Ejemplo n.º 1
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));
        }
Ejemplo n.º 2
0
        internal static int[] divide(int[] quot, int quotLength, int[] a, int aLength, int[] b, int bLength)
        {
            int[] normA = new int[aLength + 1];       // the normalized dividend
            // an extra byte is needed for correct shift
            int[] normB       = new int[bLength + 1]; // the normalized divisor;
            int   normBLength = bLength;

            /*
             * Step D1: normalize a and b and put the results to a1 and b1 the
             * normalized divisor's first digit must be >= 2^31
             */
            int divisorShift = BigDecimal.numberOfLeadingZeros(b[bLength - 1]);

            if (divisorShift != 0)
            {
                BitLevel.shiftLeft(normB, b, 0, divisorShift);
                BitLevel.shiftLeft(normA, a, 0, divisorShift);
            }
            else
            {
                Array.Copy(a, normA, aLength);
                Array.Copy(b, normB, bLength);
            }
            int firstDivisorDigit = normB[normBLength - 1];
            // Step D2: set the quotient index
            int i = quotLength - 1;
            int j = aLength;

            while (i >= 0)
            {
                // Step D3: calculate a guess digit guessDigit
                int guessDigit = 0;
                if (normA[j] == firstDivisorDigit)
                {
                    // set guessDigit to the largest unsigned int value
                    guessDigit = -1;
                }
                else
                {
                    long product = (((normA[j] & 0xffffffffL) << 32) + (normA[j - 1] & 0xffffffffL));
                    long res     = Division.divideLongByInt(product, firstDivisorDigit);
                    guessDigit = (int)res;      // the quotient of divideLongByInt
                    int rem = (int)(res >> 32); // the remainder of
                    // divideLongByInt
                    // decrease guessDigit by 1 while leftHand > rightHand
                    if (guessDigit != 0)
                    {
                        long leftHand    = 0;
                        long rightHand   = 0;
                        bool rOverflowed = false;
                        guessDigit++; // to have the proper value in the loop
                        // below
                        do
                        {
                            guessDigit--;
                            if (rOverflowed)
                            {
                                break;
                            }
                            // leftHand always fits in an unsigned long
                            leftHand = (guessDigit & 0xffffffffL)
                                       * (normB[normBLength - 2] & 0xffffffffL);

                            /*
                             * rightHand can overflow; in this case the loop
                             * condition will be true in the next step of the loop
                             */
                            rightHand = ((long)rem << 32)
                                        + (normA[j - 2] & 0xffffffffL);
                            long longR = (rem & 0xffffffffL)
                                         + (firstDivisorDigit & 0xffffffffL);

                            /*
                             * checks that longR does not fit in an unsigned int;
                             * this ensures that rightHand will overflow unsigned
                             * long in the next step
                             */
                            if (BigDecimal.numberOfLeadingZeros((int)((long)(((ulong)longR) >> 32))) < 32)
                            {
                                rOverflowed = true;
                            }
                            else
                            {
                                rem = (int)longR;
                            }
                        } while (((long)((ulong)leftHand ^ 0x8000000000000000L) > (long)((ulong)rightHand ^ 0x8000000000000000L)));
                    }
                }
                // Step D4: multiply normB by guessDigit and subtract the production
                // from normA.
                if (guessDigit != 0)
                {
                    int borrow = Division.multiplyAndSubtract(normA, j
                                                              - normBLength, normB, normBLength,
                                                              guessDigit);
                    // Step D5: check the borrow
                    if (borrow != 0)
                    {
                        // Step D6: compensating addition
                        guessDigit--;
                        long carry = 0;
                        for (int k = 0; k < normBLength; k++)
                        {
                            carry += (normA[j - normBLength + k] & 0xffffffffL)
                                     + (normB[k] & 0xffffffffL);
                            normA[j - normBLength + k] = (int)carry;
                            carry = (long)(((ulong)carry) >> 32);
                        }
                    }
                }
                if (quot != null)
                {
                    quot[i] = guessDigit;
                }
                // Step D7
                j--;
                i--;
            }

            /*
             * Step D8: we got the remainder in normA. Denormalize it id needed
             */
            if (divisorShift != 0)
            {
                // reuse normB
                BitLevel.shiftRight(normB, normBLength, normA, 0, divisorShift);
                return(normB);
            }
            Array.Copy(normA, normB, bLength);
            return(normA);
        }
Ejemplo n.º 3
0
        internal static String bigInteger2String(BigInteger val, int radix)
        {
            int sign         = val.sign;
            int numberLength = val.numberLength;

            int[] digits = val.digits;

            if (sign == 0)
            {
                return("0"); //$NON-NLS-1$
            }
            if (numberLength == 1)
            {
                int  highDigit = digits[numberLength - 1];
                long v         = highDigit & 0xFFFFFFFFL;
                if (sign < 0)
                {
                    v = -v;
                }
                return(Convert.ToString(v, radix));
            }
            if ((radix == 10) || (radix < 0) ||
                (radix > 26))
            {
                return(val.ToString());
            }
            double bitsForRadixDigit;

            bitsForRadixDigit = Math.Log(radix) / Math.Log(2);
            int resLengthInChars = (int)(val.abs().bitLength() / bitsForRadixDigit + ((sign < 0) ? 1
                                                                                       : 0)) + 1;

            char[] result      = new char[resLengthInChars];
            int    currentChar = resLengthInChars;
            int    resDigit;

            if (radix != 16)
            {
                int[] temp = new int[numberLength];
                Array.Copy(digits, 0, temp, 0, numberLength);
                int tempLen     = numberLength;
                int charsPerInt = digitFitInInt[radix];
                int i;
                // get the maximal power of radix that fits in int
                int bigRadix = bigRadices[radix - 2];
                while (true)
                {
                    // divide the array of digits by bigRadix and convert remainders
                    // to characters collecting them in the char array
                    resDigit = Division.divideArrayByInt(temp, temp, tempLen,
                                                         bigRadix);
                    int previous = currentChar;
                    do
                    {
                        result[--currentChar] = Convert.ToString(resDigit % radix, radix)[0];
                    } while (((resDigit /= radix) != 0) && (currentChar != 0));
                    int delta = charsPerInt - previous + currentChar;
                    for (i = 0; i < delta && currentChar > 0; i++)
                    {
                        result[--currentChar] = '0';
                    }
                    for (i = tempLen - 1; (i > 0) && (temp[i] == 0); i--)
                    {
                        ;
                    }
                    tempLen = i + 1;
                    if ((tempLen == 1) && (temp[0] == 0))   // the quotient is 0
                    {
                        break;
                    }
                }
            }
            else
            {
                // radix == 16
                for (int i = 0; i < numberLength; i++)
                {
                    for (int j = 0; (j < 8) && (currentChar > 0); j++)
                    {
                        resDigit = digits[i] >> (j << 2) & 0xf;
                        result[--currentChar] = Convert.ToString(resDigit % radix, 16)[0];
                    }
                }
            }
            while (result[currentChar] == '0')
            {
                currentChar++;
            }
            if (sign == -1)
            {
                result[--currentChar] = '-';
            }
            return(new String(result, currentChar, resLengthInChars - currentChar));
        }