ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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 <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!=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());
 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                 return thisexpairseq(v, f(overall_coeff));
 298 }
 299
 300 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 301 ex expairseq::eval(int level) const
 302 {
 303         if ((level==1) && (flags &status_flags::evaluated))
 304                 return *this;
 305
 306         std::auto_ptr<epvector> vp = evalchildren(level);
 307         if (vp.get() == 0)
 308                 return this->hold();
 309
 310         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 311 }
 312
 313 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 314 {
 315         // This differs from basic::match() because we want "a+b+c+d" to
 316         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 317
 318         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 319
 320                 // Check whether global wildcard (one that matches the "rest of the
 321                 // expression", like "*" above) is present
 322                 bool has_global_wildcard = false;
 323                 ex global_wildcard;
 324                 for (size_t i=0; i<pattern.nops(); i++) {
 325                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 326                                 has_global_wildcard = true;
 327                                 global_wildcard = pattern.op(i);
 328                                 break;
 329                         }
 330                 }
 331
 332                 // Unfortunately, this is an O(N^2) operation because we can't
 333                 // sort the pattern in a useful way...
 334
 335                 // Chop into terms
 336                 exvector ops;
 337                 ops.reserve(nops());
 338                 for (size_t i=0; i<nops(); i++)
 339                         ops.push_back(op(i));
 340
 341                 // Now, for every term of the pattern, look for a matching term in
 342                 // the expression and remove the match
 343                 for (size_t i=0; i<pattern.nops(); i++) {
 344                         ex p = pattern.op(i);
 345                         if (has_global_wildcard && p.is_equal(global_wildcard))
 346                                 continue;
 347                         exvector::iterator it = ops.begin(), itend = ops.end();
 348                         while (it != itend) {
 349                                 if (it->match(p, repl_lst)) {
 350                                         ops.erase(it);
 351                                         goto found;
 352                                 }
 353                                 ++it;
 354                         }
 355                         return false; // no match found
 356 found:          ;
 357                 }
 358
 359                 if (has_global_wildcard) {
 360
 361                         // Assign all the remaining terms to the global wildcard (unless
 362                         // it has already been matched before, in which case the matches
 363                         // must be equal)
 364                         size_t num = ops.size();
 365                         std::auto_ptr<epvector> vp(new epvector);
 366                         vp->reserve(num);
 367                         for (size_t i=0; i<num; i++)
 368                                 vp->push_back(split_ex_to_pair(ops[i]));
 369                         ex rest = thisexpairseq(vp, default_overall_coeff());
 370                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 371                                 if (it->op(0).is_equal(global_wildcard))
 372                                         return rest.is_equal(it->op(1));
 373                         }
 374                         repl_lst.append(global_wildcard == rest);
 375                         return true;
 376
 377                 } else {
 378
 379                         // No global wildcard, then the match fails if there are any
 380                         // unmatched terms left
 381                         return ops.empty();
 382                 }
 383         }
 384         return inherited::match(pattern, repl_lst);
 385 }
 386
 387 ex expairseq::subs(const exmap & m, unsigned options) const
 388 {
 389         std::auto_ptr<epvector> vp = subschildren(m, options);
 390         if (vp.get())
 391                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 392         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 393                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 394         else
 395                 return subs_one_level(m, options);
 396 }
 397
 398 // protected
 399
 400 int expairseq::compare_same_type(const basic &other) const
 401 {
 402         GINAC_ASSERT(is_a<expairseq>(other));
 403         const expairseq &o = static_cast<const expairseq &>(other);
 404
 405         int cmpval;
 406
 407         // compare number of elements
 408         if (seq.size() != o.seq.size())
 409                 return (seq.size()<o.seq.size()) ? -1 : 1;
 410
 411         // compare overall_coeff
 412         cmpval = overall_coeff.compare(o.overall_coeff);
 413         if (cmpval!=0)
 414                 return cmpval;
 415
 416 #if EXPAIRSEQ_USE_HASHTAB
 417         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 418         if (hashtabsize==0) {
 419 #endif // EXPAIRSEQ_USE_HASHTAB
 420                 epvector::const_iterator cit1 = seq.begin();
 421                 epvector::const_iterator cit2 = o.seq.begin();
 422                 epvector::const_iterator last1 = seq.end();
 423                 epvector::const_iterator last2 = o.seq.end();
 424
 425                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 426                         cmpval = (*cit1).compare(*cit2);
 427                         if (cmpval!=0) return cmpval;
 428                 }
 429
 430                 GINAC_ASSERT(cit1==last1);
 431                 GINAC_ASSERT(cit2==last2);
 432
 433                 return 0;
 434 #if EXPAIRSEQ_USE_HASHTAB
 435         }
 436
 437         // compare number of elements in each hashtab entry
 438         for (unsigned i=0; i<hashtabsize; ++i) {
 439                 unsigned cursize=hashtab[i].size();
 440                 if (cursize != o.hashtab[i].size())
 441                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 442         }
 443
 444         // compare individual (sorted) hashtab entries
 445         for (unsigned i=0; i<hashtabsize; ++i) {
 446                 unsigned sz = hashtab[i].size();
