ppl-1.2/src/checked_inlines.hh

/* Abstract checked arithmetic functions: fall-backs.
   Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
   Copyright (C) 2010-2016 BUGSENG srl (http://bugseng.com)

This file is part of the Parma Polyhedra Library (PPL).

The PPL is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The PPL is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.

For the most up-to-date information see the Parma Polyhedra Library
site: http://bugseng.com/products/ppl/ . */

#ifndef PPL_checked_inlines_hh
#define PPL_checked_inlines_hh 1

#include "globals_types.hh"
#include "meta_programming.hh"
#include "C_Integer.hh"
#include "assertions.hh"

/*! \brief
  Performs the test <CODE>a < b</CODE> avoiding the warning about the
  comparison being always false due to limited range of data type.
  FIXME: we have not found a working solution. The GCC option
  -Wno-type-limits suppresses the warning
*/
#define PPL_LT_SILENT(a, b) ((a) < (b))
#define PPL_GT_SILENT(a, b) ((a) > (b))

namespace Parma_Polyhedra_Library {

namespace Checked {

template <typename T1, typename T2>
struct Safe_Conversion : public False {
};
template <typename T>
struct Safe_Conversion<T, T> : public True {
};

#define PPL_SAFE_CONVERSION(To, From)                        \
  template <> struct Safe_Conversion<PPL_U(To), PPL_U(From)> \
    : public True { }

#if PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed short, char);
#endif
PPL_SAFE_CONVERSION(signed short, signed char);
#if PPL_SIZEOF_CHAR < PPL_SIZEOF_SHORT
#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed short, char);
#endif
PPL_SAFE_CONVERSION(signed short, unsigned char);
#endif

#if PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed int, char);
#endif
PPL_SAFE_CONVERSION(signed int, signed char);
PPL_SAFE_CONVERSION(signed int, signed short);
#if PPL_SIZEOF_CHAR < PPL_SIZEOF_INT
#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed int, char);
#endif
PPL_SAFE_CONVERSION(signed int, unsigned char);
#endif
#if PPL_SIZEOF_SHORT < PPL_SIZEOF_INT
PPL_SAFE_CONVERSION(signed int, unsigned short);
#endif

#if PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed long, char);
#endif
PPL_SAFE_CONVERSION(signed long, signed char);
PPL_SAFE_CONVERSION(signed long, signed short);
PPL_SAFE_CONVERSION(signed long, signed int);
#if PPL_SIZEOF_CHAR < PPL_SIZEOF_LONG
#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed long, char);
#endif
PPL_SAFE_CONVERSION(signed long, unsigned char);
#endif
#if PPL_SIZEOF_SHORT < PPL_SIZEOF_LONG
PPL_SAFE_CONVERSION(signed long, unsigned short);
#endif
#if PPL_SIZEOF_INT < PPL_SIZEOF_LONG
PPL_SAFE_CONVERSION(signed long, unsigned int);
#endif

#if PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed long long, char);
#endif
PPL_SAFE_CONVERSION(signed long long, signed char);
PPL_SAFE_CONVERSION(signed long long, signed short);
PPL_SAFE_CONVERSION(signed long long, signed int);
PPL_SAFE_CONVERSION(signed long long, signed long);
#if PPL_SIZEOF_CHAR < PPL_SIZEOF_LONG_LONG
#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(signed long long, char);
#endif
PPL_SAFE_CONVERSION(signed long long, unsigned char);
#endif
#if PPL_SIZEOF_SHORT < PPL_SIZEOF_LONG_LONG
PPL_SAFE_CONVERSION(signed long long, unsigned short);
#endif
#if PPL_SIZEOF_INT < PPL_SIZEOF_LONG_LONG
PPL_SAFE_CONVERSION(signed long long, unsigned int);
#endif
#if PPL_SIZEOF_LONG < PPL_SIZEOF_LONG_LONG
PPL_SAFE_CONVERSION(signed long long, unsigned long);
#endif

#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(unsigned short, char);
#endif
PPL_SAFE_CONVERSION(unsigned short, unsigned char);

