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 "print.h"
  35 #include "archive.h"
  36 #include "operators.h"
  37 #include "utils.h"
  38
  39 #if EXPAIRSEQ_USE_HASHTAB
  40 #include <cmath>
  41 #endif // EXPAIRSEQ_USE_HASHTAB
  42
  43 namespace GiNaC {
  44
  45
  46 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  47
  48 //////////
  49 // helper classes
  50 //////////
  51
  52 class epp_is_less
  53 {
  54 public:
  55         bool operator()(const epp &lh, const epp &rh) const
  56         {
  57                 return (*lh).is_less(*rh);
  58         }
  59 };
  60
  61 //////////
  62 // default ctor, dtor, copy ctor, assignment operator and helpers
  63 //////////
  64
  65 // public
  66
  67 expairseq::expairseq(const expairseq &other)
  68 {
  69         copy(other);
  70 }
  71
  72 const expairseq &expairseq::operator=(const expairseq &other)
  73 {
  74         if (this != &other) {
  75                 destroy(true);
  76                 copy(other);
  77         }
  78         return *this;
  79 }
  80
  81 // protected
  82
  83 /** For use by copy ctor and assignment operator. */
  84 void expairseq::copy(const expairseq &other)
  85 {
  86         inherited::copy(other);
  87         seq = other.seq;
  88         overall_coeff = other.overall_coeff;
  89 #if EXPAIRSEQ_USE_HASHTAB
  90         // copy hashtab
  91         hashtabsize = other.hashtabsize;
  92         if (hashtabsize!=0) {
  93                 hashmask = other.hashmask;
  94                 hashtab.resize(hashtabsize);
  95                 epvector::const_iterator osb = other.seq.begin();
  96                 for (unsigned i=0; i<hashtabsize; ++i) {
  97                         hashtab[i].clear();
  98                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  99                              cit!=other.hashtab[i].end(); ++cit) {
 100                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 101                         }
 102                 }
 103         } else {
 104                 hashtab.clear();
 105         }
 106 #endif // EXPAIRSEQ_USE_HASHTAB
 107 }
 108
 109 DEFAULT_DESTROY(expairseq)
 110
 111 //////////
 112 // other ctors
 113 //////////
 114
 115 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 116 {
 117         construct_from_2_ex(lh,rh);
 118         GINAC_ASSERT(is_canonical());
 119 }
 120
 121 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 122 {
 123         construct_from_exvector(v);
 124         GINAC_ASSERT(is_canonical());
 125 }
 126
 127 expairseq::expairseq(const epvector &v, const ex &oc)
 128   : inherited(TINFO_expairseq), overall_coeff(oc)
 129 {
 130         GINAC_ASSERT(is_a<numeric>(oc));
 131         construct_from_epvector(v);
 132         GINAC_ASSERT(is_canonical());
 133 }
 134
 135 expairseq::expairseq(epvector *vp, const ex &oc)
 136   : inherited(TINFO_expairseq), overall_coeff(oc)
 137 {
 138         GINAC_ASSERT(vp!=0);
 139         GINAC_ASSERT(is_a<numeric>(oc));
 140         construct_from_epvector(*vp);
 141         delete vp;
 142         GINAC_ASSERT(is_canonical());
 143 }
 144
 145 //////////
 146 // archiving
 147 //////////
 148
 149 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 150 #if EXPAIRSEQ_USE_HASHTAB
 151         , hashtabsize(0)
 152 #endif
 153
 154 {
 155
 156         canonicalize();
 157         GINAC_ASSERT(is_canonical());
 158         for (unsigned int i=0; true; i++) {
 159                 ex rest;
 160                 ex coeff;
 161                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 162                         seq.push_back(expair(rest, coeff));
 163                 else
 164                         break;
 165         }
 166         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 167 }
 168
 169 void expairseq::archive(archive_node &n) const
 170 {
 171         inherited::archive(n);
 172         epvector::const_iterator i = seq.begin(), iend = seq.end();
 173         while (i != iend) {
 174                 n.add_ex("rest", i->rest);
 175                 n.add_ex("coeff", i->coeff);
 176                 ++i;
 177         }
 178         n.add_ex("overall_coeff", overall_coeff);
 179 }
 180
 181 DEFAULT_UNARCHIVE(expairseq)
 182
 183 //////////
 184 // functions overriding virtual functions from base classes
 185 //////////
 186
 187 // public
 188
 189 basic *expairseq::duplicate() const
 190 {
 191         return new expairseq(*this);
 192 }
 193
 194 void expairseq::print(const print_context &c, unsigned level) const
 195 {
 196         if (is_a<print_tree>(c)) {
 197
 198                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 199
 200                 c.s << std::string(level, ' ') << class_name()
 201                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 202                     << ", nops=" << nops()
 203                     << std::endl;
 204                 size_t num = seq.size();
 205                 for (size_t i=0; i<num; ++i) {
 206                         seq[i].rest.print(c, level + delta_indent);
 207                         seq[i].coeff.print(c, level + delta_indent);
 208                         if (i != num - 1)
 209                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 210                 }
 211                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 212                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 213                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 214                         overall_coeff.print(c, level + delta_indent);
 215                 }
 216                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 217 #if EXPAIRSEQ_USE_HASHTAB
 218                 c.s << std::string(level + delta_indent,' ')
 219                     << "hashtab size " << hashtabsize << std::endl;
 220                 if (hashtabsize == 0) return;
 221 #define MAXCOUNT 5
 222                 unsigned count[MAXCOUNT+1];
 223                 for (int i=0; i<MAXCOUNT+1; ++i)
 224                         count[i] = 0;
 225                 unsigned this_bin_fill;
 226                 unsigned cum_fill_sq = 0;
 227                 unsigned cum_fill = 0;
 228                 for (unsigned i=0; i<hashtabsize; ++i) {
 229                         this_bin_fill = 0;
 230                         if (hashtab[i].size() > 0) {
 231                                 c.s << std::string(level + delta_indent, ' ')
 232                                     << "bin " << i << " with entries ";
 233                                 for (epplist::const_iterator it=hashtab[i].begin();
 234                                      it!=hashtab[i].end(); ++it) {
 235                                         c.s << *it-seq.begin() << " ";
 236                                         ++this_bin_fill;
 237                                 }
 238                                 c.s << std::endl;
 239                                 cum_fill += this_bin_fill;
 240                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 241                         }
 242                         if (this_bin_fill<MAXCOUNT)
 243                                 ++count[this_bin_fill];
 244                         else
 245                                 ++count[MAXCOUNT];
 246                 }
 247                 unsigned fact = 1;
 248                 double cum_prob = 0;
 249                 double lambda = (1.0*seq.size()) / hashtabsize;
 250                 for (int k=0; k<MAXCOUNT; ++k) {
 251                         if (k>0)
 252                                 fact *= k;
 253                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 254                         cum_prob += prob;
