ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <iostream>
  24 #include <algorithm>
  25 #include <string>
  26 #include <stdexcept>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "mul.h"
  31 #include "power.h"
  32 #include "relational.h"
  33 #include "wildcard.h"
  34 #include "archive.h"
  35 #include "operators.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  46   print_func<print_context>(&expairseq::do_print).
  47   print_func<print_tree>(&expairseq::do_print_tree))
  48
  49
  50 //////////
  51 // helper classes
  52 //////////
  53
  54 class epp_is_less
  55 {
  56 public:
  57         bool operator()(const epp &lh, const epp &rh) const
  58         {
  59                 return (*lh).is_less(*rh);
  60         }
  61 };
  62
  63 //////////
  64 // default constructor
  65 //////////
  66
  67 // public
  68
  69 expairseq::expairseq() : inherited(TINFO_expairseq)
  70 #if EXPAIRSEQ_USE_HASHTAB
  71                                                    , hashtabsize(0)
  72 #endif // EXPAIRSEQ_USE_HASHTAB
  73 {}
  74
  75 // protected
  76
  77 #if 0
  78 /** For use by copy ctor and assignment operator. */
  79 void expairseq::copy(const expairseq &other)
  80 {
  81         seq = other.seq;
  82         overall_coeff = other.overall_coeff;
  83 #if EXPAIRSEQ_USE_HASHTAB
  84         // copy hashtab
  85         hashtabsize = other.hashtabsize;
  86         if (hashtabsize!=0) {
  87                 hashmask = other.hashmask;
  88                 hashtab.resize(hashtabsize);
  89                 epvector::const_iterator osb = other.seq.begin();
  90                 for (unsigned i=0; i<hashtabsize; ++i) {
  91                         hashtab[i].clear();
  92                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  93                              cit!=other.hashtab[i].end(); ++cit) {
  94                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  95                         }
  96                 }
  97         } else {
  98                 hashtab.clear();
  99         }
 100 #endif // EXPAIRSEQ_USE_HASHTAB
 101 }
 102 #endif
 103
 104 //////////
 105 // other constructors
 106 //////////
 107
 108 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 109 {
 110         construct_from_2_ex(lh,rh);
 111         GINAC_ASSERT(is_canonical());
 112 }
 113
 114 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_exvector(v);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const epvector &v, const ex &oc)
 121   : inherited(TINFO_expairseq), overall_coeff(oc)
 122 {
 123         GINAC_ASSERT(is_a<numeric>(oc));
 124         construct_from_epvector(v);
 125         GINAC_ASSERT(is_canonical());
 126 }
 127
 128 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
 129   : inherited(TINFO_expairseq), overall_coeff(oc)
 130 {
 131         GINAC_ASSERT(vp.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                                 if (it->match(p, repl_lst)) {
 386                                         ops.erase(it);
 387                                         goto found;
 388                                 }
 389                                 ++it;
 390                         }
 391                         return false; // no match found
 392 found:          ;
 393                 }
 394
 395                 if (has_global_wildcard) {
 396
 397                         // Assign all the remaining terms to the global wildcard (unless
 398                         // it has already been matched before, in which case the matches
 399                         // must be equal)
 400                         size_t num = ops.size();
 401                         std::auto_ptr<epvector> vp(new epvector);
 402                         vp->reserve(num);
 403                         for (size_t i=0; i<num; i++)
 404                                 vp->push_back(split_ex_to_pair(ops[i]));
 405                         ex rest = thisexpairseq(vp, default_overall_coeff());
 406                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 407                                 if (it->op(0).is_equal(global_wildcard))
 408                                         return rest.is_equal(it->op(1));
 409                         }
 410                         repl_lst.append(global_wildcard == rest);
 411                         return true;
 412
 413                 } else {
 414
 415                         // No global wildcard, then the match fails if there are any
 416                         // unmatched terms left
 417                         return ops.empty();
 418                 }
 419         }
 420         return inherited::match(pattern, repl_lst);
 421 }
 422
 423 ex expairseq::subs(const exmap & m, unsigned options) const
 424 {
 425         std::auto_ptr<epvector> vp = subschildren(m, options);
 426         if (vp.get())
 427                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 428         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 429                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 430         else
 431                 return subs_one_level(m, options);
 432 }
 433
 434 // protected
 435
 436 int expairseq::compare_same_type(const basic &other) const
 437 {
 438         GINAC_ASSERT(is_a<expairseq>(other));
 439         const expairseq &o = static_cast<const expairseq &>(other);
 440
 441         int cmpval;
 442
 443         // compare number of elements
 444         if (seq.size() != o.seq.size())
 445                 return (seq.size()<o.seq.size()) ? -1 : 1;
 446
 447         // compare overall_coeff
 448         cmpval = overall_coeff.compare(o.overall_coeff);
 449         if (cmpval!=0)
 450                 return cmpval;
 451
 452 #if EXPAIRSEQ_USE_HASHTAB
 453         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 454         if (hashtabsize==0) {
 455 #endif // EXPAIRSEQ_USE_HASHTAB
 456                 epvector::const_iterator cit1 = seq.begin();