 447                 if (sz>0) {
 448                         const epplist &eppl1 = hashtab[i];
 449                         const epplist &eppl2 = o.hashtab[i];
 450                         epplist::const_iterator it1 = eppl1.begin();
 451                         epplist::const_iterator it2 = eppl2.begin();
 452                         while (it1!=eppl1.end()) {
 453                                 cmpval = (*(*it1)).compare(*(*it2));
 454                                 if (cmpval!=0)
 455                                         return cmpval;
 456                                 ++it1;
 457                                 ++it2;
 458                         }
 459                 }
 460         }
 461
 462         return 0; // equal
 463 #endif // EXPAIRSEQ_USE_HASHTAB
 464 }
 465
 466 bool expairseq::is_equal_same_type(const basic &other) const
 467 {
 468         const expairseq &o = static_cast<const expairseq &>(other);
 469
 470         // compare number of elements
 471         if (seq.size()!=o.seq.size())
 472                 return false;
 473
 474         // compare overall_coeff
 475         if (!overall_coeff.is_equal(o.overall_coeff))
 476                 return false;
 477
 478 #if EXPAIRSEQ_USE_HASHTAB
 479         // compare number of elements in each hashtab entry
 480         if (hashtabsize!=o.hashtabsize) {
 481                 std::cout << "this:" << std::endl;
 482                 print(print_tree(std::cout));
 483                 std::cout << "other:" << std::endl;
 484                 other.print(print_tree(std::cout));
 485         }
 486
 487         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 488
 489         if (hashtabsize==0) {
 490 #endif // EXPAIRSEQ_USE_HASHTAB
 491                 epvector::const_iterator cit1 = seq.begin();
 492                 epvector::const_iterator cit2 = o.seq.begin();
 493                 epvector::const_iterator last1 = seq.end();
 494
 495                 while (cit1!=last1) {
 496                         if (!(*cit1).is_equal(*cit2)) return false;
 497                         ++cit1;
 498                         ++cit2;
 499                 }
 500
 501                 return true;
 502 #if EXPAIRSEQ_USE_HASHTAB
 503         }
 504
 505         for (unsigned i=0; i<hashtabsize; ++i) {
 506                 if (hashtab[i].size() != o.hashtab[i].size())
 507                         return false;
 508         }
 509
 510         // compare individual sorted hashtab entries
 511         for (unsigned i=0; i<hashtabsize; ++i) {
 512                 unsigned sz = hashtab[i].size();
 513                 if (sz>0) {
 514                         const epplist &eppl1 = hashtab[i];
 515                         const epplist &eppl2 = o.hashtab[i];
 516                         epplist::const_iterator it1 = eppl1.begin();
 517                         epplist::const_iterator it2 = eppl2.begin();
 518                         while (it1!=eppl1.end()) {
 519                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 520                                 ++it1;
 521                                 ++it2;
 522                         }
 523                 }
 524         }
 525
 526         return true;
 527 #endif // EXPAIRSEQ_USE_HASHTAB
 528 }
 529
 530 unsigned expairseq::return_type() const
 531 {
 532         return return_types::noncommutative_composite;
 533 }
 534
 535 unsigned expairseq::calchash() const
 536 {
 537         unsigned v = golden_ratio_hash(this->tinfo());
 538         epvector::const_iterator i = seq.begin();
 539         const epvector::const_iterator end = seq.end();
 540         while (i != end) {
 541                 v ^= i->rest.gethash();
 542 #if !EXPAIRSEQ_USE_HASHTAB
 543                 // rotation spoils commutativity!
 544                 v = rotate_left(v);
 545                 v ^= i->coeff.gethash();
 546 #endif // !EXPAIRSEQ_USE_HASHTAB
 547                 ++i;
 548         }
 549
 550         v ^= overall_coeff.gethash();
 551
 552         // store calculated hash value only if object is already evaluated
 553         if (flags &status_flags::evaluated) {
 554                 setflag(status_flags::hash_calculated);
 555                 hashvalue = v;
 556         }
 557
 558         return v;
 559 }
 560
 561 ex expairseq::expand(unsigned options) const
 562 {
 563         std::auto_ptr<epvector> vp = expandchildren(options);
 564         if (vp.get())
 565                 return thisexpairseq(vp, overall_coeff);
 566         else {
 567                 // The terms have not changed, so it is safe to declare this expanded
 568                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 569         }
 570 }
 571
 572 //////////
 573 // new virtual functions which can be overridden by derived classes
 574 //////////
 575
 576 // protected
 577
 578 /** Create an object of this type.
 579  *  This method works similar to a constructor.  It is useful because expairseq
 580  *  has (at least) two possible different semantics but we want to inherit
 581  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 582  *  has to create a new one of the same semantics, which cannot be done by a
 583  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 584  *  order for this trick to work a derived class must of course override this
 585  *  definition. */
 586 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 587 {
 588         return expairseq(v, oc);
 589 }
 590
 591 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
 592 {
 593         return expairseq(vp, oc);
 594 }
 595
 596 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 597 {
 598         c.s << "[[";
 599         p.rest.print(c, precedence());
 600         c.s << ",";
 601         p.coeff.print(c, precedence());
 602         c.s << "]]";
 603 }
 604
 605 void expairseq::printseq(const print_context & c, char delim,
 606                          unsigned this_precedence,
 607                          unsigned upper_precedence) const
 608 {
 609         if (this_precedence <= upper_precedence)
 610                 c.s << "(";
 611         epvector::const_iterator it, it_last = seq.end() - 1;
 612         for (it=seq.begin(); it!=it_last; ++it) {
 613                 printpair(c, *it, this_precedence);
 614                 c.s << delim;
 615         }
 616         printpair(c, *it, this_precedence);
 617         if (!overall_coeff.is_equal(default_overall_coeff())) {
 618                 c.s << delim;
 619                 overall_coeff.print(c, this_precedence);
 620         }
 621
 622         if (this_precedence <= upper_precedence)
 623                 c.s << ")";
 624 }
 625
 626
 627 /** Form an expair from an ex, using the corresponding semantics.
