ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2010 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         if (newepv) {
 375                 delete newepv;
 376         }
 377         return result;
 378 }
 379
 380 bool expairseq::is_polynomial(const ex & var) const
 381 {
 382         if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
 383                 return basic::is_polynomial(var);
 384         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 385                 if (!(i->rest).is_polynomial(var))
 386                         return false;
 387         }
 388         return true;
 389 }
 390
 391 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 392 {
 393         // This differs from basic::match() because we want "a+b+c+d" to
 394         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 395
 396         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 397
 398                 // Check whether global wildcard (one that matches the "rest of the
 399                 // expression", like "*" above) is present
 400                 bool has_global_wildcard = false;
 401                 ex global_wildcard;
 402                 for (size_t i=0; i<pattern.nops(); i++) {
 403                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 404                                 has_global_wildcard = true;
 405                                 global_wildcard = pattern.op(i);
 406                                 break;
 407                         }
 408                 }
 409
 410                 // Unfortunately, this is an O(N^2) operation because we can't
 411                 // sort the pattern in a useful way...
 412
 413                 // Chop into terms
 414                 exvector ops;
 415                 ops.reserve(nops());
 416                 for (size_t i=0; i<nops(); i++)
 417                         ops.push_back(op(i));
 418
 419                 // Now, for every term of the pattern, look for a matching term in
 420                 // the expression and remove the match
 421                 for (size_t i=0; i<pattern.nops(); i++) {
 422                         ex p = pattern.op(i);
 423                         if (has_global_wildcard && p.is_equal(global_wildcard))
 424                                 continue;
 425                         exvector::iterator it = ops.begin(), itend = ops.end();
 426                         while (it != itend) {
 427                                 if (it->match(p, repl_lst)) {
 428                                         ops.erase(it);
 429                                         goto found;
 430                                 }
 431                                 ++it;
 432                         }
 433                         return false; // no match found
 434 found:          ;
 435                 }
 436
 437                 if (has_global_wildcard) {
 438
 439                         // Assign all the remaining terms to the global wildcard (unless
 440                         // it has already been matched before, in which case the matches
 441                         // must be equal)
 442                         size_t num = ops.size();
 443                         std::auto_ptr<epvector> vp(new epvector);
 444                         vp->reserve(num);
 445                         for (size_t i=0; i<num; i++)
 446                                 vp->push_back(split_ex_to_pair(ops[i]));
 447                         ex rest = thisexpairseq(vp, default_overall_coeff());
 448                         for (exmap::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 449                                 if (it->first.is_equal(global_wildcard))
 450                                         return rest.is_equal(it->second);
 451                         }
 452                         repl_lst[global_wildcard] = rest;
 453                         return true;
 454
 455                 } else {
 456
 457                         // No global wildcard, then the match fails if there are any
 458                         // unmatched terms left
 459                         return ops.empty();
 460                 }
 461         }
 462         return inherited::match(pattern, repl_lst);
 463 }
 464
 465 ex expairseq::subs(const exmap & m, unsigned options) const
 466 {
 467         std::auto_ptr<epvector> vp = subschildren(m, options);
 468         if (vp.get())
 469                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
 470         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 471                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 472         else
 473                 return subs_one_level(m, options);
 474 }
 475
 476 // protected
 477
 478 int expairseq::compare_same_type(const basic &other) const
 479 {
 480         GINAC_ASSERT(is_a<expairseq>(other));
 481         const expairseq &o = static_cast<const expairseq &>(other);
 482
 483         int cmpval;
 484
 485         // compare number of elements
 486         if (seq.size() != o.seq.size())
 487                 return (seq.size()<o.seq.size()) ? -1 : 1;
 488
 489         // compare overall_coeff
 490         cmpval = overall_coeff.compare(o.overall_coeff);
 491         if (cmpval!=0)
 492                 return cmpval;
 493
 494 #if EXPAIRSEQ_USE_HASHTAB
 495         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 496         if (hashtabsize==0) {
 497 #endif // EXPAIRSEQ_USE_HASHTAB
 498                 epvector::const_iterator cit1 = seq.begin();
 499                 epvector::const_iterator cit2 = o.seq.begin();
 500                 epvector::const_iterator last1 = seq.end();
 501                 epvector::const_iterator last2 = o.seq.end();
 502
 503                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 504                         cmpval = (*cit1).compare(*cit2);
 505                         if (cmpval!=0) return cmpval;
 506                 }
 507
 508                 GINAC_ASSERT(cit1==last1);
 509                 GINAC_ASSERT(cit2==last2);
 510
 511                 return 0;
 512 #if EXPAIRSEQ_USE_HASHTAB
 513         }
 514
 515         // compare number of elements in each hashtab entry
 516         for (unsigned i=0; i<hashtabsize; ++i) {
 517                 unsigned cursize=hashtab[i].size();
 518                 if (cursize != o.hashtab[i].size())
 519                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 520         }
 521
 522         // compare individual (sorted) hashtab entries
 523         for (unsigned i=0; i<hashtabsize; ++i) {
 524                 unsigned sz = hashtab[i].size();
 525                 if (sz>0) {
 526                         const epplist &eppl1 = hashtab[i];
