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
43 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(basic, void)
46 // default ctor, dtor, copy ctor assignment operator and helpers
51 basic::basic(const basic & other) : tinfo_key(TINFO_basic), flags(0), refcount(0)
53 debugmsg("basic copy ctor", LOGLEVEL_CONSTRUCT);
57 const basic & basic::operator=(const basic & other)
59 debugmsg("basic operator=", LOGLEVEL_ASSIGNMENT);
69 // none (all conditionally inlined)
75 // none (all conditionally inlined)
81 /** Construct object from archive_node. */
82 basic::basic(const archive_node &n, const lst &sym_lst) : flags(0), refcount(0)
84 debugmsg("basic ctor from archive_node", LOGLEVEL_CONSTRUCT);
86 // Reconstruct tinfo_key from class name
87 std::string class_name;
88 if (n.find_string("class", class_name))
89 tinfo_key = find_tinfo_key(class_name);
91 throw (std::runtime_error("archive node contains no class name"));
94 /** Unarchive the object. */
95 DEFAULT_UNARCHIVE(basic)
97 /** Archive the object. */
98 void basic::archive(archive_node &n) const
100 n.add_string("class", class_name());
104 // functions overriding virtual functions from bases classes
110 // new virtual functions which can be overridden by derived classes
115 /** Output to stream.
116 * @param c print context object that describes the output formatting
117 * @param level value that is used to identify the precedence or indentation
118 * level for placing parentheses and formatting */
119 void basic::print(const print_context & c, unsigned level) const
121 debugmsg("basic print", LOGLEVEL_PRINT);
123 if (is_of_type(c, print_tree)) {
125 c.s << std::string(level, ' ') << class_name()
126 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
127 << ", nops=" << nops()
129 for (unsigned i=0; i<nops(); ++i)
130 op(i).print(c, level + static_cast<const print_tree &>(c).delta_indent);
133 c.s << "[" << class_name() << " object]";
136 /** Little wrapper arount print to be called within a debugger.
137 * This is needed because you cannot call foo.print(cout) from within the
138 * debugger because it might not know what cout is. This method can be
139 * invoked with no argument and it will simply print to stdout.
141 * @see basic::print */
142 void basic::dbgprint(void) const
144 this->print(std::cerr);
145 std::cerr << std::endl;
148 /** Little wrapper arount printtree to be called within a debugger.
150 * @see basic::dbgprint
151 * @see basic::printtree */
152 void basic::dbgprinttree(void) const
154 this->print(print_tree(std::cerr));
157 /** Create a new copy of this on the heap. One can think of this as simulating
158 * a virtual copy constructor which is needed for instance by the refcounted
159 * construction of an ex from a basic. */
160 basic * basic::duplicate() const
162 debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
163 return new basic(*this);
166 /** Information about the object.
168 * @see class info_flags */
169 bool basic::info(unsigned inf) const
171 // all possible properties are false for basic objects
175 /** Number of operands/members. */
176 unsigned basic::nops() const
178 // iterating from 0 to nops() on atomic objects should be an empty loop,
179 // and accessing their elements is a range error. Container objects should
184 /** Return operand/member at position i. */
185 ex basic::op(int i) const
187 return (const_cast<basic *>(this))->let_op(i);
190 /** Return modifyable operand/member at position i. */
191 ex & basic::let_op(int i)
193 throw(std::out_of_range("op() out of range"));
196 ex basic::operator[](const ex & index) const
198 if (is_exactly_of_type(*index.bp,numeric))
199 return op(static_cast<const numeric &>(*index.bp).to_int());
201 throw(std::invalid_argument("non-numeric indices not supported by this type"));
204 ex basic::operator[](int i) const
209 /** Search ocurrences. An object 'has' an expression if it is the expression
210 * itself or one of the children 'has' it. As a consequence (according to
211 * the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y)
213 bool basic::has(const ex & other) const
215 GINAC_ASSERT(other.bp!=0);
216 if (is_equal(*other.bp)) return true;
218 for (unsigned i=0; i<nops(); i++)
219 if (op(i).has(other))
226 /** Return degree of highest power in object s. */
227 int basic::degree(const ex & s) const
232 /** Return degree of lowest power in object s. */
233 int basic::ldegree(const ex & s) const
238 /** Return coefficient of degree n in object s. */
239 ex basic::coeff(const ex & s, int n) const
241 return n==0 ? *this : _ex0();
244 /** Sort expression in terms of powers of some object(s).
