3 * Implementation of GiNaC's ABC. */
6 * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 #ifdef DO_GINAC_ASSERT
36 #include "relational.h"
37 #include "operators.h"
44 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(basic, void,
45 print_func<print_context>(&basic::do_print).
46 print_func<print_tree>(&basic::do_print_tree).
47 print_func<print_python_repr>(&basic::do_print_python_repr))
50 // default constructor, destructor, copy constructor and assignment operator
55 /** basic copy constructor: implicitly assumes that the other class is of
56 * the exact same type (as it's used by duplicate()), so it can copy the
57 * tinfo_key and the hash value. */
58 basic::basic(const basic & other) : tinfo_key(other.tinfo_key), flags(other.flags & ~status_flags::dynallocated), hashvalue(other.hashvalue)
62 /** basic assignment operator: the other object might be of a derived class. */
63 const basic & basic::operator=(const basic & other)
65 unsigned fl = other.flags & ~status_flags::dynallocated;
66 if (tinfo_key != other.tinfo_key) {
67 // The other object is of a derived class, so clear the flags as they
68 // might no longer apply (especially hash_calculated). Oh, and don't
69 // copy the tinfo_key: it is already set correctly for this object.
70 fl &= ~(status_flags::evaluated | status_flags::expanded | status_flags::hash_calculated);
72 // The objects are of the exact same class, so copy the hash value.
73 hashvalue = other.hashvalue;
94 /** Construct object from archive_node. */
95 basic::basic(const archive_node &n, lst &sym_lst) : flags(0)
97 // Reconstruct tinfo_key from class name
98 std::string class_name;
99 if (n.find_string("class", class_name))
100 tinfo_key = find_tinfo_key(class_name);
102 throw (std::runtime_error("archive node contains no class name"));
105 /** Unarchive the object. */
106 DEFAULT_UNARCHIVE(basic)
108 /** Archive the object. */
109 void basic::archive(archive_node &n) const
111 n.add_string("class", class_name());
115 // new virtual functions which can be overridden by derived classes
120 /** Output to stream. This performs double dispatch on the dynamic type of
121 * *this and the dynamic type of the supplied print context.
122 * @param c print context object that describes the output formatting
123 * @param level value that is used to identify the precedence or indentation
124 * level for placing parentheses and formatting */
125 void basic::print(const print_context & c, unsigned level) const
127 print_dispatch(get_class_info(), c, level);
130 /** Like print(), but dispatch to the specified class. Can be used by
131 * implementations of print methods to dispatch to the method of the
134 * @see basic::print */
135 void basic::print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const
137 // Double dispatch on object type and print_context type
138 const registered_class_info * reg_info = &ri;
139 const print_context_class_info * pc_info = &c.get_class_info();
142 const std::vector<print_functor> & pdt = reg_info->options.get_print_dispatch_table();
145 unsigned id = pc_info->options.get_id();
146 if (id >= pdt.size() || !(pdt[id].is_valid())) {
148 // Method not found, try parent print_context class
149 const print_context_class_info * parent_pc_info = pc_info->get_parent();
150 if (parent_pc_info) {
151 pc_info = parent_pc_info;
155 // Method still not found, try parent class
156 const registered_class_info * parent_reg_info = reg_info->get_parent();
157 if (parent_reg_info) {
158 reg_info = parent_reg_info;
159 pc_info = &c.get_class_info();
163 // Method still not found. This shouldn't happen because basic (the
164 // base class of the algebraic hierarchy) registers a method for
165 // print_context (the base class of the print context hierarchy),
166 // so if we end up here, there's something wrong with the class
168 throw (std::runtime_error(std::string("basic::print(): method for ") + class_name() + "/" + c.class_name() + " not found"));
173 pdt[id](*this, c, level);
177 /** Default output to stream. */
178 void basic::do_print(const print_context & c, unsigned level) const
180 c.s << "[" << class_name() << " object]";
183 /** Tree output to stream. */
184 void basic::do_print_tree(const print_tree & c, unsigned level) const
186 c.s << std::string(level, ' ') << class_name() << " @" << this
187 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec;
189 c.s << ", nops=" << nops();
191 for (size_t i=0; i<nops(); ++i)
192 op(i).print(c, level + c.delta_indent);
195 /** Python parsable output to stream. */
196 void basic::do_print_python_repr(const print_python_repr & c, unsigned level) const
198 c.s << class_name() << "()";
201 /** Little wrapper around print to be called within a debugger.
