Improved dummy index renaming.
[ginac.git] / ginac / expairseq.cpp
1 /** @file expairseq.cpp
2  *
3  *  Implementation of sequences of expression pairs. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
7  *
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.
12  *
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.
17  *
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
21  */
22
23 #include <iostream>
24 #include <algorithm>
25 #include <string>
26 #include <stdexcept>
27
28 #include "expairseq.h"
29 #include "lst.h"
30 #include "add.h"
31 #include "mul.h"
32 #include "power.h"
33 #include "relational.h"
34 #include "wildcard.h"
35 #include "archive.h"
36 #include "operators.h"
37 #include "utils.h"
38 #include "indexed.h"
39
40 #if EXPAIRSEQ_USE_HASHTAB
41 #include <cmath>
42 #endif // EXPAIRSEQ_USE_HASHTAB
43
44 namespace GiNaC {
45
46         
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))
50
51
52 //////////
53 // helper classes
54 //////////
55
56 class epp_is_less
57 {
58 public:
59         bool operator()(const epp &lh, const epp &rh) const
60         {
61                 return (*lh).is_less(*rh);
62         }
63 };
64
65 //////////
66 // default constructor
67 //////////
68
69 // public
70
71 expairseq::expairseq() : inherited(&expairseq::tinfo_static)
72 #if EXPAIRSEQ_USE_HASHTAB
73                                                    , hashtabsize(0)
74 #endif // EXPAIRSEQ_USE_HASHTAB
75 {}
76
77 // protected
78
79 #if 0
80 /** For use by copy ctor and assignment operator. */
81 void expairseq::copy(const expairseq &other)
82 {
83         seq = other.seq;
84         overall_coeff = other.overall_coeff;
85 #if EXPAIRSEQ_USE_HASHTAB
86         // copy hashtab
87         hashtabsize = other.hashtabsize;
88         if (hashtabsize!=0) {
89                 hashmask = other.hashmask;
90                 hashtab.resize(hashtabsize);
91                 epvector::const_iterator osb = other.seq.begin();
92                 for (unsigned i=0; i<hashtabsize; ++i) {
93                         hashtab[i].clear();
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));
97                         }
98                 }
99         } else {
100                 hashtab.clear();
101         }
102 #endif // EXPAIRSEQ_USE_HASHTAB
103 }
104 #endif
105
106 //////////
107 // other constructors
108 //////////
109
110 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(&expairseq::tinfo_static)
111 {
112         construct_from_2_ex(lh,rh);
113         GINAC_ASSERT(is_canonical());
114 }
115
116 expairseq::expairseq(const exvector &v) : inherited(&expairseq::tinfo_static)
117 {
118         construct_from_exvector(v);
119         GINAC_ASSERT(is_canonical());
120 }
121
122 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
123   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
124 {
125         GINAC_ASSERT(is_a<numeric>(oc));
126         construct_from_epvector(v, do_index_renaming);
127         GINAC_ASSERT(is_canonical());
128 }
129
130 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
131   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
132 {
133         GINAC_ASSERT(vp.get()!=0);
134         GINAC_ASSERT(is_a<numeric>(oc));
135         construct_from_epvector(*vp, do_index_renaming);
136         GINAC_ASSERT(is_canonical());
137 }
138
139 //////////
140 // archiving
141 //////////
142
143 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
144 #if EXPAIRSEQ_USE_HASHTAB
145         , hashtabsize(0)
146 #endif
147 {
148         for (unsigned int i=0; true; i++) {
149                 ex rest;
150                 ex coeff;
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));
153                 else
154                         break;
155         }
156
157         n.find_ex("overall_coeff", overall_coeff, sym_lst);
158
159         canonicalize();
160         GINAC_ASSERT(is_canonical());
161 }
162
163 void expairseq::archive(archive_node &n) const
164 {
165         inherited::archive(n);
166         epvector::const_iterator i = seq.begin(), iend = seq.end();
167         while (i != iend) {
168                 n.add_ex("rest", i->rest);
169                 n.add_ex("coeff", i->coeff);
170                 ++i;
171         }
172         n.add_ex("overall_coeff", overall_coeff);
173 }
174
175 DEFAULT_UNARCHIVE(expairseq)
176
177 //////////
178 // functions overriding virtual functions from base classes
179 //////////
180
181 // public
182
183 void expairseq::do_print(const print_context & c, unsigned level) const
184 {
185         c.s << "[[";
186         printseq(c, ',', precedence(), level);
187         c.s << "]]";
188 }
189
190 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
191 {
192         c.s << std::string(level, ' ') << class_name() << " @" << this
193             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
194             << ", nops=" << nops()
195             << std::endl;
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);
200                 if (i != num - 1)
201                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
202         }
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);
207         }
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;
213 #define MAXCOUNT 5
214         unsigned count[MAXCOUNT+1];
215         for (int i=0; i<MAXCOUNT+1; ++i)
216                 count[i] = 0;
217         unsigned this_bin_fill;
218         unsigned cum_fill_sq = 0;
219         unsigned cum_fill = 0;
220         for (unsigned i=0; i<hashtabsize; ++i) {
221                 this_bin_fill = 0;
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() << " ";
228                                 ++this_bin_fill;
229                         }
230                         c.s << std::endl;
231                         cum_fill += this_bin_fill;
232                         cum_fill_sq += this_bin_fill*this_bin_fill;
233                 }
234                 if (this_bin_fill<MAXCOUNT)
235                         ++count[this_bin_fill];
236                 else
237                         ++count[MAXCOUNT];
238         }
239         unsigned fact = 1;
240         double cum_prob = 0;
241         double lambda = (1.0*seq.size()) / hashtabsize;
242         for (int k=0; k<MAXCOUNT; ++k) {
243                 if (k>0)
244                         fact *= k;
245                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
246                 cum_prob += prob;
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;
250         }
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;
254
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)
257             << std::endl;
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
262 }
263
264 bool expairseq::info(unsigned inf) const
265 {
266         return inherited::info(inf);
267 }
268
269 size_t expairseq::nops() const
270 {
271         if (overall_coeff.is_equal(default_overall_coeff()))
272                 return seq.size();
273         else
274                 return seq.size()+1;
275 }
276
277 ex expairseq::op(size_t i) const
278 {
279         if (i < seq.size())
280                 return recombine_pair_to_ex(seq[i]);
281         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
282         return overall_coeff;
283 }
284
285 ex expairseq::map(map_function &f) const
286 {
287         std::auto_ptr<epvector> v(new epvector);
288         v->reserve(seq.size());
289
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))));
293                 ++cit;
294         }
295
296         if (overall_coeff.is_equal(default_overall_coeff()))
297                 return thisexpairseq(v, default_overall_coeff(), true);
298         else
299                 return thisexpairseq(v, f(overall_coeff), true);
300 }
301
302 /** Perform coefficient-wise automatic term rewriting rules in this class. */
303 ex expairseq::eval(int level) const
304 {
305         if ((level==1) && (flags &status_flags::evaluated))
306                 return *this;
307         
308         std::auto_ptr<epvector> vp = evalchildren(level);
309         if (vp.get() == 0)
310                 return this->hold();
311         
312         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
313 }
314
315 epvector* conjugateepvector(const epvector&epv)
316 {
317         epvector *newepv = 0;
318         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
319                 if(newepv) {
320                         newepv->push_back(i->conjugate());
