ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include <iostream>
  24 #include <algorithm>
  25 #include <string>
  26 #include <stdexcept>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "mul.h"
  31 #include "power.h"
  32 #include "relational.h"
  33 #include "wildcard.h"
  34 #include "archive.h"
  35 #include "operators.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  46   print_func<print_context>(&expairseq::do_print).
  47   print_func<print_tree>(&expairseq::do_print_tree))
  48
  49
  50 //////////
  51 // helper classes
  52 //////////
  53
  54 class epp_is_less
  55 {
  56 public:
  57         bool operator()(const epp &lh, const epp &rh) const
  58         {
  59                 return (*lh).is_less(*rh);
  60         }
  61 };
  62
  63 //////////
  64 // default constructor
  65 //////////
  66
  67 // public
  68
  69 expairseq::expairseq() : inherited(TINFO_expairseq)
  70 #if EXPAIRSEQ_USE_HASHTAB
  71                                                    , hashtabsize(0)
  72 #endif // EXPAIRSEQ_USE_HASHTAB
  73 {}
  74
  75 // protected
  76
  77 #if 0
  78 /** For use by copy ctor and assignment operator. */
  79 void expairseq::copy(const expairseq &other)
  80 {
  81         seq = other.seq;
  82         overall_coeff = other.overall_coeff;
  83 #if EXPAIRSEQ_USE_HASHTAB
  84         // copy hashtab
  85         hashtabsize = other.hashtabsize;
  86         if (hashtabsize!=0) {
  87                 hashmask = other.hashmask;
  88                 hashtab.resize(hashtabsize);
  89                 epvector::const_iterator osb = other.seq.begin();
  90                 for (unsigned i=0; i<hashtabsize; ++i) {
  91                         hashtab[i].clear();
  92                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  93                              cit!=other.hashtab[i].end(); ++cit) {
  94                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  95                         }
  96                 }
  97         } else {
  98                 hashtab.clear();
  99         }
 100 #endif // EXPAIRSEQ_USE_HASHTAB
 101 }
 102 #endif
 103
 104 //////////
 105 // other constructors
 106 //////////
 107
 108 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 109 {
 110         construct_from_2_ex(lh,rh);
 111         GINAC_ASSERT(is_canonical());
 112 }
 113
 114 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_exvector(v);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const epvector &v, const ex &oc)
 121   : inherited(TINFO_expairseq), overall_coeff(oc)
 122 {
 123         GINAC_ASSERT(is_a<numeric>(oc));
 124         construct_from_epvector(v);
 125         GINAC_ASSERT(is_canonical());
 126 }
 127
 128 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
 129   : inherited(TINFO_expairseq), overall_coeff(oc)
 130 {
 131         GINAC_ASSERT(vp.get()!=0);
 132         GINAC_ASSERT(is_a<numeric>(oc));
 133         construct_from_epvector(*vp);
 134         GINAC_ASSERT(is_canonical());
 135 }
 136
 137 //////////
 138 // archiving
 139 //////////
 140
 141 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 142 #if EXPAIRSEQ_USE_HASHTAB
 143         , hashtabsize(0)
 144 #endif
 145 {
 146         for (unsigned int i=0; true; i++) {
 147                 ex rest;
 148                 ex coeff;
 149                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 150                         seq.push_back(expair(rest, coeff));
 151                 else
 152                         break;
 153         }
 154
 155         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 156
 157         canonicalize();
 158         GINAC_ASSERT(is_canonical());
 159 }
 160
 161 void expairseq::archive(archive_node &n) const
 162 {
 163         inherited::archive(n);
 164         epvector::const_iterator i = seq.begin(), iend = seq.end();
 165         while (i != iend) {
 166                 n.add_ex("rest", i->rest);
 167                 n.add_ex("coeff", i->coeff);
 168                 ++i;
 169         }
 170         n.add_ex("overall_coeff", overall_coeff);
 171 }
 172
 173 DEFAULT_UNARCHIVE(expairseq)
 174
 175 //////////
 176 // functions overriding virtual functions from base classes
 177 //////////
 178
 179 // public
 180
 181 void expairseq::do_print(const print_context & c, unsigned level) const
 182 {
 183         c.s << "[[";
 184         printseq(c, ',', precedence(), level);
 185         c.s << "]]";
 186 }
 187
 188 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 189 {
 190         c.s << std::string(level, ' ') << class_name() << " @" << this
 191             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 192             << ", nops=" << nops()
 193             << std::endl;
 194         size_t num = seq.size();
 195         for (size_t i=0; i<num; ++i) {
 196                 seq[i].rest.print(c, level + c.delta_indent);
 197                 seq[i].coeff.print(c, level + c.delta_indent);
 198                 if (i != num - 1)
 199                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 200         }
 201         if (!overall_coeff.is_equal(default_overall_coeff())) {
 202                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 203                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 204                 overall_coeff.print(c, level + c.delta_indent);
 205         }
 206         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 207 #if EXPAIRSEQ_USE_HASHTAB
 208         c.s << std::string(level + c.delta_indent,' ')
 209             << "hashtab size " << hashtabsize << std::endl;
 210         if (hashtabsize == 0) return;
 211 #define MAXCOUNT 5
 212         unsigned count[MAXCOUNT+1];
 213         for (int i=0; i<MAXCOUNT+1; ++i)
 214                 count[i] = 0;
 215         unsigned this_bin_fill;
 216         unsigned cum_fill_sq = 0;
 217         unsigned cum_fill = 0;
 218         for (unsigned i=0; i<hashtabsize; ++i) {
 219                 this_bin_fill = 0;
 220                 if (hashtab[i].size() > 0) {
 221                         c.s << std::string(level + c.delta_indent, ' ')
 222                             << "bin " << i << " with entries ";
 223                         for (epplist::const_iterator it=hashtab[i].begin();
 224                              it!=hashtab[i].end(); ++it) {
 225                                 c.s << *it-seq.begin() << " ";
 226                                 ++this_bin_fill;
 227                         }
 228                         c.s << std::endl;
 229                         cum_fill += this_bin_fill;
 230                         cum_fill_sq += this_bin_fill*this_bin_fill;
 231                 }
 232                 if (this_bin_fill<MAXCOUNT)
 233                         ++count[this_bin_fill];
 234                 else
 235                         ++count[MAXCOUNT];
 236         }
 237         unsigned fact = 1;
 238         double cum_prob = 0;
 239         double lambda = (1.0*seq.size()) / hashtabsize;
 240         for (int k=0; k<MAXCOUNT; ++k) {
 241                 if (k>0)
 242                         fact *= k;
 243                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 244                 cum_prob += prob;
 245                 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
 246                     << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 247                     << int(prob*1000)/10.0 << ")" << std::endl;
 248         }
 249         c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
 250             << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 251             << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 252
 253         c.s << std::string(level + c.delta_indent, ' ') << "variance: "
 254             << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 255             << std::endl;
 256         c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
 257             << (1.0*cum_fill)/hashtabsize
 258             << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 259 #endif // EXPAIRSEQ_USE_HASHTAB
 260 }
 261
