/**************************************************************************\MODULE: vec_GF2SUMMARY:a vec_GF2 is a vector of GF2s that behaves much like generic NTL vectors(see vector.txt), but there are some differences.For efficiency, elements of a vec_GF2 are "packed" into a word.One may use subscript notation v[i] or v(i) as an r-valuein an expression, and as an l-value in the following contexts:   * on the left-hand side of an assignment operator,     * on the left-hand side of +=, -=, *=, /=,    * and as an argument to ++ and --.One may not use the expression v[i] or v(i) to initialize a non-const reference parameter.  For example, if v, w are vec_GF2's, you can write:   v[i] = 0;   v[i] = v[j] + w[k];   v[i] += 1;   v[i]++;   v[i] += w[i];It is perhaps helpful to describe how this is implemented,without going into all the details.The type of a subscript-expression is "subscript_GF2" or"const_subscript_GF2", the latter chosen if the vector is read-only.Both of these "helper" types have automatic conversions operators to GF2.  Moreover, assignment and increment operatorsare defined for "subscript_GF2" (but not for "const_subscript_GF2").These operators return references to themselves, so one caniterate assignment operators as usual (as usual in NTL, the return type of post-increment/decrement is void).As an alternative, one can use the get and put methods below to accessvector elements.There is one subtle but important difference in the semanticsof vec_GF2 and that of generic NTL vectors.  With a vec_GF2, whenever itslength is increased (via SetLength), the "new" bits are always 0.For example, if v.length() == 20, then    v.SetLength(10); v.setLength(20);will effectively clear bits 10..19 of v.This is quite different from the semantics of generic NTL vectors, wherethe above sequence would not change the value of v at all.One has to be aware of this difference, but it will not matterin most ordinary circumstances.\**************************************************************************/class vec_GF2 {public:   vec_GF2(); // 0 length vector   vec_GF2(INIT_SIZE_TYPE, long n); // initialize to length n                                      // usage: vec_GF2(INIT_SIZE, n)   vec_GF2(const vec_GF2& a); // copy constructor   vec_GF2& operator=(const vec_GF2& a); // assignment   ~vec_GF2(); // destructor   void SetLength(long n); // set length to n bits   void SetMaxLength(long n); // allocate space for n bits   long length(); // bit length   long MaxLength(); // max allocated bit length   // SIZE INVARIANT: length() <= MaxLength() < 2^(NTL_BITS_PER_LONG-4)   void FixLength(long n); // fix length to n bits      // can only be applied after default initialization or kill   long fixed(); // test if length has been fixed   void kill(); // free space and make length 0   GF2 get(long i) const; // fetch value at index i (indexing from 0)   void put(long i, GF2 a); // write value a to index i (indexing from 0)   void put(long i, long a);    // Here are the subscripting operators, defined using the   // "helper" classes subscript_GF2 and const_subscript_GF2.   subscript_GF2 operator[](long i);   subscript_GF2 operator()(long i);   const_subscript_GF2 operator[](long i) const;   const_subscript_GF2 operator()(long i) const;};void swap(vec_GF2& x, vec_GF2& y);// swap x and y (fast pointer swap)void append(vec_GF2& v, GF2 a);// append a to vvoid append(vec_GF2& v, const vec_GF2& a);// append a to v// equality operators:long operator==(const vec_GF2& a, const vec_GF2& b);long operator!=(const vec_GF2& a, const vec_GF2& b);// I/O operators:ostream& operator<<(ostream& s, const vec_GF2& a);istream& operator>>(istream& s, vec_GF2& a);// The I/O format is [a_0 a_1 ... a_{n-1}], where each a_i is "0" or "1".// On input, the a_i may be arbitrary integers, which are reduced mod 2.// utility routines:void clear(vec_GF2& x); // clear all bits--length unchangedlong IsZero(const vec_GF2& a); // test if all bits are zerovoid shift(vec_GF2& x, const vec_GF2& a, long n);vec_GF2 shift(const vec_GF2& a, long n);// x = a shifted n places, where n may be positive or negative.// Generally, x[i] = a[i-n], so positive n shifts to a higher index.// The length of x is set to the length of a, and bits // are zero-filled or discarded as necessary.void reverse(vec_GF2& x, const vec_GF2& a); // c = a reversedvec_GF2 reverse(const vec_GF2& a);long weight(const vec_GF2& a); // return number of 1 bits in avoid random(vec_GF2& x, long n);  // x = random vector of length nvec_GF2 random_vec_GF2(long n);// arithmetic operations over GF(2):void add(vec_GF2& x, const vec_GF2& a, const vec_GF2& b);void sub(vec_GF2& x, const vec_GF2& a, const vec_GF2& b);void negate(vec_GF2& x, const vec_GF2& a);void mul(vec_GF2& x, const vec_GF2& a, GF2 b);void mul(vec_GF2& x, const vec_GF2& a, long b);void mul(vec_GF2& x, GF2 a, const vec_GF2& b);void mul(vec_GF2& x, long a, const vec_GF2& b);// x = a * bvoid InnerProduct(GF2& x, const vec_GF2& a, const vec_GF2& b);// vectors may differ in lengthvoid VectorCopy(vec_GF2& x, const vec_GF2& a, long n);vec_GF2 VectorCopy(const vec_GF2& a, long n);// x = a copy of a of length exactly n.// The input is truncated or padded with zeroes, as necessary.// arithmetic operator notation:vec_GF2 operator+(const vec_GF2& a, const vec_GF2& b);vec_GF2 operator-(const vec_GF2& a, const vec_GF2& b);vec_GF2 operator-(const vec_GF2& a);// scalar mul:vec_GF2 operator*(const vec_GF2& a, GF2 b);vec_GF2 operator*(const vec_GF2& a, long b);vec_GF2 operator*(GF2 a, const vec_GF2& b); vec_GF2 operator*(long a, const vec_GF2& b); // inner product: inline GF2 operator*(const vec_GF2& a, const vec_GF2& b); // assignment operator notation:vec_GF2& operator+=(vec_GF2& x, const vec_GF2& a);vec_GF2& operator-=(vec_GF2& x, const vec_GF2& a);vec_GF2& operator*=(vec_GF2& x, GF2 a);vec_GF2& operator*=(vec_GF2& x, long a);