some more comments and cleanups to mul::expand() and ncmul::expand()
[ginac.git] / ginac / expairseq.cpp
1 /** @file expairseq.cpp
2  *
3  *  Implementation of sequences of expression pairs. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
21  */
22
23 #include <algorithm>
24 #include <string>
25 #include <stdexcept>
26
27 #include "expairseq.h"
28 #include "lst.h"
29 #include "relational.h"
30 #include "print.h"
31 #include "archive.h"
32 #include "debugmsg.h"
33 #include "utils.h"
34
35 #if EXPAIRSEQ_USE_HASHTAB
36 #include <cmath>
37 #endif // EXPAIRSEQ_USE_HASHTAB
38
39 namespace GiNaC {
40
41 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
42
43 //////////
44 // helper classes
45 //////////
46
47 class epp_is_less
48 {
49 public:
50         bool operator()(const epp &lh, const epp &rh) const
51         {
52                 return (*lh).is_less(*rh);
53         }
54 };
55
56 //////////
57 // default ctor, dtor, copy ctor assignment operator and helpers
58 //////////
59
60 // public
61
62 expairseq::expairseq(const expairseq &other)
63 {
64         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
65         copy(other);
66 }
67
68 const expairseq &expairseq::operator=(const expairseq &other)
69 {
70         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
71         if (this != &other) {
72                 destroy(true);
73                 copy(other);
74         }
75         return *this;
76 }
77
78 // protected
79
80 /** For use by copy ctor and assignment operator. */
81 void expairseq::copy(const expairseq &other)
82 {
83         inherited::copy(other);
84         seq = other.seq;
85         overall_coeff = other.overall_coeff;
86 #if EXPAIRSEQ_USE_HASHTAB
87         // copy hashtab
88         hashtabsize = other.hashtabsize;
89         if (hashtabsize!=0) {
90                 hashmask = other.hashmask;
91                 hashtab.resize(hashtabsize);
92                 epvector::const_iterator osb = other.seq.begin();
93                 for (unsigned i=0; i<hashtabsize; ++i) {
94                         hashtab[i].clear();
95                         for (epplist::const_iterator cit=other.hashtab[i].begin();
96                              cit!=other.hashtab[i].end(); ++cit) {
97                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
98                         }
99                 }
100         } else {
101                 hashtab.clear();
102         }
103 #endif // EXPAIRSEQ_USE_HASHTAB
104 }
105
106 DEFAULT_DESTROY(expairseq)
107
108 //////////
109 // other ctors
110 //////////
111
112 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
113 {
114         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
115         construct_from_2_ex(lh,rh);
116         GINAC_ASSERT(is_canonical());
117 }
118
119 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
120 {
121         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
122         construct_from_exvector(v);
123         GINAC_ASSERT(is_canonical());
124 }
125
126 expairseq::expairseq(const epvector &v, const ex &oc)
127   : inherited(TINFO_expairseq), overall_coeff(oc)
128 {
129         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
130         construct_from_epvector(v);
131         GINAC_ASSERT(is_canonical());
132 }
133
134 expairseq::expairseq(epvector *vp, const ex &oc)
135   : inherited(TINFO_expairseq), overall_coeff(oc)
136 {
137         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
138         GINAC_ASSERT(vp!=0);
139         construct_from_epvector(*vp);
140         delete vp;
141         GINAC_ASSERT(is_canonical());
142 }
143
144 //////////
145 // archiving
146 //////////
147
148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
149 #if EXPAIRSEQ_USE_HASHTAB
150         , hashtabsize(0)
151 #endif
152 {
153         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
154         for (unsigned int i=0; true; i++) {
155                 ex rest;
156                 ex coeff;
157                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
158                         seq.push_back(expair(rest, coeff));
159                 else
160                         break;
161         }
162         n.find_ex("overall_coeff", overall_coeff, sym_lst);
163 }
164
165 void expairseq::archive(archive_node &n) const
166 {
167         inherited::archive(n);
168         epvector::const_iterator i = seq.begin(), iend = seq.end();
169         while (i != iend) {
170                 n.add_ex("rest", i->rest);
171                 n.add_ex("coeff", i->coeff);
172                 ++i;
173         }
174         n.add_ex("overall_coeff", overall_coeff);
175 }
176
177 DEFAULT_UNARCHIVE(expairseq)
178
179 //////////
180 // functions overriding virtual functions from bases classes
181 //////////
182
183 // public
184
185 basic *expairseq::duplicate() const
186 {
187         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
188         return new expairseq(*this);
189 }
190
191 void expairseq::print(const print_context & c, unsigned level) const
192 {
193         debugmsg("expairseq print",LOGLEVEL_PRINT);
194
195         if (is_of_type(c, print_tree)) {
196
197                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
198
199                 c.s << std::string(level, ' ') << class_name()
200                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
201                     << ", nops=" << nops()
202                     << std::endl;
203                 unsigned num = seq.size();
204                 for (unsigned i=0; i<num; ++i) {
205                         seq[i].rest.print(c, level + delta_indent);
206                         seq[i].coeff.print(c, level + delta_indent);
207                         if (i != num - 1)
208                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
209                 }
210                 if (!overall_coeff.is_equal(default_overall_coeff())) {
211                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
212                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
213                         overall_coeff.print(c, level + delta_indent);
214                 }
215                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
216 #if EXPAIRSEQ_USE_HASHTAB
217                 c.s << std::string(level + delta_indent,' ')
218                     << "hashtab size " << hashtabsize << std::endl;
219                 if (hashtabsize == 0) return;
220 #define MAXCOUNT 5
221                 unsigned count[MAXCOUNT+1];
222                 for (int i=0; i<MAXCOUNT+1; ++i)
223                         count[i] = 0;
224                 unsigned this_bin_fill;
225                 unsigned cum_fill_sq = 0;
226                 unsigned cum_fill = 0;
227                 for (unsigned i=0; i<hashtabsize; ++i) {
228                         this_bin_fill = 0;
229                         if (hashtab[i].size() > 0) {
230                                 c.s << std::string(level + delta_indent, ' ')
231                                     << "bin " << i << " with entries ";
232                                 for (epplist::const_iterator it=hashtab[i].begin();
233                                      it!=hashtab[i].end(); ++it) {
234                                         c.s << *it-seq.begin() << " ";
235                                         ++this_bin_fill;
236                                 }
237                                 c.s << std::endl;
238                                 cum_fill += this_bin_fill;
239                                 cum_fill_sq += this_bin_fill*this_bin_fill;
240                         }
241                         if (this_bin_fill<MAXCOUNT)
242                                 ++count[this_bin_fill];
243                         else
244                                 ++count[MAXCOUNT];
245                 }