 262 bool expairseq::info(unsigned inf) const
 263 {
 264         return inherited::info(inf);
 265 }
 266
 267 size_t expairseq::nops() const
 268 {
 269         if (overall_coeff.is_equal(default_overall_coeff()))
 270                 return seq.size();
 271         else
 272                 return seq.size()+1;
 273 }
 274
 275 ex expairseq::op(size_t i) const
 276 {
 277         if (i < seq.size())
 278                 return recombine_pair_to_ex(seq[i]);
 279         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 280         return overall_coeff;
 281 }
 282
 283 ex expairseq::map(map_function &f) const
 284 {
 285         std::auto_ptr<epvector> v(new epvector);
 286         v->reserve(seq.size());
 287
 288         epvector::const_iterator cit = seq.begin(), last = seq.end();
 289         while (cit != last) {
 290                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 291                 ++cit;
 292         }
 293
 294         if (overall_coeff.is_equal(default_overall_coeff()))
 295                 return thisexpairseq(v, default_overall_coeff());
 296         else
 297                 return thisexpairseq(v, f(overall_coeff));
 298 }
 299
 300 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 301 ex expairseq::eval(int level) const
 302 {
 303         if ((level==1) && (flags &status_flags::evaluated))
 304                 return *this;
 305
 306         std::auto_ptr<epvector> vp = evalchildren(level);
 307         if (vp.get() == 0)
 308                 return this->hold();
 309
 310         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 311 }
 312
 313 epvector* conjugateepvector(const epvector&epv)
 314 {
 315         epvector *newepv = 0;
 316         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 317                 if(newepv) {
 318                         newepv->push_back(i->conjugate());
 319                         continue;
 320                 }
 321                 expair x = i->conjugate();
 322                 if (x.is_equal(*i)) {
 323                         continue;
 324                 }
 325                 newepv = new epvector;
 326                 newepv->reserve(epv.size());
 327                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 328                         newepv->push_back(*j);
 329                 }
 330                 newepv->push_back(x);
 331         }
 332         return newepv;
 333 }
 334
 335 ex expairseq::conjugate() const
 336 {
 337         epvector* newepv = conjugateepvector(seq);
 338         ex x = overall_coeff.conjugate();
 339         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 340                 return *this;
 341         }
 342         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 343         if (newepv) {
 344                 delete newepv;
 345         }
 346         return result;
 347 }
 348
 349 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 350 {
 351         // This differs from basic::match() because we want "a+b+c+d" to
 352         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 353
 354         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 355
 356                 // Check whether global wildcard (one that matches the "rest of the
 357                 // expression", like "*" above) is present
 358                 bool has_global_wildcard = false;
 359                 ex global_wildcard;
 360                 for (size_t i=0; i<pattern.nops(); i++) {
 361                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 362                                 has_global_wildcard = true;
 363                                 global_wildcard = pattern.op(i);
 364                                 break;
 365                         }
 366                 }
 367
 368                 // Unfortunately, this is an O(N^2) operation because we can't
 369                 // sort the pattern in a useful way...
 370
 371                 // Chop into terms
 372                 exvector ops;
 373                 ops.reserve(nops());
 374                 for (size_t i=0; i<nops(); i++)
 375                         ops.push_back(op(i));
 376
 377                 // Now, for every term of the pattern, look for a matching term in
 378                 // the expression and remove the match
 379                 for (size_t i=0; i<pattern.nops(); i++) {
 380                         ex p = pattern.op(i);
 381                         if (has_global_wildcard && p.is_equal(global_wildcard))
 382                                 continue;
 383                         exvector::iterator it = ops.begin(), itend = ops.end();
 384                         while (it != itend) {
 385                                 lst::const_iterator last_el = repl_lst.end();
 386                                 --last_el;
 387                                 if (it->match(p, repl_lst)) {
 388                                         ops.erase(it);
 389                                         goto found;
 390                                 }
 391                                 while(true) {
 392                                         lst::const_iterator next_el = last_el;
 393                                         ++next_el;
 394                                         if(next_el == repl_lst.end())
 395                                                 break;
 396                                         else
 397                                                 repl_lst.remove_last();
 398                                 }
 399                                 ++it;
 400                         }
 401                         return false; // no match found
 402 found:          ;
 403                 }
 404
 405                 if (has_global_wildcard) {
 406
 407                         // Assign all the remaining terms to the global wildcard (unless
 408                         // it has already been matched before, in which case the matches
 409                         // must be equal)
 410                         size_t num = ops.size();
 411                         std::auto_ptr<epvector> vp(new epvector);
 412                         vp->reserve(num);
 413                         for (size_t i=0; i<num; i++)
 414                                 vp->push_back(split_ex_to_pair(ops[i]));
 415                         ex rest = thisexpairseq(vp, default_overall_coeff());
 416                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 417                                 if (it->op(0).is_equal(global_wildcard))
 418                                         return rest.is_equal(it->op(1));
 419                         }
 420                         repl_lst.append(global_wildcard == rest);
 421                         return true;
 422
 423                 } else {
 424
 425                         // No global wildcard, then the match fails if there are any
 426                         // unmatched terms left
 427                         return ops.empty();
 428                 }
 429         }
 430         return inherited::match(pattern, repl_lst);
 431 }
 432
 433 ex expairseq::subs(const exmap & m, unsigned options) const
 434 {
 435         std::auto_ptr<epvector> vp = subschildren(m, options);
 436         if (vp.get())
 437                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 438         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 439                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 440         else
 441                 return subs_one_level(m, options);
 442 }
 443
 444 // protected
 445
 446 int expairseq::compare_same_type(const basic &other) const
 447 {
 448         GINAC_ASSERT(is_a<expairseq>(other));
 449         const expairseq &o = static_cast<const expairseq &>(other);
 450
 451         int cmpval;
 452
 453         // compare number of elements
 454         if (seq.size() != o.seq.size())
 455                 return (seq.size()<o.seq.size()) ? -1 : 1;
 456
 457         // compare overall_coeff
 458         cmpval = overall_coeff.compare(o.overall_coeff);
 459         if (cmpval!=0)
