ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2011 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 "expairseq.h"
  24 #include "lst.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "power.h"
  28 #include "relational.h"
  29 #include "wildcard.h"
  30 #include "archive.h"
  31 #include "operators.h"
  32 #include "utils.h"
  33 #include "hash_seed.h"
  34 #include "indexed.h"
  35
  36 #include <algorithm>
  37 #if EXPAIRSEQ_USE_HASHTAB
  38 #include <cmath>
  39 #endif // EXPAIRSEQ_USE_HASHTAB
  40 #include <iostream>
  41 #include <iterator>
  42 #include <stdexcept>
  43 #include <string>
  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()
  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)
 112 {
 113         construct_from_2_ex(lh,rh);
 114         GINAC_ASSERT(is_canonical());
 115 }
 116
 117 expairseq::expairseq(const exvector &v)
 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   :  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   :  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 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
 145 {
 146         inherited::read_archive(n, sym_lst);
 147         archive_node::archive_node_cit first = n.find_first("rest");
 148         archive_node::archive_node_cit last = n.find_last("coeff");
 149         ++last;
 150         seq.reserve((last-first)/2);
 151
 152         for (archive_node::archive_node_cit loc = first; loc < last;) {
 153                 ex rest;
 154                 ex coeff;
 155                 n.find_ex_by_loc(loc++, rest, sym_lst);
 156                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 157                 seq.push_back(expair(rest, coeff));
 158         }
 159
 160         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 161
 162         canonicalize();
 163         GINAC_ASSERT(is_canonical());
 164 }
 165
 166 void expairseq::archive(archive_node &n) const
 167 {
 168         inherited::archive(n);
 169         epvector::const_iterator i = seq.begin(), iend = seq.end();
 170         while (i != iend) {
 171                 n.add_ex("rest", i->rest);
 172                 n.add_ex("coeff", i->coeff);
 173                 ++i;
 174         }
 175         n.add_ex("overall_coeff", overall_coeff);
 176 }
 177
 178
 179 //////////
 180 // functions overriding virtual functions from base classes
 181 //////////
 182
 183 // public
 184
 185 void expairseq::do_print(const print_context & c, unsigned level) const
 186 {
 187         c.s << "[[";
 188         printseq(c, ',', precedence(), level);
 189         c.s << "]]";
 190 }
 191
 192 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 193 {
 194         c.s << std::string(level, ' ') << class_name() << " @" << this
 195             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 196             << ", nops=" << nops()
 197             << std::endl;
 198         size_t num = seq.size();
 199         for (size_t i=0; i<num; ++i) {
 200                 seq[i].rest.print(c, level + c.delta_indent);
 201                 seq[i].coeff.print(c, level + c.delta_indent);
 202                 if (i != num - 1)
 203                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 204         }
 205         if (!overall_coeff.is_equal(default_overall_coeff())) {
 206                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 207                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 208                 overall_coeff.print(c, level + c.delta_indent);
 209         }
 210         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 211 #if EXPAIRSEQ_USE_HASHTAB
 212         c.s << std::string(level + c.delta_indent,' ')
 213             << "hashtab size " << hashtabsize << std::endl;
 214         if (hashtabsize == 0) return;
 215 #define MAXCOUNT 5
 216         unsigned count[MAXCOUNT+1];
 217         for (int i=0; i<MAXCOUNT+1; ++i)
 218                 count[i] = 0;
 219         unsigned this_bin_fill;
 220         unsigned cum_fill_sq = 0;
 221         unsigned cum_fill = 0;
 222         for (unsigned i=0; i<hashtabsize; ++i) {
 223                 this_bin_fill = 0;
 224                 if (hashtab[i].size() > 0) {
 225                         c.s << std::string(level + c.delta_indent, ' ')
 226                             << "bin " << i << " with entries ";
 227                         for (epplist::const_iterator it=hashtab[i].begin();
 228                              it!=hashtab[i].end(); ++it) {
 229                                 c.s << *it-seq.begin() << " ";
 230                                 ++this_bin_fill;
 231                         }
 232                         c.s << std::endl;
 233                         cum_fill += this_bin_fill;
 234                         cum_fill_sq += this_bin_fill*this_bin_fill;
 235                 }
 236                 if (this_bin_fill<MAXCOUNT)
 237                         ++count[this_bin_fill];
 238                 else
 239                         ++count[MAXCOUNT];
 240         }
 241         unsigned fact = 1;
 242         double cum_prob = 0;
 243         double lambda = (1.0*seq.size()) / hashtabsize;
 244         for (int k=0; k<MAXCOUNT; ++k) {
 245                 if (k>0)
 246                         fact *= k;
 247                 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 248                 cum_prob += prob;
 249                 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
 250                     << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 251                     << int(prob*1000)/10.0 << ")" << std::endl;
 252         }
 253         c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
 254             << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 255             << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 256
 257         c.s << std::string(level + c.delta_indent, ' ') << "variance: "
 258             << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 259             << std::endl;
 260         c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
 261             << (1.0*cum_fill)/hashtabsize
 262             << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 263 #endif // EXPAIRSEQ_USE_HASHTAB
 264 }
 265
 266 bool expairseq::info(unsigned inf) const
 267 {
 268         switch(inf) {
 269                 case info_flags::expanded:
 270                         return (flags & status_flags::expanded);
 271                 case info_flags::has_indices: {
 272                         if (flags & status_flags::has_indices)
 273                                 return true;
 274                         else if (flags & status_flags::has_no_indices)
 275                                 return false;
 276                         for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
 277                                 if (i->rest.info(info_flags::has_indices)) {
 278                                         this->setflag(status_flags::has_indices);
 279                                         this->clearflag(status_flags::has_no_indices);
 280                                         return true;
 281                                 }
 282                         }
 283                         this->clearflag(status_flags::has_indices);
 284                         this->setflag(status_flags::has_no_indices);
 285                         return false;
 286                 }
 287         }
 288         return inherited::info(inf);
 289 }
 290
 291 size_t expairseq::nops() const
 292 {
 293         if (overall_coeff.is_equal(default_overall_coeff()))
 294                 return seq.size();
 295         else
 296                 return seq.size()+1;
 297 }
 298
 299 ex expairseq::op(size_t i) const
 300 {
 301         if (i < seq.size())
 302                 return recombine_pair_to_ex(seq[i]);
