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 construct_from_epvector(v);
130 GINAC_ASSERT(is_canonical());
133 expairseq::expairseq(epvector *vp, const ex &oc)
134 : inherited(TINFO_expairseq), overall_coeff(oc)
137 construct_from_epvector(*vp);
139 GINAC_ASSERT(is_canonical());
146 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
147 #if EXPAIRSEQ_USE_HASHTAB
151 for (unsigned int i=0; true; i++) {
154 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
155 seq.push_back(expair(rest, coeff));
159 n.find_ex("overall_coeff", overall_coeff, sym_lst);
162 void expairseq::archive(archive_node &n) const
164 inherited::archive(n);
165 epvector::const_iterator i = seq.begin(), iend = seq.end();
167 n.add_ex("rest", i->rest);
168 n.add_ex("coeff", i->coeff);
171 n.add_ex("overall_coeff", overall_coeff);
174 DEFAULT_UNARCHIVE(expairseq)
177 // functions overriding virtual functions from base classes
182 basic *expairseq::duplicate() const
184 return new expairseq(*this);
187 void expairseq::print(const print_context &c, unsigned level) const
189 if (is_of_type(c, print_tree)) {
191 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
193 c.s << std::string(level, ' ') << class_name()
194 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
195 << ", nops=" << nops()
197 unsigned num = seq.size();
198 for (unsigned i=0; i<num; ++i) {
199 seq[i].rest.print(c, level + delta_indent);
200 seq[i].coeff.print(c, level + delta_indent);
202 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
204 if (!overall_coeff.is_equal(default_overall_coeff())) {
205 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
206 << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
207 overall_coeff.print(c, level + delta_indent);
209 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
210 #if EXPAIRSEQ_USE_HASHTAB
211 c.s << std::string(level + delta_indent,' ')
212 << "hashtab size " << hashtabsize << std::endl;
213 if (hashtabsize == 0) return;
215 unsigned count[MAXCOUNT+1];
216 for (int i=0; i<MAXCOUNT+1; ++i)
218 unsigned this_bin_fill;
219 unsigned cum_fill_sq = 0;
220 unsigned cum_fill = 0;
221 for (unsigned i=0; i<hashtabsize; ++i) {
223 if (hashtab[i].size() > 0) {
224 c.s << std::string(level + delta_indent, ' ')
225 << "bin " << i << " with entries ";
226 for (epplist::const_iterator it=hashtab[i].begin();
227 it!=hashtab[i].end(); ++it) {
228 c.s << *it-seq.begin() << " ";
232 cum_fill += this_bin_fill;
233 cum_fill_sq += this_bin_fill*this_bin_fill;
235 if (this_bin_fill<MAXCOUNT)
236 ++count[this_bin_fill];
242 double lambda = (1.0*seq.size()) / hashtabsize;
243 for (int k=0; k<MAXCOUNT; ++k) {
246 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
248 c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
249 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
250 << int(prob*1000)/10.0 << ")" << std::endl;
252 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
253 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
254 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
256 c.s << std::string(level + delta_indent, ' ') << "variance: "
257 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
259 c.s << std::string(level + delta_indent, ' ') << "average fill: "
260 << (1.0*cum_fill)/hashtabsize
261 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
262 #endif // EXPAIRSEQ_USE_HASHTAB
266 printseq(c, ',', precedence(), level);
271 bool expairseq::info(unsigned inf) const
273 return inherited::info(inf);
276 unsigned expairseq::nops() const
278 if (overall_coeff.is_equal(default_overall_coeff()))
284 ex expairseq::op(int i) const
286 if (unsigned(i)<seq.size())
287 return recombine_pair_to_ex(seq[i]);
288 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
289 return overall_coeff;
292 ex &expairseq::let_op(int i)
294 throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
297 ex expairseq::map(map_function &f) const
299 epvector *v = new epvector;
300 v->reserve(seq.size());
302 epvector::const_iterator cit = seq.begin(), last = seq.end();
303 while (cit != last) {
304 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
308 if (overall_coeff.is_equal(default_overall_coeff()))
309 return thisexpairseq(v, default_overall_coeff());
311 return thisexpairseq(v, f(overall_coeff));
314 /** Perform coefficient-wise automatic term rewriting rules in this class. */
315 ex expairseq::eval(int level) const
317 if ((level==1) && (flags &status_flags::evaluated))
320 epvector *vp = evalchildren(level);
324 return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
327 bool expairseq::match(const ex & pattern, lst & repl_lst) const
329 // This differs from basic::match() because we want "a+b+c+d" to
330 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
332 if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
334 // Check whether global wildcard (one that matches the "rest of the
335 // expression", like "*" above) is present
336 bool has_global_wildcard = false;
338 for (unsigned int i=0; i<pattern.nops(); i++) {
339 if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
340 has_global_wildcard = true;
341 global_wildcard = pattern.op(i);
346 // Unfortunately, this is an O(N^2) operation because we can't
347 // sort the pattern in a useful way...
