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()));
}
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));
}