ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <iostream>
  24 #include <algorithm>
  25 #include <string>
  26 #include <stdexcept>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "mul.h"
  31 #include "power.h"
  32 #include "relational.h"
  33 #include "wildcard.h"
  34 #include "print.h"
  35 #include "archive.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  46
  47 //////////
  48 // helper classes
  49 //////////
  50
  51 class epp_is_less
  52 {
  53 public:
  54         bool operator()(const epp &lh, const epp &rh) const
  55         {
  56                 return (*lh).is_less(*rh);
  57         }
  58 };
  59
  60 //////////
  61 // default ctor, dtor, copy ctor, assignment operator and helpers
  62 //////////
  63
  64 // public
  65
  66 expairseq::expairseq(const expairseq &other)
  67 {
  68         copy(other);
  69 }
  70
  71 const expairseq &expairseq::operator=(const expairseq &other)
  72 {
  73         if (this != &other) {
  74                 destroy(true);
  75                 copy(other);
  76         }
  77         return *this;
  78 }
  79
  80 // protected
  81
  82 /** For use by copy ctor and assignment operator. */
  83 void expairseq::copy(const expairseq &other)
  84 {
  85         inherited::copy(other);
  86         seq = other.seq;
  87         overall_coeff = other.overall_coeff;
  88 #if EXPAIRSEQ_USE_HASHTAB
  89         // copy hashtab
  90         hashtabsize = other.hashtabsize;
  91         if (hashtabsize!=0) {
  92                 hashmask = other.hashmask;
  93                 hashtab.resize(hashtabsize);
  94                 epvector::const_iterator osb = other.seq.begin();
  95                 for (unsigned i=0; i<hashtabsize; ++i) {
  96                         hashtab[i].clear();
  97                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  98                              cit!=other.hashtab[i].end(); ++cit) {
  99                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 100                         }
 101                 }
 102         } else {
 103                 hashtab.clear();
 104         }
 105 #endif // EXPAIRSEQ_USE_HASHTAB
 106 }
 107
 108 DEFAULT_DESTROY(expairseq)
 109
 110 //////////
 111 // other ctors
 112 //////////
 113
 114 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_2_ex(lh,rh);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 121 {
 122         construct_from_exvector(v);
 123         GINAC_ASSERT(is_canonical());
 124 }
 125
 126 expairseq::expairseq(const epvector &v, const ex &oc)
 127   : inherited(TINFO_expairseq), overall_coeff(oc)
 128 {
 129         construct_from_epvector(v);
 130         GINAC_ASSERT(is_canonical());
 131 }
 132
 133 expairseq::expairseq(epvector *vp, const ex &oc)
 134   : inherited(TINFO_expairseq), overall_coeff(oc)
 135 {
 136         GINAC_ASSERT(vp!=0);
 137         construct_from_epvector(*vp);
 138         delete vp;
 139         GINAC_ASSERT(is_canonical());
 140 }
 141
 142 //////////
 143 // archiving
 144 //////////
 145
 146 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 147 #if EXPAIRSEQ_USE_HASHTAB
 148         , hashtabsize(0)
 149 #endif
 150 {
 151         for (unsigned int i=0; true; i++) {
 152                 ex rest;
 153                 ex coeff;
 154                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 155                         seq.push_back(expair(rest, coeff));
 156                 else
 157                         break;
 158         }
 159         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 160 }
 161
 162 void expairseq::archive(archive_node &n) const
 163 {
 164         inherited::archive(n);
 165         epvector::const_iterator i = seq.begin(), iend = seq.end();
 166         while (i != iend) {
 167                 n.add_ex("rest", i->rest);
 168                 n.add_ex("coeff", i->coeff);
 169                 ++i;
 170         }
 171         n.add_ex("overall_coeff", overall_coeff);
 172 }
 173
 174 DEFAULT_UNARCHIVE(expairseq)
 175
 176 //////////
 177 // functions overriding virtual functions from base classes
 178 //////////
 179
 180 // public
 181
 182 basic *expairseq::duplicate() const
 183 {
 184         return new expairseq(*this);
 185 }
 186
 187 void expairseq::print(const print_context &c, unsigned level) const
 188 {
 189         if (is_of_type(c, print_tree)) {
 190
 191                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 192
 193                 c.s << std::string(level, ' ') << class_name()
 194                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 195                     << ", nops=" << nops()
 196                     << std::endl;
 197                 unsigned num = seq.size();
 198                 for (unsigned i=0; i<num; ++i) {
 199                         seq[i].rest.print(c, level + delta_indent);
 200                         seq[i].coeff.print(c, level + delta_indent);
 201                         if (i != num - 1)
 202                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 203                 }
 204                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 205                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 206                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 207                         overall_coeff.print(c, level + delta_indent);
 208                 }
 209                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 210 #if EXPAIRSEQ_USE_HASHTAB
 211                 c.s << std::string(level + delta_indent,' ')
 212                     << "hashtab size " << hashtabsize << std::endl;
 213                 if (hashtabsize == 0) return;
 214 #define MAXCOUNT 5
 215                 unsigned count[MAXCOUNT+1];
 216                 for (int i=0; i<MAXCOUNT+1; ++i)
 217                         count[i] = 0;
 218                 unsigned this_bin_fill;
 219                 unsigned cum_fill_sq = 0;
 220                 unsigned cum_fill = 0;
 221                 for (unsigned i=0; i<hashtabsize; ++i) {
 222                         this_bin_fill = 0;
 223                         if (hashtab[i].size() > 0) {
 224                                 c.s << std::string(level + delta_indent, ' ')
 225                                     << "bin " << i << " with entries ";
 226                                 for (epplist::const_iterator it=hashtab[i].begin();
 227                                      it!=hashtab[i].end(); ++it) {
 228                                         c.s << *it-seq.begin() << " ";
 229                                         ++this_bin_fill;
 230                                 }
 231                                 c.s << std::endl;
 232                                 cum_fill += this_bin_fill;
 233                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 234                         }
 235                         if (this_bin_fill<MAXCOUNT)
 236                                 ++count[this_bin_fill];
 237                         else
 238                                 ++count[MAXCOUNT];
 239                 }
 240                 unsigned fact = 1;
 241                 double cum_prob = 0;
 242                 double lambda = (1.0*seq.size()) / hashtabsize;
 243                 for (int k=0; k<MAXCOUNT; ++k) {
 244                         if (k>0)
 245                                 fact *= k;
 246                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 247                         cum_prob += prob;