321                         continue;
322                 }
323                 expair x = i->conjugate();
324                 if (x.is_equal(*i)) {
325                         continue;
326                 }
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);
331                 }
332                 newepv->push_back(x);
333         }
334         return newepv;
335 }
336
337 ex expairseq::conjugate() const
338 {
339         epvector* newepv = conjugateepvector(seq);
340         ex x = overall_coeff.conjugate();
341         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
342                 return *this;
343         }
344         ex result = thisexpairseq(newepv ? *newepv : seq, x);
345         if (newepv) {
346                 delete newepv;
347         }
348         return result;
349 }
350
351 bool expairseq::is_polynomial(const ex & var) const
352 {
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))
357                         return false;
358         }
359         return true;
360 }
361
362 bool expairseq::match(const ex & pattern, lst & repl_lst) const
363 {
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
366
367         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
368
369                 // Check whether global wildcard (one that matches the "rest of the
370                 // expression", like "*" above) is present
371                 bool has_global_wildcard = false;
372                 ex global_wildcard;
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);
377                                 break;
378                         }
379                 }
380
381                 // Unfortunately, this is an O(N^2) operation because we can't
382                 // sort the pattern in a useful way...
383
384                 // Chop into terms
385                 exvector ops;
386                 ops.reserve(nops());
387                 for (size_t i=0; i<nops(); i++)
388                         ops.push_back(op(i));
389
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))
395                                 continue;
396                         exvector::iterator it = ops.begin(), itend = ops.end();
397                         while (it != itend) {
398                                 lst::const_iterator last_el = repl_lst.end();
399                                 --last_el;
400                                 if (it->match(p, repl_lst)) {
401                                         ops.erase(it);
402                                         goto found;
403                                 }
404                                 while(true) {
405                                         lst::const_iterator next_el = last_el;
406                                         ++next_el;
407                                         if(next_el == repl_lst.end())
408                                                 break;
409                                         else
410                                                 repl_lst.remove_last();
411                                 }
412                                 ++it;
413                         }
414                         return false; // no match found
415 found:          ;
416                 }
417
418                 if (has_global_wildcard) {
419
420                         // Assign all the remaining terms to the global wildcard (unless
421                         // it has already been matched before, in which case the matches
422                         // must be equal)
423                         size_t num = ops.size();
424                         std::auto_ptr<epvector> vp(new epvector);
425                         vp->reserve(num);
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));
432                         }
433                         repl_lst.append(global_wildcard == rest);
434                         return true;
435
436                 } else {
437
438                         // No global wildcard, then the match fails if there are any
439                         // unmatched terms left
440                         return ops.empty();
441                 }
442         }
443         return inherited::match(pattern, repl_lst);
444 }
445
446 ex expairseq::subs(const exmap & m, unsigned options) const
447 {
448         std::auto_ptr<epvector> vp = subschildren(m, options);
449         if (vp.get())
450                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
451         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
452                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
453         else
454                 return subs_one_level(m, options);
455 }
456
457 // protected
458
459 int expairseq::compare_same_type(const basic &other) const
460 {
461         GINAC_ASSERT(is_a<expairseq>(other));
462         const expairseq &o = static_cast<const expairseq &>(other);
463         
464         int cmpval;
465         
466         // compare number of elements
467         if (seq.size() != o.seq.size())
468                 return (seq.size()<o.seq.size()) ? -1 : 1;
469         
470         // compare overall_coeff
471         cmpval = overall_coeff.compare(o.overall_coeff);
472         if (cmpval!=0)
473                 return cmpval;
474         
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();
483                 
484                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
485                         cmpval = (*cit1).compare(*cit2);
486                         if (cmpval!=0) return cmpval;
487                 }
488                 
489                 GINAC_ASSERT(cit1==last1);
490                 GINAC_ASSERT(cit2==last2);
491                 
492                 return 0;
493 #if EXPAIRSEQ_USE_HASHTAB
494         }
495         
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;
501         }
502         
503         // compare individual (sorted) hashtab entries
504         for (unsigned i=0; i<hashtabsize; ++i) {
505                 unsigned sz = hashtab[i].size();
506                 if (sz>0) {
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));
513                                 if (cmpval!=0)
514                                         return cmpval;
515                                 ++it1;
516                                 ++it2;
517                         }
518                 }
519         }
520         
521         return 0; // equal
522 #endif // EXPAIRSEQ_USE_HASHTAB
523 }
524
525 bool expairseq::is_equal_same_type(const basic &other) const
526 {
527         const expairseq &o = static_cast<const expairseq &>(other);
528         
529         // compare number of elements
530         if (seq.size()!=o.seq.size())
531                 return false;
532         
533         // compare overall_coeff
534         if (!overall_coeff.is_equal(o.overall_coeff))
535                 return false;
536         
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));
544         }
545                 
546         GINAC_ASSERT(hashtabsize==o.hashtabsize);
547         
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();
553                 
554                 while (cit1!=last1) {
555                         if (!(*cit1).is_equal(*cit2)) return false;
556                         ++cit1;
557                         ++cit2;
558                 }
559                 
560                 return true;
561 #if EXPAIRSEQ_USE_HASHTAB
562         }
563         
564         for (unsigned i=0; i<hashtabsize; ++i) {
565                 if (hashtab[i].size() != o.hashtab[i].size())
566                         return false;
567         }
568
569         // compare individual sorted hashtab entries
570         for (unsigned i=0; i<hashtabsize; ++i) {
571                 unsigned sz = hashtab[i].size();
572                 if (sz>0) {
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;
579                                 ++it1;
580                                 ++it2;
581                         }
582                 }
583         }
584         
585         return true;
586 #endif // EXPAIRSEQ_USE_HASHTAB
587 }
588
589 unsigned expairseq::return_type() const
590 {
591         return return_types::noncommutative_composite;
592 }
593
594 unsigned expairseq::calchash() const
595 {
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();
599         while (i != end) {
600                 v ^= i->rest.gethash();
601 #if !EXPAIRSEQ_USE_HASHTAB
602                 // rotation spoils commutativity!