 527                         const epplist &eppl2 = o.hashtab[i];
 528                         epplist::const_iterator it1 = eppl1.begin();
 529                         epplist::const_iterator it2 = eppl2.begin();
 530                         while (it1!=eppl1.end()) {
 531                                 cmpval = (*(*it1)).compare(*(*it2));
 532                                 if (cmpval!=0)
 533                                         return cmpval;
 534                                 ++it1;
 535                                 ++it2;
 536                         }
 537                 }
 538         }
 539
 540         return 0; // equal
 541 #endif // EXPAIRSEQ_USE_HASHTAB
 542 }
 543
 544 bool expairseq::is_equal_same_type(const basic &other) const
 545 {
 546         const expairseq &o = static_cast<const expairseq &>(other);
 547
 548         // compare number of elements
 549         if (seq.size()!=o.seq.size())
 550                 return false;
 551
 552         // compare overall_coeff
 553         if (!overall_coeff.is_equal(o.overall_coeff))
 554                 return false;
 555
 556 #if EXPAIRSEQ_USE_HASHTAB
 557         // compare number of elements in each hashtab entry
 558         if (hashtabsize!=o.hashtabsize) {
 559                 std::cout << "this:" << std::endl;
 560                 print(print_tree(std::cout));
 561                 std::cout << "other:" << std::endl;
 562                 other.print(print_tree(std::cout));
 563         }
 564
 565         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 566
 567         if (hashtabsize==0) {
 568 #endif // EXPAIRSEQ_USE_HASHTAB
 569                 epvector::const_iterator cit1 = seq.begin();
 570                 epvector::const_iterator cit2 = o.seq.begin();
 571                 epvector::const_iterator last1 = seq.end();
 572
 573                 while (cit1!=last1) {
 574                         if (!(*cit1).is_equal(*cit2)) return false;
 575                         ++cit1;
 576                         ++cit2;
 577                 }
 578
 579                 return true;
 580 #if EXPAIRSEQ_USE_HASHTAB
 581         }
 582
 583         for (unsigned i=0; i<hashtabsize; ++i) {
 584                 if (hashtab[i].size() != o.hashtab[i].size())
 585                         return false;
 586         }
 587
 588         // compare individual sorted hashtab entries
 589         for (unsigned i=0; i<hashtabsize; ++i) {
 590                 unsigned sz = hashtab[i].size();
 591                 if (sz>0) {
 592                         const epplist &eppl1 = hashtab[i];
 593                         const epplist &eppl2 = o.hashtab[i];
 594                         epplist::const_iterator it1 = eppl1.begin();
 595                         epplist::const_iterator it2 = eppl2.begin();
 596                         while (it1!=eppl1.end()) {
 597                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 598                                 ++it1;
 599                                 ++it2;
 600                         }
 601                 }
 602         }
 603
 604         return true;
 605 #endif // EXPAIRSEQ_USE_HASHTAB
 606 }
 607
 608 unsigned expairseq::return_type() const
 609 {
 610         return return_types::noncommutative_composite;
 611 }
 612
 613 unsigned expairseq::calchash() const
 614 {
 615         unsigned v = make_hash_seed(typeid(*this));
 616         epvector::const_iterator i = seq.begin();
 617         const epvector::const_iterator end = seq.end();
 618         while (i != end) {
 619                 v ^= i->rest.gethash();
 620 #if !EXPAIRSEQ_USE_HASHTAB
 621                 // rotation spoils commutativity!
 622                 v = rotate_left(v);
 623                 v ^= i->coeff.gethash();
 624 #endif // !EXPAIRSEQ_USE_HASHTAB
 625                 ++i;
 626         }
 627
 628         v ^= overall_coeff.gethash();
 629
 630         // store calculated hash value only if object is already evaluated
 631         if (flags &status_flags::evaluated) {
 632                 setflag(status_flags::hash_calculated);
 633                 hashvalue = v;
 634         }
 635
 636         return v;
 637 }
 638
 639 ex expairseq::expand(unsigned options) const
 640 {
 641         std::auto_ptr<epvector> vp = expandchildren(options);
 642         if (vp.get())
 643                 return thisexpairseq(vp, overall_coeff);
 644         else {
 645                 // The terms have not changed, so it is safe to declare this expanded
 646                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 647         }
 648 }
 649
 650 //////////
 651 // new virtual functions which can be overridden by derived classes
 652 //////////
 653
 654 // protected
 655
 656 /** Create an object of this type.
 657  *  This method works similar to a constructor.  It is useful because expairseq
 658  *  has (at least) two possible different semantics but we want to inherit
 659  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 660  *  has to create a new one of the same semantics, which cannot be done by a
 661  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 662  *  order for this trick to work a derived class must of course override this
 663  *  definition. */
 664 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 665 {
 666         return expairseq(v, oc, do_index_renaming);
 667 }
 668
 669 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
 670 {
 671         return expairseq(vp, oc, do_index_renaming);
 672 }
 673
 674 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 675 {
 676         c.s << "[[";
 677         p.rest.print(c, precedence());
 678         c.s << ",";
 679         p.coeff.print(c, precedence());
 680         c.s << "]]";
 681 }
 682
 683 void expairseq::printseq(const print_context & c, char delim,
 684                          unsigned this_precedence,
 685                          unsigned upper_precedence) const
 686 {
 687         if (this_precedence <= upper_precedence)
 688                 c.s << "(";
 689         epvector::const_iterator it, it_last = seq.end() - 1;
 690         for (it=seq.begin(); it!=it_last; ++it) {
 691                 printpair(c, *it, this_precedence);
 692                 c.s << delim;
 693         }
 694         printpair(c, *it, this_precedence);
 695         if (!overall_coeff.is_equal(default_overall_coeff())) {
 696                 c.s << delim;
 697                 overall_coeff.print(c, this_precedence);
 698         }
 699
 700         if (this_precedence <= upper_precedence)
 701                 c.s << ")";
 702 }
 703
 704
 705 /** Form an expair from an ex, using the corresponding semantics.
