1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2006 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
28 #include "expairseq.h"
33 #include "relational.h"
36 #include "operators.h"
40 #if EXPAIRSEQ_USE_HASHTAB
42 #endif // EXPAIRSEQ_USE_HASHTAB
47 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
48 print_func<print_context>(&expairseq::do_print).
49 print_func<print_tree>(&expairseq::do_print_tree))
59 bool operator()(const epp &lh, const epp &rh) const
61 return (*lh).is_less(*rh);
66 // default constructor
71 expairseq::expairseq() : inherited(&expairseq::tinfo_static)
72 #if EXPAIRSEQ_USE_HASHTAB
74 #endif // EXPAIRSEQ_USE_HASHTAB
80 /** For use by copy ctor and assignment operator. */
81 void expairseq::copy(const expairseq &other)
84 overall_coeff = other.overall_coeff;
85 #if EXPAIRSEQ_USE_HASHTAB
87 hashtabsize = other.hashtabsize;
89 hashmask = other.hashmask;
90 hashtab.resize(hashtabsize);
91 epvector::const_iterator osb = other.seq.begin();
92 for (unsigned i=0; i<hashtabsize; ++i) {
94 for (epplist::const_iterator cit=other.hashtab[i].begin();
95 cit!=other.hashtab[i].end(); ++cit) {
96 hashtab[i].push_back(seq.begin()+((*cit)-osb));
102 #endif // EXPAIRSEQ_USE_HASHTAB
107 // other constructors
110 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(&expairseq::tinfo_static)
112 construct_from_2_ex(lh,rh);
113 GINAC_ASSERT(is_canonical());
116 expairseq::expairseq(const exvector &v) : inherited(&expairseq::tinfo_static)
118 construct_from_exvector(v);
119 GINAC_ASSERT(is_canonical());
122 expairseq::expairseq(const epvector &v, const ex &oc)
123 : inherited(&expairseq::tinfo_static), overall_coeff(oc)
125 GINAC_ASSERT(is_a<numeric>(oc));
126 construct_from_epvector(v);
127 GINAC_ASSERT(is_canonical());
130 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
131 : inherited(&expairseq::tinfo_static), overall_coeff(oc)
133 GINAC_ASSERT(vp.get()!=0);
134 GINAC_ASSERT(is_a<numeric>(oc));
135 construct_from_epvector(*vp);
136 GINAC_ASSERT(is_canonical());
143 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
144 #if EXPAIRSEQ_USE_HASHTAB
148 for (unsigned int i=0; true; i++) {
151 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
152 seq.push_back(expair(rest, coeff));
157 n.find_ex("overall_coeff", overall_coeff, sym_lst);
160 GINAC_ASSERT(is_canonical());
163 void expairseq::archive(archive_node &n) const
165 inherited::archive(n);
166 epvector::const_iterator i = seq.begin(), iend = seq.end();
168 n.add_ex("rest", i->rest);
169 n.add_ex("coeff", i->coeff);
172 n.add_ex("overall_coeff", overall_coeff);
175 DEFAULT_UNARCHIVE(expairseq)
178 // functions overriding virtual functions from base classes
183 void expairseq::do_print(const print_context & c, unsigned level) const
186 printseq(c, ',', precedence(), level);
190 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
192 c.s << std::string(level, ' ') << class_name() << " @" << this
193 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
194 << ", nops=" << nops()
196 size_t num = seq.size();
197 for (size_t i=0; i<num; ++i) {
198 seq[i].rest.print(c, level + c.delta_indent);
199 seq[i].coeff.print(c, level + c.delta_indent);
201 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
203 if (!overall_coeff.is_equal(default_overall_coeff())) {
204 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
205 << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
206 overall_coeff.print(c, level + c.delta_indent);
208 c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
209 #if EXPAIRSEQ_USE_HASHTAB
210 c.s << std::string(level + c.delta_indent,' ')
211 << "hashtab size " << hashtabsize << std::endl;
212 if (hashtabsize == 0) return;
214 unsigned count[MAXCOUNT+1];
215 for (int i=0; i<MAXCOUNT+1; ++i)
217 unsigned this_bin_fill;
218 unsigned cum_fill_sq = 0;
219 unsigned cum_fill = 0;
220 for (unsigned i=0; i<hashtabsize; ++i) {
222 if (hashtab[i].size() > 0) {
223 c.s << std::string(level + c.delta_indent, ' ')
224 << "bin " << i << " with entries ";
225 for (epplist::const_iterator it=hashtab[i].begin();
226 it!=hashtab[i].end(); ++it) {
227 c.s << *it-seq.begin() << " ";
231 cum_fill += this_bin_fill;
232 cum_fill_sq += this_bin_fill*this_bin_fill;
234 if (this_bin_fill<MAXCOUNT)
235 ++count[this_bin_fill];
241 double lambda = (1.0*seq.size()) / hashtabsize;
242 for (int k=0; k<MAXCOUNT; ++k) {
245 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
247 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
248 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
249 << int(prob*1000)/10.0 << ")" << std::endl;
251 c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
252 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
253 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
255 c.s << std::string(level + c.delta_indent, ' ') << "variance: "
256 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
258 c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
259 << (1.0*cum_fill)/hashtabsize
260 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
