ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2005 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 "mul.h"
  31 #include "power.h"
  32 #include "relational.h"
  33 #include "wildcard.h"
  34 #include "archive.h"
  35 #include "operators.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  46   print_func<print_context>(&expairseq::do_print).
  47   print_func<print_tree>(&expairseq::do_print_tree))
  48
  49
  50 //////////
  51 // helper classes
  52 //////////
  53
  54 class epp_is_less
  55 {
  56 public:
  57         bool operator()(const epp &lh, const epp &rh) const
  58         {
  59                 return (*lh).is_less(*rh);
  60         }
  61 };
  62
  63 //////////
  64 // default constructor
  65 //////////
  66
  67 // public
  68
  69 expairseq::expairseq() : inherited(TINFO_expairseq)
  70 #if EXPAIRSEQ_USE_HASHTAB
  71                                                    , hashtabsize(0)
  72 #endif // EXPAIRSEQ_USE_HASHTAB
  73 {}
  74
  75 // protected
  76
  77 #if 0
  78 /** For use by copy ctor and assignment operator. */
  79 void expairseq::copy(const expairseq &other)
  80 {
  81         seq = other.seq;
  82         overall_coeff = other.overall_coeff;
  83 #if EXPAIRSEQ_USE_HASHTAB
  84         // copy hashtab
  85         hashtabsize = other.hashtabsize;
  86         if (hashtabsize!=0) {
  87                 hashmask = other.hashmask;
  88                 hashtab.resize(hashtabsize);
  89                 epvector::const_iterator osb = other.seq.begin();
  90                 for (unsigned i=0; i<hashtabsize; ++i) {
  91                         hashtab[i].clear();
  92                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  93                              cit!=other.hashtab[i].end(); ++cit) {
  94                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  95                         }
  96                 }
  97         } else {
  98                 hashtab.clear();
  99         }
 100 #endif // EXPAIRSEQ_USE_HASHTAB
 101 }
 102 #endif
 103
 104 //////////
 105 // other constructors
 106 //////////
 107
 108 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 109 {
 110         construct_from_2_ex(lh,rh);
 111         GINAC_ASSERT(is_canonical());
 112 }
 113
 114 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_exvector(v);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const epvector &v, const ex &oc)
 121   : inherited(TINFO_expairseq), overall_coeff(oc)
 122 {
 123         GINAC_ASSERT(is_a<numeric>(oc));
 124         construct_from_epvector(v);
 125         GINAC_ASSERT(is_canonical());
 126 }
 127
 128 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
 129   : inherited(TINFO_expairseq), overall_coeff(oc)
 130 {
 131         GINAC_ASSERT(vp.get()!=0);
 132         GINAC_ASSERT(is_a<numeric>(oc));
 133         construct_from_epvector(*vp);
 134         GINAC_ASSERT(is_canonical());
 135 }
 136
 137 //////////
 138 // archiving
 139 //////////
 140
 141 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 142 #if EXPAIRSEQ_USE_HASHTAB
 143         , hashtabsize(0)
 144 #endif
 145 {
 146         for (unsigned int i=0; true; i++) {
 147                 ex rest;
 148                 ex coeff;
 149                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 150                         seq.push_back(expair(rest, coeff));
 151                 else
 152                         break;
 153         }
 154
 155         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 156
 157         canonicalize();
 158         GINAC_ASSERT(is_canonical());
 159 }
 160
 161 void expairseq::archive(archive_node &n) const
 162 {
 163         inherited::archive(n);
 164         epvector::const_iterator i = seq.begin(), iend = seq.end();
 165         while (i != iend) {
 166                 n.add_ex("rest", i->rest);
 167                 n.add_ex("coeff", i->coeff);
 168                 ++i;
 169         }
 170         n.add_ex("overall_coeff", overall_coeff);
 171 }
 172
 173 DEFAULT_UNARCHIVE(expairseq)
 174
 175 //////////
 176 // functions overriding virtual functions from base classes
 177 //////////
 178
 179 // public
 180
 181 void expairseq::do_print(const print_context & c, unsigned level) const
 182 {
 183         c.s << "[[";
 184         printseq(c, ',', precedence(), level);
 185         c.s << "]]";
 186 }
 187
 188 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 189 {
 190         c.s << std::string(level, ' ') << class_name() << " @" << this
 191             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 192             << ", nops=" << nops()
 193             << std::endl;
 194         size_t num = seq.size();
 195         for (size_t i=0; i<num; ++i) {
 196                 seq[i].rest.print(c, level + c.delta_indent);
 197                 seq[i].coeff.print(c, level + c.delta_indent);
 198                 if (i != num - 1)
 199                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 200         }
 201         if (!overall_coeff.is_equal(default_overall_coeff())) {
 202                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 203                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 204                 overall_coeff.print(c, level + c.delta_indent);
 205         }
 206         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 207 #if EXPAIRSEQ_USE_HASHTAB
 208         c.s << std::string(level + c.delta_indent,' ')
 209             << "hashtab size " << hashtabsize << std::endl;
 210         if (hashtabsize == 0) return;
 211 #define MAXCOUNT 5
 212         unsigned count[MAXCOUNT+1];
 213         for (int i=0; i<MAXCOUNT+1; ++i)
 214                 count[i] = 0;
 215         unsigned this_bin_fill;
 216         unsigned cum_fill_sq = 0;
 217         unsigned cum_fill = 0;
 218         for (unsigned i=0; i<hashtabsize; ++i) {
 219                 this_bin_fill = 0;
 220                 if (hashtab[i].size() > 0) {
 221                         c.s << std::string(level + c.delta_indent, ' ')
 222                             << "bin " << i << " with entries ";
 223                         for (epplist::const_iterator it=hashtab[i].begin();
 224                              it!=hashtab[i].end(); ++it) {
 225                                 c.s << *it-seq.begin() << " ";
 226                                 ++this_bin_fill;
 227                         }
 228                         c.s << std::endl;
 229                         cum_fill += this_bin_fill;
 230                         cum_fill_sq += this_bin_fill*this_bin_fill;
 231                 }
 232                 if (this_bin_fill<MAXCOUNT)
 233                         ++count[this_bin_fill];
 234                 else
 235                         ++count[MAXCOUNT];
 236         }
 237         unsigned fact = 1;
 238         double cum_prob = 0;
 239         double lambda = (1.0*seq.size()) / hashtabsize;
 240         for (int k=0; k<MAXCOUNT; ++k) {
 241                 if (k>0)
 242                         fact *= k;
 243                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 244                 cum_prob += prob;
 245                 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
 246                     << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 247                     << int(prob*1000)/10.0 << ")" << std::endl;
 248         }
 249         c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
 250             << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 251             << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 252
