text: /* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
  /*
   *  Main authors:
   *     Christian Schulte <schulte@gecode.org>
   *     Guido Tack <tack@gecode.org>
   *
   *  Copyright:
   *     Christian Schulte, 2002
   *     Guido Tack, 2004
   *
   *  This file is part of Gecode, the generic constraint
   *  development environment:
   *     http://www.gecode.org
   *
   *  Permission is hereby granted, free of charge, to any person obtaining
   *  a copy of this software and associated documentation files (the
   *  "Software"), to deal in the Software without restriction, including
   *  without limitation the rights to use, copy, modify, merge, publish,
   *  distribute, sublicense, and/or sell copies of the Software, and to
   *  permit persons to whom the Software is furnished to do so, subject to
   *  the following conditions:
   *
   *  The above copyright notice and this permission notice shall be
   *  included in all copies or substantial portions of the Software.
   *
   *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
   *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
   *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
   *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
   *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
   *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
   *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
   *
   */
  
  #ifndef __GECODE_INT_ARITHMETIC_HH__
  #define __GECODE_INT_ARITHMETIC_HH__
  
  #include <gecode/int.hh>
  
  #include <gecode/int/idx-view.hh>
  #include <gecode/int/rel.hh>
  #include <gecode/int/linear.hh>
  
  /**
   * \namespace Gecode::Int::Arithmetic
   * \brief Numerical (arithmetic) propagators
   */
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Bounds consistent absolute value propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class AbsBnd : public BinaryPropagator<View,PC_INT_BND> {
    protected:
      using BinaryPropagator<View,PC_INT_BND>::x0;
      using BinaryPropagator<View,PC_INT_BND>::x1;
  
      /// Constructor for cloning \a p
      AbsBnd(Space& home, AbsBnd& p);
      /// Constructor for posting
      AbsBnd(Home home, View x0, View x1);
    public:
  
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low unary.
       * Otherwise it is low binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus  propagate(Space& home, const ModEventDelta& med);
      /// Post bounds consistent propagator \f$ |x_0|=x_1\f$
      static  ExecStatus  post(Home home, View x0, View x1);
    };
  
    /**
     * \brief Domain consistent absolute value propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class AbsDom : public BinaryPropagator<View,PC_INT_DOM> {
    protected:
      using BinaryPropagator<View,PC_INT_DOM>::x0;
      using BinaryPropagator<View,PC_INT_DOM>::x1;
  
      /// Constructor for cloning \a p
      AbsDom(Space& home, AbsDom& p);
      /// Constructor for posting
      AbsDom(Home home, View x0, View x1);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low binary.
       * If in stage for bounds propagation, the cost is
       * low binary. Otherwise it is high binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus  propagate(Space& home, const ModEventDelta& med);
      /// Post domain consistent propagator \f$ |x_0|=x_1\f$
      static  ExecStatus  post(Home home, View x0, View x1);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/abs.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Bounds consistent ternary maximum propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class MaxBnd : public TernaryPropagator<View,PC_INT_BND> {
    protected:
      using TernaryPropagator<View,PC_INT_BND>::x0;
      using TernaryPropagator<View,PC_INT_BND>::x1;
      using TernaryPropagator<View,PC_INT_BND>::x2;
  
      /// Constructor for cloning \a p
      MaxBnd(Space& home, MaxBnd& p);
      /// Constructor for posting
      MaxBnd(Home home, View x0, View x1, View x2);
    public:
      /// Constructor for rewriting \a p during cloning
      MaxBnd(Space& home, Propagator& p, View x0, View x1, View x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator \f$ \max\{x_0,x_1\}=x_2\f$
      static  ExecStatus post(Home home, View x0, View x1, View x2);
    };
  
    /**
     * \brief Bounds consistent n-ary maximum propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class NaryMaxBnd : public NaryOnePropagator<View,PC_INT_BND> {
    protected:
      using NaryOnePropagator<View,PC_INT_BND>::x;
      using NaryOnePropagator<View,PC_INT_BND>::y;
  
      /// Constructor for cloning \a p
      NaryMaxBnd(Space& home, NaryMaxBnd& p);
      /// Constructor for posting
      NaryMaxBnd(Home home, ViewArray<View>& x, View y);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator \f$ \max x=y\f$
      static  ExecStatus post(Home home, ViewArray<View>& x, View y);
    };
  
