ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include <iostream>
  24 #include <algorithm>
  25 #include <string>
  26 #include <stdexcept>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "add.h"
  31 #include "mul.h"
  32 #include "power.h"
  33 #include "relational.h"
  34 #include "wildcard.h"
  35 #include "archive.h"
  36 #include "operators.h"
  37 #include "utils.h"
  38 #include "indexed.h"
  39
  40 #if EXPAIRSEQ_USE_HASHTAB
  41 #include <cmath>
  42 #endif // EXPAIRSEQ_USE_HASHTAB
  43
  44 namespace GiNaC {
  45
  46
  47 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  48   print_func<print_context>(&expairseq::do_print).
  49   print_func<print_tree>(&expairseq::do_print_tree))
  50
  51
  52 //////////
  53 // helper classes
  54 //////////
  55
  56 class epp_is_less
  57 {
  58 public:
  59         bool operator()(const epp &lh, const epp &rh) const
  60         {
  61                 return (*lh).is_less(*rh);
  62         }
  63 };
  64
  65 //////////
  66 // default constructor
  67 //////////
  68
  69 // public
  70
  71 expairseq::expairseq() : inherited(&expairseq::tinfo_static)
  72 #if EXPAIRSEQ_USE_HASHTAB
  73                                                    , hashtabsize(0)
  74 #endif // EXPAIRSEQ_USE_HASHTAB
  75 {}
  76
  77 // protected
  78
  79 #if 0
  80 /** For use by copy ctor and assignment operator. */
  81 void expairseq::copy(const expairseq &other)
  82 {
  83         seq = other.seq;
  84         overall_coeff = other.overall_coeff;
  85 #if EXPAIRSEQ_USE_HASHTAB
  86         // copy hashtab
  87         hashtabsize = other.hashtabsize;
  88         if (hashtabsize!=0) {
  89                 hashmask = other.hashmask;
  90                 hashtab.resize(hashtabsize);
  91                 epvector::const_iterator osb = other.seq.begin();
  92                 for (unsigned i=0; i<hashtabsize; ++i) {
  93                         hashtab[i].clear();
  94                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  95                              cit!=other.hashtab[i].end(); ++cit) {
  96                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  97                         }
  98                 }
  99         } else {
 100                 hashtab.clear();
 101         }
 102 #endif // EXPAIRSEQ_USE_HASHTAB
 103 }
 104 #endif
 105
 106 //////////
 107 // other constructors
 108 //////////
 109
 110 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(&expairseq::tinfo_static)
 111 {
 112         construct_from_2_ex(lh,rh);
 113         GINAC_ASSERT(is_canonical());
 114 }
 115
 116 expairseq::expairseq(const exvector &v) : inherited(&expairseq::tinfo_static)
 117 {
 118         construct_from_exvector(v);
 119         GINAC_ASSERT(is_canonical());
 120 }
 121
 122 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
 123   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
 124 {
 125         GINAC_ASSERT(is_a<numeric>(oc));
 126         construct_from_epvector(v, do_index_renaming);
 127         GINAC_ASSERT(is_canonical());
 128 }
 129
 130 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
 131   : inherited(&expairseq::tinfo_static), overall_coeff(oc)
 132 {
 133         GINAC_ASSERT(vp.get()!=0);
 134         GINAC_ASSERT(is_a<numeric>(oc));
 135         construct_from_epvector(*vp, do_index_renaming);
 136         GINAC_ASSERT(is_canonical());
 137 }
 138
 139 //////////
 140 // archiving
 141 //////////
 142
 143 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 144 #if EXPAIRSEQ_USE_HASHTAB
 145         , hashtabsize(0)
 146 #endif
 147 {
 148         archive_node::archive_node_cit first = n.find_first("rest");
 149         archive_node::archive_node_cit last = n.find_last("coeff");
 150         ++last;
 151         seq.reserve((last-first)/2);
 152
 153         for (archive_node::archive_node_cit loc = first; loc < last;) {
 154                 ex rest;
 155                 ex coeff;
 156                 n.find_ex_by_loc(loc++, rest, sym_lst);
 157                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 158                 seq.push_back(expair(rest, coeff));
 159         }
 160
 161         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 162
 163         canonicalize();
 164         GINAC_ASSERT(is_canonical());
 165 }
 166
 167 void expairseq::archive(archive_node &n) const
 168 {
 169         inherited::archive(n);
 170         epvector::const_iterator i = seq.begin(), iend = seq.end();
 171         while (i != iend) {
 172                 n.add_ex("rest", i->rest);
 173                 n.add_ex("coeff", i->coeff);
 174                 ++i;
 175         }
 176         n.add_ex("overall_coeff", overall_coeff);
 177 }
 178
 179 DEFAULT_UNARCHIVE(expairseq)
 180
 181 //////////
 182 // functions overriding virtual functions from base classes
 183 //////////
 184
 185 // public
 186
 187 void expairseq::do_print(const print_context & c, unsigned level) const
 188 {
 189         c.s << "[[";
 190         printseq(c, ',', precedence(), level);
 191         c.s << "]]";
 192 }
 193
 194 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 195 {
 196         c.s << std::string(level, ' ') << class_name() << " @" << this
 197             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 198             << ", nops=" << nops()
 199             << std::endl;
 200         size_t num = seq.size();
 201         for (size_t i=0; i<num; ++i) {
 202                 seq[i].rest.print(c, level + c.delta_indent);
 203                 seq[i].coeff.print(c, level + c.delta_indent);
 204                 if (i != num - 1)
 205                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 206         }
 207         if (!overall_coeff.is_equal(default_overall_coeff())) {
 208                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 209                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 210                 overall_coeff.print(c, level + c.delta_indent);
 211         }
 212         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 213 #if EXPAIRSEQ_USE_HASHTAB
 214         c.s << std::string(level + c.delta_indent,' ')
 215             << "hashtab size " << hashtabsize << std::endl;
 216         if (hashtabsize == 0) return;
 217 #define MAXCOUNT 5
 218         unsigned count[MAXCOUNT+1];
 219         for (int i=0; i<MAXCOUNT+1; ++i)
 220                 count[i] = 0;
 221         unsigned this_bin_fill;
 222         unsigned cum_fill_sq = 0;
 223         unsigned cum_fill = 0;
 224         for (unsigned i=0; i<hashtabsize; ++i) {
 225                 this_bin_fill = 0;
 226                 if (hashtab[i].size() > 0) {
 227                         c.s << std::string(level + c.delta_indent, ' ')
