ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2002 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 "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  46
  47 //////////
  48 // helper classes
  49 //////////
  50
  51 class epp_is_less
  52 {
  53 public:
  54         bool operator()(const epp &lh, const epp &rh) const
  55         {
  56                 return (*lh).is_less(*rh);
  57         }
  58 };
  59
  60 //////////
  61 // default ctor, dtor, copy ctor, assignment operator and helpers
  62 //////////
  63
  64 // public
  65
  66 expairseq::expairseq(const expairseq &other)
  67 {
  68         copy(other);
  69 }
  70
  71 const expairseq &expairseq::operator=(const expairseq &other)
  72 {
  73         if (this != &other) {
  74                 destroy(true);
  75                 copy(other);
  76         }
  77         return *this;
  78 }
  79
  80 // protected
  81
  82 /** For use by copy ctor and assignment operator. */
  83 void expairseq::copy(const expairseq &other)
  84 {
  85         inherited::copy(other);
  86         seq = other.seq;
  87         overall_coeff = other.overall_coeff;
  88 #if EXPAIRSEQ_USE_HASHTAB
  89         // copy hashtab
  90         hashtabsize = other.hashtabsize;
  91         if (hashtabsize!=0) {
  92                 hashmask = other.hashmask;
  93                 hashtab.resize(hashtabsize);
  94                 epvector::const_iterator osb = other.seq.begin();
  95                 for (unsigned i=0; i<hashtabsize; ++i) {
  96                         hashtab[i].clear();
  97                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  98                              cit!=other.hashtab[i].end(); ++cit) {
  99                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 100                         }
 101                 }
 102         } else {
 103                 hashtab.clear();
 104         }
 105 #endif // EXPAIRSEQ_USE_HASHTAB
 106 }
 107
 108 DEFAULT_DESTROY(expairseq)
 109
 110 //////////
 111 // other ctors
 112 //////////
 113
 114 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_2_ex(lh,rh);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 121 {
 122         construct_from_exvector(v);
 123         GINAC_ASSERT(is_canonical());
 124 }
 125
 126 expairseq::expairseq(const epvector &v, const ex &oc)
 127   : inherited(TINFO_expairseq), overall_coeff(oc)
 128 {
 129         GINAC_ASSERT(is_a<numeric>(oc));
 130         construct_from_epvector(v);
 131         GINAC_ASSERT(is_canonical());
 132 }
 133
 134 expairseq::expairseq(epvector *vp, const ex &oc)
 135   : inherited(TINFO_expairseq), overall_coeff(oc)
 136 {
 137         GINAC_ASSERT(vp!=0);
 138         GINAC_ASSERT(is_a<numeric>(oc));
 139         construct_from_epvector(*vp);
 140         delete vp;
 141         GINAC_ASSERT(is_canonical());
 142 }
 143
 144 //////////
 145 // archiving
 146 //////////
 147
 148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 149 #if EXPAIRSEQ_USE_HASHTAB
 150         , hashtabsize(0)
 151 #endif
 152 {
 153         for (unsigned int i=0; true; i++) {
 154                 ex rest;
 155                 ex coeff;
 156                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 157                         seq.push_back(expair(rest, coeff));
 158                 else
 159                         break;
 160         }
 161         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 162 }
 163
 164 void expairseq::archive(archive_node &n) const
 165 {
 166         inherited::archive(n);
 167         epvector::const_iterator i = seq.begin(), iend = seq.end();
 168         while (i != iend) {
 169                 n.add_ex("rest", i->rest);
 170                 n.add_ex("coeff", i->coeff);
 171                 ++i;
 172         }
 173         n.add_ex("overall_coeff", overall_coeff);
 174 }
 175
 176 DEFAULT_UNARCHIVE(expairseq)
 177
 178 //////////
 179 // functions overriding virtual functions from base classes
 180 //////////
 181
 182 // public
 183
 184 basic *expairseq::duplicate() const
 185 {
 186         return new expairseq(*this);
 187 }
 188
 189 void expairseq::print(const print_context &c, unsigned level) const
 190 {
 191         if (is_of_type(c, print_tree)) {
 192
 193                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 194
 195                 c.s << std::string(level, ' ') << class_name()
 196                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 197                     << ", nops=" << nops()
 198                     << std::endl;
 199                 unsigned num = seq.size();
 200                 for (unsigned i=0; i<num; ++i) {
 201                         seq[i].rest.print(c, level + delta_indent);
 202                         seq[i].coeff.print(c, level + delta_indent);
 203                         if (i != num - 1)
 204                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 205                 }
 206                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 207                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 208                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 209                         overall_coeff.print(c, level + delta_indent);
 210                 }