 255                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 256                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 257                             << int(prob*1000)/10.0 << ")" << std::endl;
 258                 }
 259                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 260                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 261                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 262
 263                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 264                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 265                     << std::endl;
 266                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 267                     << (1.0*cum_fill)/hashtabsize
 268                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 269 #endif // EXPAIRSEQ_USE_HASHTAB
 270
 271         } else {
 272                 c.s << "[[";
 273                 printseq(c, ',', precedence(), level);
 274                 c.s << "]]";
 275         }
 276 }
 277
 278 bool expairseq::info(unsigned inf) const
 279 {
 280         return inherited::info(inf);
 281 }
 282
 283 size_t expairseq::nops() const
 284 {
 285         if (overall_coeff.is_equal(default_overall_coeff()))
 286                 return seq.size();
 287         else
 288                 return seq.size()+1;
 289 }
 290
 291 ex expairseq::op(size_t i) const
 292 {
 293         if (i < seq.size())
 294                 return recombine_pair_to_ex(seq[i]);
 295         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 296         return overall_coeff;
 297 }
 298
 299 ex expairseq::map(map_function &f) const
 300 {
 301         epvector *v = new epvector;
 302         v->reserve(seq.size());
 303
 304         epvector::const_iterator cit = seq.begin(), last = seq.end();
 305         while (cit != last) {
 306                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 307                 ++cit;
 308         }
 309
 310         if (overall_coeff.is_equal(default_overall_coeff()))
 311                 return thisexpairseq(v, default_overall_coeff());
 312         else
 313                 return thisexpairseq(v, f(overall_coeff));
 314 }
 315
 316 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 317 ex expairseq::eval(int level) const
 318 {
 319         if ((level==1) && (flags &status_flags::evaluated))
 320                 return *this;
 321
 322         epvector *vp = evalchildren(level);
 323         if (vp==0)
 324                 return this->hold();
 325
 326         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 327 }
 328
 329 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 330 {
 331         // This differs from basic::match() because we want "a+b+c+d" to
 332         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 333
 334         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 335
 336                 // Check whether global wildcard (one that matches the "rest of the
 337                 // expression", like "*" above) is present
 338                 bool has_global_wildcard = false;
 339                 ex global_wildcard;
 340                 for (size_t i=0; i<pattern.nops(); i++) {
 341                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 342                                 has_global_wildcard = true;
 343                                 global_wildcard = pattern.op(i);
 344                                 break;
 345                         }
 346                 }
 347
 348                 // Unfortunately, this is an O(N^2) operation because we can't
 349                 // sort the pattern in a useful way...
 350
 351                 // Chop into terms
 352                 exvector ops;
 353                 ops.reserve(nops());
 354                 for (size_t i=0; i<nops(); i++)
 355                         ops.push_back(op(i));
 356
 357                 // Now, for every term of the pattern, look for a matching term in
 358                 // the expression and remove the match
 359                 for (size_t i=0; i<pattern.nops(); i++) {
 360                         ex p = pattern.op(i);
 361                         if (has_global_wildcard && p.is_equal(global_wildcard))
 362                                 continue;
 363                         exvector::iterator it = ops.begin(), itend = ops.end();
 364                         while (it != itend) {
 365                                 if (it->match(p, repl_lst)) {
 366                                         ops.erase(it);
 367                                         goto found;
 368                                 }
 369                                 ++it;
 370                         }
 371                         return false; // no match found
 372 found:          ;
 373                 }
 374
 375                 if (has_global_wildcard) {
 376
 377                         // Assign all the remaining terms to the global wildcard (unless
 378                         // it has already been matched before, in which case the matches
 379                         // must be equal)
 380                         size_t num = ops.size();
 381                         epvector *vp = new epvector();
 382                         vp->reserve(num);
 383                         for (size_t i=0; i<num; i++)
 384                                 vp->push_back(split_ex_to_pair(ops[i]));
 385                         ex rest = thisexpairseq(vp, default_overall_coeff());
 386                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 387                                 if (it->op(0).is_equal(global_wildcard))
 388                                         return rest.is_equal(it->op(1));
 389                         }
 390                         repl_lst.append(global_wildcard == rest);
 391                         return true;
 392
 393                 } else {
 394
 395                         // No global wildcard, then the match fails if there are any
 396                         // unmatched terms left
 397                         return ops.empty();
 398                 }
 399         }
 400         return inherited::match(pattern, repl_lst);
 401 }
 402
 403 ex expairseq::subs(const lst &ls, const lst &lr, unsigned options) const
 404 {
 405         epvector *vp = subschildren(ls, lr, options);
 406         if (vp)
 407                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 408         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 409                 return static_cast<const mul *>(this)->algebraic_subs_mul(ls, lr, options);
 410         else
 411                 return basic::subs(ls, lr, options);
 412 }
 413
 414 // protected
 415
 416 int expairseq::compare_same_type(const basic &other) const
 417 {
 418         GINAC_ASSERT(is_a<expairseq>(other));
 419         const expairseq &o = static_cast<const expairseq &>(other);
 420
 421         int cmpval;
 422
 423         // compare number of elements
 424         if (seq.size() != o.seq.size())
 425                 return (seq.size()<o.seq.size()) ? -1 : 1;
 426
 427         // compare overall_coeff
 428         cmpval = overall_coeff.compare(o.overall_coeff);
 429         if (cmpval!=0)
 430                 return cmpval;
 431
 432 #if EXPAIRSEQ_USE_HASHTAB
 433         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 434         if (hashtabsize==0) {
 435 #endif // EXPAIRSEQ_USE_HASHTAB
 436                 epvector::const_iterator cit1 = seq.begin();
 437                 epvector::const_iterator cit2 = o.seq.begin();
 438                 epvector::const_iterator last1 = seq.end();