 228                             << "bin " << i << " with entries ";
 229                         for (epplist::const_iterator it=hashtab[i].begin();
 230                              it!=hashtab[i].end(); ++it) {
 231                                 c.s << *it-seq.begin() << " ";
 232                                 ++this_bin_fill;
 233                         }
 234                         c.s << std::endl;
 235                         cum_fill += this_bin_fill;
 236                         cum_fill_sq += this_bin_fill*this_bin_fill;
 237                 }
 238                 if (this_bin_fill<MAXCOUNT)
 239                         ++count[this_bin_fill];
 240                 else
 241                         ++count[MAXCOUNT];
 242         }
 243         unsigned fact = 1;
 244         double cum_prob = 0;
 245         double lambda = (1.0*seq.size()) / hashtabsize;
 246         for (int k=0; k<MAXCOUNT; ++k) {
 247                 if (k>0)
 248                         fact *= k;
 249                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 250                 cum_prob += prob;
 251                 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
 252                     << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 253                     << int(prob*1000)/10.0 << ")" << std::endl;
 254         }
 255         c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
 256             << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 257             << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 258
 259         c.s << std::string(level + c.delta_indent, ' ') << "variance: "
 260             << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 261             << std::endl;
 262         c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
 263             << (1.0*cum_fill)/hashtabsize
 264             << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 265 #endif // EXPAIRSEQ_USE_HASHTAB
 266 }
 267
 268 bool expairseq::info(unsigned inf) const
 269 {
 270         if (inf == info_flags::expanded)
 271                 return (flags & status_flags::expanded);
 272         return inherited::info(inf);
 273 }
 274
 275 size_t expairseq::nops() const
 276 {
 277         if (overall_coeff.is_equal(default_overall_coeff()))
 278                 return seq.size();
 279         else
 280                 return seq.size()+1;
 281 }
 282
 283 ex expairseq::op(size_t i) const
 284 {
 285         if (i < seq.size())
 286                 return recombine_pair_to_ex(seq[i]);
 287         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 288         return overall_coeff;
 289 }
 290
 291 ex expairseq::map(map_function &f) const
 292 {
 293         std::auto_ptr<epvector> v(new epvector);
 294         v->reserve(seq.size()+1);
 295
 296         epvector::const_iterator cit = seq.begin(), last = seq.end();
 297         while (cit != last) {
 298                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 299                 ++cit;
 300         }
 301
 302         if (overall_coeff.is_equal(default_overall_coeff()))
 303                 return thisexpairseq(v, default_overall_coeff(), true);
 304         else {
 305                 ex newcoeff = f(overall_coeff);
 306                 if(is_a<numeric>(newcoeff))
 307                         return thisexpairseq(v, newcoeff, true);
 308                 else {
 309                         v->push_back(split_ex_to_pair(newcoeff));
 310                         return thisexpairseq(v, default_overall_coeff(), true);
 311                 }
 312         }
 313 }
 314
 315 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 316 ex expairseq::eval(int level) const
 317 {
 318         if ((level==1) && (flags &status_flags::evaluated))
 319                 return *this;
 320
 321         std::auto_ptr<epvector> vp = evalchildren(level);
 322         if (vp.get() == 0)
 323                 return this->hold();
 324
 325         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 326 }
 327
 328 epvector* conjugateepvector(const epvector&epv)
 329 {
 330         epvector *newepv = 0;
 331         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 332                 if(newepv) {
 333                         newepv->push_back(i->conjugate());
 334                         continue;
 335                 }
 336                 expair x = i->conjugate();
 337                 if (x.is_equal(*i)) {
 338                         continue;
 339                 }
 340                 newepv = new epvector;
 341                 newepv->reserve(epv.size());
 342                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 343                         newepv->push_back(*j);
 344                 }
 345                 newepv->push_back(x);
 346         }
 347         return newepv;
 348 }
 349
 350 ex expairseq::conjugate() const
 351 {
 352         epvector* newepv = conjugateepvector(seq);
 353         ex x = overall_coeff.conjugate();
 354         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 355                 return *this;
 356         }
 357         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 358         if (newepv) {
 359                 delete newepv;
 360         }
 361         return result;
 362 }
 363
 364 bool expairseq::is_polynomial(const ex & var) const
 365 {
 366         if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
 367                 return basic::is_polynomial(var);
 368         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 369                 if (!(i->rest).is_polynomial(var))
 370                         return false;
 371         }
 372         return true;
 373 }
 374
 375 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 376 {
 377         // This differs from basic::match() because we want "a+b+c+d" to
 378         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 379
 380         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 381
 382                 // Check whether global wildcard (one that matches the "rest of the
 383                 // expression", like "*" above) is present
 384                 bool has_global_wildcard = false;
 385                 ex global_wildcard;
 386                 for (size_t i=0; i<pattern.nops(); i++) {
 387                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 388                                 has_global_wildcard = true;
 389                                 global_wildcard = pattern.op(i);
 390                                 break;
 391                         }
 392                 }
 393
 394                 // Unfortunately, this is an O(N^2) operation because we can't
 395                 // sort the pattern in a useful way...
