3 * Implementation of GiNaC's ABC. */
6 * GiNaC Copyright (C) 1999-2016 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
31 #include "relational.h"
32 #include "operators.h"
36 #include "hash_seed.h"
45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(basic, void,
46 print_func<print_context>(&basic::do_print).
47 print_func<print_tree>(&basic::do_print_tree).
48 print_func<print_python_repr>(&basic::do_print_python_repr))
51 // default constructor, destructor, copy constructor and assignment operator
56 /** basic copy constructor: implicitly assumes that the other class is of
57 * the exact same type (as it's used by duplicate()), so it can copy the
58 * tinfo_key and the hash value. */
59 basic::basic(const basic & other) : flags(other.flags & ~status_flags::dynallocated), hashvalue(other.hashvalue)
63 /** basic assignment operator: the other object might be of a derived class. */
64 const basic & basic::operator=(const basic & other)
66 unsigned fl = other.flags & ~status_flags::dynallocated;
67 if (typeid(*this) != typeid(other)) {
68 // The other object is of a derived class, so clear the flags as they
69 // might no longer apply (especially hash_calculated). Oh, and don't
70 // copy the tinfo_key: it is already set correctly for this object.
71 fl &= ~(status_flags::evaluated | status_flags::expanded | status_flags::hash_calculated);
73 // The objects are of the exact same class, so copy the hash value.
74 hashvalue = other.hashvalue;
95 /** Construct object from archive_node. */
96 void basic::read_archive(const archive_node& n, lst& syms)
99 /** Archive the object. */
100 void basic::archive(archive_node &n) const
102 n.add_string("class", class_name());
106 // new virtual functions which can be overridden by derived classes
111 /** Output to stream. This performs double dispatch on the dynamic type of
112 * *this and the dynamic type of the supplied print context.
113 * @param c print context object that describes the output formatting
114 * @param level value that is used to identify the precedence or indentation
115 * level for placing parentheses and formatting */
116 void basic::print(const print_context & c, unsigned level) const
118 print_dispatch(get_class_info(), c, level);
121 /** Like print(), but dispatch to the specified class. Can be used by
122 * implementations of print methods to dispatch to the method of the
125 * @see basic::print */
126 void basic::print_dispatch(const registered_class_info & ri, const print_context & c, unsigned level) const
128 // Double dispatch on object type and print_context type
129 const registered_class_info * reg_info = &ri;
130 const print_context_class_info * pc_info = &c.get_class_info();
133 const std::vector<print_functor> & pdt = reg_info->options.get_print_dispatch_table();
136 unsigned id = pc_info->options.get_id();
137 if (id >= pdt.size() || !(pdt[id].is_valid())) {
139 // Method not found, try parent print_context class
140 const print_context_class_info * parent_pc_info = pc_info->get_parent();
141 if (parent_pc_info) {
142 pc_info = parent_pc_info;
146 // Method still not found, try parent class
147 const registered_class_info * parent_reg_info = reg_info->get_parent();
148 if (parent_reg_info) {
149 reg_info = parent_reg_info;
150 pc_info = &c.get_class_info();
154 // Method still not found. This shouldn't happen because basic (the
155 // base class of the algebraic hierarchy) registers a method for
156 // print_context (the base class of the print context hierarchy),
157 // so if we end up here, there's something wrong with the class
159 throw (std::runtime_error(std::string("basic::print(): method for ") + class_name() + "/" + c.class_name() + " not found"));
164 pdt[id](*this, c, level);
168 /** Default output to stream. */
169 void basic::do_print(const print_context & c, unsigned level) const
171 c.s << "[" << class_name() << " object]";
174 /** Tree output to stream. */
175 void basic::do_print_tree(const print_tree & c, unsigned level) const
177 c.s << std::string(level, ' ') << class_name() << " @" << this
178 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec;
180 c.s << ", nops=" << nops();
182 for (size_t i=0; i<nops(); ++i)
183 op(i).print(c, level + c.delta_indent);
186 /** Python parsable output to stream. */
187 void basic::do_print_python_repr(const print_python_repr & c, unsigned level) const
189 c.s << class_name() << "()";
192 /** Little wrapper around print to be called within a debugger.