246                 unsigned fact = 1;
247                 double cum_prob = 0;
248                 double lambda = (1.0*seq.size()) / hashtabsize;
249                 for (int k=0; k<MAXCOUNT; ++k) {
250                         if (k>0)
251                                 fact *= k;
252                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
253                         cum_prob += prob;
254                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
255                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
256                             << int(prob*1000)/10.0 << ")" << std::endl;
257                 }
258                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
259                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
260                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
261         
262                 c.s << std::string(level + delta_indent, ' ') << "variance: "
263                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
264                     << std::endl;
265                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
266                     << (1.0*cum_fill)/hashtabsize
267                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
268 #endif // EXPAIRSEQ_USE_HASHTAB
269
270         } else {
271                 c.s << "[[";
272                 printseq(c, ',', precedence(), level);
273                 c.s << "]]";
274         }
275 }
276
277 bool expairseq::info(unsigned inf) const
278 {
279         return inherited::info(inf);
280 }
281
282 unsigned expairseq::nops() const
283 {
284         if (overall_coeff.is_equal(default_overall_coeff()))
285                 return seq.size();
286         else
287                 return seq.size()+1;
288 }
289
290 ex expairseq::op(int i) const
291 {
292         if (unsigned(i)<seq.size())
293                 return recombine_pair_to_ex(seq[i]);
294         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
295         return overall_coeff;
296 }
297
298 ex &expairseq::let_op(int i)
299 {
300         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
301 }
302
303 ex expairseq::map(map_function & f) const
304 {
305         epvector *v = new epvector;
306         v->reserve(seq.size());
307
308         epvector::const_iterator cit = seq.begin(), last = seq.end();
309         while (cit != last) {
310                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
311                 ++cit;
312         }
313
314         if (overall_coeff.is_equal(default_overall_coeff()))
315                 return thisexpairseq(v, default_overall_coeff());
316         else
317                 return thisexpairseq(v, f(overall_coeff));
318 }
319
320 ex expairseq::eval(int level) const
321 {
322         if ((level==1) && (flags &status_flags::evaluated))
323                 return *this;
324         
325         epvector *vp = evalchildren(level);
326         if (vp==0)
327                 return this->hold();
328         
329         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
330 }
331
332 bool expairseq::match(const ex & pattern, lst & repl_lst) const
333 {
334         // This differs from basic::match() because we want "a+b+c+d" to
335         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
336
337         if (tinfo() == pattern.bp->tinfo()) {
338
339                 // Check whether global wildcard (one that matches the "rest of the
340                 // expression", like "*" above) is present
341                 bool has_global_wildcard = false;
342                 ex global_wildcard;
343                 for (unsigned int i=0; i<pattern.nops(); i++) {
344                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
345                                 has_global_wildcard = true;
346                                 global_wildcard = pattern.op(i);
347                                 break;
348                         }
349                 }
350
351                 // Unfortunately, this is an O(N^2) operation because we can't
352                 // sort the pattern in a useful way...
353
354                 // Chop into terms
355                 exvector ops;
356                 ops.reserve(nops());
357                 for (unsigned i=0; i<nops(); i++)
358                         ops.push_back(op(i));
359
360                 // Now, for every term of the pattern, look for a matching term in
361                 // the expression and remove the match
362                 for (unsigned i=0; i<pattern.nops(); i++) {
363                         ex p = pattern.op(i);
364                         if (has_global_wildcard && p.is_equal(global_wildcard))
365                                 continue;
366                         exvector::iterator it = ops.begin(), itend = ops.end();
367                         while (it != itend) {
368                                 if (it->match(p, repl_lst)) {
369                                         ops.erase(it);
370                                         goto found;
371                                 }
372                                 ++it;
373                         }
374                         return false; // no match found
375 found:          ;
376                 }
377
378                 if (has_global_wildcard) {
379
380                         // Assign all the remaining terms to the global wildcard (unless
381                         // it has already been matched before, in which case the matches
382                         // must be equal)
383                         unsigned num = ops.size();
384                         epvector *vp = new epvector();
385                         vp->reserve(num);
386                         for (unsigned i=0; i<num; i++)
387                                 vp->push_back(split_ex_to_pair(ops[i]));
388                         ex rest = thisexpairseq(vp, default_overall_coeff());
389                         for (unsigned i=0; i<repl_lst.nops(); i++) {
390                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
391                                         return rest.is_equal(*repl_lst.op(i).op(1).bp);
392                         }
393                         repl_lst.append(global_wildcard == rest);
394                         return true;
395
396                 } else {
397
398                         // No global wildcard, then the match fails if there are any
399                         // unmatched terms left
400                         return ops.empty();
401                 }
402         }
403         return inherited::match(pattern, repl_lst);
404 }
405
406 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
407 {
408         epvector *vp = subschildren(ls, lr, no_pattern);
409         if (vp)
410                 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
411         else
412                 return basic::subs(ls, lr, no_pattern);
413 }
414
415 // protected
416
417 int expairseq::compare_same_type(const basic &other) const
418 {
419         GINAC_ASSERT(is_of_type(other, expairseq));
420         const expairseq &o = static_cast<const expairseq &>(other);
421         
422         int cmpval;
423         
424         // compare number of elements
425         if (seq.size() != o.seq.size())
426                 return (seq.size()<o.seq.size()) ? -1 : 1;
427         
428         // compare overall_coeff
429         cmpval = overall_coeff.compare(o.overall_coeff);
430         if (cmpval!=0)
431                 return cmpval;
432         
433 #if EXPAIRSEQ_USE_HASHTAB
434         GINAC_ASSERT(hashtabsize==o.hashtabsize);
435         if (hashtabsize==0) {
436 #endif // EXPAIRSEQ_USE_HASHTAB
437                 epvector::const_iterator cit1 = seq.begin();
438                 epvector::const_iterator cit2 = o.seq.begin();