 460                 return cmpval;
 461
 462 #if EXPAIRSEQ_USE_HASHTAB
 463         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 464         if (hashtabsize==0) {
 465 #endif // EXPAIRSEQ_USE_HASHTAB
 466                 epvector::const_iterator cit1 = seq.begin();
 467                 epvector::const_iterator cit2 = o.seq.begin();
 468                 epvector::const_iterator last1 = seq.end();
 469                 epvector::const_iterator last2 = o.seq.end();
 470
 471                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 472                         cmpval = (*cit1).compare(*cit2);
 473                         if (cmpval!=0) return cmpval;
 474                 }
 475
 476                 GINAC_ASSERT(cit1==last1);
 477                 GINAC_ASSERT(cit2==last2);
 478
 479                 return 0;
 480 #if EXPAIRSEQ_USE_HASHTAB
 481         }
 482
 483         // compare number of elements in each hashtab entry
 484         for (unsigned i=0; i<hashtabsize; ++i) {
 485                 unsigned cursize=hashtab[i].size();
 486                 if (cursize != o.hashtab[i].size())
 487                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 488         }
 489
 490         // compare individual (sorted) hashtab entries
 491         for (unsigned i=0; i<hashtabsize; ++i) {
 492                 unsigned sz = hashtab[i].size();
 493                 if (sz>0) {
 494                         const epplist &eppl1 = hashtab[i];
 495                         const epplist &eppl2 = o.hashtab[i];
 496                         epplist::const_iterator it1 = eppl1.begin();
 497                         epplist::const_iterator it2 = eppl2.begin();
 498                         while (it1!=eppl1.end()) {
 499                                 cmpval = (*(*it1)).compare(*(*it2));
 500                                 if (cmpval!=0)
 501                                         return cmpval;
 502                                 ++it1;
 503                                 ++it2;
 504                         }
 505                 }
 506         }
 507
 508         return 0; // equal
 509 #endif // EXPAIRSEQ_USE_HASHTAB
 510 }
 511
 512 bool expairseq::is_equal_same_type(const basic &other) const
 513 {
 514         const expairseq &o = static_cast<const expairseq &>(other);
 515
 516         // compare number of elements
 517         if (seq.size()!=o.seq.size())
 518                 return false;
 519
 520         // compare overall_coeff
 521         if (!overall_coeff.is_equal(o.overall_coeff))
 522                 return false;
 523
 524 #if EXPAIRSEQ_USE_HASHTAB
 525         // compare number of elements in each hashtab entry
 526         if (hashtabsize!=o.hashtabsize) {
 527                 std::cout << "this:" << std::endl;
 528                 print(print_tree(std::cout));
 529                 std::cout << "other:" << std::endl;
 530                 other.print(print_tree(std::cout));
 531         }
 532
 533         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 534
 535         if (hashtabsize==0) {
 536 #endif // EXPAIRSEQ_USE_HASHTAB
 537                 epvector::const_iterator cit1 = seq.begin();
 538                 epvector::const_iterator cit2 = o.seq.begin();
 539                 epvector::const_iterator last1 = seq.end();
 540
 541                 while (cit1!=last1) {
 542                         if (!(*cit1).is_equal(*cit2)) return false;
 543                         ++cit1;
 544                         ++cit2;
 545                 }
 546
 547                 return true;
 548 #if EXPAIRSEQ_USE_HASHTAB
 549         }
 550
 551         for (unsigned i=0; i<hashtabsize; ++i) {
 552                 if (hashtab[i].size() != o.hashtab[i].size())
 553                         return false;
 554         }
 555
 556         // compare individual sorted hashtab entries
 557         for (unsigned i=0; i<hashtabsize; ++i) {
 558                 unsigned sz = hashtab[i].size();
 559                 if (sz>0) {
 560                         const epplist &eppl1 = hashtab[i];
 561                         const epplist &eppl2 = o.hashtab[i];
 562                         epplist::const_iterator it1 = eppl1.begin();
 563                         epplist::const_iterator it2 = eppl2.begin();
 564                         while (it1!=eppl1.end()) {
 565                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 566                                 ++it1;
 567                                 ++it2;
 568                         }
 569                 }
 570         }
 571
 572         return true;
 573 #endif // EXPAIRSEQ_USE_HASHTAB
 574 }
 575
 576 unsigned expairseq::return_type() const
 577 {
 578         return return_types::noncommutative_composite;
 579 }
 580
 581 unsigned expairseq::calchash() const
 582 {
 583         unsigned v = golden_ratio_hash(this->tinfo());
 584         epvector::const_iterator i = seq.begin();
 585         const epvector::const_iterator end = seq.end();
 586         while (i != end) {
 587                 v ^= i->rest.gethash();
 588 #if !EXPAIRSEQ_USE_HASHTAB
 589                 // rotation spoils commutativity!
 590                 v = rotate_left(v);
 591                 v ^= i->coeff.gethash();
 592 #endif // !EXPAIRSEQ_USE_HASHTAB
 593                 ++i;
 594         }
 595
 596         v ^= overall_coeff.gethash();
 597
 598         // store calculated hash value only if object is already evaluated
 599         if (flags &status_flags::evaluated) {
 600                 setflag(status_flags::hash_calculated);
 601                 hashvalue = v;
 602         }
 603
 604         return v;
 605 }
 606
 607 ex expairseq::expand(unsigned options) const
 608 {
 609         std::auto_ptr<epvector> vp = expandchildren(options);
 610         if (vp.get())
 611                 return thisexpairseq(vp, overall_coeff);
 612         else {
 613                 // The terms have not changed, so it is safe to declare this expanded
 614                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 615         }
 616 }
 617
 618 //////////
 619 // new virtual functions which can be overridden by derived classes
 620 //////////
 621
 622 // protected
 623
 624 /** Create an object of this type.
 625  *  This method works similar to a constructor.  It is useful because expairseq
 626  *  has (at least) two possible different semantics but we want to inherit
 627  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 628  *  has to create a new one of the same semantics, which cannot be done by a
 629  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 630  *  order for this trick to work a derived class must of course override this
 631  *  definition. */
 632 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 633 {
 634         return expairseq(v, oc);
 635 }
 636
 637 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
 638 {
 639         return expairseq(vp, oc);
 640 }
 641
 642 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 643 {
 644         c.s << "[[";
 645         p.rest.print(c, precedence());
 646         c.s << ",";
 647         p.coeff.print(c, precedence());
 648         c.s << "]]";
 649 }
 650
 651 void expairseq::printseq(const print_context & c, char delim,
 652                          unsigned this_precedence,
 653                          unsigned upper_precedence) const
 654 {
 655         if (this_precedence <= upper_precedence)
 656                 c.s << "(";
 657         epvector::const_iterator it, it_last = seq.end() - 1;
 658         for (it=seq.begin(); it!=it_last; ++it) {
 659                 printpair(c, *it, this_precedence);
 660                 c.s << delim;
 661         }
 662         printpair(c, *it, this_precedence);
 663         if (!overall_coeff.is_equal(default_overall_coeff())) {
 664                 c.s << delim;
 665                 overall_coeff.print(c, this_precedence);
 666         }
 667
 668         if (this_precedence <= upper_precedence)
 669                 c.s << ")";
 670 }
 671
 672
 673 /** Form an expair from an ex, using the corresponding semantics.