193 * This is needed because you cannot call foo.print(cout) from within the
194 * debugger because it might not know what cout is. This method can be
195 * invoked with no argument and it will simply print to stdout.
198 * @see basic::dbgprinttree */
199 void basic::dbgprint() const
201 this->print(print_dflt(std::cerr));
202 std::cerr << std::endl;
205 /** Little wrapper around printtree to be called within a debugger.
207 * @see basic::dbgprint */
208 void basic::dbgprinttree() const
210 this->print(print_tree(std::cerr));
213 /** Return relative operator precedence (for parenthezing output). */
214 unsigned basic::precedence() const
219 /** Information about the object.
221 * @see class info_flags */
222 bool basic::info(unsigned inf) const
224 // all possible properties are false for basic objects
228 /** Number of operands/members. */
229 size_t basic::nops() const
231 // iterating from 0 to nops() on atomic objects should be an empty loop,
232 // and accessing their elements is a range error. Container objects should
237 /** Return operand/member at position i. */
238 ex basic::op(size_t i) const
240 throw(std::range_error(std::string("basic::op(): ") + class_name() + std::string(" has no operands")));
243 /** Return modifiable operand/member at position i. */
244 ex & basic::let_op(size_t i)
246 ensure_if_modifiable();
247 throw(std::range_error(std::string("basic::let_op(): ") + class_name() + std::string(" has no operands")));
250 ex basic::operator[](const ex & index) const
252 if (is_exactly_a<numeric>(index))
253 return op(static_cast<size_t>(ex_to<numeric>(index).to_int()));
255 throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
258 ex basic::operator[](size_t i) const
263 ex & basic::operator[](const ex & index)
265 if (is_exactly_a<numeric>(index))
266 return let_op(ex_to<numeric>(index).to_int());
268 throw(std::invalid_argument(std::string("non-numeric indices not supported by ") + class_name()));
271 ex & basic::operator[](size_t i)
276 /** Test for occurrence of a pattern. An object 'has' a pattern if it matches
277 * the pattern itself or one of the children 'has' it. As a consequence
278 * (according to the definition of children) given e=x+y+z, e.has(x) is true
279 * but e.has(x+y) is false. */
280 bool basic::has(const ex & pattern, unsigned options) const
283 if (match(pattern, repl_lst))
285 for (size_t i=0; i<nops(); i++)
286 if (op(i).has(pattern, options))
292 /** Construct new expression by applying the specified function to all
293 * sub-expressions (one level only, not recursively). */
294 ex basic::map(map_function & f) const
300 basic *copy = nullptr;
301 for (size_t i=0; i<num; i++) {
302 const ex & o = op(i);
304 if (!are_ex_trivially_equal(o, n)) {
312 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
318 /** Check whether this is a polynomial in the given variables. */
319 bool basic::is_polynomial(const ex & var) const
321 return !has(var) || is_equal(ex_to<basic>(var));
324 /** Return degree of highest power in object s. */
325 int basic::degree(const ex & s) const
327 return is_equal(ex_to<basic>(s)) ? 1 : 0;
330 /** Return degree of lowest power in object s. */
331 int basic::ldegree(const ex & s) const
333 return is_equal(ex_to<basic>(s)) ? 1 : 0;
336 /** Return coefficient of degree n in object s. */
337 ex basic::coeff(const ex & s, int n) const
339 if (is_equal(ex_to<basic>(s)))
340 return n==1 ? _ex1 : _ex0;
342 return n==0 ? *this : _ex0;
345 /** Sort expanded expression in terms of powers of some object(s).