 706  *  @see expairseq::recombine_pair_to_ex() */
 707 expair expairseq::split_ex_to_pair(const ex &e) const
 708 {
 709         return expair(e,_ex1);
 710 }
 711
 712
 713 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 714                                                 const ex &c) const
 715 {
 716         GINAC_ASSERT(is_exactly_a<numeric>(c));
 717
 718         return expair(e,c);
 719 }
 720
 721
 722 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 723                                                   const ex &c) const
 724 {
 725         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 726         GINAC_ASSERT(is_exactly_a<numeric>(c));
 727
 728         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 729 }
 730
 731
 732 /** Form an ex out of an expair, using the corresponding semantics.
 733  *  @see expairseq::split_ex_to_pair() */
 734 ex expairseq::recombine_pair_to_ex(const expair &p) const
 735 {
 736         return lst(p.rest,p.coeff);
 737 }
 738
 739 bool expairseq::expair_needs_further_processing(epp it)
 740 {
 741 #if EXPAIRSEQ_USE_HASHTAB
 742         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 743 #endif // EXPAIRSEQ_USE_HASHTAB
 744         return false;
 745 }
 746
 747 ex expairseq::default_overall_coeff() const
 748 {
 749         return _ex0;
 750 }
 751
 752 void expairseq::combine_overall_coeff(const ex &c)
 753 {
 754         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 755         GINAC_ASSERT(is_exactly_a<numeric>(c));
 756         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 757 }
 758
 759 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 760 {
 761         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 762         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 763         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 764         overall_coeff = ex_to<numeric>(overall_coeff).
 765                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 766 }
 767
 768 bool expairseq::can_make_flat(const expair &p) const
 769 {
 770         return true;
 771 }
 772
 773
 774 //////////
 775 // non-virtual functions in this class
 776 //////////
 777
 778 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 779 {
 780         exvector v;
 781         v.reserve(2);
 782         v.push_back(lh);
 783         v.push_back(rh);
 784         construct_from_exvector(v);
 785 #if EXPAIRSEQ_USE_HASHTAB
 786         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 787         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 788 #endif // EXPAIRSEQ_USE_HASHTAB
 789 }
 790
 791 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 792 {
 793         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 794                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 795 #if EXPAIRSEQ_USE_HASHTAB
 796                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 797                                              ex_to<expairseq>(rh).seq.size();
 798                         if (calc_hashtabsize(totalsize)!=0) {
 799                                 construct_from_2_ex_via_exvector(lh,rh);
 800                         } else {
 801 #endif // EXPAIRSEQ_USE_HASHTAB
 802                                 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 803                                         rh.info(info_flags::has_indices)) {
 804                                         ex newrh=rename_dummy_indices_uniquely(lh, rh);
 805                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 806                                                                    ex_to<expairseq>(newrh));
 807                                 }
 808                                 else
 809                                         construct_from_2_expairseq(ex_to<expairseq>(lh),
 810                                                                    ex_to<expairseq>(rh));
 811 #if EXPAIRSEQ_USE_HASHTAB
 812                         }
 813 #endif // EXPAIRSEQ_USE_HASHTAB
 814                         return;
 815                 } else {
 816 #if EXPAIRSEQ_USE_HASHTAB
 817                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 818                         if (calc_hashtabsize(totalsize)!=0) {
 819                                 construct_from_2_ex_via_exvector(lh, rh);
 820                         } else {
 821 #endif // EXPAIRSEQ_USE_HASHTAB
 822                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 823 #if EXPAIRSEQ_USE_HASHTAB
 824                         }
 825 #endif // EXPAIRSEQ_USE_HASHTAB
 826                         return;
 827                 }
 828         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 829 #if EXPAIRSEQ_USE_HASHTAB
 830                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 831                 if (calc_hashtabsize(totalsize)!=0) {
 832                         construct_from_2_ex_via_exvector(lh,rh);
 833                 } else {
 834 #endif // EXPAIRSEQ_USE_HASHTAB
 835                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 836 #if EXPAIRSEQ_USE_HASHTAB
 837                 }
 838 #endif // EXPAIRSEQ_USE_HASHTAB
 839                 return;
 840         }
 841
 842 #if EXPAIRSEQ_USE_HASHTAB
 843         if (calc_hashtabsize(2)!=0) {
 844                 construct_from_2_ex_via_exvector(lh,rh);
 845                 return;
 846         }
 847         hashtabsize = 0;
 848 #endif // EXPAIRSEQ_USE_HASHTAB
 849
 850         if (is_exactly_a<numeric>(lh)) {
 851                 if (is_exactly_a<numeric>(rh)) {
 852                         combine_overall_coeff(lh);
 853                         combine_overall_coeff(rh);
 854                 } else {
 855                         combine_overall_coeff(lh);
 856                         seq.push_back(split_ex_to_pair(rh));
 857                 }
 858         } else {
 859                 if (is_exactly_a<numeric>(rh)) {
 860                         combine_overall_coeff(rh);
 861                         seq.push_back(split_ex_to_pair(lh));
 862                 } else {
 863                         expair p1 = split_ex_to_pair(lh);
 864                         expair p2 = split_ex_to_pair(rh);
 865
 866                         int cmpval = p1.rest.compare(p2.rest);
 867                         if (cmpval==0) {
 868                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 869                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 870                                         // no further processing is necessary, since this
 871                                         // one element will usually be recombined in eval()