352 for (unsigned i=0; i<nops(); i++)
353 ops.push_back(op(i));
355 // Now, for every term of the pattern, look for a matching term in
356 // the expression and remove the match
357 for (unsigned i=0; i<pattern.nops(); i++) {
358 ex p = pattern.op(i);
359 if (has_global_wildcard && p.is_equal(global_wildcard))
361 exvector::iterator it = ops.begin(), itend = ops.end();
362 while (it != itend) {
363 if (it->match(p, repl_lst)) {
369 return false; // no match found
373 if (has_global_wildcard) {
375 // Assign all the remaining terms to the global wildcard (unless
376 // it has already been matched before, in which case the matches
378 unsigned num = ops.size();
379 epvector *vp = new epvector();
381 for (unsigned i=0; i<num; i++)
382 vp->push_back(split_ex_to_pair(ops[i]));
383 ex rest = thisexpairseq(vp, default_overall_coeff());
384 for (unsigned i=0; i<repl_lst.nops(); i++) {
385 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
386 return rest.is_equal(repl_lst.op(i).op(1));
388 repl_lst.append(global_wildcard == rest);
393 // No global wildcard, then the match fails if there are any
394 // unmatched terms left
398 return inherited::match(pattern, repl_lst);
401 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
403 epvector *vp = subschildren(ls, lr, no_pattern);
405 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
407 return basic::subs(ls, lr, no_pattern);
412 int expairseq::compare_same_type(const basic &other) const
414 GINAC_ASSERT(is_a<expairseq>(other));
415 const expairseq &o = static_cast<const expairseq &>(other);
419 // compare number of elements
420 if (seq.size() != o.seq.size())
421 return (seq.size()<o.seq.size()) ? -1 : 1;
423 // compare overall_coeff
424 cmpval = overall_coeff.compare(o.overall_coeff);
428 #if EXPAIRSEQ_USE_HASHTAB
429 GINAC_ASSERT(hashtabsize==o.hashtabsize);
430 if (hashtabsize==0) {
431 #endif // EXPAIRSEQ_USE_HASHTAB
432 epvector::const_iterator cit1 = seq.begin();
433 epvector::const_iterator cit2 = o.seq.begin();
434 epvector::const_iterator last1 = seq.end();
435 epvector::const_iterator last2 = o.seq.end();
437 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
438 cmpval = (*cit1).compare(*cit2);
439 if (cmpval!=0) return cmpval;
442 GINAC_ASSERT(cit1==last1);
443 GINAC_ASSERT(cit2==last2);
446 #if EXPAIRSEQ_USE_HASHTAB
449 // compare number of elements in each hashtab entry
450 for (unsigned i=0; i<hashtabsize; ++i) {
451 unsigned cursize=hashtab[i].size();
452 if (cursize != o.hashtab[i].size())
453 return (cursize < o.hashtab[i].size()) ? -1 : 1;
456 // compare individual (sorted) hashtab entries
457 for (unsigned i=0; i<hashtabsize; ++i) {
458 unsigned sz = hashtab[i].size();
460 const epplist &eppl1 = hashtab[i];
461 const epplist &eppl2 = o.hashtab[i];
462 epplist::const_iterator it1 = eppl1.begin();
463 epplist::const_iterator it2 = eppl2.begin();
464 while (it1!=eppl1.end()) {
465 cmpval = (*(*it1)).compare(*(*it2));
475 #endif // EXPAIRSEQ_USE_HASHTAB
478 bool expairseq::is_equal_same_type(const basic &other) const
480 const expairseq &o = static_cast<const expairseq &>(other);
482 // compare number of elements
483 if (seq.size()!=o.seq.size())
486 // compare overall_coeff
487 if (!overall_coeff.is_equal(o.overall_coeff))
490 #if EXPAIRSEQ_USE_HASHTAB
491 // compare number of elements in each hashtab entry
492 if (hashtabsize!=o.hashtabsize) {
493 std::cout << "this:" << std::endl;
494 print(print_tree(std::cout));
495 std::cout << "other:" << std::endl;
496 other.print(print_tree(std::cout));
499 GINAC_ASSERT(hashtabsize==o.hashtabsize);
501 if (hashtabsize==0) {
502 #endif // EXPAIRSEQ_USE_HASHTAB
503 epvector::const_iterator cit1 = seq.begin();