 674  *  @see expairseq::recombine_pair_to_ex() */
 675 expair expairseq::split_ex_to_pair(const ex &e) const
 676 {
 677         return expair(e,_ex1);
 678 }
 679
 680
 681 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 682                                                 const ex &c) const
 683 {
 684         GINAC_ASSERT(is_exactly_a<numeric>(c));
 685
 686         return expair(e,c);
 687 }
 688
 689
 690 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 691                                                   const ex &c) const
 692 {
 693         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 694         GINAC_ASSERT(is_exactly_a<numeric>(c));
 695
 696         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 697 }
 698
 699
 700 /** Form an ex out of an expair, using the corresponding semantics.
 701  *  @see expairseq::split_ex_to_pair() */
 702 ex expairseq::recombine_pair_to_ex(const expair &p) const
 703 {
 704         return lst(p.rest,p.coeff);
 705 }
 706
 707 bool expairseq::expair_needs_further_processing(epp it)
 708 {
 709 #if EXPAIRSEQ_USE_HASHTAB
 710         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 711 #endif // EXPAIRSEQ_USE_HASHTAB
 712         return false;
 713 }
 714
 715 ex expairseq::default_overall_coeff() const
 716 {
 717         return _ex0;
 718 }
 719
 720 void expairseq::combine_overall_coeff(const ex &c)
 721 {
 722         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 723         GINAC_ASSERT(is_exactly_a<numeric>(c));
 724         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 725 }
 726
 727 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 728 {
 729         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 730         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 731         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 732         overall_coeff = ex_to<numeric>(overall_coeff).
 733                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 734 }
 735
 736 bool expairseq::can_make_flat(const expair &p) const
 737 {
 738         return true;
 739 }
 740
 741
 742 //////////
 743 // non-virtual functions in this class
 744 //////////
 745
 746 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 747 {
 748         exvector v;
 749         v.reserve(2);
 750         v.push_back(lh);
 751         v.push_back(rh);
 752         construct_from_exvector(v);
 753 #if EXPAIRSEQ_USE_HASHTAB
 754         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 755         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 756 #endif // EXPAIRSEQ_USE_HASHTAB
 757 }
 758
 759 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 760 {
 761         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 762                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 763 #if EXPAIRSEQ_USE_HASHTAB
 764                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 765                                              ex_to<expairseq>(rh).seq.size();
 766                         if (calc_hashtabsize(totalsize)!=0) {
 767                                 construct_from_2_ex_via_exvector(lh,rh);
 768                         } else {
 769 #endif // EXPAIRSEQ_USE_HASHTAB
 770                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 771                                                            ex_to<expairseq>(rh));
 772 #if EXPAIRSEQ_USE_HASHTAB
 773                         }
 774 #endif // EXPAIRSEQ_USE_HASHTAB
 775                         return;
 776                 } else {
 777 #if EXPAIRSEQ_USE_HASHTAB
 778                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 779                         if (calc_hashtabsize(totalsize)!=0) {
 780                                 construct_from_2_ex_via_exvector(lh, rh);
 781                         } else {
 782 #endif // EXPAIRSEQ_USE_HASHTAB
 783                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 784 #if EXPAIRSEQ_USE_HASHTAB
 785                         }
 786 #endif // EXPAIRSEQ_USE_HASHTAB
 787                         return;
 788                 }
 789         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 790 #if EXPAIRSEQ_USE_HASHTAB
 791                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 792                 if (calc_hashtabsize(totalsize)!=0) {
 793                         construct_from_2_ex_via_exvector(lh,rh);
 794                 } else {
 795 #endif // EXPAIRSEQ_USE_HASHTAB
 796                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 797 #if EXPAIRSEQ_USE_HASHTAB
 798                 }
 799 #endif // EXPAIRSEQ_USE_HASHTAB
 800                 return;
 801         }
 802
 803 #if EXPAIRSEQ_USE_HASHTAB
 804         if (calc_hashtabsize(2)!=0) {
 805                 construct_from_2_ex_via_exvector(lh,rh);
 806                 return;
 807         }
 808         hashtabsize = 0;
 809 #endif // EXPAIRSEQ_USE_HASHTAB
 810
 811         if (is_exactly_a<numeric>(lh)) {
 812                 if (is_exactly_a<numeric>(rh)) {
 813                         combine_overall_coeff(lh);
 814                         combine_overall_coeff(rh);
 815                 } else {
 816                         combine_overall_coeff(lh);
 817                         seq.push_back(split_ex_to_pair(rh));
 818                 }
 819         } else {
 820                 if (is_exactly_a<numeric>(rh)) {
 821                         combine_overall_coeff(rh);
 822                         seq.push_back(split_ex_to_pair(lh));
 823                 } else {
 824                         expair p1 = split_ex_to_pair(lh);
 825                         expair p2 = split_ex_to_pair(rh);
 826
 827                         int cmpval = p1.rest.compare(p2.rest);
 828                         if (cmpval==0) {
 829                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 830                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 831                                         // no further processing is necessary, since this
 832                                         // one element will usually be recombined in eval()
 833                                         seq.push_back(p1);
 834                                 }
 835                         } else {
 836                                 seq.reserve(2);
 837                                 if (cmpval<0) {
 838                                         seq.push_back(p1);
 839                                         seq.push_back(p2);
 840                                 } else {
 841                                         seq.push_back(p2);
 842                                         seq.push_back(p1);
 843                                 }
 844                         }
 845                 }
 846         }
 847 }
 848
 849 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 850                                                                                    const expairseq &s2)
 851 {
 852         combine_overall_coeff(s1.overall_coeff);
 853         combine_overall_coeff(s2.overall_coeff);
 854
 855         epvector::const_iterator first1 = s1.seq.begin();
 856         epvector::const_iterator last1 = s1.seq.end();
 857         epvector::const_iterator first2 = s2.seq.begin();
 858         epvector::const_iterator last2 = s2.seq.end();
