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 arount 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 arount 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)
220 bool basic::has(const ex & other) const
222 GINAC_ASSERT(other.bp!=0);
224 if (match(*other.bp, repl_lst)) return true;
226 for (unsigned i=0; i<nops(); i++)
227 if (op(i).has(other))
234 /** Return degree of highest power in object s. */
235 int basic::degree(const ex & s) const
240 /** Return degree of lowest power in object s. */
241 int basic::ldegree(const ex & s) const
246 /** Return coefficient of degree n in object s. */
247 ex basic::coeff(const ex & s, int n) const
249 return n==0 ? *this : _ex0();
252 /** Sort expression in terms of powers of some object(s).
253 * @param s object(s) to sort in
254 * @param distributed recursive or distributed form (only used when s is a list) */
255 ex basic::collect(const ex & s, bool distributed) const
258 if (is_ex_of_type(s, lst)) {
260 // List of objects specified
262 return collect(s.op(0));
264 else if (distributed) {
266 // Get lower/upper degree of all symbols in list
271 int cnt; // current degree, 'counter'
272 ex coeff; // coefficient for degree 'cnt'
274 sym_info *si = new sym_info[num];
276 for (int i=0; i<num; i++) {
278 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
279 si[i].deg = this->degree(si[i].sym);
280 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
285 // Calculate coeff*x1^c1*...*xn^cn
287 for (int i=0; i<num; i++) {
289 y *= power(si[i].sym, cnt);
291 x += y * si[num - 1].coeff;
293 // Increment counters
297 if (si[n].cnt <= si[n].deg) {
298 // Update coefficients
304 for (int i=n; i<num; i++)
305 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
310 si[n].cnt = si[n].ldeg;
321 for (int n=s.nops()-1; n>=0; n--)
327 // Only one object specified
328 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
329 x += this->coeff(s,n)*power(s,n);
332 // correct for lost fractional arguments and return
333 return x + (*this - x).expand();
336 /** Perform automatic non-interruptive symbolic evaluation on expression. */
337 ex basic::eval(int level) const
339 // There is nothing to do for basic objects:
343 /** Evaluate object numerically. */
344 ex basic::evalf(int level) const
346 // There is nothing to do for basic objects:
350 /** Perform automatic symbolic evaluations on indexed expression that
351 * contains this object as the base expression. */
352 ex basic::eval_indexed(const basic & i) const
353 // this function can't take a "const ex & i" because that would result
354 // in an infinite eval() loop
356 // There is nothing to do for basic objects
360 /** Add two indexed expressions. They are guaranteed to be of class indexed
361 * (or a subclass) and their indices are compatible. This function is used
362 * internally by simplify_indexed().
364 * @param self First indexed expression; it's base object is *this
365 * @param other Second indexed expression
366 * @return sum of self and other
367 * @see ex::simplify_indexed() */
368 ex basic::add_indexed(const ex & self, const ex & other) const
373 /** Multiply an indexed expression with a scalar. This function is used
374 * internally by simplify_indexed().
376 * @param self Indexed expression; it's base object is *this
377 * @param other Numeric value
378 * @return product of self and other
379 * @see ex::simplify_indexed() */
380 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
385 /** Try to contract two indexed expressions that appear in the same product.
386 * If a contraction exists, the function overwrites one or both of the
387 * expressions and returns true. Otherwise it returns false. It is
388 * guaranteed that both expressions are of class indexed (or a subclass)
389 * and that at least one dummy index has been found. This functions is
390 * used internally by simplify_indexed().