 303         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 304         return overall_coeff;
 305 }
 306
 307 ex expairseq::map(map_function &f) const
 308 {
 309         std::auto_ptr<epvector> v(new epvector);
 310         v->reserve(seq.size()+1);
 311
 312         epvector::const_iterator cit = seq.begin(), last = seq.end();
 313         while (cit != last) {
 314                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 315                 ++cit;
 316         }
 317
 318         if (overall_coeff.is_equal(default_overall_coeff()))
 319                 return thisexpairseq(v, default_overall_coeff(), true);
 320         else {
 321                 ex newcoeff = f(overall_coeff);
 322                 if(is_a<numeric>(newcoeff))
 323                         return thisexpairseq(v, newcoeff, true);
 324                 else {
 325                         v->push_back(split_ex_to_pair(newcoeff));
 326                         return thisexpairseq(v, default_overall_coeff(), true);
 327                 }
 328         }
 329 }
 330
 331 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 332 ex expairseq::eval(int level) const
 333 {
 334         if ((level==1) && (flags &status_flags::evaluated))
 335                 return *this;
 336
 337         std::auto_ptr<epvector> vp = evalchildren(level);
 338         if (vp.get() == 0)
 339                 return this->hold();
 340
 341         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 342 }
 343
 344 epvector* conjugateepvector(const epvector&epv)
 345 {
 346         epvector *newepv = 0;
 347         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 348                 if(newepv) {
 349                         newepv->push_back(i->conjugate());
 350                         continue;
 351                 }
 352                 expair x = i->conjugate();
 353                 if (x.is_equal(*i)) {
 354                         continue;
 355                 }
 356                 newepv = new epvector;
 357                 newepv->reserve(epv.size());
 358                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 359                         newepv->push_back(*j);
 360                 }
 361                 newepv->push_back(x);
 362         }
 363         return newepv;
 364 }
 365
 366 ex expairseq::conjugate() const
 367 {
 368         epvector* newepv = conjugateepvector(seq);
 369         ex x = overall_coeff.conjugate();
 370         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 371                 return *this;
 372         }
 373         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 374         delete newepv;
 375         return result;
 376 }
 377
 378 bool expairseq::is_polynomial(const ex & var) const
 379 {
 380         if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
 381                 return basic::is_polynomial(var);
 382         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 383                 if (!(i->rest).is_polynomial(var))
 384                         return false;
 385         }
 386         return true;
 387 }
 388
 389 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 390 {
 391         // This differs from basic::match() because we want "a+b+c+d" to
 392         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 393
 394         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 395
 396                 // Check whether global wildcard (one that matches the "rest of the
 397                 // expression", like "*" above) is present
 398                 bool has_global_wildcard = false;
 399                 ex global_wildcard;
 400                 for (size_t i=0; i<pattern.nops(); i++) {
 401                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 402                                 has_global_wildcard = true;
 403                                 global_wildcard = pattern.op(i);
 404                                 break;
 405                         }
 406                 }
 407
 408                 // Unfortunately, this is an O(N^2) operation because we can't
 409                 // sort the pattern in a useful way...
 410
 411                 // Chop into terms
 412                 exvector ops;
 413                 ops.reserve(nops());
 414                 for (size_t i=0; i<nops(); i++)
 415                         ops.push_back(op(i));
 416
 417                 // Now, for every term of the pattern, look for a matching term in
 418                 // the expression and remove the match
 419                 for (size_t i=0; i<pattern.nops(); i++) {
 420                         ex p = pattern.op(i);
 421                         if (has_global_wildcard && p.is_equal(global_wildcard))
 422                                 continue;
 423                         exvector::iterator it = ops.begin(), itend = ops.end();
 424                         while (it != itend) {
 425                                 if (it->match(p, repl_lst)) {
 426                                         ops.erase(it);
 427                                         goto found;
 428                                 }
 429                                 ++it;
 430                         }
 431                         return false; // no match found
 432 found:          ;
 433                 }
 434
 435                 if (has_global_wildcard) {
 436
 437                         // Assign all the remaining terms to the global wildcard (unless
 438                         // it has already been matched before, in which case the matches
 439                         // must be equal)
 440                         size_t num = ops.size();
 441                         std::auto_ptr<epvector> vp(new epvector);
 442                         vp->reserve(num);
 443                         for (size_t i=0; i<num; i++)
 444                                 vp->push_back(split_ex_to_pair(ops[i]));
 445                         ex rest = thisexpairseq(vp, default_overall_coeff());
 446                         for (exmap::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 447                                 if (it->first.is_equal(global_wildcard))
 448                                         return rest.is_equal(it->second);
 449                         }
 450                         repl_lst[global_wildcard] = rest;
 451                         return true;
 452
 453                 } else {
 454
 455                         // No global wildcard, then the match fails if there are any
 456                         // unmatched terms left
 457                         return ops.empty();
 458                 }
 459         }
 460         return inherited::match(pattern, repl_lst);
 461 }
 462
 463 ex expairseq::subs(const exmap & m, unsigned options) const
 464 {
 465         std::auto_ptr<epvector> vp = subschildren(m, options);
 466         if (vp.get())
 467                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
 468         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 469                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 470         else
 471                 return subs_one_level(m, options);
 472 }
 473
 474 // protected
 475
 476 int expairseq::compare_same_type(const basic &other) const
 477 {
 478         GINAC_ASSERT(is_a<expairseq>(other));
 479         const expairseq &o = static_cast<const expairseq &>(other);
 480
 481         int cmpval;
 482
 483         // compare number of elements
 484         if (seq.size() != o.seq.size())
 485                 return (seq.size()<o.seq.size()) ? -1 : 1;
 486
 487         // compare overall_coeff
 488         cmpval = overall_coeff.compare(o.overall_coeff);
 489         if (cmpval!=0)
 490                 return cmpval;
 491
 492 #if EXPAIRSEQ_USE_HASHTAB
 493         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 494         if (hashtabsize==0) {
 495 #endif // EXPAIRSEQ_USE_HASHTAB