 859
 860         seq.reserve(s1.seq.size()+s2.seq.size());
 861
 862         bool needs_further_processing=false;
 863
 864         while (first1!=last1 && first2!=last2) {
 865                 int cmpval = (*first1).rest.compare((*first2).rest);
 866                 if (cmpval==0) {
 867                         // combine terms
 868                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 869                                                    add(ex_to<numeric>(first2->coeff));
 870                         if (!newcoeff.is_zero()) {
 871                                 seq.push_back(expair(first1->rest,newcoeff));
 872                                 if (expair_needs_further_processing(seq.end()-1)) {
 873                                         needs_further_processing = true;
 874                                 }
 875                         }
 876                         ++first1;
 877                         ++first2;
 878                 } else if (cmpval<0) {
 879                         seq.push_back(*first1);
 880                         ++first1;
 881                 } else {
 882                         seq.push_back(*first2);
 883                         ++first2;
 884                 }
 885         }
 886
 887         while (first1!=last1) {
 888                 seq.push_back(*first1);
 889                 ++first1;
 890         }
 891         while (first2!=last2) {
 892                 seq.push_back(*first2);
 893                 ++first2;
 894         }
 895
 896         if (needs_further_processing) {
 897                 epvector v = seq;
 898                 seq.clear();
 899                 construct_from_epvector(v);
 900         }
 901 }
 902
 903 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 904                                                                                         const ex &e)
 905 {
 906         combine_overall_coeff(s.overall_coeff);
 907         if (is_exactly_a<numeric>(e)) {
 908                 combine_overall_coeff(e);
 909                 seq = s.seq;
 910                 return;
 911         }
 912
 913         epvector::const_iterator first = s.seq.begin();
 914         epvector::const_iterator last = s.seq.end();
 915         expair p = split_ex_to_pair(e);
 916
 917         seq.reserve(s.seq.size()+1);
 918         bool p_pushed = false;
 919
 920         bool needs_further_processing=false;
 921
 922         // merge p into s.seq
 923         while (first!=last) {
 924                 int cmpval = (*first).rest.compare(p.rest);
 925                 if (cmpval==0) {
 926                         // combine terms
 927                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 928                                                    add(ex_to<numeric>(p.coeff));
 929                         if (!newcoeff.is_zero()) {
 930                                 seq.push_back(expair(first->rest,newcoeff));
 931                                 if (expair_needs_further_processing(seq.end()-1))
 932                                         needs_further_processing = true;
 933                         }
 934                         ++first;
 935                         p_pushed = true;
 936                         break;
 937                 } else if (cmpval<0) {
 938                         seq.push_back(*first);
 939                         ++first;
 940                 } else {
 941                         seq.push_back(p);
 942                         p_pushed = true;
 943                         break;
 944                 }
 945         }
 946
 947         if (p_pushed) {
 948                 // while loop exited because p was pushed, now push rest of s.seq
 949                 while (first!=last) {
 950                         seq.push_back(*first);
 951                         ++first;
 952                 }
 953         } else {
 954                 // while loop exited because s.seq was pushed, now push p
 955                 seq.push_back(p);
 956         }
 957
 958         if (needs_further_processing) {
 959                 epvector v = seq;
 960                 seq.clear();
 961                 construct_from_epvector(v);
 962         }
 963 }
 964
 965 void expairseq::construct_from_exvector(const exvector &v)
 966 {
 967         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 968         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 969         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 970         //                  (same for (+,*) -> (*,^)
 971
 972         make_flat(v);
 973 #if EXPAIRSEQ_USE_HASHTAB
 974         combine_same_terms();
 975 #else
 976         canonicalize();
 977         combine_same_terms_sorted_seq();
 978 #endif // EXPAIRSEQ_USE_HASHTAB
 979 }
 980
 981 void expairseq::construct_from_epvector(const epvector &v)
 982 {
 983         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 984         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 985         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 986         //                  (same for (+,*) -> (*,^)
 987
 988         make_flat(v);
 989 #if EXPAIRSEQ_USE_HASHTAB
 990         combine_same_terms();
 991 #else
 992         canonicalize();
 993         combine_same_terms_sorted_seq();
 994 #endif // EXPAIRSEQ_USE_HASHTAB
 995 }
 996
 997 /** Combine this expairseq with argument exvector.
 998  *  It cares for associativity as well as for special handling of numerics. */
 999 void expairseq::make_flat(const exvector &v)
1000 {
1001         exvector::const_iterator cit;
1002
1003         // count number of operands which are of same expairseq derived type
1004         // and their cumulative number of operands
1005         int nexpairseqs = 0;
1006         int noperands = 0;
1007
1008         cit = v.begin();
1009         while (cit!=v.end()) {
1010                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1011                         ++nexpairseqs;
1012                         noperands += ex_to<expairseq>(*cit).seq.size();
1013                 }
1014                 ++cit;
1015         }
1016
1017         // reserve seq and coeffseq which will hold all operands
1018         seq.reserve(v.size()+noperands-nexpairseqs);
1019
1020         // copy elements and split off numerical part
1021         cit = v.begin();
1022         while (cit!=v.end()) {
1023                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1024                         const expairseq &subseqref = ex_to<expairseq>(*cit);
1025                         combine_overall_coeff(subseqref.overall_coeff);
1026                         epvector::const_iterator cit_s = subseqref.seq.begin();
1027                         while (cit_s!=subseqref.seq.end()) {
1028                                 seq.push_back(*cit_s);
1029                                 ++cit_s;
1030                         }
1031                 } else {
1032                         if (is_exactly_a<numeric>(*cit))
1033                                 combine_overall_coeff(*cit);
1034                         else
1035                                 seq.push_back(split_ex_to_pair(*cit));
1036                 }
1037                 ++cit;
1038         }
1039 }
1040
1041 /** Combine this expairseq with argument epvector.