 396
 397                 // Chop into terms
 398                 exvector ops;
 399                 ops.reserve(nops());
 400                 for (size_t i=0; i<nops(); i++)
 401                         ops.push_back(op(i));
 402
 403                 // Now, for every term of the pattern, look for a matching term in
 404                 // the expression and remove the match
 405                 for (size_t i=0; i<pattern.nops(); i++) {
 406                         ex p = pattern.op(i);
 407                         if (has_global_wildcard && p.is_equal(global_wildcard))
 408                                 continue;
 409                         exvector::iterator it = ops.begin(), itend = ops.end();
 410                         while (it != itend) {
 411                                 lst::const_iterator last_el = repl_lst.end();
 412                                 --last_el;
 413                                 if (it->match(p, repl_lst)) {
 414                                         ops.erase(it);
 415                                         goto found;
 416                                 }
 417                                 while(true) {
 418                                         lst::const_iterator next_el = last_el;
 419                                         ++next_el;
 420                                         if(next_el == repl_lst.end())
 421                                                 break;
 422                                         else
 423                                                 repl_lst.remove_last();
 424                                 }
 425                                 ++it;
 426                         }
 427                         return false; // no match found
 428 found:          ;
 429                 }
 430
 431                 if (has_global_wildcard) {
 432
 433                         // Assign all the remaining terms to the global wildcard (unless
 434                         // it has already been matched before, in which case the matches
 435                         // must be equal)
 436                         size_t num = ops.size();
 437                         std::auto_ptr<epvector> vp(new epvector);
 438                         vp->reserve(num);
 439                         for (size_t i=0; i<num; i++)
 440                                 vp->push_back(split_ex_to_pair(ops[i]));
 441                         ex rest = thisexpairseq(vp, default_overall_coeff());
 442                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 443                                 if (it->op(0).is_equal(global_wildcard))
 444                                         return rest.is_equal(it->op(1));
 445                         }
 446                         repl_lst.append(global_wildcard == rest);
 447                         return true;
 448
 449                 } else {
 450
 451                         // No global wildcard, then the match fails if there are any
 452                         // unmatched terms left
 453                         return ops.empty();
 454                 }
 455         }
 456         return inherited::match(pattern, repl_lst);
 457 }
 458
 459 ex expairseq::subs(const exmap & m, unsigned options) const
 460 {
 461         std::auto_ptr<epvector> vp = subschildren(m, options);
 462         if (vp.get())
 463                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
 464         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 465                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 466         else
 467                 return subs_one_level(m, options);
 468 }
 469
 470 // protected
 471
 472 int expairseq::compare_same_type(const basic &other) const
 473 {
 474         GINAC_ASSERT(is_a<expairseq>(other));
 475         const expairseq &o = static_cast<const expairseq &>(other);
 476
 477         int cmpval;
 478
 479         // compare number of elements
 480         if (seq.size() != o.seq.size())
 481                 return (seq.size()<o.seq.size()) ? -1 : 1;
 482
 483         // compare overall_coeff
 484         cmpval = overall_coeff.compare(o.overall_coeff);
 485         if (cmpval!=0)
 486                 return cmpval;
 487
 488 #if EXPAIRSEQ_USE_HASHTAB
 489         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 490         if (hashtabsize==0) {
 491 #endif // EXPAIRSEQ_USE_HASHTAB
 492                 epvector::const_iterator cit1 = seq.begin();
 493                 epvector::const_iterator cit2 = o.seq.begin();
 494                 epvector::const_iterator last1 = seq.end();
 495                 epvector::const_iterator last2 = o.seq.end();
 496
 497                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 498                         cmpval = (*cit1).compare(*cit2);
 499                         if (cmpval!=0) return cmpval;
 500                 }
 501
 502                 GINAC_ASSERT(cit1==last1);
 503                 GINAC_ASSERT(cit2==last2);
 504
 505                 return 0;
 506 #if EXPAIRSEQ_USE_HASHTAB
 507         }
 508
 509         // compare number of elements in each hashtab entry
 510         for (unsigned i=0; i<hashtabsize; ++i) {
 511                 unsigned cursize=hashtab[i].size();
 512                 if (cursize != o.hashtab[i].size())
 513                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 514         }
 515
 516         // compare individual (sorted) hashtab entries
 517         for (unsigned i=0; i<hashtabsize; ++i) {
 518                 unsigned sz = hashtab[i].size();
 519                 if (sz>0) {
 520                         const epplist &eppl1 = hashtab[i];
 521                         const epplist &eppl2 = o.hashtab[i];
 522                         epplist::const_iterator it1 = eppl1.begin();
 523                         epplist::const_iterator it2 = eppl2.begin();
 524                         while (it1!=eppl1.end()) {
 525                                 cmpval = (*(*it1)).compare(*(*it2));
 526                                 if (cmpval!=0)
 527                                         return cmpval;
 528                                 ++it1;
 529                                 ++it2;
 530                         }
 531                 }
 532         }
 533
 534         return 0; // equal
 535 #endif // EXPAIRSEQ_USE_HASHTAB
 536 }
 537
 538 bool expairseq::is_equal_same_type(const basic &other) const
 539 {
 540         const expairseq &o = static_cast<const expairseq &>(other);
 541
 542         // compare number of elements
 543         if (seq.size()!=o.seq.size())
 544                 return false;
 545
 546         // compare overall_coeff
 547         if (!overall_coeff.is_equal(o.overall_coeff))
 548                 return false;
 549
 550 #if EXPAIRSEQ_USE_HASHTAB
 551         // compare number of elements in each hashtab entry
 552         if (hashtabsize!=o.hashtabsize) {
 553                 std::cout << "this:" << std::endl;
 554                 print(print_tree(std::cout));
 555                 std::cout << "other:" << std::endl;
 556                 other.print(print_tree(std::cout));
 557         }
 558
 559         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 560
 561         if (hashtabsize==0) {
 562 #endif // EXPAIRSEQ_USE_HASHTAB
 563                 epvector::const_iterator cit1 = seq.begin();
 564                 epvector::const_iterator cit2 = o.seq.begin();
 565                 epvector::const_iterator last1 = seq.end();
 566
 567                 while (cit1!=last1) {
 568                         if (!(*cit1).is_equal(*cit2)) return false;
 569                         ++cit1;
 570                         ++cit2;
 571                 }
 572
 573                 return true;
 574 #if EXPAIRSEQ_USE_HASHTAB
 575         }
 576
 577         for (unsigned i=0; i<hashtabsize; ++i) {
 578                 if (hashtab[i].size() != o.hashtab[i].size())
 579                         return false;
 580         }
 581
 582         // compare individual sorted hashtab entries
 583         for (unsigned i=0; i<hashtabsize; ++i) {
 584                 unsigned sz = hashtab[i].size();
 585                 if (sz>0) {
 586                         const epplist &eppl1 = hashtab[i];
 587                         const epplist &eppl2 = o.hashtab[i];
 588                         epplist::const_iterator it1 = eppl1.begin();
 589                         epplist::const_iterator it2 = eppl2.begin();
 590                         while (it1!=eppl1.end()) {
 591                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 592                                 ++it1;
 593                                 ++it2;
 594                         }
 595                 }
 596         }
 597
 598         return true;
 599 #endif // EXPAIRSEQ_USE_HASHTAB
 600 }
 601
 602 unsigned expairseq::return_type() const
 603 {
 604         return return_types::noncommutative_composite;
 605 }
 606
 607 unsigned expairseq::calchash() const
 608 {
 609         unsigned v = golden_ratio_hash((p_int)this->tinfo());
 610         epvector::const_iterator i = seq.begin();
 611         const epvector::const_iterator end = seq.end();
 612         while (i != end) {
 613                 v ^= i->rest.gethash();
 614 #if !EXPAIRSEQ_USE_HASHTAB
 615                 // rotation spoils commutativity!
 616                 v = rotate_left(v);
 617                 v ^= i->coeff.gethash();
 618 #endif // !EXPAIRSEQ_USE_HASHTAB
 619                 ++i;
 620         }
 621
 622         v ^= overall_coeff.gethash();
 623
 624         // store calculated hash value only if object is already evaluated
 625         if (flags &status_flags::evaluated) {
 626                 setflag(status_flags::hash_calculated);
 627                 hashvalue = v;
 628         }
 629
 630         return v;
 631 }
 632
 633 ex expairseq::expand(unsigned options) const
 634 {
 635         std::auto_ptr<epvector> vp = expandchildren(options);
 636         if (vp.get())
 637                 return thisexpairseq(vp, overall_coeff);
 638         else {
 639                 // The terms have not changed, so it is safe to declare this expanded
 640                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 641         }
 642 }
 643
 644 //////////
 645 // new virtual functions which can be overridden by derived classes
 646 //////////
 647
 648 // protected
 649
 650 /** Create an object of this type.