202 * This is needed because you cannot call foo.print(cout) from within the
203 * debugger because it might not know what cout is. This method can be
204 * invoked with no argument and it will simply print to stdout.
207 * @see basic::dbgprinttree */
208 void basic::dbgprint() const
210 this->print(print_dflt(std::cerr));
211 std::cerr << std::endl;
214 /** Little wrapper around printtree to be called within a debugger.
216 * @see basic::dbgprint */
217 void basic::dbgprinttree() const
219 this->print(print_tree(std::cerr));
222 /** Return relative operator precedence (for parenthezing output). */
223 unsigned basic::precedence() const
228 /** Information about the object.
230 * @see class info_flags */
231 bool basic::info(unsigned inf) const
233 // all possible properties are false for basic objects
237 /** Number of operands/members. */
238 size_t basic::nops() const
240 // iterating from 0 to nops() on atomic objects should be an empty loop,
241 // and accessing their elements is a range error. Container objects should
246 /** Return operand/member at position i. */
247 ex basic::op(size_t i) const
249 throw(std::range_error(std::string("basic::op(): ") + class_name() + std::string(" has no operands")));
252 /** Return modifyable operand/member at position i. */
253 ex & basic::let_op(size_t i)
255 ensure_if_modifiable();
256 throw(std::range_error(std::string("basic::let_op(): ") + class_name() + std::string(" has no operands")));
259 ex basic::operator[](const ex & index) const
261 if (is_exactly_a<numeric>(index))
262 return op(static_cast<size_t>(ex_to<numeric>(index).to_int()));
264 throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
267 ex basic::operator[](size_t i) const
272 ex & basic::operator[](const ex & index)
274 if (is_exactly_a<numeric>(index))
275 return let_op(ex_to<numeric>(index).to_int());
277 throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
280 ex & basic::operator[](size_t i)
285 /** Test for occurrence of a pattern. An object 'has' a pattern if it matches
286 * the pattern itself or one of the children 'has' it. As a consequence
287 * (according to the definition of children) given e=x+y+z, e.has(x) is true
288 * but e.has(x+y) is false. */
289 bool basic::has(const ex & pattern) const
292 if (match(pattern, repl_lst))
294 for (size_t i=0; i<nops(); i++)
295 if (op(i).has(pattern))
301 /** Construct new expression by applying the specified function to all
302 * sub-expressions (one level only, not recursively). */
303 ex basic::map(map_function & f) const
310 for (size_t i=0; i<num; i++) {
311 const ex & o = op(i);
313 if (!are_ex_trivially_equal(o, n)) {
321 copy->setflag(status_flags::dynallocated);
322 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
328 /** Return degree of highest power in object s. */
329 int basic::degree(const ex & s) const
331 return is_equal(ex_to<basic>(s)) ? 1 : 0;
334 /** Return degree of lowest power in object s. */
335 int basic::ldegree(const ex & s) const
337 return is_equal(ex_to<basic>(s)) ? 1 : 0;
340 /** Return coefficient of degree n in object s. */
341 ex basic::coeff(const ex & s, int n) const
343 if (is_equal(ex_to<basic>(s)))
344 return n==1 ? _ex1 : _ex0;
346 return n==0 ? *this : _ex0;
349 /** Sort expanded expression in terms of powers of some object(s).
