public static BigInteger DivideAndRemainder(BigInteger dividend, BigInteger divisor, out BigInteger remainder)
{
int divisorSign = divisor.Sign;
if (divisorSign == 0)
{
// math.17=BigInteger divide by zero
throw new ArithmeticException(Messages.math17); //$NON-NLS-1$
}
int divisorLen = divisor.numberLength;
int[] divisorDigits = divisor.digits;
if (divisorLen == 1)
{
var values = Division.DivideAndRemainderByInteger(dividend, divisorDigits[0], divisorSign);
remainder = values[1];
return(values[0]);
}
int[] thisDigits = dividend.digits;
int thisLen = dividend.numberLength;
int cmp = (thisLen != divisorLen)
? ((thisLen > divisorLen) ? 1 : -1)
: Elementary.CompareArrays(thisDigits, divisorDigits, thisLen);
if (cmp < 0)
{
remainder = dividend;
return(BigInteger.Zero);
}
int thisSign = dividend.Sign;
int quotientLength = thisLen - divisorLen + 1;
int remainderLength = divisorLen;
int quotientSign = ((thisSign == divisorSign) ? 1 : -1);
int[] quotientDigits = new int[quotientLength];
int[] remainderDigits = Division.Divide(quotientDigits, quotientLength,
thisDigits, thisLen, divisorDigits, divisorLen);
var quotient = new BigInteger(quotientSign, quotientLength, quotientDigits);
remainder = new BigInteger(thisSign, remainderLength, remainderDigits);
quotient.CutOffLeadingZeroes();
remainder.CutOffLeadingZeroes();
return(quotient);
}
/// <inheritdoc cref="IComparable{T}.CompareTo"/>
public int CompareTo(BigInteger other)
{
if (sign > other.sign)
{
return(GREATER);
}
if (sign < other.sign)
{
return(LESS);
}
if (numberLength > other.numberLength)
{
return(sign);
}
if (numberLength < other.numberLength)
{
return(-other.sign);
}
// Equal sign and equal numberLength
return(sign * Elementary.CompareArrays(digits, other.digits,
numberLength));
}
private static bool TryParse(string s, int radix, out BigInteger value, out Exception exception)
{
if (String.IsNullOrEmpty(s))
{
exception = new FormatException(Messages.math11);
value = null;
return(false);
}
if ((radix < CharHelper.MIN_RADIX) || (radix > CharHelper.MAX_RADIX))
{
// math.11=Radix out of range
exception = new FormatException(Messages.math12);
value = null;
return(false);
}
int sign;
int[] digits;
int numberLength;
int stringLength = s.Length;
int startChar;
int endChar = stringLength;
if (s[0] == '-')
{
sign = -1;
startChar = 1;
stringLength--;
}
else
{
sign = 1;
startChar = 0;
}
/*
* We use the following algorithm: split a string into portions of n
* char and convert each portion to an integer according to the
* radix. Then convert an exp(radix, n) based number to binary using the
* multiplication method. See D. Knuth, The Art of Computer Programming,
* vol. 2.
*/
try
{
int charsPerInt = Conversion.digitFitInInt[radix];
int bigRadixDigitsLength = stringLength / charsPerInt;
int topChars = stringLength % charsPerInt;
if (topChars != 0)
{
bigRadixDigitsLength++;
}
digits = new int[bigRadixDigitsLength];
// Get the maximal power of radix that fits in int
int bigRadix = Conversion.bigRadices[radix - 2];
// Parse an input string and accumulate the BigInteger's magnitude
int digitIndex = 0; // index of digits array
int substrEnd = startChar + ((topChars == 0) ? charsPerInt : topChars);
int newDigit;
for (int substrStart = startChar;
substrStart < endChar;
substrStart = substrEnd, substrEnd = substrStart
+ charsPerInt)
{
int bigRadixDigit = Convert.ToInt32(s.Substring(substrStart, substrEnd - substrStart), radix);
newDigit = Multiplication.MultiplyByInt(digits, digitIndex, bigRadix);
newDigit += Elementary.inplaceAdd(digits, digitIndex, bigRadixDigit);
digits[digitIndex++] = newDigit;
}
numberLength = digitIndex;
}
catch (Exception ex)
{
exception = ex;
value = null;
return(false);
}
value = new BigInteger();
value.sign = sign;
value.numberLength = numberLength;
value.digits = digits;
value.CutOffLeadingZeroes();
exception = null;
return(true);
}
/**
* It uses the sieve of Eratosthenes to discard several composite numbers in
* some appropriate range (at the moment {@code [this, this + 1024]}). After
* this process it applies the Miller-Rabin test to the numbers that were
* not discarded in the sieve.