603                 v = rotate_left(v);
604                 v ^= i->coeff.gethash();
605 #endif // !EXPAIRSEQ_USE_HASHTAB
606                 ++i;
607         }
608
609         v ^= overall_coeff.gethash();
610
611         // store calculated hash value only if object is already evaluated
612         if (flags &status_flags::evaluated) {
613                 setflag(status_flags::hash_calculated);
614                 hashvalue = v;
615         }
616         
617         return v;
618 }
619
620 ex expairseq::expand(unsigned options) const
621 {
622         std::auto_ptr<epvector> vp = expandchildren(options);
623         if (vp.get())
624                 return thisexpairseq(vp, overall_coeff);
625         else {
626                 // The terms have not changed, so it is safe to declare this expanded
627                 return (options == 0) ? setflag(status_flags::expanded) : *this;
628         }
629 }
630
631 //////////
632 // new virtual functions which can be overridden by derived classes
633 //////////
634
635 // protected
636
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
644  *  definition. */
645 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
646 {
647         return expairseq(v, oc, do_index_renaming);
648 }
649
650 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
651 {
652         return expairseq(vp, oc, do_index_renaming);
653 }
654
655 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
656 {
657         c.s << "[[";
658         p.rest.print(c, precedence());
659         c.s << ",";
660         p.coeff.print(c, precedence());
661         c.s << "]]";
662 }
663
664 void expairseq::printseq(const print_context & c, char delim,
665                          unsigned this_precedence,
666                          unsigned upper_precedence) const
667 {
668         if (this_precedence <= upper_precedence)
669                 c.s << "(";
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);
673                 c.s << delim;
674         }
675         printpair(c, *it, this_precedence);
676         if (!overall_coeff.is_equal(default_overall_coeff())) {
677                 c.s << delim;
678                 overall_coeff.print(c, this_precedence);
679         }
680         
681         if (this_precedence <= upper_precedence)
682                 c.s << ")";
683 }
684
685
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
689 {
690         return expair(e,_ex1);
691 }
692
693
694 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
695                                                 const ex &c) const
696 {
697         GINAC_ASSERT(is_exactly_a<numeric>(c));
698         
699         return expair(e,c);
700 }
701
702
703 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
704                                                   const ex &c) const
705 {
706         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
707         GINAC_ASSERT(is_exactly_a<numeric>(c));
708         
709         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
710 }
711
712
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
716 {
717         return lst(p.rest,p.coeff);
718 }
719
720 bool expairseq::expair_needs_further_processing(epp it)
721 {
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
725         return false;
726 }
727
728 ex expairseq::default_overall_coeff() const
729 {
730         return _ex0;
731 }
732
733 void expairseq::combine_overall_coeff(const ex &c)
734 {
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));
738 }
739
740 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
741 {
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)));
747 }
748
749 bool expairseq::can_make_flat(const expair &p) const
750 {
751         return true;
752 }
753
754
755 //////////
756 // non-virtual functions in this class
757 //////////
758
759 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
760 {
761         exvector v;
762         v.reserve(2);
763         v.push_back(lh);
764         v.push_back(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
770 }
771
772 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
773 {
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);
781                         } else {
782 #endif // EXPAIRSEQ_USE_HASHTAB
783                                 if(is_a<mul>(lh))
784                                 {
785                                         ex newrh=rename_dummy_indices_uniquely(lh, rh);
786                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
787                                                                    ex_to<expairseq>(newrh));
788                                 }
789                                 else
790                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
791                                                                    ex_to<expairseq>(rh));
792 #if EXPAIRSEQ_USE_HASHTAB
793                         }
794 #endif // EXPAIRSEQ_USE_HASHTAB
795                         return;
796                 } else {
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);
801                         } else {
802 #endif // EXPAIRSEQ_USE_HASHTAB
803                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
804 #if EXPAIRSEQ_USE_HASHTAB
805                         }
806 #endif // EXPAIRSEQ_USE_HASHTAB
807                         return;
808                 }
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);
814                 } else {
815 #endif // EXPAIRSEQ_USE_HASHTAB
816                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
817 #if EXPAIRSEQ_USE_HASHTAB
818                 }
819 #endif // EXPAIRSEQ_USE_HASHTAB
820                 return;
821         }
822         
823 #if EXPAIRSEQ_USE_HASHTAB
824         if (calc_hashtabsize(2)!=0) {
825                 construct_from_2_ex_via_exvector(lh,rh);
826                 return;
827         }
828         hashtabsize = 0;
829 #endif // EXPAIRSEQ_USE_HASHTAB
830         
831         if (is_exactly_a<numeric>(lh)) {
832                 if (is_exactly_a<numeric>(rh)) {
833                         combine_overall_coeff(lh);
834                         combine_overall_coeff(rh);
