1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2002 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
28 #include "expairseq.h"
32 #include "relational.h"
38 #if EXPAIRSEQ_USE_HASHTAB
40 #endif // EXPAIRSEQ_USE_HASHTAB
45 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
54 bool operator()(const epp &lh, const epp &rh) const
56 return (*lh).is_less(*rh);
61 // default ctor, dtor, copy ctor, assignment operator and helpers
66 expairseq::expairseq(const expairseq &other)
71 const expairseq &expairseq::operator=(const expairseq &other)
82 /** For use by copy ctor and assignment operator. */
83 void expairseq::copy(const expairseq &other)
85 inherited::copy(other);
87 overall_coeff = other.overall_coeff;
88 #if EXPAIRSEQ_USE_HASHTAB
90 hashtabsize = other.hashtabsize;
92 hashmask = other.hashmask;
93 hashtab.resize(hashtabsize);
94 epvector::const_iterator osb = other.seq.begin();
95 for (unsigned i=0; i<hashtabsize; ++i) {
97 for (epplist::const_iterator cit=other.hashtab[i].begin();
98 cit!=other.hashtab[i].end(); ++cit) {
99 hashtab[i].push_back(seq.begin()+((*cit)-osb));
105 #endif // EXPAIRSEQ_USE_HASHTAB
108 DEFAULT_DESTROY(expairseq)
114 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
116 construct_from_2_ex(lh,rh);
117 GINAC_ASSERT(is_canonical());
120 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
122 construct_from_exvector(v);
123 GINAC_ASSERT(is_canonical());
126 expairseq::expairseq(const epvector &v, const ex &oc)
127 : inherited(TINFO_expairseq), overall_coeff(oc)
129 GINAC_ASSERT(is_a<numeric>(oc));
130 construct_from_epvector(v);
131 GINAC_ASSERT(is_canonical());
134 expairseq::expairseq(epvector *vp, const ex &oc)
135 : inherited(TINFO_expairseq), overall_coeff(oc)
138 GINAC_ASSERT(is_a<numeric>(oc));
139 construct_from_epvector(*vp);
141 GINAC_ASSERT(is_canonical());
148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
149 #if EXPAIRSEQ_USE_HASHTAB
153 for (unsigned int i=0; true; i++) {
156 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
157 seq.push_back(expair(rest, coeff));
161 n.find_ex("overall_coeff", overall_coeff, sym_lst);
164 void expairseq::archive(archive_node &n) const
166 inherited::archive(n);
167 epvector::const_iterator i = seq.begin(), iend = seq.end();
169 n.add_ex("rest", i->rest);
170 n.add_ex("coeff", i->coeff);
173 n.add_ex("overall_coeff", overall_coeff);
176 DEFAULT_UNARCHIVE(expairseq)
179 // functions overriding virtual functions from base classes
184 basic *expairseq::duplicate() const
186 return new expairseq(*this);
189 void expairseq::print(const print_context &c, unsigned level) const
191 if (is_of_type(c, print_tree)) {
193 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
195 c.s << std::string(level, ' ') << class_name()
196 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
197 << ", nops=" << nops()
199 unsigned num = seq.size();
200 for (unsigned i=0; i<num; ++i) {
201 seq[i].rest.print(c, level + delta_indent);
202 seq[i].coeff.print(c, level + delta_indent);
204 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
206 if (!overall_coeff.is_equal(default_overall_coeff())) {
207 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
208 << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
209 overall_coeff.print(c, level + delta_indent);
211 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
212 #if EXPAIRSEQ_USE_HASHTAB
213 c.s << std::string(level + delta_indent,' ')
214 << "hashtab size " << hashtabsize << std::endl;
215 if (hashtabsize == 0) return;
217 unsigned count[MAXCOUNT+1];
218 for (int i=0; i<MAXCOUNT+1; ++i)
220 unsigned this_bin_fill;
221 unsigned cum_fill_sq = 0;
222 unsigned cum_fill = 0;
223 for (unsigned i=0; i<hashtabsize; ++i) {
225 if (hashtab[i].size() > 0) {
226 c.s << std::string(level + delta_indent, ' ')
227 << "bin " << i << " with entries ";
228 for (epplist::const_iterator it=hashtab[i].begin();
229 it!=hashtab[i].end(); ++it) {
230 c.s << *it-seq.begin() << " ";
234 cum_fill += this_bin_fill;
235 cum_fill_sq += this_bin_fill*this_bin_fill;
237 if (this_bin_fill<MAXCOUNT)
238 ++count[this_bin_fill];
244 double lambda = (1.0*seq.size()) / hashtabsize;
245 for (int k=0; k<MAXCOUNT; ++k) {
248 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
250 c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
251 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
252 << int(prob*1000)/10.0 << ")" << std::endl;
254 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
255 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