 651  *  This method works similar to a constructor.  It is useful because expairseq
 652  *  has (at least) two possible different semantics but we want to inherit
 653  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 654  *  has to create a new one of the same semantics, which cannot be done by a
 655  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 656  *  order for this trick to work a derived class must of course override this
 657  *  definition. */
 658 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 659 {
 660         return expairseq(v, oc, do_index_renaming);
 661 }
 662
 663 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
 664 {
 665         return expairseq(vp, oc, do_index_renaming);
 666 }
 667
 668 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 669 {
 670         c.s << "[[";
 671         p.rest.print(c, precedence());
 672         c.s << ",";
 673         p.coeff.print(c, precedence());
 674         c.s << "]]";
 675 }
 676
 677 void expairseq::printseq(const print_context & c, char delim,
 678                          unsigned this_precedence,
 679                          unsigned upper_precedence) const
 680 {
 681         if (this_precedence <= upper_precedence)
 682                 c.s << "(";
 683         epvector::const_iterator it, it_last = seq.end() - 1;
 684         for (it=seq.begin(); it!=it_last; ++it) {
 685                 printpair(c, *it, this_precedence);
 686                 c.s << delim;
 687         }
 688         printpair(c, *it, this_precedence);
 689         if (!overall_coeff.is_equal(default_overall_coeff())) {
 690                 c.s << delim;
 691                 overall_coeff.print(c, this_precedence);
 692         }
 693
 694         if (this_precedence <= upper_precedence)
 695                 c.s << ")";
 696 }
 697
 698
 699 /** Form an expair from an ex, using the corresponding semantics.
 700  *  @see expairseq::recombine_pair_to_ex() */
 701 expair expairseq::split_ex_to_pair(const ex &e) const
 702 {
 703         return expair(e,_ex1);
 704 }
 705
 706
 707 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 708                                                 const ex &c) const
 709 {
 710         GINAC_ASSERT(is_exactly_a<numeric>(c));
 711
 712         return expair(e,c);
 713 }
 714
 715
 716 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 717                                                   const ex &c) const
 718 {
 719         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 720         GINAC_ASSERT(is_exactly_a<numeric>(c));
 721
 722         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 723 }
 724
 725
 726 /** Form an ex out of an expair, using the corresponding semantics.
 727  *  @see expairseq::split_ex_to_pair() */
 728 ex expairseq::recombine_pair_to_ex(const expair &p) const
 729 {
 730         return lst(p.rest,p.coeff);
 731 }
 732
 733 bool expairseq::expair_needs_further_processing(epp it)
 734 {
 735 #if EXPAIRSEQ_USE_HASHTAB
 736         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 737 #endif // EXPAIRSEQ_USE_HASHTAB
 738         return false;
 739 }
 740
 741 ex expairseq::default_overall_coeff() const
 742 {
 743         return _ex0;
 744 }
 745
 746 void expairseq::combine_overall_coeff(const ex &c)
 747 {
 748         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 749         GINAC_ASSERT(is_exactly_a<numeric>(c));
 750         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 751 }
 752
 753 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 754 {
 755         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 756         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 757         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 758         overall_coeff = ex_to<numeric>(overall_coeff).
 759                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 760 }
 761
 762 bool expairseq::can_make_flat(const expair &p) const
 763 {
 764         return true;
 765 }
 766
 767
 768 //////////
 769 // non-virtual functions in this class
 770 //////////
 771
 772 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 773 {
 774         exvector v;
 775         v.reserve(2);
 776         v.push_back(lh);
 777         v.push_back(rh);
 778         construct_from_exvector(v);
 779 #if EXPAIRSEQ_USE_HASHTAB
 780         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 781         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 782 #endif // EXPAIRSEQ_USE_HASHTAB
 783 }
 784
 785 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 786 {
 787         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 788                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 789 #if EXPAIRSEQ_USE_HASHTAB
 790                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 791                                              ex_to<expairseq>(rh).seq.size();
 792                         if (calc_hashtabsize(totalsize)!=0) {
 793                                 construct_from_2_ex_via_exvector(lh,rh);
 794                         } else {
 795 #endif // EXPAIRSEQ_USE_HASHTAB
 796                                 if(is_a<mul>(lh))
 797                                 {
 798                                         ex newrh=rename_dummy_indices_uniquely(lh, rh);
 799                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 800                                                                    ex_to<expairseq>(newrh));
 801                                 }
 802                                 else
 803                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 804                                                                    ex_to<expairseq>(rh));
 805 #if EXPAIRSEQ_USE_HASHTAB
 806                         }
 807 #endif // EXPAIRSEQ_USE_HASHTAB
 808                         return;
 809                 } else {
 810 #if EXPAIRSEQ_USE_HASHTAB
 811                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 812                         if (calc_hashtabsize(totalsize)!=0) {
 813                                 construct_from_2_ex_via_exvector(lh, rh);
 814                         } else {
 815 #endif // EXPAIRSEQ_USE_HASHTAB
 816                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 817 #if EXPAIRSEQ_USE_HASHTAB
 818                         }
 819 #endif // EXPAIRSEQ_USE_HASHTAB
 820                         return;
 821                 }
 822         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 823 #if EXPAIRSEQ_USE_HASHTAB
 824                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 825                 if (calc_hashtabsize(totalsize)!=0) {
 826                         construct_from_2_ex_via_exvector(lh,rh);
 827                 } else {
 828 #endif // EXPAIRSEQ_USE_HASHTAB
 829                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 830 #if EXPAIRSEQ_USE_HASHTAB
 831                 }
 832 #endif // EXPAIRSEQ_USE_HASHTAB
 833                 return;
 834         }
 835
 836 #if EXPAIRSEQ_USE_HASHTAB
 837         if (calc_hashtabsize(2)!=0) {
 838                 construct_from_2_ex_via_exvector(lh,rh);
 839                 return;
 840         }
 841         hashtabsize = 0;
 842 #endif // EXPAIRSEQ_USE_HASHTAB
 843
 844         if (is_exactly_a<numeric>(lh)) {
 845                 if (is_exactly_a<numeric>(rh)) {
 846                         combine_overall_coeff(lh);
 847                         combine_overall_coeff(rh);
 848                 } else {
 849                         combine_overall_coeff(lh);
 850                         seq.push_back(split_ex_to_pair(rh));
 851                 }
 852         } else {
 853                 if (is_exactly_a<numeric>(rh)) {
 854                         combine_overall_coeff(rh);
 855                         seq.push_back(split_ex_to_pair(lh));
 856                 } else {
 857                         expair p1 = split_ex_to_pair(lh);
 858                         expair p2 = split_ex_to_pair(rh);
 859
 860                         int cmpval = p1.rest.compare(p2.rest);
 861                         if (cmpval==0) {
 862                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 863                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 864                                         // no further processing is necessary, since this