#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(unsigned int, char);
#endif
PPL_SAFE_CONVERSION(unsigned int, unsigned char);
PPL_SAFE_CONVERSION(unsigned int, unsigned short);

#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(unsigned long, char);
#endif
PPL_SAFE_CONVERSION(unsigned long, unsigned char);
PPL_SAFE_CONVERSION(unsigned long, unsigned short);
PPL_SAFE_CONVERSION(unsigned long, unsigned int);

#if !PPL_CXX_PLAIN_CHAR_IS_SIGNED
PPL_SAFE_CONVERSION(unsigned long long, char);
#endif
PPL_SAFE_CONVERSION(unsigned long long, unsigned char);
PPL_SAFE_CONVERSION(unsigned long long, unsigned short);
PPL_SAFE_CONVERSION(unsigned long long, unsigned int);
PPL_SAFE_CONVERSION(unsigned long long, unsigned long);


#if PPL_SIZEOF_CHAR <= PPL_SIZEOF_FLOAT - 2
PPL_SAFE_CONVERSION(float, char);
PPL_SAFE_CONVERSION(float, signed char);
PPL_SAFE_CONVERSION(float, unsigned char);
#endif
#if PPL_SIZEOF_SHORT <= PPL_SIZEOF_FLOAT - 2
PPL_SAFE_CONVERSION(float, signed short);
PPL_SAFE_CONVERSION(float, unsigned short);
#endif
#if PPL_SIZEOF_INT <= PPL_SIZEOF_FLOAT - 2
PPL_SAFE_CONVERSION(float, signed int);
PPL_SAFE_CONVERSION(float, unsigned int);
#endif
#if PPL_SIZEOF_LONG <= PPL_SIZEOF_FLOAT - 2
PPL_SAFE_CONVERSION(float, signed long);
PPL_SAFE_CONVERSION(float, unsigned long);
#endif
#if PPL_SIZEOF_LONG_LONG <= PPL_SIZEOF_FLOAT - 2
PPL_SAFE_CONVERSION(float, signed long long);
PPL_SAFE_CONVERSION(float, unsigned long long);
#endif

#if PPL_SIZEOF_CHAR <= PPL_SIZEOF_DOUBLE - 4
PPL_SAFE_CONVERSION(double, char);
PPL_SAFE_CONVERSION(double, signed char);
PPL_SAFE_CONVERSION(double, unsigned char);
#endif
#if PPL_SIZEOF_SHORT <= PPL_SIZEOF_DOUBLE - 4
PPL_SAFE_CONVERSION(double, signed short);
PPL_SAFE_CONVERSION(double, unsigned short);
#endif
#if PPL_SIZEOF_INT <= PPL_SIZEOF_DOUBLE - 4
PPL_SAFE_CONVERSION(double, signed int);
PPL_SAFE_CONVERSION(double, unsigned int);
#endif
#if PPL_SIZEOF_LONG <= PPL_SIZEOF_DOUBLE - 4
PPL_SAFE_CONVERSION(double, signed long);
PPL_SAFE_CONVERSION(double, unsigned long);
#endif
#if PPL_SIZEOF_LONG_LONG <= PPL_SIZEOF_DOUBLE - 4
PPL_SAFE_CONVERSION(double, signed long long);
PPL_SAFE_CONVERSION(double, unsigned long long);
#endif
PPL_SAFE_CONVERSION(double, float);