 439                 epvector::const_iterator last2 = o.seq.end();
 440
 441                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 442                         cmpval = (*cit1).compare(*cit2);
 443                         if (cmpval!=0) return cmpval;
 444                 }
 445
 446                 GINAC_ASSERT(cit1==last1);
 447                 GINAC_ASSERT(cit2==last2);
 448
 449                 return 0;
 450 #if EXPAIRSEQ_USE_HASHTAB
 451         }
 452
 453         // compare number of elements in each hashtab entry
 454         for (unsigned i=0; i<hashtabsize; ++i) {
 455                 unsigned cursize=hashtab[i].size();
 456                 if (cursize != o.hashtab[i].size())
 457                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 458         }
 459
 460         // compare individual (sorted) hashtab entries
 461         for (unsigned i=0; i<hashtabsize; ++i) {
 462                 unsigned sz = hashtab[i].size();
 463                 if (sz>0) {
 464                         const epplist &eppl1 = hashtab[i];
 465                         const epplist &eppl2 = o.hashtab[i];
 466                         epplist::const_iterator it1 = eppl1.begin();
 467                         epplist::const_iterator it2 = eppl2.begin();
 468                         while (it1!=eppl1.end()) {
 469                                 cmpval = (*(*it1)).compare(*(*it2));
 470                                 if (cmpval!=0)
 471                                         return cmpval;
 472                                 ++it1;
 473                                 ++it2;
 474                         }
 475                 }
 476         }
 477
 478         return 0; // equal
 479 #endif // EXPAIRSEQ_USE_HASHTAB
 480 }
 481
 482 bool expairseq::is_equal_same_type(const basic &other) const
 483 {
 484         const expairseq &o = static_cast<const expairseq &>(other);
 485
 486         // compare number of elements
 487         if (seq.size()!=o.seq.size())
 488                 return false;
 489
 490         // compare overall_coeff
 491         if (!overall_coeff.is_equal(o.overall_coeff))
 492                 return false;
 493
 494 #if EXPAIRSEQ_USE_HASHTAB
 495         // compare number of elements in each hashtab entry
 496         if (hashtabsize!=o.hashtabsize) {
 497                 std::cout << "this:" << std::endl;
 498                 print(print_tree(std::cout));
 499                 std::cout << "other:" << std::endl;
 500                 other.print(print_tree(std::cout));
 501         }
 502
 503         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 504
 505         if (hashtabsize==0) {
 506 #endif // EXPAIRSEQ_USE_HASHTAB
 507                 epvector::const_iterator cit1 = seq.begin();
 508                 epvector::const_iterator cit2 = o.seq.begin();
 509                 epvector::const_iterator last1 = seq.end();
 510
 511                 while (cit1!=last1) {
 512                         if (!(*cit1).is_equal(*cit2)) return false;
 513                         ++cit1;
 514                         ++cit2;
 515                 }
 516
 517                 return true;
 518 #if EXPAIRSEQ_USE_HASHTAB
 519         }
 520
 521         for (unsigned i=0; i<hashtabsize; ++i) {
 522                 if (hashtab[i].size() != o.hashtab[i].size())
 523                         return false;
 524         }
 525
 526         // compare individual sorted hashtab entries
 527         for (unsigned i=0; i<hashtabsize; ++i) {
 528                 unsigned sz = hashtab[i].size();
 529                 if (sz>0) {
 530                         const epplist &eppl1 = hashtab[i];
 531                         const epplist &eppl2 = o.hashtab[i];
 532                         epplist::const_iterator it1 = eppl1.begin();
 533                         epplist::const_iterator it2 = eppl2.begin();
 534                         while (it1!=eppl1.end()) {
 535                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 536                                 ++it1;
 537                                 ++it2;
 538                         }
 539                 }
 540         }
 541
 542         return true;
 543 #endif // EXPAIRSEQ_USE_HASHTAB
 544 }
 545
 546 unsigned expairseq::return_type(void) const
 547 {
 548         return return_types::noncommutative_composite;
 549 }
 550
 551 unsigned expairseq::calchash(void) const
 552 {
 553         unsigned v = golden_ratio_hash(this->tinfo());
 554         epvector::const_iterator i = seq.begin();
 555         const epvector::const_iterator end = seq.end();
 556         while (i != end) {
 557                 v ^= i->rest.gethash();
 558 #if !EXPAIRSEQ_USE_HASHTAB
 559                 // rotation spoils commutativity!
 560                 v = rotate_left(v);
 561                 v ^= i->coeff.gethash();
 562 #endif // !EXPAIRSEQ_USE_HASHTAB
 563                 ++i;
 564         }
 565
 566         v ^= overall_coeff.gethash();
 567
 568         // store calculated hash value only if object is already evaluated
 569         if (flags &status_flags::evaluated) {
 570                 setflag(status_flags::hash_calculated);
 571                 hashvalue = v;
 572         }
 573
 574         return v;
 575 }
 576
 577 ex expairseq::expand(unsigned options) const
 578 {
 579         epvector *vp = expandchildren(options);
 580         if (vp == NULL) {
 581                 // The terms have not changed, so it is safe to declare this expanded
 582                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 583         } else
 584                 return thisexpairseq(vp, overall_coeff);
 585 }
 586
 587 //////////
 588 // new virtual functions which can be overridden by derived classes
 589 //////////
 590
 591 // protected
 592
 593 /** Create an object of this type.
 594  *  This method works similar to a constructor.  It is useful because expairseq
 595  *  has (at least) two possible different semantics but we want to inherit
 596  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 597  *  has to create a new one of the same semantics, which cannot be done by a
 598  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 599  *  order for this trick to work a derived class must of course override this
 600  *  definition. */
 601 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 602 {
 603         return expairseq(v,oc);
 604 }
 605
 606 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 607 {
 608         return expairseq(vp,oc);
 609 }
 610
 611 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 612 {
 613         c.s << "[[";
 614         p.rest.print(c, precedence());
 615         c.s << ",";
 616         p.coeff.print(c, precedence());
 617         c.s << "]]";
 618 }
 619
 620 void expairseq::printseq(const print_context & c, char delim,
 621                          unsigned this_precedence,
 622                          unsigned upper_precedence) const
 623 {
 624         if (this_precedence <= upper_precedence)
 625                 c.s << "(";
 626         epvector::const_iterator it, it_last = seq.end() - 1;
 627         for (it=seq.begin(); it!=it_last; ++it) {
 628                 printpair(c, *it, this_precedence);
 629                 c.s << delim;
 630         }
 631         printpair(c, *it, this_precedence);
 632         if (!overall_coeff.is_equal(default_overall_coeff())) {
 633                 c.s << delim;
 634                 overall_coeff.print(c, this_precedence);
 635         }
 636
 637         if (this_precedence <= upper_precedence)
 638                 c.s << ")";
 639 }
 640
 641
 642 /** Form an expair from an ex, using the corresponding semantics.