 872                                         seq.push_back(p1);
 873                                 }
 874                         } else {
 875                                 seq.reserve(2);
 876                                 if (cmpval<0) {
 877                                         seq.push_back(p1);
 878                                         seq.push_back(p2);
 879                                 } else {
 880                                         seq.push_back(p2);
 881                                         seq.push_back(p1);
 882                                 }
 883                         }
 884                 }
 885         }
 886 }
 887
 888 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 889                                                                                    const expairseq &s2)
 890 {
 891         combine_overall_coeff(s1.overall_coeff);
 892         combine_overall_coeff(s2.overall_coeff);
 893
 894         epvector::const_iterator first1 = s1.seq.begin();
 895         epvector::const_iterator last1 = s1.seq.end();
 896         epvector::const_iterator first2 = s2.seq.begin();
 897         epvector::const_iterator last2 = s2.seq.end();
 898
 899         seq.reserve(s1.seq.size()+s2.seq.size());
 900
 901         bool needs_further_processing=false;
 902
 903         while (first1!=last1 && first2!=last2) {
 904                 int cmpval = (*first1).rest.compare((*first2).rest);
 905
 906                 if (cmpval==0) {
 907                         // combine terms
 908                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 909                                                    add(ex_to<numeric>(first2->coeff));
 910                         if (!newcoeff.is_zero()) {
 911                                 seq.push_back(expair(first1->rest,newcoeff));
 912                                 if (expair_needs_further_processing(seq.end()-1)) {
 913                                         needs_further_processing = true;
 914                                 }
 915                         }
 916                         ++first1;
 917                         ++first2;
 918                 } else if (cmpval<0) {
 919                         seq.push_back(*first1);
 920                         ++first1;
 921                 } else {
 922                         seq.push_back(*first2);
 923                         ++first2;
 924                 }
 925         }
 926
 927         while (first1!=last1) {
 928                 seq.push_back(*first1);
 929                 ++first1;
 930         }
 931         while (first2!=last2) {
 932                 seq.push_back(*first2);
 933                 ++first2;
 934         }
 935
 936         if (needs_further_processing) {
 937                 epvector v = seq;
 938                 seq.clear();
 939                 construct_from_epvector(v);
 940         }
 941 }
 942
 943 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 944                                                                                         const ex &e)
 945 {
 946         combine_overall_coeff(s.overall_coeff);
 947         if (is_exactly_a<numeric>(e)) {
 948                 combine_overall_coeff(e);
 949                 seq = s.seq;
 950                 return;
 951         }
 952
 953         epvector::const_iterator first = s.seq.begin();
 954         epvector::const_iterator last = s.seq.end();
 955         expair p = split_ex_to_pair(e);
 956
 957         seq.reserve(s.seq.size()+1);
 958         bool p_pushed = false;
 959
 960         bool needs_further_processing=false;
 961
 962         // merge p into s.seq
 963         while (first!=last) {
 964                 int cmpval = (*first).rest.compare(p.rest);
 965                 if (cmpval==0) {
 966                         // combine terms
 967                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 968                                                    add(ex_to<numeric>(p.coeff));
 969                         if (!newcoeff.is_zero()) {
 970                                 seq.push_back(expair(first->rest,newcoeff));
 971                                 if (expair_needs_further_processing(seq.end()-1))
 972                                         needs_further_processing = true;
 973                         }
 974                         ++first;
 975                         p_pushed = true;
 976                         break;
 977                 } else if (cmpval<0) {
 978                         seq.push_back(*first);
 979                         ++first;
 980                 } else {
 981                         seq.push_back(p);
 982                         p_pushed = true;
 983                         break;
 984                 }
 985         }
 986
 987         if (p_pushed) {
 988                 // while loop exited because p was pushed, now push rest of s.seq
 989                 while (first!=last) {
 990                         seq.push_back(*first);
 991                         ++first;
 992                 }
 993         } else {
 994                 // while loop exited because s.seq was pushed, now push p
 995                 seq.push_back(p);
 996         }
 997
 998         if (needs_further_processing) {
 999                 epvector v = seq;
1000                 seq.clear();
1001                 construct_from_epvector(v);
1002         }
1003 }
1004
1005 void expairseq::construct_from_exvector(const exvector &v)
1006 {
1007         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1008         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1009         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1010         //                  (same for (+,*) -> (*,^)
1011
1012         make_flat(v);
1013 #if EXPAIRSEQ_USE_HASHTAB
1014         combine_same_terms();
1015 #else
1016         canonicalize();
1017         combine_same_terms_sorted_seq();
1018 #endif // EXPAIRSEQ_USE_HASHTAB
1019 }
1020
1021 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1022 {
1023         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1024         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1025         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1026         //                  (same for (+,*) -> (*,^)
1027
1028         make_flat(v, do_index_renaming);
1029 #if EXPAIRSEQ_USE_HASHTAB
1030         combine_same_terms();
1031 #else
1032         canonicalize();
1033         combine_same_terms_sorted_seq();
1034 #endif // EXPAIRSEQ_USE_HASHTAB
1035 }
1036
1037 /** Combine this expairseq with argument exvector.