 496                 epvector::const_iterator cit1 = seq.begin();
 497                 epvector::const_iterator cit2 = o.seq.begin();
 498                 epvector::const_iterator last1 = seq.end();
 499                 epvector::const_iterator last2 = o.seq.end();
 500
 501                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 502                         cmpval = (*cit1).compare(*cit2);
 503                         if (cmpval!=0) return cmpval;
 504                 }
 505
 506                 GINAC_ASSERT(cit1==last1);
 507                 GINAC_ASSERT(cit2==last2);
 508
 509                 return 0;
 510 #if EXPAIRSEQ_USE_HASHTAB
 511         }
 512
 513         // compare number of elements in each hashtab entry
 514         for (unsigned i=0; i<hashtabsize; ++i) {
 515                 unsigned cursize=hashtab[i].size();
 516                 if (cursize != o.hashtab[i].size())
 517                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 518         }
 519
 520         // compare individual (sorted) hashtab entries
 521         for (unsigned i=0; i<hashtabsize; ++i) {
 522                 unsigned sz = hashtab[i].size();
 523                 if (sz>0) {
 524                         const epplist &eppl1 = hashtab[i];
 525                         const epplist &eppl2 = o.hashtab[i];
 526                         epplist::const_iterator it1 = eppl1.begin();
 527                         epplist::const_iterator it2 = eppl2.begin();
 528                         while (it1!=eppl1.end()) {
 529                                 cmpval = (*(*it1)).compare(*(*it2));
 530                                 if (cmpval!=0)
 531                                         return cmpval;
 532                                 ++it1;
 533                                 ++it2;
 534                         }
 535                 }
 536         }
 537
 538         return 0; // equal
 539 #endif // EXPAIRSEQ_USE_HASHTAB
 540 }
 541
 542 bool expairseq::is_equal_same_type(const basic &other) const
 543 {
 544         const expairseq &o = static_cast<const expairseq &>(other);
 545
 546         // compare number of elements
 547         if (seq.size()!=o.seq.size())
 548                 return false;
 549
 550         // compare overall_coeff
 551         if (!overall_coeff.is_equal(o.overall_coeff))
 552                 return false;
 553
 554 #if EXPAIRSEQ_USE_HASHTAB
 555         // compare number of elements in each hashtab entry
 556         if (hashtabsize!=o.hashtabsize) {
 557                 std::cout << "this:" << std::endl;
 558                 print(print_tree(std::cout));
 559                 std::cout << "other:" << std::endl;
 560                 other.print(print_tree(std::cout));
 561         }
 562
 563         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 564
 565         if (hashtabsize==0) {
 566 #endif // EXPAIRSEQ_USE_HASHTAB
 567                 epvector::const_iterator cit1 = seq.begin();
 568                 epvector::const_iterator cit2 = o.seq.begin();
 569                 epvector::const_iterator last1 = seq.end();
 570
 571                 while (cit1!=last1) {
 572                         if (!(*cit1).is_equal(*cit2)) return false;
 573                         ++cit1;
 574                         ++cit2;
 575                 }
 576
 577                 return true;
 578 #if EXPAIRSEQ_USE_HASHTAB
 579         }
 580
 581         for (unsigned i=0; i<hashtabsize; ++i) {
 582                 if (hashtab[i].size() != o.hashtab[i].size())
 583                         return false;
 584         }
 585
 586         // compare individual sorted hashtab entries
 587         for (unsigned i=0; i<hashtabsize; ++i) {
 588                 unsigned sz = hashtab[i].size();
 589                 if (sz>0) {
 590                         const epplist &eppl1 = hashtab[i];
 591                         const epplist &eppl2 = o.hashtab[i];
 592                         epplist::const_iterator it1 = eppl1.begin();
 593                         epplist::const_iterator it2 = eppl2.begin();
 594                         while (it1!=eppl1.end()) {
 595                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 596                                 ++it1;
 597                                 ++it2;
 598                         }
 599                 }
 600         }
 601
 602         return true;
 603 #endif // EXPAIRSEQ_USE_HASHTAB
 604 }
 605
 606 unsigned expairseq::return_type() const
 607 {
 608         return return_types::noncommutative_composite;
 609 }
 610
 611 unsigned expairseq::calchash() const
 612 {
 613         unsigned v = make_hash_seed(typeid(*this));
 614         epvector::const_iterator i = seq.begin();
 615         const epvector::const_iterator end = seq.end();
 616         while (i != end) {
 617                 v ^= i->rest.gethash();
 618 #if !EXPAIRSEQ_USE_HASHTAB
 619                 // rotation spoils commutativity!
 620                 v = rotate_left(v);
 621                 v ^= i->coeff.gethash();
 622 #endif // !EXPAIRSEQ_USE_HASHTAB
 623                 ++i;
 624         }
 625
 626         v ^= overall_coeff.gethash();
 627
 628         // store calculated hash value only if object is already evaluated
 629         if (flags &status_flags::evaluated) {
 630                 setflag(status_flags::hash_calculated);
 631                 hashvalue = v;
 632         }
 633
 634         return v;
 635 }
 636
 637 ex expairseq::expand(unsigned options) const
 638 {
 639         std::auto_ptr<epvector> vp = expandchildren(options);
 640         if (vp.get())
 641                 return thisexpairseq(vp, overall_coeff);
 642         else {
 643                 // The terms have not changed, so it is safe to declare this expanded
 644                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 645         }
 646 }
 647
 648 //////////
 649 // new virtual functions which can be overridden by derived classes
 650 //////////
 651
 652 // protected
 653
 654 /** Create an object of this type.
 655  *  This method works similar to a constructor.  It is useful because expairseq
 656  *  has (at least) two possible different semantics but we want to inherit
 657  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 658  *  has to create a new one of the same semantics, which cannot be done by a
 659  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 660  *  order for this trick to work a derived class must of course override this
 661  *  definition. */
 662 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 663 {
 664         return expairseq(v, oc, do_index_renaming);
 665 }
 666
 667 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
 668 {
 669         return expairseq(vp, oc, do_index_renaming);
 670 }
 671
 672 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 673 {
 674         c.s << "[[";
 675         p.rest.print(c, precedence());
 676         c.s << ",";
 677         p.coeff.print(c, precedence());
 678         c.s << "]]";
 679 }
 680
 681 void expairseq::printseq(const print_context & c, char delim,
 682                          unsigned this_precedence,
 683                          unsigned upper_precedence) const
 684 {
 685         if (this_precedence <= upper_precedence)
 686                 c.s << "(";
 687         epvector::const_iterator it, it_last = seq.end() - 1;
 688         for (it=seq.begin(); it!=it_last; ++it) {
 689                 printpair(c, *it, this_precedence);
 690                 c.s << delim;
 691         }
 692         printpair(c, *it, this_precedence);
 693         if (!overall_coeff.is_equal(default_overall_coeff())) {
 694                 c.s << delim;
 695                 overall_coeff.print(c, this_precedence);
 696         }
 697
 698         if (this_precedence <= upper_precedence)
 699                 c.s << ")";
 700 }
 701
 702
 703 /** Form an expair from an ex, using the corresponding semantics.