346 * @param s object(s) to sort in
347 * @param distributed recursive or distributed form (only used when s is a list) */
348 ex basic::collect(const ex & s, bool distributed) const
353 // List of objects specified
357 return collect(s.op(0));
359 else if (distributed) {
364 const lst& l(ex_to<lst>(s));
368 for (const auto & xi : x) {
371 for (auto & li : l) {
372 int cexp = pre_coeff.degree(li);
373 pre_coeff = pre_coeff.coeff(li, cexp);
374 key *= pow(li, cexp);
376 auto ci = cmap.find(key);
377 if (ci != cmap.end())
378 ci->second += pre_coeff;
380 cmap.insert(exmap::value_type(key, pre_coeff));
384 for (auto & mi : cmap)
385 resv.push_back((mi.first)*(mi.second));
386 return dynallocate<add>(resv);
392 size_t n = s.nops() - 1;
403 // Only one object specified
404 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
405 x += this->coeff(s,n)*power(s,n);
408 // correct for lost fractional arguments and return
409 return x + (*this - x).expand();
412 /** Perform automatic non-interruptive term rewriting rules. */
413 ex basic::eval() const
415 // There is nothing to do for basic objects:
419 /** Function object to be applied by basic::evalf(). */
420 struct evalf_map_function : public map_function {
421 ex operator()(const ex & e) override { return evalf(e); }
424 /** Evaluate object numerically. */
425 ex basic::evalf() const
430 evalf_map_function map_evalf;
431 return map(map_evalf);
435 /** Function object to be applied by basic::evalm(). */
436 struct evalm_map_function : public map_function {
437 ex operator()(const ex & e) override { return evalm(e); }
440 /** Evaluate sums, products and integer powers of matrices. */
441 ex basic::evalm() const
446 return map(map_evalm);
449 /** Function object to be applied by basic::eval_integ(). */
450 struct eval_integ_map_function : public map_function {
451 ex operator()(const ex & e) override { return eval_integ(e); }
454 /** Evaluate integrals, if result is known. */
455 ex basic::eval_integ() const
460 return map(map_eval_integ);
463 /** Perform automatic symbolic evaluations on indexed expression that
464 * contains this object as the base expression. */
465 ex basic::eval_indexed(const basic & i) const
466 // this function can't take a "const ex & i" because that would result
467 // in an infinite eval() loop
469 // There is nothing to do for basic objects
473 /** Add two indexed expressions. They are guaranteed to be of class indexed
474 * (or a subclass) and their indices are compatible. This function is used
475 * internally by simplify_indexed().
477 * @param self First indexed expression; its base object is *this
478 * @param other Second indexed expression
479 * @return sum of self and other
480 * @see ex::simplify_indexed() */
481 ex basic::add_indexed(const ex & self, const ex & other) const
486 /** Multiply an indexed expression with a scalar. This function is used
487 * internally by simplify_indexed().
489 * @param self Indexed expression; its base object is *this
490 * @param other Numeric value
491 * @return product of self and other
492 * @see ex::simplify_indexed() */
493 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
498 /** Try to contract two indexed expressions that appear in the same product.
499 * If a contraction exists, the function overwrites one or both of the
500 * expressions and returns true. Otherwise it returns false. It is
501 * guaranteed that both expressions are of class indexed (or a subclass)
502 * and that at least one dummy index has been found. This functions is
503 * used internally by simplify_indexed().
