3 * Implementation of GiNaC's ABC. */
6 * GiNaC Copyright (C) 1999-2006 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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, unsigned options) const
292 if (match(pattern, repl_lst))
294 for (size_t i=0; i<nops(); i++)
295 if (op(i).has(pattern, options))
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 /** Check whether this is a polynomial in the given variables. */
329 bool basic::is_polynomial(const ex & var) const
331 return !has(var) || is_equal(ex_to<basic>(var));
334 /** Return degree of highest power in object s. */
335 int basic::degree(const ex & s) const
337 return is_equal(ex_to<basic>(s)) ? 1 : 0;
340 /** Return degree of lowest power in object s. */
341 int basic::ldegree(const ex & s) const
343 return is_equal(ex_to<basic>(s)) ? 1 : 0;
346 /** Return coefficient of degree n in object s. */
347 ex basic::coeff(const ex & s, int n) const
349 if (is_equal(ex_to<basic>(s)))
350 return n==1 ? _ex1 : _ex0;
352 return n==0 ? *this : _ex0;
355 /** Sort expanded expression in terms of powers of some object(s).
356 * @param s object(s) to sort in
357 * @param distributed recursive or distributed form (only used when s is a list) */
358 ex basic::collect(const ex & s, bool distributed) const
363 // List of objects specified
367 return collect(s.op(0));
369 else if (distributed) {
371 // Get lower/upper degree of all symbols in list
372 size_t num = s.nops();
376 int cnt; // current degree, 'counter'
377 ex coeff; // coefficient for degree 'cnt'
379 sym_info *si = new sym_info[num];
381 for (size_t i=0; i<num; i++) {
383 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
384 si[i].deg = this->degree(si[i].sym);
385 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
390 // Calculate coeff*x1^c1*...*xn^cn
392 for (size_t i=0; i<num; i++) {
394 y *= power(si[i].sym, cnt);
396 x += y * si[num - 1].coeff;
398 // Increment counters
402 if (si[n].cnt <= si[n].deg) {
403 // Update coefficients
409 for (size_t i=n; i<num; i++)
410 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
415 si[n].cnt = si[n].ldeg;
426 size_t n = s.nops() - 1;
437 // Only one object specified
438 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
439 x += this->coeff(s,n)*power(s,n);
442 // correct for lost fractional arguments and return
443 return x + (*this - x).expand();
446 /** Perform automatic non-interruptive term rewriting rules. */
447 ex basic::eval(int level) const
449 // There is nothing to do for basic objects:
453 /** Function object to be applied by basic::evalf(). */
454 struct evalf_map_function : public map_function {
456 evalf_map_function(int l) : level(l) {}
457 ex operator()(const ex & e) { return evalf(e, level); }
460 /** Evaluate object numerically. */
461 ex basic::evalf(int level) const
468 else if (level == -max_recursion_level)
469 throw(std::runtime_error("max recursion level reached"));
471 evalf_map_function map_evalf(level - 1);
472 return map(map_evalf);
477 /** Function object to be applied by basic::evalm(). */
478 struct evalm_map_function : public map_function {
479 ex operator()(const ex & e) { return evalm(e); }
482 /** Evaluate sums, products and integer powers of matrices. */
483 ex basic::evalm() const
488 return map(map_evalm);
491 /** Function object to be applied by basic::eval_integ(). */
492 struct eval_integ_map_function : public map_function {
493 ex operator()(const ex & e) { return eval_integ(e); }
496 /** Evaluate integrals, if result is known. */
497 ex basic::eval_integ() const
502 return map(map_eval_integ);
505 /** Perform automatic symbolic evaluations on indexed expression that
506 * contains this object as the base expression. */
507 ex basic::eval_indexed(const basic & i) const
508 // this function can't take a "const ex & i" because that would result
509 // in an infinite eval() loop
511 // There is nothing to do for basic objects
515 /** Add two indexed expressions. They are guaranteed to be of class indexed
516 * (or a subclass) and their indices are compatible. This function is used
517 * internally by simplify_indexed().