504 epvector::const_iterator cit2 = o.seq.begin();
505 epvector::const_iterator last1 = seq.end();
507 while (cit1!=last1) {
508 if (!(*cit1).is_equal(*cit2)) return false;
514 #if EXPAIRSEQ_USE_HASHTAB
517 for (unsigned i=0; i<hashtabsize; ++i) {
518 if (hashtab[i].size() != o.hashtab[i].size())
522 // compare individual sorted hashtab entries
523 for (unsigned i=0; i<hashtabsize; ++i) {
524 unsigned sz = hashtab[i].size();
526 const epplist &eppl1 = hashtab[i];
527 const epplist &eppl2 = o.hashtab[i];
528 epplist::const_iterator it1 = eppl1.begin();
529 epplist::const_iterator it2 = eppl2.begin();
530 while (it1!=eppl1.end()) {
531 if (!(*(*it1)).is_equal(*(*it2))) return false;
539 #endif // EXPAIRSEQ_USE_HASHTAB
542 unsigned expairseq::return_type(void) const
544 return return_types::noncommutative_composite;
547 unsigned expairseq::calchash(void) const
549 unsigned v = golden_ratio_hash(this->tinfo());
550 epvector::const_iterator i = seq.begin(), end = seq.end();
552 #if !EXPAIRSEQ_USE_HASHTAB
553 v = rotate_left_31(v); // rotation would spoil commutativity
554 #endif // EXPAIRSEQ_USE_HASHTAB
555 v ^= i->rest.gethash();
556 #if !EXPAIRSEQ_USE_HASHTAB
557 v = rotate_left_31(v);
558 v ^= i->coeff.gethash();
559 #endif // EXPAIRSEQ_USE_HASHTAB
563 v ^= overall_coeff.gethash();
566 // store calculated hash value only if object is already evaluated
567 if (flags &status_flags::evaluated) {
568 setflag(status_flags::hash_calculated);
575 ex expairseq::expand(unsigned options) const
577 epvector *vp = expandchildren(options);
579 // The terms have not changed, so it is safe to declare this expanded
580 return (options == 0) ? setflag(status_flags::expanded) : *this;
582 return thisexpairseq(vp, overall_coeff);
586 // new virtual functions which can be overridden by derived classes
591 /** Create an object of this type.
592 * This method works similar to a constructor. It is useful because expairseq
593 * has (at least) two possible different semantics but we want to inherit
594 * methods thus avoiding code duplication. Sometimes a method in expairseq
595 * has to create a new one of the same semantics, which cannot be done by a
596 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
597 * order for this trick to work a derived class must of course override this
599 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
601 return expairseq(v,oc);
604 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
606 return expairseq(vp,oc);
609 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
612 p.rest.print(c, precedence());
614 p.coeff.print(c, precedence());
618 void expairseq::printseq(const print_context & c, char delim,
619 unsigned this_precedence,
620 unsigned upper_precedence) const
622 if (this_precedence <= upper_precedence)
624 epvector::const_iterator it, it_last = seq.end() - 1;
625 for (it=seq.begin(); it!=it_last; ++it) {
626 printpair(c, *it, this_precedence);
629 printpair(c, *it, this_precedence);
630 if (!overall_coeff.is_equal(default_overall_coeff())) {
632 overall_coeff.print(c, this_precedence);
635 if (this_precedence <= upper_precedence)
640 /** Form an expair from an ex, using the corresponding semantics.
641 * @see expairseq::recombine_pair_to_ex() */
642 expair expairseq::split_ex_to_pair(const ex &e) const
644 return expair(e,_ex1);
648 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
651 GINAC_ASSERT(is_exactly_a<numeric>(c));
657 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
660 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
661 GINAC_ASSERT(is_exactly_a<numeric>(c));
663 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
667 /** Form an ex out of an expair, using the corresponding semantics.