 253         c.s << std::string(level + c.delta_indent, ' ') << "variance: "
 254             << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 255             << std::endl;
 256         c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
 257             << (1.0*cum_fill)/hashtabsize
 258             << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 259 #endif // EXPAIRSEQ_USE_HASHTAB
 260 }
 261
 262 bool expairseq::info(unsigned inf) const
 263 {
 264         return inherited::info(inf);
 265 }
 266
 267 size_t expairseq::nops() const
 268 {
 269         if (overall_coeff.is_equal(default_overall_coeff()))
 270                 return seq.size();
 271         else
 272                 return seq.size()+1;
 273 }
 274
 275 ex expairseq::op(size_t i) const
 276 {
 277         if (i < seq.size())
 278                 return recombine_pair_to_ex(seq[i]);
 279         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 280         return overall_coeff;
 281 }
 282
 283 ex expairseq::map(map_function &f) const
 284 {
 285         std::auto_ptr<epvector> v(new epvector);
 286         v->reserve(seq.size()+1);
 287
 288         epvector::const_iterator cit = seq.begin(), last = seq.end();
 289         while (cit != last) {
 290                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 291                 ++cit;
 292         }
 293
 294         if (overall_coeff.is_equal(default_overall_coeff()))
 295                 return thisexpairseq(v, default_overall_coeff());
 296         else {
 297       ex newcoeff = f(overall_coeff);
 298       if(is_a<numeric>(newcoeff))
 299          return thisexpairseq(v, newcoeff);
 300       else {
 301          v->push_back(split_ex_to_pair(newcoeff));
 302          return thisexpairseq(v, default_overall_coeff());
 303       }
 304    }
 305 }
 306
 307 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 308 ex expairseq::eval(int level) const
 309 {
 310         if ((level==1) && (flags &status_flags::evaluated))
 311                 return *this;
 312
 313         std::auto_ptr<epvector> vp = evalchildren(level);
 314         if (vp.get() == 0)
 315                 return this->hold();
 316
 317         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 318 }
 319
 320 epvector* conjugateepvector(const epvector&epv)
 321 {
 322         epvector *newepv = 0;
 323         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 324                 if(newepv) {
 325                         newepv->push_back(i->conjugate());
 326                         continue;
 327                 }
 328                 expair x = i->conjugate();
 329                 if (x.is_equal(*i)) {
 330                         continue;
 331                 }
 332                 newepv = new epvector;
 333                 newepv->reserve(epv.size());
 334                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 335                         newepv->push_back(*j);
 336                 }
 337                 newepv->push_back(x);
 338         }
 339         return newepv;
 340 }
 341
 342 ex expairseq::conjugate() const
 343 {
 344         epvector* newepv = conjugateepvector(seq);
 345         ex x = overall_coeff.conjugate();
 346         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 347                 return *this;
 348         }
 349         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 350         if (newepv) {
 351                 delete newepv;
 352         }
 353         return result;
 354 }
 355
 356 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 357 {
 358         // This differs from basic::match() because we want "a+b+c+d" to
 359         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 360
 361         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 362
 363                 // Check whether global wildcard (one that matches the "rest of the
 364                 // expression", like "*" above) is present
 365                 bool has_global_wildcard = false;
 366                 ex global_wildcard;
 367                 for (size_t i=0; i<pattern.nops(); i++) {
 368                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 369                                 has_global_wildcard = true;
 370                                 global_wildcard = pattern.op(i);
 371                                 break;
 372                         }
 373                 }
 374
 375                 // Unfortunately, this is an O(N^2) operation because we can't
 376                 // sort the pattern in a useful way...
 377
 378                 // Chop into terms
 379                 exvector ops;
 380                 ops.reserve(nops());
 381                 for (size_t i=0; i<nops(); i++)
 382                         ops.push_back(op(i));
 383
 384                 // Now, for every term of the pattern, look for a matching term in
 385                 // the expression and remove the match
 386                 for (size_t i=0; i<pattern.nops(); i++) {
 387                         ex p = pattern.op(i);
 388                         if (has_global_wildcard && p.is_equal(global_wildcard))
 389                                 continue;
 390                         exvector::iterator it = ops.begin(), itend = ops.end();
 391                         while (it != itend) {
 392                                 lst::const_iterator last_el = repl_lst.end();
 393                                 --last_el;
 394                                 if (it->match(p, repl_lst)) {
 395                                         ops.erase(it);
 396                                         goto found;
 397                                 }
 398                                 while(true) {
 399                                         lst::const_iterator next_el = last_el;
 400                                         ++next_el;
 401                                         if(next_el == repl_lst.end())
 402                                                 break;
 403                                         else
 404                                                 repl_lst.remove_last();
 405                                 }
 406                                 ++it;
 407                         }
 408                         return false; // no match found
 409 found:          ;
 410                 }
 411
 412                 if (has_global_wildcard) {
 413
 414                         // Assign all the remaining terms to the global wildcard (unless
 415                         // it has already been matched before, in which case the matches
 416                         // must be equal)
 417                         size_t num = ops.size();
 418                         std::auto_ptr<epvector> vp(new epvector);
 419                         vp->reserve(num);
 420                         for (size_t i=0; i<num; i++)
 421                                 vp->push_back(split_ex_to_pair(ops[i]));
 422                         ex rest = thisexpairseq(vp, default_overall_coeff());
 423                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 424                                 if (it->op(0).is_equal(global_wildcard))
 425                                         return rest.is_equal(it->op(1));
 426                         }
 427                         repl_lst.append(global_wildcard == rest);
 428                         return true;
 429
 430                 } else {
 431
