3 * Implementation of GiNaC's ABC. */
6 * GiNaC Copyright (C) 1999-2001 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"
44 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(basic, void)
47 // default ctor, dtor, copy ctor assignment operator and helpers
52 basic::basic(const basic & other) : tinfo_key(TINFO_basic), flags(0), refcount(0)
54 debugmsg("basic copy ctor", LOGLEVEL_CONSTRUCT);
58 const basic & basic::operator=(const basic & other)
60 debugmsg("basic operator=", LOGLEVEL_ASSIGNMENT);
70 // none (all conditionally inlined)
76 // none (all conditionally inlined)
82 /** Construct object from archive_node. */
83 basic::basic(const archive_node &n, const lst &sym_lst) : flags(0), refcount(0)
85 debugmsg("basic ctor from archive_node", LOGLEVEL_CONSTRUCT);
87 // Reconstruct tinfo_key from class name
88 std::string class_name;
89 if (n.find_string("class", class_name))
90 tinfo_key = find_tinfo_key(class_name);
92 throw (std::runtime_error("archive node contains no class name"));
95 /** Unarchive the object. */
96 DEFAULT_UNARCHIVE(basic)
98 /** Archive the object. */
99 void basic::archive(archive_node &n) const
101 n.add_string("class", class_name());
105 // functions overriding virtual functions from bases classes
111 // new virtual functions which can be overridden by derived classes
116 /** Output to stream.
117 * @param c print context object that describes the output formatting
118 * @param level value that is used to identify the precedence or indentation
119 * level for placing parentheses and formatting */
120 void basic::print(const print_context & c, unsigned level) const
122 debugmsg("basic print", LOGLEVEL_PRINT);
124 if (is_of_type(c, print_tree)) {
126 c.s << std::string(level, ' ') << class_name()
127 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
128 << ", nops=" << nops()
130 for (unsigned i=0; i<nops(); ++i)
131 op(i).print(c, level + static_cast<const print_tree &>(c).delta_indent);
134 c.s << "[" << class_name() << " object]";
137 /** Little wrapper around print to be called within a debugger.
138 * This is needed because you cannot call foo.print(cout) from within the
139 * debugger because it might not know what cout is. This method can be
140 * invoked with no argument and it will simply print to stdout.
142 * @see basic::print */
143 void basic::dbgprint(void) const
145 this->print(std::cerr);
146 std::cerr << std::endl;
149 /** Little wrapper around printtree to be called within a debugger.
151 * @see basic::dbgprint
152 * @see basic::printtree */
153 void basic::dbgprinttree(void) const
155 this->print(print_tree(std::cerr));
158 /** Return relative operator precedence (for parenthizing output). */
159 unsigned basic::precedence(void) const
164 /** Create a new copy of this on the heap. One can think of this as simulating
165 * a virtual copy constructor which is needed for instance by the refcounted
166 * construction of an ex from a basic. */
167 basic * basic::duplicate() const
169 debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
170 return new basic(*this);
173 /** Information about the object.
175 * @see class info_flags */
176 bool basic::info(unsigned inf) const
178 // all possible properties are false for basic objects
182 /** Number of operands/members. */
183 unsigned basic::nops() const
185 // iterating from 0 to nops() on atomic objects should be an empty loop,
186 // and accessing their elements is a range error. Container objects should
191 /** Return operand/member at position i. */
192 ex basic::op(int i) const
194 return (const_cast<basic *>(this))->let_op(i);
197 /** Return modifyable operand/member at position i. */
198 ex & basic::let_op(int i)
200 throw(std::out_of_range("op() out of range"));
203 ex basic::operator[](const ex & index) const
205 if (is_exactly_of_type(*index.bp,numeric))
206 return op(static_cast<const numeric &>(*index.bp).to_int());
208 throw(std::invalid_argument("non-numeric indices not supported by this type"));
211 ex basic::operator[](int i) const
216 /** Search ocurrences. An object 'has' an expression if it is the expression
217 * itself or one of the children 'has' it. As a consequence (according to
218 * the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y)
219 * is false. The expression can also contain wildcards. */
220 bool basic::has(const ex & other) const
222 GINAC_ASSERT(other.bp!=0);
224 if (match(*other.bp, repl_lst))
226 for (unsigned i=0; i<nops(); i++)
227 if (op(i).has(other))
233 /** Construct new expression by applying the specified function to all
234 * sub-expressions (one level only, not recursively). */
235 ex basic::map(map_function & f) const
237 unsigned num = nops();
241 basic *copy = duplicate();
242 copy->setflag(status_flags::dynallocated);
243 copy->clearflag(status_flags::hash_calculated | status_flags::expanded);
245 for (unsigned i=0; i<num; i++)
246 e.let_op(i) = f(e.op(i));
250 /** Return degree of highest power in object s. */
251 int basic::degree(const ex & s) const
256 /** Return degree of lowest power in object s. */
257 int basic::ldegree(const ex & s) const
262 /** Return coefficient of degree n in object s. */
263 ex basic::coeff(const ex & s, int n) const
265 return n==0 ? *this : _ex0();
268 /** Sort expanded expression in terms of powers of some object(s).