 643  *  @see expairseq::recombine_pair_to_ex() */
 644 expair expairseq::split_ex_to_pair(const ex &e) const
 645 {
 646         return expair(e,_ex1);
 647 }
 648
 649
 650 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 651                                                 const ex &c) const
 652 {
 653         GINAC_ASSERT(is_exactly_a<numeric>(c));
 654
 655         return expair(e,c);
 656 }
 657
 658
 659 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 660                                                   const ex &c) const
 661 {
 662         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 663         GINAC_ASSERT(is_exactly_a<numeric>(c));
 664
 665         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 666 }
 667
 668
 669 /** Form an ex out of an expair, using the corresponding semantics.
 670  *  @see expairseq::split_ex_to_pair() */
 671 ex expairseq::recombine_pair_to_ex(const expair &p) const
 672 {
 673         return lst(p.rest,p.coeff);
 674 }
 675
 676 bool expairseq::expair_needs_further_processing(epp it)
 677 {
 678 #if EXPAIRSEQ_USE_HASHTAB
 679         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 680 #endif // EXPAIRSEQ_USE_HASHTAB
 681         return false;
 682 }
 683
 684 ex expairseq::default_overall_coeff(void) const
 685 {
 686         return _ex0;
 687 }
 688
 689 void expairseq::combine_overall_coeff(const ex &c)
 690 {
 691         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 692         GINAC_ASSERT(is_exactly_a<numeric>(c));
 693         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 694 }
 695
 696 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 697 {
 698         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 699         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 700         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 701         overall_coeff = ex_to<numeric>(overall_coeff).
 702                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 703 }
 704
 705 bool expairseq::can_make_flat(const expair &p) const
 706 {
 707         return true;
 708 }
 709
 710
 711 //////////
 712 // non-virtual functions in this class
 713 //////////
 714
 715 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 716 {
 717         exvector v;
 718         v.reserve(2);
 719         v.push_back(lh);
 720         v.push_back(rh);
 721         construct_from_exvector(v);
 722 #if EXPAIRSEQ_USE_HASHTAB
 723         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 724         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 725 #endif // EXPAIRSEQ_USE_HASHTAB
 726 }
 727
 728 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 729 {
 730         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 731                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 732 #if EXPAIRSEQ_USE_HASHTAB
 733                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 734                                              ex_to<expairseq>(rh).seq.size();
 735                         if (calc_hashtabsize(totalsize)!=0) {
 736                                 construct_from_2_ex_via_exvector(lh,rh);
 737                         } else {
 738 #endif // EXPAIRSEQ_USE_HASHTAB
 739                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 740                                                            ex_to<expairseq>(rh));
 741 #if EXPAIRSEQ_USE_HASHTAB
 742                         }
 743 #endif // EXPAIRSEQ_USE_HASHTAB
 744                         return;
 745                 } else {
 746 #if EXPAIRSEQ_USE_HASHTAB
 747                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 748                         if (calc_hashtabsize(totalsize)!=0) {
 749                                 construct_from_2_ex_via_exvector(lh, rh);
 750                         } else {
 751 #endif // EXPAIRSEQ_USE_HASHTAB
 752                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 753 #if EXPAIRSEQ_USE_HASHTAB
 754                         }
 755 #endif // EXPAIRSEQ_USE_HASHTAB
 756                         return;
 757                 }
 758         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 759 #if EXPAIRSEQ_USE_HASHTAB
 760                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 761                 if (calc_hashtabsize(totalsize)!=0) {
 762                         construct_from_2_ex_via_exvector(lh,rh);
 763                 } else {
 764 #endif // EXPAIRSEQ_USE_HASHTAB
 765                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 766 #if EXPAIRSEQ_USE_HASHTAB
 767                 }
 768 #endif // EXPAIRSEQ_USE_HASHTAB
 769                 return;
 770         }
 771
 772 #if EXPAIRSEQ_USE_HASHTAB
 773         if (calc_hashtabsize(2)!=0) {
 774                 construct_from_2_ex_via_exvector(lh,rh);
 775                 return;
 776         }
 777         hashtabsize = 0;
 778 #endif // EXPAIRSEQ_USE_HASHTAB
 779
 780         if (is_exactly_a<numeric>(lh)) {
 781                 if (is_exactly_a<numeric>(rh)) {
 782                         combine_overall_coeff(lh);
 783                         combine_overall_coeff(rh);
 784                 } else {
 785                         combine_overall_coeff(lh);
 786                         seq.push_back(split_ex_to_pair(rh));
 787                 }
 788         } else {
 789                 if (is_exactly_a<numeric>(rh)) {
 790                         combine_overall_coeff(rh);
 791                         seq.push_back(split_ex_to_pair(lh));
 792                 } else {
 793                         expair p1 = split_ex_to_pair(lh);
 794                         expair p2 = split_ex_to_pair(rh);
 795
 796                         int cmpval = p1.rest.compare(p2.rest);
 797                         if (cmpval==0) {
 798                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 799                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 800                                         // no further processing is necessary, since this
 801                                         // one element will usually be recombined in eval()
 802                                         seq.push_back(p1);
 803                                 }
 804                         } else {
 805                                 seq.reserve(2);
 806                                 if (cmpval<0) {
 807                                         seq.push_back(p1);
 808                                         seq.push_back(p2);
 809                                 } else {
 810                                         seq.push_back(p2);
 811                                         seq.push_back(p1);
 812                                 }
 813                         }
 814                 }
 815         }
 816 }
 817
 818 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 819                                                                                    const expairseq &s2)
 820 {
 821         combine_overall_coeff(s1.overall_coeff);
 822         combine_overall_coeff(s2.overall_coeff);
 823
 824         epvector::const_iterator first1 = s1.seq.begin();
 825         epvector::const_iterator last1 = s1.seq.end();
 826         epvector::const_iterator first2 = s2.seq.begin();