245 * @param s object(s) to sort in
246 * @param distributed recursive or distributed form (only used when s is a list) */
247 ex basic::collect(const ex & s, bool distributed) const
250 if (is_ex_of_type(s, lst)) {
252 // List of objects specified
254 return collect(s.op(0));
256 else if (distributed) {
258 // Get lower/upper degree of all symbols in list
263 int cnt; // current degree, 'counter'
264 ex coeff; // coefficient for degree 'cnt'
266 sym_info *si = new sym_info[num];
268 for (int i=0; i<num; i++) {
270 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
271 si[i].deg = this->degree(si[i].sym);
272 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
277 // Calculate coeff*x1^c1*...*xn^cn
279 for (int i=0; i<num; i++) {
281 y *= power(si[i].sym, cnt);
283 x += y * si[num - 1].coeff;
285 // Increment counters
289 if (si[n].cnt <= si[n].deg) {
290 // Update coefficients
296 for (int i=n; i<num; i++)
297 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
302 si[n].cnt = si[n].ldeg;
313 for (int n=s.nops()-1; n>=0; n--)
319 // Only one object specified
320 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
321 x += this->coeff(s,n)*power(s,n);
324 // correct for lost fractional arguments and return
325 return x + (*this - x).expand();
328 /** Perform automatic non-interruptive symbolic evaluation on expression. */
329 ex basic::eval(int level) const
331 // There is nothing to do for basic objects:
335 /** Evaluate object numerically. */
336 ex basic::evalf(int level) const
338 // There is nothing to do for basic objects:
342 /** Perform automatic symbolic evaluations on indexed expression that
343 * contains this object as the base expression. */
344 ex basic::eval_indexed(const basic & i) const
345 // this function can't take a "const ex & i" because that would result
346 // in an infinite eval() loop
348 // There is nothing to do for basic objects
352 /** Add two indexed expressions. They are guaranteed to be of class indexed
353 * (or a subclass) and their indices are compatible. This function is used
354 * internally by simplify_indexed().
356 * @param self First indexed expression; it's base object is *this
357 * @param other Second indexed expression
358 * @return sum of self and other
359 * @see ex::simplify_indexed() */
360 ex basic::add_indexed(const ex & self, const ex & other) const
365 /** Multiply an indexed expression with a scalar. This function is used
366 * internally by simplify_indexed().
368 * @param self Indexed expression; it's base object is *this
369 * @param other Numeric value
370 * @return product of self and other
371 * @see ex::simplify_indexed() */
372 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
377 /** Try to contract two indexed expressions that appear in the same product.
378 * If a contraction exists, the function overwrites one or both of the
379 * expressions and returns true. Otherwise it returns false. It is
380 * guaranteed that both expressions are of class indexed (or a subclass)
381 * and that at least one dummy index has been found. This functions is
382 * used internally by simplify_indexed().
384 * @param self Pointer to first indexed expression; it's base object is *this
385 * @param other Pointer to second indexed expression
386 * @param v The complete vector of factors
387 * @return true if the contraction was successful, false otherwise
388 * @see ex::simplify_indexed() */
389 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
395 /** Substitute a set of objects by arbitrary expressions. The ex returned
396 * will already be evaluated. */
397 ex basic::subs(const lst & ls, const lst & lr) const
399 GINAC_ASSERT(ls.nops() == lr.nops());
401 for (unsigned i=0; i<ls.nops(); i++) {
402 if (is_equal(*ls.op(i).bp))
409 /** Default interface of nth derivative ex::diff(s, n). It should be called
410 * instead of ::derivative(s) for first derivatives and for nth derivatives it
411 * just recurses down.
413 * @param s symbol to differentiate in
414 * @param nth order of differentiation
416 ex basic::diff(const symbol & s, unsigned nth) const
418 // trivial: zeroth derivative
422 // evaluate unevaluated *this before differentiating
423 if (!(flags & status_flags::evaluated))
424 return ex(*this).diff(s, nth);
426 ex ndiff = this->derivative(s);
427 while (!ndiff.is_zero() && // stop differentiating zeros
429 ndiff = ndiff.diff(s);
435 /** Return a vector containing the free indices of an expression. */
436 exvector basic::get_free_indices(void) const
438 return exvector(); // return an empty exvector
441 ex basic::simplify_ncmul(const exvector & v) const
443 return simplified_ncmul(v);
448 /** Default implementation of ex::diff(). It simply throws an error message.