392 * @param self Pointer to first indexed expression; it's base object is *this
393 * @param other Pointer to second indexed expression
394 * @param v The complete vector of factors
395 * @return true if the contraction was successful, false otherwise
396 * @see ex::simplify_indexed() */
397 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
403 /** Check whether the expression matches a given pattern. For every wildcard
404 * object in the pattern, an expression of the form "wildcard == matching_expression"
405 * is added to repl_lst. */
406 bool basic::match(const ex & pattern, lst & repl_lst) const
408 //clog << "match " << *this << " with " << pattern << ", repl_lst = " << repl_lst << endl;
409 if (is_ex_exactly_of_type(pattern, wildcard)) {
411 // Wildcard matches anything, but check whether we already have found
412 // a match for that wildcard first (if so, it the earlier match must
413 // be the same expression)
414 for (unsigned i=0; i<repl_lst.nops(); i++) {
415 if (repl_lst.op(i).op(0).is_equal(pattern))
416 return is_equal(*repl_lst.op(i).op(1).bp);
418 repl_lst.append(pattern == *this);
423 // Expression must be of the same type as the pattern
424 if (tinfo() != pattern.bp->tinfo())
427 // Number of subexpressions must match
428 if (nops() != pattern.nops())
431 // No subexpressions? Then just compare the objects (there can't be
432 // wildcards in the pattern)
434 return is_equal(*pattern.bp);
436 // Otherwise the subexpressions must match one-to-one
437 for (unsigned i=0; i<nops(); i++)
438 if (!op(i).match(pattern.op(i), repl_lst))
441 // Looks similar enough, match found
446 /** Substitute a set of objects by arbitrary expressions. The ex returned
447 * will already be evaluated. */
448 ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
450 GINAC_ASSERT(ls.nops() == lr.nops());
453 for (unsigned i=0; i<ls.nops(); i++) {
454 if (is_equal(*ls.op(i).bp))
458 for (unsigned i=0; i<ls.nops(); i++) {
460 if (match(*ls.op(i).bp, repl_lst))
461 return lr.op(i).bp->subs(repl_lst, true); // avoid recursion when re-substituting the wildcards
468 /** Default interface of nth derivative ex::diff(s, n). It should be called
469 * instead of ::derivative(s) for first derivatives and for nth derivatives it
470 * just recurses down.
472 * @param s symbol to differentiate in
473 * @param nth order of differentiation
475 ex basic::diff(const symbol & s, unsigned nth) const
477 // trivial: zeroth derivative
481 // evaluate unevaluated *this before differentiating
482 if (!(flags & status_flags::evaluated))
483 return ex(*this).diff(s, nth);
485 ex ndiff = this->derivative(s);
486 while (!ndiff.is_zero() && // stop differentiating zeros
488 ndiff = ndiff.diff(s);
494 /** Return a vector containing the free indices of an expression. */
495 exvector basic::get_free_indices(void) const
497 return exvector(); // return an empty exvector
500 ex basic::simplify_ncmul(const exvector & v) const
502 return simplified_ncmul(v);
507 /** Default implementation of ex::diff(). It simply throws an error message.