 865                                         // one element will usually be recombined in eval()
 866                                         seq.push_back(p1);
 867                                 }
 868                         } else {
 869                                 seq.reserve(2);
 870                                 if (cmpval<0) {
 871                                         seq.push_back(p1);
 872                                         seq.push_back(p2);
 873                                 } else {
 874                                         seq.push_back(p2);
 875                                         seq.push_back(p1);
 876                                 }
 877                         }
 878                 }
 879         }
 880 }
 881
 882 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 883                                                                                    const expairseq &s2)
 884 {
 885         combine_overall_coeff(s1.overall_coeff);
 886         combine_overall_coeff(s2.overall_coeff);
 887
 888         epvector::const_iterator first1 = s1.seq.begin();
 889         epvector::const_iterator last1 = s1.seq.end();
 890         epvector::const_iterator first2 = s2.seq.begin();
 891         epvector::const_iterator last2 = s2.seq.end();
 892
 893         seq.reserve(s1.seq.size()+s2.seq.size());
 894
 895         bool needs_further_processing=false;
 896
 897         while (first1!=last1 && first2!=last2) {
 898                 int cmpval = (*first1).rest.compare((*first2).rest);
 899
 900                 if (cmpval==0) {
 901                         // combine terms
 902                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 903                                                    add(ex_to<numeric>(first2->coeff));
 904                         if (!newcoeff.is_zero()) {
 905                                 seq.push_back(expair(first1->rest,newcoeff));
 906                                 if (expair_needs_further_processing(seq.end()-1)) {
 907                                         needs_further_processing = true;
 908                                 }
 909                         }
 910                         ++first1;
 911                         ++first2;
 912                 } else if (cmpval<0) {
 913                         seq.push_back(*first1);
 914                         ++first1;
 915                 } else {
 916                         seq.push_back(*first2);
 917                         ++first2;
 918                 }
 919         }
 920
 921         while (first1!=last1) {
 922                 seq.push_back(*first1);
 923                 ++first1;
 924         }
 925         while (first2!=last2) {
 926                 seq.push_back(*first2);
 927                 ++first2;
 928         }
 929
 930         if (needs_further_processing) {
 931                 epvector v = seq;
 932                 seq.clear();
 933                 construct_from_epvector(v);
 934         }
 935 }
 936
 937 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 938                                                                                         const ex &e)
 939 {
 940         combine_overall_coeff(s.overall_coeff);
 941         if (is_exactly_a<numeric>(e)) {
 942                 combine_overall_coeff(e);
 943                 seq = s.seq;
 944                 return;
 945         }
 946
 947         epvector::const_iterator first = s.seq.begin();
 948         epvector::const_iterator last = s.seq.end();
 949         expair p = split_ex_to_pair(e);
 950
 951         seq.reserve(s.seq.size()+1);
 952         bool p_pushed = false;
 953
 954         bool needs_further_processing=false;
 955
 956         // merge p into s.seq
 957         while (first!=last) {
 958                 int cmpval = (*first).rest.compare(p.rest);
 959                 if (cmpval==0) {
 960                         // combine terms
 961                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 962                                                    add(ex_to<numeric>(p.coeff));
 963                         if (!newcoeff.is_zero()) {
 964                                 seq.push_back(expair(first->rest,newcoeff));
 965                                 if (expair_needs_further_processing(seq.end()-1))
 966                                         needs_further_processing = true;
 967                         }
 968                         ++first;
 969                         p_pushed = true;
 970                         break;
 971                 } else if (cmpval<0) {
 972                         seq.push_back(*first);
 973                         ++first;
 974                 } else {
 975                         seq.push_back(p);
 976                         p_pushed = true;
 977                         break;
 978                 }
 979         }
 980
 981         if (p_pushed) {
 982                 // while loop exited because p was pushed, now push rest of s.seq
 983                 while (first!=last) {
 984                         seq.push_back(*first);
 985                         ++first;
 986                 }
 987         } else {
 988                 // while loop exited because s.seq was pushed, now push p
 989                 seq.push_back(p);
 990         }
 991
 992         if (needs_further_processing) {
 993                 epvector v = seq;
 994                 seq.clear();
 995                 construct_from_epvector(v);
 996         }
 997 }
 998
 999 void expairseq::construct_from_exvector(const exvector &v)
1000 {
1001         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1002         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1003         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1004         //                  (same for (+,*) -> (*,^)
1005
1006         make_flat(v);
1007 #if EXPAIRSEQ_USE_HASHTAB
1008         combine_same_terms();
1009 #else
1010         canonicalize();
1011         combine_same_terms_sorted_seq();
1012 #endif // EXPAIRSEQ_USE_HASHTAB
1013 }
1014
1015 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1016 {
1017         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1018         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1019         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1020         //                  (same for (+,*) -> (*,^)
1021
1022         make_flat(v, do_index_renaming);
1023 #if EXPAIRSEQ_USE_HASHTAB
1024         combine_same_terms();
1025 #else
1026         canonicalize();
1027         combine_same_terms_sorted_seq();
1028 #endif // EXPAIRSEQ_USE_HASHTAB
1029 }
1030
1031 /** Combine this expairseq with argument exvector.
1032  *  It cares for associativity as well as for special handling of numerics. */
1033 void expairseq::make_flat(const exvector &v)
1034 {
1035         exvector::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).tinfo()==this->tinfo()) {
1045                         ++nexpairseqs;
1046                         noperands += ex_to<expairseq>(*cit).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         make_flat_inserter mf(v, this->tinfo() == &mul::tinfo_static);
1056         cit = v.begin();
1057         while (cit!=v.end()) {
1058                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1059                         ex newfactor = mf.handle_factor(*cit, _ex1);
1060                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
1061                         combine_overall_coeff(subseqref.overall_coeff);
1062                         epvector::const_iterator cit_s = subseqref.seq.begin();
1063                         while (cit_s!=subseqref.seq.end()) {
1064                                 seq.push_back(*cit_s);
1065                                 ++cit_s;
1066                         }
1067                 } else {
1068                         if (is_exactly_a<numeric>(*cit))
1069                                 combine_overall_coeff(*cit);
1070                         else {
1071                                 ex newfactor = mf.handle_factor(*cit, _ex1);
1072                                 seq.push_back(split_ex_to_pair(newfactor));
1073                         }
1074                 }
1075                 ++cit;
1076         }
1077 }
1078
1079 /** Combine this expairseq with argument epvector.