450 * @exception logic_error (differentiation not supported by this type)
452 ex basic::derivative(const symbol & s) const
454 throw(std::logic_error("differentiation not supported by this type"));
457 /** Returns order relation between two objects of same type. This needs to be
458 * implemented by each class. It may never return anything else than 0,
459 * signalling equality, or +1 and -1 signalling inequality and determining
460 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
461 * the spaceship operator <=> for denoting just this.) */
462 int basic::compare_same_type(const basic & other) const
464 return compare_pointers(this, &other);
467 /** Returns true if two objects of same type are equal. Normally needs
468 * not be reimplemented as long as it wasn't overwritten by some parent
469 * class, since it just calls compare_same_type(). The reason why this
470 * function exists is that sometimes it is easier to determine equality
471 * than an order relation and then it can be overridden. */
472 bool basic::is_equal_same_type(const basic & other) const
474 return this->compare_same_type(other)==0;
477 unsigned basic::return_type(void) const
479 return return_types::commutative;
482 unsigned basic::return_type_tinfo(void) const
487 /** Compute the hash value of an object and if it makes sense to store it in
488 * the objects status_flags, do so. The method inherited from class basic
489 * computes a hash value based on the type and hash values of possible
490 * members. For this reason it is well suited for container classes but
491 * atomic classes should override this implementation because otherwise they
492 * would all end up with the same hashvalue. */
493 unsigned basic::calchash(void) const
495 unsigned v = golden_ratio_hash(tinfo());
496 for (unsigned i=0; i<nops(); i++) {
497 v = rotate_left_31(v);
498 v ^= (const_cast<basic *>(this))->op(i).gethash();
501 // mask out numeric hashes:
504 // store calculated hash value only if object is already evaluated
505 if (flags & status_flags::evaluated) {
506 setflag(status_flags::hash_calculated);
513 /** Expand expression, i.e. multiply it out and return the result as a new
515 ex basic::expand(unsigned options) const
517 return this->setflag(status_flags::expanded);
522 // non-virtual functions in this class
527 /** Substitute objects in an expression (syntactic substitution) and return
528 * the result as a new expression. There are two valid types of
529 * replacement arguments: 1) a relational like object==ex and 2) a list of
530 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
531 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
532 ex basic::subs(const ex & e) const
534 if (e.info(info_flags::relation_equal)) {
537 if (!e.info(info_flags::list)) {
538 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
542 for (unsigned i=0; i<e.nops(); i++) {
544 if (!r.info(info_flags::relation_equal)) {
545 throw(std::invalid_argument("basic::subs(ex): argument must be a list or equations"));
553 /** Compare objects to establish canonical ordering.
554 * All compare functions return: -1 for *this less than other, 0 equal,
556 int basic::compare(const basic & other) const
558 unsigned hash_this = gethash();
559 unsigned hash_other = other.gethash();
561 if (hash_this<hash_other) return -1;
562 if (hash_this>hash_other) return 1;
564 unsigned typeid_this = tinfo();
565 unsigned typeid_other = other.tinfo();
567 if (typeid_this<typeid_other) {
568 // std::cout << "hash collision, different types: "
569 // << *this << " and " << other << std::endl;
570 // this->print(print_tree(std::cout));
571 // std::cout << " and ";
572 // other.print(print_tree(std::cout));
573 // std::cout << std::endl;
576 if (typeid_this>typeid_other) {
577 // std::cout << "hash collision, different types: "
578 // << *this << " and " << other << std::endl;
579 // this->print(print_tree(std::cout));
580 // std::cout << " and ";
581 // other.print(print_tree(std::cout));
582 // std::cout << std::endl;
586 GINAC_ASSERT(typeid(*this)==typeid(other));
588 // int cmpval = compare_same_type(other);
589 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
590 // std::cout << "hash collision, same type: "
591 // << *this << " and " << other << std::endl;
592 // this->print(print_tree(std::cout));
593 // std::cout << " and ";
594 // other.print(print_tree(std::cout));
595 // std::cout << std::endl;
599 return compare_same_type(other);
602 /** Test for equality.
603 * This is only a quick test, meaning objects should be in the same domain.
604 * You might have to .expand(), .normal() objects first, depending on the
605 * domain of your computation, to get a more reliable answer.
607 * @see is_equal_same_type */
608 bool basic::is_equal(const basic & other) const
610 if (this->gethash()!=other.gethash())
612 if (this->tinfo()!=other.tinfo())
615 GINAC_ASSERT(typeid(*this)==typeid(other));
617 return this->is_equal_same_type(other);
622 /** Stop further evaluation.
624 * @see basic::eval */
625 const basic & basic::hold(void) const
627 return this->setflag(status_flags::evaluated);
630 /** Ensure the object may be modified without hurting others, throws if this
631 * is not the case. */
632 void basic::ensure_if_modifiable(void) const
634 if (this->refcount>1)
635 throw(std::runtime_error("cannot modify multiply referenced object"));
639 // static member variables
644 unsigned basic::precedence = 70;
650 int max_recursion_level = 1024;