256 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
258 c.s << std::string(level + delta_indent, ' ') << "variance: "
259 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
261 c.s << std::string(level + delta_indent, ' ') << "average fill: "
262 << (1.0*cum_fill)/hashtabsize
263 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
264 #endif // EXPAIRSEQ_USE_HASHTAB
268 printseq(c, ',', precedence(), level);
273 bool expairseq::info(unsigned inf) const
275 return inherited::info(inf);
278 unsigned expairseq::nops() const
280 if (overall_coeff.is_equal(default_overall_coeff()))
286 ex expairseq::op(int i) const
288 if (unsigned(i)<seq.size())
289 return recombine_pair_to_ex(seq[i]);
290 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
291 return overall_coeff;
294 ex &expairseq::let_op(int i)
296 throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
299 ex expairseq::map(map_function &f) const
301 epvector *v = new epvector;
302 v->reserve(seq.size());
304 epvector::const_iterator cit = seq.begin(), last = seq.end();
305 while (cit != last) {
306 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
310 if (overall_coeff.is_equal(default_overall_coeff()))
311 return thisexpairseq(v, default_overall_coeff());
313 return thisexpairseq(v, f(overall_coeff));
316 /** Perform coefficient-wise automatic term rewriting rules in this class. */
317 ex expairseq::eval(int level) const
319 if ((level==1) && (flags &status_flags::evaluated))
322 epvector *vp = evalchildren(level);
326 return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
329 bool expairseq::match(const ex & pattern, lst & repl_lst) const
331 // This differs from basic::match() because we want "a+b+c+d" to
332 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
334 if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
336 // Check whether global wildcard (one that matches the "rest of the
337 // expression", like "*" above) is present
338 bool has_global_wildcard = false;
340 for (unsigned int i=0; i<pattern.nops(); i++) {
341 if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
342 has_global_wildcard = true;
343 global_wildcard = pattern.op(i);
348 // Unfortunately, this is an O(N^2) operation because we can't
349 // sort the pattern in a useful way...
354 for (unsigned i=0; i<nops(); i++)
355 ops.push_back(op(i));
357 // Now, for every term of the pattern, look for a matching term in
358 // the expression and remove the match
359 for (unsigned i=0; i<pattern.nops(); i++) {
360 ex p = pattern.op(i);
361 if (has_global_wildcard && p.is_equal(global_wildcard))
363 exvector::iterator it = ops.begin(), itend = ops.end();
364 while (it != itend) {
365 if (it->match(p, repl_lst)) {
371 return false; // no match found
375 if (has_global_wildcard) {
377 // Assign all the remaining terms to the global wildcard (unless
378 // it has already been matched before, in which case the matches
380 unsigned num = ops.size();
381 epvector *vp = new epvector();
383 for (unsigned i=0; i<num; i++)
384 vp->push_back(split_ex_to_pair(ops[i]));
385 ex rest = thisexpairseq(vp, default_overall_coeff());
386 for (unsigned i=0; i<repl_lst.nops(); i++) {
387 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
388 return rest.is_equal(repl_lst.op(i).op(1));
390 repl_lst.append(global_wildcard == rest);
395 // No global wildcard, then the match fails if there are any
396 // unmatched terms left
400 return inherited::match(pattern, repl_lst);
403 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
405 epvector *vp = subschildren(ls, lr, no_pattern);
407 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
409 return basic::subs(ls, lr, no_pattern);
414 int expairseq::compare_same_type(const basic &other) const
416 GINAC_ASSERT(is_a<expairseq>(other));
417 const expairseq &o = static_cast<const expairseq &>(other);
421 // compare number of elements
422 if (seq.size() != o.seq.size())
423 return (seq.size()<o.seq.size()) ? -1 : 1;
425 // compare overall_coeff
426 cmpval = overall_coeff.compare(o.overall_coeff);
430 #if EXPAIRSEQ_USE_HASHTAB
431 GINAC_ASSERT(hashtabsize==o.hashtabsize);
432 if (hashtabsize==0) {
433 #endif // EXPAIRSEQ_USE_HASHTAB
434 epvector::const_iterator cit1 = seq.begin();
435 epvector::const_iterator cit2 = o.seq.begin();
436 epvector::const_iterator last1 = seq.end();
437 epvector::const_iterator last2 = o.seq.end();
439 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
440 cmpval = (*cit1).compare(*cit2);
441 if (cmpval!=0) return cmpval;
444 GINAC_ASSERT(cit1==last1);
445 GINAC_ASSERT(cit2==last2);
448 #if EXPAIRSEQ_USE_HASHTAB