350 * @param s object(s) to sort in
351 * @param distributed recursive or distributed form (only used when s is a list) */
352 ex basic::collect(const ex & s, bool distributed) const
357 // List of objects specified
361 return collect(s.op(0));
363 else if (distributed) {
365 // Get lower/upper degree of all symbols in list
366 size_t num = s.nops();
370 int cnt; // current degree, 'counter'
371 ex coeff; // coefficient for degree 'cnt'
373 sym_info *si = new sym_info[num];
375 for (size_t i=0; i<num; i++) {
377 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
378 si[i].deg = this->degree(si[i].sym);
379 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
384 // Calculate coeff*x1^c1*...*xn^cn
386 for (size_t i=0; i<num; i++) {
388 y *= power(si[i].sym, cnt);
390 x += y * si[num - 1].coeff;
392 // Increment counters
396 if (si[n].cnt <= si[n].deg) {
397 // Update coefficients
403 for (size_t i=n; i<num; i++)
404 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
409 si[n].cnt = si[n].ldeg;
420 size_t n = s.nops() - 1;
431 // Only one object specified
432 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
433 x += this->coeff(s,n)*power(s,n);
436 // correct for lost fractional arguments and return
437 return x + (*this - x).expand();
440 /** Perform automatic non-interruptive term rewriting rules. */
441 ex basic::eval(int level) const
443 // There is nothing to do for basic objects:
447 /** Function object to be applied by basic::evalf(). */
448 struct evalf_map_function : public map_function {
450 evalf_map_function(int l) : level(l) {}
451 ex operator()(const ex & e) { return evalf(e, level); }
454 /** Evaluate object numerically. */
455 ex basic::evalf(int level) const
462 else if (level == -max_recursion_level)
463 throw(std::runtime_error("max recursion level reached"));
465 evalf_map_function map_evalf(level - 1);
466 return map(map_evalf);
471 /** Function object to be applied by basic::evalm(). */
472 struct evalm_map_function : public map_function {
473 ex operator()(const ex & e) { return evalm(e); }
476 /** Evaluate sums, products and integer powers of matrices. */
477 ex basic::evalm() const
482 return map(map_evalm);
485 /** Function object to be applied by basic::eval_integ(). */
486 struct eval_integ_map_function : public map_function {
487 ex operator()(const ex & e) { return eval_integ(e); }
490 /** Evaluate integrals, if result is known. */
491 ex basic::eval_integ() const
496 return map(map_eval_integ);
499 /** Perform automatic symbolic evaluations on indexed expression that
500 * contains this object as the base expression. */
501 ex basic::eval_indexed(const basic & i) const
502 // this function can't take a "const ex & i" because that would result
503 // in an infinite eval() loop
505 // There is nothing to do for basic objects
509 /** Add two indexed expressions. They are guaranteed to be of class indexed
510 * (or a subclass) and their indices are compatible. This function is used
511 * internally by simplify_indexed().
513 * @param self First indexed expression; its base object is *this
514 * @param other Second indexed expression
515 * @return sum of self and other
516 * @see ex::simplify_indexed() */
517 ex basic::add_indexed(const ex & self, const ex & other) const
522 /** Multiply an indexed expression with a scalar. This function is used
523 * internally by simplify_indexed().
525 * @param self Indexed expression; its base object is *this
526 * @param other Numeric value
527 * @return product of self and other
528 * @see ex::simplify_indexed() */
529 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
534 /** Try to contract two indexed expressions that appear in the same product.
535 * If a contraction exists, the function overwrites one or both of the
536 * expressions and returns true. Otherwise it returns false. It is
537 * guaranteed that both expressions are of class indexed (or a subclass)
538 * and that at least one dummy index has been found. This functions is
539 * used internally by simplify_indexed().