668 * @see expairseq::split_ex_to_pair() */
669 ex expairseq::recombine_pair_to_ex(const expair &p) const
671 return lst(p.rest,p.coeff);
674 bool expairseq::expair_needs_further_processing(epp it)
676 #if EXPAIRSEQ_USE_HASHTAB
677 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
678 #endif // EXPAIRSEQ_USE_HASHTAB
682 ex expairseq::default_overall_coeff(void) const
687 void expairseq::combine_overall_coeff(const ex &c)
689 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
690 GINAC_ASSERT(is_exactly_a<numeric>(c));
691 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
694 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
696 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
697 GINAC_ASSERT(is_exactly_a<numeric>(c1));
698 GINAC_ASSERT(is_exactly_a<numeric>(c2));
699 overall_coeff = ex_to<numeric>(overall_coeff).
700 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
703 bool expairseq::can_make_flat(const expair &p) const
710 // non-virtual functions in this class
713 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
719 construct_from_exvector(v);
720 #if EXPAIRSEQ_USE_HASHTAB
721 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
722 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
723 #endif // EXPAIRSEQ_USE_HASHTAB
726 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
728 if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
729 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
730 #if EXPAIRSEQ_USE_HASHTAB
731 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
732 ex_to<expairseq>(rh).seq.size();
733 if (calc_hashtabsize(totalsize)!=0) {
734 construct_from_2_ex_via_exvector(lh,rh);
736 #endif // EXPAIRSEQ_USE_HASHTAB
737 construct_from_2_expairseq(ex_to<expairseq>(lh),
738 ex_to<expairseq>(rh));
739 #if EXPAIRSEQ_USE_HASHTAB
741 #endif // EXPAIRSEQ_USE_HASHTAB
744 #if EXPAIRSEQ_USE_HASHTAB
745 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
746 if (calc_hashtabsize(totalsize)!=0) {
747 construct_from_2_ex_via_exvector(lh, rh);
749 #endif // EXPAIRSEQ_USE_HASHTAB
750 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
751 #if EXPAIRSEQ_USE_HASHTAB
753 #endif // EXPAIRSEQ_USE_HASHTAB
756 } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
757 #if EXPAIRSEQ_USE_HASHTAB
758 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
759 if (calc_hashtabsize(totalsize)!=0) {
760 construct_from_2_ex_via_exvector(lh,rh);
762 #endif // EXPAIRSEQ_USE_HASHTAB
763 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
764 #if EXPAIRSEQ_USE_HASHTAB
766 #endif // EXPAIRSEQ_USE_HASHTAB
770 #if EXPAIRSEQ_USE_HASHTAB
771 if (calc_hashtabsize(2)!=0) {
772 construct_from_2_ex_via_exvector(lh,rh);
776 #endif // EXPAIRSEQ_USE_HASHTAB
778 if (is_ex_exactly_of_type(lh,numeric)) {
779 if (is_ex_exactly_of_type(rh,numeric)) {
780 combine_overall_coeff(lh);
781 combine_overall_coeff(rh);
783 combine_overall_coeff(lh);
784 seq.push_back(split_ex_to_pair(rh));
787 if (is_ex_exactly_of_type(rh,numeric)) {
788 combine_overall_coeff(rh);
789 seq.push_back(split_ex_to_pair(lh));
791 expair p1 = split_ex_to_pair(lh);
792 expair p2 = split_ex_to_pair(rh);
794 int cmpval = p1.rest.compare(p2.rest);
796 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
797 if (!ex_to<numeric>(p1.coeff).is_zero()) {
798 // no further processing is necessary, since this
799 // one element will usually be recombined in eval()
816 void expairseq::construct_from_2_expairseq(const expairseq &s1,
819 combine_overall_coeff(s1.overall_coeff);
820 combine_overall_coeff(s2.overall_coeff);
822 epvector::const_iterator first1 = s1.seq.begin();
823 epvector::const_iterator last1 = s1.seq.end();
824 epvector::const_iterator first2 = s2.seq.begin();
825 epvector::const_iterator last2 = s2.seq.end();
827 seq.reserve(s1.seq.size()+s2.seq.size());
829 bool needs_further_processing=false;
831 while (first1!=last1 && first2!=last2) {
832 int cmpval = (*first1).rest.compare((*first2).rest);
835 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
836 add(ex_to<numeric>(first2->coeff));
837 if (!newcoeff.is_zero()) {
838 seq.push_back(expair(first1->rest,newcoeff));
839 if (expair_needs_further_processing(seq.end()-1)) {
840 needs_further_processing = true;
845 } else if (cmpval<0) {
846 seq.push_back(*first1);
849 seq.push_back(*first2);
854 while (first1!=last1) {
855 seq.push_back(*first1);
858 while (first2!=last2) {
859 seq.push_back(*first2);
863 if (needs_further_processing) {
866 construct_from_epvector(v);
870 void expairseq::construct_from_expairseq_ex(const expairseq &s,
873 combine_overall_coeff(s.overall_coeff);
874 if (is_ex_exactly_of_type(e,numeric)) {
875 combine_overall_coeff(e);
880 epvector::const_iterator first = s.seq.begin();
881 epvector::const_iterator last = s.seq.end();
882 expair p = split_ex_to_pair(e);
884 seq.reserve(s.seq.size()+1);
885 bool p_pushed = false;
887 bool needs_further_processing=false;
889 // merge p into s.seq
890 while (first!=last) {
891 int cmpval = (*first).rest.compare(p.rest);
894 const numeric &newcoeff = ex_to<numeric>(first->coeff).