 457                 epvector::const_iterator cit2 = o.seq.begin();
 458                 epvector::const_iterator last1 = seq.end();
 459                 epvector::const_iterator last2 = o.seq.end();
 460
 461                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 462                         cmpval = (*cit1).compare(*cit2);
 463                         if (cmpval!=0) return cmpval;
 464                 }
 465
 466                 GINAC_ASSERT(cit1==last1);
 467                 GINAC_ASSERT(cit2==last2);
 468
 469                 return 0;
 470 #if EXPAIRSEQ_USE_HASHTAB
 471         }
 472
 473         // compare number of elements in each hashtab entry
 474         for (unsigned i=0; i<hashtabsize; ++i) {
 475                 unsigned cursize=hashtab[i].size();
 476                 if (cursize != o.hashtab[i].size())
 477                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 478         }
 479
 480         // compare individual (sorted) hashtab entries
 481         for (unsigned i=0; i<hashtabsize; ++i) {
 482                 unsigned sz = hashtab[i].size();
 483                 if (sz>0) {
 484                         const epplist &eppl1 = hashtab[i];
 485                         const epplist &eppl2 = o.hashtab[i];
 486                         epplist::const_iterator it1 = eppl1.begin();
 487                         epplist::const_iterator it2 = eppl2.begin();
 488                         while (it1!=eppl1.end()) {
 489                                 cmpval = (*(*it1)).compare(*(*it2));
 490                                 if (cmpval!=0)
 491                                         return cmpval;
 492                                 ++it1;
 493                                 ++it2;
 494                         }
 495                 }
 496         }
 497
 498         return 0; // equal
 499 #endif // EXPAIRSEQ_USE_HASHTAB
 500 }
 501
 502 bool expairseq::is_equal_same_type(const basic &other) const
 503 {
 504         const expairseq &o = static_cast<const expairseq &>(other);
 505
 506         // compare number of elements
 507         if (seq.size()!=o.seq.size())
 508                 return false;
 509
 510         // compare overall_coeff
 511         if (!overall_coeff.is_equal(o.overall_coeff))
 512                 return false;
 513
 514 #if EXPAIRSEQ_USE_HASHTAB
 515         // compare number of elements in each hashtab entry
 516         if (hashtabsize!=o.hashtabsize) {
 517                 std::cout << "this:" << std::endl;
 518                 print(print_tree(std::cout));
 519                 std::cout << "other:" << std::endl;
 520                 other.print(print_tree(std::cout));
 521         }
 522
 523         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 524
 525         if (hashtabsize==0) {
 526 #endif // EXPAIRSEQ_USE_HASHTAB
 527                 epvector::const_iterator cit1 = seq.begin();
 528                 epvector::const_iterator cit2 = o.seq.begin();
 529                 epvector::const_iterator last1 = seq.end();
 530
 531                 while (cit1!=last1) {
 532                         if (!(*cit1).is_equal(*cit2)) return false;
 533                         ++cit1;
 534                         ++cit2;
 535                 }
 536
 537                 return true;
 538 #if EXPAIRSEQ_USE_HASHTAB
 539         }
 540
 541         for (unsigned i=0; i<hashtabsize; ++i) {
 542                 if (hashtab[i].size() != o.hashtab[i].size())
 543                         return false;
 544         }
 545
 546         // compare individual sorted hashtab entries
 547         for (unsigned i=0; i<hashtabsize; ++i) {
 548                 unsigned sz = hashtab[i].size();
 549                 if (sz>0) {
 550                         const epplist &eppl1 = hashtab[i];
 551                         const epplist &eppl2 = o.hashtab[i];
 552                         epplist::const_iterator it1 = eppl1.begin();
 553                         epplist::const_iterator it2 = eppl2.begin();
 554                         while (it1!=eppl1.end()) {
 555                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 556                                 ++it1;
 557                                 ++it2;
 558                         }
 559                 }
 560         }
 561
 562         return true;
 563 #endif // EXPAIRSEQ_USE_HASHTAB
 564 }
 565
 566 unsigned expairseq::return_type() const
 567 {
 568         return return_types::noncommutative_composite;
 569 }
 570
 571 unsigned expairseq::calchash() const
 572 {
 573         unsigned v = golden_ratio_hash(this->tinfo());
 574         epvector::const_iterator i = seq.begin();
 575         const epvector::const_iterator end = seq.end();
 576         while (i != end) {
 577                 v ^= i->rest.gethash();
 578 #if !EXPAIRSEQ_USE_HASHTAB
 579                 // rotation spoils commutativity!
 580                 v = rotate_left(v);
 581                 v ^= i->coeff.gethash();
 582 #endif // !EXPAIRSEQ_USE_HASHTAB
 583                 ++i;
 584         }
 585
 586         v ^= overall_coeff.gethash();
 587
 588         // store calculated hash value only if object is already evaluated
 589         if (flags &status_flags::evaluated) {
 590                 setflag(status_flags::hash_calculated);
 591                 hashvalue = v;
 592         }
 593
 594         return v;
 595 }
 596
 597 ex expairseq::expand(unsigned options) const
 598 {
 599         std::auto_ptr<epvector> vp = expandchildren(options);
 600         if (vp.get())
 601                 return thisexpairseq(vp, overall_coeff);
 602         else {
 603                 // The terms have not changed, so it is safe to declare this expanded
 604                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 605         }
 606 }
 607
 608 //////////
 609 // new virtual functions which can be overridden by derived classes
 610 //////////
 611
 612 // protected
 613
 614 /** Create an object of this type.