 211                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 212 #if EXPAIRSEQ_USE_HASHTAB
 213                 c.s << std::string(level + delta_indent,' ')
 214                     << "hashtab size " << hashtabsize << std::endl;
 215                 if (hashtabsize == 0) return;
 216 #define MAXCOUNT 5
 217                 unsigned count[MAXCOUNT+1];
 218                 for (int i=0; i<MAXCOUNT+1; ++i)
 219                         count[i] = 0;
 220                 unsigned this_bin_fill;
 221                 unsigned cum_fill_sq = 0;
 222                 unsigned cum_fill = 0;
 223                 for (unsigned i=0; i<hashtabsize; ++i) {
 224                         this_bin_fill = 0;
 225                         if (hashtab[i].size() > 0) {
 226                                 c.s << std::string(level + delta_indent, ' ')
 227                                     << "bin " << i << " with entries ";
 228                                 for (epplist::const_iterator it=hashtab[i].begin();
 229                                      it!=hashtab[i].end(); ++it) {
 230                                         c.s << *it-seq.begin() << " ";
 231                                         ++this_bin_fill;
 232                                 }
 233                                 c.s << std::endl;
 234                                 cum_fill += this_bin_fill;
 235                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 236                         }
 237                         if (this_bin_fill<MAXCOUNT)
 238                                 ++count[this_bin_fill];
 239                         else
 240                                 ++count[MAXCOUNT];
 241                 }
 242                 unsigned fact = 1;
 243                 double cum_prob = 0;
 244                 double lambda = (1.0*seq.size()) / hashtabsize;
 245                 for (int k=0; k<MAXCOUNT; ++k) {
 246                         if (k>0)
 247                                 fact *= k;
 248                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 249                         cum_prob += prob;
 250                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 251                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 252                             << int(prob*1000)/10.0 << ")" << std::endl;
 253                 }
 254                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 255                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 256                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 257
 258                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 259                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 260                     << std::endl;
 261                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 262                     << (1.0*cum_fill)/hashtabsize
 263                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 264 #endif // EXPAIRSEQ_USE_HASHTAB
 265
 266         } else {
 267                 c.s << "[[";
 268                 printseq(c, ',', precedence(), level);
 269                 c.s << "]]";
 270         }
 271 }
 272
 273 bool expairseq::info(unsigned inf) const
 274 {
 275         return inherited::info(inf);
 276 }
 277
 278 unsigned expairseq::nops() const
 279 {
 280         if (overall_coeff.is_equal(default_overall_coeff()))
 281                 return seq.size();
 282         else
 283                 return seq.size()+1;
 284 }
 285
 286 ex expairseq::op(int i) const
 287 {
 288         if (unsigned(i)<seq.size())
 289                 return recombine_pair_to_ex(seq[i]);
 290         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 291         return overall_coeff;
 292 }
 293
 294 ex &expairseq::let_op(int i)
 295 {
 296         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 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 (unsigned int i=0; i<pattern.nops(); i++) {
 341                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 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 (unsigned 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 (unsigned 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                         unsigned num = ops.size();
 381                         epvector *vp = new epvector();
 382                         vp->reserve(num);
 383                         for (unsigned 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 (unsigned i=0; i<repl_lst.nops(); i++) {
 387                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 388                                         return rest.is_equal(repl_lst.op(i).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, bool no_pattern) const
 404 {
 405         epvector *vp = subschildren(ls, lr, no_pattern);
 406         if (vp)
 407                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 408         else
 409                 return basic::subs(ls, lr, no_pattern);
 410 }
 411
 412 // protected
 413
 414 int expairseq::compare_same_type(const basic &other) const
 415 {
 416         GINAC_ASSERT(is_a<expairseq>(other));
 417         const expairseq &o = static_cast<const expairseq &>(other);
 418
 419         int cmpval;
 420