895 add(ex_to<numeric>(p.coeff));
896 if (!newcoeff.is_zero()) {
897 seq.push_back(expair(first->rest,newcoeff));
898 if (expair_needs_further_processing(seq.end()-1))
899 needs_further_processing = true;
904 } else if (cmpval<0) {
905 seq.push_back(*first);
915 // while loop exited because p was pushed, now push rest of s.seq
916 while (first!=last) {
917 seq.push_back(*first);
921 // while loop exited because s.seq was pushed, now push p
925 if (needs_further_processing) {
928 construct_from_epvector(v);
932 void expairseq::construct_from_exvector(const exvector &v)
934 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
935 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
936 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
937 // (same for (+,*) -> (*,^)
940 #if EXPAIRSEQ_USE_HASHTAB
941 combine_same_terms();
944 combine_same_terms_sorted_seq();
945 #endif // EXPAIRSEQ_USE_HASHTAB
948 void expairseq::construct_from_epvector(const epvector &v)
950 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
951 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
952 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
953 // (same for (+,*) -> (*,^)
956 #if EXPAIRSEQ_USE_HASHTAB
957 combine_same_terms();
960 combine_same_terms_sorted_seq();
961 #endif // EXPAIRSEQ_USE_HASHTAB
964 /** Combine this expairseq with argument exvector.
965 * It cares for associativity as well as for special handling of numerics. */
966 void expairseq::make_flat(const exvector &v)
968 exvector::const_iterator cit;
970 // count number of operands which are of same expairseq derived type
971 // and their cumulative number of operands
976 while (cit!=v.end()) {
977 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
979 noperands += ex_to<expairseq>(*cit).seq.size();
984 // reserve seq and coeffseq which will hold all operands
985 seq.reserve(v.size()+noperands-nexpairseqs);
987 // copy elements and split off numerical part
989 while (cit!=v.end()) {
990 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
991 const expairseq &subseqref = ex_to<expairseq>(*cit);
992 combine_overall_coeff(subseqref.overall_coeff);
993 epvector::const_iterator cit_s = subseqref.seq.begin();
994 while (cit_s!=subseqref.seq.end()) {
995 seq.push_back(*cit_s);
999 if (is_ex_exactly_of_type(*cit,numeric))
1000 combine_overall_coeff(*cit);
1002 seq.push_back(split_ex_to_pair(*cit));
1008 /** Combine this expairseq with argument epvector.
1009 * It cares for associativity as well as for special handling of numerics. */
1010 void expairseq::make_flat(const epvector &v)
1012 epvector::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->rest).tinfo()==this->tinfo()) {
1023 noperands += ex_to<expairseq>(cit->rest).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
1033 while (cit!=v.end()) {
1034 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1035 this->can_make_flat(*cit)) {
1036 const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1037 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1038 ex_to<numeric>(cit->coeff));
1039 epvector::const_iterator cit_s = subseqref.seq.begin();
1040 while (cit_s!=subseqref.seq.end()) {
1041 seq.push_back(expair(cit_s->rest,
1042 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1043 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1048 if (cit->is_canonical_numeric())
1049 combine_overall_coeff(cit->rest);
1051 seq.push_back(*cit);
1057 /** Brings this expairseq into a sorted (canonical) form. */
1058 void expairseq::canonicalize(void)
1060 std::sort(seq.begin(), seq.end(), expair_is_less());
1064 /** Compact a presorted expairseq by combining all matching expairs to one
1065 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1067 void expairseq::combine_same_terms_sorted_seq(void)
1069 bool needs_further_processing = false;
1072 epvector::iterator itin1 = seq.begin();
1073 epvector::iterator itin2 = itin1+1;
1074 epvector::iterator itout = itin1;
1075 epvector::iterator last = seq.end();
1076 // must_copy will be set to true the first time some combination is
1077 // possible from then on the sequence has changed and must be compacted
1078 bool must_copy = false;
1079 while (itin2!=last) {
1080 if (itin1->rest.compare(itin2->rest)==0) {
1081 itin1->coeff = ex_to<numeric>(itin1->coeff).
