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 lst::const_iterator last_el = repl_lst.end();
400 if (it->match(p, repl_lst)) {
405 lst::const_iterator next_el = last_el;
407 if(next_el == repl_lst.end())
410 repl_lst.remove_last();
414 return false; // no match found
418 if (has_global_wildcard) {
420 // Assign all the remaining terms to the global wildcard (unless
421 // it has already been matched before, in which case the matches
423 size_t num = ops.size();
424 std::auto_ptr<epvector> vp(new epvector);
426 for (size_t i=0; i<num; i++)
427 vp->push_back(split_ex_to_pair(ops[i]));
428 ex rest = thisexpairseq(vp, default_overall_coeff());
429 for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
430 if (it->op(0).is_equal(global_wildcard))
431 return rest.is_equal(it->op(1));
433 repl_lst.append(global_wildcard == rest);
438 // No global wildcard, then the match fails if there are any
439 // unmatched terms left
443 return inherited::match(pattern, repl_lst);
446 ex expairseq::subs(const exmap & m, unsigned options) const
448 std::auto_ptr<epvector> vp = subschildren(m, options);
450 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
451 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
452 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
454 return subs_one_level(m, options);
459 int expairseq::compare_same_type(const basic &other) const
461 GINAC_ASSERT(is_a<expairseq>(other));
462 const expairseq &o = static_cast<const expairseq &>(other);
466 // compare number of elements
467 if (seq.size() != o.seq.size())
468 return (seq.size()<o.seq.size()) ? -1 : 1;
470 // compare overall_coeff
471 cmpval = overall_coeff.compare(o.overall_coeff);
475 #if EXPAIRSEQ_USE_HASHTAB
476 GINAC_ASSERT(hashtabsize==o.hashtabsize);
477 if (hashtabsize==0) {
478 #endif // EXPAIRSEQ_USE_HASHTAB
479 epvector::const_iterator cit1 = seq.begin();
480 epvector::const_iterator cit2 = o.seq.begin();
481 epvector::const_iterator last1 = seq.end();
482 epvector::const_iterator last2 = o.seq.end();
484 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
485 cmpval = (*cit1).compare(*cit2);
486 if (cmpval!=0) return cmpval;
489 GINAC_ASSERT(cit1==last1);
490 GINAC_ASSERT(cit2==last2);
493 #if EXPAIRSEQ_USE_HASHTAB
496 // compare number of elements in each hashtab entry
497 for (unsigned i=0; i<hashtabsize; ++i) {
498 unsigned cursize=hashtab[i].size();
499 if (cursize != o.hashtab[i].size())
500 return (cursize < o.hashtab[i].size()) ? -1 : 1;
503 // compare individual (sorted) hashtab entries
504 for (unsigned i=0; i<hashtabsize; ++i) {
505 unsigned sz = hashtab[i].size();
507 const epplist &eppl1 = hashtab[i];
508 const epplist &eppl2 = o.hashtab[i];
509 epplist::const_iterator it1 = eppl1.begin();
510 epplist::const_iterator it2 = eppl2.begin();
511 while (it1!=eppl1.end()) {
512 cmpval = (*(*it1)).compare(*(*it2));
522 #endif // EXPAIRSEQ_USE_HASHTAB
525 bool expairseq::is_equal_same_type(const basic &other) const
527 const expairseq &o = static_cast<const expairseq &>(other);
529 // compare number of elements
530 if (seq.size()!=o.seq.size())
533 // compare overall_coeff
534 if (!overall_coeff.is_equal(o.overall_coeff))
537 #if EXPAIRSEQ_USE_HASHTAB
538 // compare number of elements in each hashtab entry
539 if (hashtabsize!=o.hashtabsize) {
540 std::cout << "this:" << std::endl;
541 print(print_tree(std::cout));
542 std::cout << "other:" << std::endl;
543 other.print(print_tree(std::cout));
546 GINAC_ASSERT(hashtabsize==o.hashtabsize);
548 if (hashtabsize==0) {
549 #endif // EXPAIRSEQ_USE_HASHTAB
550 epvector::const_iterator cit1 = seq.begin();
551 epvector::const_iterator cit2 = o.seq.begin();
552 epvector::const_iterator last1 = seq.end();
554 while (cit1!=last1) {
555 if (!(*cit1).is_equal(*cit2)) return false;
561 #if EXPAIRSEQ_USE_HASHTAB
564 for (unsigned i=0; i<hashtabsize; ++i) {
565 if (hashtab[i].size() != o.hashtab[i].size())
569 // compare individual sorted hashtab entries
570 for (unsigned i=0; i<hashtabsize; ++i) {
571 unsigned sz = hashtab[i].size();
