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_func 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 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 /** Evaluate sums and products of matrices. */
367 ex basic::evalm(void) const
372 return map(GiNaC::evalm);
375 /** Perform automatic symbolic evaluations on indexed expression that
376 * contains this object as the base expression. */
377 ex basic::eval_indexed(const basic & i) const
378 // this function can't take a "const ex & i" because that would result
379 // in an infinite eval() loop
381 // There is nothing to do for basic objects
385 /** Add two indexed expressions. They are guaranteed to be of class indexed
386 * (or a subclass) and their indices are compatible. This function is used
387 * internally by simplify_indexed().
389 * @param self First indexed expression; it's base object is *this
390 * @param other Second indexed expression
391 * @return sum of self and other
392 * @see ex::simplify_indexed() */
393 ex basic::add_indexed(const ex & self, const ex & other) const
398 /** Multiply an indexed expression with a scalar. This function is used
399 * internally by simplify_indexed().
401 * @param self Indexed expression; it's base object is *this
402 * @param other Numeric value
403 * @return product of self and other
404 * @see ex::simplify_indexed() */
405 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
410 /** Try to contract two indexed expressions that appear in the same product.
411 * If a contraction exists, the function overwrites one or both of the
412 * expressions and returns true. Otherwise it returns false. It is
413 * guaranteed that both expressions are of class indexed (or a subclass)
414 * and that at least one dummy index has been found. This functions is
415 * used internally by simplify_indexed().
417 * @param self Pointer to first indexed expression; it's base object is *this
418 * @param other Pointer to second indexed expression
419 * @param v The complete vector of factors
420 * @return true if the contraction was successful, false otherwise
421 * @see ex::simplify_indexed() */
422 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
428 /** Check whether the expression matches a given pattern. For every wildcard
429 * object in the pattern, an expression of the form "wildcard == matching_expression"
430 * is added to repl_lst. */
431 bool basic::match(const ex & pattern, lst & repl_lst) const
434 Sweet sweet shapes, sweet sweet shapes,
435 That's the key thing, right right.
436 Feed feed face, feed feed shapes,
437 But who is the king tonight?
438 Who is the king tonight?
439 Pattern is the thing, the key thing-a-ling,
440 But who is the king of pattern?
441 But who is the king, the king thing-a-ling,
442 Who is the king of Pattern?
443 Bog is the king, the king thing-a-ling,
444 Bog is the king of Pattern.
445 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
446 Bog is the king of Pattern.
449 if (is_ex_exactly_of_type(pattern, wildcard)) {
451 // Wildcard matches anything, but check whether we already have found
452 // a match for that wildcard first (if so, it the earlier match must
453 // be the same expression)
454 for (unsigned i=0; i<repl_lst.nops(); i++) {
455 if (repl_lst.op(i).op(0).is_equal(pattern))
456 return is_equal(*repl_lst.op(i).op(1).bp);
458 repl_lst.append(pattern == *this);
463 // Expression must be of the same type as the pattern
464 if (tinfo() != pattern.bp->tinfo())
467 // Number of subexpressions must match
468 if (nops() != pattern.nops())
471 // No subexpressions? Then just compare the objects (there can't be
472 // wildcards in the pattern)
474 return is_equal(*pattern.bp);
476 // Otherwise the subexpressions must match one-to-one
477 for (unsigned i=0; i<nops(); i++)
478 if (!op(i).match(pattern.op(i), repl_lst))
481 // Looks similar enough, match found
486 /** Substitute a set of objects by arbitrary expressions. The ex returned
487 * will already be evaluated. */
488 ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
490 GINAC_ASSERT(ls.nops() == lr.nops());
493 for (unsigned i=0; i<ls.nops(); i++) {
494 if (is_equal(*ls.op(i).bp))
498 for (unsigned i=0; i<ls.nops(); i++) {
500 if (match(*ls.op(i).bp, repl_lst))
501 return lr.op(i).bp->subs(repl_lst, true); // avoid infinite recursion when re-substituting the wildcards
508 /** Default interface of nth derivative ex::diff(s, n). It should be called
509 * instead of ::derivative(s) for first derivatives and for nth derivatives it
510 * just recurses down.
512 * @param s symbol to differentiate in
513 * @param nth order of differentiation
515 ex basic::diff(const symbol & s, unsigned nth) const
517 // trivial: zeroth derivative
521 // evaluate unevaluated *this before differentiating
522 if (!(flags & status_flags::evaluated))
523 return ex(*this).diff(s, nth);
525 ex ndiff = this->derivative(s);
526 while (!ndiff.is_zero() && // stop differentiating zeros
528 ndiff = ndiff.diff(s);
534 /** Return a vector containing the free indices of an expression. */
535 exvector basic::get_free_indices(void) const
537 return exvector(); // return an empty exvector
540 ex basic::simplify_ncmul(const exvector & v) const
542 return simplified_ncmul(v);
547 /** Default implementation of ex::diff(). It simply throws an error message.
