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);
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 /** Evaluate object numerically. */
360 ex basic::evalf(int level) const
362 // There is nothing to do for basic objects:
366 /** Function object to be applied by basic::evalm(). */
367 struct evalm_map_function : public map_function {
368 ex operator()(const ex & e) { return GiNaC::evalm(e); }
370 /** Evaluate sums, products and integer powers of matrices. */
371 ex basic::evalm(void) const
379 /** Perform automatic symbolic evaluations on indexed expression that
380 * contains this object as the base expression. */
381 ex basic::eval_indexed(const basic & i) const
382 // this function can't take a "const ex & i" because that would result
383 // in an infinite eval() loop
385 // There is nothing to do for basic objects
389 /** Add two indexed expressions. They are guaranteed to be of class indexed
390 * (or a subclass) and their indices are compatible. This function is used
391 * internally by simplify_indexed().
393 * @param self First indexed expression; it's base object is *this
394 * @param other Second indexed expression
395 * @return sum of self and other
396 * @see ex::simplify_indexed() */
397 ex basic::add_indexed(const ex & self, const ex & other) const
402 /** Multiply an indexed expression with a scalar. This function is used
403 * internally by simplify_indexed().
405 * @param self Indexed expression; it's base object is *this
406 * @param other Numeric value
407 * @return product of self and other
408 * @see ex::simplify_indexed() */
409 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
414 /** Try to contract two indexed expressions that appear in the same product.
415 * If a contraction exists, the function overwrites one or both of the
416 * expressions and returns true. Otherwise it returns false. It is
417 * guaranteed that both expressions are of class indexed (or a subclass)
418 * and that at least one dummy index has been found. This functions is
419 * used internally by simplify_indexed().
421 * @param self Pointer to first indexed expression; it's base object is *this
422 * @param other Pointer to second indexed expression
423 * @param v The complete vector of factors
424 * @return true if the contraction was successful, false otherwise
425 * @see ex::simplify_indexed() */
426 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
432 /** Check whether the expression matches a given pattern. For every wildcard
433 * object in the pattern, an expression of the form "wildcard == matching_expression"
434 * is added to repl_lst. */
435 bool basic::match(const ex & pattern, lst & repl_lst) const
438 Sweet sweet shapes, sweet sweet shapes,
439 That's the key thing, right right.
440 Feed feed face, feed feed shapes,
441 But who is the king tonight?
442 Who is the king tonight?
443 Pattern is the thing, the key thing-a-ling,
444 But who is the king of pattern?
445 But who is the king, the king thing-a-ling,
446 Who is the king of Pattern?
447 Bog is the king, the king thing-a-ling,
448 Bog is the king of Pattern.
449 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
450 Bog is the king of Pattern.
453 if (is_ex_exactly_of_type(pattern, wildcard)) {
455 // Wildcard matches anything, but check whether we already have found
456 // a match for that wildcard first (if so, it the earlier match must
457 // be the same expression)
458 for (unsigned i=0; i<repl_lst.nops(); i++) {
459 if (repl_lst.op(i).op(0).is_equal(pattern))
460 return is_equal(*repl_lst.op(i).op(1).bp);
462 repl_lst.append(pattern == *this);
467 // Expression must be of the same type as the pattern
468 if (tinfo() != pattern.bp->tinfo())
471 // Number of subexpressions must match
472 if (nops() != pattern.nops())
475 // No subexpressions? Then just compare the objects (there can't be
476 // wildcards in the pattern)
478 return is_equal(*pattern.bp);
480 // Otherwise the subexpressions must match one-to-one
481 for (unsigned i=0; i<nops(); i++)
482 if (!op(i).match(pattern.op(i), repl_lst))
485 // Looks similar enough, match found
490 /** Substitute a set of objects by arbitrary expressions. The ex returned
491 * will already be evaluated. */
492 ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
494 GINAC_ASSERT(ls.nops() == lr.nops());
497 for (unsigned i=0; i<ls.nops(); i++) {
498 if (is_equal(*ls.op(i).bp))
502 for (unsigned i=0; i<ls.nops(); i++) {
504 if (match(*ls.op(i).bp, repl_lst))
505 return lr.op(i).bp->subs(repl_lst, true); // avoid infinite recursion when re-substituting the wildcards
512 /** Default interface of nth derivative ex::diff(s, n). It should be called
513 * instead of ::derivative(s) for first derivatives and for nth derivatives it
514 * just recurses down.
516 * @param s symbol to differentiate in
517 * @param nth order of differentiation
519 ex basic::diff(const symbol & s, unsigned nth) const
521 // trivial: zeroth derivative
525 // evaluate unevaluated *this before differentiating
526 if (!(flags & status_flags::evaluated))
527 return ex(*this).diff(s, nth);
529 ex ndiff = this->derivative(s);
530 while (!ndiff.is_zero() && // stop differentiating zeros
532 ndiff = ndiff.diff(s);
538 /** Return a vector containing the free indices of an expression. */
539 exvector basic::get_free_indices(void) const
541 return exvector(); // return an empty exvector
544 ex basic::simplify_ncmul(const exvector & v) const
546 return simplified_ncmul(v);
551 /** Default implementation of ex::diff(). It simply throws an error message.