 615  *  This method works similar to a constructor.  It is useful because expairseq
 616  *  has (at least) two possible different semantics but we want to inherit
 617  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 618  *  has to create a new one of the same semantics, which cannot be done by a
 619  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 620  *  order for this trick to work a derived class must of course override this
 621  *  definition. */
 622 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 623 {
 624         return expairseq(v, oc);
 625 }
 626
 627 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
 628 {
 629         return expairseq(vp, oc);
 630 }
 631
 632 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 633 {
 634         c.s << "[[";
 635         p.rest.print(c, precedence());
 636         c.s << ",";
 637         p.coeff.print(c, precedence());
 638         c.s << "]]";
 639 }
 640
 641 void expairseq::printseq(const print_context & c, char delim,
 642                          unsigned this_precedence,
 643                          unsigned upper_precedence) const
 644 {
 645         if (this_precedence <= upper_precedence)
 646                 c.s << "(";
 647         epvector::const_iterator it, it_last = seq.end() - 1;
 648         for (it=seq.begin(); it!=it_last; ++it) {
 649                 printpair(c, *it, this_precedence);
 650                 c.s << delim;
 651         }
 652         printpair(c, *it, this_precedence);
 653         if (!overall_coeff.is_equal(default_overall_coeff())) {
 654                 c.s << delim;
 655                 overall_coeff.print(c, this_precedence);
 656         }
 657
 658         if (this_precedence <= upper_precedence)
 659                 c.s << ")";
 660 }
 661
 662
 663 /** Form an expair from an ex, using the corresponding semantics.
 664  *  @see expairseq::recombine_pair_to_ex() */
 665 expair expairseq::split_ex_to_pair(const ex &e) const
 666 {
 667         return expair(e,_ex1);
 668 }
 669
 670
 671 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 672                                                 const ex &c) const
 673 {
 674         GINAC_ASSERT(is_exactly_a<numeric>(c));
 675
 676         return expair(e,c);
 677 }
 678
 679
 680 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 681                                                   const ex &c) const
 682 {
 683         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 684         GINAC_ASSERT(is_exactly_a<numeric>(c));
 685
 686         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 687 }
 688
 689
 690 /** Form an ex out of an expair, using the corresponding semantics.
 691  *  @see expairseq::split_ex_to_pair() */
 692 ex expairseq::recombine_pair_to_ex(const expair &p) const
 693 {
 694         return lst(p.rest,p.coeff);
 695 }
 696
 697 bool expairseq::expair_needs_further_processing(epp it)
 698 {
 699 #if EXPAIRSEQ_USE_HASHTAB
 700         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 701 #endif // EXPAIRSEQ_USE_HASHTAB
 702         return false;
 703 }
 704
 705 ex expairseq::default_overall_coeff() const
 706 {
 707         return _ex0;
 708 }
 709
 710 void expairseq::combine_overall_coeff(const ex &c)
 711 {
 712         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 713         GINAC_ASSERT(is_exactly_a<numeric>(c));
 714         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 715 }
 716
 717 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 718 {
 719         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 720         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 721         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 722         overall_coeff = ex_to<numeric>(overall_coeff).
 723                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 724 }
 725
 726 bool expairseq::can_make_flat(const expair &p) const
 727 {
 728         return true;
 729 }
 730
 731
 732 //////////
 733 // non-virtual functions in this class
 734 //////////
 735
 736 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 737 {
 738         exvector v;
 739         v.reserve(2);
 740         v.push_back(lh);
 741         v.push_back(rh);
 742         construct_from_exvector(v);
 743 #if EXPAIRSEQ_USE_HASHTAB
 744         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 745         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 746 #endif // EXPAIRSEQ_USE_HASHTAB
 747 }
 748
 749 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 750 {
 751         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 752                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 753 #if EXPAIRSEQ_USE_HASHTAB
 754                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 755                                              ex_to<expairseq>(rh).seq.size();
 756                         if (calc_hashtabsize(totalsize)!=0) {
 757                                 construct_from_2_ex_via_exvector(lh,rh);
 758                         } else {
 759 #endif // EXPAIRSEQ_USE_HASHTAB
 760                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 761                                                            ex_to<expairseq>(rh));
 762 #if EXPAIRSEQ_USE_HASHTAB
 763                         }
 764 #endif // EXPAIRSEQ_USE_HASHTAB
 765                         return;
 766                 } else {
 767 #if EXPAIRSEQ_USE_HASHTAB
 768                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 769                         if (calc_hashtabsize(totalsize)!=0) {
 770                                 construct_from_2_ex_via_exvector(lh, rh);
 771                         } else {
 772 #endif // EXPAIRSEQ_USE_HASHTAB
 773                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 774 #if EXPAIRSEQ_USE_HASHTAB
 775                         }
 776 #endif // EXPAIRSEQ_USE_HASHTAB
 777                         return;
 778                 }
 779         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 780 #if EXPAIRSEQ_USE_HASHTAB
 781                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 782                 if (calc_hashtabsize(totalsize)!=0) {
 783                         construct_from_2_ex_via_exvector(lh,rh);
 784                 } else {
 785 #endif // EXPAIRSEQ_USE_HASHTAB
 786                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 787 #if EXPAIRSEQ_USE_HASHTAB
 788                 }
 789 #endif // EXPAIRSEQ_USE_HASHTAB
 790                 return;
 791         }
 792
 793 #if EXPAIRSEQ_USE_HASHTAB
 794         if (calc_hashtabsize(2)!=0) {
 795                 construct_from_2_ex_via_exvector(lh,rh);
 796                 return;
 797         }
 798         hashtabsize = 0;
 799 #endif // EXPAIRSEQ_USE_HASHTAB
 800
 801         if (is_exactly_a<numeric>(lh)) {
 802                 if (is_exactly_a<numeric>(rh)) {
 803                         combine_overall_coeff(lh);
 804                         combine_overall_coeff(rh);
 805                 } else {
 806                         combine_overall_coeff(lh);
 807                         seq.push_back(split_ex_to_pair(rh));
 808                 }
 809         } else {
 810                 if (is_exactly_a<numeric>(rh)) {
