basic.h

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/*
 *  GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
 *
 *  This program 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 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program 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  02110-1301  USA
 */

#ifndef GINAC_BASIC_H
#define GINAC_BASIC_H

#include "flags.h"
#include "ptr.h"
#include "assertion.h"
#include "registrar.h"

// CINT needs <algorithm> to work properly with <vector>
#include <algorithm>
#include <cstddef> // for size_t
#include <map>
#include <set>
#include <typeinfo> // for typeid
#include <vector>

namespace GiNaC {

class ex;
class ex_is_less;
class symbol;
class numeric;
class relational;
class archive_node;
class print_context;

typedef std::vector<ex> exvector;
typedef std::set<ex, ex_is_less> exset;
typedef std::map<ex, ex, ex_is_less> exmap;

// Define this to enable some statistical output for comparisons and hashing
#undef GINAC_COMPARE_STATISTICS

#ifdef GINAC_COMPARE_STATISTICS
class compare_statistics_t {
public:
    compare_statistics_t()
     : total_compares(0), nontrivial_compares(0), total_basic_compares(0), compare_same_hashvalue(0), compare_same_type(0),
       total_is_equals(0), nontrivial_is_equals(0), total_basic_is_equals(0), is_equal_same_hashvalue(0), is_equal_same_type(0),
       total_gethash(0), gethash_cached(0) {}
    ~compare_statistics_t();

    unsigned long total_compares;
    unsigned long nontrivial_compares;
    unsigned long total_basic_compares;
    unsigned long compare_same_hashvalue;
    unsigned long compare_same_type;

    unsigned long total_is_equals;
    unsigned long nontrivial_is_equals;
    unsigned long total_basic_is_equals;
    unsigned long is_equal_same_hashvalue;
    unsigned long is_equal_same_type;

    unsigned long total_gethash;
    unsigned long gethash_cached;
};

extern compare_statistics_t compare_statistics;
#endif


struct map_function {
    virtual ~map_function() {}
    typedef const ex & argument_type;
    typedef ex result_type;
    virtual ex operator()(const ex & e) = 0;
};


class visitor {
protected:
    virtual ~visitor() {}
};


class basic : public refcounted
{
    GINAC_DECLARE_REGISTERED_CLASS_NO_CTORS(basic, void)
    
    friend class ex;
    
    // default constructor, destructor, copy constructor and assignment operator
protected:
    basic() : flags(0) {}

public:
    virtual ~basic()
    {
        GINAC_ASSERT((!(flags & status_flags::dynallocated)) || (get_refcount() == 0));
    }
    basic(const basic & other);
    const basic & operator=(const basic & other);

protected:
    // new virtual functions which can be overridden by derived classes
public: // only const functions please (may break reference counting)

    virtual basic * duplicate() const { return new basic(*this); }

    // evaluation
    virtual ex eval(int level = 0) const;
    virtual ex evalf(int level = 0) const;
    virtual ex evalm() const;
    virtual ex eval_integ() const;
protected:
    virtual ex eval_ncmul(const exvector & v) const;
public:
    virtual ex eval_indexed(const basic & i) const;

    // printing
    virtual void print(const print_context & c, unsigned level = 0) const;
    virtual void dbgprint() const;
    virtual void dbgprinttree() const;
    virtual unsigned precedence() const;

    // info
    virtual bool info(unsigned inf) const;

    // operand access
    virtual size_t nops() const;
    virtual ex op(size_t i) const;
    virtual ex operator[](const ex & index) const;
    virtual ex operator[](size_t i) const;
    virtual ex & let_op(size_t i);
    virtual ex & operator[](const ex & index);
    virtual ex & operator[](size_t i);

    // pattern matching
    virtual bool has(const ex & other, unsigned options = 0) const;
    virtual bool match(const ex & pattern, exmap & repls) const;
protected:
    virtual bool match_same_type(const basic & other) const;
public:

    // substitutions
    virtual ex subs(const exmap & m, unsigned options = 0) const;

    // function mapping
    virtual ex map(map_function & f) const;

    // visitors and tree traversal
    virtual void accept(GiNaC::visitor & v) const
    {
        if (visitor *p = dynamic_cast<visitor *>(&v))
            p->visit(*this);
    }

    // degree/coeff
    virtual bool is_polynomial(const ex & var) const;
    virtual int degree(const ex & s) const;
    virtual int ldegree(const ex & s) const;
    virtual ex coeff(const ex & s, int n = 1) const;

    // expand/collect
    virtual ex expand(unsigned options = 0) const;
    virtual ex collect(const ex & s, bool distributed = false) const;

    // differentiation and series expansion
protected:
    virtual ex derivative(const symbol & s) const;
public:
    virtual ex series(const relational & r, int order, unsigned options = 0) const;

    // rational functions
    virtual ex normal(exmap & repl, exmap & rev_lookup, int level = 0) const;
    virtual ex to_rational(exmap & repl) const;
    virtual ex to_polynomial(exmap & repl) const;

    // polynomial algorithms
    virtual numeric integer_content() const;
    virtual ex smod(const numeric &xi) const;
    virtual numeric max_coefficient() const;

    // indexed objects
    virtual exvector get_free_indices() const;
    virtual ex add_indexed(const ex & self, const ex & other) const;
    virtual ex scalar_mul_indexed(const ex & self, const numeric & other) const;
    virtual bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const;

    // noncommutativity
    virtual unsigned return_type() const;
    virtual return_type_t return_type_tinfo() const;

    // functions for complex expressions
    virtual ex conjugate() const;
    virtual ex real_part() const;
    virtual ex imag_part() const;

    // functions that should be called from class ex only
protected:
    virtual int compare_same_type(const basic & other) const;
    virtual bool is_equal_same_type(const basic & other) const;

    virtual unsigned calchash() const;
    
    // non-virtual functions in this class
public:
    template <class T>
    void print_dispatch(const print_context & c, unsigned level) const
    {
        print_dispatch(T::get_class_info_static(), c, level);
    }

    void print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const;

    virtual void archive(archive_node& n) const;
    virtual void read_archive(const archive_node& n, lst& syms); // no const

    ex subs_one_level(const exmap & m, unsigned options) const;
    ex diff(const symbol & s, unsigned nth = 1) const;
    int compare(const basic & other) const;
    bool is_equal(const basic & other) const;
    const basic & hold() const;

    unsigned gethash() const
    {
#ifdef GINAC_COMPARE_STATISTICS
        compare_statistics.total_gethash++;
#endif
        if (flags & status_flags::hash_calculated) {
#ifdef GINAC_COMPARE_STATISTICS
            compare_statistics.gethash_cached++;
#endif
            return hashvalue;
        } else {
            return calchash();
        }
    }

    const basic & setflag(unsigned f) const {flags |= f; return *this;}

    const basic & clearflag(unsigned f) const {flags &= ~f; return *this;}

protected:
    void ensure_if_modifiable() const;

    void do_print(const print_context & c, unsigned level) const;
    void do_print_tree(const print_tree & c, unsigned level) const;
    void do_print_python_repr(const print_python_repr & c, unsigned level) const;
    
    // member variables
protected:
    mutable unsigned flags;             
    mutable unsigned hashvalue;         
};


// global variables

extern int max_recursion_level;


// convenience type checker template functions

template <class T>
inline bool is_a(const basic &obj)
{
    return dynamic_cast<const T *>(&obj) != 0;
}

template <class T>
inline bool is_exactly_a(const basic & obj)
{
    return typeid(T) == typeid(obj);
}

} // namespace GiNaC

#endif // ndef GINAC_BASIC_H