 704  *  @see expairseq::recombine_pair_to_ex() */
 705 expair expairseq::split_ex_to_pair(const ex &e) const
 706 {
 707         return expair(e,_ex1);
 708 }
 709
 710
 711 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 712                                                 const ex &c) const
 713 {
 714         GINAC_ASSERT(is_exactly_a<numeric>(c));
 715
 716         return expair(e,c);
 717 }
 718
 719
 720 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 721                                                   const ex &c) const
 722 {
 723         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 724         GINAC_ASSERT(is_exactly_a<numeric>(c));
 725
 726         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 727 }
 728
 729
 730 /** Form an ex out of an expair, using the corresponding semantics.
 731  *  @see expairseq::split_ex_to_pair() */
 732 ex expairseq::recombine_pair_to_ex(const expair &p) const
 733 {
 734         return lst(p.rest,p.coeff);
 735 }
 736
 737 bool expairseq::expair_needs_further_processing(epp it)
 738 {
 739 #if EXPAIRSEQ_USE_HASHTAB
 740         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 741 #endif // EXPAIRSEQ_USE_HASHTAB
 742         return false;
 743 }
 744
 745 ex expairseq::default_overall_coeff() const
 746 {
 747         return _ex0;
 748 }
 749
 750 void expairseq::combine_overall_coeff(const ex &c)
 751 {
 752         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 753         GINAC_ASSERT(is_exactly_a<numeric>(c));
 754         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 755 }
 756
 757 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 758 {
 759         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 760         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 761         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 762         overall_coeff = ex_to<numeric>(overall_coeff).
 763                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 764 }
 765
 766 bool expairseq::can_make_flat(const expair &p) const
 767 {
 768         return true;
 769 }
 770
 771
 772 //////////
 773 // non-virtual functions in this class
 774 //////////
 775
 776 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 777 {
 778         exvector v;
 779         v.reserve(2);
 780         v.push_back(lh);
 781         v.push_back(rh);
 782         construct_from_exvector(v);
 783 #if EXPAIRSEQ_USE_HASHTAB
 784         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 785         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 786 #endif // EXPAIRSEQ_USE_HASHTAB
 787 }
 788
 789 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 790 {
 791         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 792                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 793 #if EXPAIRSEQ_USE_HASHTAB
 794                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 795                                              ex_to<expairseq>(rh).seq.size();
 796                         if (calc_hashtabsize(totalsize)!=0) {
 797                                 construct_from_2_ex_via_exvector(lh,rh);
 798                         } else {
 799 #endif // EXPAIRSEQ_USE_HASHTAB
 800                                 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 801                                         rh.info(info_flags::has_indices)) {
 802                                         ex newrh=rename_dummy_indices_uniquely(lh, rh);
 803                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 804                                                                    ex_to<expairseq>(newrh));
 805                                 }
 806                                 else
 807                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 808                                                                    ex_to<expairseq>(rh));
 809 #if EXPAIRSEQ_USE_HASHTAB
 810                         }
 811 #endif // EXPAIRSEQ_USE_HASHTAB
 812                         return;
 813                 } else {
 814 #if EXPAIRSEQ_USE_HASHTAB
 815                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 816                         if (calc_hashtabsize(totalsize)!=0) {
 817                                 construct_from_2_ex_via_exvector(lh, rh);
 818                         } else {
 819 #endif // EXPAIRSEQ_USE_HASHTAB
 820                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 821 #if EXPAIRSEQ_USE_HASHTAB
 822                         }
 823 #endif // EXPAIRSEQ_USE_HASHTAB
 824                         return;
 825                 }
 826         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 827 #if EXPAIRSEQ_USE_HASHTAB
 828                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 829                 if (calc_hashtabsize(totalsize)!=0) {
 830                         construct_from_2_ex_via_exvector(lh,rh);
 831                 } else {
 832 #endif // EXPAIRSEQ_USE_HASHTAB
 833                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 834 #if EXPAIRSEQ_USE_HASHTAB
 835                 }
 836 #endif // EXPAIRSEQ_USE_HASHTAB
 837                 return;
 838         }
 839
 840 #if EXPAIRSEQ_USE_HASHTAB
 841         if (calc_hashtabsize(2)!=0) {
 842                 construct_from_2_ex_via_exvector(lh,rh);
 843                 return;
 844         }
 845         hashtabsize = 0;
 846 #endif // EXPAIRSEQ_USE_HASHTAB
 847
 848         if (is_exactly_a<numeric>(lh)) {
 849                 if (is_exactly_a<numeric>(rh)) {
 850                         combine_overall_coeff(lh);
 851                         combine_overall_coeff(rh);
 852                 } else {
 853                         combine_overall_coeff(lh);
 854                         seq.push_back(split_ex_to_pair(rh));
 855                 }
 856         } else {
 857                 if (is_exactly_a<numeric>(rh)) {
 858                         combine_overall_coeff(rh);
 859                         seq.push_back(split_ex_to_pair(lh));
 860                 } else {
 861                         expair p1 = split_ex_to_pair(lh);
 862                         expair p2 = split_ex_to_pair(rh);
 863
 864                         int cmpval = p1.rest.compare(p2.rest);
 865                         if (cmpval==0) {
 866                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 867                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 868                                         // no further processing is necessary, since this
 869                                         // one element will usually be recombined in eval()
 870                                         seq.push_back(p1);
 871                                 }
 872                         } else {
 873                                 seq.reserve(2);
 874                                 if (cmpval<0) {
 875                                         seq.push_back(p1);
 876                                         seq.push_back(p2);
 877                                 } else {
 878                                         seq.push_back(p2);
 879                                         seq.push_back(p1);
 880                                 }
 881                         }
 882                 }
 883         }
 884 }
 885
 886 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 887                                                                                    const expairseq &s2)
 888 {
 889         combine_overall_coeff(s1.overall_coeff);
 890         combine_overall_coeff(s2.overall_coeff);
 891
 892         epvector::const_iterator first1 = s1.seq.begin();
 893         epvector::const_iterator last1 = s1.seq.end();
 894         epvector::const_iterator first2 = s2.seq.begin();