519 * @param self First indexed expression; its base object is *this
520 * @param other Second indexed expression
521 * @return sum of self and other
522 * @see ex::simplify_indexed() */
523 ex basic::add_indexed(const ex & self, const ex & other) const
528 /** Multiply an indexed expression with a scalar. This function is used
529 * internally by simplify_indexed().
531 * @param self Indexed expression; its base object is *this
532 * @param other Numeric value
533 * @return product of self and other
534 * @see ex::simplify_indexed() */
535 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
540 /** Try to contract two indexed expressions that appear in the same product.
541 * If a contraction exists, the function overwrites one or both of the
542 * expressions and returns true. Otherwise it returns false. It is
543 * guaranteed that both expressions are of class indexed (or a subclass)
544 * and that at least one dummy index has been found. This functions is
545 * used internally by simplify_indexed().
547 * @param self Pointer to first indexed expression; its base object is *this
548 * @param other Pointer to second indexed expression
549 * @param v The complete vector of factors
550 * @return true if the contraction was successful, false otherwise
551 * @see ex::simplify_indexed() */
552 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
558 /** Check whether the expression matches a given pattern. For every wildcard
559 * object in the pattern, an expression of the form "wildcard == matching_expression"
560 * is added to repl_lst. */
561 bool basic::match(const ex & pattern, lst & repl_lst) const
564 Sweet sweet shapes, sweet sweet shapes,
565 That's the key thing, right right.
566 Feed feed face, feed feed shapes,
567 But who is the king tonight?
568 Who is the king tonight?
569 Pattern is the thing, the key thing-a-ling,
570 But who is the king of Pattern?
571 But who is the king, the king thing-a-ling,
572 Who is the king of Pattern?
573 Bog is the king, the king thing-a-ling,
574 Bog is the king of Pattern.
575 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
576 Bog is the king of Pattern.
579 if (is_exactly_a<wildcard>(pattern)) {
581 // Wildcard matches anything, but check whether we already have found
582 // a match for that wildcard first (if so, the earlier match must be
583 // the same expression)
584 for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
585 if (it->op(0).is_equal(pattern))
586 return is_equal(ex_to<basic>(it->op(1)));
588 repl_lst.append(pattern == *this);
593 // Expression must be of the same type as the pattern
594 if (tinfo() != ex_to<basic>(pattern).tinfo())
597 // Number of subexpressions must match
598 if (nops() != pattern.nops())
601 // No subexpressions? Then just compare the objects (there can't be
602 // wildcards in the pattern)
604 return is_equal_same_type(ex_to<basic>(pattern));
606 // Check whether attributes that are not subexpressions match
607 if (!match_same_type(ex_to<basic>(pattern)))
610 // Otherwise the subexpressions must match one-to-one
611 for (size_t i=0; i<nops(); i++)
612 if (!op(i).match(pattern.op(i), repl_lst))
615 // Looks similar enough, match found
620 /** Helper function for subs(). Does not recurse into subexpressions. */
621 ex basic::subs_one_level(const exmap & m, unsigned options) const
623 exmap::const_iterator it;
625 if (options & subs_options::no_pattern) {
632 for (it = m.begin(); it != m.end(); ++it) {
634 if (match(ex_to<basic>(it->first), repl_lst))
635 return it->second.subs(repl_lst, options | subs_options::no_pattern); // avoid infinite recursion when re-substituting the wildcards
642 /** Substitute a set of objects by arbitrary expressions. The ex returned
643 * will already be evaluated. */
644 ex basic::subs(const exmap & m, unsigned options) const
649 // Substitute in subexpressions
650 for (size_t i=0; i<num; i++) {
651 const ex & orig_op = op(i);
652 const ex & subsed_op = orig_op.subs(m, options);
653 if (!are_ex_trivially_equal(orig_op, subsed_op)) {
655 // Something changed, clone the object
656 basic *copy = duplicate();
657 copy->setflag(status_flags::dynallocated);
658 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
660 // Substitute the changed operand
661 copy->let_op(i++) = subsed_op;
663 // Substitute the other operands
665 copy->let_op(i) = op(i).subs(m, options);
667 // Perform substitutions on the new object as a whole
668 return copy->subs_one_level(m, options);
673 // Nothing changed or no subexpressions
674 return subs_one_level(m, options);
677 /** Default interface of nth derivative ex::diff(s, n). It should be called
678 * instead of ::derivative(s) for first derivatives and for nth derivatives it
679 * just recurses down.