835                 } else {
836                         combine_overall_coeff(lh);
837                         seq.push_back(split_ex_to_pair(rh));
838                 }
839         } else {
840                 if (is_exactly_a<numeric>(rh)) {
841                         combine_overall_coeff(rh);
842                         seq.push_back(split_ex_to_pair(lh));
843                 } else {
844                         expair p1 = split_ex_to_pair(lh);
845                         expair p2 = split_ex_to_pair(rh);
846                         
847                         int cmpval = p1.rest.compare(p2.rest);
848                         if (cmpval==0) {
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()
853                                         seq.push_back(p1);
854                                 }
855                         } else {
856                                 seq.reserve(2);
857                                 if (cmpval<0) {
858                                         seq.push_back(p1);
859                                         seq.push_back(p2);
860                                 } else {
861                                         seq.push_back(p2);
862                                         seq.push_back(p1);
863                                 }
864                         }
865                 }
866         }
867 }
868
869 void expairseq::construct_from_2_expairseq(const expairseq &s1,
870                                                                                    const expairseq &s2)
871 {
872         combine_overall_coeff(s1.overall_coeff);
873         combine_overall_coeff(s2.overall_coeff);
874
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();
879
880         seq.reserve(s1.seq.size()+s2.seq.size());
881
882         bool needs_further_processing=false;
883         
884         while (first1!=last1 && first2!=last2) {
885                 int cmpval = (*first1).rest.compare((*first2).rest);
886
887                 if (cmpval==0) {
888                         // combine terms
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;
895                                 }
896                         }
897                         ++first1;
898                         ++first2;
899                 } else if (cmpval<0) {
900                         seq.push_back(*first1);
901                         ++first1;
902                 } else {
903                         seq.push_back(*first2);
904                         ++first2;
905                 }
906         }
907         
908         while (first1!=last1) {
909                 seq.push_back(*first1);
910                 ++first1;
911         }
912         while (first2!=last2) {
913                 seq.push_back(*first2);
914                 ++first2;
915         }
916         
917         if (needs_further_processing) {
918                 epvector v = seq;
919                 seq.clear();
920                 construct_from_epvector(v);
921         }
922 }
923
924 void expairseq::construct_from_expairseq_ex(const expairseq &s,
925                                                                                         const ex &e)
926 {
927         combine_overall_coeff(s.overall_coeff);
928         if (is_exactly_a<numeric>(e)) {
929                 combine_overall_coeff(e);
930                 seq = s.seq;
931                 return;
932         }
933         
934         epvector::const_iterator first = s.seq.begin();
935         epvector::const_iterator last = s.seq.end();
936         expair p = split_ex_to_pair(e);
937         
938         seq.reserve(s.seq.size()+1);
939         bool p_pushed = false;
940         
941         bool needs_further_processing=false;
942         
943         // merge p into s.seq
944         while (first!=last) {
945                 int cmpval = (*first).rest.compare(p.rest);
946                 if (cmpval==0) {
947                         // combine terms
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;
954                         }
955                         ++first;
956                         p_pushed = true;
957                         break;
958                 } else if (cmpval<0) {
959                         seq.push_back(*first);
960                         ++first;
961                 } else {
962                         seq.push_back(p);
963                         p_pushed = true;
964                         break;
965                 }
966         }
967         
968         if (p_pushed) {
969                 // while loop exited because p was pushed, now push rest of s.seq
970                 while (first!=last) {
971                         seq.push_back(*first);
972                         ++first;
973                 }
974         } else {
975                 // while loop exited because s.seq was pushed, now push p
976                 seq.push_back(p);
977         }
978
979         if (needs_further_processing) {
980                 epvector v = seq;
981                 seq.clear();
982                 construct_from_epvector(v);
983         }
984 }
985
986 void expairseq::construct_from_exvector(const exvector &v)
987 {
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 (+,*) -> (*,^)
992
993         make_flat(v);
994 #if EXPAIRSEQ_USE_HASHTAB
995         combine_same_terms();
996 #else
997         canonicalize();
998         combine_same_terms_sorted_seq();
999 #endif // EXPAIRSEQ_USE_HASHTAB
1000 }
1001
1002 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1003 {
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 (+,*) -> (*,^)
1008
1009         make_flat(v, do_index_renaming);
1010 #if EXPAIRSEQ_USE_HASHTAB
1011         combine_same_terms();
1012 #else
1013         canonicalize();
1014         combine_same_terms_sorted_seq();
1015 #endif // EXPAIRSEQ_USE_HASHTAB
1016 }
1017
1018 // Class to handle the renaming of dummy indices. It holds a vector of
1019 // indices that are being used in the expression so-far. If the same
1020 // index occurs again as a dummy index in a factor, it is to be renamed.
1021 // Unless dummy index renaming was swichted of, of course ;-) .
