ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2008 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 #include <iterator>
  28
  29 #include "expairseq.h"
  30 #include "lst.h"
  31 #include "add.h"
  32 #include "mul.h"
  33 #include "power.h"
  34 #include "relational.h"
  35 #include "wildcard.h"
  36 #include "archive.h"
  37 #include "operators.h"
  38 #include "utils.h"
  39 #include "indexed.h"
  40
  41 #if EXPAIRSEQ_USE_HASHTAB
  42 #include <cmath>
  43 #endif // EXPAIRSEQ_USE_HASHTAB
  44
  45 namespace GiNaC {
  46
  47
  48 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  49   print_func<print_context>(&expairseq::do_print).
  50   print_func<print_tree>(&expairseq::do_print_tree))
  51
  52
  53 //////////
  54 // helper classes
  55 //////////
  56
  57 class epp_is_less
  58 {
  59 public:
  60         bool operator()(const epp &lh, const epp &rh) const
  61         {
  62                 return (*lh).is_less(*rh);
  63         }
  64 };
  65
  66 //////////
  67 // default constructor
  68 //////////
  69
  70 // public
  71
  72 expairseq::expairseq() : inherited(&expairseq::tinfo_static)
  73 #if EXPAIRSEQ_USE_HASHTAB
  74                                                    , hashtabsize(0)
  75 #endif // EXPAIRSEQ_USE_HASHTAB
  76 {}
  77
  78 // protected
  79
  80 #if 0
  81 /** For use by copy ctor and assignment operator. */
  82 void expairseq::copy(const expairseq &other)
  83 {
  84         seq = other.seq;
  85         overall_coeff = other.overall_coeff;
  86 #if EXPAIRSEQ_USE_HASHTAB
  87         // copy hashtab
  88         hashtabsize = other.hashtabsize;
  89         if (hashtabsize!=0) {
  90                 hashmask = other.hashmask;
  91                 hashtab.resize(hashtabsize);
  92                 epvector::const_iterator osb = other.seq.begin();
  93                 for (unsigned i=0; i<hashtabsize; ++i) {
  94                         hashtab[i].clear();
  95                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  96                              cit!=other.hashtab[i].end(); ++cit) {
  97                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  98                         }
  99                 }
 100         } else {
 101                 hashtab.clear();
 102         }
 103 #endif // EXPAIRSEQ_USE_HASHTAB
 104 }
 105 #endif
 106
 107 //////////
 108 // other constructors
 109 //////////
 110
 111 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(&expairseq::tinfo_static)
 112 {
 113         construct_from_2_ex(lh,rh);
 114         GINAC_ASSERT(is_canonical());
 115 }
 116
 117 expairseq::expairseq(const exvector &v) : inherited(&expairseq::tinfo_static)
 118 {
 119         construct_from_exvector(v);
 120         GINAC_ASSERT(is_canonical());
 121 }
 122
 123 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
 124   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
 125 {
 126         GINAC_ASSERT(is_a<numeric>(oc));
 127         construct_from_epvector(v, do_index_renaming);
 128         GINAC_ASSERT(is_canonical());
 129 }
 130
 131 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
 132   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
 133 {
 134         GINAC_ASSERT(vp.get()!=0);
 135         GINAC_ASSERT(is_a<numeric>(oc));
 136         construct_from_epvector(*vp, do_index_renaming);
 137         GINAC_ASSERT(is_canonical());
 138 }
 139
 140 //////////
 141 // archiving
 142 //////////
 143
 144 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 145 #if EXPAIRSEQ_USE_HASHTAB
 146         , hashtabsize(0)
 147 #endif
 148 {
 149         archive_node::archive_node_cit first = n.find_first("rest");
 150         archive_node::archive_node_cit last = n.find_last("coeff");
 151         ++last;
 152         seq.reserve((last-first)/2);
 153
 154         for (archive_node::archive_node_cit loc = first; loc < last;) {
 155                 ex rest;
 156                 ex coeff;
 157                 n.find_ex_by_loc(loc++, rest, sym_lst);
 158                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 159                 seq.push_back(expair(rest, coeff));
 160         }
 161
 162         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 163
 164         canonicalize();
 165         GINAC_ASSERT(is_canonical());
 166 }
 167
 168 void expairseq::archive(archive_node &n) const
 169 {
 170         inherited::archive(n);
 171         epvector::const_iterator i = seq.begin(), iend = seq.end();
 172         while (i != iend) {
 173                 n.add_ex("rest", i->rest);
 174                 n.add_ex("coeff", i->coeff);
 175                 ++i;
 176         }
 177         n.add_ex("overall_coeff", overall_coeff);
 178 }
 179
 180 DEFAULT_UNARCHIVE(expairseq)
 181
 182 //////////
 183 // functions overriding virtual functions from base classes
 184 //////////
 185
 186 // public
 187
 188 void expairseq::do_print(const print_context & c, unsigned level) const
 189 {
 190         c.s << "[[";
 191         printseq(c, ',', precedence(), level);
 192         c.s << "]]";
 193 }
 194
 195 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 196 {
 197         c.s << std::string(level, ' ') << class_name() << " @" << this
 198             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 199             << ", nops=" << nops()
 200             << std::endl;
 201         size_t num = seq.size();
 202         for (size_t i=0; i<num; ++i) {
 203                 seq[i].rest.print(c, level + c.delta_indent);
 204                 seq[i].coeff.print(c, level + c.delta_indent);
 205                 if (i != num - 1)
 206                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 207         }
 208         if (!overall_coeff.is_equal(default_overall_coeff())) {
 209                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 210                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 211                 overall_coeff.print(c, level + c.delta_indent);
 212         }
 213         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 214 #if EXPAIRSEQ_USE_HASHTAB
 215         c.s << std::string(level + c.delta_indent,' ')
 216             << "hashtab size " << hashtabsize << std::endl;
 217         if (hashtabsize == 0) return;
 218 #define MAXCOUNT 5
 219         unsigned count[MAXCOUNT+1];
 220         for (int i=0; i<MAXCOUNT+1; ++i)
 221                 count[i] = 0;
 222         unsigned this_bin_fill;
 223         unsigned cum_fill_sq = 0;
 224         unsigned cum_fill = 0;
 225         for (unsigned i=0; i<hashtabsize; ++i) {
 226                 this_bin_fill = 0;
 227                 if (hashtab[i].size() > 0) {
 228                         c.s << std::string(level + c.delta_indent, ' ')
 229                             << "bin " << i << " with entries ";
 230                         for (epplist::const_iterator it=hashtab[i].begin();
 231                              it!=hashtab[i].end(); ++it) {
 232                                 c.s << *it-seq.begin() << " ";
 233                                 ++this_bin_fill;
 234                         }
 235                         c.s << std::endl;
 236                         cum_fill += this_bin_fill;
 237                         cum_fill_sq += this_bin_fill*this_bin_fill;
