Boundary.defs.hh

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/* Interval boundary functions.
   Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
   Copyright (C) 2010-2012 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_Boundary_defs_hh
#define PPL_Boundary_defs_hh 1

#include "Checked_Number.defs.hh"

namespace Parma_Polyhedra_Library {

namespace Boundary_NS {

struct Property {
  enum Type {
    SPECIAL_,
    OPEN_,
  };
  typedef bool Value;
  static const Value default_value = true;
  static const Value unsupported_value = false;
  Property(Type t)
    : type(t) {
  }
  Type type;
};

static const Property SPECIAL(Property::SPECIAL_);
static const Property OPEN(Property::OPEN_);

enum Boundary_Type {
  LOWER = ROUND_DOWN,
  UPPER = ROUND_UP
};

inline Rounding_Dir
round_dir_check(Boundary_Type t, bool check = false) {
  if (check)
    return static_cast<Rounding_Dir>(t) | ROUND_STRICT_RELATION;
  else
    return static_cast<Rounding_Dir>(t);
}

template <typename T, typename Info>
inline Result
special_set_boundary_infinity(Boundary_Type type, T&, Info& info) {
  PPL_ASSERT(Info::store_special);
  info.set_boundary_property(type, SPECIAL);
  return V_EQ;
}

template <typename T, typename Info>
inline bool
special_is_open(Boundary_Type, const T&, const Info&) {
  return !Info::may_contain_infinity;
}

template <typename T, typename Info>
inline bool
normal_is_open(Boundary_Type type, const T& x, const Info& info) {
  if (Info::store_open)
    return info.get_boundary_property(type, OPEN);
  else
    return !Info::store_special && !Info::may_contain_infinity
      && normal_is_boundary_infinity(type, x, info);
}

template <typename T, typename Info>
inline bool
is_open(Boundary_Type type, const T& x, const Info& info) {
  if (Info::store_open)
    return info.get_boundary_property(type, OPEN);
  else
    return !Info::may_contain_infinity
      && is_boundary_infinity(type, x, info);
}

template <typename T, typename Info>
inline Result
set_unbounded(Boundary_Type type, T& x, Info& info) {
  PPL_COMPILE_TIME_CHECK(Info::store_special
                         || std::numeric_limits<T>::is_bounded
                         || std::numeric_limits<T>::has_infinity,
                         "unbounded is not representable");
  Result r;
  if (Info::store_special)
    r = special_set_boundary_infinity(type, x, info);
  else if (type == LOWER)
    r = assign_r(x, MINUS_INFINITY, ROUND_UP);
  else
    r = assign_r(x, PLUS_INFINITY, ROUND_DOWN);
  if (result_relation(r) == VR_EQ && !Info::may_contain_infinity)
    info.set_boundary_property(type, OPEN);
  return r;
}

template <typename T, typename Info>
inline Result
set_minus_infinity(Boundary_Type type, T& x, Info& info, bool open = false) {
  /*
  PPL_COMPILE_TIME_CHECK(Info::store_special
                         || std::numeric_limits<T>::has_infinity,
                         "minus infinity is not representable");
  */
  if (open) {
    PPL_ASSERT(type == LOWER);
  }
  else {
    PPL_ASSERT(Info::may_contain_infinity);
  }
  Result r;
  if (Info::store_special) {
    PPL_ASSERT(type == LOWER);
    r = special_set_boundary_infinity(type, x, info);
  }
  else {
    r = assign_r(x, MINUS_INFINITY, round_dir_check(type));
    PPL_ASSERT(result_representable(r));
  }
  if (open || result_relation(r) != VR_EQ)
    info.set_boundary_property(type, OPEN);
  return r;
}

template <typename T, typename Info>
inline Result
set_plus_infinity(Boundary_Type type, T& x, Info& info, bool open = false) {
  /*
  PPL_COMPILE_TIME_CHECK(Info::store_special
                         || std::numeric_limits<T>::has_infinity,
                         "minus infinity is not representable");
  */
  if (open) {
    PPL_ASSERT(type == UPPER);
  }
  else {
    PPL_ASSERT(Info::may_contain_infinity);
  }
  Result r;
  if (Info::store_special) {
    PPL_ASSERT(type == UPPER);
    r = special_set_boundary_infinity(type, x, info);
  }
  else {
    r = assign_r(x, PLUS_INFINITY, round_dir_check(type));
    PPL_ASSERT(result_representable(r));
  }
  if (open || result_relation(r) != VR_EQ)
    info.set_boundary_property(type, OPEN);
  return r;
}