*
* @see BigInteger#nextProbablePrime()
* @see #millerRabin(BigInteger, int)
*/
public static BigInteger NextProbablePrime(BigInteger n)
{
// PRE: n >= 0
int i, j;
int certainty;
int gapSize = 1024; // for searching of the next probable prime number
int[] modules = new int[primes.Length];
bool[] isDivisible = new bool[gapSize];
BigInteger startPoint;
BigInteger probPrime;
// If n < "last prime of table" searches next prime in the table
if ((n.numberLength == 1) && (n.Digits[0] >= 0) &&
(n.Digits[0] < primes[primes.Length - 1]))
{
for (i = 0; n.Digits[0] >= primes[i]; i++)
{
;
}
return(BIprimes[i]);
}
/*
* Creates a "N" enough big to hold the next probable prime Note that: N <
* "next prime" < 2*N
*/
startPoint = new BigInteger(1, n.numberLength,
new int[n.numberLength + 1]);
Array.Copy(n.Digits, 0, startPoint.Digits, 0, n.numberLength);
// To fix N to the "next odd number"
if (BigInteger.TestBit(n, 0))
{
Elementary.inplaceAdd(startPoint, 2);
}
else
{
startPoint.Digits[0] |= 1;
}
// To set the improved certainly of Miller-Rabin
j = startPoint.BitLength;
for (certainty = 2; j < BITS[certainty]; certainty++)
{
;
}
// To calculate modules: N mod p1, N mod p2, ... for first primes.
for (i = 0; i < primes.Length; i++)
{
modules[i] = Division.Remainder(startPoint, primes[i]) - gapSize;
}
while (true)
{
// At this point, all numbers in the gap are initialized as
// probably primes
// Arrays.fill(isDivisible, false);
for (int k = 0; k < isDivisible.Length; k++)
{
isDivisible[k] = false;
}
// To discard multiples of first primes
for (i = 0; i < primes.Length; i++)
{
modules[i] = (modules[i] + gapSize) % primes[i];
j = (modules[i] == 0) ? 0 : (primes[i] - modules[i]);
for (; j < gapSize; j += primes[i])
{
isDivisible[j] = true;
}
}
// To execute Miller-Rabin for non-divisible numbers by all first
// primes
for (j = 0; j < gapSize; j++)
{
if (!isDivisible[j])
{
probPrime = startPoint.Copy();
Elementary.inplaceAdd(probPrime, j);
if (MillerRabin(probPrime, certainty))
{
return(probPrime);
}
}
}
Elementary.inplaceAdd(startPoint, gapSize);
}
}
/**
*
* Based on "New Algorithm for Classical Modular Inverse" Róbert Lórencz.
* LNCS 2523 (2002)
*
* @return a^(-1) mod m
*/
private static BigInteger ModInverseLorencz(BigInteger a, BigInteger modulo)
{
// PRE: a is coprime with modulo, a < modulo
int max = System.Math.Max(a.numberLength, modulo.numberLength);
int[] uDigits = new int[max + 1]; // enough place to make all the inplace operation
int[] vDigits = new int[max + 1];
Array.Copy(modulo.Digits, 0, uDigits, 0, modulo.numberLength);
Array.Copy(a.Digits, 0, vDigits, 0, a.numberLength);
BigInteger u = new BigInteger(modulo.Sign,
modulo.numberLength,
uDigits);
BigInteger v = new BigInteger(a.Sign, a.numberLength, vDigits);
BigInteger r = new BigInteger(0, 1, new int[max + 1]); // BigInteger.ZERO;
BigInteger s = new BigInteger(1, 1, new int[max + 1]);
s.Digits[0] = 1;
// r == 0 && s == 1, but with enough place
int coefU = 0, coefV = 0;
int n = modulo.BitLength;
int k;
while (!IsPowerOfTwo(u, coefU) && !IsPowerOfTwo(v, coefV))
{
// modification of original algorithm: I calculate how many times the algorithm will enter in the same branch of if