261 #endif // EXPAIRSEQ_USE_HASHTAB
264 bool expairseq::info(unsigned inf) const
266 return inherited::info(inf);
269 size_t expairseq::nops() const
271 if (overall_coeff.is_equal(default_overall_coeff()))
277 ex expairseq::op(size_t i) const
280 return recombine_pair_to_ex(seq[i]);
281 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
282 return overall_coeff;
285 ex expairseq::map(map_function &f) const
287 std::auto_ptr<epvector> v(new epvector);
288 v->reserve(seq.size());
290 epvector::const_iterator cit = seq.begin(), last = seq.end();
291 while (cit != last) {
292 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
296 if (overall_coeff.is_equal(default_overall_coeff()))
297 return thisexpairseq(v, default_overall_coeff());
299 return thisexpairseq(v, f(overall_coeff));
302 /** Perform coefficient-wise automatic term rewriting rules in this class. */
303 ex expairseq::eval(int level) const
305 if ((level==1) && (flags &status_flags::evaluated))
308 std::auto_ptr<epvector> vp = evalchildren(level);
312 return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
315 epvector* conjugateepvector(const epvector&epv)
317 epvector *newepv = 0;
318 for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
320 newepv->push_back(i->conjugate());
323 expair x = i->conjugate();
324 if (x.is_equal(*i)) {
327 newepv = new epvector;
328 newepv->reserve(epv.size());
329 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
330 newepv->push_back(*j);
332 newepv->push_back(x);
337 ex expairseq::conjugate() const
339 epvector* newepv = conjugateepvector(seq);
340 ex x = overall_coeff.conjugate();
341 if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
344 ex result = thisexpairseq(newepv ? *newepv : seq, x);
351 bool expairseq::is_polynomial(const ex & var) const
353 if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
354 return basic::is_polynomial(var);
355 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
356 if (!(i->rest).is_polynomial(var))
362 bool expairseq::match(const ex & pattern, lst & repl_lst) const
364 // This differs from basic::match() because we want "a+b+c+d" to
365 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
367 if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
369 // Check whether global wildcard (one that matches the "rest of the
370 // expression", like "*" above) is present
371 bool has_global_wildcard = false;
373 for (size_t i=0; i<pattern.nops(); i++) {
374 if (is_exactly_a<wildcard>(pattern.op(i))) {
375 has_global_wildcard = true;
376 global_wildcard = pattern.op(i);
381 // Unfortunately, this is an O(N^2) operation because we can't
382 // sort the pattern in a useful way...
387 for (size_t i=0; i<nops(); i++)
388 ops.push_back(op(i));
390 // Now, for every term of the pattern, look for a matching term in
391 // the expression and remove the match
392 for (size_t i=0; i<pattern.nops(); i++) {
393 ex p = pattern.op(i);
394 if (has_global_wildcard && p.is_equal(global_wildcard))
396 exvector::iterator it = ops.begin(), itend = ops.end();
397 while (it != itend) {
398 if (it->match(p, repl_lst)) {
404 return false; // no match found
408 if (has_global_wildcard) {
410 // Assign all the remaining terms to the global wildcard (unless
411 // it has already been matched before, in which case the matches
413 size_t num = ops.size();
414 std::auto_ptr<epvector> vp(new epvector);
416 for (size_t i=0; i<num; i++)
417 vp->push_back(split_ex_to_pair(ops[i]));
418 ex rest = thisexpairseq(vp, default_overall_coeff());
419 for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
420 if (it->op(0).is_equal(global_wildcard))
421 return rest.is_equal(it->op(1));
423 repl_lst.append(global_wildcard == rest);
428 // No global wildcard, then the match fails if there are any
429 // unmatched terms left
433 return inherited::match(pattern, repl_lst);
436 ex expairseq::subs(const exmap & m, unsigned options) const
438 std::auto_ptr<epvector> vp = subschildren(m, options);
440 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
441 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
442 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
444 return subs_one_level(m, options);
449 int expairseq::compare_same_type(const basic &other) const
451 GINAC_ASSERT(is_a<expairseq>(other));
452 const expairseq &o = static_cast<const expairseq &>(other);
456 // compare number of elements
457 if (seq.size() != o.seq.size())
458 return (seq.size()<o.seq.size()) ? -1 : 1;
460 // compare overall_coeff
461 cmpval = overall_coeff.compare(o.overall_coeff);
465 #if EXPAIRSEQ_USE_HASHTAB
466 GINAC_ASSERT(hashtabsize==o.hashtabsize);
467 if (hashtabsize==0) {
468 #endif // EXPAIRSEQ_USE_HASHTAB
469 epvector::const_iterator cit1 = seq.begin();
470 epvector::const_iterator cit2 = o.seq.begin();
471 epvector::const_iterator last1 = seq.end();
472 epvector::const_iterator last2 = o.seq.end();
474 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
475 cmpval = (*cit1).compare(*cit2);
476 if (cmpval!=0) return cmpval;
479 GINAC_ASSERT(cit1==last1);