 628  *  @see expairseq::recombine_pair_to_ex() */
 629 expair expairseq::split_ex_to_pair(const ex &e) const
 630 {
 631         return expair(e,_ex1);
 632 }
 633
 634
 635 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 636                                                 const ex &c) const
 637 {
 638         GINAC_ASSERT(is_exactly_a<numeric>(c));
 639
 640         return expair(e,c);
 641 }
 642
 643
 644 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 645                                                   const ex &c) const
 646 {
 647         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 648         GINAC_ASSERT(is_exactly_a<numeric>(c));
 649
 650         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 651 }
 652
 653
 654 /** Form an ex out of an expair, using the corresponding semantics.
 655  *  @see expairseq::split_ex_to_pair() */
 656 ex expairseq::recombine_pair_to_ex(const expair &p) const
 657 {
 658         return lst(p.rest,p.coeff);
 659 }
 660
 661 bool expairseq::expair_needs_further_processing(epp it)
 662 {
 663 #if EXPAIRSEQ_USE_HASHTAB
 664         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 665 #endif // EXPAIRSEQ_USE_HASHTAB
 666         return false;
 667 }
 668
 669 ex expairseq::default_overall_coeff() const
 670 {
 671         return _ex0;
 672 }
 673
 674 void expairseq::combine_overall_coeff(const ex &c)
 675 {
 676         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 677         GINAC_ASSERT(is_exactly_a<numeric>(c));
 678         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 679 }
 680
 681 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 682 {
 683         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 684         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 685         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 686         overall_coeff = ex_to<numeric>(overall_coeff).
 687                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 688 }
 689
 690 bool expairseq::can_make_flat(const expair &p) const
 691 {
 692         return true;
 693 }
 694
 695
 696 //////////
 697 // non-virtual functions in this class
 698 //////////
 699
 700 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 701 {
 702         exvector v;
 703         v.reserve(2);
 704         v.push_back(lh);
 705         v.push_back(rh);
 706         construct_from_exvector(v);
 707 #if EXPAIRSEQ_USE_HASHTAB
 708         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 709         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 710 #endif // EXPAIRSEQ_USE_HASHTAB
 711 }
 712
 713 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 714 {
 715         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 716                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 717 #if EXPAIRSEQ_USE_HASHTAB
 718                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 719                                              ex_to<expairseq>(rh).seq.size();
 720                         if (calc_hashtabsize(totalsize)!=0) {
 721                                 construct_from_2_ex_via_exvector(lh,rh);
 722                         } else {
 723 #endif // EXPAIRSEQ_USE_HASHTAB
 724                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 725                                                            ex_to<expairseq>(rh));
 726 #if EXPAIRSEQ_USE_HASHTAB
 727                         }
 728 #endif // EXPAIRSEQ_USE_HASHTAB
 729                         return;
 730                 } else {
 731 #if EXPAIRSEQ_USE_HASHTAB
 732                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 733                         if (calc_hashtabsize(totalsize)!=0) {
 734                                 construct_from_2_ex_via_exvector(lh, rh);
 735                         } else {
 736 #endif // EXPAIRSEQ_USE_HASHTAB
 737                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 738 #if EXPAIRSEQ_USE_HASHTAB
 739                         }
 740 #endif // EXPAIRSEQ_USE_HASHTAB
 741                         return;
 742                 }
 743         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 744 #if EXPAIRSEQ_USE_HASHTAB
 745                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 746                 if (calc_hashtabsize(totalsize)!=0) {
 747                         construct_from_2_ex_via_exvector(lh,rh);
 748                 } else {
 749 #endif // EXPAIRSEQ_USE_HASHTAB
 750                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 751 #if EXPAIRSEQ_USE_HASHTAB
 752                 }
 753 #endif // EXPAIRSEQ_USE_HASHTAB
 754                 return;
 755         }
 756
 757 #if EXPAIRSEQ_USE_HASHTAB
 758         if (calc_hashtabsize(2)!=0) {
 759                 construct_from_2_ex_via_exvector(lh,rh);
 760                 return;
 761         }
 762         hashtabsize = 0;
 763 #endif // EXPAIRSEQ_USE_HASHTAB
 764
 765         if (is_exactly_a<numeric>(lh)) {
 766                 if (is_exactly_a<numeric>(rh)) {
 767                         combine_overall_coeff(lh);
 768                         combine_overall_coeff(rh);
 769                 } else {
 770                         combine_overall_coeff(lh);
 771                         seq.push_back(split_ex_to_pair(rh));
 772                 }
 773         } else {
 774                 if (is_exactly_a<numeric>(rh)) {
 775                         combine_overall_coeff(rh);
 776                         seq.push_back(split_ex_to_pair(lh));
 777                 } else {
 778                         expair p1 = split_ex_to_pair(lh);
 779                         expair p2 = split_ex_to_pair(rh);
 780
 781                         int cmpval = p1.rest.compare(p2.rest);
 782                         if (cmpval==0) {
 783                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 784                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 785                                         // no further processing is necessary, since this
 786                                         // one element will usually be recombined in eval()
 787                                         seq.push_back(p1);
 788                                 }
 789                         } else {
 790                                 seq.reserve(2);
