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)
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. */
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
369 unsigned num = nops();
373 return map(GiNaC::evalm);
376 /** Perform automatic symbolic evaluations on indexed expression that
377 * contains this object as the base expression. */
378 ex basic::eval_indexed(const basic & i) const
379 // this function can't take a "const ex & i" because that would result
380 // in an infinite eval() loop
382 // There is nothing to do for basic objects
386 /** Add two indexed expressions. They are guaranteed to be of class indexed
387 * (or a subclass) and their indices are compatible. This function is used
388 * internally by simplify_indexed().
390 * @param self First indexed expression; it's base object is *this
391 * @param other Second indexed expression
392 * @return sum of self and other
393 * @see ex::simplify_indexed() */
394 ex basic::add_indexed(const ex & self, const ex & other) const
399 /** Multiply an indexed expression with a scalar. This function is used
400 * internally by simplify_indexed().
402 * @param self Indexed expression; it's base object is *this
403 * @param other Numeric value
404 * @return product of self and other
405 * @see ex::simplify_indexed() */
406 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
411 /** Try to contract two indexed expressions that appear in the same product.
412 * If a contraction exists, the function overwrites one or both of the
413 * expressions and returns true. Otherwise it returns false. It is
414 * guaranteed that both expressions are of class indexed (or a subclass)
415 * and that at least one dummy index has been found. This functions is
416 * used internally by simplify_indexed().
418 * @param self Pointer to first indexed expression; it's base object is *this
419 * @param other Pointer to second indexed expression
420 * @param v The complete vector of factors
421 * @return true if the contraction was successful, false otherwise
422 * @see ex::simplify_indexed() */
423 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
429 /** Check whether the expression matches a given pattern. For every wildcard
430 * object in the pattern, an expression of the form "wildcard == matching_expression"
431 * is added to repl_lst. */
432 bool basic::match(const ex & pattern, lst & repl_lst) const
435 Sweet sweet shapes, sweet sweet shapes,
436 Thats the key thing, right right.
437 Feed feed face, feed feed shapes,
438 But who is the king tonight?
439 Who is the king tonight?
440 Pattern is the thing, the key thing-a-ling,
441 But who is the king of pattern?
442 But who is the king, the king thing-a-ling,
443 Who is the king of Pattern?
444 Bog is the king, the king thing-a-ling,
445 Bog is the king of Pattern.
446 Ba bu-bu-bu-bu bu-bu-bu-bu-bu-bu bu-bu
447 Bog is the king of Pattern.
450 if (is_ex_exactly_of_type(pattern, wildcard)) {
452 // Wildcard matches anything, but check whether we already have found
453 // a match for that wildcard first (if so, it the earlier match must
454 // be the same expression)
455 for (unsigned i=0; i<repl_lst.nops(); i++) {
456 if (repl_lst.op(i).op(0).is_equal(pattern))
457 return is_equal(*repl_lst.op(i).op(1).bp);
459 repl_lst.append(pattern == *this);
464 // Expression must be of the same type as the pattern
465 if (tinfo() != pattern.bp->tinfo())
468 // Number of subexpressions must match
469 if (nops() != pattern.nops())
472 // No subexpressions? Then just compare the objects (there can't be
473 // wildcards in the pattern)
475 return is_equal(*pattern.bp);
477 // Otherwise the subexpressions must match one-to-one
478 for (unsigned i=0; i<nops(); i++)
479 if (!op(i).match(pattern.op(i), repl_lst))
482 // Looks similar enough, match found
487 /** Substitute a set of objects by arbitrary expressions. The ex returned
488 * will already be evaluated. */
489 ex basic::subs(const lst & ls, const lst & lr, bool no_pattern) const
491 GINAC_ASSERT(ls.nops() == lr.nops());
494 for (unsigned i=0; i<ls.nops(); i++) {
495 if (is_equal(*ls.op(i).bp))
499 for (unsigned i=0; i<ls.nops(); i++) {
501 if (match(*ls.op(i).bp, repl_lst))
502 return lr.op(i).bp->subs(repl_lst, true); // avoid infinite recursion when re-substituting the wildcards
509 /** Default interface of nth derivative ex::diff(s, n). It should be called
510 * instead of ::derivative(s) for first derivatives and for nth derivatives it
511 * just recurses down.
513 * @param s symbol to differentiate in
514 * @param nth order of differentiation
516 ex basic::diff(const symbol & s, unsigned nth) const
518 // trivial: zeroth derivative
522 // evaluate unevaluated *this before differentiating
523 if (!(flags & status_flags::evaluated))
524 return ex(*this).diff(s, nth);
526 ex ndiff = this->derivative(s);
527 while (!ndiff.is_zero() && // stop differentiating zeros
529 ndiff = ndiff.diff(s);
535 /** Return a vector containing the free indices of an expression. */
536 exvector basic::get_free_indices(void) const
538 return exvector(); // return an empty exvector
541 ex basic::simplify_ncmul(const exvector & v) const
543 return simplified_ncmul(v);
548 /** Default implementation of ex::diff(). It simply throws an error message.