1042  *  It cares for associativity as well as for special handling of numerics. */
1043 void expairseq::make_flat(const epvector &v)
1044 {
1045         epvector::const_iterator cit;
1046
1047         // count number of operands which are of same expairseq derived type
1048         // and their cumulative number of operands
1049         int nexpairseqs = 0;
1050         int noperands = 0;
1051
1052         cit = v.begin();
1053         while (cit!=v.end()) {
1054                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1055                         ++nexpairseqs;
1056                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1057                 }
1058                 ++cit;
1059         }
1060
1061         // reserve seq and coeffseq which will hold all operands
1062         seq.reserve(v.size()+noperands-nexpairseqs);
1063
1064         // copy elements and split off numerical part
1065         cit = v.begin();
1066         while (cit!=v.end()) {
1067                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1068                     this->can_make_flat(*cit)) {
1069                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1070                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1071                                                             ex_to<numeric>(cit->coeff));
1072                         epvector::const_iterator cit_s = subseqref.seq.begin();
1073                         while (cit_s!=subseqref.seq.end()) {
1074                                 seq.push_back(expair(cit_s->rest,
1075                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1076                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1077                                 //                                              (*cit).coeff));
1078                                 ++cit_s;
1079                         }
1080                 } else {
1081                         if (cit->is_canonical_numeric())
1082                                 combine_overall_coeff(cit->rest);
1083                         else
1084                                 seq.push_back(*cit);
1085                 }
1086                 ++cit;
1087         }
1088 }
1089
1090 /** Brings this expairseq into a sorted (canonical) form. */
1091 void expairseq::canonicalize()
1092 {
1093         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1094 }
1095
1096
1097 /** Compact a presorted expairseq by combining all matching expairs to one
1098  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1099  *  instance. */
1100 void expairseq::combine_same_terms_sorted_seq()
1101 {
1102         if (seq.size()<2)
1103                 return;
1104
1105         bool needs_further_processing = false;
1106
1107         epvector::iterator itin1 = seq.begin();
1108         epvector::iterator itin2 = itin1+1;
1109         epvector::iterator itout = itin1;
1110         epvector::iterator last = seq.end();
1111         // must_copy will be set to true the first time some combination is
1112         // possible from then on the sequence has changed and must be compacted
1113         bool must_copy = false;
1114         while (itin2!=last) {
1115                 if (itin1->rest.compare(itin2->rest)==0) {
1116                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1117                                        add_dyn(ex_to<numeric>(itin2->coeff));
1118                         if (expair_needs_further_processing(itin1))
1119                                 needs_further_processing = true;
1120                         must_copy = true;
1121                 } else {
1122                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1123                                 if (must_copy)
1124                                         *itout = *itin1;
1125                                 ++itout;
1126                         }
1127                         itin1 = itin2;
1128                 }
1129                 ++itin2;
1130         }
1131         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1132                 if (must_copy)
1133                         *itout = *itin1;
1134                 ++itout;
1135         }
1136         if (itout!=last)
1137                 seq.erase(itout,last);
1138
1139         if (needs_further_processing) {
1140                 epvector v = seq;
1141                 seq.clear();
1142                 construct_from_epvector(v);
1143         }
1144 }
1145
1146 #if EXPAIRSEQ_USE_HASHTAB
1147
1148 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1149 {
1150         unsigned size;
1151         unsigned nearest_power_of_2 = 1 << log2(sz);
1152         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1153         //  size = nearest_power_of_2*hashtabfactor;
1154         size = nearest_power_of_2/hashtabfactor;
1155         if (size<minhashtabsize)
1156                 return 0;
1157
1158         // hashtabsize must be a power of 2
1159         GINAC_ASSERT((1U << log2(size))==size);
1160         return size;
1161 }
1162
1163 unsigned expairseq::calc_hashindex(const ex &e) const
1164 {
1165         // calculate hashindex
1166         unsigned hashindex;
1167         if (is_a<numeric>(e)) {
1168                 hashindex = hashmask;
1169         } else {
1170                 hashindex = e.gethash() & hashmask;
1171                 // last hashtab entry is reserved for numerics
1172                 if (hashindex==hashmask) hashindex = 0;
1173         }
1174         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1175         return hashindex;
1176 }
1177
1178 void expairseq::shrink_hashtab()
1179 {
1180         unsigned new_hashtabsize;
1181         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1182                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1183                 if (new_hashtabsize==0) {
1184                         hashtab.clear();
1185                         hashtabsize = 0;
1186                         canonicalize();
1187                         return;
1188                 }
1189
1190                 // shrink by a factor of 2
1191                 unsigned half_hashtabsize = hashtabsize/2;
1192                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1193                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1194                 // special treatment for numeric hashes
1195                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1196                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1197                 hashtab.resize(half_hashtabsize);
1198                 hashtabsize = half_hashtabsize;
1199                 hashmask = hashtabsize-1;
1200         }
1201 }
1202
1203 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1204 {
1205         if (hashtabsize==0)
1206                 return; // nothing to do
1207
1208         // calculate hashindex of element to be deleted
1209         unsigned hashindex = calc_hashindex((*element).rest);
1210
1211         // find it in hashtab and remove it
1212         epplist &eppl = hashtab[hashindex];
1213         epplist::iterator epplit = eppl.begin();
1214         bool erased = false;
1215         while (epplit!=eppl.end()) {
1216                 if (*epplit == element) {
1217                         eppl.erase(epplit);
1218                         erased = true;
1219                         break;
1220                 }
1221                 ++epplit;
1222         }
1223         if (!erased) {
1224                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1225                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1226
1227                 unsigned hashindex = calc_hashindex(element->rest);
1228                 epplist &eppl = hashtab[hashindex];
1229                 epplist::iterator epplit = eppl.begin();
1230                 bool erased = false;
1231                 while (epplit!=eppl.end()) {
1232                         if (*epplit == element) {
1233                                 eppl.erase(epplit);
1234                                 erased = true;
1235                                 break;
1236                         }
1237                         ++epplit;
1238                 }
1239                 GINAC_ASSERT(erased);
1240         }
1241         GINAC_ASSERT(erased);
1242 }
1243
1244 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1245                                    epvector::iterator newpos)
1246 {
1247         GINAC_ASSERT(hashtabsize!=0);
1248
1249         // calculate hashindex of element which was moved
1250         unsigned hashindex=calc_hashindex((*newpos).rest);
1251
1252         // find it in hashtab and modify it
1253         epplist &eppl = hashtab[hashindex];
1254         epplist::iterator epplit = eppl.begin();
1255         while (epplit!=eppl.end()) {
1256                 if (*epplit == oldpos) {
1257                         *epplit = newpos;
1258                         break;
1259                 }
1260                 ++epplit;
1261         }
1262         GINAC_ASSERT(epplit!=eppl.end());
1263 }
1264
