ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <algorithm>
  24 #include <string>
  25 #include <stdexcept>
  26
  27 #include "expairseq.h"
  28 #include "lst.h"
  29 #include "archive.h"
  30 #include "debugmsg.h"
  31 #include "utils.h"
  32
  33 #if EXPAIRSEQ_USE_HASHTAB
  34 #include <cmath>
  35 #endif // EXPAIRSEQ_USE_HASHTAB
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  40
  41 //////////
  42 // helper classes
  43 //////////
  44
  45 class epp_is_less
  46 {
  47 public:
  48         bool operator()(const epp &lh, const epp &rh) const
  49         {
  50                 return (*lh).is_less(*rh);
  51         }
  52 };
  53
  54 //////////
  55 // default ctor, dtor, copy ctor assignment operator and helpers
  56 //////////
  57
  58 // public
  59
  60 expairseq::expairseq(const expairseq &other)
  61 {
  62         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
  63         copy(other);
  64 }
  65
  66 const expairseq &expairseq::operator=(const expairseq &other)
  67 {
  68         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  69         if (this != &other) {
  70                 destroy(true);
  71                 copy(other);
  72         }
  73         return *this;
  74 }
  75
  76 // protected
  77
  78 /** For use by copy ctor and assignment operator. */
  79 void expairseq::copy(const expairseq &other)
  80 {
  81         inherited::copy(other);
  82         seq = other.seq;
  83         overall_coeff = other.overall_coeff;
  84 #if EXPAIRSEQ_USE_HASHTAB
  85         // copy hashtab
  86         hashtabsize = other.hashtabsize;
  87         if (hashtabsize!=0) {
  88                 hashmask = other.hashmask;
  89                 hashtab.resize(hashtabsize);
  90                 epvector::const_iterator osb = other.seq.begin();
  91                 for (unsigned i=0; i<hashtabsize; ++i) {
  92                         hashtab[i].clear();
  93                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  94                              cit!=other.hashtab[i].end(); ++cit) {
  95                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  96                         }
  97                 }
  98         } else {
  99                 hashtab.clear();
 100         }
 101 #endif // EXPAIRSEQ_USE_HASHTAB
 102 }
 103
 104 void expairseq::destroy(bool call_parent)
 105 {
 106         if (call_parent)
 107                 basic::destroy(call_parent);
 108 }
 109
 110 //////////
 111 // other ctors
 112 //////////
 113
 114 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 115 {
 116         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 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         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 124         construct_from_exvector(v);
 125         GINAC_ASSERT(is_canonical());
 126 }
 127
 128 expairseq::expairseq(const epvector &v, const ex &oc)
 129   : inherited(TINFO_expairseq), overall_coeff(oc)
 130 {
 131         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 132         construct_from_epvector(v);
 133         GINAC_ASSERT(is_canonical());
 134 }
 135
 136 expairseq::expairseq(epvector *vp, const ex &oc)
 137   : inherited(TINFO_expairseq), overall_coeff(oc)
 138 {
 139         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 140         GINAC_ASSERT(vp!=0);
 141         construct_from_epvector(*vp);
 142         delete vp;
 143         GINAC_ASSERT(is_canonical());
 144 }
 145
 146 //////////
 147 // archiving
 148 //////////
 149
 150 /** Construct object from archive_node. */
 151 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 152 #if EXPAIRSEQ_USE_HASHTAB
 153         , hashtabsize(0)
 154 #endif
 155 {
 156         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
 157         for (unsigned int i=0; true; i++) {
 158                 ex rest;
 159                 ex coeff;
 160                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 161                         seq.push_back(expair(rest, coeff));
 162                 else
 163                         break;
 164         }
 165         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 166 }
 167
 168 /** Unarchive the object. */
 169 ex expairseq::unarchive(const archive_node &n, const lst &sym_lst)
 170 {
 171         return (new expairseq(n, sym_lst))->setflag(status_flags::dynallocated);
 172 }
 173
 174 /** Archive the object. */
 175 void expairseq::archive(archive_node &n) const
 176 {
 177         inherited::archive(n);
 178         epvector::const_iterator i = seq.begin(), iend = seq.end();
 179         while (i != iend) {
 180                 n.add_ex("rest", i->rest);
 181                 n.add_ex("coeff", i->coeff);
 182                 ++i;
 183         }
 184         n.add_ex("overall_coeff", overall_coeff);
 185 }
 186
 187 //////////
 188 // functions overriding virtual functions from bases classes
 189 //////////
 190
 191 // public
 192
 193 basic *expairseq::duplicate() const
 194 {
 195         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 196         return new expairseq(*this);
 197 }
 198
 199 void expairseq::print(std::ostream &os, unsigned upper_precedence) const
 200 {
 201         debugmsg("expairseq print",LOGLEVEL_PRINT);
 202         os << "[[";
 203         printseq(os,',',precedence,upper_precedence);
 204         os << "]]";
 205 }
 206
 207 void expairseq::printraw(std::ostream &os) const
 208 {
 209         debugmsg("expairseq printraw",LOGLEVEL_PRINT);
 210         os << class_name() << "(";
 211         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 212                 os << "(";
 213                 (*cit).rest.printraw(os);
 214                 os << ",";
 215                 (*cit).coeff.printraw(os);
 216                 os << "),";
 217         }
 218         os << ")";
 219 }
 220
 221 void expairseq::printtree(std::ostream &os, unsigned indent) const
 222 {
 223         debugmsg("expairseq printtree",LOGLEVEL_PRINT);
 224
 225         os << std::string(indent,' ') << "type=" << class_name()
 226            << ", hash=" << hashvalue
 227            << " (0x" << std::hex << hashvalue << std::dec << ")"
 228            << ", flags=" << flags
 229            << ", nops=" << nops() << std::endl;
 230         for (unsigned i=0; i<seq.size(); ++i) {
 231                 seq[i].rest.printtree(os,indent+delta_indent);
 232                 seq[i].coeff.printtree(os,indent+delta_indent);
 233                 if (i!=seq.size()-1)
 234                         os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
 235         }
 236         if (!overall_coeff.is_equal(default_overall_coeff())) {
 237                 os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
 238                 os << std::string(indent+delta_indent,' ') << "overall_coeff" << std::endl;
 239                 overall_coeff.printtree(os,indent+delta_indent);
 240         }
 241         os << std::string(indent+delta_indent,' ') << "=====" << std::endl;
 242 #if EXPAIRSEQ_USE_HASHTAB
 243         os << std::string(indent+delta_indent,' ')
 244            << "hashtab size " << hashtabsize << std::endl;
 245         if (hashtabsize==0) return;
 246 #define MAXCOUNT 5
 247         unsigned count[MAXCOUNT+1];
 248         for (int i=0; i<MAXCOUNT+1; ++i)
 249                 count[i] = 0;
 250         unsigned this_bin_fill;
 251         unsigned cum_fill_sq = 0;