 791                                 if (cmpval<0) {
 792                                         seq.push_back(p1);
 793                                         seq.push_back(p2);
 794                                 } else {
 795                                         seq.push_back(p2);
 796                                         seq.push_back(p1);
 797                                 }
 798                         }
 799                 }
 800         }
 801 }
 802
 803 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 804                                                                                    const expairseq &s2)
 805 {
 806         combine_overall_coeff(s1.overall_coeff);
 807         combine_overall_coeff(s2.overall_coeff);
 808
 809         epvector::const_iterator first1 = s1.seq.begin();
 810         epvector::const_iterator last1 = s1.seq.end();
 811         epvector::const_iterator first2 = s2.seq.begin();
 812         epvector::const_iterator last2 = s2.seq.end();
 813
 814         seq.reserve(s1.seq.size()+s2.seq.size());
 815
 816         bool needs_further_processing=false;
 817
 818         while (first1!=last1 && first2!=last2) {
 819                 int cmpval = (*first1).rest.compare((*first2).rest);
 820                 if (cmpval==0) {
 821                         // combine terms
 822                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 823                                                    add(ex_to<numeric>(first2->coeff));
 824                         if (!newcoeff.is_zero()) {
 825                                 seq.push_back(expair(first1->rest,newcoeff));
 826                                 if (expair_needs_further_processing(seq.end()-1)) {
 827                                         needs_further_processing = true;
 828                                 }
 829                         }
 830                         ++first1;
 831                         ++first2;
 832                 } else if (cmpval<0) {
 833                         seq.push_back(*first1);
 834                         ++first1;
 835                 } else {
 836                         seq.push_back(*first2);
 837                         ++first2;
 838                 }
 839         }
 840
 841         while (first1!=last1) {
 842                 seq.push_back(*first1);
 843                 ++first1;
 844         }
 845         while (first2!=last2) {
 846                 seq.push_back(*first2);
 847                 ++first2;
 848         }
 849
 850         if (needs_further_processing) {
 851                 epvector v = seq;
 852                 seq.clear();
 853                 construct_from_epvector(v);
 854         }
 855 }
 856
 857 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 858                                                                                         const ex &e)
 859 {
 860         combine_overall_coeff(s.overall_coeff);
 861         if (is_exactly_a<numeric>(e)) {
 862                 combine_overall_coeff(e);
 863                 seq = s.seq;
 864                 return;
 865         }
 866
 867         epvector::const_iterator first = s.seq.begin();
 868         epvector::const_iterator last = s.seq.end();
 869         expair p = split_ex_to_pair(e);
 870
 871         seq.reserve(s.seq.size()+1);
 872         bool p_pushed = false;
 873
 874         bool needs_further_processing=false;
 875
 876         // merge p into s.seq
 877         while (first!=last) {
 878                 int cmpval = (*first).rest.compare(p.rest);
 879                 if (cmpval==0) {
 880                         // combine terms
 881                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 882                                                    add(ex_to<numeric>(p.coeff));
 883                         if (!newcoeff.is_zero()) {
 884                                 seq.push_back(expair(first->rest,newcoeff));
 885                                 if (expair_needs_further_processing(seq.end()-1))
 886                                         needs_further_processing = true;
 887                         }
 888                         ++first;
 889                         p_pushed = true;
 890                         break;
 891                 } else if (cmpval<0) {
 892                         seq.push_back(*first);
 893                         ++first;
 894                 } else {
 895                         seq.push_back(p);
 896                         p_pushed = true;
 897                         break;
 898                 }
 899         }
 900
 901         if (p_pushed) {
 902                 // while loop exited because p was pushed, now push rest of s.seq
 903                 while (first!=last) {
 904                         seq.push_back(*first);
 905                         ++first;
 906                 }
 907         } else {
 908                 // while loop exited because s.seq was pushed, now push p
 909                 seq.push_back(p);
 910         }
 911
 912         if (needs_further_processing) {
 913                 epvector v = seq;
 914                 seq.clear();
 915                 construct_from_epvector(v);
 916         }
 917 }
 918
 919 void expairseq::construct_from_exvector(const exvector &v)
 920 {
 921         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 922         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 923         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 924         //                  (same for (+,*) -> (*,^)
 925
 926         make_flat(v);
 927 #if EXPAIRSEQ_USE_HASHTAB
 928         combine_same_terms();
 929 #else
 930         canonicalize();
 931         combine_same_terms_sorted_seq();
 932 #endif // EXPAIRSEQ_USE_HASHTAB
 933 }
 934
 935 void expairseq::construct_from_epvector(const epvector &v)
 936 {
 937         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 938         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 939         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 940         //                  (same for (+,*) -> (*,^)
 941
 942         make_flat(v);
 943 #if EXPAIRSEQ_USE_HASHTAB
 944         combine_same_terms();
 945 #else
 946         canonicalize();
 947         combine_same_terms_sorted_seq();
 948 #endif // EXPAIRSEQ_USE_HASHTAB
 949 }
 950
 951 /** Combine this expairseq with argument exvector.