1080  *  It cares for associativity as well as for special handling of numerics. */
1081 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1082 {
1083         epvector::const_iterator cit;
1084
1085         // count number of operands which are of same expairseq derived type
1086         // and their cumulative number of operands
1087         int nexpairseqs = 0;
1088         int noperands = 0;
1089
1090         cit = v.begin();
1091         while (cit!=v.end()) {
1092                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1093                         ++nexpairseqs;
1094                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1095                 }
1096                 ++cit;
1097         }
1098
1099         // reserve seq and coeffseq which will hold all operands
1100         seq.reserve(v.size()+noperands-nexpairseqs);
1101         make_flat_inserter mf(v, do_index_renaming);
1102
1103         // copy elements and split off numerical part
1104         cit = v.begin();
1105         while (cit!=v.end()) {
1106                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1107                     this->can_make_flat(*cit)) {
1108                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1109                         const expairseq &subseqref = ex_to<expairseq>(newrest);
1110                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1111                                                             ex_to<numeric>(cit->coeff));
1112                         epvector::const_iterator cit_s = subseqref.seq.begin();
1113                         while (cit_s!=subseqref.seq.end()) {
1114                                 seq.push_back(expair(cit_s->rest,
1115                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1116                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1117                                 //                                              (*cit).coeff));
1118                                 ++cit_s;
1119                         }
1120                 } else {
1121                         if (cit->is_canonical_numeric())
1122                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1123                         else {
1124                                 ex rest = cit->rest;
1125                                 ex newrest = mf.handle_factor(rest, cit->coeff);
1126                                 if (are_ex_trivially_equal(newrest, rest))
1127                                         seq.push_back(*cit);
1128                                 else
1129                                         seq.push_back(expair(newrest, cit->coeff));
1130                         }
1131                 }
1132                 ++cit;
1133         }
1134 }
1135
1136 /** Brings this expairseq into a sorted (canonical) form. */
1137 void expairseq::canonicalize()
1138 {
1139         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1140 }
1141
1142
1143 /** Compact a presorted expairseq by combining all matching expairs to one
1144  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1145  *  instance. */
1146 void expairseq::combine_same_terms_sorted_seq()
1147 {
1148         if (seq.size()<2)
1149                 return;
1150
1151         bool needs_further_processing = false;
1152
1153         epvector::iterator itin1 = seq.begin();
1154         epvector::iterator itin2 = itin1+1;
1155         epvector::iterator itout = itin1;
1156         epvector::iterator last = seq.end();
1157         // must_copy will be set to true the first time some combination is
1158         // possible from then on the sequence has changed and must be compacted
1159         bool must_copy = false;
1160         while (itin2!=last) {
1161                 if (itin1->rest.compare(itin2->rest)==0) {
1162                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1163                                        add_dyn(ex_to<numeric>(itin2->coeff));
1164                         if (expair_needs_further_processing(itin1))
1165                                 needs_further_processing = true;
1166                         must_copy = true;
1167                 } else {
1168                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1169                                 if (must_copy)
1170                                         *itout = *itin1;
1171                                 ++itout;
1172                         }
1173                         itin1 = itin2;
1174                 }
1175                 ++itin2;
1176         }
1177         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1178                 if (must_copy)
1179                         *itout = *itin1;
1180                 ++itout;
1181         }
1182         if (itout!=last)
1183                 seq.erase(itout,last);
1184
1185         if (needs_further_processing) {
1186                 epvector v = seq;
1187                 seq.clear();
1188                 construct_from_epvector(v);
1189         }
1190 }
1191
1192 #if EXPAIRSEQ_USE_HASHTAB
1193
1194 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1195 {
1196         unsigned size;
1197         unsigned nearest_power_of_2 = 1 << log2(sz);
1198         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1199         //  size = nearest_power_of_2*hashtabfactor;
1200         size = nearest_power_of_2/hashtabfactor;
1201         if (size<minhashtabsize)
1202                 return 0;
1203
1204         // hashtabsize must be a power of 2
1205         GINAC_ASSERT((1U << log2(size))==size);
1206         return size;
1207 }
1208
1209 unsigned expairseq::calc_hashindex(const ex &e) const
1210 {
1211         // calculate hashindex
1212         unsigned hashindex;
1213         if (is_a<numeric>(e)) {
1214                 hashindex = hashmask;
1215         } else {
1216                 hashindex = e.gethash() & hashmask;
1217                 // last hashtab entry is reserved for numerics
1218                 if (hashindex==hashmask) hashindex = 0;
1219         }
1220         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1221         return hashindex;
1222 }
1223
1224 void expairseq::shrink_hashtab()
1225 {
1226         unsigned new_hashtabsize;
1227         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1228                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1229                 if (new_hashtabsize==0) {
1230                         hashtab.clear();
1231                         hashtabsize = 0;
1232                         canonicalize();
1233                         return;
1234                 }
1235
1236                 // shrink by a factor of 2
1237                 unsigned half_hashtabsize = hashtabsize/2;
1238                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1239                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1240                 // special treatment for numeric hashes
1241                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1242                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1243                 hashtab.resize(half_hashtabsize);
1244                 hashtabsize = half_hashtabsize;
1245                 hashmask = hashtabsize-1;
1246         }
1247 }
1248
1249 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1250 {
1251         if (hashtabsize==0)
1252                 return; // nothing to do
1253
1254         // calculate hashindex of element to be deleted
1255         unsigned hashindex = calc_hashindex((*element).rest);
1256
1257         // find it in hashtab and remove it
1258         epplist &eppl = hashtab[hashindex];
1259         epplist::iterator epplit = eppl.begin();
1260         bool erased = false;
1261         while (epplit!=eppl.end()) {
1262                 if (*epplit == element) {
1263                         eppl.erase(epplit);
1264                         erased = true;
1265                         break;
1266                 }
1267                 ++epplit;
1268         }
1269         if (!erased) {
1270                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1271                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1272
1273                 unsigned hashindex = calc_hashindex(element->rest);
1274                 epplist &eppl = hashtab[hashindex];
1275                 epplist::iterator epplit = eppl.begin();
1276                 bool erased = false;
1277                 while (epplit!=eppl.end()) {
1278                         if (*epplit == element) {
1279                                 eppl.erase(epplit);
1280                                 erased = true;
1281                                 break;
1282                         }
1283                         ++epplit;
1284                 }
1285                 GINAC_ASSERT(erased);
1286         }
1287         GINAC_ASSERT(erased);
1288 }
1289
1290 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1291                                    epvector::iterator newpos)
1292 {
1293         GINAC_ASSERT(hashtabsize!=0);
1294
1295         // calculate hashindex of element which was moved
1296         unsigned hashindex=calc_hashindex((*newpos).rest);
1297
1298         // find it in hashtab and modify it
1299         epplist &eppl = hashtab[hashindex];
1300         epplist::iterator epplit = eppl.begin();
1301         while (epplit!=eppl.end()) {