549 * @exception logic_error (differentiation not supported by this type)
551 ex basic::derivative(const symbol & s) const
553 throw(std::logic_error("differentiation not supported by this type"));
556 /** Returns order relation between two objects of same type. This needs to be
557 * implemented by each class. It may never return anything else than 0,
558 * signalling equality, or +1 and -1 signalling inequality and determining
559 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
560 * the spaceship operator <=> for denoting just this.) */
561 int basic::compare_same_type(const basic & other) const
563 return compare_pointers(this, &other);
566 /** Returns true if two objects of same type are equal. Normally needs
567 * not be reimplemented as long as it wasn't overwritten by some parent
568 * class, since it just calls compare_same_type(). The reason why this
569 * function exists is that sometimes it is easier to determine equality
570 * than an order relation and then it can be overridden. */
571 bool basic::is_equal_same_type(const basic & other) const
573 return this->compare_same_type(other)==0;
576 unsigned basic::return_type(void) const
578 return return_types::commutative;
581 unsigned basic::return_type_tinfo(void) const
586 /** Compute the hash value of an object and if it makes sense to store it in
587 * the objects status_flags, do so. The method inherited from class basic
588 * computes a hash value based on the type and hash values of possible
589 * members. For this reason it is well suited for container classes but
590 * atomic classes should override this implementation because otherwise they
591 * would all end up with the same hashvalue. */
592 unsigned basic::calchash(void) const
594 unsigned v = golden_ratio_hash(tinfo());
595 for (unsigned i=0; i<nops(); i++) {
596 v = rotate_left_31(v);
597 v ^= (const_cast<basic *>(this))->op(i).gethash();
600 // mask out numeric hashes:
603 // store calculated hash value only if object is already evaluated
604 if (flags & status_flags::evaluated) {
605 setflag(status_flags::hash_calculated);
612 /** Expand expression, i.e. multiply it out and return the result as a new
614 ex basic::expand(unsigned options) const
616 return this->setflag(status_flags::expanded);
621 // non-virtual functions in this class
626 /** Substitute objects in an expression (syntactic substitution) and return
627 * the result as a new expression. There are two valid types of
628 * replacement arguments: 1) a relational like object==ex and 2) a list of
629 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
630 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
631 ex basic::subs(const ex & e, bool no_pattern) const
633 if (e.info(info_flags::relation_equal)) {
634 return subs(lst(e), no_pattern);
636 if (!e.info(info_flags::list)) {
637 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
641 for (unsigned i=0; i<e.nops(); i++) {
643 if (!r.info(info_flags::relation_equal)) {
644 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
649 return subs(ls, lr, no_pattern);
652 /** Compare objects to establish canonical ordering.
653 * All compare functions return: -1 for *this less than other, 0 equal,
655 int basic::compare(const basic & other) const
657 unsigned hash_this = gethash();
658 unsigned hash_other = other.gethash();
660 if (hash_this<hash_other) return -1;
661 if (hash_this>hash_other) return 1;
663 unsigned typeid_this = tinfo();
664 unsigned typeid_other = other.tinfo();
666 if (typeid_this<typeid_other) {
667 // std::cout << "hash collision, different types: "
668 // << *this << " and " << other << std::endl;
669 // this->print(print_tree(std::cout));
670 // std::cout << " and ";
671 // other.print(print_tree(std::cout));
672 // std::cout << std::endl;
675 if (typeid_this>typeid_other) {
676 // std::cout << "hash collision, different types: "
677 // << *this << " and " << other << std::endl;
678 // this->print(print_tree(std::cout));
679 // std::cout << " and ";
680 // other.print(print_tree(std::cout));
681 // std::cout << std::endl;
685 GINAC_ASSERT(typeid(*this)==typeid(other));
687 // int cmpval = compare_same_type(other);
688 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
689 // std::cout << "hash collision, same type: "
690 // << *this << " and " << other << std::endl;
691 // this->print(print_tree(std::cout));
692 // std::cout << " and ";
693 // other.print(print_tree(std::cout));
694 // std::cout << std::endl;
698 return compare_same_type(other);
701 /** Test for equality.
702 * This is only a quick test, meaning objects should be in the same domain.
703 * You might have to .expand(), .normal() objects first, depending on the
704 * domain of your computation, to get a more reliable answer.
706 * @see is_equal_same_type */
707 bool basic::is_equal(const basic & other) const
709 if (this->gethash()!=other.gethash())
711 if (this->tinfo()!=other.tinfo())
714 GINAC_ASSERT(typeid(*this)==typeid(other));
716 return this->is_equal_same_type(other);
721 /** Stop further evaluation.
723 * @see basic::eval */
724 const basic & basic::hold(void) const
726 return this->setflag(status_flags::evaluated);
729 /** Ensure the object may be modified without hurting others, throws if this
730 * is not the case. */
731 void basic::ensure_if_modifiable(void) const
733 if (this->refcount>1)
734 throw(std::runtime_error("cannot modify multiply referenced object"));
741 int max_recursion_level = 1024;