 952  *  It cares for associativity as well as for special handling of numerics. */
 953 void expairseq::make_flat(const exvector &v)
 954 {
 955         exvector::const_iterator cit;
 956
 957         // count number of operands which are of same expairseq derived type
 958         // and their cumulative number of operands
 959         int nexpairseqs = 0;
 960         int noperands = 0;
 961
 962         cit = v.begin();
 963         while (cit!=v.end()) {
 964                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 965                         ++nexpairseqs;
 966                         noperands += ex_to<expairseq>(*cit).seq.size();
 967                 }
 968                 ++cit;
 969         }
 970
 971         // reserve seq and coeffseq which will hold all operands
 972         seq.reserve(v.size()+noperands-nexpairseqs);
 973
 974         // copy elements and split off numerical part
 975         cit = v.begin();
 976         while (cit!=v.end()) {
 977                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 978                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 979                         combine_overall_coeff(subseqref.overall_coeff);
 980                         epvector::const_iterator cit_s = subseqref.seq.begin();
 981                         while (cit_s!=subseqref.seq.end()) {
 982                                 seq.push_back(*cit_s);
 983                                 ++cit_s;
 984                         }
 985                 } else {
 986                         if (is_exactly_a<numeric>(*cit))
 987                                 combine_overall_coeff(*cit);
 988                         else
 989                                 seq.push_back(split_ex_to_pair(*cit));
 990                 }
 991                 ++cit;
 992         }
 993 }
 994
 995 /** Combine this expairseq with argument epvector.
 996  *  It cares for associativity as well as for special handling of numerics. */
 997 void expairseq::make_flat(const epvector &v)
 998 {
 999         epvector::const_iterator cit;
1000
1001         // count number of operands which are of same expairseq derived type
1002         // and their cumulative number of operands
1003         int nexpairseqs = 0;
1004         int noperands = 0;
1005
1006         cit = v.begin();
1007         while (cit!=v.end()) {
1008                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1009                         ++nexpairseqs;
1010                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1011                 }
1012                 ++cit;
1013         }
1014
1015         // reserve seq and coeffseq which will hold all operands
1016         seq.reserve(v.size()+noperands-nexpairseqs);
1017
1018         // copy elements and split off numerical part
1019         cit = v.begin();
1020         while (cit!=v.end()) {
1021                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1022                     this->can_make_flat(*cit)) {
1023                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1024                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1025                                                             ex_to<numeric>(cit->coeff));
1026                         epvector::const_iterator cit_s = subseqref.seq.begin();
1027                         while (cit_s!=subseqref.seq.end()) {
1028                                 seq.push_back(expair(cit_s->rest,
1029                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1030                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1031                                 //                                              (*cit).coeff));
1032                                 ++cit_s;
1033                         }
1034                 } else {
1035                         if (cit->is_canonical_numeric())
1036                                 combine_overall_coeff(cit->rest);
1037                         else
1038                                 seq.push_back(*cit);
1039                 }
1040                 ++cit;
1041         }
1042 }
1043
1044 /** Brings this expairseq into a sorted (canonical) form. */
1045 void expairseq::canonicalize()
1046 {
1047         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1048 }
1049
1050
1051 /** Compact a presorted expairseq by combining all matching expairs to one
1052  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1053  *  instance. */
1054 void expairseq::combine_same_terms_sorted_seq()
1055 {
1056         if (seq.size()<2)
1057                 return;
1058
1059         bool needs_further_processing = false;
1060
1061         epvector::iterator itin1 = seq.begin();
1062         epvector::iterator itin2 = itin1+1;
1063         epvector::iterator itout = itin1;
1064         epvector::iterator last = seq.end();
1065         // must_copy will be set to true the first time some combination is
1066         // possible from then on the sequence has changed and must be compacted
1067         bool must_copy = false;
1068         while (itin2!=last) {
1069                 if (itin1->rest.compare(itin2->rest)==0) {
1070                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1071                                        add_dyn(ex_to<numeric>(itin2->coeff));
1072                         if (expair_needs_further_processing(itin1))
1073                                 needs_further_processing = true;
1074                         must_copy = true;
1075                 } else {
1076                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1077                                 if (must_copy)
1078                                         *itout = *itin1;
1079                                 ++itout;
1080                         }
1081                         itin1 = itin2;
1082                 }
1083                 ++itin2;
1084         }
1085         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1086                 if (must_copy)
1087                         *itout = *itin1;
1088                 ++itout;
1089         }
1090         if (itout!=last)
1091                 seq.erase(itout,last);
1092
1093         if (needs_further_processing) {
1094                 epvector v = seq;
1095                 seq.clear();
1096                 construct_from_epvector(v);
1097         }
1098 }
1099
1100 #if EXPAIRSEQ_USE_HASHTAB
1101
1102 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1103 {
1104         unsigned size;
1105         unsigned nearest_power_of_2 = 1 << log2(sz);
1106         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1107         //  size = nearest_power_of_2*hashtabfactor;
1108         size = nearest_power_of_2/hashtabfactor;
1109         if (size<minhashtabsize)
1110                 return 0;
1111
1112         // hashtabsize must be a power of 2
1113         GINAC_ASSERT((1U << log2(size))==size);
1114         return size;
1115 }
1116
1117 unsigned expairseq::calc_hashindex(const ex &e) const
1118 {
1119         // calculate hashindex
1120         unsigned hashindex;
1121         if (is_a<numeric>(e)) {
1122                 hashindex = hashmask;
1123         } else {
1124                 hashindex = e.gethash() & hashmask;
1125                 // last hashtab entry is reserved for numerics
1126                 if (hashindex==hashmask) hashindex = 0;
1127         }
1128         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1129         return hashindex;
1130 }
1131
1132 void expairseq::shrink_hashtab()
1133 {
1134         unsigned new_hashtabsize;
1135         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1136                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1137                 if (new_hashtabsize==0) {
1138                         hashtab.clear();
1139                         hashtabsize = 0;
1140                         canonicalize();
1141                         return;
1142                 }
1143
1144                 // shrink by a factor of 2
1145                 unsigned half_hashtabsize = hashtabsize/2;
1146                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1147                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1148                 // special treatment for numeric hashes