 811                         combine_overall_coeff(rh);
 812                         seq.push_back(split_ex_to_pair(lh));
 813                 } else {
 814                         expair p1 = split_ex_to_pair(lh);
 815                         expair p2 = split_ex_to_pair(rh);
 816
 817                         int cmpval = p1.rest.compare(p2.rest);
 818                         if (cmpval==0) {
 819                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 820                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 821                                         // no further processing is necessary, since this
 822                                         // one element will usually be recombined in eval()
 823                                         seq.push_back(p1);
 824                                 }
 825                         } else {
 826                                 seq.reserve(2);
 827                                 if (cmpval<0) {
 828                                         seq.push_back(p1);
 829                                         seq.push_back(p2);
 830                                 } else {
 831                                         seq.push_back(p2);
 832                                         seq.push_back(p1);
 833                                 }
 834                         }
 835                 }
 836         }
 837 }
 838
 839 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 840                                                                                    const expairseq &s2)
 841 {
 842         combine_overall_coeff(s1.overall_coeff);
 843         combine_overall_coeff(s2.overall_coeff);
 844
 845         epvector::const_iterator first1 = s1.seq.begin();
 846         epvector::const_iterator last1 = s1.seq.end();
 847         epvector::const_iterator first2 = s2.seq.begin();
 848         epvector::const_iterator last2 = s2.seq.end();
 849
 850         seq.reserve(s1.seq.size()+s2.seq.size());
 851
 852         bool needs_further_processing=false;
 853
 854         while (first1!=last1 && first2!=last2) {
 855                 int cmpval = (*first1).rest.compare((*first2).rest);
 856                 if (cmpval==0) {
 857                         // combine terms
 858                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 859                                                    add(ex_to<numeric>(first2->coeff));
 860                         if (!newcoeff.is_zero()) {
 861                                 seq.push_back(expair(first1->rest,newcoeff));
 862                                 if (expair_needs_further_processing(seq.end()-1)) {
 863                                         needs_further_processing = true;
 864                                 }
 865                         }
 866                         ++first1;
 867                         ++first2;
 868                 } else if (cmpval<0) {
 869                         seq.push_back(*first1);
 870                         ++first1;
 871                 } else {
 872                         seq.push_back(*first2);
 873                         ++first2;
 874                 }
 875         }
 876
 877         while (first1!=last1) {
 878                 seq.push_back(*first1);
 879                 ++first1;
 880         }
 881         while (first2!=last2) {
 882                 seq.push_back(*first2);
 883                 ++first2;
 884         }
 885
 886         if (needs_further_processing) {
 887                 epvector v = seq;
 888                 seq.clear();
 889                 construct_from_epvector(v);
 890         }
 891 }
 892
 893 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 894                                                                                         const ex &e)
 895 {
 896         combine_overall_coeff(s.overall_coeff);
 897         if (is_exactly_a<numeric>(e)) {
 898                 combine_overall_coeff(e);
 899                 seq = s.seq;
 900                 return;
 901         }
 902
 903         epvector::const_iterator first = s.seq.begin();
 904         epvector::const_iterator last = s.seq.end();
 905         expair p = split_ex_to_pair(e);
 906
 907         seq.reserve(s.seq.size()+1);
 908         bool p_pushed = false;
 909
 910         bool needs_further_processing=false;
 911
 912         // merge p into s.seq
 913         while (first!=last) {
 914                 int cmpval = (*first).rest.compare(p.rest);
 915                 if (cmpval==0) {
 916                         // combine terms
 917                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 918                                                    add(ex_to<numeric>(p.coeff));
 919                         if (!newcoeff.is_zero()) {
 920                                 seq.push_back(expair(first->rest,newcoeff));
 921                                 if (expair_needs_further_processing(seq.end()-1))
 922                                         needs_further_processing = true;
 923                         }
 924                         ++first;
 925                         p_pushed = true;
 926                         break;
 927                 } else if (cmpval<0) {
 928                         seq.push_back(*first);
 929                         ++first;
 930                 } else {
 931                         seq.push_back(p);
 932                         p_pushed = true;
 933                         break;
 934                 }
 935         }
 936
 937         if (p_pushed) {
 938                 // while loop exited because p was pushed, now push rest of s.seq
 939                 while (first!=last) {
 940                         seq.push_back(*first);
 941                         ++first;
 942                 }
 943         } else {
 944                 // while loop exited because s.seq was pushed, now push p
 945                 seq.push_back(p);
 946         }
 947
 948         if (needs_further_processing) {
 949                 epvector v = seq;
 950                 seq.clear();
 951                 construct_from_epvector(v);
 952         }
 953 }
 954
 955 void expairseq::construct_from_exvector(const exvector &v)
 956 {
 957         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 958         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 959         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 960         //                  (same for (+,*) -> (*,^)
 961
 962         make_flat(v);
 963 #if EXPAIRSEQ_USE_HASHTAB
 964         combine_same_terms();
 965 #else
 966         canonicalize();
 967         combine_same_terms_sorted_seq();
 968 #endif // EXPAIRSEQ_USE_HASHTAB
 969 }
 970
 971 void expairseq::construct_from_epvector(const epvector &v)
 972 {
 973         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 974         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 975         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 976         //                  (same for (+,*) -> (*,^)
 977
 978         make_flat(v);
 979 #if EXPAIRSEQ_USE_HASHTAB
 980         combine_same_terms();
 981 #else
 982         canonicalize();
 983         combine_same_terms_sorted_seq();
 984 #endif // EXPAIRSEQ_USE_HASHTAB
 985 }
 986
 987 /** Combine this expairseq with argument exvector.