573 const epplist &eppl1 = hashtab[i];
574 const epplist &eppl2 = o.hashtab[i];
575 epplist::const_iterator it1 = eppl1.begin();
576 epplist::const_iterator it2 = eppl2.begin();
577 while (it1!=eppl1.end()) {
578 if (!(*(*it1)).is_equal(*(*it2))) return false;
586 #endif // EXPAIRSEQ_USE_HASHTAB
589 unsigned expairseq::return_type() const
591 return return_types::noncommutative_composite;
594 unsigned expairseq::calchash() const
596 unsigned v = golden_ratio_hash((p_int)this->tinfo());
597 epvector::const_iterator i = seq.begin();
598 const epvector::const_iterator end = seq.end();
600 v ^= i->rest.gethash();
601 #if !EXPAIRSEQ_USE_HASHTAB
602 // rotation spoils commutativity!
604 v ^= i->coeff.gethash();
605 #endif // !EXPAIRSEQ_USE_HASHTAB
609 v ^= overall_coeff.gethash();
611 // store calculated hash value only if object is already evaluated
612 if (flags &status_flags::evaluated) {
613 setflag(status_flags::hash_calculated);
620 ex expairseq::expand(unsigned options) const
622 std::auto_ptr<epvector> vp = expandchildren(options);
624 return thisexpairseq(vp, overall_coeff);
626 // The terms have not changed, so it is safe to declare this expanded
627 return (options == 0) ? setflag(status_flags::expanded) : *this;
632 // new virtual functions which can be overridden by derived classes
637 /** Create an object of this type.
638 * This method works similar to a constructor. It is useful because expairseq
639 * has (at least) two possible different semantics but we want to inherit
640 * methods thus avoiding code duplication. Sometimes a method in expairseq
641 * has to create a new one of the same semantics, which cannot be done by a
642 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
643 * order for this trick to work a derived class must of course override this
645 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
647 return expairseq(v, oc);
650 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
652 return expairseq(vp, oc);
655 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
658 p.rest.print(c, precedence());
660 p.coeff.print(c, precedence());
664 void expairseq::printseq(const print_context & c, char delim,
665 unsigned this_precedence,
666 unsigned upper_precedence) const
668 if (this_precedence <= upper_precedence)
670 epvector::const_iterator it, it_last = seq.end() - 1;
671 for (it=seq.begin(); it!=it_last; ++it) {
672 printpair(c, *it, this_precedence);
675 printpair(c, *it, this_precedence);
676 if (!overall_coeff.is_equal(default_overall_coeff())) {
678 overall_coeff.print(c, this_precedence);
681 if (this_precedence <= upper_precedence)
686 /** Form an expair from an ex, using the corresponding semantics.
687 * @see expairseq::recombine_pair_to_ex() */
688 expair expairseq::split_ex_to_pair(const ex &e) const
690 return expair(e,_ex1);
694 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
697 GINAC_ASSERT(is_exactly_a<numeric>(c));
703 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
706 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
707 GINAC_ASSERT(is_exactly_a<numeric>(c));
709 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
713 /** Form an ex out of an expair, using the corresponding semantics.
714 * @see expairseq::split_ex_to_pair() */
715 ex expairseq::recombine_pair_to_ex(const expair &p) const
717 return lst(p.rest,p.coeff);
720 bool expairseq::expair_needs_further_processing(epp it)
722 #if EXPAIRSEQ_USE_HASHTAB
723 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
724 #endif // EXPAIRSEQ_USE_HASHTAB
728 ex expairseq::default_overall_coeff() const
733 void expairseq::combine_overall_coeff(const ex &c)
735 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
736 GINAC_ASSERT(is_exactly_a<numeric>(c));
737 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
740 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
742 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
743 GINAC_ASSERT(is_exactly_a<numeric>(c1));
744 GINAC_ASSERT(is_exactly_a<numeric>(c2));
745 overall_coeff = ex_to<numeric>(overall_coeff).