 248                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 249                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 250                             << int(prob*1000)/10.0 << ")" << std::endl;
 251                 }
 252                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 253                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 254                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 255
 256                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 257                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 258                     << std::endl;
 259                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 260                     << (1.0*cum_fill)/hashtabsize
 261                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 262 #endif // EXPAIRSEQ_USE_HASHTAB
 263
 264         } else {
 265                 c.s << "[[";
 266                 printseq(c, ',', precedence(), level);
 267                 c.s << "]]";
 268         }
 269 }
 270
 271 bool expairseq::info(unsigned inf) const
 272 {
 273         return inherited::info(inf);
 274 }
 275
 276 unsigned expairseq::nops() const
 277 {
 278         if (overall_coeff.is_equal(default_overall_coeff()))
 279                 return seq.size();
 280         else
 281                 return seq.size()+1;
 282 }
 283
 284 ex expairseq::op(int i) const
 285 {
 286         if (unsigned(i)<seq.size())
 287                 return recombine_pair_to_ex(seq[i]);
 288         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 289         return overall_coeff;
 290 }
 291
 292 ex &expairseq::let_op(int i)
 293 {
 294         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 295 }
 296
 297 ex expairseq::map(map_function &f) const
 298 {
 299         epvector *v = new epvector;
 300         v->reserve(seq.size());
 301
 302         epvector::const_iterator cit = seq.begin(), last = seq.end();
 303         while (cit != last) {
 304                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 305                 ++cit;
 306         }
 307
 308         if (overall_coeff.is_equal(default_overall_coeff()))
 309                 return thisexpairseq(v, default_overall_coeff());
 310         else
 311                 return thisexpairseq(v, f(overall_coeff));
 312 }
 313
 314 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 315 ex expairseq::eval(int level) const
 316 {
 317         if ((level==1) && (flags &status_flags::evaluated))
 318                 return *this;
 319
 320         epvector *vp = evalchildren(level);
 321         if (vp==0)
 322                 return this->hold();
 323
 324         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 325 }
 326
 327 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 328 {
 329         // This differs from basic::match() because we want "a+b+c+d" to
 330         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 331
 332         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 333
 334                 // Check whether global wildcard (one that matches the "rest of the
 335                 // expression", like "*" above) is present
 336                 bool has_global_wildcard = false;
 337                 ex global_wildcard;
 338                 for (unsigned int i=0; i<pattern.nops(); i++) {
 339                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 340                                 has_global_wildcard = true;
 341                                 global_wildcard = pattern.op(i);
 342                                 break;
 343                         }
 344                 }
 345
 346                 // Unfortunately, this is an O(N^2) operation because we can't
 347                 // sort the pattern in a useful way...
 348
 349                 // Chop into terms
 350                 exvector ops;
 351                 ops.reserve(nops());
 352                 for (unsigned i=0; i<nops(); i++)
 353                         ops.push_back(op(i));
 354
 355                 // Now, for every term of the pattern, look for a matching term in
 356                 // the expression and remove the match
 357                 for (unsigned i=0; i<pattern.nops(); i++) {
 358                         ex p = pattern.op(i);
 359                         if (has_global_wildcard && p.is_equal(global_wildcard))
 360                                 continue;
 361                         exvector::iterator it = ops.begin(), itend = ops.end();
 362                         while (it != itend) {
 363                                 if (it->match(p, repl_lst)) {
 364                                         ops.erase(it);
 365                                         goto found;
 366                                 }
 367                                 ++it;
 368                         }
 369                         return false; // no match found
 370 found:          ;
 371                 }
 372
 373                 if (has_global_wildcard) {
 374
 375                         // Assign all the remaining terms to the global wildcard (unless
 376                         // it has already been matched before, in which case the matches
 377                         // must be equal)
 378                         unsigned num = ops.size();
 379                         epvector *vp = new epvector();
 380                         vp->reserve(num);
 381                         for (unsigned i=0; i<num; i++)
 382                                 vp->push_back(split_ex_to_pair(ops[i]));
 383                         ex rest = thisexpairseq(vp, default_overall_coeff());
 384                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 385                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 386                                         return rest.is_equal(repl_lst.op(i).op(1));
 387                         }
 388                         repl_lst.append(global_wildcard == rest);
 389                         return true;
 390
 391                 } else {
 392
 393                         // No global wildcard, then the match fails if there are any
 394                         // unmatched terms left
 395                         return ops.empty();
 396                 }
 397         }
 398         return inherited::match(pattern, repl_lst);
 399 }
 400
 401 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 402 {
 403         epvector *vp = subschildren(ls, lr, no_pattern);
 404         if (vp)
 405                 return ex_to<basic>(thisexpairseq(vp, overall_coeff)).basic::subs(ls, lr, no_pattern);
 406         else
 407                 return basic::subs(ls, lr, no_pattern);
 408 }
 409
 410 // protected
 411
 412 int expairseq::compare_same_type(const basic &other) const
 413 {
 414         GINAC_ASSERT(is_a<expairseq>(other));
 415         const expairseq &o = static_cast<const expairseq &>(other);
 416
 417         int cmpval;
 418
 419         // compare number of elements
 420         if (seq.size() != o.seq.size())
 421                 return (seq.size()<o.seq.size()) ? -1 : 1;
 422
 423         // compare overall_coeff
 424         cmpval = overall_coeff.compare(o.overall_coeff);
 425         if (cmpval!=0)
 426                 return cmpval;
 427
 428 #if EXPAIRSEQ_USE_HASHTAB
 429         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 430         if (hashtabsize==0) {