 421         // compare number of elements
 422         if (seq.size() != o.seq.size())
 423                 return (seq.size()<o.seq.size()) ? -1 : 1;
 424
 425         // compare overall_coeff
 426         cmpval = overall_coeff.compare(o.overall_coeff);
 427         if (cmpval!=0)
 428                 return cmpval;
 429
 430 #if EXPAIRSEQ_USE_HASHTAB
 431         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 432         if (hashtabsize==0) {
 433 #endif // EXPAIRSEQ_USE_HASHTAB
 434                 epvector::const_iterator cit1 = seq.begin();
 435                 epvector::const_iterator cit2 = o.seq.begin();
 436                 epvector::const_iterator last1 = seq.end();
 437                 epvector::const_iterator last2 = o.seq.end();
 438
 439                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 440                         cmpval = (*cit1).compare(*cit2);
 441                         if (cmpval!=0) return cmpval;
 442                 }
 443
 444                 GINAC_ASSERT(cit1==last1);
 445                 GINAC_ASSERT(cit2==last2);
 446
 447                 return 0;
 448 #if EXPAIRSEQ_USE_HASHTAB
 449         }
 450
 451         // compare number of elements in each hashtab entry
 452         for (unsigned i=0; i<hashtabsize; ++i) {
 453                 unsigned cursize=hashtab[i].size();
 454                 if (cursize != o.hashtab[i].size())
 455                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 456         }
 457
 458         // compare individual (sorted) hashtab entries
 459         for (unsigned i=0; i<hashtabsize; ++i) {
 460                 unsigned sz = hashtab[i].size();
 461                 if (sz>0) {
 462                         const epplist &eppl1 = hashtab[i];
 463                         const epplist &eppl2 = o.hashtab[i];
 464                         epplist::const_iterator it1 = eppl1.begin();
 465                         epplist::const_iterator it2 = eppl2.begin();
 466                         while (it1!=eppl1.end()) {
 467                                 cmpval = (*(*it1)).compare(*(*it2));
 468                                 if (cmpval!=0)
 469                                         return cmpval;
 470                                 ++it1;
 471                                 ++it2;
 472                         }
 473                 }
 474         }
 475
 476         return 0; // equal
 477 #endif // EXPAIRSEQ_USE_HASHTAB
 478 }
 479
 480 bool expairseq::is_equal_same_type(const basic &other) const
 481 {
 482         const expairseq &o = static_cast<const expairseq &>(other);
 483
 484         // compare number of elements
 485         if (seq.size()!=o.seq.size())
 486                 return false;
 487
 488         // compare overall_coeff
 489         if (!overall_coeff.is_equal(o.overall_coeff))
 490                 return false;
 491
 492 #if EXPAIRSEQ_USE_HASHTAB
 493         // compare number of elements in each hashtab entry
 494         if (hashtabsize!=o.hashtabsize) {
 495                 std::cout << "this:" << std::endl;
 496                 print(print_tree(std::cout));
 497                 std::cout << "other:" << std::endl;
 498                 other.print(print_tree(std::cout));
 499         }
 500
 501         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 502
 503         if (hashtabsize==0) {
 504 #endif // EXPAIRSEQ_USE_HASHTAB
 505                 epvector::const_iterator cit1 = seq.begin();
 506                 epvector::const_iterator cit2 = o.seq.begin();
 507                 epvector::const_iterator last1 = seq.end();
 508
 509                 while (cit1!=last1) {
 510                         if (!(*cit1).is_equal(*cit2)) return false;
 511                         ++cit1;
 512                         ++cit2;
 513                 }
 514
 515                 return true;
 516 #if EXPAIRSEQ_USE_HASHTAB
 517         }
 518
 519         for (unsigned i=0; i<hashtabsize; ++i) {
 520                 if (hashtab[i].size() != o.hashtab[i].size())
 521                         return false;
 522         }
 523
 524         // compare individual sorted hashtab entries
 525         for (unsigned i=0; i<hashtabsize; ++i) {
 526                 unsigned sz = hashtab[i].size();
 527                 if (sz>0) {
 528                         const epplist &eppl1 = hashtab[i];
 529                         const epplist &eppl2 = o.hashtab[i];
 530                         epplist::const_iterator it1 = eppl1.begin();
 531                         epplist::const_iterator it2 = eppl2.begin();
 532                         while (it1!=eppl1.end()) {
 533                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 534                                 ++it1;
 535                                 ++it2;
 536                         }
 537                 }
 538         }
 539
 540         return true;
 541 #endif // EXPAIRSEQ_USE_HASHTAB
 542 }
 543
 544 unsigned expairseq::return_type(void) const
 545 {
 546         return return_types::noncommutative_composite;
 547 }
 548
 549 unsigned expairseq::calchash(void) const
 550 {
 551         unsigned v = golden_ratio_hash(this->tinfo());
 552         epvector::const_iterator i = seq.begin(), end = seq.end();
 553         while (i != end) {