746 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
749 bool expairseq::can_make_flat(const expair &p) const
756 // non-virtual functions in this class
759 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
765 construct_from_exvector(v);
766 #if EXPAIRSEQ_USE_HASHTAB
767 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
768 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
769 #endif // EXPAIRSEQ_USE_HASHTAB
772 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
774 if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
775 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
776 #if EXPAIRSEQ_USE_HASHTAB
777 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
778 ex_to<expairseq>(rh).seq.size();
779 if (calc_hashtabsize(totalsize)!=0) {
780 construct_from_2_ex_via_exvector(lh,rh);
782 #endif // EXPAIRSEQ_USE_HASHTAB
785 ex newrh=rename_dummy_indices_uniquely(lh, rh);
786 construct_from_2_expairseq(ex_to<expairseq>(lh),
787 ex_to<expairseq>(newrh));
790 construct_from_2_expairseq(ex_to<expairseq>(lh),
791 ex_to<expairseq>(rh));
792 #if EXPAIRSEQ_USE_HASHTAB
794 #endif // EXPAIRSEQ_USE_HASHTAB
797 #if EXPAIRSEQ_USE_HASHTAB
798 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
799 if (calc_hashtabsize(totalsize)!=0) {
800 construct_from_2_ex_via_exvector(lh, rh);
802 #endif // EXPAIRSEQ_USE_HASHTAB
803 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
804 #if EXPAIRSEQ_USE_HASHTAB
806 #endif // EXPAIRSEQ_USE_HASHTAB
809 } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
810 #if EXPAIRSEQ_USE_HASHTAB
811 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
812 if (calc_hashtabsize(totalsize)!=0) {
813 construct_from_2_ex_via_exvector(lh,rh);
815 #endif // EXPAIRSEQ_USE_HASHTAB
816 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
817 #if EXPAIRSEQ_USE_HASHTAB
819 #endif // EXPAIRSEQ_USE_HASHTAB
823 #if EXPAIRSEQ_USE_HASHTAB
824 if (calc_hashtabsize(2)!=0) {
825 construct_from_2_ex_via_exvector(lh,rh);
829 #endif // EXPAIRSEQ_USE_HASHTAB
831 if (is_exactly_a<numeric>(lh)) {
832 if (is_exactly_a<numeric>(rh)) {
833 combine_overall_coeff(lh);
834 combine_overall_coeff(rh);
836 combine_overall_coeff(lh);
837 seq.push_back(split_ex_to_pair(rh));
840 if (is_exactly_a<numeric>(rh)) {
841 combine_overall_coeff(rh);
842 seq.push_back(split_ex_to_pair(lh));
844 expair p1 = split_ex_to_pair(lh);
845 expair p2 = split_ex_to_pair(rh);
847 int cmpval = p1.rest.compare(p2.rest);
849 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
850 if (!ex_to<numeric>(p1.coeff).is_zero()) {
851 // no further processing is necessary, since this
852 // one element will usually be recombined in eval()
869 void expairseq::construct_from_2_expairseq(const expairseq &s1,
872 combine_overall_coeff(s1.overall_coeff);
873 combine_overall_coeff(s2.overall_coeff);
875 epvector::const_iterator first1 = s1.seq.begin();
876 epvector::const_iterator last1 = s1.seq.end();
877 epvector::const_iterator first2 = s2.seq.begin();
878 epvector::const_iterator last2 = s2.seq.end();
880 seq.reserve(s1.seq.size()+s2.seq.size());
882 bool needs_further_processing=false;
884 while (first1!=last1 && first2!=last2) {
885 int cmpval = (*first1).rest.compare((*first2).rest);
889 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
890 add(ex_to<numeric>(first2->coeff));
891 if (!newcoeff.is_zero()) {
892 seq.push_back(expair(first1->rest,newcoeff));
893 if (expair_needs_further_processing(seq.end()-1)) {
894 needs_further_processing = true;
899 } else if (cmpval<0) {
900 seq.push_back(*first1);
903 seq.push_back(*first2);
908 while (first1!=last1) {
909 seq.push_back(*first1);
912 while (first2!=last2) {
913 seq.push_back(*first2);
917 if (needs_further_processing) {
920 construct_from_epvector(v);
924 void expairseq::construct_from_expairseq_ex(const expairseq &s,
927 combine_overall_coeff(s.overall_coeff);
928 if (is_exactly_a<numeric>(e)) {
929 combine_overall_coeff(e);
934 epvector::const_iterator first = s.seq.begin();
935 epvector::const_iterator last = s.seq.end();
936 expair p = split_ex_to_pair(e);
938 seq.reserve(s.seq.size()+1);
939 bool p_pushed = false;
941 bool needs_further_processing=false;
943 // merge p into s.seq
944 while (first!=last) {
945 int cmpval = (*first).rest.compare(p.rest);
948 const numeric &newcoeff = ex_to<numeric>(first->coeff).