451 // compare number of elements in each hashtab entry
452 for (unsigned i=0; i<hashtabsize; ++i) {
453 unsigned cursize=hashtab[i].size();
454 if (cursize != o.hashtab[i].size())
455 return (cursize < o.hashtab[i].size()) ? -1 : 1;
458 // compare individual (sorted) hashtab entries
459 for (unsigned i=0; i<hashtabsize; ++i) {
460 unsigned sz = hashtab[i].size();
462 const epplist &eppl1 = hashtab[i];
463 const epplist &eppl2 = o.hashtab[i];
464 epplist::const_iterator it1 = eppl1.begin();
465 epplist::const_iterator it2 = eppl2.begin();
466 while (it1!=eppl1.end()) {
467 cmpval = (*(*it1)).compare(*(*it2));
477 #endif // EXPAIRSEQ_USE_HASHTAB
480 bool expairseq::is_equal_same_type(const basic &other) const
482 const expairseq &o = static_cast<const expairseq &>(other);
484 // compare number of elements
485 if (seq.size()!=o.seq.size())
488 // compare overall_coeff
489 if (!overall_coeff.is_equal(o.overall_coeff))
492 #if EXPAIRSEQ_USE_HASHTAB
493 // compare number of elements in each hashtab entry
494 if (hashtabsize!=o.hashtabsize) {
495 std::cout << "this:" << std::endl;
496 print(print_tree(std::cout));
497 std::cout << "other:" << std::endl;
498 other.print(print_tree(std::cout));
501 GINAC_ASSERT(hashtabsize==o.hashtabsize);
503 if (hashtabsize==0) {
504 #endif // EXPAIRSEQ_USE_HASHTAB
505 epvector::const_iterator cit1 = seq.begin();
506 epvector::const_iterator cit2 = o.seq.begin();
507 epvector::const_iterator last1 = seq.end();
509 while (cit1!=last1) {
510 if (!(*cit1).is_equal(*cit2)) return false;
516 #if EXPAIRSEQ_USE_HASHTAB
519 for (unsigned i=0; i<hashtabsize; ++i) {
520 if (hashtab[i].size() != o.hashtab[i].size())
524 // compare individual sorted hashtab entries
525 for (unsigned i=0; i<hashtabsize; ++i) {
526 unsigned sz = hashtab[i].size();
528 const epplist &eppl1 = hashtab[i];
529 const epplist &eppl2 = o.hashtab[i];
530 epplist::const_iterator it1 = eppl1.begin();
531 epplist::const_iterator it2 = eppl2.begin();
532 while (it1!=eppl1.end()) {
533 if (!(*(*it1)).is_equal(*(*it2))) return false;
541 #endif // EXPAIRSEQ_USE_HASHTAB
544 unsigned expairseq::return_type(void) const
546 return return_types::noncommutative_composite;
549 unsigned expairseq::calchash(void) const
551 unsigned v = golden_ratio_hash(this->tinfo());
552 epvector::const_iterator i = seq.begin(), end = seq.end();
554 #if !EXPAIRSEQ_USE_HASHTAB
555 v = rotate_left_31(v); // rotation would spoil commutativity
556 #endif // EXPAIRSEQ_USE_HASHTAB
557 v ^= i->rest.gethash();
558 #if !EXPAIRSEQ_USE_HASHTAB
559 v = rotate_left_31(v);
560 v ^= i->coeff.gethash();
561 #endif // EXPAIRSEQ_USE_HASHTAB
565 v ^= overall_coeff.gethash();
568 // store calculated hash value only if object is already evaluated
569 if (flags &status_flags::evaluated) {
570 setflag(status_flags::hash_calculated);
577 ex expairseq::expand(unsigned options) const
579 epvector *vp = expandchildren(options);
581 // The terms have not changed, so it is safe to declare this expanded
582 return (options == 0) ? setflag(status_flags::expanded) : *this;
584 return thisexpairseq(vp, overall_coeff);
588 // new virtual functions which can be overridden by derived classes
593 /** Create an object of this type.
594 * This method works similar to a constructor. It is useful because expairseq
595 * has (at least) two possible different semantics but we want to inherit
596 * methods thus avoiding code duplication. Sometimes a method in expairseq
597 * has to create a new one of the same semantics, which cannot be done by a
598 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
599 * order for this trick to work a derived class must of course override this
601 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
603 return expairseq(v,oc);
606 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
608 return expairseq(vp,oc);
611 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
614 p.rest.print(c, precedence());
616 p.coeff.print(c, precedence());
620 void expairseq::printseq(const print_context & c, char delim,
621 unsigned this_precedence,
622 unsigned upper_precedence) const
624 if (this_precedence <= upper_precedence)
626 epvector::const_iterator it, it_last = seq.end() - 1;
627 for (it=seq.begin(); it!=it_last; ++it) {
628 printpair(c, *it, this_precedence);
631 printpair(c, *it, this_precedence);
632 if (!overall_coeff.is_equal(default_overall_coeff())) {
634 overall_coeff.print(c, this_precedence);
637 if (this_precedence <= upper_precedence)
642 /** Form an expair from an ex, using the corresponding semantics.