505 * @param self Pointer to first indexed expression; its base object is *this
506 * @param other Pointer to second indexed expression
507 * @param v The complete vector of factors
508 * @return true if the contraction was successful, false otherwise
509 * @see ex::simplify_indexed() */
510 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
516 /** Check whether the expression matches a given pattern. For every wildcard
517 * object in the pattern, a pair with the wildcard as a key and matching
518 * expression as a value is added to repl_lst. */
519 bool basic::match(const ex & pattern, exmap& repl_lst) const
522 Sweet sweet shapes, sweet sweet shapes,
523 That's the key thing, right right.
524 Feed feed face, feed feed shapes,
525 But who is the king tonight?
526 Who is the king tonight?
527 Pattern is the thing, the key thing-a-ling,
528 But who is the king of Pattern?
529 But who is the king, the king thing-a-ling,
530 Who is the king of Pattern?
531 Bog is the king, the king thing-a-ling,
532 Bog is the king of Pattern.
533 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
534 Bog is the king of Pattern.
537 if (is_exactly_a<wildcard>(pattern)) {
539 // Wildcard matches anything, but check whether we already have found
540 // a match for that wildcard first (if so, the earlier match must be
541 // the same expression)
542 for (auto & it : repl_lst) {
543 if (it.first.is_equal(pattern))
544 return is_equal(ex_to<basic>(it.second));
546 repl_lst[pattern] = *this;
551 // Expression must be of the same type as the pattern
552 if (typeid(*this) != typeid(ex_to<basic>(pattern)))
555 // Number of subexpressions must match
556 if (nops() != pattern.nops())
559 // No subexpressions? Then just compare the objects (there can't be
560 // wildcards in the pattern)
562 return is_equal_same_type(ex_to<basic>(pattern));
564 // Check whether attributes that are not subexpressions match
565 if (!match_same_type(ex_to<basic>(pattern)))
568 // Even if the expression does not match the pattern, some of
569 // its subexpressions could match it. For example, x^5*y^(-1)
570 // does not match the pattern $0^5, but its subexpression x^5
571 // does. So, save repl_lst in order to not add bogus entries.
572 exmap tmp_repl = repl_lst;
573 // Otherwise the subexpressions must match one-to-one
574 for (size_t i=0; i<nops(); i++)
575 if (!op(i).match(pattern.op(i), tmp_repl))
578 // Looks similar enough, match found
584 /** Helper function for subs(). Does not recurse into subexpressions. */
585 ex basic::subs_one_level(const exmap & m, unsigned options) const
587 if (options & subs_options::no_pattern) {
588 ex thisex = *this; // NB: *this may be deleted here.
589 auto it = m.find(thisex);
594 for (auto & it : m) {
596 if (match(ex_to<basic>(it.first), repl_lst))
597 return it.second.subs(repl_lst, options | subs_options::no_pattern);
598 // avoid infinite recursion when re-substituting the wildcards
605 /** Substitute a set of objects by arbitrary expressions. The ex returned
606 * will already be evaluated. */
607 ex basic::subs(const exmap & m, unsigned options) const
612 // Substitute in subexpressions
613 for (size_t i=0; i<num; i++) {
614 const ex & orig_op = op(i);
615 const ex & subsed_op = orig_op.subs(m, options);
616 if (!are_ex_trivially_equal(orig_op, subsed_op)) {
618 // Something changed, clone the object
619 basic *copy = duplicate();
620 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
622 // Substitute the changed operand
623 copy->let_op(i++) = subsed_op;
625 // Substitute the other operands
627 copy->let_op(i) = op(i).subs(m, options);
629 // Perform substitutions on the new object as a whole
630 return copy->subs_one_level(m, options);
635 // Nothing changed or no subexpressions
636 return subs_one_level(m, options);
639 /** Default interface of nth derivative ex::diff(s, n). It should be called
640 * instead of ::derivative(s) for first derivatives and for nth derivatives it
641 * just recurses down.