949 add(ex_to<numeric>(p.coeff));
950 if (!newcoeff.is_zero()) {
951 seq.push_back(expair(first->rest,newcoeff));
952 if (expair_needs_further_processing(seq.end()-1))
953 needs_further_processing = true;
958 } else if (cmpval<0) {
959 seq.push_back(*first);
969 // while loop exited because p was pushed, now push rest of s.seq
970 while (first!=last) {
971 seq.push_back(*first);
975 // while loop exited because s.seq was pushed, now push p
979 if (needs_further_processing) {
982 construct_from_epvector(v);
986 void expairseq::construct_from_exvector(const exvector &v)
988 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
989 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
990 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
991 // (same for (+,*) -> (*,^)
994 #if EXPAIRSEQ_USE_HASHTAB
995 combine_same_terms();
998 combine_same_terms_sorted_seq();
999 #endif // EXPAIRSEQ_USE_HASHTAB
1002 void expairseq::construct_from_epvector(const epvector &v)
1004 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1005 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1006 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1007 // (same for (+,*) -> (*,^)
1010 #if EXPAIRSEQ_USE_HASHTAB
1011 combine_same_terms();
1014 combine_same_terms_sorted_seq();
1015 #endif // EXPAIRSEQ_USE_HASHTAB
1018 /** Combine this expairseq with argument exvector.
1019 * It cares for associativity as well as for special handling of numerics. */
1020 void expairseq::make_flat(const exvector &v)
1022 exvector::const_iterator cit;
1024 // count number of operands which are of same expairseq derived type
1025 // and their cumulative number of operands
1026 int nexpairseqs = 0;
1030 while (cit!=v.end()) {
1031 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1033 noperands += ex_to<expairseq>(*cit).seq.size();
1038 // reserve seq and coeffseq which will hold all operands
1039 seq.reserve(v.size()+noperands-nexpairseqs);
1041 // copy elements and split off numerical part
1042 exvector dummy_indices;
1044 while (cit!=v.end()) {
1045 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1046 const expairseq *subseqref;
1050 exvector dummies_of_factor = get_all_dummy_indices(*cit);
1051 sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
1052 newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, *cit);
1053 subseqref = &(ex_to<expairseq>(newfactor));
1054 exvector new_dummy_indices;
1055 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());
1056 dummy_indices.swap(new_dummy_indices);
1059 subseqref = &ex_to<expairseq>(*cit);
1060 combine_overall_coeff(subseqref->overall_coeff);
1061 epvector::const_iterator cit_s = subseqref->seq.begin();
1062 while (cit_s!=subseqref->seq.end()) {
1063 seq.push_back(*cit_s);
1067 if (is_exactly_a<numeric>(*cit))
1068 combine_overall_coeff(*cit);
1070 seq.push_back(split_ex_to_pair(*cit));
1076 /** Combine this expairseq with argument epvector.