1149                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1150                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1151                 hashtab.resize(half_hashtabsize);
1152                 hashtabsize = half_hashtabsize;
1153                 hashmask = hashtabsize-1;
1154         }
1155 }
1156
1157 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1158 {
1159         if (hashtabsize==0)
1160                 return; // nothing to do
1161
1162         // calculate hashindex of element to be deleted
1163         unsigned hashindex = calc_hashindex((*element).rest);
1164
1165         // find it in hashtab and remove it
1166         epplist &eppl = hashtab[hashindex];
1167         epplist::iterator epplit = eppl.begin();
1168         bool erased = false;
1169         while (epplit!=eppl.end()) {
1170                 if (*epplit == element) {
1171                         eppl.erase(epplit);
1172                         erased = true;
1173                         break;
1174                 }
1175                 ++epplit;
1176         }
1177         if (!erased) {
1178                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1179                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1180
1181                 unsigned hashindex = calc_hashindex(element->rest);
1182                 epplist &eppl = hashtab[hashindex];
1183                 epplist::iterator epplit = eppl.begin();
1184                 bool erased = false;
1185                 while (epplit!=eppl.end()) {
1186                         if (*epplit == element) {
1187                                 eppl.erase(epplit);
1188                                 erased = true;
1189                                 break;
1190                         }
1191                         ++epplit;
1192                 }
1193                 GINAC_ASSERT(erased);
1194         }
1195         GINAC_ASSERT(erased);
1196 }
1197
1198 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1199                                    epvector::iterator newpos)
1200 {
1201         GINAC_ASSERT(hashtabsize!=0);
1202
1203         // calculate hashindex of element which was moved
1204         unsigned hashindex=calc_hashindex((*newpos).rest);
1205
1206         // find it in hashtab and modify it
1207         epplist &eppl = hashtab[hashindex];
1208         epplist::iterator epplit = eppl.begin();
1209         while (epplit!=eppl.end()) {
1210                 if (*epplit == oldpos) {
1211                         *epplit = newpos;
1212                         break;
1213                 }
1214                 ++epplit;
1215         }
1216         GINAC_ASSERT(epplit!=eppl.end());
1217 }
1218
1219 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1220 {
1221         epplist::const_iterator current = eppl.begin();
1222         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1223                 ++current;
1224         }
1225         eppl.insert(current,elem);
1226 }
1227
1228 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1229                                           epvector::iterator &last_non_zero,
1230                                           std::vector<bool> &touched,
1231                                           unsigned &number_of_zeroes)
1232 {
1233         epp current = seq.begin();
1234
1235         while (current!=first_numeric) {
1236                 if (is_exactly_a<numeric>(current->rest)) {
1237                         --first_numeric;
1238                         iter_swap(current,first_numeric);
1239                 } else {
1240                         // calculate hashindex
1241                         unsigned currenthashindex = calc_hashindex(current->rest);
1242
1243                         // test if there is already a matching expair in the hashtab-list
1244                         epplist &eppl=hashtab[currenthashindex];
1245                         epplist::iterator epplit = eppl.begin();
1246                         while (epplit!=eppl.end()) {
1247                                 if (current->rest.is_equal((*epplit)->rest))
1248                                         break;
1249                                 ++epplit;
1250                         }
1251                         if (epplit==eppl.end()) {
1252                                 // no matching expair found, append this to end of list
1253                                 sorted_insert(eppl,current);
1254                                 ++current;
1255                         } else {
1256                                 // epplit points to a matching expair, combine it with current
1257                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1258                                                    add_dyn(ex_to<numeric>(current->coeff));
1259
1260                                 // move obsolete current expair to end by swapping with last_non_zero element
1261                                 // if this was a numeric, it is swapped with the expair before first_numeric
1262                                 iter_swap(current,last_non_zero);
1263                                 --first_numeric;
1264                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1265                                 --last_non_zero;
1266                                 ++number_of_zeroes;
1267                                 // test if combined term has coeff 0 and can be removed is done later
1268                                 touched[(*epplit)-seq.begin()] = true;
1269                         }
1270                 }
1271         }
1272 }
1273
1274 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1275                                    epvector::iterator &last_non_zero,
1276                                    std::vector<bool> &touched,
1277                                    unsigned &number_of_zeroes)
1278 {
1279         // move terms with coeff 0 to end and remove them from hashtab
1280         // check only those elements which have been touched
1281         epp current = seq.begin();
1282         size_t i = 0;
1283         while (current!=first_numeric) {
1284                 if (!touched[i]) {
1285                         ++current;
1286                         ++i;
1287                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1288                         ++current;
1289                         ++i;
1290                 } else {
1291                         remove_hashtab_entry(current);
1292
1293                         // move element to the end, unless it is already at the end
1294                         if (current!=last_non_zero) {
1295                                 iter_swap(current,last_non_zero);
1296                                 --first_numeric;
1297                                 bool numeric_swapped = first_numeric!=last_non_zero;
1298                                 if (numeric_swapped)
1299                                         iter_swap(first_numeric,current);
1300                                 epvector::iterator changed_entry;
1301
1302                                 if (numeric_swapped)
1303                                         changed_entry = first_numeric;
1304                                 else
1305                                         changed_entry = last_non_zero;
1306
1307                                 --last_non_zero;
1308                                 ++number_of_zeroes;
1309
1310                                 if (first_numeric!=current) {
1311
1312                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1313                                         move_hashtab_entry(changed_entry,current);
1314                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1315                                 }
1316                         } else {
1317                                 --first_numeric;
1318                                 --last_non_zero;
1319                                 ++number_of_zeroes;
1320                         }
1321                 }
1322         }
1323         GINAC_ASSERT(i==current-seq.begin());
1324 }
1325
1326 /** True if one of the coeffs vanishes, otherwise false.
