public static BigInteger powerOf10(long exp)
{
// PRE: exp >= 0
int intExp = (int)exp;
// "SMALL POWERS"
if (exp < bigTenPows.Length)
{
// The largest power that fit in 'long' type
return(bigTenPows[intExp]);
}
else if (exp <= 50)
{
// To calculate: 10^exp
return(BigInteger.TEN.pow(intExp));
}
else if (exp <= 1000)
{
// To calculate: 5^exp * 2^exp
return(bigFivePows[1].pow(intExp).shiftLeft(intExp));
}
if (exp <= Int32.MaxValue)
{
// To calculate: 5^exp * 2^exp
return(bigFivePows[1].pow(intExp).shiftLeft(intExp));
}
/*
* "HUGE POWERS"
*
* This branch probably won't be executed since the power of ten is too
* big.
*/
// To calculate: 5^exp
BigInteger powerOfFive = bigFivePows[1].pow(Int32.MaxValue);
BigInteger res = powerOfFive;
long longExp = exp - Int32.MaxValue;
intExp = (int)(exp % Int32.MaxValue);
while (longExp > Int32.MaxValue)
{
res = res.multiply(powerOfFive);
longExp -= Int32.MaxValue;
}
res = res.multiply(bigFivePows[1].pow(intExp));
// To calculate: 5^exp << exp
res = res.shiftLeft(Int32.MaxValue);
longExp = exp - Int32.MaxValue;
while (longExp > Int32.MaxValue)
{
res = res.shiftLeft(Int32.MaxValue);
longExp -= Int32.MaxValue;
}
res = res.shiftLeft(intExp);
return(res);
}
internal static BigInteger oddModPow(BigInteger _base, BigInteger exponent,
BigInteger modulus)
{
// PRE: (base > 0), (exponent > 0), (modulus > 0) and (odd modulus)
int k = (modulus.numberLength << 5); // r = 2^k
// n-residue of base [base * r (mod modulus)]
BigInteger a2 = _base.shiftLeft(k).mod(modulus);
// n-residue of base [1 * r (mod modulus)]
BigInteger x2 = BigInteger.getPowerOfTwo(k).mod(modulus);
BigInteger res;
// Compute (modulus[0]^(-1)) (mod 2^32) for odd modulus
int n2 = calcN(modulus);
if (modulus.numberLength == 1)
{
res = squareAndMultiply(x2, a2, exponent, modulus, n2);
}
else
{
res = slidingWindow(x2, a2, exponent, modulus, n2);
}
return(monPro(res, BigInteger.ONE, modulus, n2));
}
public static BigInteger karatsuba(BigInteger op1, BigInteger op2)
{
BigInteger temp;
if (op2.numberLength > op1.numberLength)
{
temp = op1;
op1 = op2;
op2 = temp;
}
if (op2.numberLength < whenUseKaratsuba)
{
return(multiplyPAP(op1, op2));
}
/* Karatsuba: u = u1*B + u0
* v = v1*B + v0
* u*v = (u1*v1)*B^2 + ((u1-u0)*(v0-v1) + u1*v1 + u0*v0)*B + u0*v0
*/
// ndiv2 = (op1.numberLength / 2) * 32
int ndiv2 = (int)(op1.numberLength & 0xFFFFFFFE) << 4;
BigInteger upperOp1 = op1.shiftRight(ndiv2);
BigInteger upperOp2 = op2.shiftRight(ndiv2);
BigInteger lowerOp1 = op1.subtract(upperOp1.shiftLeft(ndiv2));
BigInteger lowerOp2 = op2.subtract(upperOp2.shiftLeft(ndiv2));
BigInteger upper = karatsuba(upperOp1, upperOp2);
BigInteger lower = karatsuba(lowerOp1, lowerOp2);
BigInteger middle = karatsuba(upperOp1.subtract(lowerOp1),
lowerOp2.subtract(upperOp2));
middle = middle.add(upper).add(lower);
middle = middle.shiftLeft(ndiv2);
upper = upper.shiftLeft(ndiv2 << 1);
return(upper.add(middle).add(lower));
}
internal static BigInteger oddModPow(BigInteger _base, BigInteger exponent,
BigInteger modulus)
{
// PRE: (base > 0), (exponent > 0), (modulus > 0) and (odd modulus)
int k = (modulus.numberLength << 5); // r = 2^k
// n-residue of base [base * r (mod modulus)]
BigInteger a2 = _base.shiftLeft(k).mod(modulus);
// n-residue of base [1 * r (mod modulus)]
BigInteger x2 = BigInteger.getPowerOfTwo(k).mod(modulus);
BigInteger res;
// Compute (modulus[0]^(-1)) (mod 2^32) for odd modulus
int n2 = calcN(modulus);
if( modulus.numberLength == 1 ){
res = squareAndMultiply(x2,a2, exponent, modulus,n2);
} else {
res = slidingWindow(x2, a2, exponent, modulus, n2);
}
return monPro(res, BigInteger.ONE, modulus, n2);
}
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);
}
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));
}