 554 #if !EXPAIRSEQ_USE_HASHTAB
 555                 v = rotate_left_31(v); // rotation would spoil commutativity
 556 #endif // EXPAIRSEQ_USE_HASHTAB
 557                 v ^= i->rest.gethash();
 558 #if !EXPAIRSEQ_USE_HASHTAB
 559                 v = rotate_left_31(v);
 560                 v ^= i->coeff.gethash();
 561 #endif // EXPAIRSEQ_USE_HASHTAB
 562                 ++i;
 563         }
 564
 565         v ^= overall_coeff.gethash();
 566         v &= 0x7FFFFFFFU;
 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_ex_exactly_of_type(lh,numeric)) {
 781                 if (is_ex_exactly_of_type(rh,numeric)) {
 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_ex_exactly_of_type(rh,numeric)) {
 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_ex_exactly_of_type(e,numeric)) {
 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_ex_exactly_of_type(*cit,numeric))
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         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
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 hash = e.gethash();
1136         unsigned hashindex;
1137         if (is_a_numeric_hash(hash)) {
1138                 hashindex = hashmask;
1139         } else {
1140                 hashindex = hash &hashmask;
1141                 // last hashtab entry is reserved for numerics
1142                 if (hashindex==hashmask) hashindex = 0;
1143         }
1144         GINAC_ASSERT(hashindex>=0);
1145         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1146         return hashindex;
1147 }
1148
1149 void expairseq::shrink_hashtab(void)
1150 {
1151         unsigned new_hashtabsize;
1152         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1153                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1154                 if (new_hashtabsize==0) {
1155                         hashtab.clear();
1156                         hashtabsize = 0;
1157                         canonicalize();
1158                         return;
1159                 }
1160
1161                 // shrink by a factor of 2
1162                 unsigned half_hashtabsize = hashtabsize/2;
1163                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1164                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1165                 // special treatment for numeric hashes
1166                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1167                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1168                 hashtab.resize(half_hashtabsize);
1169                 hashtabsize = half_hashtabsize;
1170                 hashmask = hashtabsize-1;
1171         }
1172 }
1173
1174 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1175 {
1176         if (hashtabsize==0)
1177                 return; // nothing to do
1178
1179         // calculate hashindex of element to be deleted
1180         unsigned hashindex = calc_hashindex((*element).rest);
1181
1182         // find it in hashtab and remove it
1183         epplist &eppl = hashtab[hashindex];
1184         epplist::iterator epplit = eppl.begin();
1185         bool erased = false;
1186         while (epplit!=eppl.end()) {
1187                 if (*epplit == element) {
1188                         eppl.erase(epplit);
1189                         erased = true;
1190                         break;
1191                 }
1192                 ++epplit;
1193         }
1194         if (!erased) {
1195                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1196                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1197
1198                 unsigned hashindex = calc_hashindex(element->rest);
1199                 epplist &eppl = hashtab[hashindex];
1200                 epplist::iterator epplit = eppl.begin();
1201                 bool erased = false;
1202                 while (epplit!=eppl.end()) {
1203                         if (*epplit == element) {
1204                                 eppl.erase(epplit);
1205                                 erased = true;
1206                                 break;
1207                         }
1208                         ++epplit;
1209                 }
1210                 GINAC_ASSERT(erased);
1211         }
1212         GINAC_ASSERT(erased);
1213 }
1214
1215 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1216                                    epvector::iterator newpos)
1217 {
1218         GINAC_ASSERT(hashtabsize!=0);
1219
1220         // calculate hashindex of element which was moved
1221         unsigned hashindex=calc_hashindex((*newpos).rest);
1222
1223         // find it in hashtab and modify it
1224         epplist &eppl = hashtab[hashindex];
1225         epplist::iterator epplit = eppl.begin();
1226         while (epplit!=eppl.end()) {
1227                 if (*epplit == oldpos) {
1228                         *epplit = newpos;
1229                         break;
1230                 }
1231                 ++epplit;
1232         }
1233         GINAC_ASSERT(epplit!=eppl.end());
1234 }
1235
1236 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1237 {
1238         epplist::const_iterator current = eppl.begin();
1239         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1240                 ++current;