1327  *  This would be an invariant violation, so this should only be used for
1328  *  debugging purposes. */
1329 bool expairseq::has_coeff_0() const
1330 {
1331         epvector::const_iterator i = seq.begin(), end = seq.end();
1332         while (i != end) {
1333                 if (i->coeff.is_zero())
1334                         return true;
1335                 ++i;
1336         }
1337         return false;
1338 }
1339
1340 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1341                                                                                 epvector::const_iterator last_non_zero)
1342 {
1343         if (first_numeric == seq.end()) return; // no numerics
1344
1345         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1346         while (current != last) {
1347                 sorted_insert(hashtab[hashmask], current);
1348                 ++current;
1349         }
1350 }
1351
1352 void expairseq::combine_same_terms()
1353 {
1354         // combine same terms, drop term with coeff 0, move numerics to end
1355
1356         // calculate size of hashtab
1357         hashtabsize = calc_hashtabsize(seq.size());
1358
1359         // hashtabsize is a power of 2
1360         hashmask = hashtabsize-1;
1361
1362         // allocate hashtab
1363         hashtab.clear();
1364         hashtab.resize(hashtabsize);
1365
1366         if (hashtabsize==0) {
1367                 canonicalize();
1368                 combine_same_terms_sorted_seq();
1369                 GINAC_ASSERT(!has_coeff_0());
1370                 return;
1371         }
1372
1373         // iterate through seq, move numerics to end,
1374         // fill hashtab and combine same terms
1375         epvector::iterator first_numeric = seq.end();
1376         epvector::iterator last_non_zero = seq.end()-1;
1377
1378         size_t num = seq.size();
1379         std::vector<bool> touched(num);
1380
1381         unsigned number_of_zeroes = 0;
1382
1383         GINAC_ASSERT(!has_coeff_0());
1384         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1385
1386         // there should not be any terms with coeff 0 from the beginning,
1387         // so it should be safe to skip this step
1388         if (number_of_zeroes!=0) {
1389                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1390         }
1391
1392         add_numerics_to_hashtab(first_numeric,last_non_zero);
1393
1394         // pop zero elements
1395         for (unsigned i=0; i<number_of_zeroes; ++i) {
1396                 seq.pop_back();
1397         }
1398
1399         // shrink hashtabsize to calculated value
1400         GINAC_ASSERT(!has_coeff_0());
1401
1402         shrink_hashtab();
1403
1404         GINAC_ASSERT(!has_coeff_0());
1405 }
1406
1407 #endif // EXPAIRSEQ_USE_HASHTAB
1408
1409 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1410  *  debugging or in assertions since being sorted is an invariance. */
1411 bool expairseq::is_canonical() const
1412 {
1413         if (seq.size() <= 1)
1414                 return 1;
1415
1416 #if EXPAIRSEQ_USE_HASHTAB
1417         if (hashtabsize > 0) return 1; // not canoncalized
1418 #endif // EXPAIRSEQ_USE_HASHTAB
1419
1420         epvector::const_iterator it = seq.begin(), itend = seq.end();
1421         epvector::const_iterator it_last = it;
1422         for (++it; it!=itend; it_last=it, ++it) {
1423                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1424                         if (!is_exactly_a<numeric>(it_last->rest) ||
1425                                 !is_exactly_a<numeric>(it->rest)) {
1426                                 // double test makes it easier to set a breakpoint...
1427                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1428                                         !is_exactly_a<numeric>(it->rest)) {
1429                                         printpair(std::clog, *it_last, 0);
1430                                         std::clog << ">";
1431                                         printpair(std::clog, *it, 0);
1432                                         std::clog << "\n";
1433                                         std::clog << "pair1:" << std::endl;
1434                                         it_last->rest.print(print_tree(std::clog));
1435                                         it_last->coeff.print(print_tree(std::clog));
1436                                         std::clog << "pair2:" << std::endl;
1437                                         it->rest.print(print_tree(std::clog));
1438                                         it->coeff.print(print_tree(std::clog));
1439                                         return 0;
1440                                 }
1441                         }
1442                 }
1443         }
1444         return 1;
1445 }
1446
1447
1448 /** Member-wise expand the expairs in this sequence.