480 GINAC_ASSERT(cit2==last2);
483 #if EXPAIRSEQ_USE_HASHTAB
486 // compare number of elements in each hashtab entry
487 for (unsigned i=0; i<hashtabsize; ++i) {
488 unsigned cursize=hashtab[i].size();
489 if (cursize != o.hashtab[i].size())
490 return (cursize < o.hashtab[i].size()) ? -1 : 1;
493 // compare individual (sorted) hashtab entries
494 for (unsigned i=0; i<hashtabsize; ++i) {
495 unsigned sz = hashtab[i].size();
497 const epplist &eppl1 = hashtab[i];
498 const epplist &eppl2 = o.hashtab[i];
499 epplist::const_iterator it1 = eppl1.begin();
500 epplist::const_iterator it2 = eppl2.begin();
501 while (it1!=eppl1.end()) {
502 cmpval = (*(*it1)).compare(*(*it2));
512 #endif // EXPAIRSEQ_USE_HASHTAB
515 bool expairseq::is_equal_same_type(const basic &other) const
517 const expairseq &o = static_cast<const expairseq &>(other);
519 // compare number of elements
520 if (seq.size()!=o.seq.size())
523 // compare overall_coeff
524 if (!overall_coeff.is_equal(o.overall_coeff))
527 #if EXPAIRSEQ_USE_HASHTAB
528 // compare number of elements in each hashtab entry
529 if (hashtabsize!=o.hashtabsize) {
530 std::cout << "this:" << std::endl;
531 print(print_tree(std::cout));
532 std::cout << "other:" << std::endl;
533 other.print(print_tree(std::cout));
536 GINAC_ASSERT(hashtabsize==o.hashtabsize);
538 if (hashtabsize==0) {
539 #endif // EXPAIRSEQ_USE_HASHTAB
540 epvector::const_iterator cit1 = seq.begin();
541 epvector::const_iterator cit2 = o.seq.begin();
542 epvector::const_iterator last1 = seq.end();
544 while (cit1!=last1) {
545 if (!(*cit1).is_equal(*cit2)) return false;
551 #if EXPAIRSEQ_USE_HASHTAB
554 for (unsigned i=0; i<hashtabsize; ++i) {
555 if (hashtab[i].size() != o.hashtab[i].size())
559 // compare individual sorted hashtab entries
560 for (unsigned i=0; i<hashtabsize; ++i) {
561 unsigned sz = hashtab[i].size();
563 const epplist &eppl1 = hashtab[i];
564 const epplist &eppl2 = o.hashtab[i];
565 epplist::const_iterator it1 = eppl1.begin();
566 epplist::const_iterator it2 = eppl2.begin();
567 while (it1!=eppl1.end()) {
568 if (!(*(*it1)).is_equal(*(*it2))) return false;
576 #endif // EXPAIRSEQ_USE_HASHTAB
579 unsigned expairseq::return_type() const
581 return return_types::noncommutative_composite;
584 unsigned expairseq::calchash() const
586 unsigned v = golden_ratio_hash((p_int)this->tinfo());
587 epvector::const_iterator i = seq.begin();
588 const epvector::const_iterator end = seq.end();
590 v ^= i->rest.gethash();
591 #if !EXPAIRSEQ_USE_HASHTAB
592 // rotation spoils commutativity!
594 v ^= i->coeff.gethash();
595 #endif // !EXPAIRSEQ_USE_HASHTAB
599 v ^= overall_coeff.gethash();
601 // store calculated hash value only if object is already evaluated
602 if (flags &status_flags::evaluated) {
603 setflag(status_flags::hash_calculated);
610 ex expairseq::expand(unsigned options) const
612 std::auto_ptr<epvector> vp = expandchildren(options);
614 return thisexpairseq(vp, overall_coeff);
616 // The terms have not changed, so it is safe to declare this expanded
617 return (options == 0) ? setflag(status_flags::expanded) : *this;
622 // new virtual functions which can be overridden by derived classes
627 /** Create an object of this type.
628 * This method works similar to a constructor. It is useful because expairseq
629 * has (at least) two possible different semantics but we want to inherit
630 * methods thus avoiding code duplication. Sometimes a method in expairseq
631 * has to create a new one of the same semantics, which cannot be done by a
632 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
633 * order for this trick to work a derived class must of course override this
635 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
637 return expairseq(v, oc);
640 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
642 return expairseq(vp, oc);
645 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
648 p.rest.print(c, precedence());
650 p.coeff.print(c, precedence());
654 void expairseq::printseq(const print_context & c, char delim,
655 unsigned this_precedence,
656 unsigned upper_precedence) const
658 if (this_precedence <= upper_precedence)
660 epvector::const_iterator it, it_last = seq.end() - 1;
661 for (it=seq.begin(); it!=it_last; ++it) {
662 printpair(c, *it, this_precedence);
665 printpair(c, *it, this_precedence);
666 if (!overall_coeff.is_equal(default_overall_coeff())) {
668 overall_coeff.print(c, this_precedence);
671 if (this_precedence <= upper_precedence)
676 /** Form an expair from an ex, using the corresponding semantics.
677 * @see expairseq::recombine_pair_to_ex() */
678 expair expairseq::split_ex_to_pair(const ex &e) const
680 return expair(e,_ex1);
684 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
687 GINAC_ASSERT(is_exactly_a<numeric>(c));
693 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
696 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
697 GINAC_ASSERT(is_exactly_a<numeric>(c));
699 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
703 /** Form an ex out of an expair, using the corresponding semantics.