643 * @param s symbol to differentiate in
644 * @param nth order of differentiation
646 ex basic::diff(const symbol & s, unsigned nth) const
648 // trivial: zeroth derivative
652 // evaluate unevaluated *this before differentiating
653 if (!(flags & status_flags::evaluated))
654 return ex(*this).diff(s, nth);
656 ex ndiff = this->derivative(s);
657 while (!ndiff.is_zero() && // stop differentiating zeros
659 ndiff = ndiff.diff(s);
665 /** Return a vector containing the free indices of an expression. */
666 exvector basic::get_free_indices() const
668 return exvector(); // return an empty exvector
671 ex basic::conjugate() const
676 ex basic::real_part() const
678 return real_part_function(*this).hold();
681 ex basic::imag_part() const
683 return imag_part_function(*this).hold();
686 ex basic::eval_ncmul(const exvector & v) const
688 return hold_ncmul(v);
693 /** Function object to be applied by basic::derivative(). */
694 struct derivative_map_function : public map_function {
696 derivative_map_function(const symbol &sym) : s(sym) {}
697 ex operator()(const ex & e) override { return diff(e, s); }
700 /** Default implementation of ex::diff(). It maps the operation on the
701 * operands (or returns 0 when the object has no operands).
704 ex basic::derivative(const symbol & s) const
709 derivative_map_function map_derivative(s);
710 return map(map_derivative);
714 /** Returns order relation between two objects of same type. This needs to be
715 * implemented by each class. It may never return anything else than 0,
716 * signalling equality, or +1 and -1 signalling inequality and determining
717 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
718 * the spaceship operator <=> for denoting just this.) */
719 int basic::compare_same_type(const basic & other) const
721 return compare_pointers(this, &other);
724 /** Returns true if two objects of same type are equal. Normally needs
725 * not be reimplemented as long as it wasn't overwritten by some parent
726 * class, since it just calls compare_same_type(). The reason why this
727 * function exists is that sometimes it is easier to determine equality
728 * than an order relation and then it can be overridden. */
729 bool basic::is_equal_same_type(const basic & other) const
731 return compare_same_type(other)==0;
734 /** Returns true if the attributes of two objects are similar enough for
735 * a match. This function must not match subexpressions (this is already
736 * done by basic::match()). Only attributes not accessible by op() should
737 * be compared. This is also the reason why this function doesn't take the
738 * wildcard replacement list from match() as an argument: only subexpressions
739 * are subject to wildcard matches. Also, this function only needs to be
740 * implemented for container classes because is_equal_same_type() is
741 * automatically used instead of match_same_type() if nops() == 0.
743 * @see basic::match */
744 bool basic::match_same_type(const basic & other) const
746 // The default is to only consider subexpressions, but not any other
751 unsigned basic::return_type() const
753 return return_types::commutative;
756 return_type_t basic::return_type_tinfo() const
759 rt.tinfo = &typeid(*this);
764 /** Compute the hash value of an object and if it makes sense to store it in
765 * the objects status_flags, do so. The method inherited from class basic
766 * computes a hash value based on the type and hash values of possible
767 * members. For this reason it is well suited for container classes but
768 * atomic classes should override this implementation because otherwise they
769 * would all end up with the same hashvalue. */
770 unsigned basic::calchash() const
772 unsigned v = make_hash_seed(typeid(*this));
773 for (size_t i=0; i<nops(); i++) {
775 v ^= this->op(i).gethash();
778 // store calculated hash value only if object is already evaluated
779 if (flags & status_flags::evaluated) {
780 setflag(status_flags::hash_calculated);
787 /** Function object to be applied by basic::expand(). */
788 struct expand_map_function : public map_function {
790 expand_map_function(unsigned o) : options(o) {}
791 ex operator()(const ex & e) override { return e.expand(options); }
794 /** Expand expression, i.e. multiply it out and return the result as a new
796 ex basic::expand(unsigned options) const
799 return (options == 0) ? setflag(status_flags::expanded) : *this;
801 expand_map_function map_expand(options);
802 return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
808 // non-virtual functions in this class
813 /** Compare objects syntactically to establish canonical ordering.
