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
40 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(basic, void)
43 // default ctor, dtor, copy ctor assignment operator and helpers
48 basic::basic(const basic & other) : tinfo_key(TINFO_basic), flags(0), refcount(0)
50 debugmsg("basic copy ctor", LOGLEVEL_CONSTRUCT);
54 const basic & basic::operator=(const basic & other)
56 debugmsg("basic operator=", LOGLEVEL_ASSIGNMENT);
66 // none (all conditionally inlined)
72 // none (all conditionally inlined)
78 /** Construct object from archive_node. */
79 basic::basic(const archive_node &n, const lst &sym_lst) : flags(0), refcount(0)
81 debugmsg("basic ctor from archive_node", LOGLEVEL_CONSTRUCT);
83 // Reconstruct tinfo_key from class name
84 std::string class_name;
85 if (n.find_string("class", class_name))
86 tinfo_key = find_tinfo_key(class_name);
88 throw (std::runtime_error("archive node contains no class name"));
91 /** Unarchive the object. */
92 DEFAULT_UNARCHIVE(basic)
94 /** Archive the object. */
95 void basic::archive(archive_node &n) const
97 n.add_string("class", class_name());
101 // functions overriding virtual functions from bases classes
107 // new virtual functions which can be overridden by derived classes
112 /** Output to stream.
113 * @param c print context object that describes the output formatting
114 * @param level value that is used to identify the precedence or indentation
115 * level for placing parentheses and formatting */
116 void basic::print(const print_context & c, unsigned level) const
118 debugmsg("basic print", LOGLEVEL_PRINT);
120 if (is_of_type(c, print_tree)) {
122 c.s << std::string(level, ' ') << class_name()
123 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
124 << ", nops=" << nops()
126 for (unsigned i=0; i<nops(); ++i)
127 op(i).print(c, level + static_cast<const print_tree &>(c).delta_indent);
130 c.s << "[" << class_name() << " object]";
133 /** Little wrapper arount print to be called within a debugger.
134 * This is needed because you cannot call foo.print(cout) from within the
135 * debugger because it might not know what cout is. This method can be
136 * invoked with no argument and it will simply print to stdout.
138 * @see basic::print */
139 void basic::dbgprint(void) const
141 this->print(std::cerr);
142 std::cerr << std::endl;
145 /** Little wrapper arount printtree to be called within a debugger.
147 * @see basic::dbgprint
148 * @see basic::printtree */
149 void basic::dbgprinttree(void) const
151 this->print(print_tree(std::cerr));
154 /** Create a new copy of this on the heap. One can think of this as simulating
155 * a virtual copy constructor which is needed for instance by the refcounted
156 * construction of an ex from a basic. */
157 basic * basic::duplicate() const
159 debugmsg("basic duplicate",LOGLEVEL_DUPLICATE);
160 return new basic(*this);
163 /** Information about the object.
165 * @see class info_flags */
166 bool basic::info(unsigned inf) const
168 // all possible properties are false for basic objects
172 /** Number of operands/members. */
173 unsigned basic::nops() const
175 // iterating from 0 to nops() on atomic objects should be an empty loop,
176 // and accessing their elements is a range error. Container objects should
181 /** Return operand/member at position i. */
182 ex basic::op(int i) const
184 return (const_cast<basic *>(this))->let_op(i);
187 /** Return modifyable operand/member at position i. */
188 ex & basic::let_op(int i)
190 throw(std::out_of_range("op() out of range"));
193 ex basic::operator[](const ex & index) const
195 if (is_exactly_of_type(*index.bp,numeric))
196 return op(static_cast<const numeric &>(*index.bp).to_int());
198 throw(std::invalid_argument("non-numeric indices not supported by this type"));
201 ex basic::operator[](int i) const
206 /** Search ocurrences. An object 'has' an expression if it is the expression
207 * itself or one of the children 'has' it. As a consequence (according to
208 * the definition of children) given e=x+y+z, e.has(x) is true but e.has(x+y)
210 bool basic::has(const ex & other) const
212 GINAC_ASSERT(other.bp!=0);
213 if (is_equal(*other.bp)) return true;
215 for (unsigned i=0; i<nops(); i++)
216 if (op(i).has(other))
223 /** Return degree of highest power in object s. */
224 int basic::degree(const ex & s) const
229 /** Return degree of lowest power in object s. */
230 int basic::ldegree(const ex & s) const
235 /** Return coefficient of degree n in object s. */
236 ex basic::coeff(const ex & s, int n) const
238 return n==0 ? *this : _ex0();
241 /** Sort expression in terms of powers of some object(s).