704 * @see expairseq::split_ex_to_pair() */
705 ex expairseq::recombine_pair_to_ex(const expair &p) const
707 return lst(p.rest,p.coeff);
710 bool expairseq::expair_needs_further_processing(epp it)
712 #if EXPAIRSEQ_USE_HASHTAB
713 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
714 #endif // EXPAIRSEQ_USE_HASHTAB
718 ex expairseq::default_overall_coeff() const
723 void expairseq::combine_overall_coeff(const ex &c)
725 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
726 GINAC_ASSERT(is_exactly_a<numeric>(c));
727 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
730 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
732 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
733 GINAC_ASSERT(is_exactly_a<numeric>(c1));
734 GINAC_ASSERT(is_exactly_a<numeric>(c2));
735 overall_coeff = ex_to<numeric>(overall_coeff).
736 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
739 bool expairseq::can_make_flat(const expair &p) const
746 // non-virtual functions in this class
749 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
755 construct_from_exvector(v);
756 #if EXPAIRSEQ_USE_HASHTAB
757 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
758 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
759 #endif // EXPAIRSEQ_USE_HASHTAB
762 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
764 if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
765 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
766 #if EXPAIRSEQ_USE_HASHTAB
767 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
768 ex_to<expairseq>(rh).seq.size();
769 if (calc_hashtabsize(totalsize)!=0) {
770 construct_from_2_ex_via_exvector(lh,rh);
772 #endif // EXPAIRSEQ_USE_HASHTAB
775 ex newrh=rename_dummy_indices_uniquely(lh, rh);
776 construct_from_2_expairseq(ex_to<expairseq>(lh),
777 ex_to<expairseq>(newrh));
780 construct_from_2_expairseq(ex_to<expairseq>(lh),
781 ex_to<expairseq>(rh));
782 #if EXPAIRSEQ_USE_HASHTAB
784 #endif // EXPAIRSEQ_USE_HASHTAB
787 #if EXPAIRSEQ_USE_HASHTAB
788 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
789 if (calc_hashtabsize(totalsize)!=0) {
790 construct_from_2_ex_via_exvector(lh, rh);
792 #endif // EXPAIRSEQ_USE_HASHTAB
793 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
794 #if EXPAIRSEQ_USE_HASHTAB
796 #endif // EXPAIRSEQ_USE_HASHTAB
799 } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
800 #if EXPAIRSEQ_USE_HASHTAB
801 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
802 if (calc_hashtabsize(totalsize)!=0) {
803 construct_from_2_ex_via_exvector(lh,rh);
805 #endif // EXPAIRSEQ_USE_HASHTAB
806 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
807 #if EXPAIRSEQ_USE_HASHTAB
809 #endif // EXPAIRSEQ_USE_HASHTAB
813 #if EXPAIRSEQ_USE_HASHTAB
814 if (calc_hashtabsize(2)!=0) {
815 construct_from_2_ex_via_exvector(lh,rh);
819 #endif // EXPAIRSEQ_USE_HASHTAB
821 if (is_exactly_a<numeric>(lh)) {
822 if (is_exactly_a<numeric>(rh)) {
823 combine_overall_coeff(lh);
824 combine_overall_coeff(rh);
826 combine_overall_coeff(lh);
827 seq.push_back(split_ex_to_pair(rh));
830 if (is_exactly_a<numeric>(rh)) {
831 combine_overall_coeff(rh);
832 seq.push_back(split_ex_to_pair(lh));
834 expair p1 = split_ex_to_pair(lh);
835 expair p2 = split_ex_to_pair(rh);
837 int cmpval = p1.rest.compare(p2.rest);
839 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
840 if (!ex_to<numeric>(p1.coeff).is_zero()) {
841 // no further processing is necessary, since this
842 // one element will usually be recombined in eval()
859 void expairseq::construct_from_2_expairseq(const expairseq &s1,
862 combine_overall_coeff(s1.overall_coeff);
863 combine_overall_coeff(s2.overall_coeff);
865 epvector::const_iterator first1 = s1.seq.begin();
866 epvector::const_iterator last1 = s1.seq.end();
867 epvector::const_iterator first2 = s2.seq.begin();
868 epvector::const_iterator last2 = s2.seq.end();
870 seq.reserve(s1.seq.size()+s2.seq.size());
872 bool needs_further_processing=false;
874 while (first1!=last1 && first2!=last2) {
875 int cmpval = (*first1).rest.compare((*first2).rest);
879 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
880 add(ex_to<numeric>(first2->coeff));
881 if (!newcoeff.is_zero()) {
882 seq.push_back(expair(first1->rest,newcoeff));
883 if (expair_needs_further_processing(seq.end()-1)) {
884 needs_further_processing = true;
889 } else if (cmpval<0) {
890 seq.push_back(*first1);
893 seq.push_back(*first2);
898 while (first1!=last1) {
899 seq.push_back(*first1);
902 while (first2!=last2) {
903 seq.push_back(*first2);
907 if (needs_further_processing) {
910 construct_from_epvector(v);
914 void expairseq::construct_from_expairseq_ex(const expairseq &s,
917 combine_overall_coeff(s.overall_coeff);
918 if (is_exactly_a<numeric>(e)) {
919 combine_overall_coeff(e);
924 epvector::const_iterator first = s.seq.begin();
925 epvector::const_iterator last = s.seq.end();
926 expair p = split_ex_to_pair(e);
928 seq.reserve(s.seq.size()+1);
929 bool p_pushed = false;
931 bool needs_further_processing=false;
933 // merge p into s.seq
934 while (first!=last) {
935 int cmpval = (*first).rest.compare(p.rest);
938 const numeric &newcoeff = ex_to<numeric>(first->coeff).