814 * All compare functions return: -1 for *this less than other, 0 equal,
816 int basic::compare(const basic & other) const
818 #ifdef GINAC_COMPARE_STATISTICS
819 compare_statistics.total_basic_compares++;
821 const unsigned hash_this = gethash();
822 const unsigned hash_other = other.gethash();
823 if (hash_this<hash_other) return -1;
824 if (hash_this>hash_other) return 1;
825 #ifdef GINAC_COMPARE_STATISTICS
826 compare_statistics.compare_same_hashvalue++;
829 const std::type_info& typeid_this = typeid(*this);
830 const std::type_info& typeid_other = typeid(other);
831 if (typeid_this == typeid_other) {
832 // int cmpval = compare_same_type(other);
834 // std::cout << "hash collision, same type: "
835 // << *this << " and " << other << std::endl;
836 // this->print(print_tree(std::cout));
837 // std::cout << " and ";
838 // other.print(print_tree(std::cout));
839 // std::cout << std::endl;
842 #ifdef GINAC_COMPARE_STATISTICS
843 compare_statistics.compare_same_type++;
845 return compare_same_type(other);
847 // std::cout << "hash collision, different types: "
848 // << *this << " and " << other << std::endl;
849 // this->print(print_tree(std::cout));
850 // std::cout << " and ";
851 // other.print(print_tree(std::cout));
852 // std::cout << std::endl;
853 return (typeid_this.before(typeid_other) ? -1 : 1);
857 /** Test for syntactic equality.
858 * This is only a quick test, meaning objects should be in the same domain.
859 * You might have to .expand(), .normal() objects first, depending on the
860 * domain of your computation, to get a more reliable answer.
862 * @see is_equal_same_type */
863 bool basic::is_equal(const basic & other) const
865 #ifdef GINAC_COMPARE_STATISTICS
866 compare_statistics.total_basic_is_equals++;
868 if (this->gethash()!=other.gethash())
870 #ifdef GINAC_COMPARE_STATISTICS
871 compare_statistics.is_equal_same_hashvalue++;
873 if (typeid(*this) != typeid(other))
876 #ifdef GINAC_COMPARE_STATISTICS
877 compare_statistics.is_equal_same_type++;
879 return is_equal_same_type(other);
884 /** Stop further evaluation.
886 * @see basic::eval */
887 const basic & basic::hold() const
889 return setflag(status_flags::evaluated);
892 /** Ensure the object may be modified without hurting others, throws if this
893 * is not the case. */
894 void basic::ensure_if_modifiable() const
896 if (get_refcount() > 1)
897 throw(std::runtime_error("cannot modify multiply referenced object"));
898 clearflag(status_flags::hash_calculated | status_flags::evaluated);
905 #ifdef GINAC_COMPARE_STATISTICS
906 compare_statistics_t::~compare_statistics_t()
908 std::clog << "ex::compare() called " << total_compares << " times" << std::endl;
909 std::clog << "nontrivial compares: " << nontrivial_compares << " times" << std::endl;
910 std::clog << "basic::compare() called " << total_basic_compares << " times" << std::endl;
911 std::clog << "same hashvalue in compare(): " << compare_same_hashvalue << " times" << std::endl;
912 std::clog << "compare_same_type() called " << compare_same_type << " times" << std::endl;
913 std::clog << std::endl;
914 std::clog << "ex::is_equal() called " << total_is_equals << " times" << std::endl;
915 std::clog << "nontrivial is_equals: " << nontrivial_is_equals << " times" << std::endl;
916 std::clog << "basic::is_equal() called " << total_basic_is_equals << " times" << std::endl;
917 std::clog << "same hashvalue in is_equal(): " << is_equal_same_hashvalue << " times" << std::endl;
918 std::clog << "is_equal_same_type() called " << is_equal_same_type << " times" << std::endl;
919 std::clog << std::endl;
920 std::clog << "basic::gethash() called " << total_gethash << " times" << std::endl;
921 std::clog << "used cached hashvalue " << gethash_cached << " times" << std::endl;
924 compare_statistics_t compare_statistics;