k = HowManyIterations(u, n);
if (k != 0)
{
BitLevel.InplaceShiftLeft(u, k);
if (coefU >= coefV)
{
BitLevel.InplaceShiftLeft(r, k);
}
else
{
BitLevel.InplaceShiftRight(s, System.Math.Min(coefV - coefU, k));
if (k - (coefV - coefU) > 0)
{
BitLevel.InplaceShiftLeft(r, k - coefV + coefU);
}
}
coefU += k;
}
k = HowManyIterations(v, n);
if (k != 0)
{
BitLevel.InplaceShiftLeft(v, k);
if (coefV >= coefU)
{
BitLevel.InplaceShiftLeft(s, k);
}
else
{
BitLevel.InplaceShiftRight(r, System.Math.Min(coefU - coefV, k));
if (k - (coefU - coefV) > 0)
{
BitLevel.InplaceShiftLeft(s, k - coefU + coefV);
}
}
coefV += k;
}
if (u.Sign == v.Sign)
{
if (coefU <= coefV)
{
Elementary.completeInPlaceSubtract(u, v);
Elementary.completeInPlaceSubtract(r, s);
}
else
{
Elementary.completeInPlaceSubtract(v, u);
Elementary.completeInPlaceSubtract(s, r);
}
}
else
{
if (coefU <= coefV)
{
Elementary.completeInPlaceAdd(u, v);
Elementary.completeInPlaceAdd(r, s);
}
else
{
Elementary.completeInPlaceAdd(v, u);
Elementary.completeInPlaceAdd(s, r);
}
}
if (v.Sign == 0 || u.Sign == 0)
{
// math.19: BigInteger not invertible
throw new ArithmeticException(Messages.math19);
}
}
if (IsPowerOfTwo(v, coefV))
{
r = s;
if (v.Sign != u.Sign)
{
u = -u;
}
}
if (BigInteger.TestBit(u, n))
{
if (r.Sign < 0)
{
r = -r;
}
else
{
r = modulo - r;
}
}
if (r.Sign < 0)
{
r += modulo;
}
return(r);
}
/**
* Calculates a.modInverse(p) Based on: Savas, E; Koc, C "The Montgomery Modular
* Inverse - Revised"
*/
public static BigInteger ModInverseMontgomery(BigInteger a, BigInteger p)
{
if (a.Sign == 0)
{
// ZERO hasn't inverse
// math.19: BigInteger not invertible
throw new ArithmeticException(Messages.math19);
}
if (!BigInteger.TestBit(p, 0))
{
// montgomery inverse require even modulo
return(ModInverseLorencz(a, p));
}
int m = p.numberLength * 32;
// PRE: a \in [1, p - 1]
BigInteger u, v, r, s;
u = p.Copy(); // make copy to use inplace method
v = a.Copy();
int max = System.Math.Max(v.numberLength, u.numberLength);
r = new BigInteger(1, 1, new int[max + 1]);
s = new BigInteger(1, 1, new int[max + 1]);
s.Digits[0] = 1;
// s == 1 && v == 0
int k = 0;
int lsbu = u.LowestSetBit;
int lsbv = v.LowestSetBit;
int toShift;
if (lsbu > lsbv)
{
BitLevel.InplaceShiftRight(u, lsbu);
BitLevel.InplaceShiftRight(v, lsbv);
BitLevel.InplaceShiftLeft(r, lsbv);
k += lsbu - lsbv;
}
else
{
BitLevel.InplaceShiftRight(u, lsbu);
BitLevel.InplaceShiftRight(v, lsbv);
BitLevel.InplaceShiftLeft(s, lsbu);
k += lsbv - lsbu;
}
r.Sign = 1;
while (v.Sign > 0)
{
// INV v >= 0, u >= 0, v odd, u odd (except last iteration when v is even (0))
while (u.CompareTo(v) > BigInteger.EQUALS)
{
Elementary.inplaceSubtract(u, v);
toShift = u.LowestSetBit;
BitLevel.InplaceShiftRight(u, toShift);
Elementary.inplaceAdd(r, s);
BitLevel.InplaceShiftLeft(s, toShift);
k += toShift;
}
while (u.CompareTo(v) <= BigInteger.EQUALS)
{
Elementary.inplaceSubtract(v, u);
if (v.Sign == 0)
{
break;
}
toShift = v.LowestSetBit;
BitLevel.InplaceShiftRight(v, toShift);
Elementary.inplaceAdd(s, r);
BitLevel.InplaceShiftLeft(r, toShift);
k += toShift;
}
}
if (!u.IsOne)
{
// in u is stored the gcd
// math.19: BigInteger not invertible.