 988  *  It cares for associativity as well as for special handling of numerics. */
 989 void expairseq::make_flat(const exvector &v)
 990 {
 991         exvector::const_iterator cit;
 992
 993         // count number of operands which are of same expairseq derived type
 994         // and their cumulative number of operands
 995         int nexpairseqs = 0;
 996         int noperands = 0;
 997
 998         cit = v.begin();
 999         while (cit!=v.end()) {
1000                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1001                         ++nexpairseqs;
1002                         noperands += ex_to<expairseq>(*cit).seq.size();
1003                 }
1004                 ++cit;
1005         }
1006
1007         // reserve seq and coeffseq which will hold all operands
1008         seq.reserve(v.size()+noperands-nexpairseqs);
1009
1010         // copy elements and split off numerical part
1011         cit = v.begin();
1012         while (cit!=v.end()) {
1013                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1014                         const expairseq &subseqref = ex_to<expairseq>(*cit);
1015                         combine_overall_coeff(subseqref.overall_coeff);
1016                         epvector::const_iterator cit_s = subseqref.seq.begin();
1017                         while (cit_s!=subseqref.seq.end()) {
1018                                 seq.push_back(*cit_s);
1019                                 ++cit_s;
1020                         }
1021                 } else {
1022                         if (is_exactly_a<numeric>(*cit))
1023                                 combine_overall_coeff(*cit);
1024                         else
1025                                 seq.push_back(split_ex_to_pair(*cit));
1026                 }
1027                 ++cit;
1028         }
1029 }
1030
1031 /** Combine this expairseq with argument epvector.
1032  *  It cares for associativity as well as for special handling of numerics. */
1033 void expairseq::make_flat(const epvector &v)
1034 {
1035         epvector::const_iterator cit;
1036
1037         // count number of operands which are of same expairseq derived type
1038         // and their cumulative number of operands
1039         int nexpairseqs = 0;
1040         int noperands = 0;
1041
1042         cit = v.begin();
1043         while (cit!=v.end()) {
1044                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1045                         ++nexpairseqs;
1046                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1047                 }
1048                 ++cit;
1049         }
1050
1051         // reserve seq and coeffseq which will hold all operands
1052         seq.reserve(v.size()+noperands-nexpairseqs);
1053
1054         // copy elements and split off numerical part
1055         cit = v.begin();
1056         while (cit!=v.end()) {
1057                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1058                     this->can_make_flat(*cit)) {
1059                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1060                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1061                                                             ex_to<numeric>(cit->coeff));
1062                         epvector::const_iterator cit_s = subseqref.seq.begin();
1063                         while (cit_s!=subseqref.seq.end()) {
1064                                 seq.push_back(expair(cit_s->rest,
1065                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1066                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1067                                 //                                              (*cit).coeff));
1068                                 ++cit_s;
1069                         }
1070                 } else {
1071                         if (cit->is_canonical_numeric())
1072                                 combine_overall_coeff(cit->rest);
1073                         else
1074                                 seq.push_back(*cit);
1075                 }
1076                 ++cit;
1077         }
1078 }
1079
1080 /** Brings this expairseq into a sorted (canonical) form. */
1081 void expairseq::canonicalize()
1082 {
1083         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1084 }
1085
1086
1087 /** Compact a presorted expairseq by combining all matching expairs to one
1088  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1089  *  instance. */
1090 void expairseq::combine_same_terms_sorted_seq()
1091 {
1092         if (seq.size()<2)
1093                 return;
1094
1095         bool needs_further_processing = false;
1096
1097         epvector::iterator itin1 = seq.begin();
1098         epvector::iterator itin2 = itin1+1;
1099         epvector::iterator itout = itin1;
1100         epvector::iterator last = seq.end();
1101         // must_copy will be set to true the first time some combination is
1102         // possible from then on the sequence has changed and must be compacted
1103         bool must_copy = false;
1104         while (itin2!=last) {
1105                 if (itin1->rest.compare(itin2->rest)==0) {
1106                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1107                                        add_dyn(ex_to<numeric>(itin2->coeff));
1108                         if (expair_needs_further_processing(itin1))
1109                                 needs_further_processing = true;
1110                         must_copy = true;
1111                 } else {
1112                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1113                                 if (must_copy)
1114                                         *itout = *itin1;
1115                                 ++itout;
1116                         }
1117                         itin1 = itin2;
1118                 }
1119                 ++itin2;
1120         }
1121         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1122                 if (must_copy)
1123                         *itout = *itin1;
1124                 ++itout;
1125         }
1126         if (itout!=last)
1127                 seq.erase(itout,last);
1128
1129         if (needs_further_processing) {
1130                 epvector v = seq;
1131                 seq.clear();
1132                 construct_from_epvector(v);
1133         }
1134 }
1135
1136 #if EXPAIRSEQ_USE_HASHTAB
1137
1138 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1139 {
1140         unsigned size;
1141         unsigned nearest_power_of_2 = 1 << log2(sz);
1142         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1143         //  size = nearest_power_of_2*hashtabfactor;
1144         size = nearest_power_of_2/hashtabfactor;
1145         if (size<minhashtabsize)
1146                 return 0;
1147
1148         // hashtabsize must be a power of 2
1149         GINAC_ASSERT((1U << log2(size))==size);
1150         return size;
1151 }
1152
1153 unsigned expairseq::calc_hashindex(const ex &e) const
1154 {
1155         // calculate hashindex
1156         unsigned hashindex;
1157         if (is_a<numeric>(e)) {
1158                 hashindex = hashmask;
1159         } else {
1160                 hashindex = e.gethash() & hashmask;
1161                 // last hashtab entry is reserved for numerics
1162                 if (hashindex==hashmask) hashindex = 0;
1163         }
1164         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1165         return hashindex;
1166 }
1167
1168 void expairseq::shrink_hashtab()
1169 {
1170         unsigned new_hashtabsize;
1171         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1172                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1173                 if (new_hashtabsize==0) {
1174                         hashtab.clear();
1175                         hashtabsize = 0;
1176                         canonicalize();
1177                         return;
1178                 }
1179
1180                 // shrink by a factor of 2
1181                 unsigned half_hashtabsize = hashtabsize/2;
1182                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1183                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1184                 // special treatment for numeric hashes