 432                         // No global wildcard, then the match fails if there are any
 433                         // unmatched terms left
 434                         return ops.empty();
 435                 }
 436         }
 437         return inherited::match(pattern, repl_lst);
 438 }
 439
 440 ex expairseq::subs(const exmap & m, unsigned options) const
 441 {
 442         std::auto_ptr<epvector> vp = subschildren(m, options);
 443         if (vp.get())
 444                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 445         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 446                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 447         else
 448                 return subs_one_level(m, options);
 449 }
 450
 451 // protected
 452
 453 int expairseq::compare_same_type(const basic &other) const
 454 {
 455         GINAC_ASSERT(is_a<expairseq>(other));
 456         const expairseq &o = static_cast<const expairseq &>(other);
 457
 458         int cmpval;
 459
 460         // compare number of elements
 461         if (seq.size() != o.seq.size())
 462                 return (seq.size()<o.seq.size()) ? -1 : 1;
 463
 464         // compare overall_coeff
 465         cmpval = overall_coeff.compare(o.overall_coeff);
 466         if (cmpval!=0)
 467                 return cmpval;
 468
 469 #if EXPAIRSEQ_USE_HASHTAB
 470         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 471         if (hashtabsize==0) {
 472 #endif // EXPAIRSEQ_USE_HASHTAB
 473                 epvector::const_iterator cit1 = seq.begin();
 474                 epvector::const_iterator cit2 = o.seq.begin();
 475                 epvector::const_iterator last1 = seq.end();
 476                 epvector::const_iterator last2 = o.seq.end();
 477
 478                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 479                         cmpval = (*cit1).compare(*cit2);
 480                         if (cmpval!=0) return cmpval;
 481                 }
 482
 483                 GINAC_ASSERT(cit1==last1);
 484                 GINAC_ASSERT(cit2==last2);
 485
 486                 return 0;
 487 #if EXPAIRSEQ_USE_HASHTAB
 488         }
 489
 490         // compare number of elements in each hashtab entry
 491         for (unsigned i=0; i<hashtabsize; ++i) {
 492                 unsigned cursize=hashtab[i].size();
 493                 if (cursize != o.hashtab[i].size())
 494                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 495         }
 496
 497         // compare individual (sorted) hashtab entries
 498         for (unsigned i=0; i<hashtabsize; ++i) {
 499                 unsigned sz = hashtab[i].size();
 500                 if (sz>0) {
 501                         const epplist &eppl1 = hashtab[i];
 502                         const epplist &eppl2 = o.hashtab[i];
 503                         epplist::const_iterator it1 = eppl1.begin();
 504                         epplist::const_iterator it2 = eppl2.begin();
 505                         while (it1!=eppl1.end()) {
 506                                 cmpval = (*(*it1)).compare(*(*it2));
 507                                 if (cmpval!=0)
 508                                         return cmpval;
 509                                 ++it1;
 510                                 ++it2;
 511                         }
 512                 }
 513         }
 514
 515         return 0; // equal
 516 #endif // EXPAIRSEQ_USE_HASHTAB
 517 }
 518
 519 bool expairseq::is_equal_same_type(const basic &other) const
 520 {
 521         const expairseq &o = static_cast<const expairseq &>(other);
 522
 523         // compare number of elements
 524         if (seq.size()!=o.seq.size())
 525                 return false;
 526
 527         // compare overall_coeff
 528         if (!overall_coeff.is_equal(o.overall_coeff))
 529                 return false;
 530
 531 #if EXPAIRSEQ_USE_HASHTAB
 532         // compare number of elements in each hashtab entry
 533         if (hashtabsize!=o.hashtabsize) {
 534                 std::cout << "this:" << std::endl;
 535                 print(print_tree(std::cout));
 536                 std::cout << "other:" << std::endl;
 537                 other.print(print_tree(std::cout));
 538         }
 539
 540         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 541
 542         if (hashtabsize==0) {
 543 #endif // EXPAIRSEQ_USE_HASHTAB
 544                 epvector::const_iterator cit1 = seq.begin();
 545                 epvector::const_iterator cit2 = o.seq.begin();
 546                 epvector::const_iterator last1 = seq.end();
 547
 548                 while (cit1!=last1) {
 549                         if (!(*cit1).is_equal(*cit2)) return false;
 550                         ++cit1;
 551                         ++cit2;
 552                 }
 553
 554                 return true;
 555 #if EXPAIRSEQ_USE_HASHTAB
 556         }
 557
 558         for (unsigned i=0; i<hashtabsize; ++i) {
 559                 if (hashtab[i].size() != o.hashtab[i].size())
 560                         return false;
 561         }
 562
 563         // compare individual sorted hashtab entries
 564         for (unsigned i=0; i<hashtabsize; ++i) {
 565                 unsigned sz = hashtab[i].size();
 566                 if (sz>0) {
 567                         const epplist &eppl1 = hashtab[i];
 568                         const epplist &eppl2 = o.hashtab[i];
 569                         epplist::const_iterator it1 = eppl1.begin();
 570                         epplist::const_iterator it2 = eppl2.begin();
 571                         while (it1!=eppl1.end()) {
 572                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 573                                 ++it1;
 574                                 ++it2;
 575                         }
 576                 }
 577         }
 578
 579         return true;
 580 #endif // EXPAIRSEQ_USE_HASHTAB
 581 }
 582
 583 unsigned expairseq::return_type() const
 584 {
 585         return return_types::noncommutative_composite;
 586 }
 587
 588 unsigned expairseq::calchash() const
 589 {
 590         unsigned v = golden_ratio_hash(this->tinfo());
 591         epvector::const_iterator i = seq.begin();
 592         const epvector::const_iterator end = seq.end();
 593         while (i != end) {
 594                 v ^= i->rest.gethash();
 595 #if !EXPAIRSEQ_USE_HASHTAB
 596                 // rotation spoils commutativity!
 597                 v = rotate_left(v);
 598                 v ^= i->coeff.gethash();
 599 #endif // !EXPAIRSEQ_USE_HASHTAB
 600                 ++i;
 601         }
 602
 603         v ^= overall_coeff.gethash();
 604
 605         // store calculated hash value only if object is already evaluated
 606         if (flags &status_flags::evaluated) {
 607                 setflag(status_flags::hash_calculated);
 608                 hashvalue = v;
 609         }
 610
 611         return v;
 612 }
 613
 614 ex expairseq::expand(unsigned options) const
 615 {
 616         std::auto_ptr<epvector> vp = expandchildren(options);
 617         if (vp.get())
 618                 return thisexpairseq(vp, overall_coeff);
 619         else {
 620                 // The terms have not changed, so it is safe to declare this expanded
 621                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 622         }
 623 }
 624
 625 //////////
 626 // new virtual functions which can be overridden by derived classes
 627 //////////
 628
 629 // protected
 630
 631 /** Create an object of this type.