template <typename T, typename Info>
inline Result
set_boundary_infinity(Boundary_Type type, T& x, Info& info, bool open = false) {
  PPL_ASSERT(open || Info::may_contain_infinity);
  Result r;
  if (Info::store_special)
    r = special_set_boundary_infinity(type, x, info);
  else if (type == LOWER)
    r = assign_r(x, MINUS_INFINITY, round_dir_check(type));
  else
    r = assign_r(x, PLUS_INFINITY, round_dir_check(type));
  PPL_ASSERT(result_representable(r));
  if (open)
    info.set_boundary_property(type, OPEN);
  return r;
}

template <typename T, typename Info>
inline bool
is_domain_inf(Boundary_Type type, const T& x, const Info& info) {
  if (Info::store_special && type == LOWER)
    return info.get_boundary_property(type, SPECIAL);
  else if (std::numeric_limits<T>::has_infinity)
    return Parma_Polyhedra_Library::is_minus_infinity(x);
  else if (std::numeric_limits<T>::is_bounded)
    return x == std::numeric_limits<T>::min();
  else
    return false;
}

template <typename T, typename Info>
inline bool
is_domain_sup(Boundary_Type type, const T& x, const Info& info) {
  if (Info::store_special && type == UPPER)
    return info.get_boundary_property(type, SPECIAL);
  else if (std::numeric_limits<T>::has_infinity)
    return Parma_Polyhedra_Library::is_plus_infinity(x);
  else if (std::numeric_limits<T>::is_bounded)
      return x == std::numeric_limits<T>::max();
  else
    return false;
}

template <typename T, typename Info>
inline bool
normal_is_boundary_infinity(Boundary_Type type, const T& x, const Info&) {
  if (!std::numeric_limits<T>::has_infinity)
    return false;
  if (type == LOWER)
    return Parma_Polyhedra_Library::is_minus_infinity(x);
  else
    return Parma_Polyhedra_Library::is_plus_infinity(x);
}

template <typename T, typename Info>
inline bool
is_boundary_infinity(Boundary_Type type, const T& x, const Info& info) {
  if (Info::store_special)
    return info.get_boundary_property(type, SPECIAL);
  else
    return normal_is_boundary_infinity(type, x, info);
}

template <typename T, typename Info>
inline bool
normal_is_reverse_infinity(Boundary_Type type, const T& x, const Info&) {
  if (!Info::may_contain_infinity)
    return false;
  else if (type == LOWER)
    return Parma_Polyhedra_Library::is_plus_infinity(x);
  else
    return Parma_Polyhedra_Library::is_minus_infinity(x);
}

template <typename T, typename Info>
inline bool
is_minus_infinity(Boundary_Type type, const T& x, const Info& info) {
  if (type == LOWER) {
    if (Info::store_special)
      return info.get_boundary_property(type, SPECIAL);
    else
      return normal_is_boundary_infinity(type, x, info);
  }
  else
    return !Info::store_special && normal_is_reverse_infinity(type, x, info);
}

template <typename T, typename Info>
inline bool
is_plus_infinity(Boundary_Type type, const T& x, const Info& info) {
  if (type == UPPER) {
    if (Info::store_special)
      return info.get_boundary_property(type, SPECIAL);
    else
      return normal_is_boundary_infinity(type, x, info);
  }
  else
    return !Info::store_special && normal_is_reverse_infinity(type, x, info);
}

template <typename T, typename Info>
inline bool
is_reverse_infinity(Boundary_Type type, const T& x, const Info& info) {
  return normal_is_reverse_infinity(type, x, info);
}

template <typename T, typename Info>
inline int
infinity_sign(Boundary_Type type, const T& x, const Info& info) {
  if (is_boundary_infinity(type, x, info))
    return (type == LOWER) ? -1 : 1;
  else if (is_reverse_infinity(type, x, info))
    return (type == UPPER) ? -1 : 1;
  else
    return 0;
}

template <typename T, typename Info>
inline bool
is_boundary_infinity_closed(Boundary_Type type, const T& x, const Info& info) {
  return Info::may_contain_infinity
    && !info.get_boundary_property(type, OPEN)
    && is_boundary_infinity(type, x, info);
}