 431 #endif // EXPAIRSEQ_USE_HASHTAB
 432                 epvector::const_iterator cit1 = seq.begin();
 433                 epvector::const_iterator cit2 = o.seq.begin();
 434                 epvector::const_iterator last1 = seq.end();
 435                 epvector::const_iterator last2 = o.seq.end();
 436
 437                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 438                         cmpval = (*cit1).compare(*cit2);
 439                         if (cmpval!=0) return cmpval;
 440                 }
 441
 442                 GINAC_ASSERT(cit1==last1);
 443                 GINAC_ASSERT(cit2==last2);
 444
 445                 return 0;
 446 #if EXPAIRSEQ_USE_HASHTAB
 447         }
 448
 449         // compare number of elements in each hashtab entry
 450         for (unsigned i=0; i<hashtabsize; ++i) {
 451                 unsigned cursize=hashtab[i].size();
 452                 if (cursize != o.hashtab[i].size())
 453                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 454         }
 455
 456         // compare individual (sorted) hashtab entries
 457         for (unsigned i=0; i<hashtabsize; ++i) {
 458                 unsigned sz = hashtab[i].size();
 459                 if (sz>0) {
 460                         const epplist &eppl1 = hashtab[i];
 461                         const epplist &eppl2 = o.hashtab[i];
 462                         epplist::const_iterator it1 = eppl1.begin();
 463                         epplist::const_iterator it2 = eppl2.begin();
 464                         while (it1!=eppl1.end()) {
 465                                 cmpval = (*(*it1)).compare(*(*it2));
 466                                 if (cmpval!=0)
 467                                         return cmpval;
 468                                 ++it1;
 469                                 ++it2;
 470                         }
 471                 }
 472         }
 473
 474         return 0; // equal
 475 #endif // EXPAIRSEQ_USE_HASHTAB
 476 }
 477
 478 bool expairseq::is_equal_same_type(const basic &other) const
 479 {
 480         const expairseq &o = static_cast<const expairseq &>(other);
 481
 482         // compare number of elements
 483         if (seq.size()!=o.seq.size())
 484                 return false;
 485
 486         // compare overall_coeff
 487         if (!overall_coeff.is_equal(o.overall_coeff))
 488                 return false;
 489
 490 #if EXPAIRSEQ_USE_HASHTAB
 491         // compare number of elements in each hashtab entry
 492         if (hashtabsize!=o.hashtabsize) {
 493                 std::cout << "this:" << std::endl;
 494                 print(print_tree(std::cout));
 495                 std::cout << "other:" << std::endl;
 496                 other.print(print_tree(std::cout));
 497         }
 498
 499         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 500
 501         if (hashtabsize==0) {
 502 #endif // EXPAIRSEQ_USE_HASHTAB
 503                 epvector::const_iterator cit1 = seq.begin();
 504                 epvector::const_iterator cit2 = o.seq.begin();
 505                 epvector::const_iterator last1 = seq.end();
 506
 507                 while (cit1!=last1) {
 508                         if (!(*cit1).is_equal(*cit2)) return false;
 509                         ++cit1;
 510                         ++cit2;
 511                 }
 512
 513                 return true;
 514 #if EXPAIRSEQ_USE_HASHTAB
 515         }
 516
 517         for (unsigned i=0; i<hashtabsize; ++i) {
 518                 if (hashtab[i].size() != o.hashtab[i].size())
 519                         return false;
 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                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 532                                 ++it1;
 533                                 ++it2;
 534                         }
 535                 }
 536         }
 537
 538         return true;
 539 #endif // EXPAIRSEQ_USE_HASHTAB
 540 }
 541
 542 unsigned expairseq::return_type(void) const
 543 {
 544         return return_types::noncommutative_composite;
 545 }
 546
 547 unsigned expairseq::calchash(void) const
 548 {
 549         unsigned v = golden_ratio_hash(this->tinfo());
 550         epvector::const_iterator i = seq.begin(), end = seq.end();
 551         while (i != end) {
 552 #if !EXPAIRSEQ_USE_HASHTAB
 553                 v = rotate_left_31(v); // rotation would spoil commutativity
 554 #endif // EXPAIRSEQ_USE_HASHTAB
 555                 v ^= i->rest.gethash();
 556 #if !EXPAIRSEQ_USE_HASHTAB
 557                 v = rotate_left_31(v);
 558                 v ^= i->coeff.gethash();
 559 #endif // EXPAIRSEQ_USE_HASHTAB
 560                 ++i;
 561         }
 562
 563         v ^= overall_coeff.gethash();
 564         v &= 0x7FFFFFFFU;
 565
 566         // store calculated hash value only if object is already evaluated
 567         if (flags &status_flags::evaluated) {
 568                 setflag(status_flags::hash_calculated);
 569                 hashvalue = v;
 570         }
 571
 572         return v;
 573 }
 574
 575 ex expairseq::expand(unsigned options) const
 576 {
 577         epvector *vp = expandchildren(options);
 578         if (vp == NULL) {
 579                 // The terms have not changed, so it is safe to declare this expanded
 580                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 581         } else
 582                 return thisexpairseq(vp, overall_coeff);
 583 }
 584
 585 //////////
 586 // new virtual functions which can be overridden by derived classes
 587 //////////
 588
 589 // protected
 590
 591 /** Create an object of this type.
 592  *  This method works similar to a constructor.  It is useful because expairseq
 593  *  has (at least) two possible different semantics but we want to inherit
 594  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 595  *  has to create a new one of the same semantics, which cannot be done by a
 596  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 597  *  order for this trick to work a derived class must of course override this
 598  *  definition. */
 599 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 600 {
 601         return expairseq(v,oc);
 602 }
 603
 604 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 605 {
 606         return expairseq(vp,oc);
 607 }
 608
 609 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 610 {
 611         c.s << "[[";
 612         p.rest.print(c, precedence());
 613         c.s << ",";
 614         p.coeff.print(c, precedence());
 615         c.s << "]]";
 616 }
 617
 618 void expairseq::printseq(const print_context & c, char delim,
 619                          unsigned this_precedence,
 620                          unsigned upper_precedence) const
 621 {
 622         if (this_precedence <= upper_precedence)
 623                 c.s << "(";
 624         epvector::const_iterator it, it_last = seq.end() - 1;
 625         for (it=seq.begin(); it!=it_last; ++it) {
 626                 printpair(c, *it, this_precedence);
 627                 c.s << delim;
 628         }
 629         printpair(c, *it, this_precedence);
 630         if (!overall_coeff.is_equal(default_overall_coeff())) {
 631                 c.s << delim;
 632                 overall_coeff.print(c, this_precedence);
 633         }
 634
 635         if (this_precedence <= upper_precedence)
 636                 c.s << ")";
 637 }
 638
 639
 640 /** Form an expair from an ex, using the corresponding semantics.