    /**
     * \brief Domain consistent ternary maximum propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class MaxDom : public TernaryPropagator<View,PC_INT_DOM> {
    protected:
      using TernaryPropagator<View,PC_INT_DOM>::x0;
      using TernaryPropagator<View,PC_INT_DOM>::x1;
      using TernaryPropagator<View,PC_INT_DOM>::x2;
  
      /// Constructor for cloning \a p
      MaxDom(Space& home, MaxDom& p);
      /// Constructor for posting
      MaxDom(Home home, View x0, View x1, View x2);
    public:
      /// Constructor for rewriting \a p during cloning
      MaxDom(Space& home, Propagator& p, View x0, View x1, View x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If in stage for bounds propagation, the cost is
       * low ternary. Otherwise it is high ternary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator \f$ \max\{x_0,x_1\}=x_2\f$
      static  ExecStatus post(Home home, View x0, View x1, View x2);
    };
  
    /**
     * \brief Domain consistent n-ary maximum propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View>
    class NaryMaxDom : public NaryOnePropagator<View,PC_INT_DOM> {
    protected:
      using NaryOnePropagator<View,PC_INT_DOM>::x;
      using NaryOnePropagator<View,PC_INT_DOM>::y;
  
      /// Constructor for cloning \a p
      NaryMaxDom(Space& home, NaryMaxDom& p);
      /// Constructor for posting
      NaryMaxDom(Home home, ViewArray<View>& x, View y);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If in stage for bounds propagation, the cost is
       * low linear. Otherwise it is high linear.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator \f$ \max x=y\f$
      static  ExecStatus post(Home home, ViewArray<View>& x, View y);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/max.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Argument maximum propagator
     *
     * Tiebreaking is used if \a tiebreak is true and views can be shared
     * if \a shread is true.
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class VA, class VB, bool tiebreak>
    class ArgMax : public Propagator {
    protected:
      /// Map of index and views
      IdxViewArray<VA> x;
      /// Position of maximum view (maximal argument)
      VB y;
      /// Constructor for cloning \a p
      ArgMax(Space& home, ArgMax& p);
      /// Constructor for posting
      ArgMax(Home home, IdxViewArray<VA>& x, VB y);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      // Cost function (defined as low linear)
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Schedule function
      virtual void reschedule(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Delete propagator and return its size
      virtual size_t dispose(Space& home);
      /**
       * \brief Post propagator \f$ \operatorname{argmax} x=y\f$
       *
       * Note that \a y must be constrained to be in the proper range
       * for the index values in \a x.
       */
      static  ExecStatus post(Home home, IdxViewArray<VA>& x, VB y);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/argmax.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Operations for square and square-root propagators
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    class SqrOps {
    public:
      /// Return whether exponent is even
      bool even(void) const;
      /// Return exponent
      int exp(void) const;
      /// Set exponent to \a m
      void exp(int m);
      /// Return \f$x^2\f$
      template<class IntType>
      IntType pow(IntType x) const;
      /// Return \f$x^2\f$ truncated to integer limits
      int tpow(int x) const;
      /// Return \f$\lfloor \sqrt{x}\rfloor\f$ where \a x must be non-negative and \f$n>0\f$
      int fnroot(int x) const;
      /// Return \f$\lceil \sqrt{x}\rceil\f$ where \a x must be non-negative and \f$n>0\f$
      int cnroot(int x) const;
    };
  
    /**
     * \brief Operations for power and nroot propagators
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    class PowOps {
    protected:
      /// The exponent and root index
      int n;
      /// Return whether \a m is even
      static bool even(int m);
      /// Test whether \f$r^n>x\f$
      bool powgr(long long int r, int x) const;
      /// Test whether \f$r^n<x\f$
      bool powle(long long int r, int x) const;
    public:
      /// Initialize with exponent \a n
      PowOps(int n);
      /// Return whether exponent is even
      bool even(void) const;
      /// Return exponent
      int exp(void) const;
      /// Set exponent to \a m
      void exp(int m);
      /// Return \f$x^n\f$ where \f$n>0\f$
      template<class IntType>
      IntType pow(IntType x) const;
      /// Return \f$x^n\f$ where \f$n>0\f$ truncated to integer limits
      int tpow(int x) const;
      /// Return \f$\lfloor \sqrt[n]{x}\rfloor\f$ where \a x must be non-negative and \f$n>0\f$
      int fnroot(int x) const;
      /// Return \f$\lceil \sqrt[n]{x}\rceil\f$ where \a x must be non-negative and \f$n>0\f$
      int cnroot(int x) const;
    };
  
