C# BigInteger.Signum方法代碼示例

        /// <summary>
        /// Computes the value of the Jacobi symbol (A|B). 
        /// </summary>
        /// 
        /// <param name="A">The integer value</param>
        /// <param name="B">The integer value</param>
        /// 
        /// <returns>Returns value of the jacobi symbol (A|B)</returns>
        public static int Jacobi(BigInteger A, BigInteger B)
        {
            BigInteger a, b, v;
            long k = 1;

            // test trivial cases
            if (B.Equals(ZERO))
            {
                a = A.Abs();
                return a.Equals(ONE) ? 1 : 0;
            }

            if (!A.TestBit(0) && !B.TestBit(0))
                return 0;

            a = A;
            b = B;

            if (b.Signum() == -1)
            { // b < 0
                b = b.Negate();
                if (a.Signum() == -1)
                    k = -1;
            }

            v = ZERO;
            while (!b.TestBit(0))
            {
                v = v.Add(ONE);
                b = b.Divide(TWO);
            }

            if (v.TestBit(0))
                k = k * _jacobiTable[a.ToInt32() & 7];

            if (a.Signum() < 0)
            {
                if (b.TestBit(1))
                    k = -k;
                a = a.Negate();
            }

            // main loop
            while (a.Signum() != 0)
            {
                v = ZERO;
                while (!a.TestBit(0))
                { // a is even
                    v = v.Add(ONE);
                    a = a.Divide(TWO);
                }
                if (v.TestBit(0))
                    k = k * _jacobiTable[b.ToInt32() & 7];

                if (a.CompareTo(b) < 0)
                {
                    // swap and correct intermediate result
                    BigInteger x = a;
                    a = b;
                    b = x;
                    if (a.TestBit(1) && b.TestBit(1))
                        k = -k;
                }
                a = a.Subtract(b);
            }

            return b.Equals(ONE) ? (int)k : 0;
        }

        /// <summary>
        /// Compute the next probable prime greater than <c>N</c> with the specified certainty
        /// </summary>
        /// 
        /// <param name="X">An integer number</param>
        /// <param name="Certainty">The certainty that the generated number is prime</param>
        /// 
        /// <returns>Returns the next prime greater than <c>N</c></returns>
        public static BigInteger NextProbablePrime(BigInteger X, int Certainty)
        {
            if (X.Signum() < 0 || X.Signum() == 0 || X.Equals(ONE))
                return TWO;

            BigInteger result = X.Add(ONE);

            // Ensure an odd number
            if (!result.TestBit(0))
                result = result.Add(ONE);

            while (true)
            {
                // Do cheap "pre-test" if applicable
                if (result.BitLength > 6)
                {
                    long r = result.Remainder(BigInteger.ValueOf(SMALL_PRIME_PRODUCT)).ToInt64();
                    if ((r % 3 == 0) || (r % 5 == 0) || (r % 7 == 0) ||
                        (r % 11 == 0) || (r % 13 == 0) || (r % 17 == 0) ||
                        (r % 19 == 0) || (r % 23 == 0) || (r % 29 == 0) ||
                        (r % 31 == 0) || (r % 37 == 0) || (r % 41 == 0))
                    {
                        result = result.Add(TWO);
                        continue; // Candidate is composite; try another
                    }
                }

                // All candidates of bitLength 2 and 3 are prime by this point
                if (result.BitLength < 4)
                    return result;

                // The expensive test
                if (result.IsProbablePrime(Certainty))
                    return result;

                result = result.Add(TWO);
            }
        }

        /// <summary>
        /// Divide two BigIntegers and return the rounded result
        /// </summary>
        /// 
        /// <param name="A">The first BigInteger</param>
        /// <param name="B">The second BigInteger</param>
        /// 
        /// <returns>The rounded result</returns>
        public static BigInteger DivideAndRound(BigInteger A, BigInteger B)
        {
            if (A.Signum() < 0)
                return DivideAndRound(A.Negate(), B).Negate();
            if (B.Signum() < 0)
                return DivideAndRound(A, B.Negate()).Negate();

            return A.ShiftLeft(1).Add(B).Divide(B.ShiftLeft(1));
        }

        /// <summary>
        /// Extended euclidian algorithm (computes Gcd and representation)
        /// </summary>
        /// 
        /// <param name="A">The first BigInteger</param>
        /// <param name="B">The second BigInteger</param>
        /// 
        /// <returns>Returns <c>(d,u,v)</c>, where <c>d = Gcd(A,B) = ua + vb</c></returns>
        public static BigInteger[] ExtGcd(BigInteger A, BigInteger B)
        {
            BigInteger u = ONE;
            BigInteger v = ZERO;
            BigInteger d = A;

            if (B.Signum() != 0)
            {
                BigInteger v1 = ZERO;
                BigInteger v3 = B;
                while (v3.Signum() != 0)
                {
                    BigInteger[] tmp = d.DivideAndRemainder(v3);
                    BigInteger q = tmp[0];
                    BigInteger t3 = tmp[1];
                    BigInteger t1 = u.Subtract(q.Multiply(v1));
                    u = v1;
                    d = v3;
                    v1 = t1;
                    v3 = t3;
                }
                v = d.Subtract(A.Multiply(u)).Divide(B);
            }