 641  *  @see expairseq::recombine_pair_to_ex() */
 642 expair expairseq::split_ex_to_pair(const ex &e) const
 643 {
 644         return expair(e,_ex1);
 645 }
 646
 647
 648 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 649                                                 const ex &c) const
 650 {
 651         GINAC_ASSERT(is_exactly_a<numeric>(c));
 652
 653         return expair(e,c);
 654 }
 655
 656
 657 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 658                                                   const ex &c) const
 659 {
 660         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 661         GINAC_ASSERT(is_exactly_a<numeric>(c));
 662
 663         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 664 }
 665
 666
 667 /** Form an ex out of an expair, using the corresponding semantics.
 668  *  @see expairseq::split_ex_to_pair() */
 669 ex expairseq::recombine_pair_to_ex(const expair &p) const
 670 {
 671         return lst(p.rest,p.coeff);
 672 }
 673
 674 bool expairseq::expair_needs_further_processing(epp it)
 675 {
 676 #if EXPAIRSEQ_USE_HASHTAB
 677         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 678 #endif // EXPAIRSEQ_USE_HASHTAB
 679         return false;
 680 }
 681
 682 ex expairseq::default_overall_coeff(void) const
 683 {
 684         return _ex0;
 685 }
 686
 687 void expairseq::combine_overall_coeff(const ex &c)
 688 {
 689         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 690         GINAC_ASSERT(is_exactly_a<numeric>(c));
 691         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 692 }
 693
 694 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 695 {
 696         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 697         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 698         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 699         overall_coeff = ex_to<numeric>(overall_coeff).
 700                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 701 }
 702
 703 bool expairseq::can_make_flat(const expair &p) const
 704 {
 705         return true;
 706 }
 707
 708
 709 //////////
 710 // non-virtual functions in this class
 711 //////////
 712
 713 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 714 {
 715         exvector v;
 716         v.reserve(2);
 717         v.push_back(lh);
 718         v.push_back(rh);
 719         construct_from_exvector(v);
 720 #if EXPAIRSEQ_USE_HASHTAB
 721         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 722         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 723 #endif // EXPAIRSEQ_USE_HASHTAB
 724 }
 725
 726 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 727 {
 728         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 729                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 730 #if EXPAIRSEQ_USE_HASHTAB
 731                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 732                                              ex_to<expairseq>(rh).seq.size();
 733                         if (calc_hashtabsize(totalsize)!=0) {
 734                                 construct_from_2_ex_via_exvector(lh,rh);
 735                         } else {
 736 #endif // EXPAIRSEQ_USE_HASHTAB
 737                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 738                                                            ex_to<expairseq>(rh));
 739 #if EXPAIRSEQ_USE_HASHTAB
 740                         }
 741 #endif // EXPAIRSEQ_USE_HASHTAB
 742                         return;
 743                 } else {
 744 #if EXPAIRSEQ_USE_HASHTAB
 745                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 746                         if (calc_hashtabsize(totalsize)!=0) {
 747                                 construct_from_2_ex_via_exvector(lh, rh);
 748                         } else {
 749 #endif // EXPAIRSEQ_USE_HASHTAB
 750                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 751 #if EXPAIRSEQ_USE_HASHTAB
 752                         }
 753 #endif // EXPAIRSEQ_USE_HASHTAB
 754                         return;
 755                 }
 756         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 757 #if EXPAIRSEQ_USE_HASHTAB
 758                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 759                 if (calc_hashtabsize(totalsize)!=0) {
 760                         construct_from_2_ex_via_exvector(lh,rh);
 761                 } else {
 762 #endif // EXPAIRSEQ_USE_HASHTAB
 763                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 764 #if EXPAIRSEQ_USE_HASHTAB
 765                 }
 766 #endif // EXPAIRSEQ_USE_HASHTAB
 767                 return;
 768         }
 769
 770 #if EXPAIRSEQ_USE_HASHTAB
 771         if (calc_hashtabsize(2)!=0) {
 772                 construct_from_2_ex_via_exvector(lh,rh);
 773                 return;
 774         }
 775         hashtabsize = 0;
 776 #endif // EXPAIRSEQ_USE_HASHTAB
 777
 778         if (is_ex_exactly_of_type(lh,numeric)) {
 779                 if (is_ex_exactly_of_type(rh,numeric)) {
 780                         combine_overall_coeff(lh);
 781                         combine_overall_coeff(rh);
 782                 } else {
 783                         combine_overall_coeff(lh);
 784                         seq.push_back(split_ex_to_pair(rh));
 785                 }
 786         } else {
 787                 if (is_ex_exactly_of_type(rh,numeric)) {
 788                         combine_overall_coeff(rh);
 789                         seq.push_back(split_ex_to_pair(lh));
 790                 } else {
 791                         expair p1 = split_ex_to_pair(lh);
 792                         expair p2 = split_ex_to_pair(rh);
 793
 794                         int cmpval = p1.rest.compare(p2.rest);
 795                         if (cmpval==0) {
 796                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 797                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 798                                         // no further processing is necessary, since this
 799                                         // one element will usually be recombined in eval()
 800                                         seq.push_back(p1);
 801                                 }
 802                         } else {
 803                                 seq.reserve(2);
 804                                 if (cmpval<0) {
 805                                         seq.push_back(p1);
 806                                         seq.push_back(p2);
 807                                 } else {
 808                                         seq.push_back(p2);
 809                                         seq.push_back(p1);
 810                                 }
 811                         }
 812                 }
 813         }
 814 }
 815
 816 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 817                                                                                    const expairseq &s2)
 818 {
 819         combine_overall_coeff(s1.overall_coeff);
 820         combine_overall_coeff(s2.overall_coeff);
 821
 822         epvector::const_iterator first1 = s1.seq.begin();
 823         epvector::const_iterator last1 = s1.seq.end();
 824         epvector::const_iterator first2 = s2.seq.begin();