541 * @param self Pointer to first indexed expression; its base object is *this
542 * @param other Pointer to second indexed expression
543 * @param v The complete vector of factors
544 * @return true if the contraction was successful, false otherwise
545 * @see ex::simplify_indexed() */
546 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
552 /** Check whether the expression matches a given pattern. For every wildcard
553 * object in the pattern, an expression of the form "wildcard == matching_expression"
554 * is added to repl_lst. */
555 bool basic::match(const ex & pattern, lst & repl_lst) const
558 Sweet sweet shapes, sweet sweet shapes,
559 That's the key thing, right right.
560 Feed feed face, feed feed shapes,
561 But who is the king tonight?
562 Who is the king tonight?
563 Pattern is the thing, the key thing-a-ling,
564 But who is the king of Pattern?
565 But who is the king, the king thing-a-ling,
566 Who is the king of Pattern?
567 Bog is the king, the king thing-a-ling,
568 Bog is the king of Pattern.
569 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
570 Bog is the king of Pattern.
573 if (is_exactly_a<wildcard>(pattern)) {
575 // Wildcard matches anything, but check whether we already have found
576 // a match for that wildcard first (if so, the earlier match must be
577 // the same expression)
578 for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
579 if (it->op(0).is_equal(pattern))
580 return is_equal(ex_to<basic>(it->op(1)));
582 repl_lst.append(pattern == *this);
587 // Expression must be of the same type as the pattern
588 if (tinfo() != ex_to<basic>(pattern).tinfo())
591 // Number of subexpressions must match
592 if (nops() != pattern.nops())
595 // No subexpressions? Then just compare the objects (there can't be
596 // wildcards in the pattern)
598 return is_equal_same_type(ex_to<basic>(pattern));
600 // Check whether attributes that are not subexpressions match
601 if (!match_same_type(ex_to<basic>(pattern)))
604 // Otherwise the subexpressions must match one-to-one
605 for (size_t i=0; i<nops(); i++)
606 if (!op(i).match(pattern.op(i), repl_lst))
609 // Looks similar enough, match found
614 /** Helper function for subs(). Does not recurse into subexpressions. */
615 ex basic::subs_one_level(const exmap & m, unsigned options) const
617 exmap::const_iterator it;
619 if (options & subs_options::no_pattern) {
626 for (it = m.begin(); it != m.end(); ++it) {
628 if (match(ex_to<basic>(it->first), repl_lst))
629 return it->second.subs(repl_lst, options | subs_options::no_pattern); // avoid infinite recursion when re-substituting the wildcards
636 /** Substitute a set of objects by arbitrary expressions. The ex returned
637 * will already be evaluated. */
638 ex basic::subs(const exmap & m, unsigned options) const
643 // Substitute in subexpressions
644 for (size_t i=0; i<num; i++) {
645 const ex & orig_op = op(i);
646 const ex & subsed_op = orig_op.subs(m, options);
647 if (!are_ex_trivially_equal(orig_op, subsed_op)) {
649 // Something changed, clone the object
650 basic *copy = duplicate();
651 copy->setflag(status_flags::dynallocated);
652 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
654 // Substitute the changed operand
655 copy->let_op(i++) = subsed_op;
657 // Substitute the other operands
659 copy->let_op(i) = op(i).subs(m, options);
661 // Perform substitutions on the new object as a whole
662 return copy->subs_one_level(m, options);
667 // Nothing changed or no subexpressions
668 return subs_one_level(m, options);
671 /** Default interface of nth derivative ex::diff(s, n). It should be called
672 * instead of ::derivative(s) for first derivatives and for nth derivatives it
673 * just recurses down.