 632  *  This method works similar to a constructor.  It is useful because expairseq
 633  *  has (at least) two possible different semantics but we want to inherit
 634  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 635  *  has to create a new one of the same semantics, which cannot be done by a
 636  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 637  *  order for this trick to work a derived class must of course override this
 638  *  definition. */
 639 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 640 {
 641         return expairseq(v, oc);
 642 }
 643
 644 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
 645 {
 646         return expairseq(vp, oc);
 647 }
 648
 649 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 650 {
 651         c.s << "[[";
 652         p.rest.print(c, precedence());
 653         c.s << ",";
 654         p.coeff.print(c, precedence());
 655         c.s << "]]";
 656 }
 657
 658 void expairseq::printseq(const print_context & c, char delim,
 659                          unsigned this_precedence,
 660                          unsigned upper_precedence) const
 661 {
 662         if (this_precedence <= upper_precedence)
 663                 c.s << "(";
 664         epvector::const_iterator it, it_last = seq.end() - 1;
 665         for (it=seq.begin(); it!=it_last; ++it) {
 666                 printpair(c, *it, this_precedence);
 667                 c.s << delim;
 668         }
 669         printpair(c, *it, this_precedence);
 670         if (!overall_coeff.is_equal(default_overall_coeff())) {
 671                 c.s << delim;
 672                 overall_coeff.print(c, this_precedence);
 673         }
 674
 675         if (this_precedence <= upper_precedence)
 676                 c.s << ")";
 677 }
 678
 679
 680 /** Form an expair from an ex, using the corresponding semantics.
 681  *  @see expairseq::recombine_pair_to_ex() */
 682 expair expairseq::split_ex_to_pair(const ex &e) const
 683 {
 684         return expair(e,_ex1);
 685 }
 686
 687
 688 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 689                                                 const ex &c) const
 690 {
 691         GINAC_ASSERT(is_exactly_a<numeric>(c));
 692
 693         return expair(e,c);
 694 }
 695
 696
 697 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 698                                                   const ex &c) const
 699 {
 700         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 701         GINAC_ASSERT(is_exactly_a<numeric>(c));
 702
 703         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 704 }
 705
 706
 707 /** Form an ex out of an expair, using the corresponding semantics.
 708  *  @see expairseq::split_ex_to_pair() */
 709 ex expairseq::recombine_pair_to_ex(const expair &p) const
 710 {
 711         return lst(p.rest,p.coeff);
 712 }
 713
 714 bool expairseq::expair_needs_further_processing(epp it)
 715 {
 716 #if EXPAIRSEQ_USE_HASHTAB
 717         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 718 #endif // EXPAIRSEQ_USE_HASHTAB
 719         return false;
 720 }
 721
 722 ex expairseq::default_overall_coeff() const
 723 {
 724         return _ex0;
 725 }
 726
 727 void expairseq::combine_overall_coeff(const ex &c)
 728 {
 729         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 730         GINAC_ASSERT(is_exactly_a<numeric>(c));
 731         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 732 }
 733
 734 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 735 {
 736         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 737         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 738         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 739         overall_coeff = ex_to<numeric>(overall_coeff).
 740                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 741 }
 742
 743 bool expairseq::can_make_flat(const expair &p) const
 744 {
 745         return true;
 746 }
 747
 748
 749 //////////
 750 // non-virtual functions in this class
 751 //////////
 752
 753 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 754 {
 755         exvector v;
 756         v.reserve(2);
 757         v.push_back(lh);
 758         v.push_back(rh);
 759         construct_from_exvector(v);
 760 #if EXPAIRSEQ_USE_HASHTAB
 761         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 762         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 763 #endif // EXPAIRSEQ_USE_HASHTAB
 764 }
 765
 766 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 767 {
 768         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 769                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 770 #if EXPAIRSEQ_USE_HASHTAB
 771                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 772                                              ex_to<expairseq>(rh).seq.size();
 773                         if (calc_hashtabsize(totalsize)!=0) {
 774                                 construct_from_2_ex_via_exvector(lh,rh);
 775                         } else {
 776 #endif // EXPAIRSEQ_USE_HASHTAB
 777                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 778                                                            ex_to<expairseq>(rh));
 779 #if EXPAIRSEQ_USE_HASHTAB
 780                         }
 781 #endif // EXPAIRSEQ_USE_HASHTAB
 782                         return;
 783                 } else {
 784 #if EXPAIRSEQ_USE_HASHTAB
 785                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 786                         if (calc_hashtabsize(totalsize)!=0) {
 787                                 construct_from_2_ex_via_exvector(lh, rh);
 788                         } else {
 789 #endif // EXPAIRSEQ_USE_HASHTAB
 790                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 791 #if EXPAIRSEQ_USE_HASHTAB
 792                         }
 793 #endif // EXPAIRSEQ_USE_HASHTAB
 794                         return;
 795                 }
 796         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 797 #if EXPAIRSEQ_USE_HASHTAB
 798                 unsigned totalsize=ex_to<expairseq>(rh).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>(rh),lh);
 804 #if EXPAIRSEQ_USE_HASHTAB
 805                 }
 806 #endif // EXPAIRSEQ_USE_HASHTAB
 807                 return;
 808         }
 809
 810 #if EXPAIRSEQ_USE_HASHTAB
 811         if (calc_hashtabsize(2)!=0) {
 812                 construct_from_2_ex_via_exvector(lh,rh);
 813                 return;
 814         }
 815         hashtabsize = 0;
 816 #endif // EXPAIRSEQ_USE_HASHTAB
 817
 818         if (is_exactly_a<numeric>(lh)) {
 819                 if (is_exactly_a<numeric>(rh)) {
 820                         combine_overall_coeff(lh);
 821                         combine_overall_coeff(rh);
 822                 } else {
 823                         combine_overall_coeff(lh);
 824                         seq.push_back(split_ex_to_pair(rh));
 825                 }
 826         } else {
 827                 if (is_exactly_a<numeric>(rh)) {
 828                         combine_overall_coeff(rh);
 829                         seq.push_back(split_ex_to_pair(lh));
 830                 } else {
 831                         expair p1 = split_ex_to_pair(lh);
 832                         expair p2 = split_ex_to_pair(rh);
 833
 834                         int cmpval = p1.rest.compare(p2.rest);
 835                         if (cmpval==0) {
 836                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 837                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 838                                         // no further processing is necessary, since this
 839                                         // one element will usually be recombined in eval()
 840                                         seq.push_back(p1);
 841                                 }
 842                         } else {
 843                                 seq.reserve(2);
 844                                 if (cmpval<0) {
 845                                         seq.push_back(p1);
 846                                         seq.push_back(p2);