 825         epvector::const_iterator last2 = s2.seq.end();
 826
 827         seq.reserve(s1.seq.size()+s2.seq.size());
 828
 829         bool needs_further_processing=false;
 830
 831         while (first1!=last1 && first2!=last2) {
 832                 int cmpval = (*first1).rest.compare((*first2).rest);
 833                 if (cmpval==0) {
 834                         // combine terms
 835                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 836                                                    add(ex_to<numeric>(first2->coeff));
 837                         if (!newcoeff.is_zero()) {
 838                                 seq.push_back(expair(first1->rest,newcoeff));
 839                                 if (expair_needs_further_processing(seq.end()-1)) {
 840                                         needs_further_processing = true;
 841                                 }
 842                         }
 843                         ++first1;
 844                         ++first2;
 845                 } else if (cmpval<0) {
 846                         seq.push_back(*first1);
 847                         ++first1;
 848                 } else {
 849                         seq.push_back(*first2);
 850                         ++first2;
 851                 }
 852         }
 853
 854         while (first1!=last1) {
 855                 seq.push_back(*first1);
 856                 ++first1;
 857         }
 858         while (first2!=last2) {
 859                 seq.push_back(*first2);
 860                 ++first2;
 861         }
 862
 863         if (needs_further_processing) {
 864                 epvector v = seq;
 865                 seq.clear();
 866                 construct_from_epvector(v);
 867         }
 868 }
 869
 870 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 871                                                                                         const ex &e)
 872 {
 873         combine_overall_coeff(s.overall_coeff);
 874         if (is_ex_exactly_of_type(e,numeric)) {
 875                 combine_overall_coeff(e);
 876                 seq = s.seq;
 877                 return;
 878         }
 879
 880         epvector::const_iterator first = s.seq.begin();
 881         epvector::const_iterator last = s.seq.end();
 882         expair p = split_ex_to_pair(e);
 883
 884         seq.reserve(s.seq.size()+1);
 885         bool p_pushed = false;
 886
 887         bool needs_further_processing=false;
 888
 889         // merge p into s.seq
 890         while (first!=last) {
 891                 int cmpval = (*first).rest.compare(p.rest);
 892                 if (cmpval==0) {
 893                         // combine terms
 894                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 895                                                    add(ex_to<numeric>(p.coeff));
 896                         if (!newcoeff.is_zero()) {
 897                                 seq.push_back(expair(first->rest,newcoeff));
 898                                 if (expair_needs_further_processing(seq.end()-1))
 899                                         needs_further_processing = true;
 900                         }
 901                         ++first;
 902                         p_pushed = true;
 903                         break;
 904                 } else if (cmpval<0) {
 905                         seq.push_back(*first);
 906                         ++first;
 907                 } else {
 908                         seq.push_back(p);
 909                         p_pushed = true;
 910                         break;
 911                 }
 912         }
 913
 914         if (p_pushed) {
 915                 // while loop exited because p was pushed, now push rest of s.seq
 916                 while (first!=last) {
 917                         seq.push_back(*first);
 918                         ++first;
 919                 }
 920         } else {
 921                 // while loop exited because s.seq was pushed, now push p
 922                 seq.push_back(p);
 923         }
 924
 925         if (needs_further_processing) {
 926                 epvector v = seq;
 927                 seq.clear();
 928                 construct_from_epvector(v);
 929         }
 930 }
 931
 932 void expairseq::construct_from_exvector(const exvector &v)
 933 {
 934         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 935         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 936         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 937         //                  (same for (+,*) -> (*,^)
 938
 939         make_flat(v);
 940 #if EXPAIRSEQ_USE_HASHTAB
 941         combine_same_terms();
 942 #else
 943         canonicalize();
 944         combine_same_terms_sorted_seq();
 945 #endif // EXPAIRSEQ_USE_HASHTAB
 946 }
 947
 948 void expairseq::construct_from_epvector(const epvector &v)
 949 {
 950         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 951         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 952         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 953         //                  (same for (+,*) -> (*,^)
 954
 955         make_flat(v);
 956 #if EXPAIRSEQ_USE_HASHTAB
 957         combine_same_terms();
 958 #else
 959         canonicalize();
 960         combine_same_terms_sorted_seq();
 961 #endif // EXPAIRSEQ_USE_HASHTAB
 962 }
 963
 964 /** Combine this expairseq with argument exvector.
 965  *  It cares for associativity as well as for special handling of numerics. */
 966 void expairseq::make_flat(const exvector &v)
 967 {
 968         exvector::const_iterator cit;
 969
 970         // count number of operands which are of same expairseq derived type
 971         // and their cumulative number of operands
 972         int nexpairseqs = 0;
 973         int noperands = 0;
 974
 975         cit = v.begin();
 976         while (cit!=v.end()) {
 977                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 978                         ++nexpairseqs;
 979                         noperands += ex_to<expairseq>(*cit).seq.size();
 980                 }
 981                 ++cit;
 982         }
 983
 984         // reserve seq and coeffseq which will hold all operands
 985         seq.reserve(v.size()+noperands-nexpairseqs);
 986
 987         // copy elements and split off numerical part
 988         cit = v.begin();
 989         while (cit!=v.end()) {
 990                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 991                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 992                         combine_overall_coeff(subseqref.overall_coeff);
 993                         epvector::const_iterator cit_s = subseqref.seq.begin();
 994                         while (cit_s!=subseqref.seq.end()) {
 995                                 seq.push_back(*cit_s);
 996                                 ++cit_s;
 997                         }
 998                 } else {
 999                         if (is_ex_exactly_of_type(*cit,numeric))
1000                                 combine_overall_coeff(*cit);
1001                         else
1002                                 seq.push_back(split_ex_to_pair(*cit));
1003                 }
1004                 ++cit;
1005         }
1006 }
1007
1008 /** Combine this expairseq with argument epvector.