  }}}
  
  #include <gecode/int/arithmetic/pow-ops.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Bounds consistent positive power propagator
     *
     * This propagator is for positive views only.
     */
    template<class VA, class VB, class Ops>
    class PowPlusBnd : public MixBinaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND> {
    protected:
      using MixBinaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND>::x0;
      using MixBinaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND>::x1;
      /// Operations
      Ops ops;
      /// Constructor for posting
      PowPlusBnd(Home home, VA x0, VB x1, const Ops& ops);
      /// Constructor for cloning \a p
      PowPlusBnd(Space& home, PowPlusBnd<VA,VB,Ops>& p);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator
      static ExecStatus post(Home home, VA x0, VB x1, Ops ops);
    };
  
    /**
     * \brief Bounds consistent power propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops>
    class PowBnd : public BinaryPropagator<IntView,PC_INT_BND> {
    protected:
      using BinaryPropagator<IntView,PC_INT_BND>::x0;
      using BinaryPropagator<IntView,PC_INT_BND>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      PowBnd(Space& home, PowBnd& p);
      /// Constructor for posting
      PowBnd(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
    /**
     * \brief Domain consistent positive power propagator
     *
     * This propagator is for positive views only.
     */
    template<class VA, class VB, class Ops>
    class PowPlusDom : public MixBinaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM> {
    protected:
      using MixBinaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM>::x0;
      using MixBinaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM>::x1;
      /// Operations
      Ops ops;
      /// Constructor for posting
      PowPlusDom(Home home, VA x0, VB x1, const Ops& ops);
      /// Constructor for cloning \a p
      PowPlusDom(Space& home, PowPlusDom<VA,VB,Ops>& p);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low unary.
       * If in stage for bounds propagation, the cost is
       * low binary. Otherwise it is high binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator
      static ExecStatus post(Home home, VA x0, VB x1, Ops ops);
    };
  
    /**
     * \brief Domain consistent power propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops>
    class PowDom : public BinaryPropagator<IntView,PC_INT_DOM> {
    protected:
      using BinaryPropagator<IntView,PC_INT_DOM>::x0;
      using BinaryPropagator<IntView,PC_INT_DOM>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      PowDom(Space& home, PowDom<Ops>& p);
      /// Constructor for posting
      PowDom(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low unary.
       * If in stage for bounds propagation, the cost is
       * low binary. Otherwise it is high binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/pow.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Positive bounds consistent n-th root propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops, bool minus>
    class NrootPlusBnd : public BinaryPropagator<IntView,PC_INT_BND> {
    protected:
      using BinaryPropagator<IntView,PC_INT_BND>::x0;
      using BinaryPropagator<IntView,PC_INT_BND>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      NrootPlusBnd(Space& home, NrootPlusBnd<Ops,minus>& p);
      /// Constructor for posting
      NrootPlusBnd(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
    /**
     * \brief Bounds consistent n-th root propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops>
    class NrootBnd : public BinaryPropagator<IntView,PC_INT_BND> {
    protected:
      using BinaryPropagator<IntView,PC_INT_BND>::x0;
      using BinaryPropagator<IntView,PC_INT_BND>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      NrootBnd(Space& home, NrootBnd<Ops>& p);
      /// Constructor for posting
      NrootBnd(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
    /**
     * \brief Domain consistent n-th root propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops, bool minus>
    class NrootPlusDom : public BinaryPropagator<IntView,PC_INT_DOM> {
    protected:
      using BinaryPropagator<IntView,PC_INT_DOM>::x0;
      using BinaryPropagator<IntView,PC_INT_DOM>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      NrootPlusDom(Space& home, NrootPlusDom<Ops,minus>& p);
      /// Constructor for posting
      NrootPlusDom(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low unary.
       * If in stage for bounds propagation, the cost is
       * low binary. Otherwise it is high binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
    /**
     * \brief Domain consistent n-th root propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class Ops>
    class NrootDom : public BinaryPropagator<IntView,PC_INT_DOM> {
    protected:
      using BinaryPropagator<IntView,PC_INT_DOM>::x0;
      using BinaryPropagator<IntView,PC_INT_DOM>::x1;
      /// Operations
      Ops ops;
      /// Constructor for cloning \a p
      NrootDom(Space& home, NrootDom<Ops>& p);
      /// Constructor for posting
      NrootDom(Home home, IntView x0, IntView x1, const Ops& ops);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /**
       * \brief Cost function
       *
       * If a view has been assigned, the cost is low unary.
       * If in stage for bounds propagation, the cost is
       * low binary. Otherwise it is high binary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Post propagator
      static ExecStatus post(Home home, IntView x0, IntView x1, Ops ops);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/nroot.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Bounds or domain consistent propagator for \f$x_0\times x_1=x_0\f$
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     * \ingroup FuncIntProp
     */
    template<class View, PropCond pc>
    class MultZeroOne : public BinaryPropagator<View,pc> {
    protected:
      using BinaryPropagator<View,pc>::x0;
      using BinaryPropagator<View,pc>::x1;
  