269 * @param s object(s) to sort in
270 * @param distributed recursive or distributed form (only used when s is a list) */
271 ex basic::collect(const ex & s, bool distributed) const
274 if (is_ex_of_type(s, lst)) {
276 // List of objects specified
278 return collect(s.op(0));
280 else if (distributed) {
282 // Get lower/upper degree of all symbols in list
287 int cnt; // current degree, 'counter'
288 ex coeff; // coefficient for degree 'cnt'
290 sym_info *si = new sym_info[num];
292 for (int i=0; i<num; i++) {
294 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
295 si[i].deg = this->degree(si[i].sym);
296 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
301 // Calculate coeff*x1^c1*...*xn^cn
303 for (int i=0; i<num; i++) {
305 y *= power(si[i].sym, cnt);
307 x += y * si[num - 1].coeff;
309 // Increment counters
313 if (si[n].cnt <= si[n].deg) {
314 // Update coefficients
320 for (int i=n; i<num; i++)
321 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
326 si[n].cnt = si[n].ldeg;
337 for (int n=s.nops()-1; n>=0; n--)
343 // Only one object specified
344 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
345 x += this->coeff(s,n)*power(s,n);
348 // correct for lost fractional arguments and return
349 return x + (*this - x).expand();
352 /** Perform automatic non-interruptive symbolic evaluation on expression. */
353 ex basic::eval(int level) const
355 // There is nothing to do for basic objects:
359 /** Function object to be applied by basic::evalf(). */
360 struct evalf_map_function : public map_function {
362 evalf_map_function(int l) : level(l) {}
363 ex operator()(const ex & e) { return evalf(e, level); }
366 /** Evaluate object numerically. */
367 ex basic::evalf(int level) const
374 else if (level == -max_recursion_level)
375 throw(std::runtime_error("max recursion level reached"));
377 evalf_map_function map_evalf(level - 1);
378 return map(map_evalf);
383 /** Function object to be applied by basic::evalm(). */
384 struct evalm_map_function : public map_function {
385 ex operator()(const ex & e) { return evalm(e); }
388 /** Evaluate sums, products and integer powers of matrices. */
389 ex basic::evalm(void) const
394 return map(map_evalm);
397 /** Perform automatic symbolic evaluations on indexed expression that
398 * contains this object as the base expression. */
399 ex basic::eval_indexed(const basic & i) const
400 // this function can't take a "const ex & i" because that would result
401 // in an infinite eval() loop
403 // There is nothing to do for basic objects
407 /** Add two indexed expressions. They are guaranteed to be of class indexed
408 * (or a subclass) and their indices are compatible. This function is used
409 * internally by simplify_indexed().
411 * @param self First indexed expression; it's base object is *this
412 * @param other Second indexed expression
413 * @return sum of self and other
414 * @see ex::simplify_indexed() */
415 ex basic::add_indexed(const ex & self, const ex & other) const
420 /** Multiply an indexed expression with a scalar. This function is used
421 * internally by simplify_indexed().
423 * @param self Indexed expression; it's base object is *this
424 * @param other Numeric value
425 * @return product of self and other
426 * @see ex::simplify_indexed() */
427 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
432 /** Try to contract two indexed expressions that appear in the same product.
433 * If a contraction exists, the function overwrites one or both of the
434 * expressions and returns true. Otherwise it returns false. It is
435 * guaranteed that both expressions are of class indexed (or a subclass)
436 * and that at least one dummy index has been found. This functions is
437 * used internally by simplify_indexed().