1009  *  It cares for associativity as well as for special handling of numerics. */
1010 void expairseq::make_flat(const epvector &v)
1011 {
1012         epvector::const_iterator cit;
1013
1014         // count number of operands which are of same expairseq derived type
1015         // and their cumulative number of operands
1016         int nexpairseqs = 0;
1017         int noperands = 0;
1018
1019         cit = v.begin();
1020         while (cit!=v.end()) {
1021                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1022                         ++nexpairseqs;
1023                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1024                 }
1025                 ++cit;
1026         }
1027
1028         // reserve seq and coeffseq which will hold all operands
1029         seq.reserve(v.size()+noperands-nexpairseqs);
1030
1031         // copy elements and split off numerical part
1032         cit = v.begin();
1033         while (cit!=v.end()) {
1034                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1035                     this->can_make_flat(*cit)) {
1036                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1037                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1038                                                             ex_to<numeric>(cit->coeff));
1039                         epvector::const_iterator cit_s = subseqref.seq.begin();
1040                         while (cit_s!=subseqref.seq.end()) {
1041                                 seq.push_back(expair(cit_s->rest,
1042                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1043                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1044                                 //                                              (*cit).coeff));
1045                                 ++cit_s;
1046                         }
1047                 } else {
1048                         if (cit->is_canonical_numeric())
1049                                 combine_overall_coeff(cit->rest);
1050                         else
1051                                 seq.push_back(*cit);
1052                 }
1053                 ++cit;
1054         }
1055 }
1056
1057 /** Brings this expairseq into a sorted (canonical) form. */
1058 void expairseq::canonicalize(void)
1059 {
1060         std::sort(seq.begin(), seq.end(), expair_is_less());
1061 }
1062
1063
1064 /** Compact a presorted expairseq by combining all matching expairs to one
1065  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1066  *  instance. */
1067 void expairseq::combine_same_terms_sorted_seq(void)
1068 {
1069         bool needs_further_processing = false;
1070
1071         if (seq.size()>1) {
1072                 epvector::iterator itin1 = seq.begin();
1073                 epvector::iterator itin2 = itin1+1;
1074                 epvector::iterator itout = itin1;
1075                 epvector::iterator last = seq.end();
1076                 // must_copy will be set to true the first time some combination is
1077                 // possible from then on the sequence has changed and must be compacted
1078                 bool must_copy = false;
1079                 while (itin2!=last) {
1080                         if (itin1->rest.compare(itin2->rest)==0) {
1081                                 itin1->coeff = ex_to<numeric>(itin1->coeff).
1082                                                add_dyn(ex_to<numeric>(itin2->coeff));
1083                                 if (expair_needs_further_processing(itin1))
1084                                         needs_further_processing = true;
1085                                 must_copy = true;
1086                         } else {
1087                                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1088                                         if (must_copy)
1089                                                 *itout = *itin1;
1090                                         ++itout;
1091                                 }
1092                                 itin1 = itin2;
1093                         }
1094                         ++itin2;
1095                 }
1096                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1097                         if (must_copy)
1098                                 *itout = *itin1;
1099                         ++itout;
1100                 }
1101                 if (itout!=last)
1102                         seq.erase(itout,last);
1103         }
1104
1105         if (needs_further_processing) {
1106                 epvector v = seq;
1107                 seq.clear();
1108                 construct_from_epvector(v);
1109         }
1110 }
1111
1112 #if EXPAIRSEQ_USE_HASHTAB
1113
1114 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1115 {
1116         unsigned size;
1117         unsigned nearest_power_of_2 = 1 << log2(sz);
1118         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1119         //  size = nearest_power_of_2*hashtabfactor;
1120         size = nearest_power_of_2/hashtabfactor;
1121         if (size<minhashtabsize)
1122                 return 0;
1123         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1124         // hashtabsize must be a power of 2
1125         GINAC_ASSERT((1U << log2(size))==size);
1126         return size;
1127 }
1128
1129 unsigned expairseq::calc_hashindex(const ex &e) const
1130 {
1131         // calculate hashindex
1132         unsigned hash = e.gethash();
1133         unsigned hashindex;
1134         if (is_a_numeric_hash(hash)) {
1135                 hashindex = hashmask;
1136         } else {
1137                 hashindex = hash &hashmask;
1138                 // last hashtab entry is reserved for numerics
1139                 if (hashindex==hashmask) hashindex = 0;
1140         }
1141         GINAC_ASSERT(hashindex>=0);
1142         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1143         return hashindex;
1144 }
1145
1146 void expairseq::shrink_hashtab(void)
1147 {
1148         unsigned new_hashtabsize;
1149         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1150                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1151                 if (new_hashtabsize==0) {
1152                         hashtab.clear();
1153                         hashtabsize = 0;
1154                         canonicalize();
1155                         return;
1156                 }
1157
1158                 // shrink by a factor of 2
1159                 unsigned half_hashtabsize = hashtabsize/2;
1160                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1161                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1162                 // special treatment for numeric hashes
1163                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1164                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1165                 hashtab.resize(half_hashtabsize);
1166                 hashtabsize = half_hashtabsize;
1167                 hashmask = hashtabsize-1;
1168         }
1169 }
1170
1171 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1172 {
1173         if (hashtabsize==0)
1174                 return; // nothing to do
1175
1176         // calculate hashindex of element to be deleted
1177         unsigned hashindex = calc_hashindex((*element).rest);
1178
1179         // find it in hashtab and remove it
1180         epplist &eppl = hashtab[hashindex];
