- first implementation of pattern matching

[ginac.git] / ginac / basic.cpp

/** @file basic.cpp
 *
 *  Implementation of GiNaC's ABC. */

/*
 *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include <iostream>
#include <stdexcept>
#ifdef DO_GINAC_ASSERT
#  include <typeinfo>
#endif

#include "basic.h"
#include "ex.h"
#include "numeric.h"
#include "power.h"
#include "symbol.h"
#include "lst.h"
#include "ncmul.h"
#include "relational.h"
#include "print.h"
#include "archive.h"
#include "utils.h"
#include "debugmsg.h"

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(basic, void)

//////////
// default ctor, dtor, copy ctor assignment operator and helpers
//////////

// public

basic::basic(const basic & other) : tinfo_key(TINFO_basic), flags(0), refcount(0)
{
        debugmsg("basic copy ctor", LOGLEVEL_CONSTRUCT);
        copy(other);
}

const basic & basic::operator=(const basic & other)
{
        debugmsg("basic operator=", LOGLEVEL_ASSIGNMENT);
        if (this != &other) {
                destroy(true);
                copy(other);
        }
        return *this;
}

// protected

// none (all conditionally inlined)

//////////
// other ctors
//////////

// none (all conditionally inlined)

//////////
// archiving
//////////

/** Construct object from archive_node. */
basic::basic(const archive_node &n, const lst &sym_lst) : flags(0), refcount(0)
{
        debugmsg("basic ctor from archive_node", LOGLEVEL_CONSTRUCT);

        // Reconstruct tinfo_key from class name
        std::string class_name;
        if (n.find_string("class", class_name))
                tinfo_key = find_tinfo_key(class_name);
        else
                throw (std::runtime_error("archive node contains no class name"));
}

/** Unarchive the object. */
DEFAULT_UNARCHIVE(basic)

/** Archive the object. */
void basic::archive(archive_node &n) const
{
        n.add_string("class", class_name());
}

//////////
// functions overriding virtual functions from bases classes
//////////

// none

//////////
// new virtual functions which can be overridden by derived classes
//////////

// public

/** Output to stream.
 *  @param c print context object that describes the output formatting
 *  @param level value that is used to identify the precedence or indentation
 *               level for placing parentheses and formatting */
void basic::print(const print_context & c, unsigned level) const
{
        debugmsg("basic print", LOGLEVEL_PRINT);

        if (is_of_type(c, print_tree)) {

                c.s << std::string(level, ' ') << class_name()
                    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
                    << ", nops=" << nops()
                    << std::endl;
                for (unsigned i=0; i<nops(); ++i)
                        op(i).print(c, level + static_cast<const print_tree &>(c).delta_indent);

        } else
                c.s << "[" << class_name() << " object]";
}

/** Little wrapper arount print to be called within a debugger.
 *  This is needed because you cannot call foo.print(cout) from within the
 *  debugger because it might not know what cout is.  This method can be
 *  invoked with no argument and it will simply print to stdout.
 *
 *  @see basic::print */
void basic::dbgprint(void) const
{
        this->print(std::cerr);
        std::cerr << std::endl;
}

/** Little wrapper arount printtree to be called within a debugger.
 *
 *  @see basic::dbgprint
 *  @see basic::printtree */
void basic::dbgprinttree(void) const
{
        this->print(print_tree(std::cerr));
}

/** Return relative operator precedence (for parenthizing output). */
unsigned basic::precedence(void) const
{
        return 70;
}

/** Create a new copy of this on the heap.  One can think of this as simulating
 *  a virtual copy constructor which is needed for instance by the refcounted
 *  construction of an ex from a basic. */
basic * basic::duplicate() const
{
        debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
        return new basic(*this);
}

/** Information about the object.
 *
 *  @see class info_flags */
bool basic::info(unsigned inf) const
{
        // all possible properties are false for basic objects
        return false;
}

/** Number of operands/members. */
unsigned basic::nops() const
{
        // iterating from 0 to nops() on atomic objects should be an empty loop,
        // and accessing their elements is a range error.  Container objects should
        // override this.
        return 0;
}

/** Return operand/member at position i. */
ex basic::op(int i) const
{
        return (const_cast<basic *>(this))->let_op(i);
}