439                 epvector::const_iterator last1 = seq.end();
440                 epvector::const_iterator last2 = o.seq.end();
441                 
442                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
443                         cmpval = (*cit1).compare(*cit2);
444                         if (cmpval!=0) return cmpval;
445                 }
446                 
447                 GINAC_ASSERT(cit1==last1);
448                 GINAC_ASSERT(cit2==last2);
449                 
450                 return 0;
451 #if EXPAIRSEQ_USE_HASHTAB
452         }
453         
454         // compare number of elements in each hashtab entry
455         for (unsigned i=0; i<hashtabsize; ++i) {
456                 unsigned cursize=hashtab[i].size();
457                 if (cursize != o.hashtab[i].size())
458                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
459         }
460         
461         // compare individual (sorted) hashtab entries
462         for (unsigned i=0; i<hashtabsize; ++i) {
463                 unsigned sz = hashtab[i].size();
464                 if (sz>0) {
465                         const epplist &eppl1 = hashtab[i];
466                         const epplist &eppl2 = o.hashtab[i];
467                         epplist::const_iterator it1 = eppl1.begin();
468                         epplist::const_iterator it2 = eppl2.begin();
469                         while (it1!=eppl1.end()) {
470                                 cmpval = (*(*it1)).compare(*(*it2));
471                                 if (cmpval!=0)
472                                         return cmpval;
473                                 ++it1;
474                                 ++it2;
475                         }
476                 }
477         }
478         
479         return 0; // equal
480 #endif // EXPAIRSEQ_USE_HASHTAB
481 }
482
483 bool expairseq::is_equal_same_type(const basic &other) const
484 {
485         const expairseq &o = static_cast<const expairseq &>(other);
486         
487         // compare number of elements
488         if (seq.size()!=o.seq.size())
489                 return false;
490         
491         // compare overall_coeff
492         if (!overall_coeff.is_equal(o.overall_coeff))
493                 return false;
494         
495 #if EXPAIRSEQ_USE_HASHTAB
496         // compare number of elements in each hashtab entry
497         if (hashtabsize!=o.hashtabsize) {
498                 std::cout << "this:" << std::endl;
499                 print(print_tree(std::cout));
500                 std::cout << "other:" << std::endl;
501                 other.print(print_tree(std::cout));
502         }
503                 
504         GINAC_ASSERT(hashtabsize==o.hashtabsize);
505         
506         if (hashtabsize==0) {
507 #endif // EXPAIRSEQ_USE_HASHTAB
508                 epvector::const_iterator cit1 = seq.begin();
509                 epvector::const_iterator cit2 = o.seq.begin();
510                 epvector::const_iterator last1 = seq.end();
511                 
512                 while (cit1!=last1) {
513                         if (!(*cit1).is_equal(*cit2)) return false;
514                         ++cit1;
515                         ++cit2;
516                 }
517                 
518                 return true;
519 #if EXPAIRSEQ_USE_HASHTAB
520         }
521         
522         for (unsigned i=0; i<hashtabsize; ++i) {
523                 if (hashtab[i].size() != o.hashtab[i].size())
524                         return false;
525         }
526
527         // compare individual sorted hashtab entries
528         for (unsigned i=0; i<hashtabsize; ++i) {
529                 unsigned sz = hashtab[i].size();
530                 if (sz>0) {
531                         const epplist &eppl1 = hashtab[i];
532                         const epplist &eppl2 = o.hashtab[i];
533                         epplist::const_iterator it1 = eppl1.begin();
534                         epplist::const_iterator it2 = eppl2.begin();
535                         while (it1!=eppl1.end()) {
536                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
537                                 ++it1;
538                                 ++it2;
539                         }
540                 }
541         }
542         
543         return true;
544 #endif // EXPAIRSEQ_USE_HASHTAB
545 }
546
547 unsigned expairseq::return_type(void) const
548 {
549         return return_types::noncommutative_composite;
550 }
551
552 unsigned expairseq::calchash(void) const
553 {
554         unsigned v = golden_ratio_hash(tinfo());
555         epvector::const_iterator i = seq.begin(), end = seq.end();
556         while (i != end) {
557 #if !EXPAIRSEQ_USE_HASHTAB
558                 v = rotate_left_31(v); // rotation would spoil commutativity
559 #endif // EXPAIRSEQ_USE_HASHTAB
560                 v ^= i->rest.gethash();
561 #if !EXPAIRSEQ_USE_HASHTAB
562                 v = rotate_left_31(v);
563                 v ^= i->coeff.gethash();
564 #endif // EXPAIRSEQ_USE_HASHTAB
565                 ++i;
566         }
567         
568         v ^= overall_coeff.gethash();
569         v &= 0x7FFFFFFFU;
570         
571         // store calculated hash value only if object is already evaluated
572         if (flags &status_flags::evaluated) {
573                 setflag(status_flags::hash_calculated);
574                 hashvalue = v;
575         }
576         
577         return v;
578 }
579
580 ex expairseq::expand(unsigned options) const
581 {
582         epvector *vp = expandchildren(options);
583         if (vp == NULL) {
584                 // The terms have not changed, so it is safe to declare this expanded
585                 return (options == 0) ? setflag(status_flags::expanded) : *this;
586         } else
587                 return thisexpairseq(vp, overall_coeff);
588 }
589
590 //////////
591 // new virtual functions which can be overridden by derived classes
592 //////////
593
594 // protected
595
596 /** Create an object of this type.
597  *  This method works similar to a constructor.  It is useful because expairseq
598  *  has (at least) two possible different semantics but we want to inherit
599  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
600  *  has to create a new one of the same semantics, which cannot be done by a
601  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
602  *  order for this trick to work a derived class must of course override this
603  *  definition. */
604 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
605 {
606         return expairseq(v,oc);
607 }
608
609 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
610 {
611         return expairseq(vp,oc);
612 }
613
614 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
615 {
616         c.s << "[[";
617         p.rest.bp->print(c, precedence());
618         c.s << ",";
619         p.coeff.bp->print(c, precedence());
620         c.s << "]]";
621 }
622
623 void expairseq::printseq(const print_context & c, char delim,
624                          unsigned this_precedence,
625                          unsigned upper_precedence) const
626 {
627         if (this_precedence <= upper_precedence)
628                 c.s << "(";
629         epvector::const_iterator it, it_last = seq.end() - 1;
630         for (it=seq.begin(); it!=it_last; ++it) {
631                 printpair(c, *it, this_precedence);
632                 c.s << delim;
633         }
634         printpair(c, *it, this_precedence);
635         if (!overall_coeff.is_equal(default_overall_coeff())) {
636                 c.s << delim;
637                 overall_coeff.print(c, this_precedence);
638         }
639         
640         if (this_precedence <= upper_precedence)
641                 c.s << ")";
642 }
643
644
645 /** Form an expair from an ex, using the corresponding semantics.