1241         }
1242         eppl.insert(current,elem);
1243 }
1244
1245 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1246                                           epvector::iterator &last_non_zero,
1247                                           std::vector<bool> &touched,
1248                                           unsigned &number_of_zeroes)
1249 {
1250         epp current = seq.begin();
1251
1252         while (current!=first_numeric) {
1253                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1254                         --first_numeric;
1255                         iter_swap(current,first_numeric);
1256                 } else {
1257                         // calculate hashindex
1258                         unsigned currenthashindex = calc_hashindex(current->rest);
1259
1260                         // test if there is already a matching expair in the hashtab-list
1261                         epplist &eppl=hashtab[currenthashindex];
1262                         epplist::iterator epplit = eppl.begin();
1263                         while (epplit!=eppl.end()) {
1264                                 if (current->rest.is_equal((*epplit)->rest))
1265                                         break;
1266                                 ++epplit;
1267                         }
1268                         if (epplit==eppl.end()) {
1269                                 // no matching expair found, append this to end of list
1270                                 sorted_insert(eppl,current);
1271                                 ++current;
1272                         } else {
1273                                 // epplit points to a matching expair, combine it with current
1274                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1275                                                    add_dyn(ex_to<numeric>(current->coeff));
1276
1277                                 // move obsolete current expair to end by swapping with last_non_zero element
1278                                 // if this was a numeric, it is swapped with the expair before first_numeric
1279                                 iter_swap(current,last_non_zero);
1280                                 --first_numeric;
1281                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1282                                 --last_non_zero;
1283                                 ++number_of_zeroes;
1284                                 // test if combined term has coeff 0 and can be removed is done later
1285                                 touched[(*epplit)-seq.begin()] = true;
1286                         }
1287                 }
1288         }
1289 }
1290
1291 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1292                                    epvector::iterator &last_non_zero,
1293                                    std::vector<bool> &touched,
1294                                    unsigned &number_of_zeroes)
1295 {
1296         // move terms with coeff 0 to end and remove them from hashtab
1297         // check only those elements which have been touched
1298         epp current = seq.begin();
1299         unsigned i = 0;
1300         while (current!=first_numeric) {
1301                 if (!touched[i]) {
1302                         ++current;
1303                         ++i;
1304                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1305                         ++current;
1306                         ++i;
1307                 } else {
1308                         remove_hashtab_entry(current);
1309
1310                         // move element to the end, unless it is already at the end
1311                         if (current!=last_non_zero) {
1312                                 iter_swap(current,last_non_zero);
1313                                 --first_numeric;
1314                                 bool numeric_swapped = first_numeric!=last_non_zero;
1315                                 if (numeric_swapped)
1316                                         iter_swap(first_numeric,current);
1317                                 epvector::iterator changed_entry;
1318
1319                                 if (numeric_swapped)
1320                                         changed_entry = first_numeric;
1321                                 else
1322                                         changed_entry = last_non_zero;
1323
1324                                 --last_non_zero;
1325                                 ++number_of_zeroes;
1326
1327                                 if (first_numeric!=current) {
1328
1329                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1330                                         move_hashtab_entry(changed_entry,current);
1331                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1332                                 }
1333                         } else {
1334                                 --first_numeric;
1335                                 --last_non_zero;
1336                                 ++number_of_zeroes;
1337                         }
1338                 }
1339         }
1340         GINAC_ASSERT(i==current-seq.begin());
1341 }
1342
1343 /** True if one of the coeffs vanishes, otherwise false.