 895         epvector::const_iterator last2 = s2.seq.end();
 896
 897         seq.reserve(s1.seq.size()+s2.seq.size());
 898
 899         bool needs_further_processing=false;
 900
 901         while (first1!=last1 && first2!=last2) {
 902                 int cmpval = (*first1).rest.compare((*first2).rest);
 903
 904                 if (cmpval==0) {
 905                         // combine terms
 906                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 907                                                    add(ex_to<numeric>(first2->coeff));
 908                         if (!newcoeff.is_zero()) {
 909                                 seq.push_back(expair(first1->rest,newcoeff));
 910                                 if (expair_needs_further_processing(seq.end()-1)) {
 911                                         needs_further_processing = true;
 912                                 }
 913                         }
 914                         ++first1;
 915                         ++first2;
 916                 } else if (cmpval<0) {
 917                         seq.push_back(*first1);
 918                         ++first1;
 919                 } else {
 920                         seq.push_back(*first2);
 921                         ++first2;
 922                 }
 923         }
 924
 925         while (first1!=last1) {
 926                 seq.push_back(*first1);
 927                 ++first1;
 928         }
 929         while (first2!=last2) {
 930                 seq.push_back(*first2);
 931                 ++first2;
 932         }
 933
 934         if (needs_further_processing) {
 935                 epvector v = seq;
 936                 seq.clear();
 937                 construct_from_epvector(v);
 938         }
 939 }
 940
 941 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 942                                                                                         const ex &e)
 943 {
 944         combine_overall_coeff(s.overall_coeff);
 945         if (is_exactly_a<numeric>(e)) {
 946                 combine_overall_coeff(e);
 947                 seq = s.seq;
 948                 return;
 949         }
 950
 951         epvector::const_iterator first = s.seq.begin();
 952         epvector::const_iterator last = s.seq.end();
 953         expair p = split_ex_to_pair(e);
 954
 955         seq.reserve(s.seq.size()+1);
 956         bool p_pushed = false;
 957
 958         bool needs_further_processing=false;
 959
 960         // merge p into s.seq
 961         while (first!=last) {
 962                 int cmpval = (*first).rest.compare(p.rest);
 963                 if (cmpval==0) {
 964                         // combine terms
 965                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 966                                                    add(ex_to<numeric>(p.coeff));
 967                         if (!newcoeff.is_zero()) {
 968                                 seq.push_back(expair(first->rest,newcoeff));
 969                                 if (expair_needs_further_processing(seq.end()-1))
 970                                         needs_further_processing = true;
 971                         }
 972                         ++first;
 973                         p_pushed = true;
 974                         break;
 975                 } else if (cmpval<0) {
 976                         seq.push_back(*first);
 977                         ++first;
 978                 } else {
 979                         seq.push_back(p);
 980                         p_pushed = true;
 981                         break;
 982                 }
 983         }
 984
 985         if (p_pushed) {
 986                 // while loop exited because p was pushed, now push rest of s.seq
 987                 while (first!=last) {
 988                         seq.push_back(*first);
 989                         ++first;
 990                 }
 991         } else {
 992                 // while loop exited because s.seq was pushed, now push p
 993                 seq.push_back(p);
 994         }
 995
 996         if (needs_further_processing) {
 997                 epvector v = seq;
 998                 seq.clear();
 999                 construct_from_epvector(v);
1000         }
1001 }
1002
1003 void expairseq::construct_from_exvector(const exvector &v)
1004 {
1005         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1006         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1007         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1008         //                  (same for (+,*) -> (*,^)
1009
1010         make_flat(v);
1011 #if EXPAIRSEQ_USE_HASHTAB
1012         combine_same_terms();
1013 #else
1014         canonicalize();
1015         combine_same_terms_sorted_seq();
1016 #endif // EXPAIRSEQ_USE_HASHTAB
1017 }
1018
1019 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1020 {
1021         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1022         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1023         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1024         //                  (same for (+,*) -> (*,^)
1025
1026         make_flat(v, do_index_renaming);
1027 #if EXPAIRSEQ_USE_HASHTAB
1028         combine_same_terms();
1029 #else
1030         canonicalize();
1031         combine_same_terms_sorted_seq();
1032 #endif // EXPAIRSEQ_USE_HASHTAB
1033 }
1034
1035 /** Combine this expairseq with argument exvector.
1036  *  It cares for associativity as well as for special handling of numerics. */
1037 void expairseq::make_flat(const exvector &v)
1038 {
1039         exvector::const_iterator cit;
1040
1041         // count number of operands which are of same expairseq derived type
1042         // and their cumulative number of operands
1043         int nexpairseqs = 0;
1044         int noperands = 0;
1045         bool do_idx_rename = false;
1046
1047         cit = v.begin();
1048         while (cit!=v.end()) {
1049                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1050                         ++nexpairseqs;
1051                         noperands += ex_to<expairseq>(*cit).seq.size();
1052                 }
1053                 if (is_a<mul>(*this) && (!do_idx_rename) &&
1054                                 cit->info(info_flags::has_indices))
1055                         do_idx_rename = true;
1056                 ++cit;
1057         }
1058
1059         // reserve seq and coeffseq which will hold all operands
1060         seq.reserve(v.size()+noperands-nexpairseqs);
1061
1062         // copy elements and split off numerical part
1063         make_flat_inserter mf(v, do_idx_rename);
1064         cit = v.begin();
1065         while (cit!=v.end()) {
1066                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1067                         ex newfactor = mf.handle_factor(*cit, _ex1);
1068                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
1069                         combine_overall_coeff(subseqref.overall_coeff);
1070                         epvector::const_iterator cit_s = subseqref.seq.begin();
1071                         while (cit_s!=subseqref.seq.end()) {
1072                                 seq.push_back(*cit_s);
1073                                 ++cit_s;
1074                         }
1075                 } else {
1076                         if (is_exactly_a<numeric>(*cit))
1077                                 combine_overall_coeff(*cit);
1078                         else {
1079                                 ex newfactor = mf.handle_factor(*cit, _ex1);
1080                                 seq.push_back(split_ex_to_pair(newfactor));
1081                         }
1082                 }
1083                 ++cit;
1084         }
1085 }
1086
1087 /** Combine this expairseq with argument epvector.