 847                                 } else {
 848                                         seq.push_back(p2);
 849                                         seq.push_back(p1);
 850                                 }
 851                         }
 852                 }
 853         }
 854 }
 855
 856 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 857                                                                                    const expairseq &s2)
 858 {
 859         combine_overall_coeff(s1.overall_coeff);
 860         combine_overall_coeff(s2.overall_coeff);
 861
 862         epvector::const_iterator first1 = s1.seq.begin();
 863         epvector::const_iterator last1 = s1.seq.end();
 864         epvector::const_iterator first2 = s2.seq.begin();
 865         epvector::const_iterator last2 = s2.seq.end();
 866
 867         seq.reserve(s1.seq.size()+s2.seq.size());
 868
 869         bool needs_further_processing=false;
 870
 871         while (first1!=last1 && first2!=last2) {
 872                 int cmpval = (*first1).rest.compare((*first2).rest);
 873                 if (cmpval==0) {
 874                         // combine terms
 875                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 876                                                    add(ex_to<numeric>(first2->coeff));
 877                         if (!newcoeff.is_zero()) {
 878                                 seq.push_back(expair(first1->rest,newcoeff));
 879                                 if (expair_needs_further_processing(seq.end()-1)) {
 880                                         needs_further_processing = true;
 881                                 }
 882                         }
 883                         ++first1;
 884                         ++first2;
 885                 } else if (cmpval<0) {
 886                         seq.push_back(*first1);
 887                         ++first1;
 888                 } else {
 889                         seq.push_back(*first2);
 890                         ++first2;
 891                 }
 892         }
 893
 894         while (first1!=last1) {
 895                 seq.push_back(*first1);
 896                 ++first1;
 897         }
 898         while (first2!=last2) {
 899                 seq.push_back(*first2);
 900                 ++first2;
 901         }
 902
 903         if (needs_further_processing) {
 904                 epvector v = seq;
 905                 seq.clear();
 906                 construct_from_epvector(v);
 907         }
 908 }
 909
 910 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 911                                                                                         const ex &e)
 912 {
 913         combine_overall_coeff(s.overall_coeff);
 914         if (is_exactly_a<numeric>(e)) {
 915                 combine_overall_coeff(e);
 916                 seq = s.seq;
 917                 return;
 918         }
 919
 920         epvector::const_iterator first = s.seq.begin();
 921         epvector::const_iterator last = s.seq.end();
 922         expair p = split_ex_to_pair(e);
 923
 924         seq.reserve(s.seq.size()+1);
 925         bool p_pushed = false;
 926
 927         bool needs_further_processing=false;
 928
 929         // merge p into s.seq
 930         while (first!=last) {
 931                 int cmpval = (*first).rest.compare(p.rest);
 932                 if (cmpval==0) {
 933                         // combine terms
 934                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 935                                                    add(ex_to<numeric>(p.coeff));
 936                         if (!newcoeff.is_zero()) {
 937                                 seq.push_back(expair(first->rest,newcoeff));
 938                                 if (expair_needs_further_processing(seq.end()-1))
 939                                         needs_further_processing = true;
 940                         }
 941                         ++first;
 942                         p_pushed = true;
 943                         break;
 944                 } else if (cmpval<0) {
 945                         seq.push_back(*first);
 946                         ++first;
 947                 } else {
 948                         seq.push_back(p);
 949                         p_pushed = true;
 950                         break;
 951                 }
 952         }
 953
 954         if (p_pushed) {
 955                 // while loop exited because p was pushed, now push rest of s.seq
 956                 while (first!=last) {
 957                         seq.push_back(*first);
 958                         ++first;
 959                 }
 960         } else {
 961                 // while loop exited because s.seq was pushed, now push p
 962                 seq.push_back(p);
 963         }
 964
 965         if (needs_further_processing) {
 966                 epvector v = seq;
 967                 seq.clear();
 968                 construct_from_epvector(v);
 969         }
 970 }
 971
 972 void expairseq::construct_from_exvector(const exvector &v)
 973 {
 974         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 975         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 976         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 977         //                  (same for (+,*) -> (*,^)
 978
 979         make_flat(v);
 980 #if EXPAIRSEQ_USE_HASHTAB
 981         combine_same_terms();
 982 #else
 983         canonicalize();
 984         combine_same_terms_sorted_seq();
 985 #endif // EXPAIRSEQ_USE_HASHTAB
 986 }
 987
 988 void expairseq::construct_from_epvector(const epvector &v)
 989 {
 990         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 991         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 992         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 993         //                  (same for (+,*) -> (*,^)
 994
 995         make_flat(v);
 996 #if EXPAIRSEQ_USE_HASHTAB
 997         combine_same_terms();
 998 #else
 999         canonicalize();
1000         combine_same_terms_sorted_seq();
1001 #endif // EXPAIRSEQ_USE_HASHTAB
1002 }
1003
1004 /** Combine this expairseq with argument exvector.
1005  *  It cares for associativity as well as for special handling of numerics. */
1006 void expairseq::make_flat(const exvector &v)
1007 {
1008         exvector::const_iterator cit;
1009
1010         // count number of operands which are of same expairseq derived type
1011         // and their cumulative number of operands
1012         int nexpairseqs = 0;
1013         int noperands = 0;
1014
1015         cit = v.begin();
1016         while (cit!=v.end()) {
1017                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1018                         ++nexpairseqs;
1019                         noperands += ex_to<expairseq>(*cit).seq.size();
1020                 }
1021                 ++cit;
1022         }
1023
1024         // reserve seq and coeffseq which will hold all operands
1025         seq.reserve(v.size()+noperands-nexpairseqs);
1026
1027         // copy elements and split off numerical part
1028         cit = v.begin();
1029         while (cit!=v.end()) {
1030                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1031                         const expairseq &subseqref = ex_to<expairseq>(*cit);
1032                         combine_overall_coeff(subseqref.overall_coeff);
1033                         epvector::const_iterator cit_s = subseqref.seq.begin();
1034                         while (cit_s!=subseqref.seq.end()) {
1035                                 seq.push_back(*cit_s);
1036                                 ++cit_s;
1037                         }
1038                 } else {
1039                         if (is_exactly_a<numeric>(*cit))
1040                                 combine_overall_coeff(*cit);
1041                         else
1042                                 seq.push_back(split_ex_to_pair(*cit));
1043                 }
1044                 ++cit;
1045         }
1046 }
1047
1048 /** Combine this expairseq with argument epvector.