939 add(ex_to<numeric>(p.coeff));
940 if (!newcoeff.is_zero()) {
941 seq.push_back(expair(first->rest,newcoeff));
942 if (expair_needs_further_processing(seq.end()-1))
943 needs_further_processing = true;
948 } else if (cmpval<0) {
949 seq.push_back(*first);
959 // while loop exited because p was pushed, now push rest of s.seq
960 while (first!=last) {
961 seq.push_back(*first);
965 // while loop exited because s.seq was pushed, now push p
969 if (needs_further_processing) {
972 construct_from_epvector(v);
976 void expairseq::construct_from_exvector(const exvector &v)
978 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
979 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
980 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
981 // (same for (+,*) -> (*,^)
984 #if EXPAIRSEQ_USE_HASHTAB
985 combine_same_terms();
988 combine_same_terms_sorted_seq();
989 #endif // EXPAIRSEQ_USE_HASHTAB
992 void expairseq::construct_from_epvector(const epvector &v)
994 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
995 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
996 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
997 // (same for (+,*) -> (*,^)
1000 #if EXPAIRSEQ_USE_HASHTAB
1001 combine_same_terms();
1004 combine_same_terms_sorted_seq();
1005 #endif // EXPAIRSEQ_USE_HASHTAB
1008 /** Combine this expairseq with argument exvector.
1009 * It cares for associativity as well as for special handling of numerics. */
1010 void expairseq::make_flat(const exvector &v)
1012 exvector::const_iterator cit;
1014 // count number of operands which are of same expairseq derived type
1015 // and their cumulative number of operands
1016 int nexpairseqs = 0;
1020 while (cit!=v.end()) {
1021 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1023 noperands += ex_to<expairseq>(*cit).seq.size();
1028 // reserve seq and coeffseq which will hold all operands
1029 seq.reserve(v.size()+noperands-nexpairseqs);
1031 // copy elements and split off numerical part
1032 exvector dummy_indices;
1034 while (cit!=v.end()) {
1035 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1036 const expairseq *subseqref;
1040 exvector dummies_of_factor = get_all_dummy_indices(*cit);
1041 sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
1042 newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, *cit);
1043 subseqref = &(ex_to<expairseq>(newfactor));
1044 exvector new_dummy_indices;
1045 set_union(dummy_indices.begin(), dummy_indices.end(), dummies_of_factor.begin(), dummies_of_factor.end(), std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1046 dummy_indices.swap(new_dummy_indices);
1049 subseqref = &ex_to<expairseq>(*cit);
1050 combine_overall_coeff(subseqref->overall_coeff);
1051 epvector::const_iterator cit_s = subseqref->seq.begin();
1052 while (cit_s!=subseqref->seq.end()) {
1053 seq.push_back(*cit_s);
1057 if (is_exactly_a<numeric>(*cit))
1058 combine_overall_coeff(*cit);
1060 seq.push_back(split_ex_to_pair(*cit));
1066 /** Combine this expairseq with argument epvector.
1067 * It cares for associativity as well as for special handling of numerics. */
1068 void expairseq::make_flat(const epvector &v)
1070 epvector::const_iterator cit;
1072 // count number of operands which are of same expairseq derived type
1073 // and their cumulative number of operands
1074 int nexpairseqs = 0;
1078 while (cit!=v.end()) {
1079 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1081 noperands += ex_to<expairseq>(cit->rest).seq.size();
1086 // reserve seq and coeffseq which will hold all operands
1087 seq.reserve(v.size()+noperands-nexpairseqs);
1089 // copy elements and split off numerical part
1091 while (cit!=v.end()) {
1092 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1093 this->can_make_flat(*cit)) {
1094 const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1095 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1096 ex_to<numeric>(cit->coeff));
1097 epvector::const_iterator cit_s = subseqref.seq.begin();
1098 while (cit_s!=subseqref.seq.end()) {
1099 seq.push_back(expair(cit_s->rest,
1100 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1101 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1106 if (cit->is_canonical_numeric())
1107 combine_overall_coeff(cit->rest);
1109 seq.push_back(*cit);
1115 /** Brings this expairseq into a sorted (canonical) form. */
1116 void expairseq::canonicalize()
1118 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1122 /** Compact a presorted expairseq by combining all matching expairs to one
1123 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1125 void expairseq::combine_same_terms_sorted_seq()
1130 bool needs_further_processing = false;
1132 epvector::iterator itin1 = seq.begin();
1133 epvector::iterator itin2 = itin1+1;
1134 epvector::iterator itout = itin1;
1135 epvector::iterator last = seq.end();
1136 // must_copy will be set to true the first time some combination is
1137 // possible from then on the sequence has changed and must be compacted
1138 bool must_copy = false;
1139 while (itin2!=last) {
1140 if (itin1->rest.compare(itin2->rest)==0) {
1141 itin1->coeff = ex_to<numeric>(itin1->coeff).