 252         unsigned cum_fill = 0;
 253         for (unsigned i=0; i<hashtabsize; ++i) {
 254                 this_bin_fill = 0;
 255                 if (hashtab[i].size()>0) {
 256                         os << std::string(indent+delta_indent,' ')
 257                            << "bin " << i << " with entries ";
 258                         for (epplist::const_iterator it=hashtab[i].begin();
 259                              it!=hashtab[i].end(); ++it) {
 260                                 os << *it-seq.begin() << " ";
 261                                 ++this_bin_fill;
 262                         }
 263                         os << std::endl;
 264                         cum_fill += this_bin_fill;
 265                         cum_fill_sq += this_bin_fill*this_bin_fill;
 266                 }
 267                 if (this_bin_fill<MAXCOUNT)
 268                         ++count[this_bin_fill];
 269                 else
 270                         ++count[MAXCOUNT];
 271         }
 272         unsigned fact = 1;
 273         double cum_prob = 0;
 274         double lambda = (1.0*seq.size())/hashtabsize;
 275         for (int k=0; k<MAXCOUNT; ++k) {
 276                 if (k>0)
 277                         fact *= k;
 278                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 279                 cum_prob += prob;
 280                 os << std::string(indent+delta_indent,' ') << "bins with " << k << " entries: "
 281                    << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 282                    << int(prob*1000)/10.0 << ")" << std::endl;
 283         }
 284         os << std::string(indent+delta_indent,' ') << "bins with more entries: "
 285            << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 286            << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 287
 288         os << std::string(indent+delta_indent,' ') << "variance: "
 289            << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 290            << std::endl;
 291         os << std::string(indent+delta_indent,' ') << "average fill: "
 292            << (1.0*cum_fill)/hashtabsize
 293            << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 294 #endif // EXPAIRSEQ_USE_HASHTAB
 295 }
 296
 297 bool expairseq::info(unsigned inf) const
 298 {
 299         return inherited::info(inf);
 300 }
 301
 302 unsigned expairseq::nops() const
 303 {
 304         if (overall_coeff.is_equal(default_overall_coeff()))
 305                 return seq.size();
 306         else
 307                 return seq.size()+1;
 308 }
 309
 310 ex expairseq::op(int i) const
 311 {
 312         if (unsigned(i)<seq.size())
 313                 return recombine_pair_to_ex(seq[i]);
 314         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 315         return overall_coeff;
 316 }
 317
 318 ex &expairseq::let_op(int i)
 319 {
 320         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 321 }
 322
 323 ex expairseq::eval(int level) const
 324 {
 325         if ((level==1) && (flags &status_flags::evaluated))
 326                 return *this;
 327
 328         epvector *vp = evalchildren(level);
 329         if (vp==0)
 330                 return this->hold();
 331
 332         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 333 }
 334
 335 ex expairseq::evalf(int level) const
 336 {
 337         return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
 338 }
 339
 340 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 341 {
 342         ex n = thisexpairseq(normalchildren(level),overall_coeff);
 343         return n.bp->basic::normal(sym_lst,repl_lst,level);
 344 }
 345
 346 ex expairseq::subs(const lst &ls, const lst &lr) const
 347 {
 348         epvector *vp = subschildren(ls,lr);
 349         if (vp==0)
 350                 return *this;
 351
 352         return thisexpairseq(vp,overall_coeff);
 353 }
 354
 355 // protected
 356
 357 /** Implementation of ex::diff() for an expairseq.
 358  *  It differentiates all elements of the sequence.
 359  *  @see ex::diff */
 360 ex expairseq::derivative(const symbol &s) const
 361 {
 362         return thisexpairseq(diffchildren(s),overall_coeff);
 363 }
 364
 365 int expairseq::compare_same_type(const basic &other) const
 366 {
 367         GINAC_ASSERT(is_of_type(other, expairseq));
 368         const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
 369
 370         int cmpval;
 371
 372         // compare number of elements
 373         if (seq.size() != o.seq.size())
 374                 return (seq.size()<o.seq.size()) ? -1 : 1;
 375
 376         // compare overall_coeff
 377         cmpval = overall_coeff.compare(o.overall_coeff);
 378         if (cmpval!=0)
 379                 return cmpval;
 380
 381 #if EXPAIRSEQ_USE_HASHTAB
 382         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 383         if (hashtabsize==0) {
 384 #endif // EXPAIRSEQ_USE_HASHTAB
 385                 epvector::const_iterator cit1 = seq.begin();
 386                 epvector::const_iterator cit2 = o.seq.begin();
 387                 epvector::const_iterator last1 = seq.end();
 388                 epvector::const_iterator last2 = o.seq.end();
 389
 390                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 391                         cmpval = (*cit1).compare(*cit2);
 392                         if (cmpval!=0) return cmpval;
 393                 }
 394
 395                 GINAC_ASSERT(cit1==last1);
 396                 GINAC_ASSERT(cit2==last2);
 397
 398                 return 0;
 399 #if EXPAIRSEQ_USE_HASHTAB
 400         }
 401
 402         // compare number of elements in each hashtab entry
 403         for (unsigned i=0; i<hashtabsize; ++i) {
 404                 unsigned cursize=hashtab[i].size();
 405                 if (cursize != o.hashtab[i].size())
 406                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 407         }
 408
 409         // compare individual (sorted) hashtab entries
 410         for (unsigned i=0; i<hashtabsize; ++i) {
 411                 unsigned sz = hashtab[i].size();
 412                 if (sz>0) {
 413                         const epplist &eppl1 = hashtab[i];
 414                         const epplist &eppl2 = o.hashtab[i];
 415                         epplist::const_iterator it1 = eppl1.begin();
 416                         epplist::const_iterator it2 = eppl2.begin();
 417                         while (it1!=eppl1.end()) {
 418                                 cmpval = (*(*it1)).compare(*(*it2));
 419                                 if (cmpval!=0)
 420                                         return cmpval;
 421                                 ++it1;
 422                                 ++it2;
 423                         }
 424                 }
 425         }
 426
 427         return 0; // equal
 428 #endif // EXPAIRSEQ_USE_HASHTAB
 429 }
 430
 431 bool expairseq::is_equal_same_type(const basic &other) const
 432 {
 433         const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
 434
 435         // compare number of elements
 436         if (seq.size()!=o.seq.size())
 437                 return false;
 438
 439         // compare overall_coeff
 440         if (!overall_coeff.is_equal(o.overall_coeff))
 441                 return false;
 442
 443 #if EXPAIRSEQ_USE_HASHTAB
 444         // compare number of elements in each hashtab entry