1265 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1266 {
1267         epplist::const_iterator current = eppl.begin();
1268         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1269                 ++current;
1270         }
1271         eppl.insert(current,elem);
1272 }
1273
1274 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1275                                           epvector::iterator &last_non_zero,
1276                                           std::vector<bool> &touched,
1277                                           unsigned &number_of_zeroes)
1278 {
1279         epp current = seq.begin();
1280
1281         while (current!=first_numeric) {
1282                 if (is_exactly_a<numeric>(current->rest)) {
1283                         --first_numeric;
1284                         iter_swap(current,first_numeric);
1285                 } else {
1286                         // calculate hashindex
1287                         unsigned currenthashindex = calc_hashindex(current->rest);
1288
1289                         // test if there is already a matching expair in the hashtab-list
1290                         epplist &eppl=hashtab[currenthashindex];
1291                         epplist::iterator epplit = eppl.begin();
1292                         while (epplit!=eppl.end()) {
1293                                 if (current->rest.is_equal((*epplit)->rest))
1294                                         break;
1295                                 ++epplit;
1296                         }
1297                         if (epplit==eppl.end()) {
1298                                 // no matching expair found, append this to end of list
1299                                 sorted_insert(eppl,current);
1300                                 ++current;
1301                         } else {
1302                                 // epplit points to a matching expair, combine it with current
1303                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1304                                                    add_dyn(ex_to<numeric>(current->coeff));
1305
1306                                 // move obsolete current expair to end by swapping with last_non_zero element
1307                                 // if this was a numeric, it is swapped with the expair before first_numeric
1308                                 iter_swap(current,last_non_zero);
1309                                 --first_numeric;
1310                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1311                                 --last_non_zero;
1312                                 ++number_of_zeroes;
1313                                 // test if combined term has coeff 0 and can be removed is done later
1314                                 touched[(*epplit)-seq.begin()] = true;
1315                         }
1316                 }
1317         }
1318 }
1319
1320 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1321                                    epvector::iterator &last_non_zero,
1322                                    std::vector<bool> &touched,
1323                                    unsigned &number_of_zeroes)
1324 {
1325         // move terms with coeff 0 to end and remove them from hashtab
1326         // check only those elements which have been touched
1327         epp current = seq.begin();
1328         size_t i = 0;
1329         while (current!=first_numeric) {
1330                 if (!touched[i]) {
1331                         ++current;
1332                         ++i;
1333                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1334                         ++current;
1335                         ++i;
1336                 } else {
1337                         remove_hashtab_entry(current);
1338
1339                         // move element to the end, unless it is already at the end
1340                         if (current!=last_non_zero) {
1341                                 iter_swap(current,last_non_zero);
1342                                 --first_numeric;
1343                                 bool numeric_swapped = first_numeric!=last_non_zero;
1344                                 if (numeric_swapped)
1345                                         iter_swap(first_numeric,current);
1346                                 epvector::iterator changed_entry;
1347
1348                                 if (numeric_swapped)
1349                                         changed_entry = first_numeric;
1350                                 else
1351                                         changed_entry = last_non_zero;
1352
1353                                 --last_non_zero;
1354                                 ++number_of_zeroes;
1355
1356                                 if (first_numeric!=current) {
1357
1358                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1359                                         move_hashtab_entry(changed_entry,current);
1360                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1361                                 }
1362                         } else {
1363                                 --first_numeric;
1364                                 --last_non_zero;
1365                                 ++number_of_zeroes;
1366                         }
1367                 }
1368         }
1369         GINAC_ASSERT(i==current-seq.begin());
1370 }
1371
1372 /** True if one of the coeffs vanishes, otherwise false.
1373  *  This would be an invariant violation, so this should only be used for
1374  *  debugging purposes. */
1375 bool expairseq::has_coeff_0() const
1376 {
1377         epvector::const_iterator i = seq.begin(), end = seq.end();
1378         while (i != end) {
1379                 if (i->coeff.is_zero())
1380                         return true;
1381                 ++i;
1382         }
1383         return false;
1384 }
1385
1386 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1387                                                                                 epvector::const_iterator last_non_zero)
1388 {
1389         if (first_numeric == seq.end()) return; // no numerics
1390
1391         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1392         while (current != last) {
1393                 sorted_insert(hashtab[hashmask], current);
1394                 ++current;
1395         }
1396 }
1397
1398 void expairseq::combine_same_terms()
1399 {
1400         // combine same terms, drop term with coeff 0, move numerics to end
1401
1402         // calculate size of hashtab
1403         hashtabsize = calc_hashtabsize(seq.size());
1404
1405         // hashtabsize is a power of 2
1406         hashmask = hashtabsize-1;
1407
1408         // allocate hashtab
1409         hashtab.clear();
1410         hashtab.resize(hashtabsize);
1411
1412         if (hashtabsize==0) {
1413                 canonicalize();
1414                 combine_same_terms_sorted_seq();
1415                 GINAC_ASSERT(!has_coeff_0());
1416                 return;
1417         }
1418
1419         // iterate through seq, move numerics to end,
1420         // fill hashtab and combine same terms
1421         epvector::iterator first_numeric = seq.end();
1422         epvector::iterator last_non_zero = seq.end()-1;
1423
1424         size_t num = seq.size();
1425         std::vector<bool> touched(num);
1426
1427         unsigned number_of_zeroes = 0;
1428
1429         GINAC_ASSERT(!has_coeff_0());
1430         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1431
1432         // there should not be any terms with coeff 0 from the beginning,
1433         // so it should be safe to skip this step
1434         if (number_of_zeroes!=0) {
1435                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1436         }
1437
1438         add_numerics_to_hashtab(first_numeric,last_non_zero);
1439
1440         // pop zero elements
1441         for (unsigned i=0; i<number_of_zeroes; ++i) {
1442                 seq.pop_back();
1443         }
1444
1445         // shrink hashtabsize to calculated value
1446         GINAC_ASSERT(!has_coeff_0());
1447
1448         shrink_hashtab();
1449
1450         GINAC_ASSERT(!has_coeff_0());
1451 }
1452
1453 #endif // EXPAIRSEQ_USE_HASHTAB
1454
1455 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1456  *  debugging or in assertions since being sorted is an invariance. */
1457 bool expairseq::is_canonical() const
1458 {
1459         if (seq.size() <= 1)
1460                 return 1;
1461
1462 #if EXPAIRSEQ_USE_HASHTAB
1463         if (hashtabsize > 0) return 1; // not canoncalized
1464 #endif // EXPAIRSEQ_USE_HASHTAB
1465
1466         epvector::const_iterator it = seq.begin(), itend = seq.end();
1467         epvector::const_iterator it_last = it;
1468         for (++it; it!=itend; it_last=it, ++it) {
1469                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1470                         if (!is_exactly_a<numeric>(it_last->rest) ||
1471                                 !is_exactly_a<numeric>(it->rest)) {
1472                                 // double test makes it easier to set a breakpoint...