1022 class make_flat_inserter
1023 {
1024         public:
1025                 make_flat_inserter(const epvector &epv, bool b): do_renaming(b)
1026                 {
1027                         if (!do_renaming)
1028                                 return;
1029                         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i)
1030                                 if(are_ex_trivially_equal(i->coeff, _ex1))
1031                                         combine_indices(i->rest.get_free_indices());
1032                 }
1033                 make_flat_inserter(const exvector &v, bool b): do_renaming(b)
1034                 {
1035                         if (!do_renaming)
1036                                 return;
1037                         for (exvector::const_iterator i=v.begin(); i!=v.end(); ++i)
1038                                 combine_indices(i->get_free_indices());
1039                 }
1040                 ex handle_factor(const ex &x, const ex &coeff)
1041                 {
1042                         if (!do_renaming)
1043                                 return x;
1044                         exvector dummies_of_factor;
1045                         if (coeff == _ex1)
1046                                 dummies_of_factor = get_all_dummy_indices_safely(x);
1047                         else if (coeff == _ex2)
1048                                 dummies_of_factor = x.get_free_indices();
1049                         else
1050                                 return x;
1051                         if (dummies_of_factor.size() == 0)
1052                                 return x;
1053                         sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
1054                         ex new_factor = rename_dummy_indices_uniquely(used_indices,
1055                                 dummies_of_factor, x);
1056                         combine_indices(dummies_of_factor);
1057                         return new_factor;
1058                 }
1059         private:
1060                 void combine_indices(const exvector &dummies_of_factor)
1061                 {
1062                         exvector new_dummy_indices;
1063                         set_union(used_indices.begin(), used_indices.end(),
1064                                 dummies_of_factor.begin(), dummies_of_factor.end(),
1065                                 std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
1066                         used_indices.swap(new_dummy_indices);
1067                 }
1068                 bool do_renaming;
1069                 exvector used_indices;
1070 };
1071
1072
1073 /** Combine this expairseq with argument exvector.
1074  *  It cares for associativity as well as for special handling of numerics. */
1075 void expairseq::make_flat(const exvector &v)
1076 {
1077         exvector::const_iterator cit;
1078         
1079         // count number of operands which are of same expairseq derived type
1080         // and their cumulative number of operands
1081         int nexpairseqs = 0;
1082         int noperands = 0;
1083         
1084         cit = v.begin();
1085         while (cit!=v.end()) {
1086                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1087                         ++nexpairseqs;
1088                         noperands += ex_to<expairseq>(*cit).seq.size();
1089                 }
1090                 ++cit;
1091         }
1092         
1093         // reserve seq and coeffseq which will hold all operands
1094         seq.reserve(v.size()+noperands-nexpairseqs);
1095         
1096         // copy elements and split off numerical part
1097         make_flat_inserter mf(v, this->tinfo()==&mul::tinfo_static);
1098         cit = v.begin();
1099         while (cit!=v.end()) {
1100                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1101                         ex newfactor = mf.handle_factor(*cit, _ex1);
1102                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
1103                         combine_overall_coeff(subseqref.overall_coeff);
1104                         epvector::const_iterator cit_s = subseqref.seq.begin();
1105                         while (cit_s!=subseqref.seq.end()) {
1106                                 seq.push_back(*cit_s);
1107                                 ++cit_s;
1108                         }
1109                 } else {
1110                         if (is_exactly_a<numeric>(*cit))
1111                                 combine_overall_coeff(*cit);
1112                         else {
1113                                 ex newfactor = mf.handle_factor(*cit, _ex1);
1114                                 seq.push_back(split_ex_to_pair(newfactor));
1115                         }
1116                 }
1117                 ++cit;
1118         }
1119 }
1120
1121 /** Combine this expairseq with argument epvector.
1122  *  It cares for associativity as well as for special handling of numerics. */
1123 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1124 {
1125         epvector::const_iterator cit;
1126         
1127         // count number of operands which are of same expairseq derived type
1128         // and their cumulative number of operands
1129         int nexpairseqs = 0;
1130         int noperands = 0;
1131         
1132         cit = v.begin();
1133         while (cit!=v.end()) {
1134                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1135                         ++nexpairseqs;
1136                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1137                 }
1138                 ++cit;
1139         }
1140         
1141         // reserve seq and coeffseq which will hold all operands
1142         seq.reserve(v.size()+noperands-nexpairseqs);
1143         make_flat_inserter mf(v, do_index_renaming);
1144         
1145         // copy elements and split off numerical part
1146         cit = v.begin();
1147         while (cit!=v.end()) {
1148                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1149                     this->can_make_flat(*cit)) {
1150                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1151                         const expairseq &subseqref = ex_to<expairseq>(newrest);
1152                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1153                                                             ex_to<numeric>(cit->coeff));
1154                         epvector::const_iterator cit_s = subseqref.seq.begin();
1155                         while (cit_s!=subseqref.seq.end()) {
1156                                 seq.push_back(expair(cit_s->rest,
1157                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1158                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1159                                 //                                              (*cit).coeff));
1160                                 ++cit_s;
1161                         }
1162                 } else {
1163                         if (cit->is_canonical_numeric())
1164                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1165                         else {
1166                                 ex rest = cit->rest;
1167                                 ex newrest = mf.handle_factor(rest, cit->coeff);
1168                                 if (are_ex_trivially_equal(newrest, rest))
1169                                         seq.push_back(*cit);
1170                                 else
1171                                         seq.push_back(expair(newrest, cit->coeff));
1172                         }
1173                 }
1174                 ++cit;
1175         }
1176 }
1177
1178 /** Brings this expairseq into a sorted (canonical) form. */
1179 void expairseq::canonicalize()
1180 {
1181         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1182 }
1183
1184
1185 /** Compact a presorted expairseq by combining all matching expairs to one
1186  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1187  *  instance. */
1188 void expairseq::combine_same_terms_sorted_seq()
1189 {
1190         if (seq.size()<2)
1191                 return;
1192
1193         bool needs_further_processing = false;
1194
1195         epvector::iterator itin1 = seq.begin();
1196         epvector::iterator itin2 = itin1+1;
1197         epvector::iterator itout = itin1;
1198         epvector::iterator last = seq.end();