1088  *  It cares for associativity as well as for special handling of numerics. */
1089 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1090 {
1091         epvector::const_iterator cit;
1092
1093         // count number of operands which are of same expairseq derived type
1094         // and their cumulative number of operands
1095         int nexpairseqs = 0;
1096         int noperands = 0;
1097         bool really_need_rename_inds = false;
1098
1099         cit = v.begin();
1100         while (cit!=v.end()) {
1101                 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1102                         ++nexpairseqs;
1103                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1104                 }
1105                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1106                                 cit->rest.info(info_flags::has_indices))
1107                         really_need_rename_inds = true;
1108                 ++cit;
1109         }
1110         do_index_renaming = do_index_renaming && really_need_rename_inds;
1111
1112         // reserve seq and coeffseq which will hold all operands
1113         seq.reserve(v.size()+noperands-nexpairseqs);
1114         make_flat_inserter mf(v, do_index_renaming);
1115
1116         // copy elements and split off numerical part
1117         cit = v.begin();
1118         while (cit!=v.end()) {
1119                 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1120                     this->can_make_flat(*cit)) {
1121                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1122                         const expairseq &subseqref = ex_to<expairseq>(newrest);
1123                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1124                                                             ex_to<numeric>(cit->coeff));
1125                         epvector::const_iterator cit_s = subseqref.seq.begin();
1126                         while (cit_s!=subseqref.seq.end()) {
1127                                 seq.push_back(expair(cit_s->rest,
1128                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1129                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1130                                 //                                              (*cit).coeff));
1131                                 ++cit_s;
1132                         }
1133                 } else {
1134                         if (cit->is_canonical_numeric())
1135                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1136                         else {
1137                                 ex rest = cit->rest;
1138                                 ex newrest = mf.handle_factor(rest, cit->coeff);
1139                                 if (are_ex_trivially_equal(newrest, rest))
1140                                         seq.push_back(*cit);
1141                                 else
1142                                         seq.push_back(expair(newrest, cit->coeff));
1143                         }
1144                 }
1145                 ++cit;
1146         }
1147 }
1148
1149 /** Brings this expairseq into a sorted (canonical) form. */
1150 void expairseq::canonicalize()
1151 {
1152         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1153 }
1154
1155
1156 /** Compact a presorted expairseq by combining all matching expairs to one
1157  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1158  *  instance. */
1159 void expairseq::combine_same_terms_sorted_seq()
1160 {
1161         if (seq.size()<2)
1162                 return;
1163
1164         bool needs_further_processing = false;
1165
1166         epvector::iterator itin1 = seq.begin();
1167         epvector::iterator itin2 = itin1+1;
1168         epvector::iterator itout = itin1;
1169         epvector::iterator last = seq.end();
1170         // must_copy will be set to true the first time some combination is
1171         // possible from then on the sequence has changed and must be compacted
1172         bool must_copy = false;
1173         while (itin2!=last) {
1174                 if (itin1->rest.compare(itin2->rest)==0) {
1175                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1176                                        add_dyn(ex_to<numeric>(itin2->coeff));
1177                         if (expair_needs_further_processing(itin1))
1178                                 needs_further_processing = true;
1179                         must_copy = true;
1180                 } else {
1181                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1182                                 if (must_copy)
1183                                         *itout = *itin1;
1184                                 ++itout;
1185                         }
1186                         itin1 = itin2;
1187                 }
1188                 ++itin2;
1189         }
1190         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1191                 if (must_copy)
1192                         *itout = *itin1;
1193                 ++itout;
1194         }
1195         if (itout!=last)
1196                 seq.erase(itout,last);
1197
1198         if (needs_further_processing) {
1199                 epvector v = seq;
1200                 seq.clear();
1201                 construct_from_epvector(v);
1202         }
1203 }
1204
1205 #if EXPAIRSEQ_USE_HASHTAB
1206
1207 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1208 {
1209         unsigned size;
1210         unsigned nearest_power_of_2 = 1 << log2(sz);
1211         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1212         //  size = nearest_power_of_2*hashtabfactor;
1213         size = nearest_power_of_2/hashtabfactor;
1214         if (size<minhashtabsize)
1215                 return 0;
1216
1217         // hashtabsize must be a power of 2
1218         GINAC_ASSERT((1U << log2(size))==size);
1219         return size;
1220 }
1221
1222 unsigned expairseq::calc_hashindex(const ex &e) const
1223 {
1224         // calculate hashindex
1225         unsigned hashindex;
1226         if (is_a<numeric>(e)) {
1227                 hashindex = hashmask;
1228         } else {
1229                 hashindex = e.gethash() & hashmask;
1230                 // last hashtab entry is reserved for numerics
1231                 if (hashindex==hashmask) hashindex = 0;
1232         }
1233         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1234         return hashindex;
1235 }
1236
1237 void expairseq::shrink_hashtab()
1238 {
1239         unsigned new_hashtabsize;
1240         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1241                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1242                 if (new_hashtabsize==0) {
1243                         hashtab.clear();
1244                         hashtabsize = 0;
1245                         canonicalize();
1246                         return;
1247                 }
1248
1249                 // shrink by a factor of 2
1250                 unsigned half_hashtabsize = hashtabsize/2;
1251                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1252                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1253                 // special treatment for numeric hashes
1254                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1255                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1256                 hashtab.resize(half_hashtabsize);
1257                 hashtabsize = half_hashtabsize;
1258                 hashmask = hashtabsize-1;
1259         }
1260 }
1261
1262 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1263 {
1264         if (hashtabsize==0)
1265                 return; // nothing to do
1266
1267         // calculate hashindex of element to be deleted
1268         unsigned hashindex = calc_hashindex((*element).rest);
1269
1270         // find it in hashtab and remove it
1271         epplist &eppl = hashtab[hashindex];
1272         epplist::iterator epplit = eppl.begin();
1273         bool erased = false;
1274         while (epplit!=eppl.end()) {
1275                 if (*epplit == element) {
1276                         eppl.erase(epplit);
1277                         erased = true;
1278                         break;
1279                 }
1280                 ++epplit;
1281         }
1282         if (!erased) {
1283                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1284                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1285
1286                 unsigned hashindex = calc_hashindex(element->rest);
1287                 epplist &eppl = hashtab[hashindex];
1288                 epplist::iterator epplit = eppl.begin();
1289                 bool erased = false;
1290                 while (epplit!=eppl.end()) {
1291                         if (*epplit == element) {
1292                                 eppl.erase(epplit);
1293                                 erased = true;
1294                                 break;
1295                         }
1296                         ++epplit;
1297                 }
1298                 GINAC_ASSERT(erased);
1299         }
1300         GINAC_ASSERT(erased);
1301 }
1302
1303 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1304                                    epvector::iterator newpos)
1305 {
1306         GINAC_ASSERT(hashtabsize!=0);
1307
1308         // calculate hashindex of element which was moved
1309         unsigned hashindex=calc_hashindex((*newpos).rest);
1310
1311         // find it in hashtab and modify it