 445         if (hashtabsize!=o.hashtabsize) {
 446                 std::cout << "this:" << std::endl;
 447                 printtree(std::cout,0);
 448                 std::cout << "other:" << std::endl;
 449                 other.printtree(std::cout,0);
 450         }
 451
 452         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 453
 454         if (hashtabsize==0) {
 455 #endif // EXPAIRSEQ_USE_HASHTAB
 456                 epvector::const_iterator cit1 = seq.begin();
 457                 epvector::const_iterator cit2 = o.seq.begin();
 458                 epvector::const_iterator last1 = seq.end();
 459
 460                 while (cit1!=last1) {
 461                         if (!(*cit1).is_equal(*cit2)) return false;
 462                         ++cit1;
 463                         ++cit2;
 464                 }
 465
 466                 return true;
 467 #if EXPAIRSEQ_USE_HASHTAB
 468         }
 469
 470         for (unsigned i=0; i<hashtabsize; ++i) {
 471                 if (hashtab[i].size() != o.hashtab[i].size())
 472                         return false;
 473         }
 474
 475         // compare individual sorted hashtab entries
 476         for (unsigned i=0; i<hashtabsize; ++i) {
 477                 unsigned sz = hashtab[i].size();
 478                 if (sz>0) {
 479                         const epplist &eppl1 = hashtab[i];
 480                         const epplist &eppl2 = o.hashtab[i];
 481                         epplist::const_iterator it1 = eppl1.begin();
 482                         epplist::const_iterator it2 = eppl2.begin();
 483                         while (it1!=eppl1.end()) {
 484                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 485                                 ++it1;
 486                                 ++it2;
 487                         }
 488                 }
 489         }
 490
 491         return true;
 492 #endif // EXPAIRSEQ_USE_HASHTAB
 493 }
 494
 495 unsigned expairseq::return_type(void) const
 496 {
 497         return return_types::noncommutative_composite;
 498 }
 499
 500 unsigned expairseq::calchash(void) const
 501 {
 502         unsigned v = golden_ratio_hash(tinfo());
 503         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 504 #if !EXPAIRSEQ_USE_HASHTAB
 505                 v = rotate_left_31(v); // rotation would spoil commutativity
 506 #endif // EXPAIRSEQ_USE_HASHTAB
 507                 v ^= cit->rest.gethash();
 508 #if !EXPAIRSEQ_USE_HASHTAB
 509                 v = rotate_left_31(v);
 510                 v ^= cit->coeff.gethash();
 511 #endif // EXPAIRSEQ_USE_HASHTAB
 512         }
 513
 514         v ^= overall_coeff.gethash();
 515         v &= 0x7FFFFFFFU;
 516
 517         // store calculated hash value only if object is already evaluated
 518         if (flags &status_flags::evaluated) {
 519                 setflag(status_flags::hash_calculated);
 520                 hashvalue = v;
 521         }
 522
 523         return v;
 524 }
 525
 526 ex expairseq::expand(unsigned options) const
 527 {
 528         epvector *vp = expandchildren(options);
 529         if (vp==0) {
 530                 // the terms have not changed, so it is safe to declare this expanded
 531                 setflag(status_flags::expanded);
 532                 return *this;
 533         }
 534
 535         return thisexpairseq(vp,overall_coeff);
 536 }
 537
 538 //////////
 539 // new virtual functions which can be overridden by derived classes
 540 //////////
 541
 542 // protected
 543
 544 /** Create an object of this type.
 545  *  This method works similar to a constructor.  It is useful because expairseq
 546  *  has (at least) two possible different semantics but we want to inherit
 547  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 548  *  has to create a new one of the same semantics, which cannot be done by a
 549  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 550  *  order for this trick to work a derived class must of course override this
 551  *  definition. */
 552 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 553 {
 554         return expairseq(v,oc);
 555 }
 556
 557 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 558 {
 559         return expairseq(vp,oc);
 560 }
 561
 562 void expairseq::printpair(std::ostream &os, const expair &p, unsigned upper_precedence) const
 563 {
 564         os << "[[";
 565         p.rest.bp->print(os,precedence);
 566         os << ",";
 567         p.coeff.bp->print(os,precedence);
 568         os << "]]";
 569 }
 570
 571 void expairseq::printseq(std::ostream &os, char delim,
 572                          unsigned this_precedence,
 573                          unsigned upper_precedence) const
 574 {
 575         if (this_precedence<=upper_precedence)
 576                 os << "(";
 577         epvector::const_iterator it,it_last;
 578         it_last=seq.end();
 579         --it_last;
 580         for (it=seq.begin(); it!=it_last; ++it) {
 581                 printpair(os,*it,this_precedence);
 582                 os << delim;
 583         }
 584         printpair(os,*it,this_precedence);
 585         if (!overall_coeff.is_equal(default_overall_coeff()))
 586                 os << delim << overall_coeff;
 587
 588         if (this_precedence<=upper_precedence)
 589                 os << ")";
 590 }
 591
 592
 593 /** Form an expair from an ex, using the corresponding semantics.
 594  *  @see expairseq::recombine_pair_to_ex() */
 595 expair expairseq::split_ex_to_pair(const ex &e) const
 596 {
 597         return expair(e,_ex1());
 598 }
 599
 600
 601 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 602                                                 const ex &c) const
 603 {
 604         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 605
 606         return expair(e,c);
 607 }
 608
 609
 610 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 611                                                   const ex &c) const
 612 {
 613         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 614         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 615
 616         return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 617 }
 618
 619
 620 /** Form an ex out of an expair, using the corresponding semantics.
 621  *  @see expairseq::split_ex_to_pair() */
 622 ex expairseq::recombine_pair_to_ex(const expair &p) const
 623 {
 624         return lst(p.rest,p.coeff);
 625 }
 626
 627 bool expairseq::expair_needs_further_processing(epp it)
 628 {
 629 #if EXPAIRSEQ_USE_HASHTAB
 630         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 631 #endif // EXPAIRSEQ_USE_HASHTAB
 632         return false;
 633 }
 634
 635 ex expairseq::default_overall_coeff(void) const
 636 {
 637         return _ex0();
 638 }
 639
 640 void expairseq::combine_overall_coeff(const ex &c)
 641 {
 642         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 643         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 644         overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 645 }
 646
 647 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 648 {
 649         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 650         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 651         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 652         overall_coeff = ex_to_numeric(overall_coeff).