 238                 }
 239                 if (this_bin_fill<MAXCOUNT)
 240                         ++count[this_bin_fill];
 241                 else
 242                         ++count[MAXCOUNT];
 243         }
 244         unsigned fact = 1;
 245         double cum_prob = 0;
 246         double lambda = (1.0*seq.size()) / hashtabsize;
 247         for (int k=0; k<MAXCOUNT; ++k) {
 248                 if (k>0)
 249                         fact *= k;
 250                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 251                 cum_prob += prob;
 252                 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
 253                     << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 254                     << int(prob*1000)/10.0 << ")" << std::endl;
 255         }
 256         c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
 257             << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 258             << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 259
 260         c.s << std::string(level + c.delta_indent, ' ') << "variance: "
 261             << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 262             << std::endl;
 263         c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
 264             << (1.0*cum_fill)/hashtabsize
 265             << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 266 #endif // EXPAIRSEQ_USE_HASHTAB
 267 }
 268
 269 bool expairseq::info(unsigned inf) const
 270 {
 271         switch(inf) {
 272                 case info_flags::expanded:
 273                         return (flags & status_flags::expanded);
 274                 case info_flags::has_indices: {
 275                         if (flags & status_flags::has_indices)
 276                                 return true;
 277                         else if (flags & status_flags::has_no_indices)
 278                                 return false;
 279                         for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
 280                                 if (i->rest.info(info_flags::has_indices)) {
 281                                         this->setflag(status_flags::has_indices);
 282                                         this->clearflag(status_flags::has_no_indices);
 283                                         return true;
 284                                 }
 285                         }
 286                         this->clearflag(status_flags::has_indices);
 287                         this->setflag(status_flags::has_no_indices);
 288                         return false;
 289                 }
 290         }
 291         return inherited::info(inf);
 292 }
 293
 294 size_t expairseq::nops() const
 295 {
 296         if (overall_coeff.is_equal(default_overall_coeff()))
 297                 return seq.size();
 298         else
 299                 return seq.size()+1;
 300 }
 301
 302 ex expairseq::op(size_t i) const
 303 {
 304         if (i < seq.size())
 305                 return recombine_pair_to_ex(seq[i]);
 306         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 307         return overall_coeff;
 308 }
 309
 310 ex expairseq::map(map_function &f) const
 311 {
 312         std::auto_ptr<epvector> v(new epvector);
 313         v->reserve(seq.size()+1);
 314
 315         epvector::const_iterator cit = seq.begin(), last = seq.end();
 316         while (cit != last) {
 317                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 318                 ++cit;
 319         }
 320
 321         if (overall_coeff.is_equal(default_overall_coeff()))
 322                 return thisexpairseq(v, default_overall_coeff(), true);
 323         else {
 324                 ex newcoeff = f(overall_coeff);
 325                 if(is_a<numeric>(newcoeff))
 326                         return thisexpairseq(v, newcoeff, true);
 327                 else {
 328                         v->push_back(split_ex_to_pair(newcoeff));
 329                         return thisexpairseq(v, default_overall_coeff(), true);
 330                 }
 331         }
 332 }
 333
 334 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 335 ex expairseq::eval(int level) const
 336 {
 337         if ((level==1) && (flags &status_flags::evaluated))
 338                 return *this;
 339
 340         std::auto_ptr<epvector> vp = evalchildren(level);
 341         if (vp.get() == 0)
 342                 return this->hold();
 343
 344         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 345 }
 346
 347 epvector* conjugateepvector(const epvector&epv)
 348 {
 349         epvector *newepv = 0;
 350         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 351                 if(newepv) {
 352                         newepv->push_back(i->conjugate());
 353                         continue;
 354                 }
 355                 expair x = i->conjugate();
 356                 if (x.is_equal(*i)) {
 357                         continue;
 358                 }
 359                 newepv = new epvector;
 360                 newepv->reserve(epv.size());
 361                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 362                         newepv->push_back(*j);
 363                 }
 364                 newepv->push_back(x);
 365         }
 366         return newepv;
 367 }
 368
 369 ex expairseq::conjugate() const
 370 {
 371         epvector* newepv = conjugateepvector(seq);
 372         ex x = overall_coeff.conjugate();
 373         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 374                 return *this;
 375         }
 376         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 377         if (newepv) {
 378                 delete newepv;
 379         }
 380         return result;
 381 }
 382
 383 bool expairseq::is_polynomial(const ex & var) const
 384 {
 385         if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
 386                 return basic::is_polynomial(var);
 387         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 388                 if (!(i->rest).is_polynomial(var))
 389                         return false;
 390         }
 391         return true;
 392 }
 393
 394 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 395 {
 396         // This differs from basic::match() because we want "a+b+c+d" to
 397         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 398
 399         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 400
 401                 // Check whether global wildcard (one that matches the "rest of the
 402                 // expression", like "*" above) is present
 403                 bool has_global_wildcard = false;
 404                 ex global_wildcard;
 405                 for (size_t i=0; i<pattern.nops(); i++) {
 406                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 407                                 has_global_wildcard = true;
 408                                 global_wildcard = pattern.op(i);
 409                                 break;
 410                         }
 411                 }
 412
 413                 // Unfortunately, this is an O(N^2) operation because we can't
 414                 // sort the pattern in a useful way...