643 * @see expairseq::recombine_pair_to_ex() */
644 expair expairseq::split_ex_to_pair(const ex &e) const
646 return expair(e,_ex1);
650 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
653 GINAC_ASSERT(is_exactly_a<numeric>(c));
659 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
662 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
663 GINAC_ASSERT(is_exactly_a<numeric>(c));
665 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
669 /** Form an ex out of an expair, using the corresponding semantics.
670 * @see expairseq::split_ex_to_pair() */
671 ex expairseq::recombine_pair_to_ex(const expair &p) const
673 return lst(p.rest,p.coeff);
676 bool expairseq::expair_needs_further_processing(epp it)
678 #if EXPAIRSEQ_USE_HASHTAB
679 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
680 #endif // EXPAIRSEQ_USE_HASHTAB
684 ex expairseq::default_overall_coeff(void) const
689 void expairseq::combine_overall_coeff(const ex &c)
691 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
692 GINAC_ASSERT(is_exactly_a<numeric>(c));
693 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
696 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
698 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
699 GINAC_ASSERT(is_exactly_a<numeric>(c1));
700 GINAC_ASSERT(is_exactly_a<numeric>(c2));
701 overall_coeff = ex_to<numeric>(overall_coeff).
702 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
705 bool expairseq::can_make_flat(const expair &p) const
712 // non-virtual functions in this class
715 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
721 construct_from_exvector(v);
722 #if EXPAIRSEQ_USE_HASHTAB
723 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
724 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
725 #endif // EXPAIRSEQ_USE_HASHTAB
728 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
730 if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
731 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
732 #if EXPAIRSEQ_USE_HASHTAB
733 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
734 ex_to<expairseq>(rh).seq.size();
735 if (calc_hashtabsize(totalsize)!=0) {
736 construct_from_2_ex_via_exvector(lh,rh);
738 #endif // EXPAIRSEQ_USE_HASHTAB
739 construct_from_2_expairseq(ex_to<expairseq>(lh),
740 ex_to<expairseq>(rh));
741 #if EXPAIRSEQ_USE_HASHTAB
743 #endif // EXPAIRSEQ_USE_HASHTAB
746 #if EXPAIRSEQ_USE_HASHTAB
747 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
748 if (calc_hashtabsize(totalsize)!=0) {
749 construct_from_2_ex_via_exvector(lh, rh);
751 #endif // EXPAIRSEQ_USE_HASHTAB
752 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
753 #if EXPAIRSEQ_USE_HASHTAB
755 #endif // EXPAIRSEQ_USE_HASHTAB
758 } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
759 #if EXPAIRSEQ_USE_HASHTAB
760 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
761 if (calc_hashtabsize(totalsize)!=0) {
762 construct_from_2_ex_via_exvector(lh,rh);
764 #endif // EXPAIRSEQ_USE_HASHTAB
765 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
766 #if EXPAIRSEQ_USE_HASHTAB
768 #endif // EXPAIRSEQ_USE_HASHTAB
772 #if EXPAIRSEQ_USE_HASHTAB
773 if (calc_hashtabsize(2)!=0) {
774 construct_from_2_ex_via_exvector(lh,rh);
778 #endif // EXPAIRSEQ_USE_HASHTAB
780 if (is_ex_exactly_of_type(lh,numeric)) {
781 if (is_ex_exactly_of_type(rh,numeric)) {
782 combine_overall_coeff(lh);
783 combine_overall_coeff(rh);
785 combine_overall_coeff(lh);
786 seq.push_back(split_ex_to_pair(rh));
789 if (is_ex_exactly_of_type(rh,numeric)) {
790 combine_overall_coeff(rh);
791 seq.push_back(split_ex_to_pair(lh));
793 expair p1 = split_ex_to_pair(lh);
794 expair p2 = split_ex_to_pair(rh);
796 int cmpval = p1.rest.compare(p2.rest);
798 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
799 if (!ex_to<numeric>(p1.coeff).is_zero()) {
800 // no further processing is necessary, since this
801 // one element will usually be recombined in eval()
818 void expairseq::construct_from_2_expairseq(const expairseq &s1,
821 combine_overall_coeff(s1.overall_coeff);