 653                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 654 }
 655
 656 bool expairseq::can_make_flat(const expair &p) const
 657 {
 658         return true;
 659 }
 660
 661
 662 //////////
 663 // non-virtual functions in this class
 664 //////////
 665
 666 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 667 {
 668         exvector v;
 669         v.reserve(2);
 670         v.push_back(lh);
 671         v.push_back(rh);
 672         construct_from_exvector(v);
 673 #if EXPAIRSEQ_USE_HASHTAB
 674         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 675         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 676 #endif // EXPAIRSEQ_USE_HASHTAB
 677 }
 678
 679 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 680 {
 681         if (lh.bp->tinfo()==tinfo()) {
 682                 if (rh.bp->tinfo()==tinfo()) {
 683 #if EXPAIRSEQ_USE_HASHTAB
 684                         unsigned totalsize = ex_to_expairseq(lh).seq.size() +
 685                                              ex_to_expairseq(rh).seq.size();
 686                         if (calc_hashtabsize(totalsize)!=0) {
 687                                 construct_from_2_ex_via_exvector(lh,rh);
 688                         } else {
 689 #endif // EXPAIRSEQ_USE_HASHTAB
 690                                 construct_from_2_expairseq(ex_to_expairseq(lh),
 691                                                            ex_to_expairseq(rh));
 692 #if EXPAIRSEQ_USE_HASHTAB
 693                         }
 694 #endif // EXPAIRSEQ_USE_HASHTAB
 695                         return;
 696                 } else {
 697 #if EXPAIRSEQ_USE_HASHTAB
 698                         unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
 699                         if (calc_hashtabsize(totalsize)!=0) {
 700                                 construct_from_2_ex_via_exvector(lh, rh);
 701                         } else {
 702 #endif // EXPAIRSEQ_USE_HASHTAB
 703                                 construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
 704 #if EXPAIRSEQ_USE_HASHTAB
 705                         }
 706 #endif // EXPAIRSEQ_USE_HASHTAB
 707                         return;
 708                 }
 709         } else if (rh.bp->tinfo()==tinfo()) {
 710 #if EXPAIRSEQ_USE_HASHTAB
 711                 unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 712                 if (calc_hashtabsize(totalsize)!=0) {
 713                         construct_from_2_ex_via_exvector(lh,rh);
 714                 } else {
 715 #endif // EXPAIRSEQ_USE_HASHTAB
 716                         construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 717 #if EXPAIRSEQ_USE_HASHTAB
 718                 }
 719 #endif // EXPAIRSEQ_USE_HASHTAB
 720                 return;
 721         }
 722
 723 #if EXPAIRSEQ_USE_HASHTAB
 724         if (calc_hashtabsize(2)!=0) {
 725                 construct_from_2_ex_via_exvector(lh,rh);
 726                 return;
 727         }
 728         hashtabsize = 0;
 729 #endif // EXPAIRSEQ_USE_HASHTAB
 730
 731         if (is_ex_exactly_of_type(lh,numeric)) {
 732                 if (is_ex_exactly_of_type(rh,numeric)) {
 733                         combine_overall_coeff(lh);
 734                         combine_overall_coeff(rh);
 735                 } else {
 736                         combine_overall_coeff(lh);
 737                         seq.push_back(split_ex_to_pair(rh));
 738                 }
 739         } else {
 740                 if (is_ex_exactly_of_type(rh,numeric)) {
 741                         combine_overall_coeff(rh);
 742                         seq.push_back(split_ex_to_pair(lh));
 743                 } else {
 744                         expair p1 = split_ex_to_pair(lh);
 745                         expair p2 = split_ex_to_pair(rh);
 746
 747                         int cmpval = p1.rest.compare(p2.rest);
 748                         if (cmpval==0) {
 749                                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 750                                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 751                                         // no further processing is necessary, since this
 752                                         // one element will usually be recombined in eval()
 753                                         seq.push_back(p1);
 754                                 }
 755                         } else {
 756                                 seq.reserve(2);
 757                                 if (cmpval<0) {
 758                                         seq.push_back(p1);
 759                                         seq.push_back(p2);
 760                                 } else {
 761                                         seq.push_back(p2);
 762                                         seq.push_back(p1);
 763                                 }
 764                         }
 765                 }
 766         }
 767 }
 768
 769 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 770                                                                                    const expairseq &s2)
 771 {
 772         combine_overall_coeff(s1.overall_coeff);
 773         combine_overall_coeff(s2.overall_coeff);
 774
 775         epvector::const_iterator first1 = s1.seq.begin();
 776         epvector::const_iterator last1 = s1.seq.end();
 777         epvector::const_iterator first2 = s2.seq.begin();
 778         epvector::const_iterator last2 = s2.seq.end();
 779
 780         seq.reserve(s1.seq.size()+s2.seq.size());
 781
 782         bool needs_further_processing=false;
 783
 784         while (first1!=last1 && first2!=last2) {
 785                 int cmpval = (*first1).rest.compare((*first2).rest);
 786                 if (cmpval==0) {
 787                         // combine terms
 788                         const numeric &newcoeff = ex_to_numeric((*first1).coeff).
 789                                                    add(ex_to_numeric((*first2).coeff));
 790                         if (!newcoeff.is_zero()) {
 791                                 seq.push_back(expair((*first1).rest,newcoeff));
 792                                 if (expair_needs_further_processing(seq.end()-1)) {
 793                                         needs_further_processing = true;
 794                                 }
 795                         }
 796                         ++first1;
 797                         ++first2;
 798                 } else if (cmpval<0) {
 799                         seq.push_back(*first1);
 800                         ++first1;
 801                 } else {
 802                         seq.push_back(*first2);
 803                         ++first2;
 804                 }
 805         }
 806
 807         while (first1!=last1) {
 808                 seq.push_back(*first1);
 809                 ++first1;
 810         }
 811         while (first2!=last2) {
 812                 seq.push_back(*first2);
 813                 ++first2;
 814         }
 815
 816         if (needs_further_processing) {
 817                 epvector v = seq;
 818                 seq.clear();
 819                 construct_from_epvector(v);
 820         }
 821 }
 822
 823 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 824                                                                                         const ex &e)
 825 {
 826         combine_overall_coeff(s.overall_coeff);
 827         if (is_ex_exactly_of_type(e,numeric)) {
 828                 combine_overall_coeff(e);
 829                 seq = s.seq;
 830                 return;
 831         }
 832
 833         epvector::const_iterator first = s.seq.begin();
 834         epvector::const_iterator last = s.seq.end();
 835         expair p = split_ex_to_pair(e);
 836
 837         seq.reserve(s.seq.size()+1);
 838         bool p_pushed = false;
 839
 840         bool needs_further_processing=false;
 841
 842         // merge p into s.seq
 843         while (first!=last) {
 844                 int cmpval=(*first).rest.compare(p.rest);
 845                 if (cmpval==0) {
 846                         // combine terms
 847                         const numeric &newcoeff = ex_to_numeric((*first).coeff).