1185                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1186                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1187                 hashtab.resize(half_hashtabsize);
1188                 hashtabsize = half_hashtabsize;
1189                 hashmask = hashtabsize-1;
1190         }
1191 }
1192
1193 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1194 {
1195         if (hashtabsize==0)
1196                 return; // nothing to do
1197
1198         // calculate hashindex of element to be deleted
1199         unsigned hashindex = calc_hashindex((*element).rest);
1200
1201         // find it in hashtab and remove it
1202         epplist &eppl = hashtab[hashindex];
1203         epplist::iterator epplit = eppl.begin();
1204         bool erased = false;
1205         while (epplit!=eppl.end()) {
1206                 if (*epplit == element) {
1207                         eppl.erase(epplit);
1208                         erased = true;
1209                         break;
1210                 }
1211                 ++epplit;
1212         }
1213         if (!erased) {
1214                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1215                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1216
1217                 unsigned hashindex = calc_hashindex(element->rest);
1218                 epplist &eppl = hashtab[hashindex];
1219                 epplist::iterator epplit = eppl.begin();
1220                 bool erased = false;
1221                 while (epplit!=eppl.end()) {
1222                         if (*epplit == element) {
1223                                 eppl.erase(epplit);
1224                                 erased = true;
1225                                 break;
1226                         }
1227                         ++epplit;
1228                 }
1229                 GINAC_ASSERT(erased);
1230         }
1231         GINAC_ASSERT(erased);
1232 }
1233
1234 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1235                                    epvector::iterator newpos)
1236 {
1237         GINAC_ASSERT(hashtabsize!=0);
1238
1239         // calculate hashindex of element which was moved
1240         unsigned hashindex=calc_hashindex((*newpos).rest);
1241
1242         // find it in hashtab and modify it
1243         epplist &eppl = hashtab[hashindex];
1244         epplist::iterator epplit = eppl.begin();
1245         while (epplit!=eppl.end()) {
1246                 if (*epplit == oldpos) {
1247                         *epplit = newpos;
1248                         break;
1249                 }
1250                 ++epplit;
1251         }
1252         GINAC_ASSERT(epplit!=eppl.end());
1253 }
1254
1255 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1256 {
1257         epplist::const_iterator current = eppl.begin();
1258         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1259                 ++current;
1260         }
1261         eppl.insert(current,elem);
1262 }
1263
1264 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1265                                           epvector::iterator &last_non_zero,
1266                                           std::vector<bool> &touched,
1267                                           unsigned &number_of_zeroes)
1268 {
1269         epp current = seq.begin();
1270
1271         while (current!=first_numeric) {
1272                 if (is_exactly_a<numeric>(current->rest)) {
1273                         --first_numeric;
1274                         iter_swap(current,first_numeric);
1275                 } else {
1276                         // calculate hashindex
1277                         unsigned currenthashindex = calc_hashindex(current->rest);
1278
1279                         // test if there is already a matching expair in the hashtab-list
1280                         epplist &eppl=hashtab[currenthashindex];
1281                         epplist::iterator epplit = eppl.begin();
1282                         while (epplit!=eppl.end()) {
1283                                 if (current->rest.is_equal((*epplit)->rest))
1284                                         break;
1285                                 ++epplit;
1286                         }
1287                         if (epplit==eppl.end()) {
1288                                 // no matching expair found, append this to end of list
1289                                 sorted_insert(eppl,current);
1290                                 ++current;
1291                         } else {
1292                                 // epplit points to a matching expair, combine it with current
1293                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1294                                                    add_dyn(ex_to<numeric>(current->coeff));
1295
1296                                 // move obsolete current expair to end by swapping with last_non_zero element
1297                                 // if this was a numeric, it is swapped with the expair before first_numeric
1298                                 iter_swap(current,last_non_zero);
1299                                 --first_numeric;
1300                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1301                                 --last_non_zero;
1302                                 ++number_of_zeroes;
1303                                 // test if combined term has coeff 0 and can be removed is done later
1304                                 touched[(*epplit)-seq.begin()] = true;
1305                         }
1306                 }
1307         }
1308 }
1309
1310 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1311                                    epvector::iterator &last_non_zero,
1312                                    std::vector<bool> &touched,
1313                                    unsigned &number_of_zeroes)
1314 {
1315         // move terms with coeff 0 to end and remove them from hashtab
1316         // check only those elements which have been touched
1317         epp current = seq.begin();
1318         size_t i = 0;
1319         while (current!=first_numeric) {
1320                 if (!touched[i]) {
1321                         ++current;
1322                         ++i;
1323                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1324                         ++current;
1325                         ++i;
1326                 } else {
1327                         remove_hashtab_entry(current);
1328
1329                         // move element to the end, unless it is already at the end
1330                         if (current!=last_non_zero) {
1331                                 iter_swap(current,last_non_zero);
1332                                 --first_numeric;
1333                                 bool numeric_swapped = first_numeric!=last_non_zero;
1334                                 if (numeric_swapped)
1335                                         iter_swap(first_numeric,current);
1336                                 epvector::iterator changed_entry;
1337
1338                                 if (numeric_swapped)
1339                                         changed_entry = first_numeric;
1340                                 else
1341                                         changed_entry = last_non_zero;
1342
1343                                 --last_non_zero;
1344                                 ++number_of_zeroes;
1345
1346                                 if (first_numeric!=current) {
1347
1348                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1349                                         move_hashtab_entry(changed_entry,current);
1350                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1351                                 }
1352                         } else {
1353                                 --first_numeric;
1354                                 --last_non_zero;
1355                                 ++number_of_zeroes;
1356                         }
1357                 }
1358         }
1359         GINAC_ASSERT(i==current-seq.begin());
1360 }
1361
1362 /** True if one of the coeffs vanishes, otherwise false.
