ize() { mpq_canonicalize(mp); }

  // constructors and destructor
  __gmp_expr() { mpq_init(mp); }

  __gmp_expr(const __gmp_expr &q) { mpq_init(mp); mpq_set(mp, q.mp); }
  template <class T, class U>
  __gmp_expr(const __gmp_expr<T, U> &expr)
  { mpq_init(mp); __gmp_set_expr(mp, expr); }

  __gmp_expr(signed char c) { mpq_init(mp); mpq_set_si(mp, c, 1); }
  __gmp_expr(unsigned char c) { mpq_init(mp); mpq_set_ui(mp, c, 1); }

  __gmp_expr(signed int i) { mpq_init(mp); mpq_set_si(mp, i, 1); }
  __gmp_expr(unsigned int i) { mpq_init(mp); mpq_set_ui(mp, i, 1); }

  __gmp_expr(signed short int s) { mpq_init(mp); mpq_set_si(mp, s, 1); }
  __gmp_expr(unsigned short int s) { mpq_init(mp); mpq_set_ui(mp, s, 1); }

  __gmp_expr(signed long int l) { mpq_init(mp); mpq_set_si(mp, l, 1); }
  __gmp_expr(unsigned long int l) { mpq_init(mp); mpq_set_ui(mp, l, 1); }

  __gmp_expr(float f) { mpq_init(mp); mpq_set_d(mp, f); }
  __gmp_expr(double d) { mpq_init(mp); mpq_set_d(mp, d); }
  // __gmp_expr(long double ld) { mpq_init(mp); mpq_set_ld(mp, ld); }

  explicit __gmp_expr(const char *s)
  {
    mpq_init (mp);
    if (mpq_set_str (mp, s, 0) != 0)
      {
        mpq_clear (mp);
        throw std::invalid_argument ("mpq_set_str");
      }
  }
  __gmp_expr(const char *s, int base)
  {
    mpq_init (mp);
    if (mpq_set_str(mp, s, base) != 0)
      {
        mpq_clear (mp);
        throw std::invalid_argument ("mpq_set_str");
      }
  }
  explicit __gmp_expr(const std::string &s)
  {
    mpq_init (mp);
    if (mpq_set_str (mp, s.c_str(), 0) != 0)
      {
        mpq_clear (mp);
        throw std::invalid_argument ("mpq_set_str");
      }
  }
  __gmp_expr(const std::string &s, int base)
  {
    mpq_init(mp);
    if (mpq_set_str (mp, s.c_str(), base) != 0)
      {
        mpq_clear (mp);
        throw std::invalid_argument ("mpq_set_str");
      }
  }
  explicit __gmp_expr(mpq_srcptr q) { mpq_init(mp); mpq_set(mp, q); }

  __gmp_expr(const mpz_class &num, const mpz_class &den)
  {
    mpq_init(mp);
    mpz_set(mpq_numref(mp), num.get_mpz_t());
    mpz_set(mpq_denref(mp), den.get_mpz_t());
  }

  ~__gmp_expr() { mpq_clear(mp); }

  // assignment operators
  __gmp_expr & operator=(const __gmp_expr &q)
  { mpq_set(mp, q.mp); return *this; }
  template <class T, class U>
  __gmp_expr<value_type, value_type> & operator=(const __gmp_expr<T, U> &expr)
  { __gmp_set_expr(mp, expr); return *this; }

  __gmp_expr & operator=(signed char c)
  { mpq_set_si(mp, c, 1); return *this; }
  __gmp_expr & operator=(unsigned char c)
  { mpq_set_ui(mp, c, 1); return *this; }

  __gmp_expr & operator=(signed int i) { mpq_set_si(mp, i, 1); return *this; }
  __gmp_expr & operator=(unsigned int i)
  { mpq_set_ui(mp, i, 1); return *this; }

  __gmp_expr & operator=(signed short int s)
  { mpq_set_si(mp, s, 1); return *this; }
  __gmp_expr & operator=(unsigned short int s)
  { mpq_set_ui(mp, s, 1); return *this; }

  __gmp_expr & operator=(signed long int l)
  { mpq_set_si(mp, l, 1); return *this; }
  __gmp_expr & operator=(unsigned long int l)
  { mpq_set_ui(mp, l, 1); return *this; }