 848                                                    add(ex_to_numeric(p.coeff));
 849                         if (!newcoeff.is_zero()) {
 850                                 seq.push_back(expair((*first).rest,newcoeff));
 851                                 if (expair_needs_further_processing(seq.end()-1)) {
 852                                         needs_further_processing = true;
 853                                 }
 854                         }
 855                         ++first;
 856                         p_pushed = true;
 857                         break;
 858                 } else if (cmpval<0) {
 859                         seq.push_back(*first);
 860                         ++first;
 861                 } else {
 862                         seq.push_back(p);
 863                         p_pushed = true;
 864                         break;
 865                 }
 866         }
 867
 868         if (p_pushed) {
 869                 // while loop exited because p was pushed, now push rest of s.seq
 870                 while (first!=last) {
 871                         seq.push_back(*first);
 872                         ++first;
 873                 }
 874         } else {
 875                 // while loop exited because s.seq was pushed, now push p
 876                 seq.push_back(p);
 877         }
 878
 879         if (needs_further_processing) {
 880                 epvector v = seq;
 881                 seq.clear();
 882                 construct_from_epvector(v);
 883         }
 884 }
 885
 886 void expairseq::construct_from_exvector(const exvector &v)
 887 {
 888         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 889         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 890         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 891         //                  (same for (+,*) -> (*,^)
 892
 893         make_flat(v);
 894 #if EXPAIRSEQ_USE_HASHTAB
 895         combine_same_terms();
 896 #else
 897         canonicalize();
 898         combine_same_terms_sorted_seq();
 899 #endif // EXPAIRSEQ_USE_HASHTAB
 900         return;
 901 }
 902
 903 void expairseq::construct_from_epvector(const epvector &v)
 904 {
 905         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 906         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 907         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 908         //                  (same for (+,*) -> (*,^)
 909
 910         make_flat(v);
 911 #if EXPAIRSEQ_USE_HASHTAB
 912         combine_same_terms();
 913 #else
 914         canonicalize();
 915         combine_same_terms_sorted_seq();
 916 #endif // EXPAIRSEQ_USE_HASHTAB
 917         return;
 918 }
 919
 920 /** Combine this expairseq with argument exvector.
 921  *  It cares for associativity as well as for special handling of numerics. */
 922 void expairseq::make_flat(const exvector &v)
 923 {
 924         exvector::const_iterator cit;
 925
 926         // count number of operands which are of same expairseq derived type
 927         // and their cumulative number of operands
 928         int nexpairseqs = 0;
 929         int noperands = 0;
 930
 931         cit = v.begin();
 932         while (cit!=v.end()) {
 933                 if (cit->bp->tinfo()==this->tinfo()) {
 934                         ++nexpairseqs;
 935                         noperands += ex_to_expairseq(*cit).seq.size();
 936                 }
 937                 ++cit;
 938         }
 939
 940         // reserve seq and coeffseq which will hold all operands
 941         seq.reserve(v.size()+noperands-nexpairseqs);
 942
 943         // copy elements and split off numerical part
 944         cit = v.begin();
 945         while (cit!=v.end()) {
 946                 if (cit->bp->tinfo()==this->tinfo()) {
 947                         const expairseq &subseqref = ex_to_expairseq(*cit);
 948                         combine_overall_coeff(subseqref.overall_coeff);
 949                         epvector::const_iterator cit_s = subseqref.seq.begin();
 950                         while (cit_s!=subseqref.seq.end()) {
 951                                 seq.push_back(*cit_s);
 952                                 ++cit_s;
 953                         }
 954                 } else {
 955                         if (is_ex_exactly_of_type(*cit,numeric))
 956                                 combine_overall_coeff(*cit);
 957                         else
 958                                 seq.push_back(split_ex_to_pair(*cit));
 959                 }
 960                 ++cit;
 961         }
 962
 963         return;
 964 }
 965
 966 /** Combine this expairseq with argument epvector.
 967  *  It cares for associativity as well as for special handling of numerics. */
 968 void expairseq::make_flat(const epvector &v)
 969 {
 970         epvector::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 (cit->rest.bp->tinfo()==this->tinfo()) {
 980                         ++nexpairseqs;
 981                         noperands += ex_to_expairseq((*cit).rest).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 (cit->rest.bp->tinfo()==this->tinfo() &&
 993                     this->can_make_flat(*cit)) {
 994                         const expairseq &subseqref = ex_to_expairseq((*cit).rest);
 995                         combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 996                                                             ex_to_numeric((*cit).coeff));
 997                         epvector::const_iterator cit_s = subseqref.seq.begin();
 998                         while (cit_s!=subseqref.seq.end()) {
 999                                 seq.push_back(expair((*cit_s).rest,
1000                                                      ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
1001                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1002                                 //                                              (*cit).coeff));
1003                                 ++cit_s;
1004                         }
1005                 } else {
1006                         if (cit->is_canonical_numeric())
1007                                 combine_overall_coeff(cit->rest);
1008                         else
1009                                 seq.push_back(*cit);
1010                 }
1011                 ++cit;
1012         }
1013         return;
1014 }
1015
1016
1017 /** Brings this expairseq into a sorted (canonical) form. */
1018 void expairseq::canonicalize(void)
1019 {
1020         // canonicalize
1021         sort(seq.begin(),seq.end(),expair_is_less());
1022         return;
1023 }
1024
1025
1026 /** Compact a presorted expairseq by combining all matching expairs to one
1027  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1028  *  instance. */
1029 void expairseq::combine_same_terms_sorted_seq(void)
1030 {
1031         bool needs_further_processing = false;
1032
1033         if (seq.size()>1) {
1034                 epvector::iterator itin1 = seq.begin();
1035                 epvector::iterator itin2 = itin1+1;
1036                 epvector::iterator itout = itin1;
1037                 epvector::iterator last = seq.end();
1038                 // must_copy will be set to true the first time some combination is
1039                 // possible from then on the sequence has changed and must be compacted
1040                 bool must_copy = false;
1041                 while (itin2!=last) {
1042                         if ((*itin1).rest.compare((*itin2).rest)==0) {
1043                                 (*itin1).coeff = ex_to_numeric((*itin1).coeff).