#if PPL_SIZEOF_CHAR <= PPL_SIZEOF_LONG_DOUBLE - 4
PPL_SAFE_CONVERSION(long double, char);
PPL_SAFE_CONVERSION(long double, signed char);
PPL_SAFE_CONVERSION(long double, unsigned char);
#endif
#if PPL_SIZEOF_SHORT <= PPL_SIZEOF_LONG_DOUBLE - 4
PPL_SAFE_CONVERSION(long double, signed short);
PPL_SAFE_CONVERSION(long double, unsigned short);
#endif
#if PPL_SIZEOF_INT <= PPL_SIZEOF_LONG_DOUBLE - 4
PPL_SAFE_CONVERSION(long double, signed int);
PPL_SAFE_CONVERSION(long double, unsigned int);
#endif
#if PPL_SIZEOF_LONG <= PPL_SIZEOF_LONG_DOUBLE - 4
PPL_SAFE_CONVERSION(long double, signed long);
PPL_SAFE_CONVERSION(long double, unsigned long);
#endif
#if PPL_SIZEOF_LONG_LONG <= PPL_SIZEOF_LONG_DOUBLE - 4
PPL_SAFE_CONVERSION(long double, signed long long);
PPL_SAFE_CONVERSION(long double, unsigned long long);
#endif
PPL_SAFE_CONVERSION(long double, float);
PPL_SAFE_CONVERSION(long double, double);

PPL_SAFE_CONVERSION(mpz_class, char);
PPL_SAFE_CONVERSION(mpz_class, signed char);
PPL_SAFE_CONVERSION(mpz_class, signed short);
PPL_SAFE_CONVERSION(mpz_class, signed int);
PPL_SAFE_CONVERSION(mpz_class, signed long);
// GMP's API does not support signed long long.
PPL_SAFE_CONVERSION(mpz_class, unsigned char);
PPL_SAFE_CONVERSION(mpz_class, unsigned short);
PPL_SAFE_CONVERSION(mpz_class, unsigned int);
PPL_SAFE_CONVERSION(mpz_class, unsigned long);
// GMP's API does not support unsigned long long.

PPL_SAFE_CONVERSION(mpq_class, char);
PPL_SAFE_CONVERSION(mpq_class, signed char);
PPL_SAFE_CONVERSION(mpq_class, signed short);
PPL_SAFE_CONVERSION(mpq_class, signed int);
PPL_SAFE_CONVERSION(mpq_class, signed long);
// GMP's API does not support signed long long.
PPL_SAFE_CONVERSION(mpq_class, unsigned char);
PPL_SAFE_CONVERSION(mpq_class, unsigned short);
PPL_SAFE_CONVERSION(mpq_class, unsigned int);
PPL_SAFE_CONVERSION(mpq_class, unsigned long);
// GMP's API does not support unsigned long long.
PPL_SAFE_CONVERSION(mpq_class, float);
PPL_SAFE_CONVERSION(mpq_class, double);
// GMP's API does not support long double.

#undef PPL_SAFE_CONVERSION

template <typename Policy, typename Type>
struct PPL_FUNCTION_CLASS(construct)<Policy, Policy, Type, Type> {
  static inline Result function(Type& to, const Type& from, Rounding_Dir) {
    new(&to) Type(from);
    return V_EQ;
  }
};

template <typename To_Policy, typename From_Policy, typename To, typename From>
struct PPL_FUNCTION_CLASS(construct) {
  static inline Result function(To& to, const From& from, Rounding_Dir dir) {
    new(&to) To();
    return assign<To_Policy, From_Policy>(to, from, dir);
  }
};

template <typename To_Policy, typename To>
struct PPL_FUNCTION_CLASS(construct_special) {
  static inline Result function(To& to, Result_Class r, Rounding_Dir dir) {
    new(&to) To();
    return assign_special<To_Policy>(to, r, dir);
  }
};

template <typename To_Policy, typename From_Policy, typename To, typename From>
inline Result
assign_exact(To& to, const From& from, Rounding_Dir) {
  to = from;
  return V_EQ;
}

template <typename To_Policy, typename From_Policy, typename Type>
inline typename Enable_If<Is_Same<To_Policy, From_Policy>::value, void>::type
copy_generic(Type& to, const Type& from) {
  to = from;
}

template <typename To_Policy, typename From_Policy, typename To, typename From>
inline Result
abs_generic(To& to, const From& from, Rounding_Dir dir) {
  if (from < 0) {
    return neg<To_Policy, From_Policy>(to, from, dir);
  }
  else {
    return assign<To_Policy, From_Policy>(to, from, dir);
  }
}

