public BigInteger gcd(BigInteger val)
{
BigInteger val1 = this.abs();
BigInteger val2 = val.abs();
// To avoid a possible division by zero
if (val1.signum() == 0)
{
return(val2);
}
else if (val2.signum() == 0)
{
return(val1);
}
// Optimization for small operands
// (op2.bitLength() < 64) and (op1.bitLength() < 64)
if (((val1.numberLength == 1) || ((val1.numberLength == 2) && (val1.digits[1] > 0))) &&
(val2.numberLength == 1 || (val2.numberLength == 2 && val2.digits[1] > 0)))
{
return(BigInteger.valueOf(Division.gcdBinary(val1.longValue(), val2
.longValue())));
}
return(Division.gcdBinary(val1.copy(), val2.copy()));
}
static BigInteger()
{
TWO_POWS = new BigInteger[32];
for (int i = 0; i < TWO_POWS.Length; i++)
{
TWO_POWS[i] = BigInteger.valueOf(1L << i);
}
}
static Primality() // To initialize the dual table of BigInteger primes
{
for (int i = 0; i < primes.Length; i++)
{
BIprimes[i] = BigInteger.valueOf(primes[i]);
}
offsetPrimes = new int[][] { null, null, new int[] { 0, 2 },
new int[] { 2, 2 }, new int[] { 4, 2 }, new int[] { 6, 5 }, new int[] { 11, 7 }, new int[] { 18, 13 }, new int[] { 31, 23 },
new int[] { 54, 43 }, new int[] { 97, 75 } };
}
static Multiplication()
{
int i;
long fivePow = 1L;
for (i = 0; i <= 18; i++)
{
bigFivePows[i] = BigInteger.valueOf(fivePow);
bigTenPows[i] = BigInteger.valueOf(fivePow << i);
fivePow *= 5;
}
for (; i < bigTenPows.Length; i++)
{
bigFivePows[i] = bigFivePows[i - 1].multiply(bigFivePows[1]);
bigTenPows[i] = bigTenPows[i - 1].multiply(BigInteger.TEN);
}
}
internal static BigInteger[] divideAndRemainderByInteger(BigInteger val,
int divisor, int divisorSign)
{
// res[0] is a quotient and res[1] is a remainder:
int[] valDigits = val.digits;
int valLen = val.numberLength;
int valSign = val.sign;
if (valLen == 1)
{
long a = (valDigits[0] & 0xffffffffL);
long b = (divisor & 0xffffffffL);
long quo = a / b;
long rem = a % b;
if (valSign != divisorSign)
{
quo = -quo;
}
if (valSign < 0)
{
rem = -rem;
}
return(new BigInteger[] { BigInteger.valueOf(quo),
BigInteger.valueOf(rem) });
}
int quotientLength = valLen;
int quotientSign = ((valSign == divisorSign) ? 1 : -1);
int[] quotientDigits = new int[quotientLength];
int[] remainderDigits;
remainderDigits = new int[] { Division.divideArrayByInt(
quotientDigits, valDigits, valLen, divisor) };
BigInteger result0 = new BigInteger(quotientSign, quotientLength,
quotientDigits);
BigInteger result1 = new BigInteger(valSign, 1, remainderDigits);
result0.cutOffLeadingZeroes();
result1.cutOffLeadingZeroes();
return(new BigInteger[] { result0, result1 });
}
internal static BigInteger add(BigInteger op1, BigInteger op2)
{
int[] resDigits;
int resSign;
int op1Sign = op1.sign;
int op2Sign = op2.sign;
if (op1Sign == 0)
{
return(op2);
}
if (op2Sign == 0)
{
return(op1);
}
int op1Len = op1.numberLength;
int op2Len = op2.numberLength;
if (op1Len + op2Len == 2)
{
long a = (op1.digits[0] & 0xFFFFFFFFL);
long b = (op2.digits[0] & 0xFFFFFFFFL);
long ress;
int valueLo;
int valueHi;
if (op1Sign == op2Sign)
{
ress = a + b;
valueLo = (int)ress;
valueHi = (int)((long)(((ulong)ress) >> 32));
return((valueHi == 0) ? new BigInteger(op1Sign, valueLo)
: new BigInteger(op1Sign, 2, new int[] { valueLo,
valueHi }));
}
return(BigInteger.valueOf((op1Sign < 0) ? (b - a) : (a - b)));
}
else if (op1Sign == op2Sign)
{
resSign = op1Sign;
// an augend should not be shorter than addend
resDigits = (op1Len >= op2Len) ? add(op1.digits, op1Len,
op2.digits, op2Len) : add(op2.digits, op2Len, op1.digits,
op1Len);
}
else // signs are different
{
int cmp = ((op1Len != op2Len) ? ((op1Len > op2Len) ? 1 : -1)
: compareArrays(op1.digits, op2.digits, op1Len));
if (cmp == BigInteger.EQUALS)
{
return(BigInteger.ZERO);
}
// a minuend should not be shorter than subtrahend
if (cmp == BigInteger.GREATER)
{
resSign = op1Sign;
resDigits = subtract(op1.digits, op1Len, op2.digits, op2Len);
}
else
{
resSign = op2Sign;
resDigits = subtract(op2.digits, op2Len, op1.digits, op1Len);
}
}
BigInteger res = new BigInteger(resSign, resDigits.Length, resDigits);
res.cutOffLeadingZeroes();
return(res);
}
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.negate());
}
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.valueOf(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);
}
internal 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.getLowestSetBit();
int lsb2 = op2.getLowestSetBit();
int pow2Count = 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.valueOf(Division.gcdBinary(op1.longValue(),
op2.longValue()));
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 = op2.remainder(op1);
if (op2.signum() != 0)
{
BitLevel.inplaceShiftRight(op2, op2.getLowestSetBit());
}
}
else
{
// Use Knuth's algorithm of successive subtract and shifting
do
{
Elementary.inplaceSubtract(op2, op1); // both are odd
BitLevel.inplaceShiftRight(op2, op2.getLowestSetBit()); // op2 is even
} while (op2.compareTo(op1) >= BigInteger.EQUALS);
}
// now op1 >= op2
swap = op2;
op2 = op1;
op1 = swap;
} while (op1.sign != 0);
return(op2.shiftLeft(pow2Count));
}