1044                                                  add_dyn(ex_to_numeric((*itin2).coeff));
1045                                 if (expair_needs_further_processing(itin1))
1046                                         needs_further_processing = true;
1047                                 must_copy = true;
1048                         } else {
1049                                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1050                                         if (must_copy)
1051                                                 *itout = *itin1;
1052                                         ++itout;
1053                                 }
1054                                 itin1 = itin2;
1055                         }
1056                         ++itin2;
1057                 }
1058                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1059                         if (must_copy)
1060                                 *itout = *itin1;
1061                         ++itout;
1062                 }
1063                 if (itout!=last)
1064                         seq.erase(itout,last);
1065         }
1066
1067         if (needs_further_processing) {
1068                 epvector v = seq;
1069                 seq.clear();
1070                 construct_from_epvector(v);
1071         }
1072         return;
1073 }
1074
1075 #if EXPAIRSEQ_USE_HASHTAB
1076
1077 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1078 {
1079         unsigned size;
1080         unsigned nearest_power_of_2 = 1 << log2(sz);
1081         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1082         //  size = nearest_power_of_2*hashtabfactor;
1083         size = nearest_power_of_2/hashtabfactor;
1084         if (size<minhashtabsize)
1085                 return 0;
1086         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1087         // hashtabsize must be a power of 2
1088         GINAC_ASSERT((1U << log2(size))==size);
1089         return size;
1090 }
1091
1092 unsigned expairseq::calc_hashindex(const ex &e) const
1093 {
1094         // calculate hashindex
1095         unsigned hash = e.gethash();
1096         unsigned hashindex;
1097         if (is_a_numeric_hash(hash)) {
1098                 hashindex = hashmask;
1099         } else {
1100                 hashindex = hash &hashmask;
1101                 // last hashtab entry is reserved for numerics
1102                 if (hashindex==hashmask) hashindex = 0;
1103         }
1104         GINAC_ASSERT(hashindex>=0);
1105         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1106         return hashindex;
1107 }
1108
1109 void expairseq::shrink_hashtab(void)
1110 {
1111         unsigned new_hashtabsize;
1112         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1113                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1114                 if (new_hashtabsize==0) {
1115                         hashtab.clear();
1116                         hashtabsize = 0;
1117                         canonicalize();
1118                         return;
1119                 }
1120
1121                 // shrink by a factor of 2
1122                 unsigned half_hashtabsize = hashtabsize/2;
1123                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1124                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1125                 // special treatment for numeric hashes
1126                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1127                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1128                 hashtab.resize(half_hashtabsize);
1129                 hashtabsize = half_hashtabsize;
1130                 hashmask = hashtabsize-1;
1131         }
1132 }
1133
1134 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1135 {
1136         if (hashtabsize==0)
1137                 return; // nothing to do
1138
1139         // calculate hashindex of element to be deleted
1140         unsigned hashindex = calc_hashindex((*element).rest);
1141
1142         // find it in hashtab and remove it
1143         epplist &eppl = hashtab[hashindex];
1144         epplist::iterator epplit = eppl.begin();
1145         bool erased = false;
1146         while (epplit!=eppl.end()) {
1147                 if (*epplit == element) {
1148                         eppl.erase(epplit);
1149                         erased = true;
1150                         break;
1151                 }
1152                 ++epplit;
1153         }
1154         if (!erased) {
1155                 printtree(cout,0);
1156                 cout << "tried to erase " << element-seq.begin() << std::endl;
1157                 cout << "size " << seq.end()-seq.begin() << std::endl;
1158
1159                 unsigned hashindex = calc_hashindex((*element).rest);
1160                 epplist &eppl = hashtab[hashindex];
1161                 epplist::iterator epplit=eppl.begin();
1162                 bool erased=false;
1163                 while (epplit!=eppl.end()) {
1164                         if (*epplit == element) {
1165                                 eppl.erase(epplit);
1166                                 erased = true;
1167                                 break;
1168                         }
1169                         ++epplit;
1170                 }
1171                 GINAC_ASSERT(erased);
1172         }
1173         GINAC_ASSERT(erased);
1174 }
1175
1176 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1177                                    epvector::iterator newpos)
1178 {
1179         GINAC_ASSERT(hashtabsize!=0);
1180
1181         // calculate hashindex of element which was moved
1182         unsigned hashindex=calc_hashindex((*newpos).rest);
1183
1184         // find it in hashtab and modify it
1185         epplist &eppl = hashtab[hashindex];
1186         epplist::iterator epplit = eppl.begin();
1187         while (epplit!=eppl.end()) {
1188                 if (*epplit == oldpos) {
1189                         *epplit = newpos;
1190                         break;
1191                 }
1192                 ++epplit;
1193         }
1194         GINAC_ASSERT(epplit!=eppl.end());
1195 }
1196
1197 void expairseq::sorted_insert(epplist &eppl, epp elem)
1198 {
1199         epplist::iterator current = eppl.begin();
1200         while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1201                 ++current;
1202         }
1203         eppl.insert(current,elem);
1204 }
1205
1206 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1207                                           epvector::iterator &last_non_zero,
1208                                           vector<bool> &touched,
1209                                           unsigned &number_of_zeroes)
1210 {
1211         epp current=seq.begin();
1212
1213         while (current!=first_numeric) {
1214                 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1215                         --first_numeric;
1216                         iter_swap(current,first_numeric);
1217                 } else {
1218                         // calculate hashindex
1219                         unsigned currenthashindex = calc_hashindex((*current).rest);
1220
1221                         // test if there is already a matching expair in the hashtab-list
1222                         epplist &eppl=hashtab[currenthashindex];
1223                         epplist::iterator epplit = eppl.begin();
1224                         while (epplit!=eppl.end()) {
1225                                 if ((*current).rest.is_equal((*(*epplit)).rest))
1226                                         break;
1227                                 ++epplit;
1228                         }
1229                         if (epplit==eppl.end()) {
1230                                 // no matching expair found, append this to end of list
1231                                 sorted_insert(eppl,current);
1232                                 ++current;
1233                         } else {
1234                                 // epplit points to a matching expair, combine it with current
1235                                 (*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
1236                                                      add_dyn(ex_to_numeric((*current).coeff));
1237
1238                                 // move obsolete current expair to end by swapping with last_non_zero element
1239                                 // if this was a numeric, it is swapped with the expair before first_numeric
1240                                 iter_swap(current,last_non_zero);
1241                                 --first_numeric;
1242                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1243                                 --last_non_zero;
1244                                 ++number_of_zeroes;
1245                                 // test if combined term has coeff 0 and can be removed is done later
1246                                 touched[(*epplit)-seq.begin()]=true;
1247                         }
1248                 }
1249         }
1250 }
1251
1252 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1253                                    epvector::iterator &last_non_zero,
1254                                    vector<bool> &touched,
1255                                    unsigned &number_of_zeroes)
1256 {
1257         // move terms with coeff 0 to end and remove them from hashtab
1258         // check only those elements which have been touched
1259         epp current = seq.begin();
1260         unsigned i = 0;
1261         while (current!=first_numeric) {
1262                 if (!touched[i]) {
1263                         ++current;
1264                         ++i;
1265                 } else if (!ex_to_numeric((*current).coeff).is_zero()) {
1266                         ++current;
1267                         ++i;
1268                 } else {
1269                         remove_hashtab_entry(current);
1270
1271                         // move element to the end, unless it is already at the end
1272                         if (current!=last_non_zero) {
1273                                 iter_swap(current,last_non_zero);
1274                                 --first_numeric;
1275                                 bool numeric_swapped=first_numeric!=last_non_zero;
1276                                 if (numeric_swapped) iter_swap(first_numeric,current);
1277                                 epvector::iterator changed_entry;
1278
1279                                 if (numeric_swapped)
1280                                         changed_entry = first_numeric;
1281                                 else
1282                                         changed_entry = last_non_zero;
1283
1284                                 --last_non_zero;
1285                                 ++number_of_zeroes;
1286
1287                                 if (first_numeric!=current) {
1288
1289                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1290                                         move_hashtab_entry(changed_entry,current);
1291                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1292                                 }
1293                         } else {
1294                                 --first_numeric;
1295                                 --last_non_zero;
1296                                 ++number_of_zeroes;
1297                         }
1298                 }
1299         }
1300         GINAC_ASSERT(i==current-seq.begin());
1301 }
1302
1303 /** True if one of the coeffs vanishes, otherwise false.