1142 add_dyn(ex_to<numeric>(itin2->coeff));
1143 if (expair_needs_further_processing(itin1))
1144 needs_further_processing = true;
1147 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1156 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1162 seq.erase(itout,last);
1164 if (needs_further_processing) {
1167 construct_from_epvector(v);
1171 #if EXPAIRSEQ_USE_HASHTAB
1173 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1176 unsigned nearest_power_of_2 = 1 << log2(sz);
1177 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1178 // size = nearest_power_of_2*hashtabfactor;
1179 size = nearest_power_of_2/hashtabfactor;
1180 if (size<minhashtabsize)
1183 // hashtabsize must be a power of 2
1184 GINAC_ASSERT((1U << log2(size))==size);
1188 unsigned expairseq::calc_hashindex(const ex &e) const
1190 // calculate hashindex
1192 if (is_a<numeric>(e)) {
1193 hashindex = hashmask;
1195 hashindex = e.gethash() & hashmask;
1196 // last hashtab entry is reserved for numerics
1197 if (hashindex==hashmask) hashindex = 0;
1199 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1203 void expairseq::shrink_hashtab()
1205 unsigned new_hashtabsize;
1206 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1207 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1208 if (new_hashtabsize==0) {
1215 // shrink by a factor of 2
1216 unsigned half_hashtabsize = hashtabsize/2;
1217 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1218 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1219 // special treatment for numeric hashes
1220 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1221 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1222 hashtab.resize(half_hashtabsize);
1223 hashtabsize = half_hashtabsize;
1224 hashmask = hashtabsize-1;
1228 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1231 return; // nothing to do
1233 // calculate hashindex of element to be deleted
1234 unsigned hashindex = calc_hashindex((*element).rest);
1236 // find it in hashtab and remove it
1237 epplist &eppl = hashtab[hashindex];
1238 epplist::iterator epplit = eppl.begin();
1239 bool erased = false;
1240 while (epplit!=eppl.end()) {
1241 if (*epplit == element) {
1249 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1250 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1252 unsigned hashindex = calc_hashindex(element->rest);
1253 epplist &eppl = hashtab[hashindex];
1254 epplist::iterator epplit = eppl.begin();
1255 bool erased = false;
1256 while (epplit!=eppl.end()) {
1257 if (*epplit == element) {
1264 GINAC_ASSERT(erased);
1266 GINAC_ASSERT(erased);
1269 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1270 epvector::iterator newpos)
1272 GINAC_ASSERT(hashtabsize!=0);
1274 // calculate hashindex of element which was moved
1275 unsigned hashindex=calc_hashindex((*newpos).rest);
1277 // find it in hashtab and modify it
1278 epplist &eppl = hashtab[hashindex];
1279 epplist::iterator epplit = eppl.begin();
1280 while (epplit!=eppl.end()) {
1281 if (*epplit == oldpos) {
1287 GINAC_ASSERT(epplit!=eppl.end());
1290 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1292 epplist::const_iterator current = eppl.begin();
1293 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1296 eppl.insert(current,elem);
1299 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1300 epvector::iterator &last_non_zero,
1301 std::vector<bool> &touched,
1302 unsigned &number_of_zeroes)
1304 epp current = seq.begin();
1306 while (current!=first_numeric) {
1307 if (is_exactly_a<numeric>(current->rest)) {
1309 iter_swap(current,first_numeric);
1311 // calculate hashindex
1312 unsigned currenthashindex = calc_hashindex(current->rest);
1314 // test if there is already a matching expair in the hashtab-list
1315 epplist &eppl=hashtab[currenthashindex];
1316 epplist::iterator epplit = eppl.begin();
1317 while (epplit!=eppl.end()) {
1318 if (current->rest.is_equal((*epplit)->rest))
1322 if (epplit==eppl.end()) {
1323 // no matching expair found, append this to end of list
1324 sorted_insert(eppl,current);
1327 // epplit points to a matching expair, combine it with current
1328 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1329 add_dyn(ex_to<numeric>(current->coeff));
1331 // move obsolete current expair to end by swapping with last_non_zero element
1332 // if this was a numeric, it is swapped with the expair before first_numeric
1333 iter_swap(current,last_non_zero);
1335 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1338 // test if combined term has coeff 0 and can be removed is done later
1339 touched[(*epplit)-seq.begin()] = true;
1345 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1346 epvector::iterator &last_non_zero,
1347 std::vector<bool> &touched,
1348 unsigned &number_of_zeroes)
1350 // move terms with coeff 0 to end and remove them from hashtab
1351 // check only those elements which have been touched
1352 epp current = seq.begin();
1354 while (current!=first_numeric) {
1358 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1362 remove_hashtab_entry(current);
1364 // move element to the end, unless it is already at the end
1365 if (current!=last_non_zero) {
1366 iter_swap(current,last_non_zero);
1368 bool numeric_swapped = first_numeric!=last_non_zero;
1369 if (numeric_swapped)
1370 iter_swap(first_numeric,current);
1371 epvector::iterator changed_entry;
1373 if (numeric_swapped)
1374 changed_entry = first_numeric;
1376 changed_entry = last_non_zero;
1381 if (first_numeric!=current) {
1383 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1384 move_hashtab_entry(changed_entry,current);
1385 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1394 GINAC_ASSERT(i==current-seq.begin());
1397 /** True if one of the coeffs vanishes, otherwise false.