throw new ArithmeticException(Messages.math19);
}
if (r.CompareTo(p) >= BigInteger.EQUALS)
{
Elementary.inplaceSubtract(r, p);
}
r = p - r;
// Have pair: ((BigInteger)r, (Integer)k) where r == a^(-1) * 2^k mod (module)
int n1 = CalcN(p);
if (k > m)
{
r = MonPro(r, BigInteger.One, p, n1);
k = k - m;
}
r = MonPro(r, BigInteger.GetPowerOfTwo(m - k), p, n1);
return(r);
}
/**
* @param m a positive modulus
* Return the greatest common divisor of op1 and op2,
*
* @param op1
* must be greater than zero
* @param op2
* must be greater than zero
* @see BigInteger#gcd(BigInteger)
* @return {@code GCD(op1, op2)}
*/
public static BigInteger GcdBinary(BigInteger op1, BigInteger op2)
{
// PRE: (op1 > 0) and (op2 > 0)
/*
* Divide both number the maximal possible times by 2 without rounding
* gcd(2*a, 2*b) = 2 * gcd(a,b)
*/
int lsb1 = op1.LowestSetBit;
int lsb2 = op2.LowestSetBit;
int pow2Count = System.Math.Min(lsb1, lsb2);
BitLevel.InplaceShiftRight(op1, lsb1);
BitLevel.InplaceShiftRight(op2, lsb2);
BigInteger swap;
// I want op2 > op1
if (op1.CompareTo(op2) == BigInteger.GREATER)
{
swap = op1;
op1 = op2;
op2 = swap;
}
do
{
// INV: op2 >= op1 && both are odd unless op1 = 0
// Optimization for small operands
// (op2.bitLength() < 64) implies by INV (op1.bitLength() < 64)
if ((op2.numberLength == 1) ||
((op2.numberLength == 2) && (op2.Digits[1] > 0)))
{
op2 = BigInteger.FromInt64(Division.GcdBinary(op1.ToInt64(),
op2.ToInt64()));
break;
}
// Implements one step of the Euclidean algorithm
// To reduce one operand if it's much smaller than the other one
if (op2.numberLength > op1.numberLength * 1.2)
{
op2 = BigMath.Remainder(op2, op1);
if (op2.Sign != 0)
{
BitLevel.InplaceShiftRight(op2, op2.LowestSetBit);
}
}
else
{
// Use Knuth's algorithm of successive subtract and shifting
do
{
Elementary.inplaceSubtract(op2, op1); // both are odd
BitLevel.InplaceShiftRight(op2, op2.LowestSetBit); // op2 is even
} while (op2.CompareTo(op1) >= BigInteger.EQUALS);
}
// now op1 >= op2
swap = op2;
op2 = op1;
op1 = swap;
} while (op1.Sign != 0);
return(op2 << pow2Count);
}
/** @see BigInteger#subtract(BigInteger) */
internal static BigInteger subtract(BigInteger op1, BigInteger op2)
{
int resSign;
int[] resDigits;
int op1Sign = op1.Sign;
int op2Sign = op2.Sign;
if (op2Sign == 0)
{
return(op1);
}
if (op1Sign == 0)
{
return(-op2);
}
int op1Len = op1.numberLength;
int op2Len = op2.numberLength;
if (op1Len + op2Len == 2)
{
long a = (op1.Digits[0] & 0xFFFFFFFFL);
long b = (op2.Digits[0] & 0xFFFFFFFFL);
if (op1Sign < 0)
{
a = -a;
}
if (op2Sign < 0)
{
b = -b;
}
return(BigInteger.FromInt64(a - b));
}
int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
: Elementary.CompareArrays(op1.Digits, op2.Digits, op1Len));
if (cmp == BigInteger.LESS)
{
resSign = -op2Sign;
resDigits = (op1Sign == op2Sign) ? subtract(op2.Digits, op2Len,
op1.Digits, op1Len) : add(op2.Digits, op2Len, op1.Digits,
op1Len);
}
else
{
resSign = op1Sign;
if (op1Sign == op2Sign)
{
if (cmp == BigInteger.EQUALS)
{
return(BigInteger.Zero);
}
resDigits = subtract(op1.Digits, op1Len, op2.Digits, op2Len);
}
else
{
resDigits = add(op1.Digits, op1Len, op2.Digits, op2Len);
}
}
BigInteger res = new BigInteger(resSign, resDigits.Length, resDigits);
res.CutOffLeadingZeroes();
return(res);
}
/// <summary>
/// Subtracts a big integer value from another
/// </summary>
/// <param name="a">The subtrahend value</param>
/// <param name="b">The subtractor value</param>
/// <returns>
/// </returns>
public static BigInteger Subtract(BigInteger a, BigInteger b)
{
return(Elementary.subtract(a, b));
}
/// <summary>
/// Computes an addition between two big integer numbers
/// </summary>
/// <param name="a">The first term of the addition</param>
/// <param name="b">The second term of the addition</param>
/// <returns>Returns a new <see cref="BigInteger"/> that
/// is the result of the addition of the two integers specified</returns>
public static BigInteger Add(BigInteger a, BigInteger b)
{
return(Elementary.Add(a, b));
}