1082 add_dyn(ex_to<numeric>(itin2->coeff));
1083 if (expair_needs_further_processing(itin1))
1084 needs_further_processing = true;
1087 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1096 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1102 seq.erase(itout,last);
1105 if (needs_further_processing) {
1108 construct_from_epvector(v);
1112 #if EXPAIRSEQ_USE_HASHTAB
1114 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1117 unsigned nearest_power_of_2 = 1 << log2(sz);
1118 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1119 // size = nearest_power_of_2*hashtabfactor;
1120 size = nearest_power_of_2/hashtabfactor;
1121 if (size<minhashtabsize)
1123 GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1124 // hashtabsize must be a power of 2
1125 GINAC_ASSERT((1U << log2(size))==size);
1129 unsigned expairseq::calc_hashindex(const ex &e) const
1131 // calculate hashindex
1132 unsigned hash = e.gethash();
1134 if (is_a_numeric_hash(hash)) {
1135 hashindex = hashmask;
1137 hashindex = hash &hashmask;
1138 // last hashtab entry is reserved for numerics
1139 if (hashindex==hashmask) hashindex = 0;
1141 GINAC_ASSERT(hashindex>=0);
1142 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1146 void expairseq::shrink_hashtab(void)
1148 unsigned new_hashtabsize;
1149 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1150 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1151 if (new_hashtabsize==0) {
1158 // shrink by a factor of 2
1159 unsigned half_hashtabsize = hashtabsize/2;
1160 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1161 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1162 // special treatment for numeric hashes
1163 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1164 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1165 hashtab.resize(half_hashtabsize);
1166 hashtabsize = half_hashtabsize;
1167 hashmask = hashtabsize-1;
1171 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1174 return; // nothing to do
1176 // calculate hashindex of element to be deleted
1177 unsigned hashindex = calc_hashindex((*element).rest);
1179 // find it in hashtab and remove it
1180 epplist &eppl = hashtab[hashindex];
1181 epplist::iterator epplit = eppl.begin();
1182 bool erased = false;
1183 while (epplit!=eppl.end()) {
1184 if (*epplit == element) {
1192 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1193 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1195 unsigned hashindex = calc_hashindex(element->rest);
1196 epplist &eppl = hashtab[hashindex];
1197 epplist::iterator epplit = eppl.begin();
1198 bool erased = false;
1199 while (epplit!=eppl.end()) {
1200 if (*epplit == element) {
1207 GINAC_ASSERT(erased);
1209 GINAC_ASSERT(erased);
1212 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1213 epvector::iterator newpos)
1215 GINAC_ASSERT(hashtabsize!=0);
1217 // calculate hashindex of element which was moved
1218 unsigned hashindex=calc_hashindex((*newpos).rest);
1220 // find it in hashtab and modify it
1221 epplist &eppl = hashtab[hashindex];
1222 epplist::iterator epplit = eppl.begin();
1223 while (epplit!=eppl.end()) {
1224 if (*epplit == oldpos) {
1230 GINAC_ASSERT(epplit!=eppl.end());
1233 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1235 epplist::const_iterator current = eppl.begin();
1236 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1239 eppl.insert(current,elem);
1242 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1243 epvector::iterator &last_non_zero,
1244 std::vector<bool> &touched,
1245 unsigned &number_of_zeroes)
1247 epp current = seq.begin();
1249 while (current!=first_numeric) {
1250 if (is_ex_exactly_of_type(current->rest,numeric)) {
1252 iter_swap(current,first_numeric);
1254 // calculate hashindex
1255 unsigned currenthashindex = calc_hashindex(current->rest);
1257 // test if there is already a matching expair in the hashtab-list
1258 epplist &eppl=hashtab[currenthashindex];
1259 epplist::iterator epplit = eppl.begin();
1260 while (epplit!=eppl.end()) {
1261 if (current->rest.is_equal((*epplit)->rest))
1265 if (epplit==eppl.end()) {
1266 // no matching expair found, append this to end of list
1267 sorted_insert(eppl,current);
1270 // epplit points to a matching expair, combine it with current