646  *  @see expairseq::recombine_pair_to_ex() */
647 expair expairseq::split_ex_to_pair(const ex &e) const
648 {
649         return expair(e,_ex1());
650 }
651
652
653 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
654                                                 const ex &c) const
655 {
656         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
657         
658         return expair(e,c);
659 }
660
661
662 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
663                                                   const ex &c) const
664 {
665         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
666         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
667         
668         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
669 }
670
671
672 /** Form an ex out of an expair, using the corresponding semantics.
673  *  @see expairseq::split_ex_to_pair() */
674 ex expairseq::recombine_pair_to_ex(const expair &p) const
675 {
676         return lst(p.rest,p.coeff);
677 }
678
679 bool expairseq::expair_needs_further_processing(epp it)
680 {
681 #if EXPAIRSEQ_USE_HASHTAB
682         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
683 #endif // EXPAIRSEQ_USE_HASHTAB
684         return false;
685 }
686
687 ex expairseq::default_overall_coeff(void) const
688 {
689         return _ex0();
690 }
691
692 void expairseq::combine_overall_coeff(const ex &c)
693 {
694         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
695         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
696         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
697 }
698
699 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
700 {
701         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
702         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
703         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
704         overall_coeff = ex_to<numeric>(overall_coeff).
705                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
706 }
707
708 bool expairseq::can_make_flat(const expair &p) const
709 {
710         return true;
711 }
712
713
714 //////////
715 // non-virtual functions in this class
716 //////////
717
718 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
719 {
720         exvector v;
721         v.reserve(2);
722         v.push_back(lh);
723         v.push_back(rh);
724         construct_from_exvector(v);
725 #if EXPAIRSEQ_USE_HASHTAB
726         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
727         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
728 #endif // EXPAIRSEQ_USE_HASHTAB
729 }
730
731 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
732 {
733         if (lh.bp->tinfo()==tinfo()) {
734                 if (rh.bp->tinfo()==tinfo()) {
735 #if EXPAIRSEQ_USE_HASHTAB
736                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
737                                              ex_to<expairseq>(rh).seq.size();
738                         if (calc_hashtabsize(totalsize)!=0) {
739                                 construct_from_2_ex_via_exvector(lh,rh);
740                         } else {
741 #endif // EXPAIRSEQ_USE_HASHTAB
742                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
743                                                            ex_to<expairseq>(rh));
744 #if EXPAIRSEQ_USE_HASHTAB
745                         }
746 #endif // EXPAIRSEQ_USE_HASHTAB
747                         return;
748                 } else {
749 #if EXPAIRSEQ_USE_HASHTAB
750                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
751                         if (calc_hashtabsize(totalsize)!=0) {
752                                 construct_from_2_ex_via_exvector(lh, rh);
753                         } else {
754 #endif // EXPAIRSEQ_USE_HASHTAB
755                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
756 #if EXPAIRSEQ_USE_HASHTAB
757                         }
758 #endif // EXPAIRSEQ_USE_HASHTAB
759                         return;
760                 }
761         } else if (rh.bp->tinfo()==tinfo()) {
762 #if EXPAIRSEQ_USE_HASHTAB
763                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
764                 if (calc_hashtabsize(totalsize)!=0) {
765                         construct_from_2_ex_via_exvector(lh,rh);
766                 } else {
767 #endif // EXPAIRSEQ_USE_HASHTAB
768                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
769 #if EXPAIRSEQ_USE_HASHTAB
770                 }
771 #endif // EXPAIRSEQ_USE_HASHTAB
772                 return;
773         }
774         
775 #if EXPAIRSEQ_USE_HASHTAB
776         if (calc_hashtabsize(2)!=0) {
777                 construct_from_2_ex_via_exvector(lh,rh);
778                 return;
779         }
780         hashtabsize = 0;
781 #endif // EXPAIRSEQ_USE_HASHTAB
782         
783         if (is_ex_exactly_of_type(lh,numeric)) {
784                 if (is_ex_exactly_of_type(rh,numeric)) {
785                         combine_overall_coeff(lh);
786                         combine_overall_coeff(rh);
787                 } else {
788                         combine_overall_coeff(lh);
789                         seq.push_back(split_ex_to_pair(rh));
790                 }
791         } else {
792                 if (is_ex_exactly_of_type(rh,numeric)) {
793                         combine_overall_coeff(rh);
794                         seq.push_back(split_ex_to_pair(lh));
795                 } else {
796                         expair p1 = split_ex_to_pair(lh);
797                         expair p2 = split_ex_to_pair(rh);
798                         
799                         int cmpval = p1.rest.compare(p2.rest);
800                         if (cmpval==0) {
801                                 p1.coeff=ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
802                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
803                                         // no further processing is necessary, since this
804                                         // one element will usually be recombined in eval()
805                                         seq.push_back(p1);
806                                 }
807                         } else {
808                                 seq.reserve(2);
809                                 if (cmpval<0) {
810                                         seq.push_back(p1);
811                                         seq.push_back(p2);
812                                 } else {
813                                         seq.push_back(p2);
814                                         seq.push_back(p1);
815                                 }
816                         }
817                 }
818         }
819 }
820
821 void expairseq::construct_from_2_expairseq(const expairseq &s1,
822                                                                                    const expairseq &s2)
823 {
824         combine_overall_coeff(s1.overall_coeff);
825         combine_overall_coeff(s2.overall_coeff);
826
827         epvector::const_iterator first1 = s1.seq.begin();
828         epvector::const_iterator last1 = s1.seq.end();
829         epvector::const_iterator first2 = s2.seq.begin();
830         epvector::const_iterator last2 = s2.seq.end();
831
832         seq.reserve(s1.seq.size()+s2.seq.size());
833
834         bool needs_further_processing=false;
835         
836         while (first1!=last1 && first2!=last2) {
837                 int cmpval = (*first1).rest.compare((*first2).rest);
838                 if (cmpval==0) {
839                         // combine terms
840                         const numeric &newcoeff = ex_to<numeric>((*first1).coeff).