681 * @param s symbol to differentiate in
682 * @param nth order of differentiation
684 ex basic::diff(const symbol & s, unsigned nth) const
686 // trivial: zeroth derivative
690 // evaluate unevaluated *this before differentiating
691 if (!(flags & status_flags::evaluated))
692 return ex(*this).diff(s, nth);
694 ex ndiff = this->derivative(s);
695 while (!ndiff.is_zero() && // stop differentiating zeros
697 ndiff = ndiff.diff(s);
703 /** Return a vector containing the free indices of an expression. */
704 exvector basic::get_free_indices() const
706 return exvector(); // return an empty exvector
709 ex basic::conjugate() const
714 ex basic::eval_ncmul(const exvector & v) const
716 return hold_ncmul(v);
721 /** Function object to be applied by basic::derivative(). */
722 struct derivative_map_function : public map_function {
724 derivative_map_function(const symbol &sym) : s(sym) {}
725 ex operator()(const ex & e) { return diff(e, s); }
728 /** Default implementation of ex::diff(). It maps the operation on the
729 * operands (or returns 0 when the object has no operands).
732 ex basic::derivative(const symbol & s) const
737 derivative_map_function map_derivative(s);
738 return map(map_derivative);
742 /** Returns order relation between two objects of same type. This needs to be
743 * implemented by each class. It may never return anything else than 0,
744 * signalling equality, or +1 and -1 signalling inequality and determining
745 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
746 * the spaceship operator <=> for denoting just this.) */
747 int basic::compare_same_type(const basic & other) const
749 return compare_pointers(this, &other);
752 /** Returns true if two objects of same type are equal. Normally needs
753 * not be reimplemented as long as it wasn't overwritten by some parent
754 * class, since it just calls compare_same_type(). The reason why this
755 * function exists is that sometimes it is easier to determine equality
756 * than an order relation and then it can be overridden. */
757 bool basic::is_equal_same_type(const basic & other) const
759 return compare_same_type(other)==0;
762 /** Returns true if the attributes of two objects are similar enough for
763 * a match. This function must not match subexpressions (this is already
764 * done by basic::match()). Only attributes not accessible by op() should
765 * be compared. This is also the reason why this function doesn't take the
766 * wildcard replacement list from match() as an argument: only subexpressions
767 * are subject to wildcard matches. Also, this function only needs to be
768 * implemented for container classes because is_equal_same_type() is
769 * automatically used instead of match_same_type() if nops() == 0.
771 * @see basic::match */
772 bool basic::match_same_type(const basic & other) const
774 // The default is to only consider subexpressions, but not any other
779 unsigned basic::return_type() const
781 return return_types::commutative;
784 tinfo_t basic::return_type_tinfo() const
789 /** Compute the hash value of an object and if it makes sense to store it in
790 * the objects status_flags, do so. The method inherited from class basic
791 * computes a hash value based on the type and hash values of possible
792 * members. For this reason it is well suited for container classes but
793 * atomic classes should override this implementation because otherwise they
794 * would all end up with the same hashvalue. */
795 unsigned basic::calchash() const
797 unsigned v = golden_ratio_hash((p_int)tinfo());
798 for (size_t i=0; i<nops(); i++) {
800 v ^= this->op(i).gethash();
803 // store calculated hash value only if object is already evaluated
804 if (flags & status_flags::evaluated) {
805 setflag(status_flags::hash_calculated);
812 /** Function object to be applied by basic::expand(). */
813 struct expand_map_function : public map_function {
815 expand_map_function(unsigned o) : options(o) {}
816 ex operator()(const ex & e) { return e.expand(options); }
819 /** Expand expression, i.e. multiply it out and return the result as a new
821 ex basic::expand(unsigned options) const
824 return (options == 0) ? setflag(status_flags::expanded) : *this;
826 expand_map_function map_expand(options);
827 return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
833 // non-virtual functions in this class
838 /** Compare objects syntactically to establish canonical ordering.