1271 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1272 add_dyn(ex_to<numeric>(current->coeff));
1274 // move obsolete current expair to end by swapping with last_non_zero element
1275 // if this was a numeric, it is swapped with the expair before first_numeric
1276 iter_swap(current,last_non_zero);
1278 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1281 // test if combined term has coeff 0 and can be removed is done later
1282 touched[(*epplit)-seq.begin()] = true;
1288 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1289 epvector::iterator &last_non_zero,
1290 std::vector<bool> &touched,
1291 unsigned &number_of_zeroes)
1293 // move terms with coeff 0 to end and remove them from hashtab
1294 // check only those elements which have been touched
1295 epp current = seq.begin();
1297 while (current!=first_numeric) {
1301 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1305 remove_hashtab_entry(current);
1307 // move element to the end, unless it is already at the end
1308 if (current!=last_non_zero) {
1309 iter_swap(current,last_non_zero);
1311 bool numeric_swapped = first_numeric!=last_non_zero;
1312 if (numeric_swapped)
1313 iter_swap(first_numeric,current);
1314 epvector::iterator changed_entry;
1316 if (numeric_swapped)
1317 changed_entry = first_numeric;
1319 changed_entry = last_non_zero;
1324 if (first_numeric!=current) {
1326 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1327 move_hashtab_entry(changed_entry,current);
1328 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1337 GINAC_ASSERT(i==current-seq.begin());
1340 /** True if one of the coeffs vanishes, otherwise false.
1341 * This would be an invariant violation, so this should only be used for
1342 * debugging purposes. */
1343 bool expairseq::has_coeff_0(void) const
1345 epvector::const_iterator i = seq.begin(), end = seq.end();
1347 if (i->coeff.is_zero())
1354 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1355 epvector::const_iterator last_non_zero)
1357 if (first_numeric == seq.end()) return; // no numerics
1359 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1360 while (current != last) {
1361 sorted_insert(hashtab[hashmask], current);
1366 void expairseq::combine_same_terms(void)
1368 // combine same terms, drop term with coeff 0, move numerics to end
1370 // calculate size of hashtab
1371 hashtabsize = calc_hashtabsize(seq.size());
1373 // hashtabsize is a power of 2
1374 hashmask = hashtabsize-1;
1378 hashtab.resize(hashtabsize);
1380 if (hashtabsize==0) {
1382 combine_same_terms_sorted_seq();
1383 GINAC_ASSERT(!has_coeff_0());
1387 // iterate through seq, move numerics to end,
1388 // fill hashtab and combine same terms
1389 epvector::iterator first_numeric = seq.end();
1390 epvector::iterator last_non_zero = seq.end()-1;
1392 unsigned num = seq.size();
1393 std::vector<bool> touched(num);
1395 unsigned number_of_zeroes = 0;
1397 GINAC_ASSERT(!has_coeff_0());
1398 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1400 // there should not be any terms with coeff 0 from the beginning,
1401 // so it should be safe to skip this step
1402 if (number_of_zeroes!=0) {
1403 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1406 add_numerics_to_hashtab(first_numeric,last_non_zero);
1408 // pop zero elements
1409 for (unsigned i=0; i<number_of_zeroes; ++i) {
1413 // shrink hashtabsize to calculated value
1414 GINAC_ASSERT(!has_coeff_0());
1418 GINAC_ASSERT(!has_coeff_0());
1421 #endif // EXPAIRSEQ_USE_HASHTAB
1423 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1424 * debugging or in assertions since being sorted is an invariance. */
1425 bool expairseq::is_canonical() const
1427 if (seq.size() <= 1)
1430 #if EXPAIRSEQ_USE_HASHTAB
1431 if (hashtabsize > 0) return 1; // not canoncalized
1432 #endif // EXPAIRSEQ_USE_HASHTAB
1434 epvector::const_iterator it = seq.begin(), itend = seq.end();
1435 epvector::const_iterator it_last = it;
1436 for (++it; it!=itend; it_last=it, ++it) {
1437 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1438 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1439 !is_ex_exactly_of_type(it->rest,numeric)) {
1440 // double test makes it easier to set a breakpoint...