841                                                    add(ex_to<numeric>((*first2).coeff));
842                         if (!newcoeff.is_zero()) {
843                                 seq.push_back(expair((*first1).rest,newcoeff));
844                                 if (expair_needs_further_processing(seq.end()-1)) {
845                                         needs_further_processing = true;
846                                 }
847                         }
848                         ++first1;
849                         ++first2;
850                 } else if (cmpval<0) {
851                         seq.push_back(*first1);
852                         ++first1;
853                 } else {
854                         seq.push_back(*first2);
855                         ++first2;
856                 }
857         }
858         
859         while (first1!=last1) {
860                 seq.push_back(*first1);
861                 ++first1;
862         }
863         while (first2!=last2) {
864                 seq.push_back(*first2);
865                 ++first2;
866         }
867         
868         if (needs_further_processing) {
869                 epvector v = seq;
870                 seq.clear();
871                 construct_from_epvector(v);
872         }
873 }
874
875 void expairseq::construct_from_expairseq_ex(const expairseq &s,
876                                                                                         const ex &e)
877 {
878         combine_overall_coeff(s.overall_coeff);
879         if (is_ex_exactly_of_type(e,numeric)) {
880                 combine_overall_coeff(e);
881                 seq = s.seq;
882                 return;
883         }
884         
885         epvector::const_iterator first = s.seq.begin();
886         epvector::const_iterator last = s.seq.end();
887         expair p = split_ex_to_pair(e);
888         
889         seq.reserve(s.seq.size()+1);
890         bool p_pushed = false;
891         
892         bool needs_further_processing=false;
893         
894         // merge p into s.seq
895         while (first!=last) {
896                 int cmpval = (*first).rest.compare(p.rest);
897                 if (cmpval==0) {
898                         // combine terms
899                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
900                                                    add(ex_to<numeric>(p.coeff));
901                         if (!newcoeff.is_zero()) {
902                                 seq.push_back(expair(first->rest,newcoeff));
903                                 if (expair_needs_further_processing(seq.end()-1))
904                                         needs_further_processing = true;
905                         }
906                         ++first;
907                         p_pushed = true;
908                         break;
909                 } else if (cmpval<0) {
910                         seq.push_back(*first);
911                         ++first;
912                 } else {
913                         seq.push_back(p);
914                         p_pushed = true;
915                         break;
916                 }
917         }
918         
919         if (p_pushed) {
920                 // while loop exited because p was pushed, now push rest of s.seq
921                 while (first!=last) {
922                         seq.push_back(*first);
923                         ++first;
924                 }
925         } else {
926                 // while loop exited because s.seq was pushed, now push p
927                 seq.push_back(p);
928         }
929
930         if (needs_further_processing) {
931                 epvector v = seq;
932                 seq.clear();
933                 construct_from_epvector(v);
934         }
935 }
936
937 void expairseq::construct_from_exvector(const exvector &v)
938 {
939         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
940         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
941         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
942         //                  (same for (+,*) -> (*,^)
943
944         make_flat(v);
945 #if EXPAIRSEQ_USE_HASHTAB
946         combine_same_terms();
947 #else
948         canonicalize();
949         combine_same_terms_sorted_seq();
950 #endif // EXPAIRSEQ_USE_HASHTAB
951 }
952
953 void expairseq::construct_from_epvector(const epvector &v)
954 {
955         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
956         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
957         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
958         //                  (same for (+,*) -> (*,^)
959
960         make_flat(v);
961 #if EXPAIRSEQ_USE_HASHTAB
962         combine_same_terms();
963 #else
964         canonicalize();
965         combine_same_terms_sorted_seq();
966 #endif // EXPAIRSEQ_USE_HASHTAB
967 }
968
969 /** Combine this expairseq with argument exvector.
970  *  It cares for associativity as well as for special handling of numerics. */
971 void expairseq::make_flat(const exvector &v)
972 {
973         exvector::const_iterator cit;
974         
975         // count number of operands which are of same expairseq derived type
976         // and their cumulative number of operands
977         int nexpairseqs = 0;
978         int noperands = 0;
979         
980         cit = v.begin();
981         while (cit!=v.end()) {
982                 if (cit->bp->tinfo()==this->tinfo()) {
983                         ++nexpairseqs;
984                         noperands += ex_to<expairseq>(*cit).seq.size();
985                 }
986                 ++cit;
987         }
988         
989         // reserve seq and coeffseq which will hold all operands
990         seq.reserve(v.size()+noperands-nexpairseqs);
991         
992         // copy elements and split off numerical part
993         cit = v.begin();
994         while (cit!=v.end()) {
995                 if (cit->bp->tinfo()==this->tinfo()) {
996                         const expairseq &subseqref = ex_to<expairseq>(*cit);
997                         combine_overall_coeff(subseqref.overall_coeff);
998                         epvector::const_iterator cit_s = subseqref.seq.begin();
999                         while (cit_s!=subseqref.seq.end()) {
1000                                 seq.push_back(*cit_s);
1001                                 ++cit_s;
1002                         }
1003                 } else {
1004                         if (is_ex_exactly_of_type(*cit,numeric))
1005                                 combine_overall_coeff(*cit);
1006                         else
1007                                 seq.push_back(split_ex_to_pair(*cit));
1008                 }
1009                 ++cit;
1010         }
1011 }
1012
1013 /** Combine this expairseq with argument epvector.