1312         epplist &eppl = hashtab[hashindex];
1313         epplist::iterator epplit = eppl.begin();
1314         while (epplit!=eppl.end()) {
1315                 if (*epplit == oldpos) {
1316                         *epplit = newpos;
1317                         break;
1318                 }
1319                 ++epplit;
1320         }
1321         GINAC_ASSERT(epplit!=eppl.end());
1322 }
1323
1324 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1325 {
1326         epplist::const_iterator current = eppl.begin();
1327         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1328                 ++current;
1329         }
1330         eppl.insert(current,elem);
1331 }
1332
1333 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1334                                           epvector::iterator &last_non_zero,
1335                                           std::vector<bool> &touched,
1336                                           unsigned &number_of_zeroes)
1337 {
1338         epp current = seq.begin();
1339
1340         while (current!=first_numeric) {
1341                 if (is_exactly_a<numeric>(current->rest)) {
1342                         --first_numeric;
1343                         iter_swap(current,first_numeric);
1344                 } else {
1345                         // calculate hashindex
1346                         unsigned currenthashindex = calc_hashindex(current->rest);
1347
1348                         // test if there is already a matching expair in the hashtab-list
1349                         epplist &eppl=hashtab[currenthashindex];
1350                         epplist::iterator epplit = eppl.begin();
1351                         while (epplit!=eppl.end()) {
1352                                 if (current->rest.is_equal((*epplit)->rest))
1353                                         break;
1354                                 ++epplit;
1355                         }
1356                         if (epplit==eppl.end()) {
1357                                 // no matching expair found, append this to end of list
1358                                 sorted_insert(eppl,current);
1359                                 ++current;
1360                         } else {
1361                                 // epplit points to a matching expair, combine it with current
1362                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1363                                                    add_dyn(ex_to<numeric>(current->coeff));
1364
1365                                 // move obsolete current expair to end by swapping with last_non_zero element
1366                                 // if this was a numeric, it is swapped with the expair before first_numeric
1367                                 iter_swap(current,last_non_zero);
1368                                 --first_numeric;
1369                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1370                                 --last_non_zero;
1371                                 ++number_of_zeroes;
1372                                 // test if combined term has coeff 0 and can be removed is done later
1373                                 touched[(*epplit)-seq.begin()] = true;
1374                         }
1375                 }
1376         }
1377 }
1378
1379 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1380                                    epvector::iterator &last_non_zero,
1381                                    std::vector<bool> &touched,
1382                                    unsigned &number_of_zeroes)
1383 {
1384         // move terms with coeff 0 to end and remove them from hashtab
1385         // check only those elements which have been touched
1386         epp current = seq.begin();
1387         size_t i = 0;
1388         while (current!=first_numeric) {
1389                 if (!touched[i]) {
1390                         ++current;
1391                         ++i;
1392                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1393                         ++current;
1394                         ++i;
1395                 } else {
1396                         remove_hashtab_entry(current);
1397
1398                         // move element to the end, unless it is already at the end
1399                         if (current!=last_non_zero) {
1400                                 iter_swap(current,last_non_zero);
1401                                 --first_numeric;
1402                                 bool numeric_swapped = first_numeric!=last_non_zero;
1403                                 if (numeric_swapped)
1404                                         iter_swap(first_numeric,current);
1405                                 epvector::iterator changed_entry;
1406
1407                                 if (numeric_swapped)
1408                                         changed_entry = first_numeric;
1409                                 else
1410                                         changed_entry = last_non_zero;
1411
1412                                 --last_non_zero;
1413                                 ++number_of_zeroes;
1414
1415                                 if (first_numeric!=current) {
1416
1417                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1418                                         move_hashtab_entry(changed_entry,current);
1419                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1420                                 }
1421                         } else {
1422                                 --first_numeric;
1423                                 --last_non_zero;
1424                                 ++number_of_zeroes;
1425                         }
1426                 }
1427         }
1428         GINAC_ASSERT(i==current-seq.begin());
1429 }
1430
1431 /** True if one of the coeffs vanishes, otherwise false.
1432  *  This would be an invariant violation, so this should only be used for
1433  *  debugging purposes. */
1434 bool expairseq::has_coeff_0() const
1435 {
1436         epvector::const_iterator i = seq.begin(), end = seq.end();
1437         while (i != end) {
1438                 if (i->coeff.is_zero())
1439                         return true;
1440                 ++i;
1441         }
1442         return false;
1443 }
1444
1445 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1446                                                                                 epvector::const_iterator last_non_zero)
1447 {
1448         if (first_numeric == seq.end()) return; // no numerics
1449
1450         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1451         while (current != last) {
1452                 sorted_insert(hashtab[hashmask], current);
1453                 ++current;
1454         }
1455 }
1456
1457 void expairseq::combine_same_terms()
1458 {
1459         // combine same terms, drop term with coeff 0, move numerics to end
1460
1461         // calculate size of hashtab
1462         hashtabsize = calc_hashtabsize(seq.size());
1463
1464         // hashtabsize is a power of 2
1465         hashmask = hashtabsize-1;
1466
1467         // allocate hashtab
1468         hashtab.clear();
1469         hashtab.resize(hashtabsize);
1470
1471         if (hashtabsize==0) {
1472                 canonicalize();
1473                 combine_same_terms_sorted_seq();
1474                 GINAC_ASSERT(!has_coeff_0());
1475                 return;
1476         }
1477
1478         // iterate through seq, move numerics to end,
1479         // fill hashtab and combine same terms
1480         epvector::iterator first_numeric = seq.end();
1481         epvector::iterator last_non_zero = seq.end()-1;
1482
1483         size_t num = seq.size();
1484         std::vector<bool> touched(num);
1485
1486         unsigned number_of_zeroes = 0;
1487
1488         GINAC_ASSERT(!has_coeff_0());
1489         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1490
1491         // there should not be any terms with coeff 0 from the beginning,
1492         // so it should be safe to skip this step
1493         if (number_of_zeroes!=0) {
1494                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1495         }
1496
1497         add_numerics_to_hashtab(first_numeric,last_non_zero);
1498
1499         // pop zero elements
1500         for (unsigned i=0; i<number_of_zeroes; ++i) {
1501                 seq.pop_back();
1502         }
1503
1504         // shrink hashtabsize to calculated value
1505         GINAC_ASSERT(!has_coeff_0());
1506
1507         shrink_hashtab();
1508
1509         GINAC_ASSERT(!has_coeff_0());
1510 }
1511
1512 #endif // EXPAIRSEQ_USE_HASHTAB
1513
1514 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1515  *  debugging or in assertions since being sorted is an invariance. */
1516 bool expairseq::is_canonical() const
1517 {
1518         if (seq.size() <= 1)
1519                 return 1;
1520
1521 #if EXPAIRSEQ_USE_HASHTAB
1522         if (hashtabsize > 0) return 1; // not canoncalized
1523 #endif // EXPAIRSEQ_USE_HASHTAB
1524
1525         epvector::const_iterator it = seq.begin(), itend = seq.end();
1526         epvector::const_iterator it_last = it;
1527         for (++it; it!=itend; it_last=it, ++it) {
1528                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1529                         if (!is_exactly_a<numeric>(it_last->rest) ||
1530                                 !is_exactly_a<numeric>(it->rest)) {
1531                                 // double test makes it easier to set a breakpoint...