/** Return modifyable operand/member at position i. */
ex & basic::let_op(int i)
{
        throw(std::out_of_range("op() out of range"));
}

ex basic::operator[](const ex & index) const
{
        if (is_exactly_of_type(*index.bp,numeric))
                return op(static_cast<const numeric &>(*index.bp).to_int());
        
        throw(std::invalid_argument("non-numeric indices not supported by this type"));
}

ex basic::operator[](int i) const
{
        return op(i);
}

/** Search ocurrences.  An object  'has' an expression if it is the expression
 *  itself or one of the children 'has' it.  As a consequence (according to
 *  the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y)
 *  is false. */
bool basic::has(const ex & other) const
{
        GINAC_ASSERT(other.bp!=0);
        lst repl_lst;
        if (match(*other.bp, repl_lst)) return true;
        if (nops()>0) {
                for (unsigned i=0; i<nops(); i++)
                        if (op(i).has(other))
                                return true;
        }
        
        return false;
}

/** Return degree of highest power in object s. */
int basic::degree(const ex & s) const
{
        return 0;
}

/** Return degree of lowest power in object s. */
int basic::ldegree(const ex & s) const
{
        return 0;
}

/** Return coefficient of degree n in object s. */
ex basic::coeff(const ex & s, int n) const
{
        return n==0 ? *this : _ex0();
}

/** Sort expression in terms of powers of some object(s).
 *  @param s object(s) to sort in
 *  @param distributed recursive or distributed form (only used when s is a list) */
ex basic::collect(const ex & s, bool distributed) const
{
        ex x;
        if (is_ex_of_type(s, lst)) {

                // List of objects specified
                if (s.nops() == 1)
                        return collect(s.op(0));

                else if (distributed) {

                        // Get lower/upper degree of all symbols in list
                        int num = s.nops();
                        struct sym_info {
                                ex sym;
                                int ldeg, deg;
                                int cnt;  // current degree, 'counter'
                                ex coeff; // coefficient for degree 'cnt'
                        };
                        sym_info *si = new sym_info[num];
                        ex c = *this;
                        for (int i=0; i<num; i++) {
                                si[i].sym = s.op(i);
                                si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
                                si[i].deg = this->degree(si[i].sym);
                                c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
                        }

                        while (true) {

                                // Calculate coeff*x1^c1*...*xn^cn
                                ex y = _ex1();
                                for (int i=0; i<num; i++) {
                                        int cnt = si[i].cnt;
                                        y *= power(si[i].sym, cnt);
                                }
                                x += y * si[num - 1].coeff;

                                // Increment counters
                                int n = num - 1;
                                while (true) {
                                        si[n].cnt++;
                                        if (si[n].cnt <= si[n].deg) {
                                                // Update coefficients
                                                ex c;
                                                if (n == 0)
                                                        c = *this;
                                                else
                                                        c = si[n - 1].coeff;
                                                for (int i=n; i<num; i++)
                                                        c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
                                                break;
                                        }
                                        if (n == 0)
                                                goto done;
                                        si[n].cnt = si[n].ldeg;
                                        n--;
                                }
                        }

done:           delete[] si;

                } else {

                        // Recursive form
                        x = *this;
                        for (int n=s.nops()-1; n>=0; n--)
                                x = x.collect(s[n]);
                }

        } else {

                // Only one object specified
                for (int n=this->ldegree(s); n<=this->degree(s); ++n)
                        x += this->coeff(s,n)*power(s,n);
        }
        
        // correct for lost fractional arguments and return
        return x + (*this - x).expand();
}

/** Perform automatic non-interruptive symbolic evaluation on expression. */
ex basic::eval(int level) const
{
        // There is nothing to do for basic objects:
        return this->hold();
}

/** Evaluate object numerically. */
ex basic::evalf(int level) const
{
        // There is nothing to do for basic objects:
        return *this;
}

/** Perform automatic symbolic evaluations on indexed expression that
 *  contains this object as the base expression. */
ex basic::eval_indexed(const basic & i) const
 // this function can't take a "const ex & i" because that would result
 // in an infinite eval() loop
{
        // There is nothing to do for basic objects
        return i.hold();
}

/** Add two indexed expressions. They are guaranteed to be of class indexed
 *  (or a subclass) and their indices are compatible. This function is used
 *  internally by simplify_indexed().
 *
 *  @param self First indexed expression; it's base object is *this
 *  @param other Second indexed expression
 *  @return sum of self and other 
 *  @see ex::simplify_indexed() */
ex basic::add_indexed(const ex & self, const ex & other) const
{
        return self + other;
}

/** Multiply an indexed expression with a scalar. This function is used
 *  internally by simplify_indexed().
 *
 *  @param self Indexed expression; it's base object is *this
 *  @param other Numeric value
 *  @return product of self and other
 *  @see ex::simplify_indexed() */
ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
{
        return self * other;
}