template <typename Info>
inline bool
boundary_infinity_is_open(Boundary_Type type, const Info& info) {
  return !Info::may_contain_infinity
    || info.get_boundary_property(type, OPEN);
}

template <typename T, typename Info>
inline int
sgn_b(Boundary_Type type, const T& x, const Info& info) {
  if (info.get_boundary_property(type, SPECIAL))
    return (type == LOWER) ? -1 : 1;
  else
    // The following Parma_Polyhedra_Library:: qualification is to work
    // around a bug of GCC 4.0.x.
    return Parma_Polyhedra_Library::sgn(x);
}

template <typename T, typename Info>
inline int
sgn(Boundary_Type type, const T& x, const Info& info) {
  int sign = sgn_b(type, x, info);
  if (x == 0 && info.get_boundary_property(type, OPEN))
    return (type == LOWER) ? -1 : 1;
  else
    return sign;
}

template <typename T1, typename Info1, typename T2, typename Info2>
inline bool
eq(Boundary_Type type1, const T1& x1, const Info1& info1,
   Boundary_Type type2, const T2& x2, const Info2& info2) {
  if (type1 == type2) {
    if (is_open(type1, x1, info1)
        != is_open(type2, x2, info2))
      return false;
  }
  else if (is_open(type1, x1, info1)
           || is_open(type2, x2, info2))
    return false;
  if (is_minus_infinity(type1, x1, info1))
    return is_minus_infinity(type2, x2, info2);
  else if (is_plus_infinity(type1, x1, info1))
    return is_plus_infinity(type2, x2, info2);
  else if (is_minus_infinity(type2, x2, info2)
           || is_plus_infinity(type2, x2, info2))
    return false;
  else
    return equal(x1, x2);
}

template <typename T1, typename Info1, typename T2, typename Info2>
inline bool
lt(Boundary_Type type1, const T1& x1, const Info1& info1,
   Boundary_Type type2, const T2& x2, const Info2& info2) {
  if (is_open(type1, x1, info1)) {
    if (type1 == UPPER
        && (type2 == LOWER
            || !is_open(type2, x2, info2)))
      goto le;
  }
  else if (type2 == LOWER
           && is_open(type2, x2, info2)) {
  le:
    if (is_minus_infinity(type1, x1, info1)
        || is_plus_infinity(type2, x2, info2))
      return true;
    if (is_plus_infinity(type1, x1, info1)
        || is_minus_infinity(type2, x2, info2))
      return false;
    else
      return less_or_equal(x1, x2);
  }
  if (is_plus_infinity(type1, x1, info1)
      || is_minus_infinity(type2, x2, info2))
    return false;
  if (is_minus_infinity(type1, x1, info1)
      || is_plus_infinity(type2, x2, info2))
    return true;
  else
    return less_than(x1, x2);
}

template <typename T1, typename Info1, typename T2, typename Info2>
inline bool
gt(Boundary_Type type1, const T1& x1, const Info1& info1,
   Boundary_Type type2, const T2& x2, const Info2& info2) {
  return lt(type2, x2, info2, type1, x1, info1);
}

template <typename T1, typename Info1, typename T2, typename Info2>
inline bool
le(Boundary_Type type1, const T1& x1, const Info1& info1,
   Boundary_Type type2, const T2& x2, const Info2& info2) {
  return !gt(type1, x1, info1, type2, x2, info2);
}

template <typename T1, typename Info1, typename T2, typename Info2>
inline bool
ge(Boundary_Type type1, const T1& x1, const Info1& info1,
   Boundary_Type type2, const T2& x2, const Info2& info2) {
  return !lt(type1, x1, info1, type2, x2, info2);
}