 827         epvector::const_iterator last2 = s2.seq.end();
 828
 829         seq.reserve(s1.seq.size()+s2.seq.size());
 830
 831         bool needs_further_processing=false;
 832
 833         while (first1!=last1 && first2!=last2) {
 834                 int cmpval = (*first1).rest.compare((*first2).rest);
 835                 if (cmpval==0) {
 836                         // combine terms
 837                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 838                                                    add(ex_to<numeric>(first2->coeff));
 839                         if (!newcoeff.is_zero()) {
 840                                 seq.push_back(expair(first1->rest,newcoeff));
 841                                 if (expair_needs_further_processing(seq.end()-1)) {
 842                                         needs_further_processing = true;
 843                                 }
 844                         }
 845                         ++first1;
 846                         ++first2;
 847                 } else if (cmpval<0) {
 848                         seq.push_back(*first1);
 849                         ++first1;
 850                 } else {
 851                         seq.push_back(*first2);
 852                         ++first2;
 853                 }
 854         }
 855
 856         while (first1!=last1) {
 857                 seq.push_back(*first1);
 858                 ++first1;
 859         }
 860         while (first2!=last2) {
 861                 seq.push_back(*first2);
 862                 ++first2;
 863         }
 864
 865         if (needs_further_processing) {
 866                 epvector v = seq;
 867                 seq.clear();
 868                 construct_from_epvector(v);
 869         }
 870 }
 871
 872 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 873                                                                                         const ex &e)
 874 {
 875         combine_overall_coeff(s.overall_coeff);
 876         if (is_exactly_a<numeric>(e)) {
 877                 combine_overall_coeff(e);
 878                 seq = s.seq;
 879                 return;
 880         }
 881
 882         epvector::const_iterator first = s.seq.begin();
 883         epvector::const_iterator last = s.seq.end();
 884         expair p = split_ex_to_pair(e);
 885
 886         seq.reserve(s.seq.size()+1);
 887         bool p_pushed = false;
 888
 889         bool needs_further_processing=false;
 890
 891         // merge p into s.seq
 892         while (first!=last) {
 893                 int cmpval = (*first).rest.compare(p.rest);
 894                 if (cmpval==0) {
 895                         // combine terms
 896                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 897                                                    add(ex_to<numeric>(p.coeff));
 898                         if (!newcoeff.is_zero()) {
 899                                 seq.push_back(expair(first->rest,newcoeff));
 900                                 if (expair_needs_further_processing(seq.end()-1))
 901                                         needs_further_processing = true;
 902                         }
 903                         ++first;
 904                         p_pushed = true;
 905                         break;
 906                 } else if (cmpval<0) {
 907                         seq.push_back(*first);
 908                         ++first;
 909                 } else {
 910                         seq.push_back(p);
 911                         p_pushed = true;
 912                         break;
 913                 }
 914         }
 915
 916         if (p_pushed) {
 917                 // while loop exited because p was pushed, now push rest of s.seq
 918                 while (first!=last) {
 919                         seq.push_back(*first);
 920                         ++first;
 921                 }
 922         } else {
 923                 // while loop exited because s.seq was pushed, now push p
 924                 seq.push_back(p);
 925         }
 926
 927         if (needs_further_processing) {
 928                 epvector v = seq;
 929                 seq.clear();
 930                 construct_from_epvector(v);
 931         }
 932 }
 933
 934 void expairseq::construct_from_exvector(const exvector &v)
 935 {
 936         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 937         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 938         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 939         //                  (same for (+,*) -> (*,^)
 940
 941         make_flat(v);
 942 #if EXPAIRSEQ_USE_HASHTAB
 943         combine_same_terms();
 944 #else
 945         canonicalize();
 946         combine_same_terms_sorted_seq();
 947 #endif // EXPAIRSEQ_USE_HASHTAB
 948 }
 949
 950 void expairseq::construct_from_epvector(const epvector &v)
 951 {
 952         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 953         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 954         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 955         //                  (same for (+,*) -> (*,^)
 956
 957         make_flat(v);
 958 #if EXPAIRSEQ_USE_HASHTAB
 959         combine_same_terms();
 960 #else
 961         canonicalize();
 962         combine_same_terms_sorted_seq();
 963 #endif // EXPAIRSEQ_USE_HASHTAB
 964 }
 965
 966 /** Combine this expairseq with argument exvector.
 967  *  It cares for associativity as well as for special handling of numerics. */
 968 void expairseq::make_flat(const exvector &v)
 969 {
 970         exvector::const_iterator cit;
 971
 972         // count number of operands which are of same expairseq derived type
 973         // and their cumulative number of operands
 974         int nexpairseqs = 0;
 975         int noperands = 0;
 976
 977         cit = v.begin();
 978         while (cit!=v.end()) {
 979                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 980                         ++nexpairseqs;
 981                         noperands += ex_to<expairseq>(*cit).seq.size();
 982                 }
 983                 ++cit;
 984         }
 985
 986         // reserve seq and coeffseq which will hold all operands
 987         seq.reserve(v.size()+noperands-nexpairseqs);
 988
 989         // copy elements and split off numerical part
 990         cit = v.begin();
 991         while (cit!=v.end()) {
 992                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 993                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 994                         combine_overall_coeff(subseqref.overall_coeff);
 995                         epvector::const_iterator cit_s = subseqref.seq.begin();
 996                         while (cit_s!=subseqref.seq.end()) {
 997                                 seq.push_back(*cit_s);
 998                                 ++cit_s;
 999                         }
1000                 } else {
1001                         if (is_exactly_a<numeric>(*cit))
1002                                 combine_overall_coeff(*cit);
1003                         else
1004                                 seq.push_back(split_ex_to_pair(*cit));
1005                 }
1006                 ++cit;
1007         }
1008 }
1009
1010 /** Combine this expairseq with argument epvector.