  __gmp_expr & operator=(float f) { mpq_set_d(mp, f); return *this; }
  __gmp_expr & operator=(double d) { mpq_set_d(mp, d); return *this; }
  // __gmp_expr & operator=(long double ld)
  // { mpq_set_ld(mp, ld); return *this; }

  __gmp_expr & operator=(const char *s)
  {
    if (mpq_set_str (mp, s, 0) != 0)
      throw std::invalid_argument ("mpq_set_str");
    return *this;
  }
  __gmp_expr & operator=(const std::string &s)
  {
    if (mpq_set_str(mp, s.c_str(), 0) != 0)
      throw std::invalid_argument ("mpq_set_str");
    return *this;
  }

  // string input/output functions
  int set_str(const char *s, int base)
  { return mpq_set_str(mp, s, base); }
  int set_str(const std::string &s, int base)
  { return mpq_set_str(mp, s.c_str(), base); }
  std::string get_str(int base = 10) const
  {
    __gmp_alloc_cstring temp(mpq_get_str(0, base, mp));
    return std::string(temp.str);
  }

  // conversion functions

  // casting a reference to an mpz_t to mpz_class & is a dirty hack,
  // al2);
    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
  }
  void eval(typename __gmp_resolve_expr<T>::ptr_type p,
	    unsigned long int prec) const
  {
    __gmp_expr<T, T> temp1(expr.val1, prec), temp2(expr.val2, prec);
    Op::eval(p, temp1.__get_mp(), temp2.__get_mp());
  }
  const val1_type & get_val1() const { return expr.val1; }
  const val2_type & get_val2() const { return expr.val2; }
  unsigned long int get_prec() const
  {
    unsigned long int prec1 = expr.val1.get_prec(),
      prec2 = expr.val2.get_prec();
    return (prec1 > prec2) ? prec1 : prec2;
  }
};


/**************** Special cases ****************/

/* Some operations (i.e., add and subtract) with mixed mpz/mpq arguments
   can be done directly without first converting the mpz to mpq.
   Appropriate specializations of __gmp_expr are required. */


#define __GMPZQ_DEFINE_EXPR(eval_fun)                                       \
                                                                            \
template <>                                                                 \
class __gmp_expr<mpq_t, __gmp_binary_expr<mpz_class, mpq_class, eval_fun> > \
{                                                                           \
private:                                                                    \
  typedef mpz_class val1_type;                                              \
  typedef mpq_class val2_type;                                              \
                                                                            \
  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
public:                                                                     \
  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
    : expr(val1, val2) { }                                                  \
  void eval(mpq_ptr q) const                                                \
  { eval_fun::eval(q, expr.val1.get_mpz_t(), expr.val2.get_mpq_t()); }      \
  const val1_type & get_val1() const { return expr.val1; }                  \
  const val2_type & get_val2() const { return expr.val2; }                  \
  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
};                                                                          \
                                                                            \
template <>                                                                 \
class __gmp_expr<mpq_t, __gmp_binary_expr<mpq_class, mpz_class, eval_fun> > \
{                                                                           \
private:                                                                    \
  typedef mpq_class val1_type;                                              \
  typedef mpz_class val2_type;                                              \
                                                                            \
  __gmp_binary_expr<val1_type, val2_type, eval_fun> expr;                   \
public:                                                                     \
  __gmp_expr(const val1_type &val1, const val2_type &val2)                  \
    : expr(val1, val2) { }                                                  \
  void eval(mpq_ptr q) const                                                \
  { eval_fun::eval(q, expr.val1.get_mpq_t(), expr.val2.get_mpz_t()); }      \
  const val1_type & get_val1() const { return expr.val1; }                  \
  const val2_type & get_val2() const { return expr.val2; }                  \
  unsigned long int get_prec() const { return mpf_get_default_prec(); }     \
};                                                                          \
                                                                            \
template <class T>                                                          \
class __gmp_expr                                                            \
<mpq_t, __gmp_binary_expr<mpz_class, __gmp_expr<mpq_t, T>, eval_fun> >      \
{