1302                 if (*epplit == oldpos) {
1303                         *epplit = newpos;
1304                         break;
1305                 }
1306                 ++epplit;
1307         }
1308         GINAC_ASSERT(epplit!=eppl.end());
1309 }
1310
1311 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1312 {
1313         epplist::const_iterator current = eppl.begin();
1314         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1315                 ++current;
1316         }
1317         eppl.insert(current,elem);
1318 }
1319
1320 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1321                                           epvector::iterator &last_non_zero,
1322                                           std::vector<bool> &touched,
1323                                           unsigned &number_of_zeroes)
1324 {
1325         epp current = seq.begin();
1326
1327         while (current!=first_numeric) {
1328                 if (is_exactly_a<numeric>(current->rest)) {
1329                         --first_numeric;
1330                         iter_swap(current,first_numeric);
1331                 } else {
1332                         // calculate hashindex
1333                         unsigned currenthashindex = calc_hashindex(current->rest);
1334
1335                         // test if there is already a matching expair in the hashtab-list
1336                         epplist &eppl=hashtab[currenthashindex];
1337                         epplist::iterator epplit = eppl.begin();
1338                         while (epplit!=eppl.end()) {
1339                                 if (current->rest.is_equal((*epplit)->rest))
1340                                         break;
1341                                 ++epplit;
1342                         }
1343                         if (epplit==eppl.end()) {
1344                                 // no matching expair found, append this to end of list
1345                                 sorted_insert(eppl,current);
1346                                 ++current;
1347                         } else {
1348                                 // epplit points to a matching expair, combine it with current
1349                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1350                                                    add_dyn(ex_to<numeric>(current->coeff));
1351
1352                                 // move obsolete current expair to end by swapping with last_non_zero element
1353                                 // if this was a numeric, it is swapped with the expair before first_numeric
1354                                 iter_swap(current,last_non_zero);
1355                                 --first_numeric;
1356                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1357                                 --last_non_zero;
1358                                 ++number_of_zeroes;
1359                                 // test if combined term has coeff 0 and can be removed is done later
1360                                 touched[(*epplit)-seq.begin()] = true;
1361                         }
1362                 }
1363         }
1364 }
1365
1366 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1367                                    epvector::iterator &last_non_zero,
1368                                    std::vector<bool> &touched,
1369                                    unsigned &number_of_zeroes)
1370 {
1371         // move terms with coeff 0 to end and remove them from hashtab
1372         // check only those elements which have been touched
1373         epp current = seq.begin();
1374         size_t i = 0;
1375         while (current!=first_numeric) {
1376                 if (!touched[i]) {
1377                         ++current;
1378                         ++i;
1379                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1380                         ++current;
1381                         ++i;
1382                 } else {
1383                         remove_hashtab_entry(current);
1384
1385                         // move element to the end, unless it is already at the end
1386                         if (current!=last_non_zero) {
1387                                 iter_swap(current,last_non_zero);
1388                                 --first_numeric;
1389                                 bool numeric_swapped = first_numeric!=last_non_zero;
1390                                 if (numeric_swapped)
1391                                         iter_swap(first_numeric,current);
1392                                 epvector::iterator changed_entry;
1393
1394                                 if (numeric_swapped)
1395                                         changed_entry = first_numeric;
1396                                 else
1397                                         changed_entry = last_non_zero;
1398
1399                                 --last_non_zero;
1400                                 ++number_of_zeroes;
1401
1402                                 if (first_numeric!=current) {
1403
1404                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1405                                         move_hashtab_entry(changed_entry,current);
1406                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1407                                 }
1408                         } else {
1409                                 --first_numeric;
1410                                 --last_non_zero;
1411                                 ++number_of_zeroes;
1412                         }
1413                 }
1414         }
1415         GINAC_ASSERT(i==current-seq.begin());
1416 }
1417
1418 /** True if one of the coeffs vanishes, otherwise false.
1419  *  This would be an invariant violation, so this should only be used for
1420  *  debugging purposes. */
1421 bool expairseq::has_coeff_0() const
1422 {
1423         epvector::const_iterator i = seq.begin(), end = seq.end();
1424         while (i != end) {
1425                 if (i->coeff.is_zero())
1426                         return true;
1427                 ++i;
1428         }
1429         return false;
1430 }
1431
1432 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1433                                                                                 epvector::const_iterator last_non_zero)
1434 {
1435         if (first_numeric == seq.end()) return; // no numerics
1436
1437         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1438         while (current != last) {
1439                 sorted_insert(hashtab[hashmask], current);
1440                 ++current;
1441         }
1442 }
1443
1444 void expairseq::combine_same_terms()
1445 {
1446         // combine same terms, drop term with coeff 0, move numerics to end
1447
1448         // calculate size of hashtab
1449         hashtabsize = calc_hashtabsize(seq.size());
1450
1451         // hashtabsize is a power of 2
1452         hashmask = hashtabsize-1;
1453
1454         // allocate hashtab
1455         hashtab.clear();
1456         hashtab.resize(hashtabsize);
1457
1458         if (hashtabsize==0) {
1459                 canonicalize();
1460                 combine_same_terms_sorted_seq();
1461                 GINAC_ASSERT(!has_coeff_0());
1462                 return;
1463         }
1464
1465         // iterate through seq, move numerics to end,
1466         // fill hashtab and combine same terms
1467         epvector::iterator first_numeric = seq.end();
1468         epvector::iterator last_non_zero = seq.end()-1;
1469
1470         size_t num = seq.size();
1471         std::vector<bool> touched(num);
1472
1473         unsigned number_of_zeroes = 0;
1474
1475         GINAC_ASSERT(!has_coeff_0());
1476         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1477
1478         // there should not be any terms with coeff 0 from the beginning,
1479         // so it should be safe to skip this step
1480         if (number_of_zeroes!=0) {
1481                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1482         }
1483
1484         add_numerics_to_hashtab(first_numeric,last_non_zero);
1485
1486         // pop zero elements
1487         for (unsigned i=0; i<number_of_zeroes; ++i) {
1488                 seq.pop_back();
1489         }
1490
1491         // shrink hashtabsize to calculated value
1492         GINAC_ASSERT(!has_coeff_0());
1493
1494         shrink_hashtab();
1495
1496         GINAC_ASSERT(!has_coeff_0());
1497 }
1498
1499 #endif // EXPAIRSEQ_USE_HASHTAB
1500
1501 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1502  *  debugging or in assertions since being sorted is an invariance. */
1503 bool expairseq::is_canonical() const
1504 {
1505         if (seq.size() <= 1)
1506                 return 1;
1507
1508 #if EXPAIRSEQ_USE_HASHTAB
1509         if (hashtabsize > 0) return 1; // not canoncalized
1510 #endif // EXPAIRSEQ_USE_HASHTAB
1511
1512         epvector::const_iterator it = seq.begin(), itend = seq.end();
1513         epvector::const_iterator it_last = it;
1514         for (++it; it!=itend; it_last=it, ++it) {
1515                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1516                         if (!is_exactly_a<numeric>(it_last->rest) ||
1517                                 !is_exactly_a<numeric>(it->rest)) {
1518                                 // double test makes it easier to set a breakpoint...