1038  *  It cares for associativity as well as for special handling of numerics. */
1039 void expairseq::make_flat(const exvector &v)
1040 {
1041         exvector::const_iterator cit;
1042
1043         // count number of operands which are of same expairseq derived type
1044         // and their cumulative number of operands
1045         int nexpairseqs = 0;
1046         int noperands = 0;
1047         bool do_idx_rename = false;
1048
1049         cit = v.begin();
1050         while (cit!=v.end()) {
1051                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1052                         ++nexpairseqs;
1053                         noperands += ex_to<expairseq>(*cit).seq.size();
1054                 }
1055                 if (is_a<mul>(*this) && (!do_idx_rename) &&
1056                                 cit->info(info_flags::has_indices))
1057                         do_idx_rename = true;
1058                 ++cit;
1059         }
1060
1061         // reserve seq and coeffseq which will hold all operands
1062         seq.reserve(v.size()+noperands-nexpairseqs);
1063
1064         // copy elements and split off numerical part
1065         make_flat_inserter mf(v, do_idx_rename);
1066         cit = v.begin();
1067         while (cit!=v.end()) {
1068                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1069                         ex newfactor = mf.handle_factor(*cit, _ex1);
1070                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
1071                         combine_overall_coeff(subseqref.overall_coeff);
1072                         epvector::const_iterator cit_s = subseqref.seq.begin();
1073                         while (cit_s!=subseqref.seq.end()) {
1074                                 seq.push_back(*cit_s);
1075                                 ++cit_s;
1076                         }
1077                 } else {
1078                         if (is_exactly_a<numeric>(*cit))
1079                                 combine_overall_coeff(*cit);
1080                         else {
1081                                 ex newfactor = mf.handle_factor(*cit, _ex1);
1082                                 seq.push_back(split_ex_to_pair(newfactor));
1083                         }
1084                 }
1085                 ++cit;
1086         }
1087 }
1088
1089 /** Combine this expairseq with argument epvector.
1090  *  It cares for associativity as well as for special handling of numerics. */
1091 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1092 {
1093         epvector::const_iterator cit;
1094
1095         // count number of operands which are of same expairseq derived type
1096         // and their cumulative number of operands
1097         int nexpairseqs = 0;
1098         int noperands = 0;
1099         bool really_need_rename_inds = false;
1100
1101         cit = v.begin();
1102         while (cit!=v.end()) {
1103                 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1104                         ++nexpairseqs;
1105                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1106                 }
1107                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1108                                 cit->rest.info(info_flags::has_indices))
1109                         really_need_rename_inds = true;
1110                 ++cit;
1111         }
1112         do_index_renaming = do_index_renaming && really_need_rename_inds;
1113
1114         // reserve seq and coeffseq which will hold all operands
1115         seq.reserve(v.size()+noperands-nexpairseqs);
1116         make_flat_inserter mf(v, do_index_renaming);
1117
1118         // copy elements and split off numerical part
1119         cit = v.begin();
1120         while (cit!=v.end()) {
1121                 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1122                     this->can_make_flat(*cit)) {
1123                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1124                         const expairseq &subseqref = ex_to<expairseq>(newrest);
1125                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1126                                                             ex_to<numeric>(cit->coeff));
1127                         epvector::const_iterator cit_s = subseqref.seq.begin();
1128                         while (cit_s!=subseqref.seq.end()) {
1129                                 seq.push_back(expair(cit_s->rest,
1130                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1131                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1132                                 //                                              (*cit).coeff));
1133                                 ++cit_s;
1134                         }
1135                 } else {
1136                         if (cit->is_canonical_numeric())
1137                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1138                         else {
1139                                 ex rest = cit->rest;
1140                                 ex newrest = mf.handle_factor(rest, cit->coeff);
1141                                 if (are_ex_trivially_equal(newrest, rest))
1142                                         seq.push_back(*cit);
1143                                 else
1144                                         seq.push_back(expair(newrest, cit->coeff));
1145                         }
1146                 }
1147                 ++cit;
1148         }
1149 }
1150
1151 /** Brings this expairseq into a sorted (canonical) form. */
1152 void expairseq::canonicalize()
1153 {
1154         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1155 }
1156
1157
1158 /** Compact a presorted expairseq by combining all matching expairs to one
1159  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1160  *  instance. */
1161 void expairseq::combine_same_terms_sorted_seq()
1162 {
1163         if (seq.size()<2)
1164                 return;
1165
1166         bool needs_further_processing = false;
1167
1168         epvector::iterator itin1 = seq.begin();
1169         epvector::iterator itin2 = itin1+1;
1170         epvector::iterator itout = itin1;
1171         epvector::iterator last = seq.end();
1172         // must_copy will be set to true the first time some combination is
1173         // possible from then on the sequence has changed and must be compacted
1174         bool must_copy = false;
1175         while (itin2!=last) {
1176                 if (itin1->rest.compare(itin2->rest)==0) {
1177                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1178                                        add_dyn(ex_to<numeric>(itin2->coeff));
1179                         if (expair_needs_further_processing(itin1))
1180                                 needs_further_processing = true;
1181                         must_copy = true;
1182                 } else {
1183                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1184                                 if (must_copy)
1185                                         *itout = *itin1;
1186                                 ++itout;
1187                         }
1188                         itin1 = itin2;
1189                 }
1190                 ++itin2;
1191         }
1192         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1193                 if (must_copy)
1194                         *itout = *itin1;
1195                 ++itout;
1196         }
1197         if (itout!=last)
1198                 seq.erase(itout,last);
1199
1200         if (needs_further_processing) {
1201                 epvector v = seq;
1202                 seq.clear();
1203                 construct_from_epvector(v);
1204         }
1205 }
1206
1207 #if EXPAIRSEQ_USE_HASHTAB
1208
1209 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1210 {
1211         unsigned size;
1212         unsigned nearest_power_of_2 = 1 << log2(sz);
1213         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1214         //  size = nearest_power_of_2*hashtabfactor;
1215         size = nearest_power_of_2/hashtabfactor;
1216         if (size<minhashtabsize)
1217                 return 0;
1218
1219         // hashtabsize must be a power of 2
1220         GINAC_ASSERT((1U << log2(size))==size);
1221         return size;
1222 }
1223
1224 unsigned expairseq::calc_hashindex(const ex &e) const
1225 {
1226         // calculate hashindex
1227         unsigned hashindex;
1228         if (is_a<numeric>(e)) {
1229                 hashindex = hashmask;
1230         } else {
1231                 hashindex = e.gethash() & hashmask;
1232                 // last hashtab entry is reserved for numerics
1233                 if (hashindex==hashmask) hashindex = 0;
1234         }
1235         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1236         return hashindex;
1237 }
1238
1239 void expairseq::shrink_hashtab()
1240 {