      /// Constructor for cloning \a p
      MultZeroOne(Space& home, MultZeroOne<View,pc>& p);
      /// Constructor for posting
      MultZeroOne(Home home, View x0, View x1);
      /// Test whether \a x is equal to \a n
      static RelTest equal(View x, int n);
    public:
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
      /// Post propagator \f$x_0\cdot x_1=x_0\f$
      static ExecStatus post(Home home, View x0, View x1);
    };
  
  
  
    /**
     * \brief Bounds consistent positive multiplication propagator
     *
     * This propagator provides multiplication for positive views only.
     */
    template<class VA, class VB, class VC>
    class MultPlusBnd :
      public MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND> {
    protected:
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x0;
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x1;
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x2;
    public:
      /// Constructor for posting
      MultPlusBnd(Home home, VA x0, VB x1, VC x2);
      /// Constructor for cloning \a p
      MultPlusBnd(Space& home, MultPlusBnd<VA,VB,VC>& p);
      /// Post propagator \f$x_0\cdot x_1=x_2\f$
      static ExecStatus post(Home home, VA x0, VB x1, VC x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
    /**
     * \brief Bounds consistent multiplication propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     *
     * \ingroup FuncIntProp
     */
    class MultBnd : public TernaryPropagator<IntView,PC_INT_BND> {
    protected:
      using TernaryPropagator<IntView,PC_INT_BND>::x0;
      using TernaryPropagator<IntView,PC_INT_BND>::x1;
      using TernaryPropagator<IntView,PC_INT_BND>::x2;
      /// Constructor for cloning \a p
      MultBnd(Space& home, MultBnd& p);
    public:
      /// Constructor for posting
      MultBnd(Home home, IntView x0, IntView x1, IntView x2);
      /// Post propagator \f$x_0\cdot x_1=x_2\f$
      GECODE_INT_EXPORT
      static ExecStatus post(Home home, IntView x0, IntView x1, IntView x2);
      /// Copy propagator during cloning
      GECODE_INT_EXPORT
      virtual Actor* copy(Space& home);
      /// Perform propagation
      GECODE_INT_EXPORT
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
  