/** Try to contract two indexed expressions that appear in the same product. 
 *  If a contraction exists, the function overwrites one or both of the
 *  expressions and returns true. Otherwise it returns false. It is
 *  guaranteed that both expressions are of class indexed (or a subclass)
 *  and that at least one dummy index has been found. This functions is
 *  used internally by simplify_indexed().
 *
 *  @param self Pointer to first indexed expression; it's base object is *this
 *  @param other Pointer to second indexed expression
 *  @param v The complete vector of factors
 *  @return true if the contraction was successful, false otherwise
 *  @see ex::simplify_indexed() */
bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
        // Do nothing
        return false;
}

/** Check whether the expression matches a given pattern. For every wildcard
 *  object in the pattern, an expression of the form "wildcard == matching_expression"
 *  is added to repl_lst. */
bool basic::match(const ex & pattern, lst & repl_lst) const
{
//clog << "match " << *this << " with " << pattern << ", repl_lst = " << repl_lst << endl;
        if (is_ex_exactly_of_type(pattern, wildcard)) {

                // Wildcard matches anything, but check whether we already have found
                // a match for that wildcard first (if so, it the earlier match must
                // be the same expression)
                for (unsigned i=0; i<repl_lst.nops(); i++) {
                        if (repl_lst.op(i).op(0).is_equal(pattern))
                                return is_equal(*repl_lst.op(i).op(1).bp);
                }
                repl_lst.append(pattern == *this);
                return true;

        } else {

                // Expression must be of the same type as the pattern
                if (tinfo() != pattern.bp->tinfo())
                        return false;

                // Number of subexpressions must match
                if (nops() != pattern.nops())
                        return false;

                // No subexpressions? Then just compare the objects (there can't be
                // wildcards in the pattern)
                if (nops() == 0)
                        return is_equal(*pattern.bp);

                // Otherwise the subexpressions must match one-to-one
                for (unsigned i=0; i<nops(); i++)
                        if (!op(i).match(pattern.op(i), repl_lst))
                                return false;

                // Looks similar enough, match found
                return true;
        }
}

/** Substitute a set of objects by arbitrary expressions. The ex returned
 *  will already be evaluated. */
ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
{
        GINAC_ASSERT(ls.nops() == lr.nops());

        if (no_pattern) {
                for (unsigned i=0; i<ls.nops(); i++) {
                        if (is_equal(*ls.op(i).bp))
                                return lr.op(i);
                }
        } else {
                for (unsigned i=0; i<ls.nops(); i++) {
                        lst repl_lst;
                        if (match(*ls.op(i).bp, repl_lst))
                                return lr.op(i).bp->subs(repl_lst, true); // avoid recursion when re-substituting the wildcards
                }
        }

        return *this;
}

/** Default interface of nth derivative ex::diff(s, n).  It should be called
 *  instead of ::derivative(s) for first derivatives and for nth derivatives it
 *  just recurses down.
 *
 *  @param s symbol to differentiate in
 *  @param nth order of differentiation
 *  @see ex::diff */
ex basic::diff(const symbol & s, unsigned nth) const
{
        // trivial: zeroth derivative
        if (nth==0)
                return ex(*this);
        
        // evaluate unevaluated *this before differentiating
        if (!(flags & status_flags::evaluated))
                return ex(*this).diff(s, nth);
        
        ex ndiff = this->derivative(s);
        while (!ndiff.is_zero() &&    // stop differentiating zeros
               nth>1) {
                ndiff = ndiff.diff(s);
                --nth;
        }
        return ndiff;
}

/** Return a vector containing the free indices of an expression. */
exvector basic::get_free_indices(void) const
{
        return exvector(); // return an empty exvector
}

ex basic::simplify_ncmul(const exvector & v) const
{
        return simplified_ncmul(v);
}

// protected

/** Default implementation of ex::diff(). It simply throws an error message.
 *
 *  @exception logic_error (differentiation not supported by this type)
 *  @see ex::diff */
ex basic::derivative(const symbol & s) const
{
        throw(std::logic_error("differentiation not supported by this type"));
}

/** Returns order relation between two objects of same type.  This needs to be
 *  implemented by each class. It may never return anything else than 0,
 *  signalling equality, or +1 and -1 signalling inequality and determining
 *  the canonical ordering.  (Perl hackers will wonder why C++ doesn't feature
 *  the spaceship operator <=> for denoting just this.) */
int basic::compare_same_type(const basic & other) const
{
        return compare_pointers(this, &other);
}

