コード例 #1
0
        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);
        }
コード例 #2
0
        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));
        }
コード例 #3
0
        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));
        }
コード例 #4
0
ファイル: Division.cs プロジェクト: vic/ioke
        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);
        }
コード例 #5
0
ファイル: Division.cs プロジェクト: vic/ioke
        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);
        }
コード例 #6
0
        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));
        }