template <typename To_Policy, typename From1_Policy, typename From2_Policy,
          typename To, typename From>
inline void
gcd_exact_no_abs(To& to, const From& x, const From& y) {
  To w_x = x;
  To w_y = y;
  To remainder;
  while (w_y != 0) {
    // The following is derived from the assumption that w_x % w_y
    // is always representable. This is true for both native integers
    // and IEC 559 floating point numbers.
    rem<To_Policy, From1_Policy, From2_Policy>(remainder, w_x, w_y,
                                               ROUND_NOT_NEEDED);
    w_x = w_y;
    w_y = remainder;
  }
  to = w_x;
}

template <typename To_Policy, typename From1_Policy, typename From2_Policy,
          typename To, typename From1, typename From2>
inline Result
gcd_exact(To& to, const From1& x, const From2& y, Rounding_Dir dir) {
  gcd_exact_no_abs<To_Policy, From1_Policy, From2_Policy>(to, x, y);
  return abs<To_Policy, To_Policy>(to, to, dir);
}

template <typename To1_Policy, typename To2_Policy, typename To3_Policy,
          typename From1_Policy, typename From2_Policy,
          typename To1, typename To2, typename To3,
          typename From1, typename From2>
inline Result
gcdext_exact(To1& to, To2& s, To3& t, const From1& x, const From2& y,
             Rounding_Dir dir) {
  // In case this becomes a bottleneck, we may consider using the
  // Stehle'-Zimmermann algorithm (see R. Crandall and C. Pomerance,
  // Prime Numbers - A Computational Perspective, Second Edition,
  // Springer, 2005).
  if (y == 0) {
    if (x == 0) {
      s = 0;
      t = 1;
      return V_EQ;
    }
    else {
      if (x < 0) {
        s = -1;
      }
      else {
        s = 1;
      }
      t = 0;
      return abs<To1_Policy, From1_Policy>(to, x, dir);
    }
  }

  s = 1;
  t = 0;
  bool negative_x = x < 0;
  bool negative_y = y < 0;

  Result r;
  r = abs<To1_Policy, From1_Policy>(to, x, dir);
  if (r != V_EQ) {
    return r;
  }

  From2 a_y;
  r = abs<To1_Policy, From2_Policy>(a_y, y, dir);
  if (r != V_EQ) {
    return r;
  }

  // If PPL_MATCH_GMP_GCDEXT is defined then s is favored when the absolute
  // values of the given numbers are equal.  For instance if x and y
  // are both 5 then s will be 1 and t will be 0, instead of the other
  // way round.  This is to match the behavior of GMP.
#define PPL_MATCH_GMP_GCDEXT 1
#ifdef PPL_MATCH_GMP_GCDEXT
  if (to == a_y) {
    goto sign_check;
  }
#endif

  {
    To2 v1 = 0;
    To3 v2 = 1;
    To1 v3 = static_cast<To1>(a_y);
    while (true) {
      To1 q = to / v3;
      // Remainder, next candidate GCD.
      To1 t3 = to - q*v3;
      To2 t1 = s - static_cast<To2>(q)*v1;
      To3 t2 = t - static_cast<To3>(q)*v2;
      s = v1;
      t = v2;
      to = v3;
      if (t3 == 0) {
        break;
      }
      v1 = t1;
      v2 = t2;
      v3 = t3;
    }
  }

#ifdef PPL_MATCH_GMP_GCDEXT
 sign_check:
#endif
  if (negative_x) {
    r = neg<To2_Policy, To2_Policy>(s, s, dir);
    if (r != V_EQ) {
      return r;
    }
  }
  if (negative_y) {
    return neg<To3_Policy, To3_Policy>(t, t, dir);
  }
  return V_EQ;
#undef PPL_MATCH_GMP_GCDEXT
}