1199         // must_copy will be set to true the first time some combination is 
1200         // possible from then on the sequence has changed and must be compacted
1201         bool must_copy = false;
1202         while (itin2!=last) {
1203                 if (itin1->rest.compare(itin2->rest)==0) {
1204                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1205                                        add_dyn(ex_to<numeric>(itin2->coeff));
1206                         if (expair_needs_further_processing(itin1))
1207                                 needs_further_processing = true;
1208                         must_copy = true;
1209                 } else {
1210                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1211                                 if (must_copy)
1212                                         *itout = *itin1;
1213                                 ++itout;
1214                         }
1215                         itin1 = itin2;
1216                 }
1217                 ++itin2;
1218         }
1219         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1220                 if (must_copy)
1221                         *itout = *itin1;
1222                 ++itout;
1223         }
1224         if (itout!=last)
1225                 seq.erase(itout,last);
1226
1227         if (needs_further_processing) {
1228                 epvector v = seq;
1229                 seq.clear();
1230                 construct_from_epvector(v);
1231         }
1232 }
1233
1234 #if EXPAIRSEQ_USE_HASHTAB
1235
1236 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1237 {
1238         unsigned size;
1239         unsigned nearest_power_of_2 = 1 << log2(sz);
1240         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1241         //  size = nearest_power_of_2*hashtabfactor;
1242         size = nearest_power_of_2/hashtabfactor;
1243         if (size<minhashtabsize)
1244                 return 0;
1245
1246         // hashtabsize must be a power of 2
1247         GINAC_ASSERT((1U << log2(size))==size);
1248         return size;
1249 }
1250
1251 unsigned expairseq::calc_hashindex(const ex &e) const
1252 {
1253         // calculate hashindex
1254         unsigned hashindex;
1255         if (is_a<numeric>(e)) {
1256                 hashindex = hashmask;
1257         } else {
1258                 hashindex = e.gethash() & hashmask;
1259                 // last hashtab entry is reserved for numerics
1260                 if (hashindex==hashmask) hashindex = 0;
1261         }
1262         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1263         return hashindex;
1264 }
1265
1266 void expairseq::shrink_hashtab()
1267 {
1268         unsigned new_hashtabsize;
1269         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1270                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1271                 if (new_hashtabsize==0) {
1272                         hashtab.clear();
1273                         hashtabsize = 0;
1274                         canonicalize();
1275                         return;
1276                 }
1277                 
1278                 // shrink by a factor of 2
1279                 unsigned half_hashtabsize = hashtabsize/2;
1280                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1281                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1282                 // special treatment for numeric hashes
1283                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1284                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1285                 hashtab.resize(half_hashtabsize);
1286                 hashtabsize = half_hashtabsize;
1287                 hashmask = hashtabsize-1;
1288         }
1289 }
1290
1291 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1292 {
1293         if (hashtabsize==0)
1294                 return; // nothing to do
1295         
1296         // calculate hashindex of element to be deleted
1297         unsigned hashindex = calc_hashindex((*element).rest);
1298
1299         // find it in hashtab and remove it
1300         epplist &eppl = hashtab[hashindex];
1301         epplist::iterator epplit = eppl.begin();
1302         bool erased = false;
1303         while (epplit!=eppl.end()) {
1304                 if (*epplit == element) {
1305                         eppl.erase(epplit);
1306                         erased = true;
1307                         break;
1308                 }
1309                 ++epplit;
1310         }
1311         if (!erased) {
1312                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1313                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1314
1315                 unsigned hashindex = calc_hashindex(element->rest);
1316                 epplist &eppl = hashtab[hashindex];
1317                 epplist::iterator epplit = eppl.begin();
1318                 bool erased = false;
1319                 while (epplit!=eppl.end()) {
1320                         if (*epplit == element) {
1321                                 eppl.erase(epplit);
1322                                 erased = true;
1323                                 break;
1324                         }
1325                         ++epplit;
1326                 }
1327                 GINAC_ASSERT(erased);
1328         }
1329         GINAC_ASSERT(erased);
1330 }
1331
1332 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1333                                    epvector::iterator newpos)
1334 {
1335         GINAC_ASSERT(hashtabsize!=0);
1336         
1337         // calculate hashindex of element which was moved
1338         unsigned hashindex=calc_hashindex((*newpos).rest);
1339
1340         // find it in hashtab and modify it
1341         epplist &eppl = hashtab[hashindex];
1342         epplist::iterator epplit = eppl.begin();
1343         while (epplit!=eppl.end()) {
1344                 if (*epplit == oldpos) {
1345                         *epplit = newpos;
1346                         break;
1347                 }
1348                 ++epplit;
1349         }
1350         GINAC_ASSERT(epplit!=eppl.end());
1351 }
1352
1353 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1354 {
1355         epplist::const_iterator current = eppl.begin();
1356         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1357                 ++current;
1358         }
1359         eppl.insert(current,elem);
1360 }    
1361
1362 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1363                                           epvector::iterator &last_non_zero,
1364                                           std::vector<bool> &touched,
1365                                           unsigned &number_of_zeroes)
1366 {
1367         epp current = seq.begin();
1368
1369         while (current!=first_numeric) {
1370                 if (is_exactly_a<numeric>(current->rest)) {
1371                         --first_numeric;
1372                         iter_swap(current,first_numeric);
1373                 } else {
1374                         // calculate hashindex
1375                         unsigned currenthashindex = calc_hashindex(current->rest);
1376
1377                         // test if there is already a matching expair in the hashtab-list
1378                         epplist &eppl=hashtab[currenthashindex];
1379                         epplist::iterator epplit = eppl.begin();
1380                         while (epplit!=eppl.end()) {
1381                                 if (current->rest.is_equal((*epplit)->rest))
1382                                         break;
1383                                 ++epplit;
1384                         }
1385                         if (epplit==eppl.end()) {
1386                                 // no matching expair found, append this to end of list
1387                                 sorted_insert(eppl,current);
1388                                 ++current;
1389                         } else {
1390                                 // epplit points to a matching expair, combine it with current
1391                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1392                                                    add_dyn(ex_to<numeric>(current->coeff));
1393                                 
1394                                 // move obsolete current expair to end by swapping with last_non_zero element