1344  *  This would be an invariant violation, so this should only be used for
1345  *  debugging purposes. */
1346 bool expairseq::has_coeff_0(void) const
1347 {
1348         epvector::const_iterator i = seq.begin(), end = seq.end();
1349         while (i != end) {
1350                 if (i->coeff.is_zero())
1351                         return true;
1352                 ++i;
1353         }
1354         return false;
1355 }
1356
1357 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1358                                                                                 epvector::const_iterator last_non_zero)
1359 {
1360         if (first_numeric == seq.end()) return; // no numerics
1361
1362         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1363         while (current != last) {
1364                 sorted_insert(hashtab[hashmask], current);
1365                 ++current;
1366         }
1367 }
1368
1369 void expairseq::combine_same_terms(void)
1370 {
1371         // combine same terms, drop term with coeff 0, move numerics to end
1372
1373         // calculate size of hashtab
1374         hashtabsize = calc_hashtabsize(seq.size());
1375
1376         // hashtabsize is a power of 2
1377         hashmask = hashtabsize-1;
1378
1379         // allocate hashtab
1380         hashtab.clear();
1381         hashtab.resize(hashtabsize);
1382
1383         if (hashtabsize==0) {
1384                 canonicalize();
1385                 combine_same_terms_sorted_seq();
1386                 GINAC_ASSERT(!has_coeff_0());
1387                 return;
1388         }
1389
1390         // iterate through seq, move numerics to end,
1391         // fill hashtab and combine same terms
1392         epvector::iterator first_numeric = seq.end();
1393         epvector::iterator last_non_zero = seq.end()-1;
1394
1395         unsigned num = seq.size();
1396         std::vector<bool> touched(num);
1397
1398         unsigned number_of_zeroes = 0;
1399
1400         GINAC_ASSERT(!has_coeff_0());
1401         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1402
1403         // there should not be any terms with coeff 0 from the beginning,
1404         // so it should be safe to skip this step
1405         if (number_of_zeroes!=0) {
1406                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1407         }
1408
1409         add_numerics_to_hashtab(first_numeric,last_non_zero);
1410
1411         // pop zero elements
1412         for (unsigned i=0; i<number_of_zeroes; ++i) {
1413                 seq.pop_back();
1414         }
1415
1416         // shrink hashtabsize to calculated value
1417         GINAC_ASSERT(!has_coeff_0());
1418
1419         shrink_hashtab();
1420
1421         GINAC_ASSERT(!has_coeff_0());
1422 }
1423
1424 #endif // EXPAIRSEQ_USE_HASHTAB
1425
1426 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1427  *  debugging or in assertions since being sorted is an invariance. */
1428 bool expairseq::is_canonical() const
1429 {
1430         if (seq.size() <= 1)
1431                 return 1;
1432
1433 #if EXPAIRSEQ_USE_HASHTAB
1434         if (hashtabsize > 0) return 1; // not canoncalized
1435 #endif // EXPAIRSEQ_USE_HASHTAB
1436
1437         epvector::const_iterator it = seq.begin(), itend = seq.end();
1438         epvector::const_iterator it_last = it;
1439         for (++it; it!=itend; it_last=it, ++it) {
1440                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1441                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1442                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1443                                 // double test makes it easier to set a breakpoint...
1444                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1445                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1446                                         printpair(std::clog, *it_last, 0);
1447                                         std::clog << ">";
1448                                         printpair(std::clog, *it, 0);
1449                                         std::clog << "\n";
1450                                         std::clog << "pair1:" << std::endl;
1451                                         it_last->rest.print(print_tree(std::clog));
1452                                         it_last->coeff.print(print_tree(std::clog));
1453                                         std::clog << "pair2:" << std::endl;
1454                                         it->rest.print(print_tree(std::clog));
1455                                         it->coeff.print(print_tree(std::clog));
1456                                         return 0;
1457                                 }
1458                         }
1459                 }
1460         }
1461         return 1;
1462 }
1463
1464
1465 /** Member-wise expand the expairs in this sequence.
1466  *
1467  *  @see expairseq::expand()
1468  *  @return pointer to epvector containing expanded pairs or zero pointer,
1469  *  if no members were changed. */
1470 epvector * expairseq::expandchildren(unsigned options) const
1471 {
1472         const epvector::const_iterator last = seq.end();
1473         epvector::const_iterator cit = seq.begin();
1474         while (cit!=last) {
1475                 const ex &expanded_ex = cit->rest.expand(options);
1476                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1477
1478                         // something changed, copy seq, eval and return it
1479                         epvector *s = new epvector;
1480                         s->reserve(seq.size());
1481
1482                         // copy parts of seq which are known not to have changed
1483                         epvector::const_iterator cit2 = seq.begin();
1484                         while (cit2!=cit) {
1485                                 s->push_back(*cit2);
1486                                 ++cit2;
1487                         }
1488                         // copy first changed element
1489                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1490                                                                    cit2->coeff));
1491                         ++cit2;
1492                         // copy rest
1493                         while (cit2!=last) {
1494                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1495                                                                            cit2->coeff));
1496                                 ++cit2;
1497                         }
1498                         return s;
1499                 }
1500                 ++cit;
1501         }
1502
1503         return 0; // signalling nothing has changed
1504 }
1505
1506
1507 /** Member-wise evaluate the expairs in this sequence.