1181         epplist::iterator epplit = eppl.begin();
1182         bool erased = false;
1183         while (epplit!=eppl.end()) {
1184                 if (*epplit == element) {
1185                         eppl.erase(epplit);
1186                         erased = true;
1187                         break;
1188                 }
1189                 ++epplit;
1190         }
1191         if (!erased) {
1192                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1193                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1194
1195                 unsigned hashindex = calc_hashindex(element->rest);
1196                 epplist &eppl = hashtab[hashindex];
1197                 epplist::iterator epplit = eppl.begin();
1198                 bool erased = false;
1199                 while (epplit!=eppl.end()) {
1200                         if (*epplit == element) {
1201                                 eppl.erase(epplit);
1202                                 erased = true;
1203                                 break;
1204                         }
1205                         ++epplit;
1206                 }
1207                 GINAC_ASSERT(erased);
1208         }
1209         GINAC_ASSERT(erased);
1210 }
1211
1212 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1213                                    epvector::iterator newpos)
1214 {
1215         GINAC_ASSERT(hashtabsize!=0);
1216
1217         // calculate hashindex of element which was moved
1218         unsigned hashindex=calc_hashindex((*newpos).rest);
1219
1220         // find it in hashtab and modify it
1221         epplist &eppl = hashtab[hashindex];
1222         epplist::iterator epplit = eppl.begin();
1223         while (epplit!=eppl.end()) {
1224                 if (*epplit == oldpos) {
1225                         *epplit = newpos;
1226                         break;
1227                 }
1228                 ++epplit;
1229         }
1230         GINAC_ASSERT(epplit!=eppl.end());
1231 }
1232
1233 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1234 {
1235         epplist::const_iterator current = eppl.begin();
1236         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1237                 ++current;
1238         }
1239         eppl.insert(current,elem);
1240 }
1241
1242 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1243                                           epvector::iterator &last_non_zero,
1244                                           std::vector<bool> &touched,
1245                                           unsigned &number_of_zeroes)
1246 {
1247         epp current = seq.begin();
1248
1249         while (current!=first_numeric) {
1250                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1251                         --first_numeric;
1252                         iter_swap(current,first_numeric);
1253                 } else {
1254                         // calculate hashindex
1255                         unsigned currenthashindex = calc_hashindex(current->rest);
1256
1257                         // test if there is already a matching expair in the hashtab-list
1258                         epplist &eppl=hashtab[currenthashindex];
1259                         epplist::iterator epplit = eppl.begin();
1260                         while (epplit!=eppl.end()) {
1261                                 if (current->rest.is_equal((*epplit)->rest))
1262                                         break;
1263                                 ++epplit;
1264                         }
1265                         if (epplit==eppl.end()) {
1266                                 // no matching expair found, append this to end of list
1267                                 sorted_insert(eppl,current);
1268                                 ++current;
1269                         } else {
1270                                 // epplit points to a matching expair, combine it with current
1271                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1272                                                    add_dyn(ex_to<numeric>(current->coeff));
1273
1274                                 // move obsolete current expair to end by swapping with last_non_zero element
1275                                 // if this was a numeric, it is swapped with the expair before first_numeric
1276                                 iter_swap(current,last_non_zero);
1277                                 --first_numeric;
1278                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1279                                 --last_non_zero;
1280                                 ++number_of_zeroes;
1281                                 // test if combined term has coeff 0 and can be removed is done later
1282                                 touched[(*epplit)-seq.begin()] = true;
1283                         }
1284                 }
1285         }
1286 }
1287
1288 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1289                                    epvector::iterator &last_non_zero,
1290                                    std::vector<bool> &touched,
1291                                    unsigned &number_of_zeroes)
1292 {
1293         // move terms with coeff 0 to end and remove them from hashtab
1294         // check only those elements which have been touched
1295         epp current = seq.begin();
1296         unsigned i = 0;
1297         while (current!=first_numeric) {
1298                 if (!touched[i]) {
1299                         ++current;
1300                         ++i;
1301                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1302                         ++current;
1303                         ++i;
1304                 } else {
1305                         remove_hashtab_entry(current);
1306
1307                         // move element to the end, unless it is already at the end
1308                         if (current!=last_non_zero) {
1309                                 iter_swap(current,last_non_zero);
1310                                 --first_numeric;
1311                                 bool numeric_swapped = first_numeric!=last_non_zero;
1312                                 if (numeric_swapped)
1313                                         iter_swap(first_numeric,current);
1314                                 epvector::iterator changed_entry;
1315
1316                                 if (numeric_swapped)
1317                                         changed_entry = first_numeric;
1318                                 else
1319                                         changed_entry = last_non_zero;
1320
1321                                 --last_non_zero;
1322                                 ++number_of_zeroes;
1323
1324                                 if (first_numeric!=current) {
1325
1326                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1327                                         move_hashtab_entry(changed_entry,current);
1328                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1329                                 }
1330                         } else {
1331                                 --first_numeric;
1332                                 --last_non_zero;
1333                                 ++number_of_zeroes;
1334                         }
1335                 }
1336         }
1337         GINAC_ASSERT(i==current-seq.begin());
1338 }
1339
1340 /** True if one of the coeffs vanishes, otherwise false.