1049  *  It cares for associativity as well as for special handling of numerics. */
1050 void expairseq::make_flat(const epvector &v)
1051 {
1052         epvector::const_iterator cit;
1053
1054         // count number of operands which are of same expairseq derived type
1055         // and their cumulative number of operands
1056         int nexpairseqs = 0;
1057         int noperands = 0;
1058
1059         cit = v.begin();
1060         while (cit!=v.end()) {
1061                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1062                         ++nexpairseqs;
1063                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1064                 }
1065                 ++cit;
1066         }
1067
1068         // reserve seq and coeffseq which will hold all operands
1069         seq.reserve(v.size()+noperands-nexpairseqs);
1070
1071         // copy elements and split off numerical part
1072         cit = v.begin();
1073         while (cit!=v.end()) {
1074                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1075                     this->can_make_flat(*cit)) {
1076                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1077                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1078                                                             ex_to<numeric>(cit->coeff));
1079                         epvector::const_iterator cit_s = subseqref.seq.begin();
1080                         while (cit_s!=subseqref.seq.end()) {
1081                                 seq.push_back(expair(cit_s->rest,
1082                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1083                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1084                                 //                                              (*cit).coeff));
1085                                 ++cit_s;
1086                         }
1087                 } else {
1088                         if (cit->is_canonical_numeric())
1089                                 combine_overall_coeff(cit->rest);
1090                         else
1091                                 seq.push_back(*cit);
1092                 }
1093                 ++cit;
1094         }
1095 }
1096
1097 /** Brings this expairseq into a sorted (canonical) form. */
1098 void expairseq::canonicalize()
1099 {
1100         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1101 }
1102
1103
1104 /** Compact a presorted expairseq by combining all matching expairs to one
1105  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1106  *  instance. */
1107 void expairseq::combine_same_terms_sorted_seq()
1108 {
1109         if (seq.size()<2)
1110                 return;
1111
1112         bool needs_further_processing = false;
1113
1114         epvector::iterator itin1 = seq.begin();
1115         epvector::iterator itin2 = itin1+1;
1116         epvector::iterator itout = itin1;
1117         epvector::iterator last = seq.end();
1118         // must_copy will be set to true the first time some combination is
1119         // possible from then on the sequence has changed and must be compacted
1120         bool must_copy = false;
1121         while (itin2!=last) {
1122                 if (itin1->rest.compare(itin2->rest)==0) {
1123                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1124                                        add_dyn(ex_to<numeric>(itin2->coeff));
1125                         if (expair_needs_further_processing(itin1))
1126                                 needs_further_processing = true;
1127                         must_copy = true;
1128                 } else {
1129                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1130                                 if (must_copy)
1131                                         *itout = *itin1;
1132                                 ++itout;
1133                         }
1134                         itin1 = itin2;
1135                 }
1136                 ++itin2;
1137         }
1138         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1139                 if (must_copy)
1140                         *itout = *itin1;
1141                 ++itout;
1142         }
1143         if (itout!=last)
1144                 seq.erase(itout,last);
1145
1146         if (needs_further_processing) {
1147                 epvector v = seq;
1148                 seq.clear();
1149                 construct_from_epvector(v);
1150         }
1151 }
1152
1153 #if EXPAIRSEQ_USE_HASHTAB
1154
1155 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1156 {
1157         unsigned size;
1158         unsigned nearest_power_of_2 = 1 << log2(sz);
1159         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1160         //  size = nearest_power_of_2*hashtabfactor;
1161         size = nearest_power_of_2/hashtabfactor;
1162         if (size<minhashtabsize)
1163                 return 0;
1164
1165         // hashtabsize must be a power of 2
1166         GINAC_ASSERT((1U << log2(size))==size);
1167         return size;
1168 }
1169
1170 unsigned expairseq::calc_hashindex(const ex &e) const
1171 {
1172         // calculate hashindex
1173         unsigned hashindex;
1174         if (is_a<numeric>(e)) {
1175                 hashindex = hashmask;
1176         } else {
1177                 hashindex = e.gethash() & hashmask;
1178                 // last hashtab entry is reserved for numerics
1179                 if (hashindex==hashmask) hashindex = 0;
1180         }
1181         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1182         return hashindex;
1183 }
1184
1185 void expairseq::shrink_hashtab()
1186 {
1187         unsigned new_hashtabsize;
1188         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1189                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1190                 if (new_hashtabsize==0) {
1191                         hashtab.clear();
1192                         hashtabsize = 0;
1193                         canonicalize();
1194                         return;
1195                 }
1196
1197                 // shrink by a factor of 2
1198                 unsigned half_hashtabsize = hashtabsize/2;
1199                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1200                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1201                 // special treatment for numeric hashes
1202                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1203                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1204                 hashtab.resize(half_hashtabsize);
1205                 hashtabsize = half_hashtabsize;
1206                 hashmask = hashtabsize-1;
1207         }
1208 }
1209
1210 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1211 {
1212         if (hashtabsize==0)
1213                 return; // nothing to do
1214
1215         // calculate hashindex of element to be deleted
1216         unsigned hashindex = calc_hashindex((*element).rest);
1217
1218         // find it in hashtab and remove it
1219         epplist &eppl = hashtab[hashindex];
1220         epplist::iterator epplit = eppl.begin();
1221         bool erased = false;
1222         while (epplit!=eppl.end()) {
1223                 if (*epplit == element) {
1224                         eppl.erase(epplit);
1225                         erased = true;
1226                         break;
1227                 }
1228                 ++epplit;
1229         }
1230         if (!erased) {
1231                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1232                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1233
1234                 unsigned hashindex = calc_hashindex(element->rest);
1235                 epplist &eppl = hashtab[hashindex];
1236                 epplist::iterator epplit = eppl.begin();
1237                 bool erased = false;
1238                 while (epplit!=eppl.end()) {
1239                         if (*epplit == element) {
1240                                 eppl.erase(epplit);
1241                                 erased = true;
1242                                 break;
1243                         }
1244                         ++epplit;
1245                 }
1246                 GINAC_ASSERT(erased);
1247         }
1248         GINAC_ASSERT(erased);
1249 }
1250
1251 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1252                                    epvector::iterator newpos)
1253 {
1254         GINAC_ASSERT(hashtabsize!=0);
1255
1256         // calculate hashindex of element which was moved
1257         unsigned hashindex=calc_hashindex((*newpos).rest);
1258
1259         // find it in hashtab and modify it
1260         epplist &eppl = hashtab[hashindex];
1261         epplist::iterator epplit = eppl.begin();
1262         while (epplit!=eppl.end()) {
1263                 if (*epplit == oldpos) {
1264                         *epplit = newpos;
1265                         break;
1266                 }
1267                 ++epplit;
1268         }
1269         GINAC_ASSERT(epplit!=eppl.end());
1270 }
1271