 415
 416                 // Chop into terms
 417                 exvector ops;
 418                 ops.reserve(nops());
 419                 for (size_t i=0; i<nops(); i++)
 420                         ops.push_back(op(i));
 421
 422                 // Now, for every term of the pattern, look for a matching term in
 423                 // the expression and remove the match
 424                 for (size_t i=0; i<pattern.nops(); i++) {
 425                         ex p = pattern.op(i);
 426                         if (has_global_wildcard && p.is_equal(global_wildcard))
 427                                 continue;
 428                         exvector::iterator it = ops.begin(), itend = ops.end();
 429                         while (it != itend) {
 430                                 lst::const_iterator last_el = repl_lst.end();
 431                                 --last_el;
 432                                 if (it->match(p, repl_lst)) {
 433                                         ops.erase(it);
 434                                         goto found;
 435                                 }
 436                                 while(true) {
 437                                         lst::const_iterator next_el = last_el;
 438                                         ++next_el;
 439                                         if(next_el == repl_lst.end())
 440                                                 break;
 441                                         else
 442                                                 repl_lst.remove_last();
 443                                 }
 444                                 ++it;
 445                         }
 446                         return false; // no match found
 447 found:          ;
 448                 }
 449
 450                 if (has_global_wildcard) {
 451
 452                         // Assign all the remaining terms to the global wildcard (unless
 453                         // it has already been matched before, in which case the matches
 454                         // must be equal)
 455                         size_t num = ops.size();
 456                         std::auto_ptr<epvector> vp(new epvector);
 457                         vp->reserve(num);
 458                         for (size_t i=0; i<num; i++)
 459                                 vp->push_back(split_ex_to_pair(ops[i]));
 460                         ex rest = thisexpairseq(vp, default_overall_coeff());
 461                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 462                                 if (it->op(0).is_equal(global_wildcard))
 463                                         return rest.is_equal(it->op(1));
 464                         }
 465                         repl_lst.append(global_wildcard == rest);
 466                         return true;
 467
 468                 } else {
 469
 470                         // No global wildcard, then the match fails if there are any
 471                         // unmatched terms left
 472                         return ops.empty();
 473                 }
 474         }
 475         return inherited::match(pattern, repl_lst);
 476 }
 477
 478 ex expairseq::subs(const exmap & m, unsigned options) const
 479 {
 480         std::auto_ptr<epvector> vp = subschildren(m, options);
 481         if (vp.get())
 482                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
 483         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 484                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 485         else
 486                 return subs_one_level(m, options);
 487 }
 488
 489 // protected
 490
 491 int expairseq::compare_same_type(const basic &other) const
 492 {
 493         GINAC_ASSERT(is_a<expairseq>(other));
 494         const expairseq &o = static_cast<const expairseq &>(other);
 495
 496         int cmpval;
 497
 498         // compare number of elements
 499         if (seq.size() != o.seq.size())
 500                 return (seq.size()<o.seq.size()) ? -1 : 1;
 501
 502         // compare overall_coeff
 503         cmpval = overall_coeff.compare(o.overall_coeff);
 504         if (cmpval!=0)
 505                 return cmpval;
 506
 507 #if EXPAIRSEQ_USE_HASHTAB
 508         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 509         if (hashtabsize==0) {
 510 #endif // EXPAIRSEQ_USE_HASHTAB
 511                 epvector::const_iterator cit1 = seq.begin();
 512                 epvector::const_iterator cit2 = o.seq.begin();
 513                 epvector::const_iterator last1 = seq.end();
 514                 epvector::const_iterator last2 = o.seq.end();
 515
 516                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 517                         cmpval = (*cit1).compare(*cit2);
 518                         if (cmpval!=0) return cmpval;
 519                 }
 520
 521                 GINAC_ASSERT(cit1==last1);
 522                 GINAC_ASSERT(cit2==last2);
 523
 524                 return 0;
 525 #if EXPAIRSEQ_USE_HASHTAB
 526         }
 527
 528         // compare number of elements in each hashtab entry
 529         for (unsigned i=0; i<hashtabsize; ++i) {
 530                 unsigned cursize=hashtab[i].size();
 531                 if (cursize != o.hashtab[i].size())
 532                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 533         }
 534
 535         // compare individual (sorted) hashtab entries
 536         for (unsigned i=0; i<hashtabsize; ++i) {
 537                 unsigned sz = hashtab[i].size();
 538                 if (sz>0) {
 539                         const epplist &eppl1 = hashtab[i];
 540                         const epplist &eppl2 = o.hashtab[i];
 541                         epplist::const_iterator it1 = eppl1.begin();
 542                         epplist::const_iterator it2 = eppl2.begin();
 543                         while (it1!=eppl1.end()) {
 544                                 cmpval = (*(*it1)).compare(*(*it2));
 545                                 if (cmpval!=0)
 546                                         return cmpval;
 547                                 ++it1;
 548                                 ++it2;
 549                         }
 550                 }
 551         }
 552
 553         return 0; // equal
 554 #endif // EXPAIRSEQ_USE_HASHTAB
 555 }
 556
 557 bool expairseq::is_equal_same_type(const basic &other) const
 558 {
 559         const expairseq &o = static_cast<const expairseq &>(other);
 560
 561         // compare number of elements
 562         if (seq.size()!=o.seq.size())
 563                 return false;
 564
 565         // compare overall_coeff
 566         if (!overall_coeff.is_equal(o.overall_coeff))
 567                 return false;
 568
 569 #if EXPAIRSEQ_USE_HASHTAB
 570         // compare number of elements in each hashtab entry
 571         if (hashtabsize!=o.hashtabsize) {
 572                 std::cout << "this:" << std::endl;
 573                 print(print_tree(std::cout));
 574                 std::cout << "other:" << std::endl;
 575                 other.print(print_tree(std::cout));
 576         }
 577
 578         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 579
 580         if (hashtabsize==0) {
 581 #endif // EXPAIRSEQ_USE_HASHTAB
 582                 epvector::const_iterator cit1 = seq.begin();
 583                 epvector::const_iterator cit2 = o.seq.begin();
 584                 epvector::const_iterator last1 = seq.end();
 585
 586                 while (cit1!=last1) {
 587                         if (!(*cit1).is_equal(*cit2)) return false;
 588                         ++cit1;
 589                         ++cit2;
 590                 }
 591
 592                 return true;
 593 #if EXPAIRSEQ_USE_HASHTAB
 594         }
 595
 596         for (unsigned i=0; i<hashtabsize; ++i) {
 597                 if (hashtab[i].size() != o.hashtab[i].size())
 598                         return false;
 599         }
 600
 601         // compare individual sorted hashtab entries
 602         for (unsigned i=0; i<hashtabsize; ++i) {
 603                 unsigned sz = hashtab[i].size();
 604                 if (sz>0) {
 605                         const epplist &eppl1 = hashtab[i];
 606                         const epplist &eppl2 = o.hashtab[i];
 607                         epplist::const_iterator it1 = eppl1.begin();
 608                         epplist::const_iterator it2 = eppl2.begin();
 609                         while (it1!=eppl1.end()) {
 610                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 611                                 ++it1;
 612                                 ++it2;
 613                         }
 614                 }
 615         }
 616
 617         return true;
 618 #endif // EXPAIRSEQ_USE_HASHTAB
 619 }
 620
 621 unsigned expairseq::return_type() const
 622 {
 623         return return_types::noncommutative_composite;
 624 }
 625
 626 unsigned expairseq::calchash() const
 627 {
 628         unsigned v = golden_ratio_hash((p_int)this->tinfo());
 629         epvector::const_iterator i = seq.begin();
 630         const epvector::const_iterator end = seq.end();
 631         while (i != end) {
 632                 v ^= i->rest.gethash();
 633 #if !EXPAIRSEQ_USE_HASHTAB
 634                 // rotation spoils commutativity!
 635                 v = rotate_left(v);
 636                 v ^= i->coeff.gethash();
 637 #endif // !EXPAIRSEQ_USE_HASHTAB
 638                 ++i;
 639         }
 640
 641         v ^= overall_coeff.gethash();
 642
 643         // store calculated hash value only if object is already evaluated
 644         if (flags &status_flags::evaluated) {
 645                 setflag(status_flags::hash_calculated);
 646                 hashvalue = v;
 647         }
 648
 649         return v;
 650 }
 651
 652 ex expairseq::expand(unsigned options) const
 653 {
 654         std::auto_ptr<epvector> vp = expandchildren(options);
 655         if (vp.get())
 656                 return thisexpairseq(vp, overall_coeff);
 657         else {
 658                 // The terms have not changed, so it is safe to declare this expanded
 659                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 660         }
 661 }
 662
 663 //////////
 664 // new virtual functions which can be overridden by derived classes
 665 //////////
 666
 667 // protected
 668
 669 /** Create an object of this type.