822 combine_overall_coeff(s2.overall_coeff);
824 epvector::const_iterator first1 = s1.seq.begin();
825 epvector::const_iterator last1 = s1.seq.end();
826 epvector::const_iterator first2 = s2.seq.begin();
827 epvector::const_iterator last2 = s2.seq.end();
829 seq.reserve(s1.seq.size()+s2.seq.size());
831 bool needs_further_processing=false;
833 while (first1!=last1 && first2!=last2) {
834 int cmpval = (*first1).rest.compare((*first2).rest);
837 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
838 add(ex_to<numeric>(first2->coeff));
839 if (!newcoeff.is_zero()) {
840 seq.push_back(expair(first1->rest,newcoeff));
841 if (expair_needs_further_processing(seq.end()-1)) {
842 needs_further_processing = true;
847 } else if (cmpval<0) {
848 seq.push_back(*first1);
851 seq.push_back(*first2);
856 while (first1!=last1) {
857 seq.push_back(*first1);
860 while (first2!=last2) {
861 seq.push_back(*first2);
865 if (needs_further_processing) {
868 construct_from_epvector(v);
872 void expairseq::construct_from_expairseq_ex(const expairseq &s,
875 combine_overall_coeff(s.overall_coeff);
876 if (is_ex_exactly_of_type(e,numeric)) {
877 combine_overall_coeff(e);
882 epvector::const_iterator first = s.seq.begin();
883 epvector::const_iterator last = s.seq.end();
884 expair p = split_ex_to_pair(e);
886 seq.reserve(s.seq.size()+1);
887 bool p_pushed = false;
889 bool needs_further_processing=false;
891 // merge p into s.seq
892 while (first!=last) {
893 int cmpval = (*first).rest.compare(p.rest);
896 const numeric &newcoeff = ex_to<numeric>(first->coeff).
897 add(ex_to<numeric>(p.coeff));
898 if (!newcoeff.is_zero()) {
899 seq.push_back(expair(first->rest,newcoeff));
900 if (expair_needs_further_processing(seq.end()-1))
901 needs_further_processing = true;
906 } else if (cmpval<0) {
907 seq.push_back(*first);
917 // while loop exited because p was pushed, now push rest of s.seq
918 while (first!=last) {
919 seq.push_back(*first);
923 // while loop exited because s.seq was pushed, now push p
927 if (needs_further_processing) {
930 construct_from_epvector(v);
934 void expairseq::construct_from_exvector(const exvector &v)
936 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
937 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
938 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
939 // (same for (+,*) -> (*,^)
942 #if EXPAIRSEQ_USE_HASHTAB
943 combine_same_terms();
946 combine_same_terms_sorted_seq();
947 #endif // EXPAIRSEQ_USE_HASHTAB
950 void expairseq::construct_from_epvector(const epvector &v)
952 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
953 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
954 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
955 // (same for (+,*) -> (*,^)
958 #if EXPAIRSEQ_USE_HASHTAB
959 combine_same_terms();
962 combine_same_terms_sorted_seq();
963 #endif // EXPAIRSEQ_USE_HASHTAB
966 /** Combine this expairseq with argument exvector.
967 * It cares for associativity as well as for special handling of numerics. */
968 void expairseq::make_flat(const exvector &v)
970 exvector::const_iterator cit;
972 // count number of operands which are of same expairseq derived type
973 // and their cumulative number of operands
978 while (cit!=v.end()) {
979 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
981 noperands += ex_to<expairseq>(*cit).seq.size();
986 // reserve seq and coeffseq which will hold all operands
987 seq.reserve(v.size()+noperands-nexpairseqs);
989 // copy elements and split off numerical part
991 while (cit!=v.end()) {
992 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
993 const expairseq &subseqref = ex_to<expairseq>(*cit);
994 combine_overall_coeff(subseqref.overall_coeff);
995 epvector::const_iterator cit_s = subseqref.seq.begin();
996 while (cit_s!=subseqref.seq.end()) {
997 seq.push_back(*cit_s);
1001 if (is_ex_exactly_of_type(*cit,numeric))
1002 combine_overall_coeff(*cit);
1004 seq.push_back(split_ex_to_pair(*cit));
1010 /** Combine this expairseq with argument epvector.