1272 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1273 {
1274         epplist::const_iterator current = eppl.begin();
1275         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1276                 ++current;
1277         }
1278         eppl.insert(current,elem);
1279 }
1280
1281 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1282                                           epvector::iterator &last_non_zero,
1283                                           std::vector<bool> &touched,
1284                                           unsigned &number_of_zeroes)
1285 {
1286         epp current = seq.begin();
1287
1288         while (current!=first_numeric) {
1289                 if (is_exactly_a<numeric>(current->rest)) {
1290                         --first_numeric;
1291                         iter_swap(current,first_numeric);
1292                 } else {
1293                         // calculate hashindex
1294                         unsigned currenthashindex = calc_hashindex(current->rest);
1295
1296                         // test if there is already a matching expair in the hashtab-list
1297                         epplist &eppl=hashtab[currenthashindex];
1298                         epplist::iterator epplit = eppl.begin();
1299                         while (epplit!=eppl.end()) {
1300                                 if (current->rest.is_equal((*epplit)->rest))
1301                                         break;
1302                                 ++epplit;
1303                         }
1304                         if (epplit==eppl.end()) {
1305                                 // no matching expair found, append this to end of list
1306                                 sorted_insert(eppl,current);
1307                                 ++current;
1308                         } else {
1309                                 // epplit points to a matching expair, combine it with current
1310                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1311                                                    add_dyn(ex_to<numeric>(current->coeff));
1312
1313                                 // move obsolete current expair to end by swapping with last_non_zero element
1314                                 // if this was a numeric, it is swapped with the expair before first_numeric
1315                                 iter_swap(current,last_non_zero);
1316                                 --first_numeric;
1317                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1318                                 --last_non_zero;
1319                                 ++number_of_zeroes;
1320                                 // test if combined term has coeff 0 and can be removed is done later
1321                                 touched[(*epplit)-seq.begin()] = true;
1322                         }
1323                 }
1324         }
1325 }
1326
1327 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1328                                    epvector::iterator &last_non_zero,
1329                                    std::vector<bool> &touched,
1330                                    unsigned &number_of_zeroes)
1331 {
1332         // move terms with coeff 0 to end and remove them from hashtab
1333         // check only those elements which have been touched
1334         epp current = seq.begin();
1335         size_t i = 0;
1336         while (current!=first_numeric) {
1337                 if (!touched[i]) {
1338                         ++current;
1339                         ++i;
1340                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1341                         ++current;
1342                         ++i;
1343                 } else {
1344                         remove_hashtab_entry(current);
1345
1346                         // move element to the end, unless it is already at the end
1347                         if (current!=last_non_zero) {
1348                                 iter_swap(current,last_non_zero);
1349                                 --first_numeric;
1350                                 bool numeric_swapped = first_numeric!=last_non_zero;
1351                                 if (numeric_swapped)
1352                                         iter_swap(first_numeric,current);
1353                                 epvector::iterator changed_entry;
1354
1355                                 if (numeric_swapped)
1356                                         changed_entry = first_numeric;
1357                                 else
1358                                         changed_entry = last_non_zero;
1359
1360                                 --last_non_zero;
1361                                 ++number_of_zeroes;
1362
1363                                 if (first_numeric!=current) {
1364
1365                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1366                                         move_hashtab_entry(changed_entry,current);
1367                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1368                                 }
1369                         } else {
1370                                 --first_numeric;
1371                                 --last_non_zero;
1372                                 ++number_of_zeroes;
1373                         }
1374                 }
1375         }
1376         GINAC_ASSERT(i==current-seq.begin());
1377 }
1378
1379 /** True if one of the coeffs vanishes, otherwise false.
1380  *  This would be an invariant violation, so this should only be used for
1381  *  debugging purposes. */
1382 bool expairseq::has_coeff_0() const
1383 {
1384         epvector::const_iterator i = seq.begin(), end = seq.end();
1385         while (i != end) {
1386                 if (i->coeff.is_zero())
1387                         return true;
1388                 ++i;
1389         }
1390         return false;
1391 }
1392
1393 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1394                                                                                 epvector::const_iterator last_non_zero)
1395 {
1396         if (first_numeric == seq.end()) return; // no numerics
1397
1398         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1399         while (current != last) {
1400                 sorted_insert(hashtab[hashmask], current);
1401                 ++current;
1402         }
1403 }
1404
1405 void expairseq::combine_same_terms()
1406 {
1407         // combine same terms, drop term with coeff 0, move numerics to end
1408
1409         // calculate size of hashtab
1410         hashtabsize = calc_hashtabsize(seq.size());
1411
1412         // hashtabsize is a power of 2
1413         hashmask = hashtabsize-1;
1414
1415         // allocate hashtab
1416         hashtab.clear();
1417         hashtab.resize(hashtabsize);
1418
1419         if (hashtabsize==0) {
1420                 canonicalize();
1421                 combine_same_terms_sorted_seq();
1422                 GINAC_ASSERT(!has_coeff_0());
1423                 return;
1424         }
1425
1426         // iterate through seq, move numerics to end,
1427         // fill hashtab and combine same terms
1428         epvector::iterator first_numeric = seq.end();
1429         epvector::iterator last_non_zero = seq.end()-1;
1430
1431         size_t num = seq.size();
1432         std::vector<bool> touched(num);
1433
1434         unsigned number_of_zeroes = 0;
1435
1436         GINAC_ASSERT(!has_coeff_0());
1437         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1438
1439         // there should not be any terms with coeff 0 from the beginning,
1440         // so it should be safe to skip this step
1441         if (number_of_zeroes!=0) {
1442                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1443         }
1444
1445         add_numerics_to_hashtab(first_numeric,last_non_zero);
1446
1447         // pop zero elements
1448         for (unsigned i=0; i<number_of_zeroes; ++i) {
1449                 seq.pop_back();
1450         }
1451
1452         // shrink hashtabsize to calculated value
1453         GINAC_ASSERT(!has_coeff_0());
1454
1455         shrink_hashtab();
1456
1457         GINAC_ASSERT(!has_coeff_0());
1458 }
1459
1460 #endif // EXPAIRSEQ_USE_HASHTAB
1461
1462 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1463  *  debugging or in assertions since being sorted is an invariance. */
1464 bool expairseq::is_canonical() const
1465 {
1466         if (seq.size() <= 1)
1467                 return 1;
1468
1469 #if EXPAIRSEQ_USE_HASHTAB
1470         if (hashtabsize > 0) return 1; // not canoncalized
1471 #endif // EXPAIRSEQ_USE_HASHTAB
1472
1473         epvector::const_iterator it = seq.begin(), itend = seq.end();
1474         epvector::const_iterator it_last = it;
1475         for (++it; it!=itend; it_last=it, ++it) {
1476                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1477                         if (!is_exactly_a<numeric>(it_last->rest) ||
1478                                 !is_exactly_a<numeric>(it->rest)) {
1479                                 // double test makes it easier to set a breakpoint...