 670  *  This method works similar to a constructor.  It is useful because expairseq
 671  *  has (at least) two possible different semantics but we want to inherit
 672  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 673  *  has to create a new one of the same semantics, which cannot be done by a
 674  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 675  *  order for this trick to work a derived class must of course override this
 676  *  definition. */
 677 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 678 {
 679         return expairseq(v, oc, do_index_renaming);
 680 }
 681
 682 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
 683 {
 684         return expairseq(vp, oc, do_index_renaming);
 685 }
 686
 687 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 688 {
 689         c.s << "[[";
 690         p.rest.print(c, precedence());
 691         c.s << ",";
 692         p.coeff.print(c, precedence());
 693         c.s << "]]";
 694 }
 695
 696 void expairseq::printseq(const print_context & c, char delim,
 697                          unsigned this_precedence,
 698                          unsigned upper_precedence) const
 699 {
 700         if (this_precedence <= upper_precedence)
 701                 c.s << "(";
 702         epvector::const_iterator it, it_last = seq.end() - 1;
 703         for (it=seq.begin(); it!=it_last; ++it) {
 704                 printpair(c, *it, this_precedence);
 705                 c.s << delim;
 706         }
 707         printpair(c, *it, this_precedence);
 708         if (!overall_coeff.is_equal(default_overall_coeff())) {
 709                 c.s << delim;
 710                 overall_coeff.print(c, this_precedence);
 711         }
 712
 713         if (this_precedence <= upper_precedence)
 714                 c.s << ")";
 715 }
 716
 717
 718 /** Form an expair from an ex, using the corresponding semantics.
 719  *  @see expairseq::recombine_pair_to_ex() */
 720 expair expairseq::split_ex_to_pair(const ex &e) const
 721 {
 722         return expair(e,_ex1);
 723 }
 724
 725
 726 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 727                                                 const ex &c) const
 728 {
 729         GINAC_ASSERT(is_exactly_a<numeric>(c));
 730
 731         return expair(e,c);
 732 }
 733
 734
 735 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 736                                                   const ex &c) const
 737 {
 738         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 739         GINAC_ASSERT(is_exactly_a<numeric>(c));
 740
 741         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 742 }
 743
 744
 745 /** Form an ex out of an expair, using the corresponding semantics.
 746  *  @see expairseq::split_ex_to_pair() */
 747 ex expairseq::recombine_pair_to_ex(const expair &p) const
 748 {
 749         return lst(p.rest,p.coeff);
 750 }
 751
 752 bool expairseq::expair_needs_further_processing(epp it)
 753 {
 754 #if EXPAIRSEQ_USE_HASHTAB
 755         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 756 #endif // EXPAIRSEQ_USE_HASHTAB
 757         return false;
 758 }
 759
 760 ex expairseq::default_overall_coeff() const
 761 {
 762         return _ex0;
 763 }
 764
 765 void expairseq::combine_overall_coeff(const ex &c)
 766 {
 767         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 768         GINAC_ASSERT(is_exactly_a<numeric>(c));
 769         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 770 }
 771
 772 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 773 {
 774         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 775         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 776         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 777         overall_coeff = ex_to<numeric>(overall_coeff).
 778                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 779 }
 780
 781 bool expairseq::can_make_flat(const expair &p) const
 782 {
 783         return true;
 784 }
 785
 786
 787 //////////
 788 // non-virtual functions in this class
 789 //////////
 790
 791 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 792 {
 793         exvector v;
 794         v.reserve(2);
 795         v.push_back(lh);
 796         v.push_back(rh);
 797         construct_from_exvector(v);
 798 #if EXPAIRSEQ_USE_HASHTAB
 799         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 800         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 801 #endif // EXPAIRSEQ_USE_HASHTAB
 802 }
 803
 804 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 805 {
 806         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 807                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 808 #if EXPAIRSEQ_USE_HASHTAB
 809                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 810                                              ex_to<expairseq>(rh).seq.size();
 811                         if (calc_hashtabsize(totalsize)!=0) {
 812                                 construct_from_2_ex_via_exvector(lh,rh);
 813                         } else {
 814 #endif // EXPAIRSEQ_USE_HASHTAB
 815                                 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 816                                         rh.info(info_flags::has_indices)) {
 817                                         ex newrh=rename_dummy_indices_uniquely(lh, rh);
 818                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 819                                                                    ex_to<expairseq>(newrh));
 820                                 }
 821                                 else
 822                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 823                                                                    ex_to<expairseq>(rh));
 824 #if EXPAIRSEQ_USE_HASHTAB
 825                         }
 826 #endif // EXPAIRSEQ_USE_HASHTAB
 827                         return;
 828                 } else {
 829 #if EXPAIRSEQ_USE_HASHTAB
 830                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 831                         if (calc_hashtabsize(totalsize)!=0) {
 832                                 construct_from_2_ex_via_exvector(lh, rh);
 833                         } else {
 834 #endif // EXPAIRSEQ_USE_HASHTAB
 835                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 836 #if EXPAIRSEQ_USE_HASHTAB
 837                         }
 838 #endif // EXPAIRSEQ_USE_HASHTAB
 839                         return;
 840                 }
 841         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 842 #if EXPAIRSEQ_USE_HASHTAB
 843                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 844                 if (calc_hashtabsize(totalsize)!=0) {
 845                         construct_from_2_ex_via_exvector(lh,rh);
 846                 } else {
 847 #endif // EXPAIRSEQ_USE_HASHTAB
 848                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 849 #if EXPAIRSEQ_USE_HASHTAB
 850                 }
 851 #endif // EXPAIRSEQ_USE_HASHTAB
 852                 return;
 853         }
 854
 855 #if EXPAIRSEQ_USE_HASHTAB
 856         if (calc_hashtabsize(2)!=0) {
 857                 construct_from_2_ex_via_exvector(lh,rh);
 858                 return;
 859         }
 860         hashtabsize = 0;
 861 #endif // EXPAIRSEQ_USE_HASHTAB
 862
 863         if (is_exactly_a<numeric>(lh)) {
 864                 if (is_exactly_a<numeric>(rh)) {
 865                         combine_overall_coeff(lh);
 866                         combine_overall_coeff(rh);
 867                 } else {
 868                         combine_overall_coeff(lh);
 869                         seq.push_back(split_ex_to_pair(rh));
 870                 }
 871         } else {
 872                 if (is_exactly_a<numeric>(rh)) {
 873                         combine_overall_coeff(rh);
 874                         seq.push_back(split_ex_to_pair(lh));
 875                 } else {
 876                         expair p1 = split_ex_to_pair(lh);
 877                         expair p2 = split_ex_to_pair(rh);
 878
 879                         int cmpval = p1.rest.compare(p2.rest);
 880                         if (cmpval==0) {
 881                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 882                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 883                                         // no further processing is necessary, since this
 884                                         // one element will usually be recombined in eval()
 885                                         seq.push_back(p1);
 886                                 }
 887                         } else {
 888                                 seq.reserve(2);