1077 * It cares for associativity as well as for special handling of numerics. */
1078 void expairseq::make_flat(const epvector &v)
1080 epvector::const_iterator cit;
1082 // count number of operands which are of same expairseq derived type
1083 // and their cumulative number of operands
1084 int nexpairseqs = 0;
1088 while (cit!=v.end()) {
1089 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1091 noperands += ex_to<expairseq>(cit->rest).seq.size();
1096 // reserve seq and coeffseq which will hold all operands
1097 seq.reserve(v.size()+noperands-nexpairseqs);
1099 // copy elements and split off numerical part
1101 while (cit!=v.end()) {
1102 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1103 this->can_make_flat(*cit)) {
1104 const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1105 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1106 ex_to<numeric>(cit->coeff));
1107 epvector::const_iterator cit_s = subseqref.seq.begin();
1108 while (cit_s!=subseqref.seq.end()) {
1109 seq.push_back(expair(cit_s->rest,
1110 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1111 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1116 if (cit->is_canonical_numeric())
1117 combine_overall_coeff(cit->rest);
1119 seq.push_back(*cit);
1125 /** Brings this expairseq into a sorted (canonical) form. */
1126 void expairseq::canonicalize()
1128 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1132 /** Compact a presorted expairseq by combining all matching expairs to one
1133 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1135 void expairseq::combine_same_terms_sorted_seq()
1140 bool needs_further_processing = false;
1142 epvector::iterator itin1 = seq.begin();
1143 epvector::iterator itin2 = itin1+1;
1144 epvector::iterator itout = itin1;
1145 epvector::iterator last = seq.end();
1146 // must_copy will be set to true the first time some combination is
1147 // possible from then on the sequence has changed and must be compacted
1148 bool must_copy = false;
1149 while (itin2!=last) {
1150 if (itin1->rest.compare(itin2->rest)==0) {
1151 itin1->coeff = ex_to<numeric>(itin1->coeff).
1152 add_dyn(ex_to<numeric>(itin2->coeff));
1153 if (expair_needs_further_processing(itin1))
1154 needs_further_processing = true;
1157 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1166 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1172 seq.erase(itout,last);
1174 if (needs_further_processing) {
1177 construct_from_epvector(v);
1181 #if EXPAIRSEQ_USE_HASHTAB
1183 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1186 unsigned nearest_power_of_2 = 1 << log2(sz);
1187 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1188 // size = nearest_power_of_2*hashtabfactor;
1189 size = nearest_power_of_2/hashtabfactor;
1190 if (size<minhashtabsize)
1193 // hashtabsize must be a power of 2
1194 GINAC_ASSERT((1U << log2(size))==size);
1198 unsigned expairseq::calc_hashindex(const ex &e) const
1200 // calculate hashindex
1202 if (is_a<numeric>(e)) {
1203 hashindex = hashmask;
1205 hashindex = e.gethash() & hashmask;
1206 // last hashtab entry is reserved for numerics
1207 if (hashindex==hashmask) hashindex = 0;
1209 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1213 void expairseq::shrink_hashtab()
1215 unsigned new_hashtabsize;
1216 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1217 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1218 if (new_hashtabsize==0) {
1225 // shrink by a factor of 2
1226 unsigned half_hashtabsize = hashtabsize/2;
1227 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1228 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1229 // special treatment for numeric hashes
1230 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1231 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1232 hashtab.resize(half_hashtabsize);
1233 hashtabsize = half_hashtabsize;
1234 hashmask = hashtabsize-1;
1238 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1241 return; // nothing to do
1243 // calculate hashindex of element to be deleted
1244 unsigned hashindex = calc_hashindex((*element).rest);
1246 // find it in hashtab and remove it
1247 epplist &eppl = hashtab[hashindex];
1248 epplist::iterator epplit = eppl.begin();
1249 bool erased = false;
1250 while (epplit!=eppl.end()) {
1251 if (*epplit == element) {
1259 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1260 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1262 unsigned hashindex = calc_hashindex(element->rest);
1263 epplist &eppl = hashtab[hashindex];
1264 epplist::iterator epplit = eppl.begin();
1265 bool erased = false;
1266 while (epplit!=eppl.end()) {
1267 if (*epplit == element) {
1274 GINAC_ASSERT(erased);
1276 GINAC_ASSERT(erased);
1279 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1280 epvector::iterator newpos)
1282 GINAC_ASSERT(hashtabsize!=0);
1284 // calculate hashindex of element which was moved
1285 unsigned hashindex=calc_hashindex((*newpos).rest);
1287 // find it in hashtab and modify it
1288 epplist &eppl = hashtab[hashindex];
1289 epplist::iterator epplit = eppl.begin();
1290 while (epplit!=eppl.end()) {
1291 if (*epplit == oldpos) {
1297 GINAC_ASSERT(epplit!=eppl.end());