550 * @exception logic_error (differentiation not supported by this type)
552 ex basic::derivative(const symbol & s) const
554 throw(std::logic_error("differentiation not supported by this type"));
557 /** Returns order relation between two objects of same type. This needs to be
558 * implemented by each class. It may never return anything else than 0,
559 * signalling equality, or +1 and -1 signalling inequality and determining
560 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
561 * the spaceship operator <=> for denoting just this.) */
562 int basic::compare_same_type(const basic & other) const
564 return compare_pointers(this, &other);
567 /** Returns true if two objects of same type are equal. Normally needs
568 * not be reimplemented as long as it wasn't overwritten by some parent
569 * class, since it just calls compare_same_type(). The reason why this
570 * function exists is that sometimes it is easier to determine equality
571 * than an order relation and then it can be overridden. */
572 bool basic::is_equal_same_type(const basic & other) const
574 return this->compare_same_type(other)==0;
577 unsigned basic::return_type(void) const
579 return return_types::commutative;
582 unsigned basic::return_type_tinfo(void) const
587 /** Compute the hash value of an object and if it makes sense to store it in
588 * the objects status_flags, do so. The method inherited from class basic
589 * computes a hash value based on the type and hash values of possible
590 * members. For this reason it is well suited for container classes but
591 * atomic classes should override this implementation because otherwise they
592 * would all end up with the same hashvalue. */
593 unsigned basic::calchash(void) const
595 unsigned v = golden_ratio_hash(tinfo());
596 for (unsigned i=0; i<nops(); i++) {
597 v = rotate_left_31(v);
598 v ^= (const_cast<basic *>(this))->op(i).gethash();
601 // mask out numeric hashes:
604 // store calculated hash value only if object is already evaluated
605 if (flags & status_flags::evaluated) {
606 setflag(status_flags::hash_calculated);
613 /** Expand expression, i.e. multiply it out and return the result as a new
615 ex basic::expand(unsigned options) const
617 return this->setflag(status_flags::expanded);
622 // non-virtual functions in this class
627 /** Substitute objects in an expression (syntactic substitution) and return
628 * the result as a new expression. There are two valid types of
629 * replacement arguments: 1) a relational like object==ex and 2) a list of
630 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
631 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
632 ex basic::subs(const ex & e, bool no_pattern) const
634 if (e.info(info_flags::relation_equal)) {
635 return subs(lst(e), no_pattern);
637 if (!e.info(info_flags::list)) {
638 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
642 for (unsigned i=0; i<e.nops(); i++) {
644 if (!r.info(info_flags::relation_equal)) {
645 throw(std::invalid_argument("basic::subs(ex): argument must be a list of equations"));
650 return subs(ls, lr, no_pattern);
653 /** Compare objects to establish canonical ordering.
654 * All compare functions return: -1 for *this less than other, 0 equal,
656 int basic::compare(const basic & other) const
658 unsigned hash_this = gethash();
659 unsigned hash_other = other.gethash();
661 if (hash_this<hash_other) return -1;
662 if (hash_this>hash_other) return 1;
664 unsigned typeid_this = tinfo();
665 unsigned typeid_other = other.tinfo();
667 if (typeid_this<typeid_other) {
668 // std::cout << "hash collision, different types: "
669 // << *this << " and " << other << std::endl;
670 // this->print(print_tree(std::cout));
671 // std::cout << " and ";
672 // other.print(print_tree(std::cout));
673 // std::cout << std::endl;
676 if (typeid_this>typeid_other) {
677 // std::cout << "hash collision, different types: "
678 // << *this << " and " << other << std::endl;
679 // this->print(print_tree(std::cout));
680 // std::cout << " and ";
681 // other.print(print_tree(std::cout));
682 // std::cout << std::endl;
686 GINAC_ASSERT(typeid(*this)==typeid(other));
688 // int cmpval = compare_same_type(other);
689 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
690 // std::cout << "hash collision, same type: "
691 // << *this << " and " << other << std::endl;
692 // this->print(print_tree(std::cout));
693 // std::cout << " and ";
694 // other.print(print_tree(std::cout));
695 // std::cout << std::endl;
699 return compare_same_type(other);
702 /** Test for equality.
703 * This is only a quick test, meaning objects should be in the same domain.
704 * You might have to .expand(), .normal() objects first, depending on the
705 * domain of your computation, to get a more reliable answer.
707 * @see is_equal_same_type */
708 bool basic::is_equal(const basic & other) const
710 if (this->gethash()!=other.gethash())
712 if (this->tinfo()!=other.tinfo())
715 GINAC_ASSERT(typeid(*this)==typeid(other));
717 return this->is_equal_same_type(other);
722 /** Stop further evaluation.
724 * @see basic::eval */
725 const basic & basic::hold(void) const
727 return this->setflag(status_flags::evaluated);
730 /** Ensure the object may be modified without hurting others, throws if this
731 * is not the case. */
732 void basic::ensure_if_modifiable(void) const
734 if (this->refcount>1)
735 throw(std::runtime_error("cannot modify multiply referenced object"));
742 int max_recursion_level = 1024;