1398 * This would be an invariant violation, so this should only be used for
1399 * debugging purposes. */
1400 bool expairseq::has_coeff_0() const
1402 epvector::const_iterator i = seq.begin(), end = seq.end();
1404 if (i->coeff.is_zero())
1411 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1412 epvector::const_iterator last_non_zero)
1414 if (first_numeric == seq.end()) return; // no numerics
1416 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1417 while (current != last) {
1418 sorted_insert(hashtab[hashmask], current);
1423 void expairseq::combine_same_terms()
1425 // combine same terms, drop term with coeff 0, move numerics to end
1427 // calculate size of hashtab
1428 hashtabsize = calc_hashtabsize(seq.size());
1430 // hashtabsize is a power of 2
1431 hashmask = hashtabsize-1;
1435 hashtab.resize(hashtabsize);
1437 if (hashtabsize==0) {
1439 combine_same_terms_sorted_seq();
1440 GINAC_ASSERT(!has_coeff_0());
1444 // iterate through seq, move numerics to end,
1445 // fill hashtab and combine same terms
1446 epvector::iterator first_numeric = seq.end();
1447 epvector::iterator last_non_zero = seq.end()-1;
1449 size_t num = seq.size();
1450 std::vector<bool> touched(num);
1452 unsigned number_of_zeroes = 0;
1454 GINAC_ASSERT(!has_coeff_0());
1455 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1457 // there should not be any terms with coeff 0 from the beginning,
1458 // so it should be safe to skip this step
1459 if (number_of_zeroes!=0) {
1460 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1463 add_numerics_to_hashtab(first_numeric,last_non_zero);
1465 // pop zero elements
1466 for (unsigned i=0; i<number_of_zeroes; ++i) {
1470 // shrink hashtabsize to calculated value
1471 GINAC_ASSERT(!has_coeff_0());
1475 GINAC_ASSERT(!has_coeff_0());
1478 #endif // EXPAIRSEQ_USE_HASHTAB
1480 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1481 * debugging or in assertions since being sorted is an invariance. */
1482 bool expairseq::is_canonical() const
1484 if (seq.size() <= 1)
1487 #if EXPAIRSEQ_USE_HASHTAB
1488 if (hashtabsize > 0) return 1; // not canoncalized
1489 #endif // EXPAIRSEQ_USE_HASHTAB
1491 epvector::const_iterator it = seq.begin(), itend = seq.end();
1492 epvector::const_iterator it_last = it;
1493 for (++it; it!=itend; it_last=it, ++it) {
1494 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1495 if (!is_exactly_a<numeric>(it_last->rest) ||
1496 !is_exactly_a<numeric>(it->rest)) {
1497 // double test makes it easier to set a breakpoint...
1498 if (!is_exactly_a<numeric>(it_last->rest) ||
1499 !is_exactly_a<numeric>(it->rest)) {
1500 printpair(std::clog, *it_last, 0);
1502 printpair(std::clog, *it, 0);
1504 std::clog << "pair1:" << std::endl;
1505 it_last->rest.print(print_tree(std::clog));
1506 it_last->coeff.print(print_tree(std::clog));
1507 std::clog << "pair2:" << std::endl;
1508 it->rest.print(print_tree(std::clog));
1509 it->coeff.print(print_tree(std::clog));
1519 /** Member-wise expand the expairs in this sequence.
1521 * @see expairseq::expand()
1522 * @return pointer to epvector containing expanded pairs or zero pointer,
1523 * if no members were changed. */
1524 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1526 const epvector::const_iterator last = seq.end();
1527 epvector::const_iterator cit = seq.begin();
1529 const ex &expanded_ex = cit->rest.expand(options);
1530 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1532 // something changed, copy seq, eval and return it
1533 std::auto_ptr<epvector> s(new epvector);
1534 s->reserve(seq.size());
1536 // copy parts of seq which are known not to have changed
1537 epvector::const_iterator cit2 = seq.begin();
1539 s->push_back(*cit2);
1543 // copy first changed element
1544 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1549 while (cit2!=last) {
1550 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1559 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1563 /** Member-wise evaluate the expairs in this sequence.