1363  *  This would be an invariant violation, so this should only be used for
1364  *  debugging purposes. */
1365 bool expairseq::has_coeff_0() const
1366 {
1367         epvector::const_iterator i = seq.begin(), end = seq.end();
1368         while (i != end) {
1369                 if (i->coeff.is_zero())
1370                         return true;
1371                 ++i;
1372         }
1373         return false;
1374 }
1375
1376 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1377                                                                                 epvector::const_iterator last_non_zero)
1378 {
1379         if (first_numeric == seq.end()) return; // no numerics
1380
1381         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1382         while (current != last) {
1383                 sorted_insert(hashtab[hashmask], current);
1384                 ++current;
1385         }
1386 }
1387
1388 void expairseq::combine_same_terms()
1389 {
1390         // combine same terms, drop term with coeff 0, move numerics to end
1391
1392         // calculate size of hashtab
1393         hashtabsize = calc_hashtabsize(seq.size());
1394
1395         // hashtabsize is a power of 2
1396         hashmask = hashtabsize-1;
1397
1398         // allocate hashtab
1399         hashtab.clear();
1400         hashtab.resize(hashtabsize);
1401
1402         if (hashtabsize==0) {
1403                 canonicalize();
1404                 combine_same_terms_sorted_seq();
1405                 GINAC_ASSERT(!has_coeff_0());
1406                 return;
1407         }
1408
1409         // iterate through seq, move numerics to end,
1410         // fill hashtab and combine same terms
1411         epvector::iterator first_numeric = seq.end();
1412         epvector::iterator last_non_zero = seq.end()-1;
1413
1414         size_t num = seq.size();
1415         std::vector<bool> touched(num);
1416
1417         unsigned number_of_zeroes = 0;
1418
1419         GINAC_ASSERT(!has_coeff_0());
1420         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1421
1422         // there should not be any terms with coeff 0 from the beginning,
1423         // so it should be safe to skip this step
1424         if (number_of_zeroes!=0) {
1425                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1426         }
1427
1428         add_numerics_to_hashtab(first_numeric,last_non_zero);
1429
1430         // pop zero elements
1431         for (unsigned i=0; i<number_of_zeroes; ++i) {
1432                 seq.pop_back();
1433         }
1434
1435         // shrink hashtabsize to calculated value
1436         GINAC_ASSERT(!has_coeff_0());
1437
1438         shrink_hashtab();
1439
1440         GINAC_ASSERT(!has_coeff_0());
1441 }
1442
1443 #endif // EXPAIRSEQ_USE_HASHTAB
1444
1445 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1446  *  debugging or in assertions since being sorted is an invariance. */
1447 bool expairseq::is_canonical() const
1448 {
1449         if (seq.size() <= 1)
1450                 return 1;
1451
1452 #if EXPAIRSEQ_USE_HASHTAB
1453         if (hashtabsize > 0) return 1; // not canoncalized
1454 #endif // EXPAIRSEQ_USE_HASHTAB
1455
1456         epvector::const_iterator it = seq.begin(), itend = seq.end();
1457         epvector::const_iterator it_last = it;
1458         for (++it; it!=itend; it_last=it, ++it) {
1459                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1460                         if (!is_exactly_a<numeric>(it_last->rest) ||
1461                                 !is_exactly_a<numeric>(it->rest)) {
1462                                 // double test makes it easier to set a breakpoint...
1463                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1464                                         !is_exactly_a<numeric>(it->rest)) {
1465                                         printpair(std::clog, *it_last, 0);
1466                                         std::clog << ">";
1467                                         printpair(std::clog, *it, 0);
1468                                         std::clog << "\n";
1469                                         std::clog << "pair1:" << std::endl;
1470                                         it_last->rest.print(print_tree(std::clog));
1471                                         it_last->coeff.print(print_tree(std::clog));
1472                                         std::clog << "pair2:" << std::endl;
1473                                         it->rest.print(print_tree(std::clog));
1474                                         it->coeff.print(print_tree(std::clog));
1475                                         return 0;
1476                                 }
1477                         }
1478                 }
1479         }
1480         return 1;
1481 }
1482
1483
1484 /** Member-wise expand the expairs in this sequence.