1011 * It cares for associativity as well as for special handling of numerics. */
1012 void expairseq::make_flat(const epvector &v)
1014 epvector::const_iterator cit;
1016 // count number of operands which are of same expairseq derived type
1017 // and their cumulative number of operands
1018 int nexpairseqs = 0;
1022 while (cit!=v.end()) {
1023 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1025 noperands += ex_to<expairseq>(cit->rest).seq.size();
1030 // reserve seq and coeffseq which will hold all operands
1031 seq.reserve(v.size()+noperands-nexpairseqs);
1033 // copy elements and split off numerical part
1035 while (cit!=v.end()) {
1036 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1037 this->can_make_flat(*cit)) {
1038 const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1039 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1040 ex_to<numeric>(cit->coeff));
1041 epvector::const_iterator cit_s = subseqref.seq.begin();
1042 while (cit_s!=subseqref.seq.end()) {
1043 seq.push_back(expair(cit_s->rest,
1044 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1045 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1050 if (cit->is_canonical_numeric())
1051 combine_overall_coeff(cit->rest);
1053 seq.push_back(*cit);
1059 /** Brings this expairseq into a sorted (canonical) form. */
1060 void expairseq::canonicalize(void)
1062 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1066 /** Compact a presorted expairseq by combining all matching expairs to one
1067 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1069 void expairseq::combine_same_terms_sorted_seq(void)
1074 bool needs_further_processing = false;
1076 epvector::iterator itin1 = seq.begin();
1077 epvector::iterator itin2 = itin1+1;
1078 epvector::iterator itout = itin1;
1079 epvector::iterator last = seq.end();
1080 // must_copy will be set to true the first time some combination is
1081 // possible from then on the sequence has changed and must be compacted
1082 bool must_copy = false;
1083 while (itin2!=last) {
1084 if (itin1->rest.compare(itin2->rest)==0) {
1085 itin1->coeff = ex_to<numeric>(itin1->coeff).
1086 add_dyn(ex_to<numeric>(itin2->coeff));
1087 if (expair_needs_further_processing(itin1))
1088 needs_further_processing = true;
1091 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1100 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1106 seq.erase(itout,last);
1108 if (needs_further_processing) {
1111 construct_from_epvector(v);
1115 #if EXPAIRSEQ_USE_HASHTAB
1117 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1120 unsigned nearest_power_of_2 = 1 << log2(sz);
1121 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1122 // size = nearest_power_of_2*hashtabfactor;
1123 size = nearest_power_of_2/hashtabfactor;
1124 if (size<minhashtabsize)
1126 GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1127 // hashtabsize must be a power of 2
1128 GINAC_ASSERT((1U << log2(size))==size);
1132 unsigned expairseq::calc_hashindex(const ex &e) const
1134 // calculate hashindex
1135 unsigned hash = e.gethash();
1137 if (is_a_numeric_hash(hash)) {
1138 hashindex = hashmask;
1140 hashindex = hash &hashmask;
1141 // last hashtab entry is reserved for numerics
1142 if (hashindex==hashmask) hashindex = 0;
1144 GINAC_ASSERT(hashindex>=0);
1145 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1149 void expairseq::shrink_hashtab(void)
1151 unsigned new_hashtabsize;
1152 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1153 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1154 if (new_hashtabsize==0) {
1161 // shrink by a factor of 2
1162 unsigned half_hashtabsize = hashtabsize/2;
1163 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1164 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1165 // special treatment for numeric hashes
1166 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1167 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1168 hashtab.resize(half_hashtabsize);
1169 hashtabsize = half_hashtabsize;
1170 hashmask = hashtabsize-1;
1174 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1177 return; // nothing to do
1179 // calculate hashindex of element to be deleted
1180 unsigned hashindex = calc_hashindex((*element).rest);
1182 // find it in hashtab and remove it
1183 epplist &eppl = hashtab[hashindex];
1184 epplist::iterator epplit = eppl.begin();
1185 bool erased = false;
1186 while (epplit!=eppl.end()) {
1187 if (*epplit == element) {
1195 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1196 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1198 unsigned hashindex = calc_hashindex(element->rest);
1199 epplist &eppl = hashtab[hashindex];
1200 epplist::iterator epplit = eppl.begin();
1201 bool erased = false;
1202 while (epplit!=eppl.end()) {
1203 if (*epplit == element) {
1210 GINAC_ASSERT(erased);
1212 GINAC_ASSERT(erased);
1215 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1216 epvector::iterator newpos)
1218 GINAC_ASSERT(hashtabsize!=0);
1220 // calculate hashindex of element which was moved
1221 unsigned hashindex=calc_hashindex((*newpos).rest);
1223 // find it in hashtab and modify it
1224 epplist &eppl = hashtab[hashindex];
1225 epplist::iterator epplit = eppl.begin();
1226 while (epplit!=eppl.end()) {
1227 if (*epplit == oldpos) {