439 * @param self Pointer to first indexed expression; it's base object is *this
440 * @param other Pointer to second indexed expression
441 * @param v The complete vector of factors
442 * @return true if the contraction was successful, false otherwise
443 * @see ex::simplify_indexed() */
444 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
450 /** Check whether the expression matches a given pattern. For every wildcard
451 * object in the pattern, an expression of the form "wildcard == matching_expression"
452 * is added to repl_lst. */
453 bool basic::match(const ex & pattern, lst & repl_lst) const
456 Sweet sweet shapes, sweet sweet shapes,
457 That's the key thing, right right.
458 Feed feed face, feed feed shapes,
459 But who is the king tonight?
460 Who is the king tonight?
461 Pattern is the thing, the key thing-a-ling,
462 But who is the king of pattern?
463 But who is the king, the king thing-a-ling,
464 Who is the king of Pattern?
465 Bog is the king, the king thing-a-ling,
466 Bog is the king of Pattern.
467 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
468 Bog is the king of Pattern.
471 if (is_ex_exactly_of_type(pattern, wildcard)) {
473 // Wildcard matches anything, but check whether we already have found
474 // a match for that wildcard first (if so, it the earlier match must
475 // be the same expression)
476 for (unsigned i=0; i<repl_lst.nops(); i++) {
477 if (repl_lst.op(i).op(0).is_equal(pattern))
478 return is_equal(*repl_lst.op(i).op(1).bp);
480 repl_lst.append(pattern == *this);
485 // Expression must be of the same type as the pattern
486 if (tinfo() != pattern.bp->tinfo())
489 // Number of subexpressions must match
490 if (nops() != pattern.nops())
493 // No subexpressions? Then just compare the objects (there can't be
494 // wildcards in the pattern)
496 return is_equal(*pattern.bp);
498 // Otherwise the subexpressions must match one-to-one
499 for (unsigned i=0; i<nops(); i++)
500 if (!op(i).match(pattern.op(i), repl_lst))
503 // Looks similar enough, match found
508 /** Substitute a set of objects by arbitrary expressions. The ex returned
509 * will already be evaluated. */
510 ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
512 GINAC_ASSERT(ls.nops() == lr.nops());
515 for (unsigned i=0; i<ls.nops(); i++) {
516 if (is_equal(*ls.op(i).bp))
520 for (unsigned i=0; i<ls.nops(); i++) {
522 if (match(*ls.op(i).bp, repl_lst))
523 return lr.op(i).bp->subs(repl_lst, true); // avoid infinite recursion when re-substituting the wildcards
530 /** Default interface of nth derivative ex::diff(s, n). It should be called
531 * instead of ::derivative(s) for first derivatives and for nth derivatives it
532 * just recurses down.
534 * @param s symbol to differentiate in
535 * @param nth order of differentiation
537 ex basic::diff(const symbol & s, unsigned nth) const
539 // trivial: zeroth derivative
543 // evaluate unevaluated *this before differentiating
544 if (!(flags & status_flags::evaluated))
545 return ex(*this).diff(s, nth);
547 ex ndiff = this->derivative(s);
548 while (!ndiff.is_zero() && // stop differentiating zeros
550 ndiff = ndiff.diff(s);
556 /** Return a vector containing the free indices of an expression. */
557 exvector basic::get_free_indices(void) const
559 return exvector(); // return an empty exvector
562 ex basic::simplify_ncmul(const exvector & v) const
564 return simplified_ncmul(v);
569 /** Function object to be applied by basic::derivative(). */
570 struct derivative_map_function : public map_function {
572 derivative_map_function(const symbol &sym) : s(sym) {}
573 ex operator()(const ex & e) { return diff(e, s); }
576 /** Default implementation of ex::diff(). It maps the operation on the
577 * operands (or returns 0 when the object has no operands).