            return new BigInteger[] { d, u, v };
        }

        /// <summary>
        /// Performs Value >>= count where Value is a positive number.
        /// </summary>
        /// 
        /// <param name="Value">The source BigIntger</param>
        /// <param name="N">Shift distance</param>
        internal static void InplaceShiftRight(BigInteger Value, int N)
        {
            int sign = Value.Signum();

            if (N == 0 || Value.Signum() == 0)
                return;

            int intCount = N >> 5; // count of integers
            Value._numberLength -= intCount;
            if (!ShiftRight(Value._digits, Value._numberLength, Value._digits, intCount, N & 31) && sign < 0)
            {
                // remainder not zero: add one to the result
                int i;
                for (i = 0; (i < Value._numberLength) && (Value._digits[i] == -1); i++)
                    Value._digits[i] = 0;

                if (i == Value._numberLength)
                    Value._numberLength++;

                Value._digits[i]++;
            }
            Value.CutOffLeadingZeroes();
            Value.UnCache();
        }

        /// <summary>
        /// Multiplies two BigIntegers using the Schönhage-Strassen algorithm.
        /// </summary>
        /// 
        /// <param name="A">Factor A</param>
        /// <param name="B">Factor B</param>
        /// 
        /// <returns>BigInteger equal to <c>A.Multiply(B)</c></returns>
        public static BigInteger Multiply(BigInteger A, BigInteger B)
        {
            // remove any minus signs, multiply, then fix sign
            int signum = A.Signum() * B.Signum();

            if (A.Signum() < 0)
                A = A.Negate();
            if (B.Signum() < 0)
                B = B.Negate();

            int[] aIntArr = ToIntArray(A);
            int[] bIntArr = ToIntArray(B);
            int[] cIntArr = Multiply(aIntArr, A.BitLength, bIntArr, B.BitLength);

            BigInteger c = ToBigInteger(cIntArr);

            if (signum < 0)
                c = c.Negate();

            return c;
        }

        private void TestDiv(BigInteger i1, BigInteger i2)
        {
            BigInteger q = i1.Divide(i2);
            BigInteger r = i1.Remainder(i2);
            BigInteger[] q2 = i1.DivideAndRemainder(i2);
            BigInteger quotient = q2[0];
            BigInteger remainder = q2[1];

            IsTrue(q.Equals(quotient), "Divide and DivideAndRemainder do not agree");
            IsTrue(r.Equals(remainder), "Remainder and DivideAndRemainder do not agree");
            IsTrue(q.Signum() != 0 || q.Equals(zero), "signum and equals(zero) do not agree on quotient");
            IsTrue(r.Signum() != 0 || r.Equals(zero), "signum and equals(zero) do not agree on remainder");
            IsTrue(q.Signum() == 0 || q.Signum() == i1.Signum() * i2.Signum(), "wrong sign on quotient");
            IsTrue(r.Signum() == 0 || r.Signum() == i1.Signum(), "wrong sign on remainder");
            IsTrue(r.Abs().CompareTo(i2.Abs()) < 0, "remainder out of range");
            IsTrue(q.Abs().Add(one).Multiply(i2.Abs()).CompareTo(i1.Abs()) > 0, "quotient too small");
            IsTrue(q.Abs().Multiply(i2.Abs()).CompareTo(i1.Abs()) <= 0, "quotient too large");
            BigInteger p = q.Multiply(i2);
            BigInteger a = p.Add(r);
            IsTrue(a.Equals(i1), "(a/b)*b+(a%b) != a");
            try
            {
                BigInteger mod = i1.Mod(i2);
                IsTrue(mod.Signum() >= 0, "mod is negative");
                IsTrue(mod.Abs().CompareTo(i2.Abs()) < 0, "mod out of range");
                IsTrue(r.Signum() < 0 || r.Equals(mod), "positive remainder == mod");
                IsTrue(r.Signum() >= 0 || r.Equals(mod.Subtract(i2)), "negative remainder == mod - divisor");
            }
            catch
            {
                IsTrue(i2.Signum() <= 0, "mod fails on negative divisor only");
            }
        }

        private static BigInteger ModInverseLorencz(BigInteger X, BigInteger Modulo)
        {
            // Based on "New Algorithm for Classical Modular Inverse" Róbert Lórencz. LNCS 2523 (2002)
            // PRE: a is coprime with modulo, a < modulo
            int max = System.Math.Max(X._numberLength, Modulo._numberLength);
            int[] uDigits = new int[max + 1]; // enough place to make all the inplace operation
            int[] vDigits = new int[max + 1];
            Array.Copy(Modulo._digits, 0, uDigits, 0, Modulo._numberLength);
            Array.Copy(X._digits, 0, vDigits, 0, X._numberLength);