1233 GINAC_ASSERT(epplit!=eppl.end());
1236 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1238 epplist::const_iterator current = eppl.begin();
1239 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1242 eppl.insert(current,elem);
1245 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1246 epvector::iterator &last_non_zero,
1247 std::vector<bool> &touched,
1248 unsigned &number_of_zeroes)
1250 epp current = seq.begin();
1252 while (current!=first_numeric) {
1253 if (is_ex_exactly_of_type(current->rest,numeric)) {
1255 iter_swap(current,first_numeric);
1257 // calculate hashindex
1258 unsigned currenthashindex = calc_hashindex(current->rest);
1260 // test if there is already a matching expair in the hashtab-list
1261 epplist &eppl=hashtab[currenthashindex];
1262 epplist::iterator epplit = eppl.begin();
1263 while (epplit!=eppl.end()) {
1264 if (current->rest.is_equal((*epplit)->rest))
1268 if (epplit==eppl.end()) {
1269 // no matching expair found, append this to end of list
1270 sorted_insert(eppl,current);
1273 // epplit points to a matching expair, combine it with current
1274 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1275 add_dyn(ex_to<numeric>(current->coeff));
1277 // move obsolete current expair to end by swapping with last_non_zero element
1278 // if this was a numeric, it is swapped with the expair before first_numeric
1279 iter_swap(current,last_non_zero);
1281 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1284 // test if combined term has coeff 0 and can be removed is done later
1285 touched[(*epplit)-seq.begin()] = true;
1291 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1292 epvector::iterator &last_non_zero,
1293 std::vector<bool> &touched,
1294 unsigned &number_of_zeroes)
1296 // move terms with coeff 0 to end and remove them from hashtab
1297 // check only those elements which have been touched
1298 epp current = seq.begin();
1300 while (current!=first_numeric) {
1304 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1308 remove_hashtab_entry(current);
1310 // move element to the end, unless it is already at the end
1311 if (current!=last_non_zero) {
1312 iter_swap(current,last_non_zero);
1314 bool numeric_swapped = first_numeric!=last_non_zero;
1315 if (numeric_swapped)
1316 iter_swap(first_numeric,current);
1317 epvector::iterator changed_entry;
1319 if (numeric_swapped)
1320 changed_entry = first_numeric;
1322 changed_entry = last_non_zero;
1327 if (first_numeric!=current) {
1329 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1330 move_hashtab_entry(changed_entry,current);
1331 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1340 GINAC_ASSERT(i==current-seq.begin());
1343 /** True if one of the coeffs vanishes, otherwise false.
1344 * This would be an invariant violation, so this should only be used for
1345 * debugging purposes. */
1346 bool expairseq::has_coeff_0(void) const
1348 epvector::const_iterator i = seq.begin(), end = seq.end();
1350 if (i->coeff.is_zero())
1357 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1358 epvector::const_iterator last_non_zero)
1360 if (first_numeric == seq.end()) return; // no numerics
1362 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1363 while (current != last) {
1364 sorted_insert(hashtab[hashmask], current);
1369 void expairseq::combine_same_terms(void)
1371 // combine same terms, drop term with coeff 0, move numerics to end
1373 // calculate size of hashtab
1374 hashtabsize = calc_hashtabsize(seq.size());
1376 // hashtabsize is a power of 2
1377 hashmask = hashtabsize-1;
1381 hashtab.resize(hashtabsize);
1383 if (hashtabsize==0) {
1385 combine_same_terms_sorted_seq();
1386 GINAC_ASSERT(!has_coeff_0());
1390 // iterate through seq, move numerics to end,
1391 // fill hashtab and combine same terms
1392 epvector::iterator first_numeric = seq.end();
1393 epvector::iterator last_non_zero = seq.end()-1;
1395 unsigned num = seq.size();
1396 std::vector<bool> touched(num);
1398 unsigned number_of_zeroes = 0;
1400 GINAC_ASSERT(!has_coeff_0());
1401 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1403 // there should not be any terms with coeff 0 from the beginning,
1404 // so it should be safe to skip this step
1405 if (number_of_zeroes!=0) {
1406 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1409 add_numerics_to_hashtab(first_numeric,last_non_zero);
1411 // pop zero elements
1412 for (unsigned i=0; i<number_of_zeroes; ++i) {
1416 // shrink hashtabsize to calculated value
1417 GINAC_ASSERT(!has_coeff_0());
1421 GINAC_ASSERT(!has_coeff_0());
1424 #endif // EXPAIRSEQ_USE_HASHTAB
1426 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1427 * debugging or in assertions since being sorted is an invariance. */
1428 bool expairseq::is_canonical() const
1430 if (seq.size() <= 1)
1433 #if EXPAIRSEQ_USE_HASHTAB
1434 if (hashtabsize > 0) return 1; // not canoncalized
1435 #endif // EXPAIRSEQ_USE_HASHTAB
1437 epvector::const_iterator it = seq.begin(), itend = seq.end();
1438 epvector::const_iterator it_last = it;
1439 for (++it; it!=itend; it_last=it, ++it) {
1440 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1441 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1442 !is_ex_exactly_of_type(it->rest,numeric)) {
1443 // double test makes it easier to set a breakpoint...
