magEnd];
for (var i = magEnd; i > nInts; --i)
{
var next = mag[i - 1];
mag[i] = (int) ((uint) m >> nBits) | (next << nBits2);
m = next;
}
mag[nInts] = (int) ((uint) mag[nInts] >> nBits);
}
}
/**
* do a right shift by one - this does it in place.
*/
private static void ShiftRightOneInPlace(
int start,
int[] mag)
{
var i = mag.Length;
var m = mag[i - 1];
while (--i > start)
{
var next = mag[i - 1];
mag[i] = (int) ((uint) m >> 1) | (next << 31);
m = next;
}
mag[start] = (int) ((uint) mag[start] >> 1);
}
public BigInteger ShiftRight(
int n)
{
if (n == 0)
return this;
if (n < 0)
return ShiftLeft(-n);
if (n >= BitLength)
return SignValue < 0 ? One.Negate() : Zero;
// int[] res = (int[]) this.magnitude.Clone();
//
// ShiftRightInPlace(0, res, n);
//
// return new BigInteger(this.sign, res, true);
var resultLength = (BitLength - n + 31) >> 5;
var res = new int[resultLength];
var numInts = n >> 5;
var numBits = n & 31;
if (numBits == 0)
{
Array.Copy(magnitude, 0, res, 0, res.Length);
}
else
{
var numBits2 = 32 - numBits;
var magPos = magnitude.Length - 1 - numInts;
for (var i = resultLength - 1; i >= 0; --i)
{
res[i] = (int) ((uint) magnitude[magPos--] >> numBits);
if (magPos >= 0)
res[i] |= magnitude[magPos] << numBits2;
}
}
Debug.Assert(res[0] != 0);
return new BigInteger(SignValue, res, false);
}
/**
* returns x = x - y - we assume x is >= y
*/
private static int[] Subtract(
int xStart,
int[] x,
int yStart,
int[] y)
{
Debug.Assert(yStart < y.Length);
Debug.Assert(x.Length - xStart >= y.Length - yStart);
var iT = x.Length;
var iV = y.Length;
long m;
var borrow = 0;
do
{
m = (x[--iT] & IMASK) - (y[--iV] & IMASK) + borrow;
x[iT] = (int) m;
// borrow = (m < 0) ? -1 : 0;
borrow = (int) (m >> 63);
} while (iV > yStart);
if (borrow != 0)
while (--x[--iT] == -1)
{
}
return x;
}
public BigInteger Subtract(
BigInteger n)
{
if (n.SignValue == 0)
return this;
if (SignValue == 0)
return n.Negate();
if (SignValue != n.SignValue)
return Add(n.Negate());
var compare = CompareNoLeadingZeroes(0, magnitude, 0, n.magnitude);
if (compare == 0)
return Zero;
BigInteger bigun, lilun;
if (compare < 0)
{
bigun = n;
lilun = this;
}
else
{
bigun = this;
lilun = n;
}
return new BigInteger(SignValue * compare, doSubBigLil(bigun.magnitude, lilun.magnitude), true);
}
private static int[] doSubBigLil(
int[] bigMag,
int[] lilMag)
{
var res = (int[]) bigMag.Clone();
return Subtract(0, res, 0, lilMag);
}
public byte[] ToByteArray()
{
return ToByteArray(false);
}
public byte[] ToByteArrayUnsigned()
{
return ToByteArray(true);
}
private byte[] ToByteArray(
bool unsigned)
{
if (SignValue == 0)
return unsigned ? ZeroEncoding : new byte[1];
var nBits = unsigned && SignValue > 0
? BitLength
: BitLength + 1;
var nBytes = GetByteLength(nBits);
var bytes = new byte[nBytes];
var magIndex = magnitude.Length;
var bytesIndex = bytes.Length;
if (SignValue > 0)
{
while (magIndex > 1)
{
var mag = (uint) magnitude[--magIndex];
bytes[--bytesIndex] = (byte) mag;
bytes[--bytesIndex] = (byte) (mag >> 8);
bytes[--bytesIndex] = (byte) (mag >> 16);
bytes[--bytesIndex] = (byte) (mag >> 24);
}
var lastMag = (uint) magnitude[0];
while (lastMag > byte.MaxValue)
{
bytes[--bytesIndex] = (byte) lastMag;
lastMag >>= 8;
}
bytes[--bytesIndex] = (byte) lastMag;
}
else // sign < 0
{
var carry = true;
while (magIndex > 1)
{
var mag = ~(uint) magnitude[--magIndex];
if (carry)
carry = ++mag == uint.MinValue;
bytes[--bytesIndex] = (byte) mag;
bytes[--bytesIndex] = (byte) (mag >> 8);
bytes[--bytesIndex] = (byte) (mag >> 16);
bytes[--bytesIndex] = (byte) (mag >> 24);
}
var lastMag = (uint) magnitude[0];
if (carry)
--lastMag;
while (lastMag > byte.MaxValue)
{
bytes[--bytesIndex] = (byte) ~lastMag;
lastMag >>= 8;
}
bytes[--bytesIndex] = (byte) ~lastMag;
if (bytesIndex > 0)
bytes[--bytesIndex] = byte.MaxValue;
}
return bytes;
}
public override string ToString()
{
return ToString(10);
}
public string ToString(
int radix)
{
// TODO Make this method work for other radices (ideally 2 <= radix <= 16)
switch (radix)
{
case 2:
case 10:
case 16:
break;
default:
throw new FormatException("Only bases 2, 10, 16 are allowed");
}
// NB: Can only happen to internally managed instances
if (magnitude == null)
return "null";
if (SignValue == 0)
return "0";
Debug.Assert(magnitude.Length > 0);
var sb = new StringBuilder();
if (radix == 16)
{
sb.Append(magnitude[0].ToString("x"));
for (var i = 1; i < magnitude.Length; i++)
sb.Append(magnitude[i].ToString("x8"));
}
else if (radix == 2)
{
sb.Append('1');
for (var i = BitLength - 2; i >= 0; --i)
sb.Append(TestBit(i) ? '1' : '0');
}
else
{
// This is algorithm 1a from chapter 4.4 in Seminumerical Algorithms, slow but it works
IList S = new List