1011  *  It cares for associativity as well as for special handling of numerics. */
1012 void expairseq::make_flat(const epvector &v)
1013 {
1014         epvector::const_iterator cit;
1015
1016         // count number of operands which are of same expairseq derived type
1017         // and their cumulative number of operands
1018         int nexpairseqs = 0;
1019         int noperands = 0;
1020
1021         cit = v.begin();
1022         while (cit!=v.end()) {
1023                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1024                         ++nexpairseqs;
1025                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1026                 }
1027                 ++cit;
1028         }
1029
1030         // reserve seq and coeffseq which will hold all operands
1031         seq.reserve(v.size()+noperands-nexpairseqs);
1032
1033         // copy elements and split off numerical part
1034         cit = v.begin();
1035         while (cit!=v.end()) {
1036                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1037                     this->can_make_flat(*cit)) {
1038                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1039                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1040                                                             ex_to<numeric>(cit->coeff));
1041                         epvector::const_iterator cit_s = subseqref.seq.begin();
1042                         while (cit_s!=subseqref.seq.end()) {
1043                                 seq.push_back(expair(cit_s->rest,
1044                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1045                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1046                                 //                                              (*cit).coeff));
1047                                 ++cit_s;
1048                         }
1049                 } else {
1050                         if (cit->is_canonical_numeric())
1051                                 combine_overall_coeff(cit->rest);
1052                         else
1053                                 seq.push_back(*cit);
1054                 }
1055                 ++cit;
1056         }
1057 }
1058
1059 /** Brings this expairseq into a sorted (canonical) form. */
1060 void expairseq::canonicalize(void)
1061 {
1062         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1063 }
1064
1065
1066 /** Compact a presorted expairseq by combining all matching expairs to one
1067  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1068  *  instance. */
1069 void expairseq::combine_same_terms_sorted_seq(void)
1070 {
1071         if (seq.size()<2)
1072                 return;
1073
1074         bool needs_further_processing = false;
1075
1076         epvector::iterator itin1 = seq.begin();
1077         epvector::iterator itin2 = itin1+1;
1078         epvector::iterator itout = itin1;
1079         epvector::iterator last = seq.end();
1080         // must_copy will be set to true the first time some combination is
1081         // possible from then on the sequence has changed and must be compacted
1082         bool must_copy = false;
1083         while (itin2!=last) {
1084                 if (itin1->rest.compare(itin2->rest)==0) {
1085                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1086                                        add_dyn(ex_to<numeric>(itin2->coeff));
1087                         if (expair_needs_further_processing(itin1))
1088                                 needs_further_processing = true;
1089                         must_copy = true;
1090                 } else {
1091                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1092                                 if (must_copy)
1093                                         *itout = *itin1;
1094                                 ++itout;
1095                         }
1096                         itin1 = itin2;
1097                 }
1098                 ++itin2;
1099         }
1100         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1101                 if (must_copy)
1102                         *itout = *itin1;
1103                 ++itout;
1104         }
1105         if (itout!=last)
1106                 seq.erase(itout,last);
1107
1108         if (needs_further_processing) {
1109                 epvector v = seq;
1110                 seq.clear();
1111                 construct_from_epvector(v);
1112         }
1113 }
1114
1115 #if EXPAIRSEQ_USE_HASHTAB
1116
1117 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1118 {
1119         unsigned size;
1120         unsigned nearest_power_of_2 = 1 << log2(sz);
1121         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1122         //  size = nearest_power_of_2*hashtabfactor;
1123         size = nearest_power_of_2/hashtabfactor;
1124         if (size<minhashtabsize)
1125                 return 0;
1126
1127         // hashtabsize must be a power of 2
1128         GINAC_ASSERT((1U << log2(size))==size);
1129         return size;
1130 }
1131
1132 unsigned expairseq::calc_hashindex(const ex &e) const
1133 {
1134         // calculate hashindex
1135         unsigned hashindex;
1136         if (is_a<numeric>(e)) {
1137                 hashindex = hashmask;
1138         } else {
1139                 hashindex = e.gethash() & hashmask;
1140                 // last hashtab entry is reserved for numerics
1141                 if (hashindex==hashmask) hashindex = 0;
1142         }
1143         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1144         return hashindex;
1145 }
1146
1147 void expairseq::shrink_hashtab(void)
1148 {
1149         unsigned new_hashtabsize;
1150         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1151                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1152                 if (new_hashtabsize==0) {
1153                         hashtab.clear();
1154                         hashtabsize = 0;
1155                         canonicalize();
1156                         return;
1157                 }
1158
1159                 // shrink by a factor of 2
1160                 unsigned half_hashtabsize = hashtabsize/2;
1161                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1162                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1163                 // special treatment for numeric hashes
1164                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1165                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1166                 hashtab.resize(half_hashtabsize);
1167                 hashtabsize = half_hashtabsize;
1168                 hashmask = hashtabsize-1;
1169         }
1170 }
1171
1172 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1173 {
1174         if (hashtabsize==0)
1175                 return; // nothing to do
1176
1177         // calculate hashindex of element to be deleted
1178         unsigned hashindex = calc_hashindex((*element).rest);
1179
1180         // find it in hashtab and remove it
1181         epplist &eppl = hashtab[hashindex];
1182         epplist::iterator epplit = eppl.begin();
1183         bool erased = false;
1184         while (epplit!=eppl.end()) {
1185                 if (*epplit == element) {
1186                         eppl.erase(epplit);
1187                         erased = true;
1188                         break;
1189                 }
1190                 ++epplit;
1191         }
1192         if (!erased) {
1193                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1194                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1195
1196                 unsigned hashindex = calc_hashindex(element->rest);
1197                 epplist &eppl = hashtab[hashindex];
1198                 epplist::iterator epplit = eppl.begin();
1199                 bool erased = false;
1200                 while (epplit!=eppl.end()) {
1201                         if (*epplit == element) {
1202                                 eppl.erase(epplit);
1203                                 erased = true;
1204                                 break;
1205                         }
1206                         ++epplit;
1207                 }
1208                 GINAC_ASSERT(erased);
1209         }
1210         GINAC_ASSERT(erased);
1211 }
1212
1213 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1214                                    epvector::iterator newpos)
1215 {
1216         GINAC_ASSERT(hashtabsize!=0);
1217
1218         // calculate hashindex of element which was moved
1219         unsigned hashindex=calc_hashindex((*newpos).rest);
1220
1221         // find it in hashtab and modify it
1222         epplist &eppl = hashtab[hashindex];
1223         epplist::iterator epplit = eppl.begin();
1224         while (epplit!=eppl.end()) {
1225                 if (*epplit == oldpos) {
1226                         *epplit = newpos;
1227                         break;
1228                 }
1229                 ++epplit;
1230         }
1231         GINAC_ASSERT(epplit!=eppl.end());
1232 }
1233
1234 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1235 {
1236         epplist::const_iterator current = eppl.begin();
1237         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1238                 ++current;
1239         }
1240         eppl.insert(current,elem);
1241 }
1242
1243 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1244                                           epvector::iterator &last_non_zero,
1245                                           std::vector<bool> &touched,
1246                                           unsigned &number_of_zeroes)
1247 {
1248         epp current = seq.begin();