1519                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1520                                         !is_exactly_a<numeric>(it->rest)) {
1521                                         printpair(std::clog, *it_last, 0);
1522                                         std::clog << ">";
1523                                         printpair(std::clog, *it, 0);
1524                                         std::clog << "\n";
1525                                         std::clog << "pair1:" << std::endl;
1526                                         it_last->rest.print(print_tree(std::clog));
1527                                         it_last->coeff.print(print_tree(std::clog));
1528                                         std::clog << "pair2:" << std::endl;
1529                                         it->rest.print(print_tree(std::clog));
1530                                         it->coeff.print(print_tree(std::clog));
1531                                         return 0;
1532                                 }
1533                         }
1534                 }
1535         }
1536         return 1;
1537 }
1538
1539
1540 /** Member-wise expand the expairs in this sequence.
1541  *
1542  *  @see expairseq::expand()
1543  *  @return pointer to epvector containing expanded pairs or zero pointer,
1544  *  if no members were changed. */
1545 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1546 {
1547         const epvector::const_iterator last = seq.end();
1548         epvector::const_iterator cit = seq.begin();
1549         while (cit!=last) {
1550                 const ex &expanded_ex = cit->rest.expand(options);
1551                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1552
1553                         // something changed, copy seq, eval and return it
1554                         std::auto_ptr<epvector> s(new epvector);
1555                         s->reserve(seq.size());
1556
1557                         // copy parts of seq which are known not to have changed
1558                         epvector::const_iterator cit2 = seq.begin();
1559                         while (cit2!=cit) {
1560                                 s->push_back(*cit2);
1561                                 ++cit2;
1562                         }
1563
1564                         // copy first changed element
1565                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1566                                                                    cit2->coeff));
1567                         ++cit2;
1568
1569                         // copy rest
1570                         while (cit2!=last) {
1571                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1572                                                                            cit2->coeff));
1573                                 ++cit2;
1574                         }
1575                         return s;
1576                 }
1577                 ++cit;
1578         }
1579
1580         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1581 }
1582
1583
1584 /** Member-wise evaluate the expairs in this sequence.
1585  *
1586  *  @see expairseq::eval()
1587  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1588  *  if no members were changed. */
1589 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1590 {
1591         // returns a NULL pointer if nothing had to be evaluated
1592         // returns a pointer to a newly created epvector otherwise
1593         // (which has to be deleted somewhere else)
1594
1595         if (level==1)
1596                 return std::auto_ptr<epvector>(0);
1597
1598         if (level == -max_recursion_level)
1599                 throw(std::runtime_error("max recursion level reached"));
1600
1601         --level;
1602         epvector::const_iterator last = seq.end();
1603         epvector::const_iterator cit = seq.begin();
1604         while (cit!=last) {
1605                 const ex &evaled_ex = cit->rest.eval(level);
1606                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1607
1608                         // something changed, copy seq, eval and return it
1609                         std::auto_ptr<epvector> s(new epvector);
1610                         s->reserve(seq.size());
1611
1612                         // copy parts of seq which are known not to have changed
1613                         epvector::const_iterator cit2=seq.begin();
1614                         while (cit2!=cit) {
1615                                 s->push_back(*cit2);
1616                                 ++cit2;
1617                         }
1618
1619                         // copy first changed element
1620                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1621                                                                    cit2->coeff));
1622                         ++cit2;
1623
1624                         // copy rest
1625                         while (cit2!=last) {
1626                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1627                                                                            cit2->coeff));
1628                                 ++cit2;
1629                         }
1630                         return s;
1631                 }
1632                 ++cit;
1633         }
1634
1635         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1636 }
1637
1638 /** Member-wise substitute in this sequence.
1639  *
1640  *  @see expairseq::subs()
1641  *  @return pointer to epvector containing pairs after application of subs,
1642  *    or NULL pointer if no members were changed. */
1643 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1644 {
1645         // When any of the objects to be substituted is a product or power
1646         // we have to recombine the pairs because the numeric coefficients may
1647         // be part of the search pattern.
1648         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1649
1650                 // Search the list of substitutions and cache our findings
1651                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1652                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1653                                 options |= subs_options::pattern_is_product;
1654                                 break;
1655                         }
1656                 }
1657                 if (!(options & subs_options::pattern_is_product))
1658                         options |= subs_options::pattern_is_not_product;
1659         }
1660
1661         if (options & subs_options::pattern_is_product) {
1662
1663                 // Substitute in the recombined pairs
1664                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1665                 while (cit != last) {
1666
1667                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1668                         const ex &subsed_ex = orig_ex.subs(m, options);
1669                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1670
1671                                 // Something changed, copy seq, subs and return it
1672                                 std::auto_ptr<epvector> s(new epvector);
1673                                 s->reserve(seq.size());
1674
1675                                 // Copy parts of seq which are known not to have changed
1676                                 s->insert(s->begin(), seq.begin(), cit);
1677
1678                                 // Copy first changed element
1679                                 s->push_back(split_ex_to_pair(subsed_ex));
1680                                 ++cit;
1681
1682                                 // Copy rest
1683                                 while (cit != last) {
1684                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1685                                         ++cit;
1686                                 }
1687                                 return s;
1688                         }
1689
1690                         ++cit;
1691                 }
1692
1693         } else {
1694
1695                 // Substitute only in the "rest" part of the pairs
1696                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1697                 while (cit != last) {
1698
1699                         const ex &subsed_ex = cit->rest.subs(m, options);
1700                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1701
1702                                 // Something changed, copy seq, subs and return it
1703                                 std::auto_ptr<epvector> s(new epvector);
1704                                 s->reserve(seq.size());
1705
1706                                 // Copy parts of seq which are known not to have changed
1707                                 s->insert(s->begin(), seq.begin(), cit);
1708
1709                                 // Copy first changed element
1710                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1711                                 ++cit;
1712
1713                                 // Copy rest
1714                                 while (cit != last) {
1715                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1716                                         ++cit;
1717                                 }
1718                                 return s;
1719                         }
1720
1721                         ++cit;
1722                 }
1723         }
1724
1725         // Nothing has changed
1726         return std::auto_ptr<epvector>(0);
1727 }
1728
1729 //////////
1730 // static member variables
1731 //////////
1732
1733 #if EXPAIRSEQ_USE_HASHTAB
1734 unsigned expairseq::maxhashtabsize = 0x4000000U;
1735 unsigned expairseq::minhashtabsize = 0x1000U;
1736 unsigned expairseq::hashtabfactor = 1;
1737 #endif // EXPAIRSEQ_USE_HASHTAB
1738
1739 } // namespace GiNaC