1508  *
1509  *  @see expairseq::eval()
1510  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1511  *  if no members were changed. */
1512 epvector * expairseq::evalchildren(int level) const
1513 {
1514         // returns a NULL pointer if nothing had to be evaluated
1515         // returns a pointer to a newly created epvector otherwise
1516         // (which has to be deleted somewhere else)
1517
1518         if (level==1)
1519                 return 0;
1520
1521         if (level == -max_recursion_level)
1522                 throw(std::runtime_error("max recursion level reached"));
1523
1524         --level;
1525         epvector::const_iterator last = seq.end();
1526         epvector::const_iterator cit = seq.begin();
1527         while (cit!=last) {
1528                 const ex &evaled_ex = cit->rest.eval(level);
1529                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1530
1531                         // something changed, copy seq, eval and return it
1532                         epvector *s = new epvector;
1533                         s->reserve(seq.size());
1534
1535                         // copy parts of seq which are known not to have changed
1536                         epvector::const_iterator cit2=seq.begin();
1537                         while (cit2!=cit) {
1538                                 s->push_back(*cit2);
1539                                 ++cit2;
1540                         }
1541                         // copy first changed element
1542                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1543                                                                    cit2->coeff));
1544                         ++cit2;
1545                         // copy rest
1546                         while (cit2!=last) {
1547                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1548                                                                            cit2->coeff));
1549                                 ++cit2;
1550                         }
1551                         return s;
1552                 }
1553                 ++cit;
1554         }
1555
1556         return 0; // signalling nothing has changed
1557 }
1558
1559
1560 /** Member-wise substitute in this sequence.
1561  *
1562  *  @see expairseq::subs()
1563  *  @return pointer to epvector containing pairs after application of subs,
1564  *    or NULL pointer if no members were changed. */
1565 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1566 {
1567         GINAC_ASSERT(ls.nops()==lr.nops());
1568
1569         // The substitution is "complex" when any of the objects to be substituted
1570         // is a product or power. In this case we have to recombine the pairs
1571         // because the numeric coefficients may be part of the search pattern.
1572         bool complex_subs = false;
1573         for (unsigned i=0; i<ls.nops(); ++i)
1574                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1575                         complex_subs = true;
1576                         break;
1577                 }
1578
1579         if (complex_subs) {
1580
1581                 // Substitute in the recombined pairs
1582                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1583                 while (cit != last) {
1584
1585                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1586                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1587                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1588
1589                                 // Something changed, copy seq, subs and return it
1590                                 epvector *s = new epvector;
1591                                 s->reserve(seq.size());
1592
1593                                 // Copy parts of seq which are known not to have changed
1594                                 s->insert(s->begin(), seq.begin(), cit);
1595
1596                                 // Copy first changed element
1597                                 s->push_back(split_ex_to_pair(subsed_ex));
1598                                 ++cit;
1599
1600                                 // Copy rest
1601                                 while (cit != last) {
1602                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1603                                         ++cit;
1604                                 }
1605                                 return s;
1606                         }
1607
1608                         ++cit;
1609                 }
1610
1611         } else {
1612
1613                 // Substitute only in the "rest" part of the pairs
1614                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1615                 while (cit != last) {
1616
1617                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1618                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1619
1620                                 // Something changed, copy seq, subs and return it
1621                                 epvector *s = new epvector;
1622                                 s->reserve(seq.size());
1623
1624                                 // Copy parts of seq which are known not to have changed
1625                                 s->insert(s->begin(), seq.begin(), cit);
1626
1627                                 // Copy first changed element
1628                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1629                                 ++cit;
1630
1631                                 // Copy rest
1632                                 while (cit != last) {
1633                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1634                                                                                    cit->coeff));
1635                                         ++cit;
1636                                 }
1637                                 return s;
1638                         }
1639
1640                         ++cit;
1641                 }
1642         }
1643
1644         // Nothing has changed
1645         return NULL;
1646 }
1647
1648 //////////
1649 // static member variables
1650 //////////
1651
1652 #if EXPAIRSEQ_USE_HASHTAB
1653 unsigned expairseq::maxhashtabsize = 0x4000000U;
1654 unsigned expairseq::minhashtabsize = 0x1000U;
1655 unsigned expairseq::hashtabfactor = 1;
1656 #endif // EXPAIRSEQ_USE_HASHTAB
1657
1658 } // namespace GiNaC