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 auto it = m.find(*this);
593 for (auto & it : m) {
595 if (match(ex_to<basic>(it.first), repl_lst))
596 return it.second.subs(repl_lst, options | subs_options::no_pattern);
597 // avoid infinite recursion when re-substituting the wildcards
604 /** Substitute a set of objects by arbitrary expressions. The ex returned
605 * will already be evaluated. */
606 ex basic::subs(const exmap & m, unsigned options) const
611 // Substitute in subexpressions
612 for (size_t i=0; i<num; i++) {
613 const ex & orig_op = op(i);
614 const ex & subsed_op = orig_op.subs(m, options);
615 if (!are_ex_trivially_equal(orig_op, subsed_op)) {
617 // Something changed, clone the object
618 basic *copy = duplicate();
619 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
621 // Substitute the changed operand
622 copy->let_op(i++) = subsed_op;
624 // Substitute the other operands
626 copy->let_op(i) = op(i).subs(m, options);
628 // Perform substitutions on the new object as a whole
629 return copy->subs_one_level(m, options);
634 // Nothing changed or no subexpressions
635 return subs_one_level(m, options);
638 /** Default interface of nth derivative ex::diff(s, n). It should be called
639 * instead of ::derivative(s) for first derivatives and for nth derivatives it
640 * just recurses down.
642 * @param s symbol to differentiate in
643 * @param nth order of differentiation
645 ex basic::diff(const symbol & s, unsigned nth) const
647 // trivial: zeroth derivative
651 // evaluate unevaluated *this before differentiating
652 if (!(flags & status_flags::evaluated))
653 return ex(*this).diff(s, nth);
655 ex ndiff = this->derivative(s);
656 while (!ndiff.is_zero() && // stop differentiating zeros
658 ndiff = ndiff.diff(s);
664 /** Return a vector containing the free indices of an expression. */
665 exvector basic::get_free_indices() const
667 return exvector(); // return an empty exvector
670 ex basic::conjugate() const
675 ex basic::real_part() const
677 return real_part_function(*this).hold();
680 ex basic::imag_part() const
682 return imag_part_function(*this).hold();
685 ex basic::eval_ncmul(const exvector & v) const
687 return hold_ncmul(v);
692 /** Function object to be applied by basic::derivative(). */
693 struct derivative_map_function : public map_function {
695 derivative_map_function(const symbol &sym) : s(sym) {}
696 ex operator()(const ex & e) override { return diff(e, s); }
699 /** Default implementation of ex::diff(). It maps the operation on the
700 * operands (or returns 0 when the object has no operands).
703 ex basic::derivative(const symbol & s) const
708 derivative_map_function map_derivative(s);
709 return map(map_derivative);
713 /** Returns order relation between two objects of same type. This needs to be
714 * implemented by each class. It may never return anything else than 0,
715 * signalling equality, or +1 and -1 signalling inequality and determining
716 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
717 * the spaceship operator <=> for denoting just this.) */
718 int basic::compare_same_type(const basic & other) const
720 return compare_pointers(this, &other);
723 /** Returns true if two objects of same type are equal. Normally needs
724 * not be reimplemented as long as it wasn't overwritten by some parent
725 * class, since it just calls compare_same_type(). The reason why this
726 * function exists is that sometimes it is easier to determine equality
727 * than an order relation and then it can be overridden. */
728 bool basic::is_equal_same_type(const basic & other) const
730 return compare_same_type(other)==0;
733 /** Returns true if the attributes of two objects are similar enough for
734 * a match. This function must not match subexpressions (this is already
735 * done by basic::match()). Only attributes not accessible by op() should
736 * be compared. This is also the reason why this function doesn't take the
737 * wildcard replacement list from match() as an argument: only subexpressions
738 * are subject to wildcard matches. Also, this function only needs to be
739 * implemented for container classes because is_equal_same_type() is
740 * automatically used instead of match_same_type() if nops() == 0.
742 * @see basic::match */
743 bool basic::match_same_type(const basic & other) const
745 // The default is to only consider subexpressions, but not any other
750 unsigned basic::return_type() const
752 return return_types::commutative;
755 return_type_t basic::return_type_tinfo() const
758 rt.tinfo = &typeid(*this);
763 /** Compute the hash value of an object and if it makes sense to store it in
764 * the objects status_flags, do so. The method inherited from class basic
765 * computes a hash value based on the type and hash values of possible
766 * members. For this reason it is well suited for container classes but
767 * atomic classes should override this implementation because otherwise they
768 * would all end up with the same hashvalue. */
769 unsigned basic::calchash() const
771 unsigned v = make_hash_seed(typeid(*this));
772 for (size_t i=0; i<nops(); i++) {
774 v ^= this->op(i).gethash();
777 // store calculated hash value only if object is already evaluated
778 if (flags & status_flags::evaluated) {
779 setflag(status_flags::hash_calculated);
786 /** Function object to be applied by basic::expand(). */
787 struct expand_map_function : public map_function {
789 expand_map_function(unsigned o) : options(o) {}
790 ex operator()(const ex & e) override { return e.expand(options); }
793 /** Expand expression, i.e. multiply it out and return the result as a new
795 ex basic::expand(unsigned options) const
798 return (options == 0) ? setflag(status_flags::expanded) : *this;
800 expand_map_function map_expand(options);
801 return ex_to<basic>(map(map_expand)).setflag(options == 0 ? status_flags::expanded : 0);
807 // non-virtual functions in this class
812 /** Compare objects syntactically to establish canonical ordering.