1241         unsigned new_hashtabsize;
1242         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1243                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1244                 if (new_hashtabsize==0) {
1245                         hashtab.clear();
1246                         hashtabsize = 0;
1247                         canonicalize();
1248                         return;
1249                 }
1250
1251                 // shrink by a factor of 2
1252                 unsigned half_hashtabsize = hashtabsize/2;
1253                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1254                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1255                 // special treatment for numeric hashes
1256                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1257                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1258                 hashtab.resize(half_hashtabsize);
1259                 hashtabsize = half_hashtabsize;
1260                 hashmask = hashtabsize-1;
1261         }
1262 }
1263
1264 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1265 {
1266         if (hashtabsize==0)
1267                 return; // nothing to do
1268
1269         // calculate hashindex of element to be deleted
1270         unsigned hashindex = calc_hashindex((*element).rest);
1271
1272         // find it in hashtab and remove it
1273         epplist &eppl = hashtab[hashindex];
1274         epplist::iterator epplit = eppl.begin();
1275         bool erased = false;
1276         while (epplit!=eppl.end()) {
1277                 if (*epplit == element) {
1278                         eppl.erase(epplit);
1279                         erased = true;
1280                         break;
1281                 }
1282                 ++epplit;
1283         }
1284         if (!erased) {
1285                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1286                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1287
1288                 unsigned hashindex = calc_hashindex(element->rest);
1289                 epplist &eppl = hashtab[hashindex];
1290                 epplist::iterator epplit = eppl.begin();
1291                 bool erased = false;
1292                 while (epplit!=eppl.end()) {
1293                         if (*epplit == element) {
1294                                 eppl.erase(epplit);
1295                                 erased = true;
1296                                 break;
1297                         }
1298                         ++epplit;
1299                 }
1300                 GINAC_ASSERT(erased);
1301         }
1302         GINAC_ASSERT(erased);
1303 }
1304
1305 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1306                                    epvector::iterator newpos)
1307 {
1308         GINAC_ASSERT(hashtabsize!=0);
1309
1310         // calculate hashindex of element which was moved
1311         unsigned hashindex=calc_hashindex((*newpos).rest);
1312
1313         // find it in hashtab and modify it
1314         epplist &eppl = hashtab[hashindex];
1315         epplist::iterator epplit = eppl.begin();
1316         while (epplit!=eppl.end()) {
1317                 if (*epplit == oldpos) {
1318                         *epplit = newpos;
1319                         break;
1320                 }
1321                 ++epplit;
1322         }
1323         GINAC_ASSERT(epplit!=eppl.end());
1324 }
1325
1326 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1327 {
1328         epplist::const_iterator current = eppl.begin();
1329         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1330                 ++current;
1331         }
1332         eppl.insert(current,elem);
1333 }
1334
1335 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1336                                           epvector::iterator &last_non_zero,
1337                                           std::vector<bool> &touched,
1338                                           unsigned &number_of_zeroes)
1339 {
1340         epp current = seq.begin();
1341
1342         while (current!=first_numeric) {
1343                 if (is_exactly_a<numeric>(current->rest)) {
1344                         --first_numeric;
1345                         iter_swap(current,first_numeric);
1346                 } else {
1347                         // calculate hashindex
1348                         unsigned currenthashindex = calc_hashindex(current->rest);
1349
1350                         // test if there is already a matching expair in the hashtab-list
1351                         epplist &eppl=hashtab[currenthashindex];
1352                         epplist::iterator epplit = eppl.begin();
1353                         while (epplit!=eppl.end()) {
1354                                 if (current->rest.is_equal((*epplit)->rest))
1355                                         break;
1356                                 ++epplit;
1357                         }
1358                         if (epplit==eppl.end()) {
1359                                 // no matching expair found, append this to end of list
1360                                 sorted_insert(eppl,current);
1361                                 ++current;
1362                         } else {
1363                                 // epplit points to a matching expair, combine it with current
1364                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1365                                                    add_dyn(ex_to<numeric>(current->coeff));
1366
1367                                 // move obsolete current expair to end by swapping with last_non_zero element
1368                                 // if this was a numeric, it is swapped with the expair before first_numeric
1369                                 iter_swap(current,last_non_zero);
1370                                 --first_numeric;
1371                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1372                                 --last_non_zero;
1373                                 ++number_of_zeroes;
1374                                 // test if combined term has coeff 0 and can be removed is done later
1375                                 touched[(*epplit)-seq.begin()] = true;
1376                         }
1377                 }
1378         }
1379 }
1380
1381 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1382                                    epvector::iterator &last_non_zero,
1383                                    std::vector<bool> &touched,
1384                                    unsigned &number_of_zeroes)
1385 {
1386         // move terms with coeff 0 to end and remove them from hashtab
1387         // check only those elements which have been touched
1388         epp current = seq.begin();
1389         size_t i = 0;
1390         while (current!=first_numeric) {
1391                 if (!touched[i]) {
1392                         ++current;
1393                         ++i;
1394                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1395                         ++current;
1396                         ++i;
1397                 } else {
1398                         remove_hashtab_entry(current);
1399
1400                         // move element to the end, unless it is already at the end
1401                         if (current!=last_non_zero) {
1402                                 iter_swap(current,last_non_zero);
1403                                 --first_numeric;
1404                                 bool numeric_swapped = first_numeric!=last_non_zero;
1405                                 if (numeric_swapped)
1406                                         iter_swap(first_numeric,current);
1407                                 epvector::iterator changed_entry;
1408
1409                                 if (numeric_swapped)
1410                                         changed_entry = first_numeric;
1411                                 else
1412                                         changed_entry = last_non_zero;
1413
1414                                 --last_non_zero;
1415                                 ++number_of_zeroes;
1416
1417                                 if (first_numeric!=current) {
1418
1419                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1420                                         move_hashtab_entry(changed_entry,current);
1421                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1422                                 }
1423                         } else {
1424                                 --first_numeric;
1425                                 --last_non_zero;
1426                                 ++number_of_zeroes;
1427                         }
1428                 }
1429         }
1430         GINAC_ASSERT(i==current-seq.begin());
1431 }
1432
1433 /** True if one of the coeffs vanishes, otherwise false.