675 * @param s symbol to differentiate in
676 * @param nth order of differentiation
678 ex basic::diff(const symbol & s, unsigned nth) const
680 // trivial: zeroth derivative
684 // evaluate unevaluated *this before differentiating
685 if (!(flags & status_flags::evaluated))
686 return ex(*this).diff(s, nth);
688 ex ndiff = this->derivative(s);
689 while (!ndiff.is_zero() && // stop differentiating zeros
691 ndiff = ndiff.diff(s);
697 /** Return a vector containing the free indices of an expression. */
698 exvector basic::get_free_indices() const
700 return exvector(); // return an empty exvector
703 ex basic::conjugate() const
708 ex basic::eval_ncmul(const exvector & v) const
710 return hold_ncmul(v);
715 /** Function object to be applied by basic::derivative(). */
716 struct derivative_map_function : public map_function {
718 derivative_map_function(const symbol &sym) : s(sym) {}
719 ex operator()(const ex & e) { return diff(e, s); }
722 /** Default implementation of ex::diff(). It maps the operation on the
723 * operands (or returns 0 when the object has no operands).
726 ex basic::derivative(const symbol & s) const
731 derivative_map_function map_derivative(s);
732 return map(map_derivative);
736 /** Returns order relation between two objects of same type. This needs to be
737 * implemented by each class. It may never return anything else than 0,
738 * signalling equality, or +1 and -1 signalling inequality and determining
739 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
740 * the spaceship operator <=> for denoting just this.) */
741 int basic::compare_same_type(const basic & other) const
743 return compare_pointers(this, &other);
746 /** Returns true if two objects of same type are equal. Normally needs
747 * not be reimplemented as long as it wasn't overwritten by some parent
748 * class, since it just calls compare_same_type(). The reason why this
749 * function exists is that sometimes it is easier to determine equality
750 * than an order relation and then it can be overridden. */
751 bool basic::is_equal_same_type(const basic & other) const
753 return compare_same_type(other)==0;
756 /** Returns true if the attributes of two objects are similar enough for
757 * a match. This function must not match subexpressions (this is already
758 * done by basic::match()). Only attributes not accessible by op() should
759 * be compared. This is also the reason why this function doesn't take the
760 * wildcard replacement list from match() as an argument: only subexpressions
761 * are subject to wildcard matches. Also, this function only needs to be
762 * implemented for container classes because is_equal_same_type() is
763 * automatically used instead of match_same_type() if nops() == 0.
765 * @see basic::match */
766 bool basic::match_same_type(const basic & other) const
768 // The default is to only consider subexpressions, but not any other
773 unsigned basic::return_type() const
775 return return_types::commutative;
778 unsigned basic::return_type_tinfo() const
783 /** Compute the hash value of an object and if it makes sense to store it in
784 * the objects status_flags, do so. The method inherited from class basic
785 * computes a hash value based on the type and hash values of possible
786 * members. For this reason it is well suited for container classes but
787 * atomic classes should override this implementation because otherwise they
788 * would all end up with the same hashvalue. */
789 unsigned basic::calchash() const
791 unsigned v = golden_ratio_hash(tinfo());
792 for (size_t i=0; i<nops(); i++) {
794 v ^= this->op(i).gethash();
797 // store calculated hash value only if object is already evaluated
798 if (flags & status_flags::evaluated) {
799 setflag(status_flags::hash_calculated);
806 /** Function object to be applied by basic::expand(). */
807 struct expand_map_function : public map_function {
809 expand_map_function(unsigned o) : options(o) {}
810 ex operator()(const ex & e) { return e.expand(options); }
813 /** Expand expression, i.e. multiply it out and return the result as a new
815 ex basic::expand(unsigned options) const
818 return (options == 0) ? setflag(status_flags::expanded) : *this;
820 expand_map_function map_expand(options);
821 return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
827 // non-virtual functions in this class
832 /** Compare objects syntactically to establish canonical ordering.