242 * @param s object(s) to sort in
243 * @param distributed recursive or distributed form (only used when s is a list) */
244 ex basic::collect(const ex & s, bool distributed) const
247 if (is_ex_of_type(s, lst)) {
249 // List of objects specified
251 return collect(s.op(0));
253 else if (distributed) {
255 // Get lower/upper degree of all symbols in list
260 int cnt; // current degree, 'counter'
261 ex coeff; // coefficient for degree 'cnt'
263 sym_info *si = new sym_info[num];
265 for (int i=0; i<num; i++) {
267 si[i].ldeg = si[i].cnt = this->ldegree(si[i].sym);
268 si[i].deg = this->degree(si[i].sym);
269 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
274 // Calculate coeff*x1^c1*...*xn^cn
276 for (int i=0; i<num; i++) {
278 y *= power(si[i].sym, cnt);
280 x += y * si[num - 1].coeff;
282 // Increment counters
286 if (si[n].cnt <= si[n].deg) {
287 // Update coefficients
293 for (int i=n; i<num; i++)
294 c = si[i].coeff = c.coeff(si[i].sym, si[i].cnt);
299 si[n].cnt = si[n].ldeg;
310 for (int n=s.nops()-1; n>=0; n--)
316 // Only one object specified
317 for (int n=this->ldegree(s); n<=this->degree(s); ++n)
318 x += this->coeff(s,n)*power(s,n);
321 // correct for lost fractional arguments and return
322 return x + (*this - x).expand();
325 /** Perform automatic non-interruptive symbolic evaluation on expression. */
326 ex basic::eval(int level) const
328 // There is nothing to do for basic objects:
332 /** Evaluate object numerically. */
333 ex basic::evalf(int level) const
335 // There is nothing to do for basic objects:
339 /** Perform automatic symbolic evaluations on indexed expression that
340 * contains this object as the base expression. */
341 ex basic::eval_indexed(const basic & i) const
342 // this function can't take a "const ex & i" because that would result
343 // in an infinite eval() loop
345 // There is nothing to do for basic objects
349 /** Add two indexed expressions. They are guaranteed to be of class indexed
350 * (or a subclass) and their indices are compatible. This function is used
351 * internally by simplify_indexed().
353 * @param self First indexed expression; it's base object is *this
354 * @param other Second indexed expression
355 * @return sum of self and other
356 * @see ex::simplify_indexed() */
357 ex basic::add_indexed(const ex & self, const ex & other) const
362 /** Multiply an indexed expression with a scalar. This function is used
363 * internally by simplify_indexed().
365 * @param self Indexed expression; it's base object is *this
366 * @param other Numeric value
367 * @return product of self and other
368 * @see ex::simplify_indexed() */
369 ex basic::scalar_mul_indexed(const ex & self, const numeric & other) const
374 /** Try to contract two indexed expressions that appear in the same product.
375 * If a contraction exists, the function overwrites one or both of the
376 * expressions and returns true. Otherwise it returns false. It is
377 * guaranteed that both expressions are of class indexed (or a subclass)
378 * and that at least one dummy index has been found. This functions is
379 * used internally by simplify_indexed().
381 * @param self Pointer to first indexed expression; it's base object is *this
382 * @param other Pointer to second indexed expression
383 * @param v The complete vector of factors
384 * @return true if the contraction was successful, false otherwise
385 * @see ex::simplify_indexed() */
386 bool basic::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
392 /** Substitute a set of objects by arbitrary expressions. The ex returned
393 * will already be evaluated. */
394 ex basic::subs(const lst & ls, const lst & lr) const
396 GINAC_ASSERT(ls.nops() == lr.nops());
398 for (unsigned i=0; i<ls.nops(); i++) {
399 if (is_equal(*ls.op(i).bp))
406 /** Default interface of nth derivative ex::diff(s, n). It should be called
407 * instead of ::derivative(s) for first derivatives and for nth derivatives it
408 * just recurses down.
410 * @param s symbol to differentiate in
411 * @param nth order of differentiation
413 ex basic::diff(const symbol & s, unsigned nth) const
415 // trivial: zeroth derivative
419 // evaluate unevaluated *this before differentiating
420 if (!(flags & status_flags::evaluated))
421 return ex(*this).diff(s, nth);
423 ex ndiff = this->derivative(s);
424 while (!ndiff.is_zero() && // stop differentiating zeros
426 ndiff = ndiff.diff(s);
432 /** Return a vector containing the free indices of an expression. */
433 exvector basic::get_free_indices(void) const
435 return exvector(); // return an empty exvector
438 ex basic::simplify_ncmul(const exvector & v) const
440 return simplified_ncmul(v);
445 /** Default implementation of ex::diff(). It simply throws an error message.