1434  *  This would be an invariant violation, so this should only be used for
1435  *  debugging purposes. */
1436 bool expairseq::has_coeff_0() const
1437 {
1438         epvector::const_iterator i = seq.begin(), end = seq.end();
1439         while (i != end) {
1440                 if (i->coeff.is_zero())
1441                         return true;
1442                 ++i;
1443         }
1444         return false;
1445 }
1446
1447 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1448                                                                                 epvector::const_iterator last_non_zero)
1449 {
1450         if (first_numeric == seq.end()) return; // no numerics
1451
1452         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1453         while (current != last) {
1454                 sorted_insert(hashtab[hashmask], current);
1455                 ++current;
1456         }
1457 }
1458
1459 void expairseq::combine_same_terms()
1460 {
1461         // combine same terms, drop term with coeff 0, move numerics to end
1462
1463         // calculate size of hashtab
1464         hashtabsize = calc_hashtabsize(seq.size());
1465
1466         // hashtabsize is a power of 2
1467         hashmask = hashtabsize-1;
1468
1469         // allocate hashtab
1470         hashtab.clear();
1471         hashtab.resize(hashtabsize);
1472
1473         if (hashtabsize==0) {
1474                 canonicalize();
1475                 combine_same_terms_sorted_seq();
1476                 GINAC_ASSERT(!has_coeff_0());
1477                 return;
1478         }
1479
1480         // iterate through seq, move numerics to end,
1481         // fill hashtab and combine same terms
1482         epvector::iterator first_numeric = seq.end();
1483         epvector::iterator last_non_zero = seq.end()-1;
1484
1485         size_t num = seq.size();
1486         std::vector<bool> touched(num);
1487
1488         unsigned number_of_zeroes = 0;
1489
1490         GINAC_ASSERT(!has_coeff_0());
1491         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1492
1493         // there should not be any terms with coeff 0 from the beginning,
1494         // so it should be safe to skip this step
1495         if (number_of_zeroes!=0) {
1496                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1497         }
1498
1499         add_numerics_to_hashtab(first_numeric,last_non_zero);
1500
1501         // pop zero elements
1502         for (unsigned i=0; i<number_of_zeroes; ++i) {
1503                 seq.pop_back();
1504         }
1505
1506         // shrink hashtabsize to calculated value
1507         GINAC_ASSERT(!has_coeff_0());
1508
1509         shrink_hashtab();
1510
1511         GINAC_ASSERT(!has_coeff_0());
1512 }
1513
1514 #endif // EXPAIRSEQ_USE_HASHTAB
1515
1516 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1517  *  debugging or in assertions since being sorted is an invariance. */
1518 bool expairseq::is_canonical() const
1519 {
1520         if (seq.size() <= 1)
1521                 return 1;
1522
1523 #if EXPAIRSEQ_USE_HASHTAB
1524         if (hashtabsize > 0) return 1; // not canoncalized
1525 #endif // EXPAIRSEQ_USE_HASHTAB
1526
1527         epvector::const_iterator it = seq.begin(), itend = seq.end();
1528         epvector::const_iterator it_last = it;
1529         for (++it; it!=itend; it_last=it, ++it) {
1530                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1531                         if (!is_exactly_a<numeric>(it_last->rest) ||
1532                                 !is_exactly_a<numeric>(it->rest)) {
1533                                 // double test makes it easier to set a breakpoint...
1534                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1535                                         !is_exactly_a<numeric>(it->rest)) {
1536                                         printpair(std::clog, *it_last, 0);
1537                                         std::clog << ">";
1538                                         printpair(std::clog, *it, 0);
1539                                         std::clog << "\n";
1540                                         std::clog << "pair1:" << std::endl;
1541                                         it_last->rest.print(print_tree(std::clog));
1542                                         it_last->coeff.print(print_tree(std::clog));
1543                                         std::clog << "pair2:" << std::endl;
1544                                         it->rest.print(print_tree(std::clog));
1545                                         it->coeff.print(print_tree(std::clog));
1546                                         return 0;
1547                                 }
1548                         }
1549                 }
1550         }
1551         return 1;
1552 }
1553
1554
1555 /** Member-wise expand the expairs in this sequence.