813 * All compare functions return: -1 for *this less than other, 0 equal,
815 int basic::compare(const basic & other) const
817 #ifdef GINAC_COMPARE_STATISTICS
818 compare_statistics.total_basic_compares++;
820 const unsigned hash_this = gethash();
821 const unsigned hash_other = other.gethash();
822 if (hash_this<hash_other) return -1;
823 if (hash_this>hash_other) return 1;
824 #ifdef GINAC_COMPARE_STATISTICS
825 compare_statistics.compare_same_hashvalue++;
828 const std::type_info& typeid_this = typeid(*this);
829 const std::type_info& typeid_other = typeid(other);
830 if (typeid_this == typeid_other) {
831 // int cmpval = compare_same_type(other);
833 // std::cout << "hash collision, same type: "
834 // << *this << " and " << other << std::endl;
835 // this->print(print_tree(std::cout));
836 // std::cout << " and ";
837 // other.print(print_tree(std::cout));
838 // std::cout << std::endl;
841 #ifdef GINAC_COMPARE_STATISTICS
842 compare_statistics.compare_same_type++;
844 return compare_same_type(other);
846 // std::cout << "hash collision, different types: "
847 // << *this << " and " << other << std::endl;
848 // this->print(print_tree(std::cout));
849 // std::cout << " and ";
850 // other.print(print_tree(std::cout));
851 // std::cout << std::endl;
852 return (typeid_this.before(typeid_other) ? -1 : 1);
856 /** Test for syntactic equality.
857 * This is only a quick test, meaning objects should be in the same domain.
858 * You might have to .expand(), .normal() objects first, depending on the
859 * domain of your computation, to get a more reliable answer.
861 * @see is_equal_same_type */
862 bool basic::is_equal(const basic & other) const
864 #ifdef GINAC_COMPARE_STATISTICS
865 compare_statistics.total_basic_is_equals++;
867 if (this->gethash()!=other.gethash())
869 #ifdef GINAC_COMPARE_STATISTICS
870 compare_statistics.is_equal_same_hashvalue++;
872 if (typeid(*this) != typeid(other))
875 #ifdef GINAC_COMPARE_STATISTICS
876 compare_statistics.is_equal_same_type++;
878 return is_equal_same_type(other);
883 /** Stop further evaluation.
885 * @see basic::eval */
886 const basic & basic::hold() const
888 return setflag(status_flags::evaluated);
891 /** Ensure the object may be modified without hurting others, throws if this
892 * is not the case. */
893 void basic::ensure_if_modifiable() const
895 if (get_refcount() > 1)
896 throw(std::runtime_error("cannot modify multiply referenced object"));
897 clearflag(status_flags::hash_calculated | status_flags::evaluated);
904 #ifdef GINAC_COMPARE_STATISTICS
905 compare_statistics_t::~compare_statistics_t()
907 std::clog << "ex::compare() called " << total_compares << " times" << std::endl;
908 std::clog << "nontrivial compares: " << nontrivial_compares << " times" << std::endl;
909 std::clog << "basic::compare() called " << total_basic_compares << " times" << std::endl;
910 std::clog << "same hashvalue in compare(): " << compare_same_hashvalue << " times" << std::endl;
911 std::clog << "compare_same_type() called " << compare_same_type << " times" << std::endl;
912 std::clog << std::endl;
913 std::clog << "ex::is_equal() called " << total_is_equals << " times" << std::endl;
914 std::clog << "nontrivial is_equals: " << nontrivial_is_equals << " times" << std::endl;
915 std::clog << "basic::is_equal() called " << total_basic_is_equals << " times" << std::endl;
916 std::clog << "same hashvalue in is_equal(): " << is_equal_same_hashvalue << " times" << std::endl;
917 std::clog << "is_equal_same_type() called " << is_equal_same_type << " times" << std::endl;
918 std::clog << std::endl;
919 std::clog << "basic::gethash() called " << total_gethash << " times" << std::endl;
920 std::clog << "used cached hashvalue " << gethash_cached << " times" << std::endl;
923 compare_statistics_t compare_statistics;