  
    /**
     * \brief Domain consistent positive multiplication propagator
     *
     * This propagator provides multiplication for positive views only.
     */
    template<class VA, class VB, class VC>
    class MultPlusDom :
      public MixTernaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM,VC,PC_INT_DOM> {
    protected:
      using MixTernaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM,VC,PC_INT_DOM>::x0;
      using MixTernaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM,VC,PC_INT_DOM>::x1;
      using MixTernaryPropagator<VA,PC_INT_DOM,VB,PC_INT_DOM,VC,PC_INT_DOM>::x2;
    public:
      /// Constructor for posting
      MultPlusDom(Home home, VA x0, VB x1, VC x2);
      /// Constructor for cloning \a p
      MultPlusDom(Space& home, MultPlusDom<VA,VB,VC>& p);
      /// Post propagator \f$x_0\cdot x_1=x_2\f$
      static ExecStatus post(Home home, VA x0, VB x1, VC x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If in stage for bounds propagation, the cost is
       * low ternary. Otherwise it is high ternary.
       */
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
    /**
     * \brief Domain consistent multiplication propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     *
     * \ingroup FuncIntProp
     */
    class MultDom : public TernaryPropagator<IntView,PC_INT_DOM> {
    protected:
      using TernaryPropagator<IntView,PC_INT_DOM>::x0;
      using TernaryPropagator<IntView,PC_INT_DOM>::x1;
      using TernaryPropagator<IntView,PC_INT_DOM>::x2;
      /// Constructor for cloning \a p
      MultDom(Space& home, MultDom& p);
    public:
      /// Constructor for posting
      MultDom(Home home, IntView x0, IntView x1, IntView x2);
      /// Post propagator \f$x_0\cdot x_1=x_2\f$
      GECODE_INT_EXPORT
      static ExecStatus post(Home home, IntView x0, IntView x1, IntView x2);
      /// Copy propagator during cloning
      GECODE_INT_EXPORT
      virtual Actor* copy(Space& home);
      /**
       * \brief Cost function
       *
       * If in stage for bounds propagation, the cost is
       * low ternary. Otherwise it is high ternary.
       */
      GECODE_INT_EXPORT
      virtual PropCost cost(const Space& home, const ModEventDelta& med) const;
      /// Perform propagation
      GECODE_INT_EXPORT
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/mult.hpp>
  
  namespace Gecode { namespace Int { namespace Arithmetic {
  
    /**
     * \brief Bounds consistent positive division propagator
     *
     * This propagator provides division for positive views only.
     */
    template<class VA, class VB, class VC>
    class DivPlusBnd :
      public MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND> {
    protected:
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x0;
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x1;
      using MixTernaryPropagator<VA,PC_INT_BND,VB,PC_INT_BND,VC,PC_INT_BND>::x2;
    public:
      /// Constructor for posting
      DivPlusBnd(Home home, VA x0, VB x1, VC x2);
      /// Constructor for cloning \a p
      DivPlusBnd(Space& home, DivPlusBnd<VA,VB,VC>& p);
      /// Post propagator \f$x_0\mathrm{div} x_1=x_2\f$ (rounding towards 0)
      static ExecStatus post(Home home, VA x0, VB x1, VC x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
    /**
     * \brief Bounds consistent division propagator
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     *
     * \ingroup FuncIntProp
     */
    template<class View>
    class DivBnd : public TernaryPropagator<View,PC_INT_BND> {
    protected:
      using TernaryPropagator<View,PC_INT_BND>::x0;
      using TernaryPropagator<View,PC_INT_BND>::x1;
      using TernaryPropagator<View,PC_INT_BND>::x2;
  
      /// Constructor for cloning \a p
      DivBnd(Space& home, DivBnd<View>& p);
    public:
      /// Constructor for posting
      DivBnd(Home home, View x0, View x1, View x2);
      /// Post propagator \f$x_0\mathrm{div} x_1=x_2\f$ (rounding towards 0)
      static  ExecStatus post(Home home, View x0, View x1, View x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
    /**
     * \brief Integer division/modulo propagator
     *
     * This propagator implements the relation between divisor and
     * modulo of an integer division.
     *
     * Requires \code #include <gecode/int/arithmetic.hh> \endcode
     *
     * \ingroup FuncIntProp
     */
    template<class View>
    class DivMod : public TernaryPropagator<View,PC_INT_BND> {
    protected:
      using TernaryPropagator<View,PC_INT_BND>::x0;
      using TernaryPropagator<View,PC_INT_BND>::x1;
      using TernaryPropagator<View,PC_INT_BND>::x2;
  
      /// Constructor for cloning \a p
      DivMod(Space& home, DivMod<View>& p);
    public:
      /// Constructor for posting
      DivMod(Home home, View x0, View x1, View x2);
      /// Post propagator \f$x_1\neq 0 \land (x_2\neq 0\Rightarrow x_0\times x_2>0) \land \mathrm{abs}(x_2)<\mathrm{abs}(x_1)\f$
      static  ExecStatus post(Home home, View x0, View x1, View x2);
      /// Copy propagator during cloning
      virtual Actor* copy(Space& home);
      /// Perform propagation
      virtual ExecStatus propagate(Space& home, const ModEventDelta& med);
    };
  
  }}}
  
  #include <gecode/int/arithmetic/divmod.hpp>
  
  #endif
  
  // STATISTICS: int-prop
  
  