1249
1250         while (current!=first_numeric) {
1251                 if (is_exactly_a<numeric>(current->rest)) {
1252                         --first_numeric;
1253                         iter_swap(current,first_numeric);
1254                 } else {
1255                         // calculate hashindex
1256                         unsigned currenthashindex = calc_hashindex(current->rest);
1257
1258                         // test if there is already a matching expair in the hashtab-list
1259                         epplist &eppl=hashtab[currenthashindex];
1260                         epplist::iterator epplit = eppl.begin();
1261                         while (epplit!=eppl.end()) {
1262                                 if (current->rest.is_equal((*epplit)->rest))
1263                                         break;
1264                                 ++epplit;
1265                         }
1266                         if (epplit==eppl.end()) {
1267                                 // no matching expair found, append this to end of list
1268                                 sorted_insert(eppl,current);
1269                                 ++current;
1270                         } else {
1271                                 // epplit points to a matching expair, combine it with current
1272                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1273                                                    add_dyn(ex_to<numeric>(current->coeff));
1274
1275                                 // move obsolete current expair to end by swapping with last_non_zero element
1276                                 // if this was a numeric, it is swapped with the expair before first_numeric
1277                                 iter_swap(current,last_non_zero);
1278                                 --first_numeric;
1279                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1280                                 --last_non_zero;
1281                                 ++number_of_zeroes;
1282                                 // test if combined term has coeff 0 and can be removed is done later
1283                                 touched[(*epplit)-seq.begin()] = true;
1284                         }
1285                 }
1286         }
1287 }
1288
1289 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1290                                    epvector::iterator &last_non_zero,
1291                                    std::vector<bool> &touched,
1292                                    unsigned &number_of_zeroes)
1293 {
1294         // move terms with coeff 0 to end and remove them from hashtab
1295         // check only those elements which have been touched
1296         epp current = seq.begin();
1297         size_t i = 0;
1298         while (current!=first_numeric) {
1299                 if (!touched[i]) {
1300                         ++current;
1301                         ++i;
1302                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1303                         ++current;
1304                         ++i;
1305                 } else {
1306                         remove_hashtab_entry(current);
1307
1308                         // move element to the end, unless it is already at the end
1309                         if (current!=last_non_zero) {
1310                                 iter_swap(current,last_non_zero);
1311                                 --first_numeric;
1312                                 bool numeric_swapped = first_numeric!=last_non_zero;
1313                                 if (numeric_swapped)
1314                                         iter_swap(first_numeric,current);
1315                                 epvector::iterator changed_entry;
1316
1317                                 if (numeric_swapped)
1318                                         changed_entry = first_numeric;
1319                                 else
1320                                         changed_entry = last_non_zero;
1321
1322                                 --last_non_zero;
1323                                 ++number_of_zeroes;
1324
1325                                 if (first_numeric!=current) {
1326
1327                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1328                                         move_hashtab_entry(changed_entry,current);
1329                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1330                                 }
1331                         } else {
1332                                 --first_numeric;
1333                                 --last_non_zero;
1334                                 ++number_of_zeroes;
1335                         }
1336                 }
1337         }
1338         GINAC_ASSERT(i==current-seq.begin());
1339 }
1340
1341 /** True if one of the coeffs vanishes, otherwise false.
1342  *  This would be an invariant violation, so this should only be used for
1343  *  debugging purposes. */
1344 bool expairseq::has_coeff_0(void) const
1345 {
1346         epvector::const_iterator i = seq.begin(), end = seq.end();
1347         while (i != end) {
1348                 if (i->coeff.is_zero())
1349                         return true;
1350                 ++i;
1351         }
1352         return false;
1353 }
1354
1355 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1356                                                                                 epvector::const_iterator last_non_zero)
1357 {
1358         if (first_numeric == seq.end()) return; // no numerics
1359
1360         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1361         while (current != last) {
1362                 sorted_insert(hashtab[hashmask], current);
1363                 ++current;
1364         }
1365 }
1366
1367 void expairseq::combine_same_terms(void)
1368 {
1369         // combine same terms, drop term with coeff 0, move numerics to end
1370
1371         // calculate size of hashtab
1372         hashtabsize = calc_hashtabsize(seq.size());
1373
1374         // hashtabsize is a power of 2
1375         hashmask = hashtabsize-1;
1376
1377         // allocate hashtab
1378         hashtab.clear();
1379         hashtab.resize(hashtabsize);
1380
1381         if (hashtabsize==0) {
1382                 canonicalize();
1383                 combine_same_terms_sorted_seq();
1384                 GINAC_ASSERT(!has_coeff_0());
1385                 return;
1386         }
1387
1388         // iterate through seq, move numerics to end,
1389         // fill hashtab and combine same terms
1390         epvector::iterator first_numeric = seq.end();
1391         epvector::iterator last_non_zero = seq.end()-1;
1392
1393         size_t num = seq.size();
1394         std::vector<bool> touched(num);
1395
1396         unsigned number_of_zeroes = 0;
1397
1398         GINAC_ASSERT(!has_coeff_0());
1399         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1400
1401         // there should not be any terms with coeff 0 from the beginning,
1402         // so it should be safe to skip this step
1403         if (number_of_zeroes!=0) {
1404                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1405         }
1406
1407         add_numerics_to_hashtab(first_numeric,last_non_zero);
1408
1409         // pop zero elements
1410         for (unsigned i=0; i<number_of_zeroes; ++i) {
1411                 seq.pop_back();
1412         }
1413
1414         // shrink hashtabsize to calculated value
1415         GINAC_ASSERT(!has_coeff_0());
1416
1417         shrink_hashtab();
1418
1419         GINAC_ASSERT(!has_coeff_0());
1420 }
1421
1422 #endif // EXPAIRSEQ_USE_HASHTAB
1423
1424 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1425  *  debugging or in assertions since being sorted is an invariance. */
1426 bool expairseq::is_canonical() const
1427 {
1428         if (seq.size() <= 1)
1429                 return 1;
1430
1431 #if EXPAIRSEQ_USE_HASHTAB
1432         if (hashtabsize > 0) return 1; // not canoncalized
1433 #endif // EXPAIRSEQ_USE_HASHTAB
1434
1435         epvector::const_iterator it = seq.begin(), itend = seq.end();
1436         epvector::const_iterator it_last = it;
1437         for (++it; it!=itend; it_last=it, ++it) {
1438                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1439                         if (!is_exactly_a<numeric>(it_last->rest) ||
1440                                 !is_exactly_a<numeric>(it->rest)) {
1441                                 // double test makes it easier to set a breakpoint...
1442                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1443                                         !is_exactly_a<numeric>(it->rest)) {
1444                                         printpair(std::clog, *it_last, 0);
1445                                         std::clog << ">";
1446                                         printpair(std::clog, *it, 0);
1447                                         std::clog << "\n";
1448                                         std::clog << "pair1:" << std::endl;
1449                                         it_last->rest.print(print_tree(std::clog));
1450                                         it_last->coeff.print(print_tree(std::clog));
1451                                         std::clog << "pair2:" << std::endl;
1452                                         it->rest.print(print_tree(std::clog));
1453                                         it->coeff.print(print_tree(std::clog));
1454                                         return 0;
1455                                 }
1456                         }
1457                 }
1458         }
1459         return 1;
1460 }
1461
1462
1463 /** Member-wise expand the expairs in this sequence.