580 ex basic::derivative(const symbol & s) const
585 derivative_map_function map_derivative(s);
586 return map(map_derivative);
590 /** Returns order relation between two objects of same type. This needs to be
591 * implemented by each class. It may never return anything else than 0,
592 * signalling equality, or +1 and -1 signalling inequality and determining
593 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
594 * the spaceship operator <=> for denoting just this.) */
595 int basic::compare_same_type(const basic & other) const
597 return compare_pointers(this, &other);
600 /** Returns true if two objects of same type are equal. Normally needs
601 * not be reimplemented as long as it wasn't overwritten by some parent
602 * class, since it just calls compare_same_type(). The reason why this
603 * function exists is that sometimes it is easier to determine equality
604 * than an order relation and then it can be overridden. */
605 bool basic::is_equal_same_type(const basic & other) const
607 return this->compare_same_type(other)==0;
610 unsigned basic::return_type(void) const
612 return return_types::commutative;
615 unsigned basic::return_type_tinfo(void) const
620 /** Compute the hash value of an object and if it makes sense to store it in
621 * the objects status_flags, do so. The method inherited from class basic
622 * computes a hash value based on the type and hash values of possible
623 * members. For this reason it is well suited for container classes but
624 * atomic classes should override this implementation because otherwise they
625 * would all end up with the same hashvalue. */
626 unsigned basic::calchash(void) const
628 unsigned v = golden_ratio_hash(tinfo());
629 for (unsigned i=0; i<nops(); i++) {
630 v = rotate_left_31(v);
631 v ^= (const_cast<basic *>(this))->op(i).gethash();
634 // mask out numeric hashes:
637 // store calculated hash value only if object is already evaluated
638 if (flags & status_flags::evaluated) {
639 setflag(status_flags::hash_calculated);
646 /** Function object to be applied by basic::expand(). */
647 struct expand_map_function : public map_function {
649 expand_map_function(unsigned o) : options(o) {}
650 ex operator()(const ex & e) { return expand(e, options); }
653 /** Expand expression, i.e. multiply it out and return the result as a new
655 ex basic::expand(unsigned options) const
658 return this->setflag(status_flags::expanded);
660 expand_map_function map_expand(options);
661 return map(map_expand).bp->setflag(status_flags::expanded);
667 // non-virtual functions in this class
672 /** Substitute objects in an expression (syntactic substitution) and return
673 * the result as a new expression. There are two valid types of
674 * replacement arguments: 1) a relational like object==ex and 2) a list of
675 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
676 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
677 ex basic::subs(const ex & e, bool no_pattern) const
679 if (e.info(info_flags::relation_equal)) {
680 return subs(lst(e), no_pattern);
682 if (!e.info(info_flags::list)) {
683 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
687 for (unsigned i=0; i<e.nops(); i++) {
689 if (!r.info(info_flags::relation_equal)) {
690 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
695 return subs(ls, lr, no_pattern);
698 /** Compare objects to establish canonical ordering.
699 * All compare functions return: -1 for *this less than other, 0 equal,
701 int basic::compare(const basic & other) const
703 unsigned hash_this = gethash();
704 unsigned hash_other = other.gethash();
706 if (hash_this<hash_other) return -1;
707 if (hash_this>hash_other) return 1;
709 unsigned typeid_this = tinfo();
710 unsigned typeid_other = other.tinfo();
712 if (typeid_this<typeid_other) {
713 // std::cout << "hash collision, different types: "
714 // << *this << " and " << other << std::endl;
715 // this->print(print_tree(std::cout));
716 // std::cout << " and ";
717 // other.print(print_tree(std::cout));
718 // std::cout << std::endl;
721 if (typeid_this>typeid_other) {
722 // std::cout << "hash collision, different types: "
723 // << *this << " and " << other << std::endl;
724 // this->print(print_tree(std::cout));
725 // std::cout << " and ";
726 // other.print(print_tree(std::cout));
727 // std::cout << std::endl;
731 GINAC_ASSERT(typeid(*this)==typeid(other));
733 // int cmpval = compare_same_type(other);
734 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
735 // std::cout << "hash collision, same type: "
736 // << *this << " and " << other << std::endl;
737 // this->print(print_tree(std::cout));
738 // std::cout << " and ";
739 // other.print(print_tree(std::cout));
740 // std::cout << std::endl;
744 return compare_same_type(other);
747 /** Test for equality.
748 * This is only a quick test, meaning objects should be in the same domain.
749 * You might have to .expand(), .normal() objects first, depending on the
750 * domain of your computation, to get a more reliable answer.
752 * @see is_equal_same_type */
753 bool basic::is_equal(const basic & other) const
755 if (this->gethash()!=other.gethash())
757 if (this->tinfo()!=other.tinfo())
760 GINAC_ASSERT(typeid(*this)==typeid(other));
762 return this->is_equal_same_type(other);
767 /** Stop further evaluation.
769 * @see basic::eval */
770 const basic & basic::hold(void) const
772 return this->setflag(status_flags::evaluated);
775 /** Ensure the object may be modified without hurting others, throws if this
776 * is not the case. */
777 void basic::ensure_if_modifiable(void) const
779 if (this->refcount>1)
780 throw(std::runtime_error("cannot modify multiply referenced object"));
781 clearflag(status_flags::hash_calculated);
788 int max_recursion_level = 1024;