1449  *
1450  *  @see expairseq::expand()
1451  *  @return pointer to epvector containing expanded pairs or zero pointer,
1452  *  if no members were changed. */
1453 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1454 {
1455         const epvector::const_iterator last = seq.end();
1456         epvector::const_iterator cit = seq.begin();
1457         while (cit!=last) {
1458                 const ex &expanded_ex = cit->rest.expand(options);
1459                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1460
1461                         // something changed, copy seq, eval and return it
1462                         std::auto_ptr<epvector> s(new epvector);
1463                         s->reserve(seq.size());
1464
1465                         // copy parts of seq which are known not to have changed
1466                         epvector::const_iterator cit2 = seq.begin();
1467                         while (cit2!=cit) {
1468                                 s->push_back(*cit2);
1469                                 ++cit2;
1470                         }
1471
1472                         // copy first changed element
1473                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1474                                                                    cit2->coeff));
1475                         ++cit2;
1476
1477                         // copy rest
1478                         while (cit2!=last) {
1479                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1480                                                                            cit2->coeff));
1481                                 ++cit2;
1482                         }
1483                         return s;
1484                 }
1485                 ++cit;
1486         }
1487
1488         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1489 }
1490
1491
1492 /** Member-wise evaluate the expairs in this sequence.
1493  *
1494  *  @see expairseq::eval()
1495  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1496  *  if no members were changed. */
1497 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1498 {
1499         // returns a NULL pointer if nothing had to be evaluated
1500         // returns a pointer to a newly created epvector otherwise
1501         // (which has to be deleted somewhere else)
1502
1503         if (level==1)
1504                 return std::auto_ptr<epvector>(0);
1505
1506         if (level == -max_recursion_level)
1507                 throw(std::runtime_error("max recursion level reached"));
1508
1509         --level;
1510         epvector::const_iterator last = seq.end();
1511         epvector::const_iterator cit = seq.begin();
1512         while (cit!=last) {
1513                 const ex &evaled_ex = cit->rest.eval(level);
1514                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1515
1516                         // something changed, copy seq, eval and return it
1517                         std::auto_ptr<epvector> s(new epvector);
1518                         s->reserve(seq.size());
1519
1520                         // copy parts of seq which are known not to have changed
1521                         epvector::const_iterator cit2=seq.begin();
1522                         while (cit2!=cit) {
1523                                 s->push_back(*cit2);
1524                                 ++cit2;
1525                         }
1526
1527                         // copy first changed element
1528                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1529                                                                    cit2->coeff));
1530                         ++cit2;
1531
1532                         // copy rest
1533                         while (cit2!=last) {
1534                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1535                                                                            cit2->coeff));
1536                                 ++cit2;
1537                         }
1538                         return s;
1539                 }
1540                 ++cit;
1541         }
1542
1543         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1544 }
1545
1546
1547 /** Member-wise substitute in this sequence.
1548  *
1549  *  @see expairseq::subs()
1550  *  @return pointer to epvector containing pairs after application of subs,
1551  *    or NULL pointer if no members were changed. */
1552 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1553 {
1554         // When any of the objects to be substituted is a product or power
1555         // we have to recombine the pairs because the numeric coefficients may
1556         // be part of the search pattern.
1557         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1558
1559                 // Search the list of substitutions and cache our findings
1560                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1561                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1562                                 options |= subs_options::pattern_is_product;
1563                                 break;
1564                         }
1565                 }
1566                 if (!(options & subs_options::pattern_is_product))
1567                         options |= subs_options::pattern_is_not_product;
1568         }
1569
1570         if (options & subs_options::pattern_is_product) {
1571
1572                 // Substitute in the recombined pairs
1573                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1574                 while (cit != last) {
1575
1576                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1577                         const ex &subsed_ex = orig_ex.subs(m, options);
1578                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1579
1580                                 // Something changed, copy seq, subs and return it
1581                                 std::auto_ptr<epvector> s(new epvector);
1582                                 s->reserve(seq.size());
1583
1584                                 // Copy parts of seq which are known not to have changed
1585                                 s->insert(s->begin(), seq.begin(), cit);
1586
1587                                 // Copy first changed element
1588                                 s->push_back(split_ex_to_pair(subsed_ex));
1589                                 ++cit;
1590
1591                                 // Copy rest
1592                                 while (cit != last) {
1593                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1594                                         ++cit;
1595                                 }
1596                                 return s;
1597                         }
1598
1599                         ++cit;
1600                 }
1601
1602         } else {
1603
1604                 // Substitute only in the "rest" part of the pairs
1605                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1606                 while (cit != last) {
1607
1608                         const ex &subsed_ex = cit->rest.subs(m, options);
1609                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1610
1611                                 // Something changed, copy seq, subs and return it
1612                                 std::auto_ptr<epvector> s(new epvector);
1613                                 s->reserve(seq.size());
1614
1615                                 // Copy parts of seq which are known not to have changed
1616                                 s->insert(s->begin(), seq.begin(), cit);
1617
1618                                 // Copy first changed element
1619                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1620                                 ++cit;
1621
1622                                 // Copy rest
1623                                 while (cit != last) {
1624                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options),
1625                                                                                    cit->coeff));
1626                                         ++cit;
1627                                 }
1628                                 return s;
1629                         }
1630
1631                         ++cit;
1632                 }
1633         }
1634
1635         // Nothing has changed
1636         return std::auto_ptr<epvector>(0);
1637 }
1638
1639 //////////
1640 // static member variables
1641 //////////
1642
1643 #if EXPAIRSEQ_USE_HASHTAB
1644 unsigned expairseq::maxhashtabsize = 0x4000000U;
1645 unsigned expairseq::minhashtabsize = 0x1000U;
1646 unsigned expairseq::hashtabfactor = 1;
1647 #endif // EXPAIRSEQ_USE_HASHTAB
1648
1649 } // namespace GiNaC