1480                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1481                                         !is_exactly_a<numeric>(it->rest)) {
1482                                         printpair(std::clog, *it_last, 0);
1483                                         std::clog << ">";
1484                                         printpair(std::clog, *it, 0);
1485                                         std::clog << "\n";
1486                                         std::clog << "pair1:" << std::endl;
1487                                         it_last->rest.print(print_tree(std::clog));
1488                                         it_last->coeff.print(print_tree(std::clog));
1489                                         std::clog << "pair2:" << std::endl;
1490                                         it->rest.print(print_tree(std::clog));
1491                                         it->coeff.print(print_tree(std::clog));
1492                                         return 0;
1493                                 }
1494                         }
1495                 }
1496         }
1497         return 1;
1498 }
1499
1500
1501 /** Member-wise expand the expairs in this sequence.
1502  *
1503  *  @see expairseq::expand()
1504  *  @return pointer to epvector containing expanded pairs or zero pointer,
1505  *  if no members were changed. */
1506 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1507 {
1508         const epvector::const_iterator last = seq.end();
1509         epvector::const_iterator cit = seq.begin();
1510         while (cit!=last) {
1511                 const ex &expanded_ex = cit->rest.expand(options);
1512                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1513
1514                         // something changed, copy seq, eval and return it
1515                         std::auto_ptr<epvector> s(new epvector);
1516                         s->reserve(seq.size());
1517
1518                         // copy parts of seq which are known not to have changed
1519                         epvector::const_iterator cit2 = seq.begin();
1520                         while (cit2!=cit) {
1521                                 s->push_back(*cit2);
1522                                 ++cit2;
1523                         }
1524
1525                         // copy first changed element
1526                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1527                                                                    cit2->coeff));
1528                         ++cit2;
1529
1530                         // copy rest
1531                         while (cit2!=last) {
1532                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1533                                                                            cit2->coeff));
1534                                 ++cit2;
1535                         }
1536                         return s;
1537                 }
1538                 ++cit;
1539         }
1540
1541         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1542 }
1543
1544
1545 /** Member-wise evaluate the expairs in this sequence.
1546  *
1547  *  @see expairseq::eval()
1548  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1549  *  if no members were changed. */
1550 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1551 {
1552         // returns a NULL pointer if nothing had to be evaluated
1553         // returns a pointer to a newly created epvector otherwise
1554         // (which has to be deleted somewhere else)
1555
1556         if (level==1)
1557                 return std::auto_ptr<epvector>(0);
1558
1559         if (level == -max_recursion_level)
1560                 throw(std::runtime_error("max recursion level reached"));
1561
1562         --level;
1563         epvector::const_iterator last = seq.end();
1564         epvector::const_iterator cit = seq.begin();
1565         while (cit!=last) {
1566                 const ex &evaled_ex = cit->rest.eval(level);
1567                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1568
1569                         // something changed, copy seq, eval and return it
1570                         std::auto_ptr<epvector> s(new epvector);
1571                         s->reserve(seq.size());
1572
1573                         // copy parts of seq which are known not to have changed
1574                         epvector::const_iterator cit2=seq.begin();
1575                         while (cit2!=cit) {
1576                                 s->push_back(*cit2);
1577                                 ++cit2;
1578                         }
1579
1580                         // copy first changed element
1581                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1582                                                                    cit2->coeff));
1583                         ++cit2;
1584
1585                         // copy rest
1586                         while (cit2!=last) {
1587                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1588                                                                            cit2->coeff));
1589                                 ++cit2;
1590                         }
1591                         return s;
1592                 }
1593                 ++cit;
1594         }
1595
1596         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1597 }
1598
1599
1600 /** Member-wise substitute in this sequence.
1601  *
1602  *  @see expairseq::subs()
1603  *  @return pointer to epvector containing pairs after application of subs,
1604  *    or NULL pointer if no members were changed. */
1605 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1606 {
1607         // When any of the objects to be substituted is a product or power
1608         // we have to recombine the pairs because the numeric coefficients may
1609         // be part of the search pattern.
1610         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1611
1612                 // Search the list of substitutions and cache our findings
1613                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1614                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1615                                 options |= subs_options::pattern_is_product;
1616                                 break;
1617                         }
1618                 }
1619                 if (!(options & subs_options::pattern_is_product))
1620                         options |= subs_options::pattern_is_not_product;
1621         }
1622
1623         if (options & subs_options::pattern_is_product) {
1624
1625                 // Substitute in the recombined pairs
1626                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1627                 while (cit != last) {
1628
1629                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1630                         const ex &subsed_ex = orig_ex.subs(m, options);
1631                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1632
1633                                 // Something changed, copy seq, subs and return it
1634                                 std::auto_ptr<epvector> s(new epvector);
1635                                 s->reserve(seq.size());
1636
1637                                 // Copy parts of seq which are known not to have changed
1638                                 s->insert(s->begin(), seq.begin(), cit);
1639
1640                                 // Copy first changed element
1641                                 s->push_back(split_ex_to_pair(subsed_ex));
1642                                 ++cit;
1643
1644                                 // Copy rest
1645                                 while (cit != last) {
1646                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1647                                         ++cit;
1648                                 }
1649                                 return s;
1650                         }
1651
1652                         ++cit;
1653                 }
1654
1655         } else {
1656
1657                 // Substitute only in the "rest" part of the pairs
1658                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1659                 while (cit != last) {
1660
1661                         const ex &subsed_ex = cit->rest.subs(m, options);
1662                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1663
1664                                 // Something changed, copy seq, subs and return it
1665                                 std::auto_ptr<epvector> s(new epvector);
1666                                 s->reserve(seq.size());
1667
1668                                 // Copy parts of seq which are known not to have changed
1669                                 s->insert(s->begin(), seq.begin(), cit);
1670
1671                                 // Copy first changed element
1672                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1673                                 ++cit;
1674
1675                                 // Copy rest
1676                                 while (cit != last) {
1677                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options),
1678                                                                                    cit->coeff));
1679                                         ++cit;
1680                                 }
1681                                 return s;
1682                         }
1683
1684                         ++cit;
1685                 }
1686         }
1687
1688         // Nothing has changed
1689         return std::auto_ptr<epvector>(0);
1690 }
1691
1692 //////////
1693 // static member variables
1694 //////////
1695
1696 #if EXPAIRSEQ_USE_HASHTAB
1697 unsigned expairseq::maxhashtabsize = 0x4000000U;
1698 unsigned expairseq::minhashtabsize = 0x1000U;
1699 unsigned expairseq::hashtabfactor = 1;
1700 #endif // EXPAIRSEQ_USE_HASHTAB
1701
1702 } // namespace GiNaC