1304  *  This would be an invariant violation, so this should only be used for
1305  *  debugging purposes. */
1306 bool expairseq::has_coeff_0(void) const
1307 {
1308         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1309                 if ((*cit).coeff.is_zero())
1310                         return true;
1311         }
1312         return false;
1313 }
1314
1315 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1316                                                                                 epvector::const_iterator last_non_zero)
1317 {
1318         if (first_numeric==seq.end()) return; // no numerics
1319
1320         epvector::iterator current = first_numeric;
1321         epvector::const_iterator last = last_non_zero+1;
1322         while (current!=last) {
1323                 sorted_insert(hashtab[hashmask],current);
1324                 ++current;
1325         }
1326 }
1327
1328 void expairseq::combine_same_terms(void)
1329 {
1330         // combine same terms, drop term with coeff 0, move numerics to end
1331
1332         // calculate size of hashtab
1333         hashtabsize = calc_hashtabsize(seq.size());
1334
1335         // hashtabsize is a power of 2
1336         hashmask = hashtabsize-1;
1337
1338         // allocate hashtab
1339         hashtab.clear();
1340         hashtab.resize(hashtabsize);
1341
1342         if (hashtabsize==0) {
1343                 canonicalize();
1344                 combine_same_terms_sorted_seq();
1345                 GINAC_ASSERT(!has_coeff_0());
1346                 return;
1347         }
1348
1349         // iterate through seq, move numerics to end,
1350         // fill hashtab and combine same terms
1351         epvector::iterator first_numeric = seq.end();
1352         epvector::iterator last_non_zero = seq.end()-1;
1353
1354         vector<bool> touched;
1355         touched.reserve(seq.size());
1356         for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1357
1358         unsigned number_of_zeroes = 0;
1359
1360         GINAC_ASSERT(!has_coeff_0());
1361         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1362         /*
1363         cout << "in combine:" << std::endl;
1364         printtree(cout,0);
1365         cout << "size=" << seq.end() - seq.begin() << std::endl;
1366         cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1367         cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1368         for (unsigned i=0; i<seq.size(); ++i) {
1369                 if (touched[i]) cout << i << " is touched" << std::endl;
1370         }
1371         cout << "end in combine" << std::endl;
1372         */
1373
1374         // there should not be any terms with coeff 0 from the beginning,
1375         // so it should be safe to skip this step
1376         if (number_of_zeroes!=0) {
1377                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1378                 /*
1379                 cout << "in combine after drop:" << std::endl;
1380                 printtree(cout,0);
1381                 cout << "size=" << seq.end() - seq.begin() << std::endl;
1382                 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1383                 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1384                 for (unsigned i=0; i<seq.size(); ++i) {
1385                         if (touched[i]) cout << i << " is touched" << std::endl;
1386                 }
1387                 cout << "end in combine after drop" << std::endl;
1388                 */
1389         }
1390
1391         add_numerics_to_hashtab(first_numeric,last_non_zero);
1392
1393         // pop zero elements
1394         for (unsigned i=0; i<number_of_zeroes; ++i) {
1395                 seq.pop_back();
1396         }
1397
1398         // shrink hashtabsize to calculated value
1399         GINAC_ASSERT(!has_coeff_0());
1400
1401         shrink_hashtab();
1402
1403         GINAC_ASSERT(!has_coeff_0());
1404 }
1405
1406 #endif // EXPAIRSEQ_USE_HASHTAB
1407
1408 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1409  *  debugging or in assertions since being sorted is an invariance. */
1410 bool expairseq::is_canonical() const
1411 {
1412         if (seq.size()<=1)
1413                 return 1;
1414
1415 #if EXPAIRSEQ_USE_HASHTAB
1416         if (hashtabsize>0) return 1; // not canoncalized
1417 #endif // EXPAIRSEQ_USE_HASHTAB
1418
1419         epvector::const_iterator it = seq.begin();
1420         epvector::const_iterator it_last = it;
1421         for (++it; it!=seq.end(); it_last=it, ++it) {
1422                 if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
1423                         if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1424                                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1425                                 // double test makes it easier to set a breakpoint...
1426                                 if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1427                                         !is_ex_exactly_of_type((*it).rest,numeric)) {
1428                                         printpair(std::clog,*it_last,0);
1429                                         std::clog << ">";
1430                                         printpair(std::clog,*it,0);
1431                                         std::clog << "\n";
1432                                         std::clog << "pair1:" << std::endl;
1433                                         (*it_last).rest.printtree(std::clog);
1434                                         (*it_last).coeff.printtree(std::clog);
1435                                         std::clog << "pair2:" << std::endl;
1436                                         (*it).rest.printtree(std::clog);
1437                                         (*it).coeff.printtree(std::clog);
1438                                         return 0;
1439                                 }
1440                         }
1441                 }
1442         }
1443         return 1;
1444 }
1445
1446
1447 /** Member-wise expand the expairs in this sequence.