1395                                 // if this was a numeric, it is swapped with the expair before first_numeric 
1396                                 iter_swap(current,last_non_zero);
1397                                 --first_numeric;
1398                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1399                                 --last_non_zero;
1400                                 ++number_of_zeroes;
1401                                 // test if combined term has coeff 0 and can be removed is done later
1402                                 touched[(*epplit)-seq.begin()] = true;
1403                         }
1404                 }
1405         }
1406 }
1407
1408 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1409                                    epvector::iterator &last_non_zero,
1410                                    std::vector<bool> &touched,
1411                                    unsigned &number_of_zeroes)
1412 {
1413         // move terms with coeff 0 to end and remove them from hashtab
1414         // check only those elements which have been touched
1415         epp current = seq.begin();
1416         size_t i = 0;
1417         while (current!=first_numeric) {
1418                 if (!touched[i]) {
1419                         ++current;
1420                         ++i;
1421                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1422                         ++current;
1423                         ++i;
1424                 } else {
1425                         remove_hashtab_entry(current);
1426                         
1427                         // move element to the end, unless it is already at the end
1428                         if (current!=last_non_zero) {
1429                                 iter_swap(current,last_non_zero);
1430                                 --first_numeric;
1431                                 bool numeric_swapped = first_numeric!=last_non_zero;
1432                                 if (numeric_swapped)
1433                                         iter_swap(first_numeric,current);
1434                                 epvector::iterator changed_entry;
1435
1436                                 if (numeric_swapped)
1437                                         changed_entry = first_numeric;
1438                                 else
1439                                         changed_entry = last_non_zero;
1440                                 
1441                                 --last_non_zero;
1442                                 ++number_of_zeroes;
1443
1444                                 if (first_numeric!=current) {
1445
1446                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1447                                         move_hashtab_entry(changed_entry,current);
1448                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1449                                 }
1450                         } else {
1451                                 --first_numeric;
1452                                 --last_non_zero;
1453                                 ++number_of_zeroes;
1454                         }
1455                 }
1456         }
1457         GINAC_ASSERT(i==current-seq.begin());
1458 }
1459
1460 /** True if one of the coeffs vanishes, otherwise false.
1461  *  This would be an invariant violation, so this should only be used for
1462  *  debugging purposes. */
1463 bool expairseq::has_coeff_0() const
1464 {
1465         epvector::const_iterator i = seq.begin(), end = seq.end();
1466         while (i != end) {
1467                 if (i->coeff.is_zero())
1468                         return true;
1469                 ++i;
1470         }
1471         return false;
1472 }
1473
1474 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1475                                                                                 epvector::const_iterator last_non_zero)
1476 {
1477         if (first_numeric == seq.end()) return; // no numerics
1478         
1479         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1480         while (current != last) {
1481                 sorted_insert(hashtab[hashmask], current);
1482                 ++current;
1483         }
1484 }
1485
1486 void expairseq::combine_same_terms()
1487 {
1488         // combine same terms, drop term with coeff 0, move numerics to end
1489         
1490         // calculate size of hashtab
1491         hashtabsize = calc_hashtabsize(seq.size());
1492         
1493         // hashtabsize is a power of 2
1494         hashmask = hashtabsize-1;
1495         
1496         // allocate hashtab
1497         hashtab.clear();
1498         hashtab.resize(hashtabsize);
1499         
1500         if (hashtabsize==0) {
1501                 canonicalize();
1502                 combine_same_terms_sorted_seq();
1503                 GINAC_ASSERT(!has_coeff_0());
1504                 return;
1505         }
1506         
1507         // iterate through seq, move numerics to end,
1508         // fill hashtab and combine same terms
1509         epvector::iterator first_numeric = seq.end();
1510         epvector::iterator last_non_zero = seq.end()-1;
1511         
1512         size_t num = seq.size();
1513         std::vector<bool> touched(num);
1514         
1515         unsigned number_of_zeroes = 0;
1516         
1517         GINAC_ASSERT(!has_coeff_0());
1518         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1519         
1520         // there should not be any terms with coeff 0 from the beginning,
1521         // so it should be safe to skip this step
1522         if (number_of_zeroes!=0) {
1523                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1524         }
1525         
1526         add_numerics_to_hashtab(first_numeric,last_non_zero);
1527         
1528         // pop zero elements
1529         for (unsigned i=0; i<number_of_zeroes; ++i) {
1530                 seq.pop_back();
1531         }
1532         
1533         // shrink hashtabsize to calculated value
1534         GINAC_ASSERT(!has_coeff_0());
1535         
1536         shrink_hashtab();
1537         
1538         GINAC_ASSERT(!has_coeff_0());
1539 }
1540
1541 #endif // EXPAIRSEQ_USE_HASHTAB
1542
1543 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1544  *  debugging or in assertions since being sorted is an invariance. */
1545 bool expairseq::is_canonical() const
1546 {
1547         if (seq.size() <= 1)
1548                 return 1;
1549         
1550 #if EXPAIRSEQ_USE_HASHTAB
1551         if (hashtabsize > 0) return 1; // not canoncalized
1552 #endif // EXPAIRSEQ_USE_HASHTAB
1553         
1554         epvector::const_iterator it = seq.begin(), itend = seq.end();
1555         epvector::const_iterator it_last = it;
1556         for (++it; it!=itend; it_last=it, ++it) {
1557                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1558                         if (!is_exactly_a<numeric>(it_last->rest) ||
1559                                 !is_exactly_a<numeric>(it->rest)) {
1560                                 // double test makes it easier to set a breakpoint...
1561                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1562                                         !is_exactly_a<numeric>(it->rest)) {
1563                                         printpair(std::clog, *it_last, 0);
1564                                         std::clog << ">";
1565                                         printpair(std::clog, *it, 0);
1566                                         std::clog << "\n";
1567                                         std::clog << "pair1:" << std::endl;
1568                                         it_last->rest.print(print_tree(std::clog));
1569                                         it_last->coeff.print(print_tree(std::clog));
1570                                         std::clog << "pair2:" << std::endl;
1571                                         it->rest.print(print_tree(std::clog));
1572                                         it->coeff.print(print_tree(std::clog));
1573                                         return 0;
1574                                 }
1575                         }
1576                 }
1577         }
1578         return 1;
1579 }
1580
1581
1582 /** Member-wise expand the expairs in this sequence.