1300 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1302 epplist::const_iterator current = eppl.begin();
1303 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1306 eppl.insert(current,elem);
1309 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1310 epvector::iterator &last_non_zero,
1311 std::vector<bool> &touched,
1312 unsigned &number_of_zeroes)
1314 epp current = seq.begin();
1316 while (current!=first_numeric) {
1317 if (is_exactly_a<numeric>(current->rest)) {
1319 iter_swap(current,first_numeric);
1321 // calculate hashindex
1322 unsigned currenthashindex = calc_hashindex(current->rest);
1324 // test if there is already a matching expair in the hashtab-list
1325 epplist &eppl=hashtab[currenthashindex];
1326 epplist::iterator epplit = eppl.begin();
1327 while (epplit!=eppl.end()) {
1328 if (current->rest.is_equal((*epplit)->rest))
1332 if (epplit==eppl.end()) {
1333 // no matching expair found, append this to end of list
1334 sorted_insert(eppl,current);
1337 // epplit points to a matching expair, combine it with current
1338 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1339 add_dyn(ex_to<numeric>(current->coeff));
1341 // move obsolete current expair to end by swapping with last_non_zero element
1342 // if this was a numeric, it is swapped with the expair before first_numeric
1343 iter_swap(current,last_non_zero);
1345 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1348 // test if combined term has coeff 0 and can be removed is done later
1349 touched[(*epplit)-seq.begin()] = true;
1355 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1356 epvector::iterator &last_non_zero,
1357 std::vector<bool> &touched,
1358 unsigned &number_of_zeroes)
1360 // move terms with coeff 0 to end and remove them from hashtab
1361 // check only those elements which have been touched
1362 epp current = seq.begin();
1364 while (current!=first_numeric) {
1368 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1372 remove_hashtab_entry(current);
1374 // move element to the end, unless it is already at the end
1375 if (current!=last_non_zero) {
1376 iter_swap(current,last_non_zero);
1378 bool numeric_swapped = first_numeric!=last_non_zero;
1379 if (numeric_swapped)
1380 iter_swap(first_numeric,current);
1381 epvector::iterator changed_entry;
1383 if (numeric_swapped)
1384 changed_entry = first_numeric;
1386 changed_entry = last_non_zero;
1391 if (first_numeric!=current) {
1393 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1394 move_hashtab_entry(changed_entry,current);
1395 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1404 GINAC_ASSERT(i==current-seq.begin());
1407 /** True if one of the coeffs vanishes, otherwise false.
1408 * This would be an invariant violation, so this should only be used for
1409 * debugging purposes. */
1410 bool expairseq::has_coeff_0() const
1412 epvector::const_iterator i = seq.begin(), end = seq.end();
1414 if (i->coeff.is_zero())
1421 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1422 epvector::const_iterator last_non_zero)
1424 if (first_numeric == seq.end()) return; // no numerics
1426 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1427 while (current != last) {
1428 sorted_insert(hashtab[hashmask], current);
1433 void expairseq::combine_same_terms()
1435 // combine same terms, drop term with coeff 0, move numerics to end
1437 // calculate size of hashtab
1438 hashtabsize = calc_hashtabsize(seq.size());
1440 // hashtabsize is a power of 2
1441 hashmask = hashtabsize-1;
1445 hashtab.resize(hashtabsize);
1447 if (hashtabsize==0) {
1449 combine_same_terms_sorted_seq();
1450 GINAC_ASSERT(!has_coeff_0());
1454 // iterate through seq, move numerics to end,
1455 // fill hashtab and combine same terms
1456 epvector::iterator first_numeric = seq.end();
1457 epvector::iterator last_non_zero = seq.end()-1;
1459 size_t num = seq.size();
1460 std::vector<bool> touched(num);
1462 unsigned number_of_zeroes = 0;
1464 GINAC_ASSERT(!has_coeff_0());
1465 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1467 // there should not be any terms with coeff 0 from the beginning,
1468 // so it should be safe to skip this step
1469 if (number_of_zeroes!=0) {
1470 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1473 add_numerics_to_hashtab(first_numeric,last_non_zero);
1475 // pop zero elements
1476 for (unsigned i=0; i<number_of_zeroes; ++i) {
1480 // shrink hashtabsize to calculated value
1481 GINAC_ASSERT(!has_coeff_0());
1485 GINAC_ASSERT(!has_coeff_0());
1488 #endif // EXPAIRSEQ_USE_HASHTAB
1490 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1491 * debugging or in assertions since being sorted is an invariance. */
1492 bool expairseq::is_canonical() const
1494 if (seq.size() <= 1)
1497 #if EXPAIRSEQ_USE_HASHTAB
1498 if (hashtabsize > 0) return 1; // not canoncalized
1499 #endif // EXPAIRSEQ_USE_HASHTAB
1501 epvector::const_iterator it = seq.begin(), itend = seq.end();
1502 epvector::const_iterator it_last = it;
1503 for (++it; it!=itend; it_last=it, ++it) {
1504 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1505 if (!is_exactly_a<numeric>(it_last->rest) ||
1506 !is_exactly_a<numeric>(it->rest)) {
1507 // double test makes it easier to set a breakpoint...