553 * @exception logic_error (differentiation not supported by this type)
555 ex basic::derivative(const symbol & s) const
557 throw(std::logic_error("differentiation not supported by this type"));
560 /** Returns order relation between two objects of same type. This needs to be
561 * implemented by each class. It may never return anything else than 0,
562 * signalling equality, or +1 and -1 signalling inequality and determining
563 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
564 * the spaceship operator <=> for denoting just this.) */
565 int basic::compare_same_type(const basic & other) const
567 return compare_pointers(this, &other);
570 /** Returns true if two objects of same type are equal. Normally needs
571 * not be reimplemented as long as it wasn't overwritten by some parent
572 * class, since it just calls compare_same_type(). The reason why this
573 * function exists is that sometimes it is easier to determine equality
574 * than an order relation and then it can be overridden. */
575 bool basic::is_equal_same_type(const basic & other) const
577 return this->compare_same_type(other)==0;
580 unsigned basic::return_type(void) const
582 return return_types::commutative;
585 unsigned basic::return_type_tinfo(void) const
590 /** Compute the hash value of an object and if it makes sense to store it in
591 * the objects status_flags, do so. The method inherited from class basic
592 * computes a hash value based on the type and hash values of possible
593 * members. For this reason it is well suited for container classes but
594 * atomic classes should override this implementation because otherwise they
595 * would all end up with the same hashvalue. */
596 unsigned basic::calchash(void) const
598 unsigned v = golden_ratio_hash(tinfo());
599 for (unsigned i=0; i<nops(); i++) {
600 v = rotate_left_31(v);
601 v ^= (const_cast<basic *>(this))->op(i).gethash();
604 // mask out numeric hashes:
607 // store calculated hash value only if object is already evaluated
608 if (flags & status_flags::evaluated) {
609 setflag(status_flags::hash_calculated);
616 /** Expand expression, i.e. multiply it out and return the result as a new
618 ex basic::expand(unsigned options) const
620 return this->setflag(status_flags::expanded);
625 // non-virtual functions in this class
630 /** Substitute objects in an expression (syntactic substitution) and return
631 * the result as a new expression. There are two valid types of
632 * replacement arguments: 1) a relational like object==ex and 2) a list of
633 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
634 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
635 ex basic::subs(const ex & e, bool no_pattern) const
637 if (e.info(info_flags::relation_equal)) {
638 return subs(lst(e), no_pattern);
640 if (!e.info(info_flags::list)) {
641 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
645 for (unsigned i=0; i<e.nops(); i++) {
647 if (!r.info(info_flags::relation_equal)) {
648 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
653 return subs(ls, lr, no_pattern);
656 /** Compare objects to establish canonical ordering.
657 * All compare functions return: -1 for *this less than other, 0 equal,
659 int basic::compare(const basic & other) const
661 unsigned hash_this = gethash();
662 unsigned hash_other = other.gethash();
664 if (hash_this<hash_other) return -1;
665 if (hash_this>hash_other) return 1;
667 unsigned typeid_this = tinfo();
668 unsigned typeid_other = other.tinfo();
670 if (typeid_this<typeid_other) {
671 // std::cout << "hash collision, different types: "
672 // << *this << " and " << other << std::endl;
673 // this->print(print_tree(std::cout));
674 // std::cout << " and ";
675 // other.print(print_tree(std::cout));
676 // std::cout << std::endl;
679 if (typeid_this>typeid_other) {
680 // std::cout << "hash collision, different types: "
681 // << *this << " and " << other << std::endl;
682 // this->print(print_tree(std::cout));
683 // std::cout << " and ";
684 // other.print(print_tree(std::cout));
685 // std::cout << std::endl;
689 GINAC_ASSERT(typeid(*this)==typeid(other));
691 // int cmpval = compare_same_type(other);
692 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
693 // std::cout << "hash collision, same type: "
694 // << *this << " and " << other << std::endl;
695 // this->print(print_tree(std::cout));
696 // std::cout << " and ";
697 // other.print(print_tree(std::cout));
698 // std::cout << std::endl;
702 return compare_same_type(other);
705 /** Test for equality.
706 * This is only a quick test, meaning objects should be in the same domain.
707 * You might have to .expand(), .normal() objects first, depending on the
708 * domain of your computation, to get a more reliable answer.
710 * @see is_equal_same_type */
711 bool basic::is_equal(const basic & other) const
713 if (this->gethash()!=other.gethash())
715 if (this->tinfo()!=other.tinfo())
718 GINAC_ASSERT(typeid(*this)==typeid(other));
720 return this->is_equal_same_type(other);
725 /** Stop further evaluation.
727 * @see basic::eval */
728 const basic & basic::hold(void) const
730 return this->setflag(status_flags::evaluated);
733 /** Ensure the object may be modified without hurting others, throws if this
734 * is not the case. */
735 void basic::ensure_if_modifiable(void) const
737 if (this->refcount>1)
738 throw(std::runtime_error("cannot modify multiply referenced object"));
739 clearflag(status_flags::hash_calculated);
746 int max_recursion_level = 1024;