1532                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1533                                         !is_exactly_a<numeric>(it->rest)) {
1534                                         printpair(std::clog, *it_last, 0);
1535                                         std::clog << ">";
1536                                         printpair(std::clog, *it, 0);
1537                                         std::clog << "\n";
1538                                         std::clog << "pair1:" << std::endl;
1539                                         it_last->rest.print(print_tree(std::clog));
1540                                         it_last->coeff.print(print_tree(std::clog));
1541                                         std::clog << "pair2:" << std::endl;
1542                                         it->rest.print(print_tree(std::clog));
1543                                         it->coeff.print(print_tree(std::clog));
1544                                         return 0;
1545                                 }
1546                         }
1547                 }
1548         }
1549         return 1;
1550 }
1551
1552
1553 /** Member-wise expand the expairs in this sequence.
1554  *
1555  *  @see expairseq::expand()
1556  *  @return pointer to epvector containing expanded pairs or zero pointer,
1557  *  if no members were changed. */
1558 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1559 {
1560         const epvector::const_iterator last = seq.end();
1561         epvector::const_iterator cit = seq.begin();
1562         while (cit!=last) {
1563                 const ex &expanded_ex = cit->rest.expand(options);
1564                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1565
1566                         // something changed, copy seq, eval and return it
1567                         std::auto_ptr<epvector> s(new epvector);
1568                         s->reserve(seq.size());
1569
1570                         // copy parts of seq which are known not to have changed
1571                         epvector::const_iterator cit2 = seq.begin();
1572                         while (cit2!=cit) {
1573                                 s->push_back(*cit2);
1574                                 ++cit2;
1575                         }
1576
1577                         // copy first changed element
1578                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1579                                                                    cit2->coeff));
1580                         ++cit2;
1581
1582                         // copy rest
1583                         while (cit2!=last) {
1584                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1585                                                                            cit2->coeff));
1586                                 ++cit2;
1587                         }
1588                         return s;
1589                 }
1590                 ++cit;
1591         }
1592
1593         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1594 }
1595
1596
1597 /** Member-wise evaluate the expairs in this sequence.
1598  *
1599  *  @see expairseq::eval()
1600  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1601  *  if no members were changed. */
1602 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1603 {
1604         // returns a NULL pointer if nothing had to be evaluated
1605         // returns a pointer to a newly created epvector otherwise
1606         // (which has to be deleted somewhere else)
1607
1608         if (level==1)
1609                 return std::auto_ptr<epvector>(0);
1610
1611         if (level == -max_recursion_level)
1612                 throw(std::runtime_error("max recursion level reached"));
1613
1614         --level;
1615         epvector::const_iterator last = seq.end();
1616         epvector::const_iterator cit = seq.begin();
1617         while (cit!=last) {
1618                 const ex &evaled_ex = cit->rest.eval(level);
1619                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1620
1621                         // something changed, copy seq, eval and return it
1622                         std::auto_ptr<epvector> s(new epvector);
1623                         s->reserve(seq.size());
1624
1625                         // copy parts of seq which are known not to have changed
1626                         epvector::const_iterator cit2=seq.begin();
1627                         while (cit2!=cit) {
1628                                 s->push_back(*cit2);
1629                                 ++cit2;
1630                         }
1631
1632                         // copy first changed element
1633                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1634                                                                    cit2->coeff));
1635                         ++cit2;
1636
1637                         // copy rest
1638                         while (cit2!=last) {
1639                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1640                                                                            cit2->coeff));
1641                                 ++cit2;
1642                         }
1643                         return s;
1644                 }
1645                 ++cit;
1646         }
1647
1648         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1649 }
1650
1651 /** Member-wise substitute in this sequence.
1652  *
1653  *  @see expairseq::subs()
1654  *  @return pointer to epvector containing pairs after application of subs,
1655  *    or NULL pointer if no members were changed. */
1656 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1657 {
1658         // When any of the objects to be substituted is a product or power
1659         // we have to recombine the pairs because the numeric coefficients may
1660         // be part of the search pattern.
1661         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1662
1663                 // Search the list of substitutions and cache our findings
1664                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1665                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1666                                 options |= subs_options::pattern_is_product;
1667                                 break;
1668                         }
1669                 }
1670                 if (!(options & subs_options::pattern_is_product))
1671                         options |= subs_options::pattern_is_not_product;
1672         }
1673
1674         if (options & subs_options::pattern_is_product) {
1675
1676                 // Substitute in the recombined pairs
1677                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1678                 while (cit != last) {
1679
1680                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1681                         const ex &subsed_ex = orig_ex.subs(m, options);
1682                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1683
1684                                 // Something changed, copy seq, subs and return it
1685                                 std::auto_ptr<epvector> s(new epvector);
1686                                 s->reserve(seq.size());
1687
1688                                 // Copy parts of seq which are known not to have changed
1689                                 s->insert(s->begin(), seq.begin(), cit);
1690
1691                                 // Copy first changed element
1692                                 s->push_back(split_ex_to_pair(subsed_ex));
1693                                 ++cit;
1694
1695                                 // Copy rest
1696                                 while (cit != last) {
1697                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1698                                         ++cit;
1699                                 }
1700                                 return s;
1701                         }
1702
1703                         ++cit;
1704                 }
1705
1706         } else {
1707
1708                 // Substitute only in the "rest" part of the pairs
1709                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1710                 while (cit != last) {
1711
1712                         const ex &subsed_ex = cit->rest.subs(m, options);
1713                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1714
1715                                 // Something changed, copy seq, subs and return it
1716                                 std::auto_ptr<epvector> s(new epvector);
1717                                 s->reserve(seq.size());
1718
1719                                 // Copy parts of seq which are known not to have changed
1720                                 s->insert(s->begin(), seq.begin(), cit);
1721
1722                                 // Copy first changed element
1723                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1724                                 ++cit;
1725
1726                                 // Copy rest
1727                                 while (cit != last) {
1728                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1729                                         ++cit;
1730                                 }
1731                                 return s;
1732                         }
1733
1734                         ++cit;
1735                 }
1736         }
1737
1738         // Nothing has changed
1739         return std::auto_ptr<epvector>(0);
1740 }
1741
1742 //////////
1743 // static member variables
1744 //////////
1745
1746 #if EXPAIRSEQ_USE_HASHTAB
1747 unsigned expairseq::maxhashtabsize = 0x4000000U;
1748 unsigned expairseq::minhashtabsize = 0x1000U;
1749 unsigned expairseq::hashtabfactor = 1;
1750 #endif // EXPAIRSEQ_USE_HASHTAB
1751
1752 } // namespace GiNaC