1444 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1445 !is_ex_exactly_of_type(it->rest,numeric)) {
1446 printpair(std::clog, *it_last, 0);
1448 printpair(std::clog, *it, 0);
1450 std::clog << "pair1:" << std::endl;
1451 it_last->rest.print(print_tree(std::clog));
1452 it_last->coeff.print(print_tree(std::clog));
1453 std::clog << "pair2:" << std::endl;
1454 it->rest.print(print_tree(std::clog));
1455 it->coeff.print(print_tree(std::clog));
1465 /** Member-wise expand the expairs in this sequence.
1467 * @see expairseq::expand()
1468 * @return pointer to epvector containing expanded pairs or zero pointer,
1469 * if no members were changed. */
1470 epvector * expairseq::expandchildren(unsigned options) const
1472 const epvector::const_iterator last = seq.end();
1473 epvector::const_iterator cit = seq.begin();
1475 const ex &expanded_ex = cit->rest.expand(options);
1476 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1478 // something changed, copy seq, eval and return it
1479 epvector *s = new epvector;
1480 s->reserve(seq.size());
1482 // copy parts of seq which are known not to have changed
1483 epvector::const_iterator cit2 = seq.begin();
1485 s->push_back(*cit2);
1488 // copy first changed element
1489 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1493 while (cit2!=last) {
1494 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1503 return 0; // signalling nothing has changed
1507 /** Member-wise evaluate the expairs in this sequence.
1509 * @see expairseq::eval()
1510 * @return pointer to epvector containing evaluated pairs or zero pointer,
1511 * if no members were changed. */
1512 epvector * expairseq::evalchildren(int level) const
1514 // returns a NULL pointer if nothing had to be evaluated
1515 // returns a pointer to a newly created epvector otherwise
1516 // (which has to be deleted somewhere else)
1521 if (level == -max_recursion_level)
1522 throw(std::runtime_error("max recursion level reached"));
1525 epvector::const_iterator last = seq.end();
1526 epvector::const_iterator cit = seq.begin();
1528 const ex &evaled_ex = cit->rest.eval(level);
1529 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1531 // something changed, copy seq, eval and return it
1532 epvector *s = new epvector;
1533 s->reserve(seq.size());
1535 // copy parts of seq which are known not to have changed
1536 epvector::const_iterator cit2=seq.begin();
1538 s->push_back(*cit2);
1541 // copy first changed element
1542 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1546 while (cit2!=last) {
1547 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1556 return 0; // signalling nothing has changed
1560 /** Member-wise substitute in this sequence.
1562 * @see expairseq::subs()
1563 * @return pointer to epvector containing pairs after application of subs,
1564 * or NULL pointer if no members were changed. */
1565 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1567 GINAC_ASSERT(ls.nops()==lr.nops());
1569 // The substitution is "complex" when any of the objects to be substituted
1570 // is a product or power. In this case we have to recombine the pairs
1571 // because the numeric coefficients may be part of the search pattern.
1572 bool complex_subs = false;
1573 for (unsigned i=0; i<ls.nops(); ++i)
1574 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1575 complex_subs = true;
1581 // Substitute in the recombined pairs
1582 epvector::const_iterator cit = seq.begin(), last = seq.end();
1583 while (cit != last) {
1585 const ex &orig_ex = recombine_pair_to_ex(*cit);
1586 const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1587 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1589 // Something changed, copy seq, subs and return it
1590 epvector *s = new epvector;
1591 s->reserve(seq.size());
1593 // Copy parts of seq which are known not to have changed
1594 s->insert(s->begin(), seq.begin(), cit);
1596 // Copy first changed element
1597 s->push_back(split_ex_to_pair(subsed_ex));
1601 while (cit != last) {
1602 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1613 // Substitute only in the "rest" part of the pairs
1614 epvector::const_iterator cit = seq.begin(), last = seq.end();
1615 while (cit != last) {
1617 const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1618 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1620 // Something changed, copy seq, subs and return it
1621 epvector *s = new epvector;
1622 s->reserve(seq.size());
1624 // Copy parts of seq which are known not to have changed
1625 s->insert(s->begin(), seq.begin(), cit);
1627 // Copy first changed element
1628 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1632 while (cit != last) {
1633 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1644 // Nothing has changed
1649 // static member variables
1652 #if EXPAIRSEQ_USE_HASHTAB
1653 unsigned expairseq::maxhashtabsize = 0x4000000U;
1654 unsigned expairseq::minhashtabsize = 0x1000U;
1655 unsigned expairseq::hashtabfactor = 1;
1656 #endif // EXPAIRSEQ_USE_HASHTAB
1658 } // namespace GiNaC