1565 * @see expairseq::eval()
1566 * @return pointer to epvector containing evaluated pairs or zero pointer,
1567 * if no members were changed. */
1568 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1570 // returns a NULL pointer if nothing had to be evaluated
1571 // returns a pointer to a newly created epvector otherwise
1572 // (which has to be deleted somewhere else)
1575 return std::auto_ptr<epvector>(0);
1577 if (level == -max_recursion_level)
1578 throw(std::runtime_error("max recursion level reached"));
1581 epvector::const_iterator last = seq.end();
1582 epvector::const_iterator cit = seq.begin();
1584 const ex &evaled_ex = cit->rest.eval(level);
1585 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1587 // something changed, copy seq, eval and return it
1588 std::auto_ptr<epvector> s(new epvector);
1589 s->reserve(seq.size());
1591 // copy parts of seq which are known not to have changed
1592 epvector::const_iterator cit2=seq.begin();
1594 s->push_back(*cit2);
1598 // copy first changed element
1599 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1604 while (cit2!=last) {
1605 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1614 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1620 safe_inserter(const ex&, const bool disable_renaming=false);
1621 std::auto_ptr<epvector> getseq(){return epv;}
1622 void insert_old_pair(const expair &p)
1626 void insert_new_pair(const expair &p, const ex &orig_ex);
1628 std::auto_ptr<epvector> epv;
1630 exvector dummy_indices;
1631 void update_dummy_indices(const exvector&);
1634 safe_inserter::safe_inserter(const ex&e, const bool disable_renaming)
1637 epv->reserve(e.nops());
1638 dodummies=is_a<mul>(e);
1639 if(disable_renaming)
1642 dummy_indices = get_all_dummy_indices_safely(e);
1643 sort(dummy_indices.begin(), dummy_indices.end(), ex_is_less());
1647 void safe_inserter::update_dummy_indices(const exvector &v)
1649 exvector new_dummy_indices;
1650 set_union(dummy_indices.begin(), dummy_indices.end(), v.begin(), v.end(),
1651 std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1652 dummy_indices.swap(new_dummy_indices);
1655 void safe_inserter::insert_new_pair(const expair &p, const ex &orig_ex)
1661 exvector dummies_of_factor = get_all_dummy_indices_safely(p.rest);
1662 if(dummies_of_factor.size() == 0) {
1666 sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
1667 exvector dummies_of_orig_ex = get_all_dummy_indices_safely(orig_ex);
1668 sort(dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(), ex_is_less());
1669 exvector new_dummy_indices;
1670 new_dummy_indices.reserve(dummy_indices.size());
1671 set_difference(dummy_indices.begin(), dummy_indices.end(), dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(),
1672 std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1673 dummy_indices.swap(new_dummy_indices);
1674 ex newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, p.rest);
1675 update_dummy_indices(dummies_of_factor);
1676 epv -> push_back(expair(newfactor, p.coeff));
1679 /** Member-wise substitute in this sequence.
1681 * @see expairseq::subs()
1682 * @return pointer to epvector containing pairs after application of subs,
1683 * or NULL pointer if no members were changed. */
1684 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1686 // When any of the objects to be substituted is a product or power
1687 // we have to recombine the pairs because the numeric coefficients may
1688 // be part of the search pattern.
1689 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1691 // Search the list of substitutions and cache our findings
1692 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1693 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1694 options |= subs_options::pattern_is_product;
1698 if (!(options & subs_options::pattern_is_product))
1699 options |= subs_options::pattern_is_not_product;
1702 if (options & subs_options::pattern_is_product) {
1704 // Substitute in the recombined pairs
1705 epvector::const_iterator cit = seq.begin(), last = seq.end();
1706 while (cit != last) {
1708 const ex &orig_ex = recombine_pair_to_ex(*cit);
1709 const ex &subsed_ex = orig_ex.subs(m, options);
1710 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1712 // Something changed, copy seq, subs and return it
1713 safe_inserter s(*this, options & subs_options::no_index_renaming);
1715 // Copy parts of seq which are known not to have changed
1716 for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
1717 s.insert_old_pair(*i);
1719 // Copy first changed element
1720 s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
1724 while (cit != last) {
1725 ex orig_ex = recombine_pair_to_ex(*cit);
1726 ex subsed_ex = orig_ex.subs(m, options);
1727 if(are_ex_trivially_equal(orig_ex, subsed_ex))
1728 s.insert_old_pair(*cit);
1730 s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
1741 // Substitute only in the "rest" part of the pairs
1742 epvector::const_iterator cit = seq.begin(), last = seq.end();
1743 while (cit != last) {
1745 const ex &subsed_ex = cit->rest.subs(m, options);
1746 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1748 // Something changed, copy seq, subs and return it
1749 safe_inserter s(*this, options & subs_options::no_index_renaming);
1751 // Copy parts of seq which are known not to have changed
1752 for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
1753 s.insert_old_pair(*i);
1755 // Copy first changed element
1756 s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), cit->rest);
1760 while (cit != last) {
1761 const ex &orig_ex = cit->rest;
1762 const ex &subsed_ex = cit->rest.subs(m, options);
1763 if(are_ex_trivially_equal(orig_ex, subsed_ex))
1764 s.insert_old_pair(*cit);
1766 s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), orig_ex);
1776 // Nothing has changed
1777 return std::auto_ptr<epvector>(0);
1781 // static member variables
1784 #if EXPAIRSEQ_USE_HASHTAB
1785 unsigned expairseq::maxhashtabsize = 0x4000000U;
1786 unsigned expairseq::minhashtabsize = 0x1000U;
1787 unsigned expairseq::hashtabfactor = 1;
1788 #endif // EXPAIRSEQ_USE_HASHTAB
1790 } // namespace GiNaC