1473                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1474                                         !is_exactly_a<numeric>(it->rest)) {
1475                                         printpair(std::clog, *it_last, 0);
1476                                         std::clog << ">";
1477                                         printpair(std::clog, *it, 0);
1478                                         std::clog << "\n";
1479                                         std::clog << "pair1:" << std::endl;
1480                                         it_last->rest.print(print_tree(std::clog));
1481                                         it_last->coeff.print(print_tree(std::clog));
1482                                         std::clog << "pair2:" << std::endl;
1483                                         it->rest.print(print_tree(std::clog));
1484                                         it->coeff.print(print_tree(std::clog));
1485                                         return 0;
1486                                 }
1487                         }
1488                 }
1489         }
1490         return 1;
1491 }
1492
1493
1494 /** Member-wise expand the expairs in this sequence.
1495  *
1496  *  @see expairseq::expand()
1497  *  @return pointer to epvector containing expanded pairs or zero pointer,
1498  *  if no members were changed. */
1499 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1500 {
1501         const epvector::const_iterator last = seq.end();
1502         epvector::const_iterator cit = seq.begin();
1503         while (cit!=last) {
1504                 const ex &expanded_ex = cit->rest.expand(options);
1505                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1506
1507                         // something changed, copy seq, eval and return it
1508                         std::auto_ptr<epvector> s(new epvector);
1509                         s->reserve(seq.size());
1510
1511                         // copy parts of seq which are known not to have changed
1512                         epvector::const_iterator cit2 = seq.begin();
1513                         while (cit2!=cit) {
1514                                 s->push_back(*cit2);
1515                                 ++cit2;
1516                         }
1517
1518                         // copy first changed element
1519                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1520                                                                    cit2->coeff));
1521                         ++cit2;
1522
1523                         // copy rest
1524                         while (cit2!=last) {
1525                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1526                                                                            cit2->coeff));
1527                                 ++cit2;
1528                         }
1529                         return s;
1530                 }
1531                 ++cit;
1532         }
1533
1534         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1535 }
1536
1537
1538 /** Member-wise evaluate the expairs in this sequence.
1539  *
1540  *  @see expairseq::eval()
1541  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1542  *  if no members were changed. */
1543 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1544 {
1545         // returns a NULL pointer if nothing had to be evaluated
1546         // returns a pointer to a newly created epvector otherwise
1547         // (which has to be deleted somewhere else)
1548
1549         if (level==1)
1550                 return std::auto_ptr<epvector>(0);
1551
1552         if (level == -max_recursion_level)
1553                 throw(std::runtime_error("max recursion level reached"));
1554
1555         --level;
1556         epvector::const_iterator last = seq.end();
1557         epvector::const_iterator cit = seq.begin();
1558         while (cit!=last) {
1559                 const ex &evaled_ex = cit->rest.eval(level);
1560                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1561
1562                         // something changed, copy seq, eval and return it
1563                         std::auto_ptr<epvector> s(new epvector);
1564                         s->reserve(seq.size());
1565
1566                         // copy parts of seq which are known not to have changed
1567                         epvector::const_iterator cit2=seq.begin();
1568                         while (cit2!=cit) {
1569                                 s->push_back(*cit2);
1570                                 ++cit2;
1571                         }
1572
1573                         // copy first changed element
1574                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1575                                                                    cit2->coeff));
1576                         ++cit2;
1577
1578                         // copy rest
1579                         while (cit2!=last) {
1580                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1581                                                                            cit2->coeff));
1582                                 ++cit2;
1583                         }
1584                         return s;
1585                 }
1586                 ++cit;
1587         }
1588
1589         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1590 }
1591
1592
1593 /** Member-wise substitute in this sequence.
1594  *
1595  *  @see expairseq::subs()
1596  *  @return pointer to epvector containing pairs after application of subs,
1597  *    or NULL pointer if no members were changed. */
1598 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1599 {
1600         // When any of the objects to be substituted is a product or power
1601         // we have to recombine the pairs because the numeric coefficients may
1602         // be part of the search pattern.
1603         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1604
1605                 // Search the list of substitutions and cache our findings
1606                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1607                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1608                                 options |= subs_options::pattern_is_product;
1609                                 break;
1610                         }
1611                 }
1612                 if (!(options & subs_options::pattern_is_product))
1613                         options |= subs_options::pattern_is_not_product;
1614         }
1615
1616         if (options & subs_options::pattern_is_product) {
1617
1618                 // Substitute in the recombined pairs
1619                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1620                 while (cit != last) {
1621
1622                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1623                         const ex &subsed_ex = orig_ex.subs(m, options);
1624                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1625
1626                                 // Something changed, copy seq, subs and return it
1627                                 std::auto_ptr<epvector> s(new epvector);
1628                                 s->reserve(seq.size());
1629
1630                                 // Copy parts of seq which are known not to have changed
1631                                 s->insert(s->begin(), seq.begin(), cit);
1632
1633                                 // Copy first changed element
1634                                 s->push_back(split_ex_to_pair(subsed_ex));
1635                                 ++cit;
1636
1637                                 // Copy rest
1638                                 while (cit != last) {
1639                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1640                                         ++cit;
1641                                 }
1642                                 return s;
1643                         }
1644
1645                         ++cit;
1646                 }
1647
1648         } else {
1649
1650                 // Substitute only in the "rest" part of the pairs
1651                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1652                 while (cit != last) {
1653
1654                         const ex &subsed_ex = cit->rest.subs(m, options);
1655                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1656
1657                                 // Something changed, copy seq, subs and return it
1658                                 std::auto_ptr<epvector> s(new epvector);
1659                                 s->reserve(seq.size());
1660
1661                                 // Copy parts of seq which are known not to have changed
1662                                 s->insert(s->begin(), seq.begin(), cit);
1663
1664                                 // Copy first changed element
1665                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1666                                 ++cit;
1667
1668                                 // Copy rest
1669                                 while (cit != last) {
1670                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options),
1671                                                                                    cit->coeff));
1672                                         ++cit;
1673                                 }
1674                                 return s;
1675                         }
1676
1677                         ++cit;
1678                 }
1679         }
1680
1681         // Nothing has changed
1682         return std::auto_ptr<epvector>(0);
1683 }
1684
1685 //////////
1686 // static member variables
1687 //////////
1688
1689 #if EXPAIRSEQ_USE_HASHTAB
1690 unsigned expairseq::maxhashtabsize = 0x4000000U;
1691 unsigned expairseq::minhashtabsize = 0x1000U;
1692 unsigned expairseq::hashtabfactor = 1;
1693 #endif // EXPAIRSEQ_USE_HASHTAB
1694
1695 } // namespace GiNaC