 889                                 if (cmpval<0) {
 890                                         seq.push_back(p1);
 891                                         seq.push_back(p2);
 892                                 } else {
 893                                         seq.push_back(p2);
 894                                         seq.push_back(p1);
 895                                 }
 896                         }
 897                 }
 898         }
 899 }
 900
 901 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 902                                                                                    const expairseq &s2)
 903 {
 904         combine_overall_coeff(s1.overall_coeff);
 905         combine_overall_coeff(s2.overall_coeff);
 906
 907         epvector::const_iterator first1 = s1.seq.begin();
 908         epvector::const_iterator last1 = s1.seq.end();
 909         epvector::const_iterator first2 = s2.seq.begin();
 910         epvector::const_iterator last2 = s2.seq.end();
 911
 912         seq.reserve(s1.seq.size()+s2.seq.size());
 913
 914         bool needs_further_processing=false;
 915
 916         while (first1!=last1 && first2!=last2) {
 917                 int cmpval = (*first1).rest.compare((*first2).rest);
 918
 919                 if (cmpval==0) {
 920                         // combine terms
 921                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 922                                                    add(ex_to<numeric>(first2->coeff));
 923                         if (!newcoeff.is_zero()) {
 924                                 seq.push_back(expair(first1->rest,newcoeff));
 925                                 if (expair_needs_further_processing(seq.end()-1)) {
 926                                         needs_further_processing = true;
 927                                 }
 928                         }
 929                         ++first1;
 930                         ++first2;
 931                 } else if (cmpval<0) {
 932                         seq.push_back(*first1);
 933                         ++first1;
 934                 } else {
 935                         seq.push_back(*first2);
 936                         ++first2;
 937                 }
 938         }
 939
 940         while (first1!=last1) {
 941                 seq.push_back(*first1);
 942                 ++first1;
 943         }
 944         while (first2!=last2) {
 945                 seq.push_back(*first2);
 946                 ++first2;
 947         }
 948
 949         if (needs_further_processing) {
 950                 epvector v = seq;
 951                 seq.clear();
 952                 construct_from_epvector(v);
 953         }
 954 }
 955
 956 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 957                                                                                         const ex &e)
 958 {
 959         combine_overall_coeff(s.overall_coeff);
 960         if (is_exactly_a<numeric>(e)) {
 961                 combine_overall_coeff(e);
 962                 seq = s.seq;
 963                 return;
 964         }
 965
 966         epvector::const_iterator first = s.seq.begin();
 967         epvector::const_iterator last = s.seq.end();
 968         expair p = split_ex_to_pair(e);
 969
 970         seq.reserve(s.seq.size()+1);
 971         bool p_pushed = false;
 972
 973         bool needs_further_processing=false;
 974
 975         // merge p into s.seq
 976         while (first!=last) {
 977                 int cmpval = (*first).rest.compare(p.rest);
 978                 if (cmpval==0) {
 979                         // combine terms
 980                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 981                                                    add(ex_to<numeric>(p.coeff));
 982                         if (!newcoeff.is_zero()) {
 983                                 seq.push_back(expair(first->rest,newcoeff));
 984                                 if (expair_needs_further_processing(seq.end()-1))
 985                                         needs_further_processing = true;
 986                         }
 987                         ++first;
 988                         p_pushed = true;
 989                         break;
 990                 } else if (cmpval<0) {
 991                         seq.push_back(*first);
 992                         ++first;
 993                 } else {
 994                         seq.push_back(p);
 995                         p_pushed = true;
 996                         break;
 997                 }
 998         }
 999
1000         if (p_pushed) {
1001                 // while loop exited because p was pushed, now push rest of s.seq
1002                 while (first!=last) {
1003                         seq.push_back(*first);
1004                         ++first;
1005                 }
1006         } else {
1007                 // while loop exited because s.seq was pushed, now push p
1008                 seq.push_back(p);
1009         }
1010
1011         if (needs_further_processing) {
1012                 epvector v = seq;
1013                 seq.clear();
1014                 construct_from_epvector(v);
1015         }
1016 }
1017
1018 void expairseq::construct_from_exvector(const exvector &v)
1019 {
1020         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1021         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1022         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1023         //                  (same for (+,*) -> (*,^)
1024
1025         make_flat(v);
1026 #if EXPAIRSEQ_USE_HASHTAB
1027         combine_same_terms();
1028 #else
1029         canonicalize();
1030         combine_same_terms_sorted_seq();
1031 #endif // EXPAIRSEQ_USE_HASHTAB
1032 }
1033
1034 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1035 {
1036         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1037         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1038         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1039         //                  (same for (+,*) -> (*,^)
1040
1041         make_flat(v, do_index_renaming);
1042 #if EXPAIRSEQ_USE_HASHTAB
1043         combine_same_terms();
1044 #else
1045         canonicalize();
1046         combine_same_terms_sorted_seq();
1047 #endif // EXPAIRSEQ_USE_HASHTAB
1048 }
1049
1050 /** Combine this expairseq with argument exvector.
1051  *  It cares for associativity as well as for special handling of numerics. */
1052 void expairseq::make_flat(const exvector &v)
1053 {
1054         exvector::const_iterator cit;
1055
1056         // count number of operands which are of same expairseq derived type
1057         // and their cumulative number of operands
1058         int nexpairseqs = 0;
1059         int noperands = 0;
1060         bool do_idx_rename = false;
1061
1062         cit = v.begin();
1063         while (cit!=v.end()) {
1064                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1065                         ++nexpairseqs;
1066                         noperands += ex_to<expairseq>(*cit).seq.size();
1067                 }
1068                 if (is_a<mul>(*this) && (!do_idx_rename) &&
1069                                 cit->info(info_flags::has_indices))
1070                         do_idx_rename = true;
1071                 ++cit;
1072         }
1073
1074         // reserve seq and coeffseq which will hold all operands
1075         seq.reserve(v.size()+noperands-nexpairseqs);
1076
1077         // copy elements and split off numerical part
1078         make_flat_inserter mf(v, do_idx_rename);
1079         cit = v.begin();
1080         while (cit!=v.end()) {
1081                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1082                         ex newfactor = mf.handle_factor(*cit, _ex1);
1083                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
1084                         combine_overall_coeff(subseqref.overall_coeff);
1085                         epvector::const_iterator cit_s = subseqref.seq.begin();
1086                         while (cit_s!=subseqref.seq.end()) {
1087                                 seq.push_back(*cit_s);
1088                                 ++cit_s;
1089                         }
1090                 } else {
1091                         if (is_exactly_a<numeric>(*cit))
1092                                 combine_overall_coeff(*cit);
1093                         else {
1094                                 ex newfactor = mf.handle_factor(*cit, _ex1);
1095                                 seq.push_back(split_ex_to_pair(newfactor));
1096                         }
1097                 }
1098                 ++cit;
1099         }
1100 }
1101
1102 /** Combine this expairseq with argument epvector.