/** Returns true if two objects of same type are equal.  Normally needs
 *  not be reimplemented as long as it wasn't overwritten by some parent
 *  class, since it just calls compare_same_type().  The reason why this
 *  function exists is that sometimes it is easier to determine equality
 *  than an order relation and then it can be overridden. */
bool basic::is_equal_same_type(const basic & other) const
{
        return this->compare_same_type(other)==0;
}

unsigned basic::return_type(void) const
{
        return return_types::commutative;
}

unsigned basic::return_type_tinfo(void) const
{
        return tinfo();
}

/** Compute the hash value of an object and if it makes sense to store it in
 *  the objects status_flags, do so.  The method inherited from class basic
 *  computes a hash value based on the type and hash values of possible
 *  members.  For this reason it is well suited for container classes but
 *  atomic classes should override this implementation because otherwise they
 *  would all end up with the same hashvalue. */
unsigned basic::calchash(void) const
{
        unsigned v = golden_ratio_hash(tinfo());
        for (unsigned i=0; i<nops(); i++) {
                v = rotate_left_31(v);
                v ^= (const_cast<basic *>(this))->op(i).gethash();
        }
        
        // mask out numeric hashes:
        v &= 0x7FFFFFFFU;
        
        // store calculated hash value only if object is already evaluated
        if (flags & status_flags::evaluated) {
                setflag(status_flags::hash_calculated);
                hashvalue = v;
        }

        return v;
}

/** Expand expression, i.e. multiply it out and return the result as a new
 *  expression. */
ex basic::expand(unsigned options) const
{
        return this->setflag(status_flags::expanded);
}


//////////
// non-virtual functions in this class
//////////

// public

/** Substitute objects in an expression (syntactic substitution) and return
 *  the result as a new expression.  There are two valid types of
 *  replacement arguments: 1) a relational like object==ex and 2) a list of
 *  relationals lst(object1==ex1,object2==ex2,...), which is converted to
 *  subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
ex basic::subs(const ex & e, bool no_pattern) const
{
        if (e.info(info_flags::relation_equal)) {
                return subs(lst(e), no_pattern);
        }
        if (!e.info(info_flags::list)) {
                throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
        }
        lst ls;
        lst lr;
        for (unsigned i=0; i<e.nops(); i++) {
                ex r = e.op(i);
                if (!r.info(info_flags::relation_equal)) {
                        throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
                }
                ls.append(r.op(0));
                lr.append(r.op(1));
        }
        return subs(ls, lr, no_pattern);
}

/** Compare objects to establish canonical ordering.
 *  All compare functions return: -1 for *this less than other, 0 equal,
 *  1 greater. */
int basic::compare(const basic & other) const
{
        unsigned hash_this = gethash();
        unsigned hash_other = other.gethash();
        
        if (hash_this<hash_other) return -1;
        if (hash_this>hash_other) return 1;
        
        unsigned typeid_this = tinfo();
        unsigned typeid_other = other.tinfo();
        
        if (typeid_this<typeid_other) {
//              std::cout << "hash collision, different types: " 
//                        << *this << " and " << other << std::endl;
//              this->print(print_tree(std::cout));
//              std::cout << " and ";
//              other.print(print_tree(std::cout));
//              std::cout << std::endl;
                return -1;
        }
        if (typeid_this>typeid_other) {
//              std::cout << "hash collision, different types: " 
//                        << *this << " and " << other << std::endl;
//              this->print(print_tree(std::cout));
//              std::cout << " and ";
//              other.print(print_tree(std::cout));
//              std::cout << std::endl;
                return 1;
        }
        
        GINAC_ASSERT(typeid(*this)==typeid(other));
        
//      int cmpval = compare_same_type(other);
//      if ((cmpval!=0) && (hash_this<0x80000000U)) {
//              std::cout << "hash collision, same type: " 
//                        << *this << " and " << other << std::endl;
//              this->print(print_tree(std::cout));
//              std::cout << " and ";
//              other.print(print_tree(std::cout));
//              std::cout << std::endl;
//      }
//      return cmpval;
        
        return compare_same_type(other);
}

/** Test for equality.
 *  This is only a quick test, meaning objects should be in the same domain.
 *  You might have to .expand(), .normal() objects first, depending on the
 *  domain of your computation, to get a more reliable answer.
 *
 *  @see is_equal_same_type */
bool basic::is_equal(const basic & other) const
{
        if (this->gethash()!=other.gethash())
                return false;
        if (this->tinfo()!=other.tinfo())
                return false;
        
        GINAC_ASSERT(typeid(*this)==typeid(other));
        
        return this->is_equal_same_type(other);
}

// protected

/** Stop further evaluation.
 *
 *  @see basic::eval */
const basic & basic::hold(void) const
{
        return this->setflag(status_flags::evaluated);
}

/** Ensure the object may be modified without hurting others, throws if this
 *  is not the case. */
void basic::ensure_if_modifiable(void) const
{
        if (this->refcount>1)
                throw(std::runtime_error("cannot modify multiply referenced object"));
}

//////////
// global variables
//////////

int max_recursion_level = 1024;

} // namespace GiNaC