template <typename T, typename Info>
inline Result
adjust_boundary(Boundary_Type type, T& x, Info& info,
                bool open, Result r) {
  r = result_relation_class(r);
  if (type == LOWER) {
    switch (r) {
    case V_GT_MINUS_INFINITY:
      open = true;
      /* Fall through */
    case V_EQ_MINUS_INFINITY:
      if (!Info::store_special)
        return r;
      if (open)
        info.set_boundary_property(type, OPEN);
      return special_set_boundary_infinity(type, x, info);
    case V_GT:
      open = true;
      /* Fall through */
    case V_GE:
    case V_EQ:
      if (open)
        info.set_boundary_property(type, OPEN);
      return r;
    default:
      PPL_UNREACHABLE;
      return V_NAN;
    }
  }
  else {
    switch (r) {
    case V_LT_PLUS_INFINITY:
      open = true;
      /* Fall through */
    case V_EQ_PLUS_INFINITY:
      if (!Info::store_special)
        return r;
      if (open)
        info.set_boundary_property(type, OPEN);
      return special_set_boundary_infinity(type, x, info);
    case V_LT:
      open = true;
      /* Fall through */
    case V_LE:
    case V_EQ:
      if (open)
        info.set_boundary_property(type, OPEN);
      return r;
    default:
      PPL_UNREACHABLE;
      return V_NAN;
    }
  }
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
complement(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type, const T& x, const Info& info) {
  PPL_ASSERT(to_type != type);
  bool should_shrink;
  if (info.get_boundary_property(type, SPECIAL)) {
    should_shrink = !special_is_open(type, x, info);
    if (type == LOWER)
      return set_minus_infinity(to_type, to, to_info, should_shrink);
    else
      return set_plus_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = !normal_is_open(type, x, info);
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = assign_r(to, x, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
assign(Boundary_Type to_type, To& to, To_Info& to_info,
       Boundary_Type type, const T& x, const Info& info,
       bool should_shrink = false) {
  PPL_ASSERT(to_type == type);
  if (info.get_boundary_property(type, SPECIAL)) {
    should_shrink = (should_shrink || special_is_open(type, x, info));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = (should_shrink || normal_is_open(type, x, info));
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = assign_r(to, x, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
min_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type, const T& x, const Info& info) {
  if (lt(type, x, info, to_type, to, to_info)) {
    to_info.clear_boundary_properties(to_type);
    return assign(to_type, to, to_info, type, x, info);
  }
  return V_EQ;
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
min_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  if (lt(type1, x1, info1, type2, x2, info2))
    return assign(to_type, to, to_info, type1, x1, info1);
  else
    return assign(to_type, to, to_info, type2, x2, info2);
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
max_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type, const T& x, const Info& info) {
  if (gt(type, x, info, to_type, to, to_info)) {
    to_info.clear_boundary_properties(to_type);
    return assign(to_type, to, to_info, type, x, info);
  }
  return V_EQ;
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
max_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  if (gt(type1, x1, info1, type2, x2, info2))
    return assign(to_type, to, to_info, type1, x1, info1);
  else
    return assign(to_type, to, to_info, type2, x2, info2);
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
neg_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type, const T& x, const Info& info) {
  PPL_ASSERT(to_type != type);
  bool should_shrink;
  if (info.get_boundary_property(type, SPECIAL)) {
    should_shrink = special_is_open(type, x, info);
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = normal_is_open(type, x, info);
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = neg_assign_r(to, x, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
add_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  PPL_ASSERT(type1 == type2);
  bool should_shrink;
  if (is_boundary_infinity(type1, x1, info1)) {
    should_shrink = (boundary_infinity_is_open(type1, info1)
                     && !is_boundary_infinity_closed(type2, x2, info2));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  else if (is_boundary_infinity(type2, x2, info2)) {
    should_shrink = (boundary_infinity_is_open(type2, info2)
                     && !is_boundary_infinity_closed(type1, x1, info1));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = (normal_is_open(type1, x1, info1)
                   || normal_is_open(type2, x2, info2));
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  // FIXME: extended handling is not needed
  Result r = add_assign_r(to, x1, x2, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
sub_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  PPL_ASSERT(type1 != type2);
  bool should_shrink;
  if (is_boundary_infinity(type1, x1, info1)) {
    should_shrink = (boundary_infinity_is_open(type1, info1)
                     && !is_boundary_infinity_closed(type2, x2, info2));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  else if (is_boundary_infinity(type2, x2, info2)) {
    should_shrink = (boundary_infinity_is_open(type2, info2)
                     && !is_boundary_infinity_closed(type1, x1, info1));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = (normal_is_open(type1, x1, info1)
                   || normal_is_open(type2, x2, info2));
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  // FIXME: extended handling is not needed
  Result r = sub_assign_r(to, x1, x2, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
mul_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  bool should_shrink;
  if (is_boundary_infinity(type1, x1, info1)) {
    should_shrink = (boundary_infinity_is_open(type1, info1)
                     && !is_boundary_infinity_closed(type2, x2, info2));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  else if (is_boundary_infinity(type2, x2, info2)) {
    should_shrink = (boundary_infinity_is_open(type2, info2)
                     && !is_boundary_infinity_closed(type1, x1, info1));
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = (normal_is_open(type1, x1, info1)
                   || normal_is_open(type2, x2, info2));
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  PPL_ASSERT(x1 != Constant<0>::value && x2 != Constant<0>::value);
  // FIXME: extended handling is not needed
  Result r = mul_assign_r(to, x1, x2, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info>
inline Result
set_zero(Boundary_Type to_type, To& to, To_Info& to_info, bool should_shrink) {
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = assign_r(to, Constant<0>::value, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
mul_assign_z(Boundary_Type to_type, To& to, To_Info& to_info,
             Boundary_Type type1, const T1& x1, const Info1& info1, int x1s,
             Boundary_Type type2, const T2& x2, const Info2& info2, int x2s) {
  bool should_shrink;
  if (x1s != 0) {
    if (x2s != 0)
      return mul_assign(to_type, to, to_info,
                        type1, x1, info1,
                        type2, x2, info2);
    else
      should_shrink = info2.get_boundary_property(type2, OPEN);
  }
  else {
    should_shrink = (info1.get_boundary_property(type1, OPEN)
                     && (x2s != 0 || info2.get_boundary_property(type2, OPEN)));
  }
  return set_zero(to_type, to, to_info, should_shrink);
}