1103  *  It cares for associativity as well as for special handling of numerics. */
1104 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1105 {
1106         epvector::const_iterator cit;
1107
1108         // count number of operands which are of same expairseq derived type
1109         // and their cumulative number of operands
1110         int nexpairseqs = 0;
1111         int noperands = 0;
1112         bool really_need_rename_inds = false;
1113
1114         cit = v.begin();
1115         while (cit!=v.end()) {
1116                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1117                         ++nexpairseqs;
1118                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1119                 }
1120                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1121                                 cit->rest.info(info_flags::has_indices))
1122                         really_need_rename_inds = true;
1123                 ++cit;
1124         }
1125         do_index_renaming = do_index_renaming && really_need_rename_inds;
1126
1127         // reserve seq and coeffseq which will hold all operands
1128         seq.reserve(v.size()+noperands-nexpairseqs);
1129         make_flat_inserter mf(v, do_index_renaming);
1130
1131         // copy elements and split off numerical part
1132         cit = v.begin();
1133         while (cit!=v.end()) {
1134                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1135                     this->can_make_flat(*cit)) {
1136                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1137                         const expairseq &subseqref = ex_to<expairseq>(newrest);
1138                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1139                                                             ex_to<numeric>(cit->coeff));
1140                         epvector::const_iterator cit_s = subseqref.seq.begin();
1141                         while (cit_s!=subseqref.seq.end()) {
1142                                 seq.push_back(expair(cit_s->rest,
1143                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1144                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1145                                 //                                              (*cit).coeff));
1146                                 ++cit_s;
1147                         }
1148                 } else {
1149                         if (cit->is_canonical_numeric())
1150                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1151                         else {
1152                                 ex rest = cit->rest;
1153                                 ex newrest = mf.handle_factor(rest, cit->coeff);
1154                                 if (are_ex_trivially_equal(newrest, rest))
1155                                         seq.push_back(*cit);
1156                                 else
1157                                         seq.push_back(expair(newrest, cit->coeff));
1158                         }
1159                 }
1160                 ++cit;
1161         }
1162 }
1163
1164 /** Brings this expairseq into a sorted (canonical) form. */
1165 void expairseq::canonicalize()
1166 {
1167         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1168 }
1169
1170
1171 /** Compact a presorted expairseq by combining all matching expairs to one
1172  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1173  *  instance. */
1174 void expairseq::combine_same_terms_sorted_seq()
1175 {
1176         if (seq.size()<2)
1177                 return;
1178
1179         bool needs_further_processing = false;
1180
1181         epvector::iterator itin1 = seq.begin();
1182         epvector::iterator itin2 = itin1+1;
1183         epvector::iterator itout = itin1;
1184         epvector::iterator last = seq.end();
1185         // must_copy will be set to true the first time some combination is
1186         // possible from then on the sequence has changed and must be compacted
1187         bool must_copy = false;
1188         while (itin2!=last) {
1189                 if (itin1->rest.compare(itin2->rest)==0) {
1190                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1191                                        add_dyn(ex_to<numeric>(itin2->coeff));
1192                         if (expair_needs_further_processing(itin1))
1193                                 needs_further_processing = true;
1194                         must_copy = true;
1195                 } else {
1196                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1197                                 if (must_copy)
1198                                         *itout = *itin1;
1199                                 ++itout;
1200                         }
1201                         itin1 = itin2;
1202                 }
1203                 ++itin2;
1204         }
1205         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1206                 if (must_copy)
1207                         *itout = *itin1;
1208                 ++itout;
1209         }
1210         if (itout!=last)
1211                 seq.erase(itout,last);
1212
1213         if (needs_further_processing) {
1214                 epvector v = seq;
1215                 seq.clear();
1216                 construct_from_epvector(v);
1217         }
1218 }
1219
1220 #if EXPAIRSEQ_USE_HASHTAB
1221
1222 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1223 {
1224         unsigned size;
1225         unsigned nearest_power_of_2 = 1 << log2(sz);
1226         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1227         //  size = nearest_power_of_2*hashtabfactor;
1228         size = nearest_power_of_2/hashtabfactor;
1229         if (size<minhashtabsize)
1230                 return 0;
1231
1232         // hashtabsize must be a power of 2
1233         GINAC_ASSERT((1U << log2(size))==size);
1234         return size;
1235 }
1236
1237 unsigned expairseq::calc_hashindex(const ex &e) const
1238 {
1239         // calculate hashindex
1240         unsigned hashindex;
1241         if (is_a<numeric>(e)) {
1242                 hashindex = hashmask;
1243         } else {
1244                 hashindex = e.gethash() & hashmask;
1245                 // last hashtab entry is reserved for numerics
1246                 if (hashindex==hashmask) hashindex = 0;
1247         }
1248         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1249         return hashindex;
1250 }
1251
1252 void expairseq::shrink_hashtab()
1253 {
1254         unsigned new_hashtabsize;
1255         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1256                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1257                 if (new_hashtabsize==0) {
1258                         hashtab.clear();
1259                         hashtabsize = 0;
1260                         canonicalize();
1261                         return;
1262                 }
1263
1264                 // shrink by a factor of 2
1265                 unsigned half_hashtabsize = hashtabsize/2;
1266                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1267                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1268                 // special treatment for numeric hashes
1269                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1270                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1271                 hashtab.resize(half_hashtabsize);
1272                 hashtabsize = half_hashtabsize;
1273                 hashmask = hashtabsize-1;
1274         }
1275 }
1276
1277 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1278 {
1279         if (hashtabsize==0)
1280                 return; // nothing to do
1281
1282         // calculate hashindex of element to be deleted
1283         unsigned hashindex = calc_hashindex((*element).rest);
1284
1285         // find it in hashtab and remove it
1286         epplist &eppl = hashtab[hashindex];
1287         epplist::iterator epplit = eppl.begin();
1288         bool erased = false;
1289         while (epplit!=eppl.end()) {
1290                 if (*epplit == element) {
1291                         eppl.erase(epplit);
1292                         erased = true;
1293                         break;
1294                 }
1295                 ++epplit;
1296         }
1297         if (!erased) {
1298                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1299                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1300
1301                 unsigned hashindex = calc_hashindex(element->rest);
1302                 epplist &eppl = hashtab[hashindex];
1303                 epplist::iterator epplit = eppl.begin();
1304                 bool erased = false;
1305                 while (epplit!=eppl.end()) {
1306                         if (*epplit == element) {
1307                                 eppl.erase(epplit);
1308                                 erased = true;
1309                                 break;
1310                         }
1311                         ++epplit;
1312                 }
1313                 GINAC_ASSERT(erased);
1314         }
1315         GINAC_ASSERT(erased);
1316 }
1317
1318 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1319                                    epvector::iterator newpos)
1320 {
1321         GINAC_ASSERT(hashtabsize!=0);
1322
1323         // calculate hashindex of element which was moved
1324         unsigned hashindex=calc_hashindex((*newpos).rest);
1325
1326         // find it in hashtab and modify it