1014  *  It cares for associativity as well as for special handling of numerics. */
1015 void expairseq::make_flat(const epvector &v)
1016 {
1017         epvector::const_iterator cit;
1018         
1019         // count number of operands which are of same expairseq derived type
1020         // and their cumulative number of operands
1021         int nexpairseqs = 0;
1022         int noperands = 0;
1023         
1024         cit = v.begin();
1025         while (cit!=v.end()) {
1026                 if (cit->rest.bp->tinfo()==this->tinfo()) {
1027                         ++nexpairseqs;
1028                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1029                 }
1030                 ++cit;
1031         }
1032         
1033         // reserve seq and coeffseq which will hold all operands
1034         seq.reserve(v.size()+noperands-nexpairseqs);
1035         
1036         // copy elements and split off numerical part
1037         cit = v.begin();
1038         while (cit!=v.end()) {
1039                 if (cit->rest.bp->tinfo()==this->tinfo() &&
1040                     this->can_make_flat(*cit)) {
1041                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1042                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1043                                                             ex_to<numeric>(cit->coeff));
1044                         epvector::const_iterator cit_s = subseqref.seq.begin();
1045                         while (cit_s!=subseqref.seq.end()) {
1046                                 seq.push_back(expair(cit_s->rest,
1047                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1048                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1049                                 //                                              (*cit).coeff));
1050                                 ++cit_s;
1051                         }
1052                 } else {
1053                         if (cit->is_canonical_numeric())
1054                                 combine_overall_coeff(cit->rest);
1055                         else
1056                                 seq.push_back(*cit);
1057                 }
1058                 ++cit;
1059         }
1060 }
1061
1062 /** Brings this expairseq into a sorted (canonical) form. */
1063 void expairseq::canonicalize(void)
1064 {
1065         sort(seq.begin(), seq.end(), expair_is_less());
1066 }
1067
1068
1069 /** Compact a presorted expairseq by combining all matching expairs to one
1070  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1071  *  instance. */
1072 void expairseq::combine_same_terms_sorted_seq(void)
1073 {
1074         bool needs_further_processing = false;
1075         
1076         if (seq.size()>1) {
1077                 epvector::iterator itin1 = seq.begin();
1078                 epvector::iterator itin2 = itin1+1;
1079                 epvector::iterator itout = itin1;
1080                 epvector::iterator last = seq.end();
1081                 // must_copy will be set to true the first time some combination is 
1082                 // possible from then on the sequence has changed and must be compacted
1083                 bool must_copy = false;
1084                 while (itin2!=last) {
1085                         if ((*itin1).rest.compare(itin2->rest)==0) {
1086                                 (*itin1).coeff = ex_to<numeric>(itin1->coeff).
1087                                                  add_dyn(ex_to<numeric>(itin2->coeff));
1088                                 if (expair_needs_further_processing(itin1))
1089                                         needs_further_processing = true;
1090                                 must_copy = true;
1091                         } else {
1092                                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1093                                         if (must_copy)
1094                                                 *itout = *itin1;
1095                                         ++itout;
1096                                 }
1097                                 itin1 = itin2;
1098                         }
1099                         ++itin2;
1100                 }
1101                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1102                         if (must_copy)
1103                                 *itout = *itin1;
1104                         ++itout;
1105                 }
1106                 if (itout!=last)
1107                         seq.erase(itout,last);
1108         }
1109         
1110         if (needs_further_processing) {
1111                 epvector v = seq;
1112                 seq.clear();
1113                 construct_from_epvector(v);
1114         }
1115 }
1116
1117 #if EXPAIRSEQ_USE_HASHTAB
1118
1119 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1120 {
1121         unsigned size;
1122         unsigned nearest_power_of_2 = 1 << log2(sz);
1123         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1124         //  size = nearest_power_of_2*hashtabfactor;
1125         size = nearest_power_of_2/hashtabfactor;
1126         if (size<minhashtabsize)
1127                 return 0;
1128         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1129         // hashtabsize must be a power of 2
1130         GINAC_ASSERT((1U << log2(size))==size);
1131         return size;
1132 }
1133
1134 unsigned expairseq::calc_hashindex(const ex &e) const
1135 {
1136         // calculate hashindex
1137         unsigned hash = e.gethash();
1138         unsigned hashindex;
1139         if (is_a_numeric_hash(hash)) {
1140                 hashindex = hashmask;
1141         } else {
1142                 hashindex = hash &hashmask;
1143                 // last hashtab entry is reserved for numerics
1144                 if (hashindex==hashmask) hashindex = 0;
1145         }
1146         GINAC_ASSERT(hashindex>=0);
1147         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1148         return hashindex;
1149 }
1150
1151 void expairseq::shrink_hashtab(void)
1152 {
1153         unsigned new_hashtabsize;
1154         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1155                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1156                 if (new_hashtabsize==0) {
1157                         hashtab.clear();
1158                         hashtabsize = 0;
1159                         canonicalize();
1160                         return;
1161                 }
1162                 
1163                 // shrink by a factor of 2
1164                 unsigned half_hashtabsize = hashtabsize/2;
1165                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1166                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1167                 // special treatment for numeric hashes
1168                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1169                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1170                 hashtab.resize(half_hashtabsize);
1171                 hashtabsize = half_hashtabsize;
1172                 hashmask = hashtabsize-1;
1173         }
1174 }
1175
1176 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1177 {
1178         if (hashtabsize==0)
1179                 return; // nothing to do
1180         
1181         // calculate hashindex of element to be deleted
1182         unsigned hashindex = calc_hashindex((*element).rest);
1183
1184         // find it in hashtab and remove it
1185         epplist &eppl = hashtab[hashindex];
1186         epplist::iterator epplit = eppl.begin();
1187         bool erased = false;
1188         while (epplit!=eppl.end()) {
1189                 if (*epplit == element) {
1190                         eppl.erase(epplit);
1191                         erased = true;
1192                         break;
1193                 }
1194                 ++epplit;
1195         }
1196         if (!erased) {
1197                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1198                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1199
1200                 unsigned hashindex = calc_hashindex(element->rest);
1201                 epplist &eppl = hashtab[hashindex];
1202                 epplist::iterator epplit = eppl.begin();
1203                 bool erased = false;
1204                 while (epplit!=eppl.end()) {
1205                         if (*epplit == element) {
1206                                 eppl.erase(epplit);
1207                                 erased = true;
1208                                 break;
1209                         }
1210                         ++epplit;
1211                 }
1212                 GINAC_ASSERT(erased);
1213         }
1214         GINAC_ASSERT(erased);
1215 }
1216
1217 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1218                                    epvector::iterator newpos)
1219 {
1220         GINAC_ASSERT(hashtabsize!=0);
1221         
1222         // calculate hashindex of element which was moved
1223         unsigned hashindex=calc_hashindex((*newpos).rest);
1224
1225         // find it in hashtab and modify it
1226         epplist &eppl = hashtab[hashindex];
1227         epplist::iterator epplit = eppl.begin();
1228         while (epplit!=eppl.end()) {
1229                 if (*epplit == oldpos) {
1230                         *epplit = newpos;
1231                         break;
1232                 }
1233                 ++epplit;