1556  *
1557  *  @see expairseq::expand()
1558  *  @return pointer to epvector containing expanded pairs or zero pointer,
1559  *  if no members were changed. */
1560 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1561 {
1562         const epvector::const_iterator last = seq.end();
1563         epvector::const_iterator cit = seq.begin();
1564         while (cit!=last) {
1565                 const ex &expanded_ex = cit->rest.expand(options);
1566                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1567
1568                         // something changed, copy seq, eval and return it
1569                         std::auto_ptr<epvector> s(new epvector);
1570                         s->reserve(seq.size());
1571
1572                         // copy parts of seq which are known not to have changed
1573                         epvector::const_iterator cit2 = seq.begin();
1574                         while (cit2!=cit) {
1575                                 s->push_back(*cit2);
1576                                 ++cit2;
1577                         }
1578
1579                         // copy first changed element
1580                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1581                                                                    cit2->coeff));
1582                         ++cit2;
1583
1584                         // copy rest
1585                         while (cit2!=last) {
1586                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1587                                                                            cit2->coeff));
1588                                 ++cit2;
1589                         }
1590                         return s;
1591                 }
1592                 ++cit;
1593         }
1594
1595         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1596 }
1597
1598
1599 /** Member-wise evaluate the expairs in this sequence.
1600  *
1601  *  @see expairseq::eval()
1602  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1603  *  if no members were changed. */
1604 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1605 {
1606         // returns a NULL pointer if nothing had to be evaluated
1607         // returns a pointer to a newly created epvector otherwise
1608         // (which has to be deleted somewhere else)
1609
1610         if (level==1)
1611                 return std::auto_ptr<epvector>(0);
1612
1613         if (level == -max_recursion_level)
1614                 throw(std::runtime_error("max recursion level reached"));
1615
1616         --level;
1617         epvector::const_iterator last = seq.end();
1618         epvector::const_iterator cit = seq.begin();
1619         while (cit!=last) {
1620                 const ex &evaled_ex = cit->rest.eval(level);
1621                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1622
1623                         // something changed, copy seq, eval and return it
1624                         std::auto_ptr<epvector> s(new epvector);
1625                         s->reserve(seq.size());
1626
1627                         // copy parts of seq which are known not to have changed
1628                         epvector::const_iterator cit2=seq.begin();
1629                         while (cit2!=cit) {
1630                                 s->push_back(*cit2);
1631                                 ++cit2;
1632                         }
1633
1634                         // copy first changed element
1635                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1636                                                                    cit2->coeff));
1637                         ++cit2;
1638
1639                         // copy rest
1640                         while (cit2!=last) {
1641                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1642                                                                            cit2->coeff));
1643                                 ++cit2;
1644                         }
1645                         return s;
1646                 }
1647                 ++cit;
1648         }
1649
1650         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1651 }
1652
1653 /** Member-wise substitute in this sequence.
1654  *
1655  *  @see expairseq::subs()
1656  *  @return pointer to epvector containing pairs after application of subs,
1657  *    or NULL pointer if no members were changed. */
1658 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1659 {
1660         // When any of the objects to be substituted is a product or power
1661         // we have to recombine the pairs because the numeric coefficients may
1662         // be part of the search pattern.
1663         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1664
1665                 // Search the list of substitutions and cache our findings
1666                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1667                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1668                                 options |= subs_options::pattern_is_product;
1669                                 break;
1670                         }
1671                 }
1672                 if (!(options & subs_options::pattern_is_product))
1673                         options |= subs_options::pattern_is_not_product;
1674         }
1675
1676         if (options & subs_options::pattern_is_product) {
1677
1678                 // Substitute in the recombined pairs
1679                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1680                 while (cit != last) {
1681
1682                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1683                         const ex &subsed_ex = orig_ex.subs(m, options);
1684                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1685
1686                                 // Something changed, copy seq, subs and return it
1687                                 std::auto_ptr<epvector> s(new epvector);
1688                                 s->reserve(seq.size());
1689
1690                                 // Copy parts of seq which are known not to have changed
1691                                 s->insert(s->begin(), seq.begin(), cit);
1692
1693                                 // Copy first changed element
1694                                 s->push_back(split_ex_to_pair(subsed_ex));
1695                                 ++cit;
1696
1697                                 // Copy rest
1698                                 while (cit != last) {
1699                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1700                                         ++cit;
1701                                 }
1702                                 return s;
1703                         }
1704
1705                         ++cit;
1706                 }
1707
1708         } else {
1709
1710                 // Substitute only in the "rest" part of the pairs
1711                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1712                 while (cit != last) {
1713
1714                         const ex &subsed_ex = cit->rest.subs(m, options);
1715                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1716
1717                                 // Something changed, copy seq, subs and return it
1718                                 std::auto_ptr<epvector> s(new epvector);
1719                                 s->reserve(seq.size());
1720
1721                                 // Copy parts of seq which are known not to have changed
1722                                 s->insert(s->begin(), seq.begin(), cit);
1723
1724                                 // Copy first changed element
1725                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1726                                 ++cit;
1727
1728                                 // Copy rest
1729                                 while (cit != last) {
1730                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1731                                         ++cit;
1732                                 }
1733                                 return s;
1734                         }
1735
1736                         ++cit;
1737                 }
1738         }
1739
1740         // Nothing has changed
1741         return std::auto_ptr<epvector>(0);
1742 }
1743
1744 //////////
1745 // static member variables
1746 //////////
1747
1748 #if EXPAIRSEQ_USE_HASHTAB
1749 unsigned expairseq::maxhashtabsize = 0x4000000U;
1750 unsigned expairseq::minhashtabsize = 0x1000U;
1751 unsigned expairseq::hashtabfactor = 1;
1752 #endif // EXPAIRSEQ_USE_HASHTAB
1753
1754 } // namespace GiNaC