1327         epplist &eppl = hashtab[hashindex];
1328         epplist::iterator epplit = eppl.begin();
1329         while (epplit!=eppl.end()) {
1330                 if (*epplit == oldpos) {
1331                         *epplit = newpos;
1332                         break;
1333                 }
1334                 ++epplit;
1335         }
1336         GINAC_ASSERT(epplit!=eppl.end());
1337 }
1338
1339 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1340 {
1341         epplist::const_iterator current = eppl.begin();
1342         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1343                 ++current;
1344         }
1345         eppl.insert(current,elem);
1346 }
1347
1348 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1349                                           epvector::iterator &last_non_zero,
1350                                           std::vector<bool> &touched,
1351                                           unsigned &number_of_zeroes)
1352 {
1353         epp current = seq.begin();
1354
1355         while (current!=first_numeric) {
1356                 if (is_exactly_a<numeric>(current->rest)) {
1357                         --first_numeric;
1358                         iter_swap(current,first_numeric);
1359                 } else {
1360                         // calculate hashindex
1361                         unsigned currenthashindex = calc_hashindex(current->rest);
1362
1363                         // test if there is already a matching expair in the hashtab-list
1364                         epplist &eppl=hashtab[currenthashindex];
1365                         epplist::iterator epplit = eppl.begin();
1366                         while (epplit!=eppl.end()) {
1367                                 if (current->rest.is_equal((*epplit)->rest))
1368                                         break;
1369                                 ++epplit;
1370                         }
1371                         if (epplit==eppl.end()) {
1372                                 // no matching expair found, append this to end of list
1373                                 sorted_insert(eppl,current);
1374                                 ++current;
1375                         } else {
1376                                 // epplit points to a matching expair, combine it with current
1377                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1378                                                    add_dyn(ex_to<numeric>(current->coeff));
1379
1380                                 // move obsolete current expair to end by swapping with last_non_zero element
1381                                 // if this was a numeric, it is swapped with the expair before first_numeric
1382                                 iter_swap(current,last_non_zero);
1383                                 --first_numeric;
1384                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1385                                 --last_non_zero;
1386                                 ++number_of_zeroes;
1387                                 // test if combined term has coeff 0 and can be removed is done later
1388                                 touched[(*epplit)-seq.begin()] = true;
1389                         }
1390                 }
1391         }
1392 }
1393
1394 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1395                                    epvector::iterator &last_non_zero,
1396                                    std::vector<bool> &touched,
1397                                    unsigned &number_of_zeroes)
1398 {
1399         // move terms with coeff 0 to end and remove them from hashtab
1400         // check only those elements which have been touched
1401         epp current = seq.begin();
1402         size_t i = 0;
1403         while (current!=first_numeric) {
1404                 if (!touched[i]) {
1405                         ++current;
1406                         ++i;
1407                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1408                         ++current;
1409                         ++i;
1410                 } else {
1411                         remove_hashtab_entry(current);
1412
1413                         // move element to the end, unless it is already at the end
1414                         if (current!=last_non_zero) {
1415                                 iter_swap(current,last_non_zero);
1416                                 --first_numeric;
1417                                 bool numeric_swapped = first_numeric!=last_non_zero;
1418                                 if (numeric_swapped)
1419                                         iter_swap(first_numeric,current);
1420                                 epvector::iterator changed_entry;
1421
1422                                 if (numeric_swapped)
1423                                         changed_entry = first_numeric;
1424                                 else
1425                                         changed_entry = last_non_zero;
1426
1427                                 --last_non_zero;
1428                                 ++number_of_zeroes;
1429
1430                                 if (first_numeric!=current) {
1431
1432                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1433                                         move_hashtab_entry(changed_entry,current);
1434                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1435                                 }
1436                         } else {
1437                                 --first_numeric;
1438                                 --last_non_zero;
1439                                 ++number_of_zeroes;
1440                         }
1441                 }
1442         }
1443         GINAC_ASSERT(i==current-seq.begin());
1444 }
1445
1446 /** True if one of the coeffs vanishes, otherwise false.
1447  *  This would be an invariant violation, so this should only be used for
1448  *  debugging purposes. */
1449 bool expairseq::has_coeff_0() const
1450 {
1451         epvector::const_iterator i = seq.begin(), end = seq.end();
1452         while (i != end) {
1453                 if (i->coeff.is_zero())
1454                         return true;
1455                 ++i;
1456         }
1457         return false;
1458 }
1459
1460 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1461                                                                                 epvector::const_iterator last_non_zero)
1462 {
1463         if (first_numeric == seq.end()) return; // no numerics
1464
1465         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1466         while (current != last) {
1467                 sorted_insert(hashtab[hashmask], current);
1468                 ++current;
1469         }
1470 }
1471
1472 void expairseq::combine_same_terms()
1473 {
1474         // combine same terms, drop term with coeff 0, move numerics to end
1475
1476         // calculate size of hashtab
1477         hashtabsize = calc_hashtabsize(seq.size());
1478
1479         // hashtabsize is a power of 2
1480         hashmask = hashtabsize-1;
1481
1482         // allocate hashtab
1483         hashtab.clear();
1484         hashtab.resize(hashtabsize);
1485
1486         if (hashtabsize==0) {
1487                 canonicalize();
1488                 combine_same_terms_sorted_seq();
1489                 GINAC_ASSERT(!has_coeff_0());
1490                 return;
1491         }
1492
1493         // iterate through seq, move numerics to end,
1494         // fill hashtab and combine same terms
1495         epvector::iterator first_numeric = seq.end();
1496         epvector::iterator last_non_zero = seq.end()-1;
1497
1498         size_t num = seq.size();
1499         std::vector<bool> touched(num);
1500
1501         unsigned number_of_zeroes = 0;
1502
1503         GINAC_ASSERT(!has_coeff_0());
1504         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1505
1506         // there should not be any terms with coeff 0 from the beginning,
1507         // so it should be safe to skip this step
1508         if (number_of_zeroes!=0) {
1509                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1510         }
1511
1512         add_numerics_to_hashtab(first_numeric,last_non_zero);
1513
1514         // pop zero elements
1515         for (unsigned i=0; i<number_of_zeroes; ++i) {
1516                 seq.pop_back();
1517         }
1518
1519         // shrink hashtabsize to calculated value
1520         GINAC_ASSERT(!has_coeff_0());
1521
1522         shrink_hashtab();
1523
1524         GINAC_ASSERT(!has_coeff_0());
1525 }
1526
1527 #endif // EXPAIRSEQ_USE_HASHTAB
1528
1529 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1530  *  debugging or in assertions since being sorted is an invariance. */
1531 bool expairseq::is_canonical() const
1532 {
1533         if (seq.size() <= 1)
1534                 return 1;
1535
1536 #if EXPAIRSEQ_USE_HASHTAB
1537         if (hashtabsize > 0) return 1; // not canoncalized
1538 #endif // EXPAIRSEQ_USE_HASHTAB
1539
1540         epvector::const_iterator it = seq.begin(), itend = seq.end();
1541         epvector::const_iterator it_last = it;
1542         for (++it; it!=itend; it_last=it, ++it) {
1543                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1544                         if (!is_exactly_a<numeric>(it_last->rest) ||
1545                                 !is_exactly_a<numeric>(it->rest)) {
1546                                 // double test makes it easier to set a breakpoint...