1234         }
1235         GINAC_ASSERT(epplit!=eppl.end());
1236 }
1237
1238 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1239 {
1240         epplist::const_iterator current = eppl.begin();
1241         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1242                 ++current;
1243         }
1244         eppl.insert(current,elem);
1245 }    
1246
1247 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1248                                           epvector::iterator &last_non_zero,
1249                                           std::vector<bool> &touched,
1250                                           unsigned &number_of_zeroes)
1251 {
1252         epp current = seq.begin();
1253
1254         while (current!=first_numeric) {
1255                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1256                         --first_numeric;
1257                         iter_swap(current,first_numeric);
1258                 } else {
1259                         // calculate hashindex
1260                         unsigned currenthashindex = calc_hashindex(current->rest);
1261
1262                         // test if there is already a matching expair in the hashtab-list
1263                         epplist &eppl=hashtab[currenthashindex];
1264                         epplist::iterator epplit = eppl.begin();
1265                         while (epplit!=eppl.end()) {
1266                                 if (current->rest.is_equal((*epplit)->rest))
1267                                         break;
1268                                 ++epplit;
1269                         }
1270                         if (epplit==eppl.end()) {
1271                                 // no matching expair found, append this to end of list
1272                                 sorted_insert(eppl,current);
1273                                 ++current;
1274                         } else {
1275                                 // epplit points to a matching expair, combine it with current
1276                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1277                                                    add_dyn(ex_to<numeric>(current->coeff));
1278                                 
1279                                 // move obsolete current expair to end by swapping with last_non_zero element
1280                                 // if this was a numeric, it is swapped with the expair before first_numeric 
1281                                 iter_swap(current,last_non_zero);
1282                                 --first_numeric;
1283                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1284                                 --last_non_zero;
1285                                 ++number_of_zeroes;
1286                                 // test if combined term has coeff 0 and can be removed is done later
1287                                 touched[(*epplit)-seq.begin()] = true;
1288                         }
1289                 }
1290         }
1291 }
1292
1293 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1294                                    epvector::iterator &last_non_zero,
1295                                    std::vector<bool> &touched,
1296                                    unsigned &number_of_zeroes)
1297 {
1298         // move terms with coeff 0 to end and remove them from hashtab
1299         // check only those elements which have been touched
1300         epp current = seq.begin();
1301         unsigned i = 0;
1302         while (current!=first_numeric) {
1303                 if (!touched[i]) {
1304                         ++current;
1305                         ++i;
1306                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1307                         ++current;
1308                         ++i;
1309                 } else {
1310                         remove_hashtab_entry(current);
1311                         
1312                         // move element to the end, unless it is already at the end
1313                         if (current!=last_non_zero) {
1314                                 iter_swap(current,last_non_zero);
1315                                 --first_numeric;
1316                                 bool numeric_swapped = first_numeric!=last_non_zero;
1317                                 if (numeric_swapped)
1318                                         iter_swap(first_numeric,current);
1319                                 epvector::iterator changed_entry;
1320
1321                                 if (numeric_swapped)
1322                                         changed_entry = first_numeric;
1323                                 else
1324                                         changed_entry = last_non_zero;
1325                                 
1326                                 --last_non_zero;
1327                                 ++number_of_zeroes;
1328
1329                                 if (first_numeric!=current) {
1330
1331                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1332                                         move_hashtab_entry(changed_entry,current);
1333                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1334                                 }
1335                         } else {
1336                                 --first_numeric;
1337                                 --last_non_zero;
1338                                 ++number_of_zeroes;
1339                         }
1340                 }
1341         }
1342         GINAC_ASSERT(i==current-seq.begin());
1343 }
1344
1345 /** True if one of the coeffs vanishes, otherwise false.
1346  *  This would be an invariant violation, so this should only be used for
1347  *  debugging purposes. */
1348 bool expairseq::has_coeff_0(void) const
1349 {
1350         epvector::const_iterator i = seq.begin(), end = seq.end();
1351         while (i != end) {
1352                 if (i->coeff.is_zero())
1353                         return true;
1354                 ++i;
1355         }
1356         return false;
1357 }
1358
1359 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1360                                                                                 epvector::const_iterator last_non_zero)
1361 {
1362         if (first_numeric == seq.end()) return; // no numerics
1363         
1364         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1365         while (current != last) {
1366                 sorted_insert(hashtab[hashmask], current);
1367                 ++current;
1368         }
1369 }
1370
1371 void expairseq::combine_same_terms(void)
1372 {
1373         // combine same terms, drop term with coeff 0, move numerics to end
1374         
1375         // calculate size of hashtab
1376         hashtabsize = calc_hashtabsize(seq.size());
1377         
1378         // hashtabsize is a power of 2
1379         hashmask = hashtabsize-1;
1380         
1381         // allocate hashtab
1382         hashtab.clear();
1383         hashtab.resize(hashtabsize);
1384         
1385         if (hashtabsize==0) {
1386                 canonicalize();
1387                 combine_same_terms_sorted_seq();
1388                 GINAC_ASSERT(!has_coeff_0());
1389                 return;
1390         }
1391         
1392         // iterate through seq, move numerics to end,
1393         // fill hashtab and combine same terms
1394         epvector::iterator first_numeric = seq.end();
1395         epvector::iterator last_non_zero = seq.end()-1;
1396         
1397         unsigned num = seq.size();
1398         std::vector<bool> touched(num);
1399         
1400         unsigned number_of_zeroes = 0;
1401         
1402         GINAC_ASSERT(!has_coeff_0());
1403         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1404         
1405         // there should not be any terms with coeff 0 from the beginning,
1406         // so it should be safe to skip this step
1407         if (number_of_zeroes!=0) {
1408                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1409         }
1410         
1411         add_numerics_to_hashtab(first_numeric,last_non_zero);
1412         
1413         // pop zero elements
1414         for (unsigned i=0; i<number_of_zeroes; ++i) {
1415                 seq.pop_back();
1416         }
1417         
1418         // shrink hashtabsize to calculated value
1419         GINAC_ASSERT(!has_coeff_0());
1420         
1421         shrink_hashtab();
1422         
1423         GINAC_ASSERT(!has_coeff_0());
1424 }
1425
1426 #endif // EXPAIRSEQ_USE_HASHTAB
1427
1428 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1429  *  debugging or in assertions since being sorted is an invariance. */
1430 bool expairseq::is_canonical() const
1431 {
1432         if (seq.size() <= 1)
1433                 return 1;
1434         
1435 #if EXPAIRSEQ_USE_HASHTAB
1436         if (hashtabsize > 0) return 1; // not canoncalized
1437 #endif // EXPAIRSEQ_USE_HASHTAB
1438         
1439         epvector::const_iterator it = seq.begin(), itend = seq.end();
1440         epvector::const_iterator it_last = it;
1441         for (++it; it!=itend; it_last=it, ++it) {
1442                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1443                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1444                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1445                                 // double test makes it easier to set a breakpoint...