template <typename To_Policy, typename From1_Policy, typename From2_Policy,
          typename To, typename From1, typename From2>
inline Result
lcm_gcd_exact(To& to, const From1& x, const From2& y, Rounding_Dir dir) {
  if (x == 0 || y == 0) {
    to = 0;
    return V_EQ;
  }
  To a_x;
  To a_y;
  Result r;
  r = abs<From1_Policy, From1_Policy>(a_x, x, dir);
  if (r != V_EQ) {
    return r;
  }
  r = abs<From2_Policy, From2_Policy>(a_y, y, dir);
  if (r != V_EQ) {
    return r;
  }
  To gcd;
  gcd_exact_no_abs<To_Policy, From1_Policy, From2_Policy>(gcd, a_x, a_y);
  // The following is derived from the assumption that a_x / gcd(a_x, a_y)
  // is always representable. This is true for both native integers
  // and IEC 559 floating point numbers.
  div<To_Policy, From1_Policy, To_Policy>(to, a_x, gcd, ROUND_NOT_NEEDED);
  return mul<To_Policy, To_Policy, From2_Policy>(to, to, a_y, dir);
}

template <typename Policy, typename Type>
inline Result_Relation
sgn_generic(const Type& x) {
  if (x > 0) {
    return VR_GT;
  }
  if (x == 0) {
    return VR_EQ;
  }
  return VR_LT;
}

template <typename T1, typename T2, typename Enable = void>
struct Safe_Int_Comparison : public False {
};

template <typename T1, typename T2>
struct Safe_Int_Comparison<T1, T2, typename Enable_If<(C_Integer<T1>::value && C_Integer<T2>::value)>::type>
  : public Bool<(C_Integer<T1>::is_signed
                 ? (C_Integer<T2>::is_signed
                    || sizeof(T2) < sizeof(T1)
                    || sizeof(T2) < sizeof(int))
                 : (!C_Integer<T2>::is_signed
                    || sizeof(T1) < sizeof(T2)
                    || sizeof(T1) < sizeof(int)))> {
};


template <typename T1, typename T2>
inline typename Enable_If<(Safe_Int_Comparison<T1, T2>::value
                           || Safe_Conversion<T1, T2>::value
                           || Safe_Conversion<T2, T1>::value), bool>::type
lt(const T1& x, const T2& y) {
  return x < y;
}
template <typename T1, typename T2>
inline typename Enable_If<(Safe_Int_Comparison<T1, T2>::value
                           || Safe_Conversion<T1, T2>::value
                           || Safe_Conversion<T2, T1>::value), bool>::type
le(const T1& x, const T2& y) {
  return x <= y;
}
template <typename T1, typename T2>
inline typename Enable_If<(Safe_Int_Comparison<T1, T2>::value
                           || Safe_Conversion<T1, T2>::value
                           || Safe_Conversion<T2, T1>::value), bool>::type
eq(const T1& x, const T2& y) {
  return x == y;
}

template <typename S, typename U>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
lt(const S& x, const U& y) {
  return x < 0 || static_cast<typename C_Integer<S>::other_type>(x) < y;
}

template <typename U, typename S>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
lt(const U& x, const S& y) {
  return y >= 0 && x < static_cast<typename C_Integer<S>::other_type>(y);
}

template <typename S, typename U>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
le(const S& x, const U& y) {
  return x < 0 || static_cast<typename C_Integer<S>::other_type>(x) <= y;
}

template <typename U, typename S>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
le(const U& x, const S& y) {
  return y >= 0 && x <= static_cast<typename C_Integer<S>::other_type>(y);
}

template <typename S, typename U>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
eq(const S& x, const U& y) {
  return x >= 0 && static_cast<typename C_Integer<S>::other_type>(x) == y;
}

template <typename U, typename S>
inline typename Enable_If<(!Safe_Int_Comparison<S, U>::value
                           && C_Integer<U>::value
                           && C_Integer<S>::is_signed), bool>::type
eq(const U& x, const S& y) {
  return y >= 0 && x == static_cast<typename C_Integer<S>::other_type>(y);
}