509 * @exception logic_error (differentiation not supported by this type)
511 ex basic::derivative(const symbol & s) const
513 throw(std::logic_error("differentiation not supported by this type"));
516 /** Returns order relation between two objects of same type. This needs to be
517 * implemented by each class. It may never return anything else than 0,
518 * signalling equality, or +1 and -1 signalling inequality and determining
519 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
520 * the spaceship operator <=> for denoting just this.) */
521 int basic::compare_same_type(const basic & other) const
523 return compare_pointers(this, &other);
526 /** Returns true if two objects of same type are equal. Normally needs
527 * not be reimplemented as long as it wasn't overwritten by some parent
528 * class, since it just calls compare_same_type(). The reason why this
529 * function exists is that sometimes it is easier to determine equality
530 * than an order relation and then it can be overridden. */
531 bool basic::is_equal_same_type(const basic & other) const
533 return this->compare_same_type(other)==0;
536 unsigned basic::return_type(void) const
538 return return_types::commutative;
541 unsigned basic::return_type_tinfo(void) const
546 /** Compute the hash value of an object and if it makes sense to store it in
547 * the objects status_flags, do so. The method inherited from class basic
548 * computes a hash value based on the type and hash values of possible
549 * members. For this reason it is well suited for container classes but
550 * atomic classes should override this implementation because otherwise they
551 * would all end up with the same hashvalue. */
552 unsigned basic::calchash(void) const
554 unsigned v = golden_ratio_hash(tinfo());
555 for (unsigned i=0; i<nops(); i++) {
556 v = rotate_left_31(v);
557 v ^= (const_cast<basic *>(this))->op(i).gethash();
560 // mask out numeric hashes:
563 // store calculated hash value only if object is already evaluated
564 if (flags & status_flags::evaluated) {
565 setflag(status_flags::hash_calculated);
572 /** Expand expression, i.e. multiply it out and return the result as a new
574 ex basic::expand(unsigned options) const
576 return this->setflag(status_flags::expanded);
581 // non-virtual functions in this class
586 /** Substitute objects in an expression (syntactic substitution) and return
587 * the result as a new expression. There are two valid types of
588 * replacement arguments: 1) a relational like object==ex and 2) a list of
589 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
590 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
591 ex basic::subs(const ex & e, bool no_pattern) const
593 if (e.info(info_flags::relation_equal)) {
594 return subs(lst(e), no_pattern);
596 if (!e.info(info_flags::list)) {
597 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
601 for (unsigned i=0; i<e.nops(); i++) {
603 if (!r.info(info_flags::relation_equal)) {
604 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
609 return subs(ls, lr, no_pattern);
612 /** Compare objects to establish canonical ordering.
613 * All compare functions return: -1 for *this less than other, 0 equal,
615 int basic::compare(const basic & other) const
617 unsigned hash_this = gethash();
618 unsigned hash_other = other.gethash();
620 if (hash_this<hash_other) return -1;
621 if (hash_this>hash_other) return 1;
623 unsigned typeid_this = tinfo();
624 unsigned typeid_other = other.tinfo();
626 if (typeid_this<typeid_other) {
627 // std::cout << "hash collision, different types: "
628 // << *this << " and " << other << std::endl;
629 // this->print(print_tree(std::cout));
630 // std::cout << " and ";
631 // other.print(print_tree(std::cout));
632 // std::cout << std::endl;
635 if (typeid_this>typeid_other) {
636 // std::cout << "hash collision, different types: "
637 // << *this << " and " << other << std::endl;
638 // this->print(print_tree(std::cout));
639 // std::cout << " and ";
640 // other.print(print_tree(std::cout));
641 // std::cout << std::endl;
645 GINAC_ASSERT(typeid(*this)==typeid(other));
647 // int cmpval = compare_same_type(other);
648 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
649 // std::cout << "hash collision, same type: "
650 // << *this << " and " << other << std::endl;
651 // this->print(print_tree(std::cout));
652 // std::cout << " and ";
653 // other.print(print_tree(std::cout));
654 // std::cout << std::endl;
658 return compare_same_type(other);
661 /** Test for equality.
662 * This is only a quick test, meaning objects should be in the same domain.
663 * You might have to .expand(), .normal() objects first, depending on the
664 * domain of your computation, to get a more reliable answer.
666 * @see is_equal_same_type */
667 bool basic::is_equal(const basic & other) const
669 if (this->gethash()!=other.gethash())
671 if (this->tinfo()!=other.tinfo())
674 GINAC_ASSERT(typeid(*this)==typeid(other));
676 return this->is_equal_same_type(other);
681 /** Stop further evaluation.
683 * @see basic::eval */
684 const basic & basic::hold(void) const
686 return this->setflag(status_flags::evaluated);
689 /** Ensure the object may be modified without hurting others, throws if this
690 * is not the case. */
691 void basic::ensure_if_modifiable(void) const
693 if (this->refcount>1)
694 throw(std::runtime_error("cannot modify multiply referenced object"));
701 int max_recursion_level = 1024;