1446                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1447                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1448                                         printpair(std::clog, *it_last, 0);
1449                                         std::clog << ">";
1450                                         printpair(std::clog, *it, 0);
1451                                         std::clog << "\n";
1452                                         std::clog << "pair1:" << std::endl;
1453                                         it_last->rest.print(print_tree(std::clog));
1454                                         it_last->coeff.print(print_tree(std::clog));
1455                                         std::clog << "pair2:" << std::endl;
1456                                         it->rest.print(print_tree(std::clog));
1457                                         it->coeff.print(print_tree(std::clog));
1458                                         return 0;
1459                                 }
1460                         }
1461                 }
1462         }
1463         return 1;
1464 }
1465
1466
1467 /** Member-wise expand the expairs in this sequence.
1468  *
1469  *  @see expairseq::expand()
1470  *  @return pointer to epvector containing expanded pairs or zero pointer,
1471  *  if no members were changed. */
1472 epvector * expairseq::expandchildren(unsigned options) const
1473 {
1474         epvector::const_iterator last = seq.end();
1475         epvector::const_iterator cit = seq.begin();
1476         while (cit!=last) {
1477                 const ex &expanded_ex = cit->rest.expand(options);
1478                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1479                         
1480                         // something changed, copy seq, eval and return it
1481                         epvector *s = new epvector;
1482                         s->reserve(seq.size());
1483                         
1484                         // copy parts of seq which are known not to have changed
1485                         epvector::const_iterator cit2 = seq.begin();
1486                         while (cit2!=cit) {
1487                                 s->push_back(*cit2);
1488                                 ++cit2;
1489                         }
1490                         // copy first changed element
1491                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1492                                                                    cit2->coeff));
1493                         ++cit2;
1494                         // copy rest
1495                         while (cit2!=last) {
1496                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1497                                                                            cit2->coeff));
1498                                 ++cit2;
1499                         }
1500                         return s;
1501                 }
1502                 ++cit;
1503         }
1504         
1505         return 0; // signalling nothing has changed
1506 }
1507
1508
1509 /** Member-wise evaluate the expairs in this sequence.
1510  *
1511  *  @see expairseq::eval()
1512  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1513  *  if no members were changed. */
1514 epvector * expairseq::evalchildren(int level) const
1515 {
1516         // returns a NULL pointer if nothing had to be evaluated
1517         // returns a pointer to a newly created epvector otherwise
1518         // (which has to be deleted somewhere else)
1519
1520         if (level==1)
1521                 return 0;
1522         
1523         if (level == -max_recursion_level)
1524                 throw(std::runtime_error("max recursion level reached"));
1525         
1526         --level;
1527         epvector::const_iterator last = seq.end();
1528         epvector::const_iterator cit = seq.begin();
1529         while (cit!=last) {
1530                 const ex &evaled_ex = cit->rest.eval(level);
1531                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1532                         
1533                         // something changed, copy seq, eval and return it
1534                         epvector *s = new epvector;
1535                         s->reserve(seq.size());
1536                         
1537                         // copy parts of seq which are known not to have changed
1538                         epvector::const_iterator cit2=seq.begin();
1539                         while (cit2!=cit) {
1540                                 s->push_back(*cit2);
1541                                 ++cit2;
1542                         }
1543                         // copy first changed element
1544                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1545                                                                    cit2->coeff));
1546                         ++cit2;
1547                         // copy rest
1548                         while (cit2!=last) {
1549                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1550                                                                            cit2->coeff));
1551                                 ++cit2;
1552                         }
1553                         return s;
1554                 }
1555                 ++cit;
1556         }
1557         
1558         return 0; // signalling nothing has changed
1559 }
1560
1561
1562 /** Member-wise substitute in this sequence.
1563  *
1564  *  @see expairseq::subs()
1565  *  @return pointer to epvector containing pairs after application of subs,
1566  *    or NULL pointer if no members were changed. */
1567 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1568 {
1569         GINAC_ASSERT(ls.nops()==lr.nops());
1570
1571         // The substitution is "complex" when any of the objects to be substituted
1572         // is a product or power. In this case we have to recombine the pairs
1573         // because the numeric coefficients may be part of the search pattern.
1574         bool complex_subs = false;
1575         for (unsigned i=0; i<ls.nops(); ++i)
1576                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1577                         complex_subs = true;
1578                         break;
1579                 }
1580
1581         if (complex_subs) {
1582
1583                 // Substitute in the recombined pairs
1584                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1585                 while (cit != last) {
1586
1587                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1588                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1589                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1590
1591                                 // Something changed, copy seq, subs and return it
1592                                 epvector *s = new epvector;
1593                                 s->reserve(seq.size());
1594
1595                                 // Copy parts of seq which are known not to have changed
1596                                 s->insert(s->begin(), seq.begin(), cit);
1597
1598                                 // Copy first changed element
1599                                 s->push_back(split_ex_to_pair(subsed_ex));
1600                                 ++cit;
1601
1602                                 // Copy rest
1603                                 while (cit != last) {
1604                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1605                                         ++cit;
1606                                 }
1607                                 return s;
1608                         }
1609
1610                         ++cit;
1611                 }
1612
1613         } else {
1614
1615                 // Substitute only in the "rest" part of the pairs
1616                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1617                 while (cit != last) {
1618
1619                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1620                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1621                         
1622                                 // Something changed, copy seq, subs and return it
1623                                 epvector *s = new epvector;
1624                                 s->reserve(seq.size());
1625
1626                                 // Copy parts of seq which are known not to have changed
1627                                 s->insert(s->begin(), seq.begin(), cit);
1628                         
1629                                 // Copy first changed element
1630                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1631                                 ++cit;
1632
1633                                 // Copy rest
1634                                 while (cit != last) {
1635                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1636                                                                                    cit->coeff));
1637                                         ++cit;
1638                                 }
1639                                 return s;
1640                         }
1641
1642                         ++cit;
1643                 }
1644         }
1645         
1646         // Nothing has changed
1647         return NULL;
1648 }
1649
1650 //////////
1651 // static member variables
1652 //////////
1653
1654 #if EXPAIRSEQ_USE_HASHTAB
1655 unsigned expairseq::maxhashtabsize = 0x4000000U;
1656 unsigned expairseq::minhashtabsize = 0x1000U;
1657 unsigned expairseq::hashtabfactor = 1;
1658 #endif // EXPAIRSEQ_USE_HASHTAB
1659
1660 } // namespace GiNaC