            BigInteger u = new BigInteger(Modulo._sign, Modulo._numberLength, uDigits);
            BigInteger v = new BigInteger(X._sign, X._numberLength, vDigits);
            BigInteger r = new BigInteger(0, 1, new int[max + 1]); // BigInteger.ZERO;
            BigInteger s = new BigInteger(1, 1, new int[max + 1]);
            s._digits[0] = 1;
            // r == 0 && s == 1, but with enough place

            int coefU = 0, coefV = 0;
            int n = Modulo.BitLength;
            int k;

            while (!IsPowerOfTwo(u, coefU) && !IsPowerOfTwo(v, coefV))
            {
                // modification of original algorithm: I calculate how many times the algorithm will enter in the same branch of if
                k = HowManyIterations(u, n);
                if (k != 0)
                {
                    BitLevel.InplaceShiftLeft(u, k);
                    if (coefU >= coefV)
                    {
                        BitLevel.InplaceShiftLeft(r, k);
                    }
                    else
                    {
                        BitLevel.InplaceShiftRight(s, System.Math.Min(coefV - coefU, k));

                        if (k - (coefV - coefU) > 0)
                            BitLevel.InplaceShiftLeft(r, k - coefV + coefU);
                    }
                    coefU += k;
                }

                k = HowManyIterations(v, n);
                if (k != 0)
                {
                    BitLevel.InplaceShiftLeft(v, k);
                    if (coefV >= coefU)
                    {
                        BitLevel.InplaceShiftLeft(s, k);
                    }
                    else
                    {
                        BitLevel.InplaceShiftRight(r, System.Math.Min(coefU - coefV, k));

                        if (k - (coefU - coefV) > 0)
                            BitLevel.InplaceShiftLeft(s, k - coefU + coefV);
                    }
                    coefV += k;

                }

                if (u.Signum() == v.Signum())
                {
                    if (coefU <= coefV)
                    {
                        Elementary.CompleteInPlaceSubtract(u, v);
                        Elementary.CompleteInPlaceSubtract(r, s);
                    }
                    else
                    {
                        Elementary.CompleteInPlaceSubtract(v, u);
                        Elementary.CompleteInPlaceSubtract(s, r);
                    }
                }
                else
                {
                    if (coefU <= coefV)
                    {
                        Elementary.CompleteInPlaceAdd(u, v);
                        Elementary.CompleteInPlaceAdd(r, s);
                    }
                    else
                    {
                        Elementary.CompleteInPlaceAdd(v, u);
                        Elementary.CompleteInPlaceAdd(s, r);
                    }
                }

                if (v.Signum() == 0 || u.Signum() == 0)
                    throw new ArithmeticException("BigInteger not invertible");
            }

            if (IsPowerOfTwo(v, coefV))
            {
                r = s;
                if (v.Signum() != u.Signum())
                    u = u.Negate();
            }
            if (u.TestBit(n))
            {
//.........這裏部分代碼省略.........

        /// <summary>
        /// Return the greatest common divisor of X and Y
        /// </summary>
        /// 
        /// <param name="X">Operand 1, must be greater than zero</param>
        /// <param name="Y">Operand 2, must be greater than zero</param>
        /// 
        /// <returns>Returns <c>GCD(X, Y)</c></returns>
        internal static BigInteger GcdBinary(BigInteger X, BigInteger Y)
        {
            // Divide both number the maximal possible times by 2 without rounding * gcd(2*a, 2*b) = 2 * gcd(a,b)
            int lsb1 = X.LowestSetBit;
            int lsb2 = Y.LowestSetBit;
            int pow2Count = System.Math.Min(lsb1, lsb2);

            BitLevel.InplaceShiftRight(X, lsb1);
            BitLevel.InplaceShiftRight(Y, lsb2);
            BigInteger swap;

            // I want op2 > op1
            if (X.CompareTo(Y) == BigInteger.GREATER)
            {
                swap = X;
                X = Y;
                Y = 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 ((Y._numberLength == 1) || ((Y._numberLength == 2) && (Y._digits[1] > 0)))
                {
                    Y = BigInteger.ValueOf(Division.GcdBinary(X.ToInt64(), Y.ToInt64()));
                    break;
                }

                // Implements one step of the Euclidean algorithm
                // To reduce one operand if it's much smaller than the other one
                if (Y._numberLength > X._numberLength * 1.2)
                {
                    Y = Y.Remainder(X);

                    if (Y.Signum() != 0)
                        BitLevel.InplaceShiftRight(Y, Y.LowestSetBit);
                }
                else
                {

                    // Use Knuth's algorithm of successive subtract and shifting
                    do
                    {
                        Elementary.InplaceSubtract(Y, X); // both are odd
                        BitLevel.InplaceShiftRight(Y, Y.LowestSetBit); // op2 is even
                    } while (Y.CompareTo(X) >= BigInteger.EQUALS);
                }
                // now op1 >= op2
                swap = Y;
                Y = X;
                X = swap;
            } while (X._sign != 0);

            return Y.ShiftLeft(pow2Count);
        }