833 * All compare functions return: -1 for *this less than other, 0 equal,
835 int basic::compare(const basic & other) const
837 #ifdef GINAC_COMPARE_STATISTICS
838 compare_statistics.total_basic_compares++;
840 const unsigned hash_this = gethash();
841 const unsigned hash_other = other.gethash();
842 if (hash_this<hash_other) return -1;
843 if (hash_this>hash_other) return 1;
844 #ifdef GINAC_COMPARE_STATISTICS
845 compare_statistics.compare_same_hashvalue++;
848 const unsigned typeid_this = tinfo();
849 const unsigned typeid_other = other.tinfo();
850 if (typeid_this==typeid_other) {
851 GINAC_ASSERT(typeid(*this)==typeid(other));
852 // int cmpval = compare_same_type(other);
854 // std::cout << "hash collision, same type: "
855 // << *this << " and " << other << std::endl;
856 // this->print(print_tree(std::cout));
857 // std::cout << " and ";
858 // other.print(print_tree(std::cout));
859 // std::cout << std::endl;
862 #ifdef GINAC_COMPARE_STATISTICS
863 compare_statistics.compare_same_type++;
865 return compare_same_type(other);
867 // std::cout << "hash collision, different types: "
868 // << *this << " and " << other << std::endl;
869 // this->print(print_tree(std::cout));
870 // std::cout << " and ";
871 // other.print(print_tree(std::cout));
872 // std::cout << std::endl;
873 return (typeid_this<typeid_other ? -1 : 1);
877 /** Test for syntactic equality.
878 * This is only a quick test, meaning objects should be in the same domain.
879 * You might have to .expand(), .normal() objects first, depending on the
880 * domain of your computation, to get a more reliable answer.
882 * @see is_equal_same_type */
883 bool basic::is_equal(const basic & other) const
885 #ifdef GINAC_COMPARE_STATISTICS
886 compare_statistics.total_basic_is_equals++;
888 if (this->gethash()!=other.gethash())
890 #ifdef GINAC_COMPARE_STATISTICS
891 compare_statistics.is_equal_same_hashvalue++;
893 if (this->tinfo()!=other.tinfo())
896 GINAC_ASSERT(typeid(*this)==typeid(other));
898 #ifdef GINAC_COMPARE_STATISTICS
899 compare_statistics.is_equal_same_type++;
901 return is_equal_same_type(other);
906 /** Stop further evaluation.
908 * @see basic::eval */
909 const basic & basic::hold() const
911 return setflag(status_flags::evaluated);
914 /** Ensure the object may be modified without hurting others, throws if this
915 * is not the case. */
916 void basic::ensure_if_modifiable() const
918 if (get_refcount() > 1)
919 throw(std::runtime_error("cannot modify multiply referenced object"));
920 clearflag(status_flags::hash_calculated | status_flags::evaluated);
927 int max_recursion_level = 1024;
930 #ifdef GINAC_COMPARE_STATISTICS
931 compare_statistics_t::~compare_statistics_t()
933 std::clog << "ex::compare() called " << total_compares << " times" << std::endl;
934 std::clog << "nontrivial compares: " << nontrivial_compares << " times" << std::endl;
935 std::clog << "basic::compare() called " << total_basic_compares << " times" << std::endl;
936 std::clog << "same hashvalue in compare(): " << compare_same_hashvalue << " times" << std::endl;
937 std::clog << "compare_same_type() called " << compare_same_type << " times" << std::endl;
938 std::clog << std::endl;
939 std::clog << "ex::is_equal() called " << total_is_equals << " times" << std::endl;
940 std::clog << "nontrivial is_equals: " << nontrivial_is_equals << " times" << std::endl;
941 std::clog << "basic::is_equal() called " << total_basic_is_equals << " times" << std::endl;
942 std::clog << "same hashvalue in is_equal(): " << is_equal_same_hashvalue << " times" << std::endl;
943 std::clog << "is_equal_same_type() called " << is_equal_same_type << " times" << std::endl;
944 std::clog << std::endl;
945 std::clog << "basic::gethash() called " << total_gethash << " times" << std::endl;
946 std::clog << "used cached hashvalue " << gethash_cached << " times" << std::endl;
949 compare_statistics_t compare_statistics;