1547                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1548                                         !is_exactly_a<numeric>(it->rest)) {
1549                                         printpair(std::clog, *it_last, 0);
1550                                         std::clog << ">";
1551                                         printpair(std::clog, *it, 0);
1552                                         std::clog << "\n";
1553                                         std::clog << "pair1:" << std::endl;
1554                                         it_last->rest.print(print_tree(std::clog));
1555                                         it_last->coeff.print(print_tree(std::clog));
1556                                         std::clog << "pair2:" << std::endl;
1557                                         it->rest.print(print_tree(std::clog));
1558                                         it->coeff.print(print_tree(std::clog));
1559                                         return 0;
1560                                 }
1561                         }
1562                 }
1563         }
1564         return 1;
1565 }
1566
1567
1568 /** Member-wise expand the expairs in this sequence.
1569  *
1570  *  @see expairseq::expand()
1571  *  @return pointer to epvector containing expanded pairs or zero pointer,
1572  *  if no members were changed. */
1573 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1574 {
1575         const epvector::const_iterator last = seq.end();
1576         epvector::const_iterator cit = seq.begin();
1577         while (cit!=last) {
1578                 const ex &expanded_ex = cit->rest.expand(options);
1579                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1580
1581                         // something changed, copy seq, eval and return it
1582                         std::auto_ptr<epvector> s(new epvector);
1583                         s->reserve(seq.size());
1584
1585                         // copy parts of seq which are known not to have changed
1586                         epvector::const_iterator cit2 = seq.begin();
1587                         while (cit2!=cit) {
1588                                 s->push_back(*cit2);
1589                                 ++cit2;
1590                         }
1591
1592                         // copy first changed element
1593                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1594                                                                    cit2->coeff));
1595                         ++cit2;
1596
1597                         // copy rest
1598                         while (cit2!=last) {
1599                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1600                                                                            cit2->coeff));
1601                                 ++cit2;
1602                         }
1603                         return s;
1604                 }
1605                 ++cit;
1606         }
1607
1608         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1609 }
1610
1611
1612 /** Member-wise evaluate the expairs in this sequence.
1613  *
1614  *  @see expairseq::eval()
1615  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1616  *  if no members were changed. */
1617 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1618 {
1619         // returns a NULL pointer if nothing had to be evaluated
1620         // returns a pointer to a newly created epvector otherwise
1621         // (which has to be deleted somewhere else)
1622
1623         if (level==1)
1624                 return std::auto_ptr<epvector>(0);
1625
1626         if (level == -max_recursion_level)
1627                 throw(std::runtime_error("max recursion level reached"));
1628
1629         --level;
1630         epvector::const_iterator last = seq.end();
1631         epvector::const_iterator cit = seq.begin();
1632         while (cit!=last) {
1633                 const ex &evaled_ex = cit->rest.eval(level);
1634                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1635
1636                         // something changed, copy seq, eval and return it
1637                         std::auto_ptr<epvector> s(new epvector);
1638                         s->reserve(seq.size());
1639
1640                         // copy parts of seq which are known not to have changed
1641                         epvector::const_iterator cit2=seq.begin();
1642                         while (cit2!=cit) {
1643                                 s->push_back(*cit2);
1644                                 ++cit2;
1645                         }
1646
1647                         // copy first changed element
1648                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1649                                                                    cit2->coeff));
1650                         ++cit2;
1651
1652                         // copy rest
1653                         while (cit2!=last) {
1654                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1655                                                                            cit2->coeff));
1656                                 ++cit2;
1657                         }
1658                         return s;
1659                 }
1660                 ++cit;
1661         }
1662
1663         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1664 }
1665
1666 /** Member-wise substitute in this sequence.
1667  *
1668  *  @see expairseq::subs()
1669  *  @return pointer to epvector containing pairs after application of subs,
1670  *    or NULL pointer if no members were changed. */
1671 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1672 {
1673         // When any of the objects to be substituted is a product or power
1674         // we have to recombine the pairs because the numeric coefficients may
1675         // be part of the search pattern.
1676         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1677
1678                 // Search the list of substitutions and cache our findings
1679                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1680                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1681                                 options |= subs_options::pattern_is_product;
1682                                 break;
1683                         }
1684                 }
1685                 if (!(options & subs_options::pattern_is_product))
1686                         options |= subs_options::pattern_is_not_product;
1687         }
1688
1689         if (options & subs_options::pattern_is_product) {
1690
1691                 // Substitute in the recombined pairs
1692                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1693                 while (cit != last) {
1694
1695                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1696                         const ex &subsed_ex = orig_ex.subs(m, options);
1697                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1698
1699                                 // Something changed, copy seq, subs and return it
1700                                 std::auto_ptr<epvector> s(new epvector);
1701                                 s->reserve(seq.size());
1702
1703                                 // Copy parts of seq which are known not to have changed
1704                                 s->insert(s->begin(), seq.begin(), cit);
1705
1706                                 // Copy first changed element
1707                                 s->push_back(split_ex_to_pair(subsed_ex));
1708                                 ++cit;
1709
1710                                 // Copy rest
1711                                 while (cit != last) {
1712                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1713                                         ++cit;
1714                                 }
1715                                 return s;
1716                         }
1717
1718                         ++cit;
1719                 }
1720
1721         } else {
1722
1723                 // Substitute only in the "rest" part of the pairs
1724                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1725                 while (cit != last) {
1726
1727                         const ex &subsed_ex = cit->rest.subs(m, options);
1728                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1729
1730                                 // Something changed, copy seq, subs and return it
1731                                 std::auto_ptr<epvector> s(new epvector);
1732                                 s->reserve(seq.size());
1733
1734                                 // Copy parts of seq which are known not to have changed
1735                                 s->insert(s->begin(), seq.begin(), cit);
1736
1737                                 // Copy first changed element
1738                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1739                                 ++cit;
1740
1741                                 // Copy rest
1742                                 while (cit != last) {
1743                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1744                                         ++cit;
1745                                 }
1746                                 return s;
1747                         }
1748
1749                         ++cit;
1750                 }
1751         }
1752
1753         // Nothing has changed
1754         return std::auto_ptr<epvector>(0);
1755 }
1756
1757 //////////
1758 // static member variables
1759 //////////
1760
1761 #if EXPAIRSEQ_USE_HASHTAB
1762 unsigned expairseq::maxhashtabsize = 0x4000000U;
1763 unsigned expairseq::minhashtabsize = 0x1000U;
1764 unsigned expairseq::hashtabfactor = 1;
1765 #endif // EXPAIRSEQ_USE_HASHTAB
1766
1767 } // namespace GiNaC