1464  *
1465  *  @see expairseq::expand()
1466  *  @return pointer to epvector containing expanded pairs or zero pointer,
1467  *  if no members were changed. */
1468 epvector * expairseq::expandchildren(unsigned options) const
1469 {
1470         const epvector::const_iterator last = seq.end();
1471         epvector::const_iterator cit = seq.begin();
1472         while (cit!=last) {
1473                 const ex &expanded_ex = cit->rest.expand(options);
1474                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1475
1476                         // something changed, copy seq, eval and return it
1477                         epvector *s = new epvector;
1478                         s->reserve(seq.size());
1479
1480                         // copy parts of seq which are known not to have changed
1481                         epvector::const_iterator cit2 = seq.begin();
1482                         while (cit2!=cit) {
1483                                 s->push_back(*cit2);
1484                                 ++cit2;
1485                         }
1486                         // copy first changed element
1487                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1488                                                                    cit2->coeff));
1489                         ++cit2;
1490                         // copy rest
1491                         while (cit2!=last) {
1492                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1493                                                                            cit2->coeff));
1494                                 ++cit2;
1495                         }
1496                         return s;
1497                 }
1498                 ++cit;
1499         }
1500
1501         return 0; // signalling nothing has changed
1502 }
1503
1504
1505 /** Member-wise evaluate the expairs in this sequence.
1506  *
1507  *  @see expairseq::eval()
1508  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1509  *  if no members were changed. */
1510 epvector * expairseq::evalchildren(int level) const
1511 {
1512         // returns a NULL pointer if nothing had to be evaluated
1513         // returns a pointer to a newly created epvector otherwise
1514         // (which has to be deleted somewhere else)
1515
1516         if (level==1)
1517                 return 0;
1518
1519         if (level == -max_recursion_level)
1520                 throw(std::runtime_error("max recursion level reached"));
1521
1522         --level;
1523         epvector::const_iterator last = seq.end();
1524         epvector::const_iterator cit = seq.begin();
1525         while (cit!=last) {
1526                 const ex &evaled_ex = cit->rest.eval(level);
1527                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1528
1529                         // something changed, copy seq, eval and return it
1530                         epvector *s = new epvector;
1531                         s->reserve(seq.size());
1532
1533                         // copy parts of seq which are known not to have changed
1534                         epvector::const_iterator cit2=seq.begin();
1535                         while (cit2!=cit) {
1536                                 s->push_back(*cit2);
1537                                 ++cit2;
1538                         }
1539                         // copy first changed element
1540                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1541                                                                    cit2->coeff));
1542                         ++cit2;
1543                         // copy rest
1544                         while (cit2!=last) {
1545                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1546                                                                            cit2->coeff));
1547                                 ++cit2;
1548                         }
1549                         return s;
1550                 }
1551                 ++cit;
1552         }
1553
1554         return 0; // signalling nothing has changed
1555 }
1556
1557
1558 /** Member-wise substitute in this sequence.
1559  *
1560  *  @see expairseq::subs()
1561  *  @return pointer to epvector containing pairs after application of subs,
1562  *    or NULL pointer if no members were changed. */
1563 epvector * expairseq::subschildren(const lst &ls, const lst &lr, unsigned options) const
1564 {
1565         GINAC_ASSERT(ls.nops()==lr.nops());
1566
1567         // When any of the objects to be substituted is a product or power
1568         // we have to recombine the pairs because the numeric coefficients may
1569         // be part of the search pattern.
1570         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1571
1572                 // Search the list of substitutions and cache our findings
1573                 for (lst::const_iterator it = ls.begin(); it != ls.end(); ++it) {
1574                         if (is_exactly_a<mul>(*it) || is_exactly_a<power>(*it)) {
1575                                 options |= subs_options::pattern_is_product;
1576                                 break;
1577                         }
1578                 }
1579                 if (!(options & subs_options::pattern_is_product))
1580                         options |= subs_options::pattern_is_not_product;
1581         }
1582
1583         if (options & subs_options::pattern_is_product) {
1584
1585                 // Substitute in the recombined pairs
1586                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1587                 while (cit != last) {
1588
1589                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1590                         const ex &subsed_ex = orig_ex.subs(ls, lr, options);
1591                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1592
1593                                 // Something changed, copy seq, subs and return it
1594                                 epvector *s = new epvector;
1595                                 s->reserve(seq.size());
1596
1597                                 // Copy parts of seq which are known not to have changed
1598                                 s->insert(s->begin(), seq.begin(), cit);
1599
1600                                 // Copy first changed element
1601                                 s->push_back(split_ex_to_pair(subsed_ex));
1602                                 ++cit;
1603
1604                                 // Copy rest
1605                                 while (cit != last) {
1606                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, options)));
1607                                         ++cit;
1608                                 }
1609                                 return s;
1610                         }
1611
1612                         ++cit;
1613                 }
1614
1615         } else {
1616
1617                 // Substitute only in the "rest" part of the pairs
1618                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1619                 while (cit != last) {
1620
1621                         const ex &subsed_ex = cit->rest.subs(ls, lr, options);
1622                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1623
1624                                 // Something changed, copy seq, subs and return it
1625                                 epvector *s = new epvector;
1626                                 s->reserve(seq.size());
1627
1628                                 // Copy parts of seq which are known not to have changed
1629                                 s->insert(s->begin(), seq.begin(), cit);
1630
1631                                 // Copy first changed element
1632                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1633                                 ++cit;
1634
1635                                 // Copy rest
1636                                 while (cit != last) {
1637                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, options),
1638                                                                                    cit->coeff));
1639                                         ++cit;
1640                                 }
1641                                 return s;
1642                         }
1643
1644                         ++cit;
1645                 }
1646         }
1647
1648         // Nothing has changed
1649         return NULL;
1650 }
1651
1652 //////////
1653 // static member variables
1654 //////////
1655
1656 #if EXPAIRSEQ_USE_HASHTAB
1657 unsigned expairseq::maxhashtabsize = 0x4000000U;
1658 unsigned expairseq::minhashtabsize = 0x1000U;
1659 unsigned expairseq::hashtabfactor = 1;
1660 #endif // EXPAIRSEQ_USE_HASHTAB
1661
1662 } // namespace GiNaC