1441 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1442 !is_ex_exactly_of_type(it->rest,numeric)) {
1443 printpair(std::clog, *it_last, 0);
1445 printpair(std::clog, *it, 0);
1447 std::clog << "pair1:" << std::endl;
1448 it_last->rest.print(print_tree(std::clog));
1449 it_last->coeff.print(print_tree(std::clog));
1450 std::clog << "pair2:" << std::endl;
1451 it->rest.print(print_tree(std::clog));
1452 it->coeff.print(print_tree(std::clog));
1462 /** Member-wise expand the expairs in this sequence.
1464 * @see expairseq::expand()
1465 * @return pointer to epvector containing expanded pairs or zero pointer,
1466 * if no members were changed. */
1467 epvector * expairseq::expandchildren(unsigned options) const
1469 const epvector::const_iterator last = seq.end();
1470 epvector::const_iterator cit = seq.begin();
1472 const ex &expanded_ex = cit->rest.expand(options);
1473 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1475 // something changed, copy seq, eval and return it
1476 epvector *s = new epvector;
1477 s->reserve(seq.size());
1479 // copy parts of seq which are known not to have changed
1480 epvector::const_iterator cit2 = seq.begin();
1482 s->push_back(*cit2);
1485 // copy first changed element
1486 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1490 while (cit2!=last) {
1491 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1500 return 0; // signalling nothing has changed
1504 /** Member-wise evaluate the expairs in this sequence.
1506 * @see expairseq::eval()
1507 * @return pointer to epvector containing evaluated pairs or zero pointer,
1508 * if no members were changed. */
1509 epvector * expairseq::evalchildren(int level) const
1511 // returns a NULL pointer if nothing had to be evaluated
1512 // returns a pointer to a newly created epvector otherwise
1513 // (which has to be deleted somewhere else)
1518 if (level == -max_recursion_level)
1519 throw(std::runtime_error("max recursion level reached"));
1522 epvector::const_iterator last = seq.end();
1523 epvector::const_iterator cit = seq.begin();
1525 const ex &evaled_ex = cit->rest.eval(level);
1526 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1528 // something changed, copy seq, eval and return it
1529 epvector *s = new epvector;
1530 s->reserve(seq.size());
1532 // copy parts of seq which are known not to have changed
1533 epvector::const_iterator cit2=seq.begin();
1535 s->push_back(*cit2);
1538 // copy first changed element
1539 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1543 while (cit2!=last) {
1544 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1553 return 0; // signalling nothing has changed
1557 /** Member-wise substitute in this sequence.
1559 * @see expairseq::subs()
1560 * @return pointer to epvector containing pairs after application of subs,
1561 * or NULL pointer if no members were changed. */
1562 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1564 GINAC_ASSERT(ls.nops()==lr.nops());
1566 // The substitution is "complex" when any of the objects to be substituted
1567 // is a product or power. In this case we have to recombine the pairs
1568 // because the numeric coefficients may be part of the search pattern.
1569 bool complex_subs = false;
1570 for (unsigned i=0; i<ls.nops(); ++i)
1571 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1572 complex_subs = true;
1578 // Substitute in the recombined pairs
1579 epvector::const_iterator cit = seq.begin(), last = seq.end();
1580 while (cit != last) {
1582 const ex &orig_ex = recombine_pair_to_ex(*cit);
1583 const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1584 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1586 // Something changed, copy seq, subs and return it
1587 epvector *s = new epvector;
1588 s->reserve(seq.size());
1590 // Copy parts of seq which are known not to have changed
1591 s->insert(s->begin(), seq.begin(), cit);
1593 // Copy first changed element
1594 s->push_back(split_ex_to_pair(subsed_ex));
1598 while (cit != last) {
1599 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1610 // Substitute only in the "rest" part of the pairs
1611 epvector::const_iterator cit = seq.begin(), last = seq.end();
1612 while (cit != last) {
1614 const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1615 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1617 // Something changed, copy seq, subs and return it
1618 epvector *s = new epvector;
1619 s->reserve(seq.size());
1621 // Copy parts of seq which are known not to have changed
1622 s->insert(s->begin(), seq.begin(), cit);
1624 // Copy first changed element
1625 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1629 while (cit != last) {
1630 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1641 // Nothing has changed
1646 // static member variables
1649 #if EXPAIRSEQ_USE_HASHTAB
1650 unsigned expairseq::maxhashtabsize = 0x4000000U;
1651 unsigned expairseq::minhashtabsize = 0x1000U;
1652 unsigned expairseq::hashtabfactor = 1;
1653 #endif // EXPAIRSEQ_USE_HASHTAB
1655 } // namespace GiNaC