839 * All compare functions return: -1 for *this less than other, 0 equal,
841 int basic::compare(const basic & other) const
843 #ifdef GINAC_COMPARE_STATISTICS
844 compare_statistics.total_basic_compares++;
846 const unsigned hash_this = gethash();
847 const unsigned hash_other = other.gethash();
848 if (hash_this<hash_other) return -1;
849 if (hash_this>hash_other) return 1;
850 #ifdef GINAC_COMPARE_STATISTICS
851 compare_statistics.compare_same_hashvalue++;
854 const tinfo_t typeid_this = tinfo();
855 const tinfo_t typeid_other = other.tinfo();
856 if (typeid_this==typeid_other) {
857 GINAC_ASSERT(typeid(*this)==typeid(other));
858 // int cmpval = compare_same_type(other);
860 // std::cout << "hash collision, same type: "
861 // << *this << " and " << other << std::endl;
862 // this->print(print_tree(std::cout));
863 // std::cout << " and ";
864 // other.print(print_tree(std::cout));
865 // std::cout << std::endl;
868 #ifdef GINAC_COMPARE_STATISTICS
869 compare_statistics.compare_same_type++;
871 return compare_same_type(other);
873 // std::cout << "hash collision, different types: "
874 // << *this << " and " << other << std::endl;
875 // this->print(print_tree(std::cout));
876 // std::cout << " and ";
877 // other.print(print_tree(std::cout));
878 // std::cout << std::endl;
879 return (typeid_this<typeid_other ? -1 : 1);
883 /** Test for syntactic equality.
884 * This is only a quick test, meaning objects should be in the same domain.
885 * You might have to .expand(), .normal() objects first, depending on the
886 * domain of your computation, to get a more reliable answer.
888 * @see is_equal_same_type */
889 bool basic::is_equal(const basic & other) const
891 #ifdef GINAC_COMPARE_STATISTICS
892 compare_statistics.total_basic_is_equals++;
894 if (this->gethash()!=other.gethash())
896 #ifdef GINAC_COMPARE_STATISTICS
897 compare_statistics.is_equal_same_hashvalue++;
899 if (this->tinfo()!=other.tinfo())
902 GINAC_ASSERT(typeid(*this)==typeid(other));
904 #ifdef GINAC_COMPARE_STATISTICS
905 compare_statistics.is_equal_same_type++;
907 return is_equal_same_type(other);
912 /** Stop further evaluation.
914 * @see basic::eval */
915 const basic & basic::hold() const
917 return setflag(status_flags::evaluated);
920 /** Ensure the object may be modified without hurting others, throws if this
921 * is not the case. */
922 void basic::ensure_if_modifiable() const
924 if (get_refcount() > 1)
925 throw(std::runtime_error("cannot modify multiply referenced object"));
926 clearflag(status_flags::hash_calculated | status_flags::evaluated);
933 int max_recursion_level = 1024;
936 #ifdef GINAC_COMPARE_STATISTICS
937 compare_statistics_t::~compare_statistics_t()
939 std::clog << "ex::compare() called " << total_compares << " times" << std::endl;
940 std::clog << "nontrivial compares: " << nontrivial_compares << " times" << std::endl;
941 std::clog << "basic::compare() called " << total_basic_compares << " times" << std::endl;
942 std::clog << "same hashvalue in compare(): " << compare_same_hashvalue << " times" << std::endl;
943 std::clog << "compare_same_type() called " << compare_same_type << " times" << std::endl;
944 std::clog << std::endl;
945 std::clog << "ex::is_equal() called " << total_is_equals << " times" << std::endl;
946 std::clog << "nontrivial is_equals: " << nontrivial_is_equals << " times" << std::endl;
947 std::clog << "basic::is_equal() called " << total_basic_is_equals << " times" << std::endl;
948 std::clog << "same hashvalue in is_equal(): " << is_equal_same_hashvalue << " times" << std::endl;
949 std::clog << "is_equal_same_type() called " << is_equal_same_type << " times" << std::endl;
950 std::clog << std::endl;
951 std::clog << "basic::gethash() called " << total_gethash << " times" << std::endl;
952 std::clog << "used cached hashvalue " << gethash_cached << " times" << std::endl;
955 compare_statistics_t compare_statistics;