1508 if (!is_exactly_a<numeric>(it_last->rest) ||
1509 !is_exactly_a<numeric>(it->rest)) {
1510 printpair(std::clog, *it_last, 0);
1512 printpair(std::clog, *it, 0);
1514 std::clog << "pair1:" << std::endl;
1515 it_last->rest.print(print_tree(std::clog));
1516 it_last->coeff.print(print_tree(std::clog));
1517 std::clog << "pair2:" << std::endl;
1518 it->rest.print(print_tree(std::clog));
1519 it->coeff.print(print_tree(std::clog));
1529 /** Member-wise expand the expairs in this sequence.
1531 * @see expairseq::expand()
1532 * @return pointer to epvector containing expanded pairs or zero pointer,
1533 * if no members were changed. */
1534 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1536 const epvector::const_iterator last = seq.end();
1537 epvector::const_iterator cit = seq.begin();
1539 const ex &expanded_ex = cit->rest.expand(options);
1540 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1542 // something changed, copy seq, eval and return it
1543 std::auto_ptr<epvector> s(new epvector);
1544 s->reserve(seq.size());
1546 // copy parts of seq which are known not to have changed
1547 epvector::const_iterator cit2 = seq.begin();
1549 s->push_back(*cit2);
1553 // copy first changed element
1554 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1559 while (cit2!=last) {
1560 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1569 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1573 /** Member-wise evaluate the expairs in this sequence.
1575 * @see expairseq::eval()
1576 * @return pointer to epvector containing evaluated pairs or zero pointer,
1577 * if no members were changed. */
1578 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1580 // returns a NULL pointer if nothing had to be evaluated
1581 // returns a pointer to a newly created epvector otherwise
1582 // (which has to be deleted somewhere else)
1585 return std::auto_ptr<epvector>(0);
1587 if (level == -max_recursion_level)
1588 throw(std::runtime_error("max recursion level reached"));
1591 epvector::const_iterator last = seq.end();
1592 epvector::const_iterator cit = seq.begin();
1594 const ex &evaled_ex = cit->rest.eval(level);
1595 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1597 // something changed, copy seq, eval and return it
1598 std::auto_ptr<epvector> s(new epvector);
1599 s->reserve(seq.size());
1601 // copy parts of seq which are known not to have changed
1602 epvector::const_iterator cit2=seq.begin();
1604 s->push_back(*cit2);
1608 // copy first changed element
1609 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1614 while (cit2!=last) {
1615 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1624 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1630 safe_inserter(const ex&, const bool disable_renaming=false);
1631 std::auto_ptr<epvector> getseq(){return epv;}
1632 void insert_old_pair(const expair &p)
1636 void insert_new_pair(const expair &p, const ex &orig_ex);
1638 std::auto_ptr<epvector> epv;
1640 exvector dummy_indices;
1641 void update_dummy_indices(const exvector&);
1644 safe_inserter::safe_inserter(const ex&e, const bool disable_renaming)
1647 epv->reserve(e.nops());
1648 dodummies=is_a<mul>(e);
1649 if(disable_renaming)
1652 dummy_indices = get_all_dummy_indices_safely(e);
1653 sort(dummy_indices.begin(), dummy_indices.end(), ex_is_less());
1657 void safe_inserter::update_dummy_indices(const exvector &v)
1659 exvector new_dummy_indices;
1660 set_union(dummy_indices.begin(), dummy_indices.end(), v.begin(), v.end(),
1661 std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1662 dummy_indices.swap(new_dummy_indices);
1665 void safe_inserter::insert_new_pair(const expair &p, const ex &orig_ex)
1671 exvector dummies_of_factor = get_all_dummy_indices_safely(p.rest);
1672 if(dummies_of_factor.size() == 0) {