1448  *
1449  *  @see expairseq::expand()
1450  *  @return pointer to epvector containing expanded pairs or zero pointer,
1451  *  if no members were changed. */
1452 epvector * expairseq::expandchildren(unsigned options) const
1453 {
1454         epvector::const_iterator last = seq.end();
1455         epvector::const_iterator cit = seq.begin();
1456         while (cit!=last) {
1457                 const ex &expanded_ex = (*cit).rest.expand(options);
1458                 if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1459
1460                         // something changed, copy seq, eval and return it
1461                         epvector *s = new epvector;
1462                         s->reserve(seq.size());
1463
1464                         // copy parts of seq which are known not to have changed
1465                         epvector::const_iterator cit2 = seq.begin();
1466                         while (cit2!=cit) {
1467                                 s->push_back(*cit2);
1468                                 ++cit2;
1469                         }
1470                         // copy first changed element
1471                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1472                                                                    (*cit2).coeff));
1473                         ++cit2;
1474                         // copy rest
1475                         while (cit2!=last) {
1476                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1477                                                                            (*cit2).coeff));
1478                                 ++cit2;
1479                         }
1480                         return s;
1481                 }
1482                 ++cit;
1483         }
1484
1485         return 0; // signalling nothing has changed
1486 }
1487
1488
1489 /** Member-wise evaluate the expairs in this sequence.
1490  *
1491  *  @see expairseq::eval()
1492  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1493  *  if no members were changed. */
1494 epvector * expairseq::evalchildren(int level) const
1495 {
1496         // returns a NULL pointer if nothing had to be evaluated
1497         // returns a pointer to a newly created epvector otherwise
1498         // (which has to be deleted somewhere else)
1499
1500         if (level==1)
1501                 return 0;
1502
1503         if (level == -max_recursion_level)
1504                 throw(std::runtime_error("max recursion level reached"));
1505
1506         --level;
1507         epvector::const_iterator last=seq.end();
1508         epvector::const_iterator cit=seq.begin();
1509         while (cit!=last) {
1510                 const ex &evaled_ex = (*cit).rest.eval(level);
1511                 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1512
1513                         // something changed, copy seq, eval and return it
1514                         epvector *s = new epvector;
1515                         s->reserve(seq.size());
1516
1517                         // copy parts of seq which are known not to have changed
1518                         epvector::const_iterator cit2=seq.begin();
1519                         while (cit2!=cit) {
1520                                 s->push_back(*cit2);
1521                                 ++cit2;
1522                         }
1523                         // copy first changed element
1524                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1525                                                                    (*cit2).coeff));
1526                         ++cit2;
1527                         // copy rest
1528                         while (cit2!=last) {
1529                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1530                                                                            (*cit2).coeff));
1531                                 ++cit2;
1532                         }
1533                         return s;
1534                 }
1535                 ++cit;
1536         }
1537
1538         return 0; // signalling nothing has changed
1539 }
1540
1541
1542 /** Member-wise evaluate numerically all expairs in this sequence.
1543  *
1544  *  @see expairseq::evalf()
1545  *  @return epvector with all entries evaluated numerically. */
1546 epvector expairseq::evalfchildren(int level) const
1547 {
1548         if (level==1)
1549                 return seq;
1550
1551         if (level==-max_recursion_level)
1552                 throw(std::runtime_error("max recursion level reached"));
1553
1554         epvector s;
1555         s.reserve(seq.size());
1556
1557         --level;
1558         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1559                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1560                                                           (*it).coeff.evalf(level)));
1561         }
1562         return s;
1563 }
1564
1565
1566 /** Member-wise normalize all expairs in this sequence.
1567  *
1568  *  @see expairseq::normal()
1569  *  @return epvector with all entries normalized. */
1570 epvector expairseq::normalchildren(int level) const
1571 {
1572         if (level==1)
1573                 return seq;
1574
1575         if (level==-max_recursion_level)
1576                 throw(std::runtime_error("max recursion level reached"));
1577
1578         epvector s;
1579         s.reserve(seq.size());
1580
1581         --level;
1582         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1583                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1584                                                           (*it).coeff));
1585         }
1586         return s;
1587 }
1588
1589
1590 /** Member-wise differentiate all expairs in this sequence.
1591  *
1592  *  @see expairseq::diff()
1593  *  @return epvector with all entries differentiated. */
1594 epvector expairseq::diffchildren(const symbol &y) const
1595 {
1596         epvector s;
1597         s.reserve(seq.size());
1598
1599         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1600                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1601                                                           (*it).coeff));
1602         }
1603         return s;
1604 }
1605
1606
1607 /** Member-wise substitute in this sequence.
1608  *
1609  *  @see expairseq::subs()
1610  *  @return pointer to epvector containing pairs after application of subs or zero
1611  *  pointer, if no members were changed. */
1612 epvector * expairseq::subschildren(const lst &ls, const lst &lr) const
1613 {
1614         // returns a NULL pointer if nothing had to be substituted
1615         // returns a pointer to a newly created epvector otherwise
1616         // (which has to be deleted somewhere else)
1617         GINAC_ASSERT(ls.nops()==lr.nops());
1618
1619         epvector::const_iterator last = seq.end();
1620         epvector::const_iterator cit = seq.begin();
1621         while (cit!=last) {
1622                 const ex &subsed_ex=(*cit).rest.subs(ls,lr);
1623                 if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1624
1625                         // something changed, copy seq, subs and return it
1626                         epvector *s = new epvector;
1627                         s->reserve(seq.size());
1628
1629                         // copy parts of seq which are known not to have changed
1630                         epvector::const_iterator cit2 = seq.begin();
1631                         while (cit2!=cit) {
1632                                 s->push_back(*cit2);
1633                                 ++cit2;
1634                         }
1635                         // copy first changed element
1636                         s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1637                                                                    (*cit2).coeff));
1638                         ++cit2;
1639                         // copy rest
1640                         while (cit2!=last) {
1641                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
1642                                                                            (*cit2).coeff));
1643                                 ++cit2;
1644                         }
1645                         return s;
1646                 }
1647                 ++cit;
1648         }
1649
1650         return 0; // signalling nothing has changed
1651 }
1652
1653 //////////
1654 // static member variables
1655 //////////
1656
1657 // protected
1658
1659 unsigned expairseq::precedence = 10;
1660
1661 #if EXPAIRSEQ_USE_HASHTAB
1662 unsigned expairseq::maxhashtabsize = 0x4000000U;
1663 unsigned expairseq::minhashtabsize = 0x1000U;
1664 unsigned expairseq::hashtabfactor = 1;
1665 #endif // EXPAIRSEQ_USE_HASHTAB
1666
1667 } // namespace GiNaC