447 * @exception logic_error (differentiation not supported by this type)
449 ex basic::derivative(const symbol & s) const
451 throw(std::logic_error("differentiation not supported by this type"));
454 /** Returns order relation between two objects of same type. This needs to be
455 * implemented by each class. It may never return anything else than 0,
456 * signalling equality, or +1 and -1 signalling inequality and determining
457 * the canonical ordering. (Perl hackers will wonder why C++ doesn't feature
458 * the spaceship operator <=> for denoting just this.) */
459 int basic::compare_same_type(const basic & other) const
461 return compare_pointers(this, &other);
464 /** Returns true if two objects of same type are equal. Normally needs
465 * not be reimplemented as long as it wasn't overwritten by some parent
466 * class, since it just calls compare_same_type(). The reason why this
467 * function exists is that sometimes it is easier to determine equality
468 * than an order relation and then it can be overridden. */
469 bool basic::is_equal_same_type(const basic & other) const
471 return this->compare_same_type(other)==0;
474 unsigned basic::return_type(void) const
476 return return_types::commutative;
479 unsigned basic::return_type_tinfo(void) const
484 /** Compute the hash value of an object and if it makes sense to store it in
485 * the objects status_flags, do so. The method inherited from class basic
486 * computes a hash value based on the type and hash values of possible
487 * members. For this reason it is well suited for container classes but
488 * atomic classes should override this implementation because otherwise they
489 * would all end up with the same hashvalue. */
490 unsigned basic::calchash(void) const
492 unsigned v = golden_ratio_hash(tinfo());
493 for (unsigned i=0; i<nops(); i++) {
494 v = rotate_left_31(v);
495 v ^= (const_cast<basic *>(this))->op(i).gethash();
498 // mask out numeric hashes:
501 // store calculated hash value only if object is already evaluated
502 if (flags & status_flags::evaluated) {
503 setflag(status_flags::hash_calculated);
510 /** Expand expression, i.e. multiply it out and return the result as a new
512 ex basic::expand(unsigned options) const
514 return this->setflag(status_flags::expanded);
519 // non-virtual functions in this class
524 /** Substitute objects in an expression (syntactic substitution) and return
525 * the result as a new expression. There are two valid types of
526 * replacement arguments: 1) a relational like object==ex and 2) a list of
527 * relationals lst(object1==ex1,object2==ex2,...), which is converted to
528 * subs(lst(object1,object2,...),lst(ex1,ex2,...)). */
529 ex basic::subs(const ex & e) const
531 if (e.info(info_flags::relation_equal)) {
534 if (!e.info(info_flags::list)) {
535 throw(std::invalid_argument("basic::subs(ex): argument must be a list"));
539 for (unsigned i=0; i<e.nops(); i++) {
541 if (!r.info(info_flags::relation_equal)) {
542 throw(std::invalid_argument("basic::subs(ex): argument must be a list or equations"));
550 /** Compare objects to establish canonical ordering.
551 * All compare functions return: -1 for *this less than other, 0 equal,
553 int basic::compare(const basic & other) const
555 unsigned hash_this = gethash();
556 unsigned hash_other = other.gethash();
558 if (hash_this<hash_other) return -1;
559 if (hash_this>hash_other) return 1;
561 unsigned typeid_this = tinfo();
562 unsigned typeid_other = other.tinfo();
564 if (typeid_this<typeid_other) {
565 // std::cout << "hash collision, different types: "
566 // << *this << " and " << other << std::endl;
567 // this->print(print_tree(std::cout));
568 // std::cout << " and ";
569 // other.print(print_tree(std::cout));
570 // std::cout << std::endl;
573 if (typeid_this>typeid_other) {
574 // std::cout << "hash collision, different types: "
575 // << *this << " and " << other << std::endl;
576 // this->print(print_tree(std::cout));
577 // std::cout << " and ";
578 // other.print(print_tree(std::cout));
579 // std::cout << std::endl;
583 GINAC_ASSERT(typeid(*this)==typeid(other));
585 // int cmpval = compare_same_type(other);
586 // if ((cmpval!=0) && (hash_this<0x80000000U)) {
587 // std::cout << "hash collision, same type: "
588 // << *this << " and " << other << std::endl;
589 // this->print(print_tree(std::cout));
590 // std::cout << " and ";
591 // other.print(print_tree(std::cout));
592 // std::cout << std::endl;
596 return compare_same_type(other);
599 /** Test for equality.
600 * This is only a quick test, meaning objects should be in the same domain.
601 * You might have to .expand(), .normal() objects first, depending on the
602 * domain of your computation, to get a more reliable answer.
604 * @see is_equal_same_type */
605 bool basic::is_equal(const basic & other) const
607 if (this->gethash()!=other.gethash())
609 if (this->tinfo()!=other.tinfo())
612 GINAC_ASSERT(typeid(*this)==typeid(other));
614 return this->is_equal_same_type(other);
619 /** Stop further evaluation.
621 * @see basic::eval */
622 const basic & basic::hold(void) const
624 return this->setflag(status_flags::evaluated);
627 /** Ensure the object may be modified without hurting others, throws if this
628 * is not the case. */
629 void basic::ensure_if_modifiable(void) const
631 if (this->refcount>1)
632 throw(std::runtime_error("cannot modify multiply referenced object"));
636 // static member variables
641 unsigned basic::precedence = 70;
647 int max_recursion_level = 1024;