1485  *
1486  *  @see expairseq::expand()
1487  *  @return pointer to epvector containing expanded pairs or zero pointer,
1488  *  if no members were changed. */
1489 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1490 {
1491         const epvector::const_iterator last = seq.end();
1492         epvector::const_iterator cit = seq.begin();
1493         while (cit!=last) {
1494                 const ex &expanded_ex = cit->rest.expand(options);
1495                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1496
1497                         // something changed, copy seq, eval and return it
1498                         std::auto_ptr<epvector> s(new epvector);
1499                         s->reserve(seq.size());
1500
1501                         // copy parts of seq which are known not to have changed
1502                         epvector::const_iterator cit2 = seq.begin();
1503                         while (cit2!=cit) {
1504                                 s->push_back(*cit2);
1505                                 ++cit2;
1506                         }
1507
1508                         // copy first changed element
1509                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1510                                                                    cit2->coeff));
1511                         ++cit2;
1512
1513                         // copy rest
1514                         while (cit2!=last) {
1515                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1516                                                                            cit2->coeff));
1517                                 ++cit2;
1518                         }
1519                         return s;
1520                 }
1521                 ++cit;
1522         }
1523
1524         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1525 }
1526
1527
1528 /** Member-wise evaluate the expairs in this sequence.
1529  *
1530  *  @see expairseq::eval()
1531  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1532  *  if no members were changed. */
1533 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1534 {
1535         // returns a NULL pointer if nothing had to be evaluated
1536         // returns a pointer to a newly created epvector otherwise
1537         // (which has to be deleted somewhere else)
1538
1539         if (level==1)
1540                 return std::auto_ptr<epvector>(0);
1541
1542         if (level == -max_recursion_level)
1543                 throw(std::runtime_error("max recursion level reached"));
1544
1545         --level;
1546         epvector::const_iterator last = seq.end();
1547         epvector::const_iterator cit = seq.begin();
1548         while (cit!=last) {
1549                 const ex &evaled_ex = cit->rest.eval(level);
1550                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1551
1552                         // something changed, copy seq, eval and return it
1553                         std::auto_ptr<epvector> s(new epvector);
1554                         s->reserve(seq.size());
1555
1556                         // copy parts of seq which are known not to have changed
1557                         epvector::const_iterator cit2=seq.begin();
1558                         while (cit2!=cit) {
1559                                 s->push_back(*cit2);
1560                                 ++cit2;
1561                         }
1562
1563                         // copy first changed element
1564                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1565                                                                    cit2->coeff));
1566                         ++cit2;
1567
1568                         // copy rest
1569                         while (cit2!=last) {
1570                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1571                                                                            cit2->coeff));
1572                                 ++cit2;
1573                         }
1574                         return s;
1575                 }
1576                 ++cit;
1577         }
1578
1579         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1580 }
1581
1582
1583 /** Member-wise substitute in this sequence.
1584  *
1585  *  @see expairseq::subs()
1586  *  @return pointer to epvector containing pairs after application of subs,
1587  *    or NULL pointer if no members were changed. */
1588 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1589 {
1590         // When any of the objects to be substituted is a product or power
1591         // we have to recombine the pairs because the numeric coefficients may
1592         // be part of the search pattern.
1593         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1594
1595                 // Search the list of substitutions and cache our findings
1596                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1597                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1598                                 options |= subs_options::pattern_is_product;
1599                                 break;
1600                         }
1601                 }
1602                 if (!(options & subs_options::pattern_is_product))
1603                         options |= subs_options::pattern_is_not_product;
1604         }
1605
1606         if (options & subs_options::pattern_is_product) {
1607
1608                 // Substitute in the recombined pairs
1609                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1610                 while (cit != last) {
1611
1612                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1613                         const ex &subsed_ex = orig_ex.subs(m, options);
1614                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1615
1616                                 // Something changed, copy seq, subs and return it
1617                                 std::auto_ptr<epvector> s(new epvector);
1618                                 s->reserve(seq.size());
1619
1620                                 // Copy parts of seq which are known not to have changed
1621                                 s->insert(s->begin(), seq.begin(), cit);
1622
1623                                 // Copy first changed element
1624                                 s->push_back(split_ex_to_pair(subsed_ex));
1625                                 ++cit;
1626
1627                                 // Copy rest
1628                                 while (cit != last) {
1629                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1630                                         ++cit;
1631                                 }
1632                                 return s;
1633                         }
1634
1635                         ++cit;
1636                 }
1637
1638         } else {
1639
1640                 // Substitute only in the "rest" part of the pairs
1641                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1642                 while (cit != last) {
1643
1644                         const ex &subsed_ex = cit->rest.subs(m, options);
1645                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1646
1647                                 // Something changed, copy seq, subs and return it
1648                                 std::auto_ptr<epvector> s(new epvector);
1649                                 s->reserve(seq.size());
1650
1651                                 // Copy parts of seq which are known not to have changed
1652                                 s->insert(s->begin(), seq.begin(), cit);
1653
1654                                 // Copy first changed element
1655                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1656                                 ++cit;
1657
1658                                 // Copy rest
1659                                 while (cit != last) {
1660                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options),
1661                                                                                    cit->coeff));
1662                                         ++cit;
1663                                 }
1664                                 return s;
1665                         }
1666
1667                         ++cit;
1668                 }
1669         }
1670
1671         // Nothing has changed
1672         return std::auto_ptr<epvector>(0);
1673 }
1674
1675 //////////
1676 // static member variables
1677 //////////
1678
1679 #if EXPAIRSEQ_USE_HASHTAB
1680 unsigned expairseq::maxhashtabsize = 0x4000000U;
1681 unsigned expairseq::minhashtabsize = 0x1000U;
1682 unsigned expairseq::hashtabfactor = 1;
1683 #endif // EXPAIRSEQ_USE_HASHTAB
1684
1685 } // namespace GiNaC