1676 sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
1677 exvector dummies_of_orig_ex = get_all_dummy_indices_safely(orig_ex);
1678 sort(dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(), ex_is_less());
1679 exvector new_dummy_indices;
1680 new_dummy_indices.reserve(dummy_indices.size());
1681 set_difference(dummy_indices.begin(), dummy_indices.end(), dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(),
1682 std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1683 dummy_indices.swap(new_dummy_indices);
1684 ex newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, p.rest);
1685 update_dummy_indices(dummies_of_factor);
1686 epv -> push_back(expair(newfactor, p.coeff));
1689 /** Member-wise substitute in this sequence.
1691 * @see expairseq::subs()
1692 * @return pointer to epvector containing pairs after application of subs,
1693 * or NULL pointer if no members were changed. */
1694 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1696 // When any of the objects to be substituted is a product or power
1697 // we have to recombine the pairs because the numeric coefficients may
1698 // be part of the search pattern.
1699 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1701 // Search the list of substitutions and cache our findings
1702 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1703 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1704 options |= subs_options::pattern_is_product;
1708 if (!(options & subs_options::pattern_is_product))
1709 options |= subs_options::pattern_is_not_product;
1712 if (options & subs_options::pattern_is_product) {
1714 // Substitute in the recombined pairs
1715 epvector::const_iterator cit = seq.begin(), last = seq.end();
1716 while (cit != last) {
1718 const ex &orig_ex = recombine_pair_to_ex(*cit);
1719 const ex &subsed_ex = orig_ex.subs(m, options);
1720 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1722 // Something changed, copy seq, subs and return it
1723 safe_inserter s(*this, options & subs_options::no_index_renaming);
1725 // Copy parts of seq which are known not to have changed
1726 for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
1727 s.insert_old_pair(*i);
1729 // Copy first changed element
1730 s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
1734 while (cit != last) {
1735 ex orig_ex = recombine_pair_to_ex(*cit);
1736 ex subsed_ex = orig_ex.subs(m, options);
1737 if(are_ex_trivially_equal(orig_ex, subsed_ex))
1738 s.insert_old_pair(*cit);
1740 s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
1751 // Substitute only in the "rest" part of the pairs
1752 epvector::const_iterator cit = seq.begin(), last = seq.end();
1753 while (cit != last) {
1755 const ex &subsed_ex = cit->rest.subs(m, options);
1756 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1758 // Something changed, copy seq, subs and return it
1759 safe_inserter s(*this, options & subs_options::no_index_renaming);
1761 // Copy parts of seq which are known not to have changed
1762 for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
1763 s.insert_old_pair(*i);
1765 // Copy first changed element
1766 s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), cit->rest);
1770 while (cit != last) {
1771 const ex &orig_ex = cit->rest;
1772 const ex &subsed_ex = cit->rest.subs(m, options);
1773 if(are_ex_trivially_equal(orig_ex, subsed_ex))
1774 s.insert_old_pair(*cit);
1776 s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), orig_ex);
1786 // Nothing has changed
1787 return std::auto_ptr<epvector>(0);
1791 // static member variables
1794 #if EXPAIRSEQ_USE_HASHTAB
1795 unsigned expairseq::maxhashtabsize = 0x4000000U;
1796 unsigned expairseq::minhashtabsize = 0x1000U;
1797 unsigned expairseq::hashtabfactor = 1;
1798 #endif // EXPAIRSEQ_USE_HASHTAB
1800 } // namespace GiNaC