1583  *
1584  *  @see expairseq::expand()
1585  *  @return pointer to epvector containing expanded pairs or zero pointer,
1586  *  if no members were changed. */
1587 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1588 {
1589         const epvector::const_iterator last = seq.end();
1590         epvector::const_iterator cit = seq.begin();
1591         while (cit!=last) {
1592                 const ex &expanded_ex = cit->rest.expand(options);
1593                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1594                         
1595                         // something changed, copy seq, eval and return it
1596                         std::auto_ptr<epvector> s(new epvector);
1597                         s->reserve(seq.size());
1598                         
1599                         // copy parts of seq which are known not to have changed
1600                         epvector::const_iterator cit2 = seq.begin();
1601                         while (cit2!=cit) {
1602                                 s->push_back(*cit2);
1603                                 ++cit2;
1604                         }
1605
1606                         // copy first changed element
1607                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1608                                                                    cit2->coeff));
1609                         ++cit2;
1610
1611                         // copy rest
1612                         while (cit2!=last) {
1613                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1614                                                                            cit2->coeff));
1615                                 ++cit2;
1616                         }
1617                         return s;
1618                 }
1619                 ++cit;
1620         }
1621         
1622         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1623 }
1624
1625
1626 /** Member-wise evaluate the expairs in this sequence.
1627  *
1628  *  @see expairseq::eval()
1629  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1630  *  if no members were changed. */
1631 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1632 {
1633         // returns a NULL pointer if nothing had to be evaluated
1634         // returns a pointer to a newly created epvector otherwise
1635         // (which has to be deleted somewhere else)
1636
1637         if (level==1)
1638                 return std::auto_ptr<epvector>(0);
1639         
1640         if (level == -max_recursion_level)
1641                 throw(std::runtime_error("max recursion level reached"));
1642         
1643         --level;
1644         epvector::const_iterator last = seq.end();
1645         epvector::const_iterator cit = seq.begin();
1646         while (cit!=last) {
1647                 const ex &evaled_ex = cit->rest.eval(level);
1648                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1649                         
1650                         // something changed, copy seq, eval and return it
1651                         std::auto_ptr<epvector> s(new epvector);
1652                         s->reserve(seq.size());
1653                         
1654                         // copy parts of seq which are known not to have changed
1655                         epvector::const_iterator cit2=seq.begin();
1656                         while (cit2!=cit) {
1657                                 s->push_back(*cit2);
1658                                 ++cit2;
1659                         }
1660
1661                         // copy first changed element
1662                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1663                                                                    cit2->coeff));
1664                         ++cit2;
1665
1666                         // copy rest
1667                         while (cit2!=last) {
1668                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1669                                                                            cit2->coeff));
1670                                 ++cit2;
1671                         }
1672                         return s;
1673                 }
1674                 ++cit;
1675         }
1676         
1677         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1678 }
1679
1680 /** Member-wise substitute in this sequence.
1681  *
1682  *  @see expairseq::subs()
1683  *  @return pointer to epvector containing pairs after application of subs,
1684  *    or NULL pointer if no members were changed. */
1685 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1686 {
1687         // When any of the objects to be substituted is a product or power
1688         // we have to recombine the pairs because the numeric coefficients may
1689         // be part of the search pattern.
1690         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1691
1692                 // Search the list of substitutions and cache our findings
1693                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1694                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1695                                 options |= subs_options::pattern_is_product;
1696                                 break;
1697                         }
1698                 }
1699                 if (!(options & subs_options::pattern_is_product))
1700                         options |= subs_options::pattern_is_not_product;
1701         }
1702
1703         if (options & subs_options::pattern_is_product) {
1704
1705                 // Substitute in the recombined pairs
1706                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1707                 while (cit != last) {
1708
1709                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1710                         const ex &subsed_ex = orig_ex.subs(m, options);
1711                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1712
1713                                 // Something changed, copy seq, subs and return it
1714                                 std::auto_ptr<epvector> s(new epvector);
1715                                 s->reserve(seq.size());
1716
1717                                 // Copy parts of seq which are known not to have changed
1718                                 s->insert(s->begin(), seq.begin(), cit);
1719
1720                                 // Copy first changed element
1721                                 s->push_back(split_ex_to_pair(subsed_ex));
1722                                 ++cit;
1723
1724                                 // Copy rest
1725                                 while (cit != last) {
1726                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1727                                         ++cit;
1728                                 }
1729                                 return s;
1730                         }
1731
1732                         ++cit;
1733                 }
1734
1735         } else {
1736
1737                 // Substitute only in the "rest" part of the pairs
1738                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1739                 while (cit != last) {
1740
1741                         const ex &subsed_ex = cit->rest.subs(m, options);
1742                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1743                         
1744                                 // Something changed, copy seq, subs and return it
1745                                 std::auto_ptr<epvector> s(new epvector);
1746                                 s->reserve(seq.size());
1747
1748                                 // Copy parts of seq which are known not to have changed
1749                                 s->insert(s->begin(), seq.begin(), cit);
1750                         
1751                                 // Copy first changed element
1752                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1753                                 ++cit;
1754
1755                                 // Copy rest
1756                                 while (cit != last) {
1757                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1758                                         ++cit;
1759                                 }
1760                                 return s;
1761                         }
1762
1763                         ++cit;
1764                 }
1765         }
1766         
1767         // Nothing has changed
1768         return std::auto_ptr<epvector>(0);
1769 }
1770
1771 //////////
1772 // static member variables
1773 //////////
1774
1775 #if EXPAIRSEQ_USE_HASHTAB
1776 unsigned expairseq::maxhashtabsize = 0x4000000U;
1777 unsigned expairseq::minhashtabsize = 0x1000U;
1778 unsigned expairseq::hashtabfactor = 1;
1779 #endif // EXPAIRSEQ_USE_HASHTAB
1780
1781 } // namespace GiNaC