template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
div_assign(Boundary_Type to_type, To& to, To_Info& to_info,
           Boundary_Type type1, const T1& x1, const Info1& info1,
           Boundary_Type type2, const T2& x2, const Info2& info2) {
  bool should_shrink;
  if (is_boundary_infinity(type1, x1, info1)) {
    should_shrink = boundary_infinity_is_open(type1, info1);
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  else if (is_boundary_infinity(type2, x2, info2)) {
    should_shrink = boundary_infinity_is_open(type2, info2);
    return set_zero(to_type, to, to_info, should_shrink);
  }
  should_shrink = (normal_is_open(type1, x1, info1)
                   || normal_is_open(type2, x2, info2));
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  PPL_ASSERT(x1 != Constant<0>::value && x2 != Constant<0>::value);
  // FIXME: extended handling is not needed
  Result r = div_assign_r(to, x1, x2, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}


template <typename To, typename To_Info, typename T1, typename Info1, typename T2, typename Info2>
inline Result
div_assign_z(Boundary_Type to_type, To& to, To_Info& to_info,
             Boundary_Type type1, const T1& x1, const Info1& info1, int x1s,
             Boundary_Type type2, const T2& x2, const Info2& info2, int x2s) {
  if (x1s != 0) {
    if (x2s != 0)
      return div_assign(to_type, to, to_info,
                        type1, x1, info1,
                        type2, x2, info2);
    else {
      return set_boundary_infinity(to_type, to, to_info, true);
    }
  }
  else {
    bool should_shrink = info1.get_boundary_property(type1, OPEN)
      && !is_boundary_infinity_closed(type2, x2, info2);
    return set_zero(to_type, to, to_info, should_shrink);
  }
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
umod_2exp_assign(Boundary_Type to_type, To& to, To_Info& to_info,
                 Boundary_Type type, const T& x, const Info& info,
                 unsigned int exp) {
  PPL_ASSERT(to_type == type);
  bool should_shrink;
  if (is_boundary_infinity(type, x, info)) {
    should_shrink = boundary_infinity_is_open(type, info);
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = normal_is_open(type, x, info);
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = umod_2exp_assign_r(to, x, exp, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

template <typename To, typename To_Info, typename T, typename Info>
inline Result
smod_2exp_assign(Boundary_Type to_type, To& to, To_Info& to_info,
                 Boundary_Type type, const T& x, const Info& info,
                 unsigned int exp) {
  PPL_ASSERT(to_type == type);
  bool should_shrink;
  if (is_boundary_infinity(type, x, info)) {
    should_shrink = boundary_infinity_is_open(type, info);
    return set_boundary_infinity(to_type, to, to_info, should_shrink);
  }
  should_shrink = normal_is_open(type, x, info);
  bool check = (To_Info::check_inexact || (!should_shrink && To_Info::store_open));
  Result r = smod_2exp_assign_r(to, x, exp, round_dir_check(to_type, check));
  return adjust_boundary(to_type, to, to_info, should_shrink, r);
}

} // namespace Boundary_NS

} // namespace Parma_Polyhedra_Library

#endif // !defined(PPL_Boundary_defs_hh)