template <typename T1, typename T2>
inline typename Enable_If<(!Safe_Conversion<T1, T2>::value
                           && !Safe_Conversion<T2, T1>::value
                           && (!C_Integer<T1>::value || !C_Integer<T2>::value)), bool>::type
eq(const T1& x, const T2& y) {
  PPL_DIRTY_TEMP(T1, tmp);
  Result r = assign_r(tmp, y, ROUND_CHECK);
  // FIXME: We can do this also without fpu inexact check using a
  // conversion back and forth and then testing equality.  We should
  // code this in checked_float_inlines.hh, probably it's faster also
  // if fpu supports inexact check.
  PPL_ASSERT(r != V_LE && r != V_GE && r != V_LGE);
  return r == V_EQ && x == tmp;
}

template <typename T1, typename T2>
inline typename Enable_If<(!Safe_Conversion<T1, T2>::value
                           && !Safe_Conversion<T2, T1>::value
                           && (!C_Integer<T1>::value || !C_Integer<T2>::value)), bool>::type
lt(const T1& x, const T2& y) {
  PPL_DIRTY_TEMP(T1, tmp);
  Result r = assign_r(tmp, y, ROUND_UP);
  if (!result_representable(r)) {
    return true;
  }
  switch (result_relation(r)) {
  case VR_EQ:
  case VR_LT:
  case VR_LE:
    return x < tmp;
  default:
    return false;
  }
}

template <typename T1, typename T2>
inline typename
Enable_If<(!Safe_Conversion<T1, T2>::value
           && !Safe_Conversion<T2, T1>::value
           && (!C_Integer<T1>::value || !C_Integer<T2>::value)), bool>::type
le(const T1& x, const T2& y) {
  PPL_DIRTY_TEMP(T1, tmp);
  Result r = assign_r(tmp, y, (ROUND_UP | ROUND_STRICT_RELATION));
  // FIXME: We can do this also without fpu inexact check using a
  // conversion back and forth and then testing equality.  We should
  // code this in checked_float_inlines.hh, probably it's faster also
  // if fpu supports inexact check.
  PPL_ASSERT(r != V_LE && r != V_GE && r != V_LGE);
  if (!result_representable(r)) {
    return true;
  }
  switch (result_relation(r)) {
  case VR_EQ:
    return x <= tmp;
  case VR_LT:
    return x < tmp;
  case VR_LE:
  case VR_GE:
  case VR_LGE:
    // See comment above.
    PPL_UNREACHABLE;
    return false;
  default:
    return false;
  }
}

template <typename Policy1, typename Policy2,
          typename Type1, typename Type2>
inline bool
lt_p(const Type1& x, const Type2& y) {
  return lt(x, y);
}

template <typename Policy1, typename Policy2,
          typename Type1, typename Type2>
inline bool
le_p(const Type1& x, const Type2& y) {
  return le(x, y);
}

template <typename Policy1, typename Policy2,
          typename Type1, typename Type2>
inline bool
eq_p(const Type1& x, const Type2& y) {
  return eq(x, y);
}

template <typename Policy1, typename Policy2,
          typename Type1, typename Type2>
inline Result_Relation
cmp_generic(const Type1& x, const Type2& y) {
  if (lt(y, x)) {
    return VR_GT;
  }
  if (lt(x, y)) {
    return VR_LT;
  }
  return VR_EQ;
}

template <typename Policy, typename Type>
inline Result
assign_nan(Type& to, Result r) {
  assign_special<Policy>(to, VC_NAN, ROUND_IGNORE);
  return r;
}

template <typename Policy, typename Type>
inline Result
input_generic(Type& to, std::istream& is, Rounding_Dir dir) {
  PPL_DIRTY_TEMP(mpq_class, q);
  Result r = input_mpq(q, is);
  Result_Class c = result_class(r);
  switch (c) {
  case VC_MINUS_INFINITY:
  case VC_PLUS_INFINITY:
    return assign_special<Policy>(to, c, dir);
  case VC_NAN:
    return assign_nan<Policy>(to, r);
  default:
    break;
  }
  PPL_ASSERT(r == V_EQ);
  return assign<Policy, void>(to, q, dir);
}

} // namespace Checked

} // namespace Parma_Polyhedra_Library

#endif // !defined(PPL_checked_inlines_hh)