1341  *  This would be an invariant violation, so this should only be used for
1342  *  debugging purposes. */
1343 bool expairseq::has_coeff_0(void) const
1344 {
1345         epvector::const_iterator i = seq.begin(), end = seq.end();
1346         while (i != end) {
1347                 if (i->coeff.is_zero())
1348                         return true;
1349                 ++i;
1350         }
1351         return false;
1352 }
1353
1354 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1355                                                                                 epvector::const_iterator last_non_zero)
1356 {
1357         if (first_numeric == seq.end()) return; // no numerics
1358
1359         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1360         while (current != last) {
1361                 sorted_insert(hashtab[hashmask], current);
1362                 ++current;
1363         }
1364 }
1365
1366 void expairseq::combine_same_terms(void)
1367 {
1368         // combine same terms, drop term with coeff 0, move numerics to end
1369
1370         // calculate size of hashtab
1371         hashtabsize = calc_hashtabsize(seq.size());
1372
1373         // hashtabsize is a power of 2
1374         hashmask = hashtabsize-1;
1375
1376         // allocate hashtab
1377         hashtab.clear();
1378         hashtab.resize(hashtabsize);
1379
1380         if (hashtabsize==0) {
1381                 canonicalize();
1382                 combine_same_terms_sorted_seq();
1383                 GINAC_ASSERT(!has_coeff_0());
1384                 return;
1385         }
1386
1387         // iterate through seq, move numerics to end,
1388         // fill hashtab and combine same terms
1389         epvector::iterator first_numeric = seq.end();
1390         epvector::iterator last_non_zero = seq.end()-1;
1391
1392         unsigned num = seq.size();
1393         std::vector<bool> touched(num);
1394
1395         unsigned number_of_zeroes = 0;
1396
1397         GINAC_ASSERT(!has_coeff_0());
1398         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1399
1400         // there should not be any terms with coeff 0 from the beginning,
1401         // so it should be safe to skip this step
1402         if (number_of_zeroes!=0) {
1403                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1404         }
1405
1406         add_numerics_to_hashtab(first_numeric,last_non_zero);
1407
1408         // pop zero elements
1409         for (unsigned i=0; i<number_of_zeroes; ++i) {
1410                 seq.pop_back();
1411         }
1412
1413         // shrink hashtabsize to calculated value
1414         GINAC_ASSERT(!has_coeff_0());
1415
1416         shrink_hashtab();
1417
1418         GINAC_ASSERT(!has_coeff_0());
1419 }
1420
1421 #endif // EXPAIRSEQ_USE_HASHTAB
1422
1423 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1424  *  debugging or in assertions since being sorted is an invariance. */
1425 bool expairseq::is_canonical() const
1426 {
1427         if (seq.size() <= 1)
1428                 return 1;
1429
1430 #if EXPAIRSEQ_USE_HASHTAB
1431         if (hashtabsize > 0) return 1; // not canoncalized
1432 #endif // EXPAIRSEQ_USE_HASHTAB
1433
1434         epvector::const_iterator it = seq.begin(), itend = seq.end();
1435         epvector::const_iterator it_last = it;
1436         for (++it; it!=itend; it_last=it, ++it) {
1437                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1438                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1439                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1440                                 // double test makes it easier to set a breakpoint...
1441                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1442                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1443                                         printpair(std::clog, *it_last, 0);
1444                                         std::clog << ">";
1445                                         printpair(std::clog, *it, 0);
1446                                         std::clog << "\n";
1447                                         std::clog << "pair1:" << std::endl;
1448                                         it_last->rest.print(print_tree(std::clog));
1449                                         it_last->coeff.print(print_tree(std::clog));
1450                                         std::clog << "pair2:" << std::endl;
1451                                         it->rest.print(print_tree(std::clog));
1452                                         it->coeff.print(print_tree(std::clog));
1453                                         return 0;
1454                                 }
1455                         }
1456                 }
1457         }
1458         return 1;
1459 }
1460
1461
1462 /** Member-wise expand the expairs in this sequence.
1463  *
1464  *  @see expairseq::expand()
1465  *  @return pointer to epvector containing expanded pairs or zero pointer,
1466  *  if no members were changed. */
1467 epvector * expairseq::expandchildren(unsigned options) const
1468 {
1469         const epvector::const_iterator last = seq.end();
1470         epvector::const_iterator cit = seq.begin();
1471         while (cit!=last) {
1472                 const ex &expanded_ex = cit->rest.expand(options);
1473                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1474
1475                         // something changed, copy seq, eval and return it
1476                         epvector *s = new epvector;
1477                         s->reserve(seq.size());
1478
1479                         // copy parts of seq which are known not to have changed
1480                         epvector::const_iterator cit2 = seq.begin();
1481                         while (cit2!=cit) {
1482                                 s->push_back(*cit2);
1483                                 ++cit2;
1484                         }
1485                         // copy first changed element
1486                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1487                                                                    cit2->coeff));
1488                         ++cit2;
1489                         // copy rest
1490                         while (cit2!=last) {
1491                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1492                                                                            cit2->coeff));
1493                                 ++cit2;
1494                         }
1495                         return s;
1496                 }
1497                 ++cit;
1498         }
1499
1500         return 0; // signalling nothing has changed
1501 }
1502
1503
1504 /** Member-wise evaluate the expairs in this sequence.
1505  *
1506  *  @see expairseq::eval()
1507  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1508  *  if no members were changed. */
1509 epvector * expairseq::evalchildren(int level) const
1510 {
1511         // returns a NULL pointer if nothing had to be evaluated
1512         // returns a pointer to a newly created epvector otherwise
1513         // (which has to be deleted somewhere else)
1514
1515         if (level==1)
1516                 return 0;
1517
1518         if (level == -max_recursion_level)
1519                 throw(std::runtime_error("max recursion level reached"));
1520
1521         --level;
1522         epvector::const_iterator last = seq.end();
1523         epvector::const_iterator cit = seq.begin();
1524         while (cit!=last) {
1525                 const ex &evaled_ex = cit->rest.eval(level);
1526                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1527
1528                         // something changed, copy seq, eval and return it
1529                         epvector *s = new epvector;
1530                         s->reserve(seq.size());
1531
1532                         // copy parts of seq which are known not to have changed
1533                         epvector::const_iterator cit2=seq.begin();
1534                         while (cit2!=cit) {
1535                                 s->push_back(*cit2);
1536                                 ++cit2;
1537                         }
1538                         // copy first changed element
1539                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1540                                                                    cit2->coeff));
1541                         ++cit2;
1542                         // copy rest
1543                         while (cit2!=last) {
1544                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1545                                                                            cit2->coeff));
1546                                 ++cit2;
1547                         }
1548                         return s;
1549                 }
1550                 ++cit;
1551         }
1552
1553         return 0; // signalling nothing has changed
1554 }
1555
1556
1557 /** Member-wise substitute in this sequence.
1558  *
1559  *  @see expairseq::subs()
1560  *  @return pointer to epvector containing pairs after application of subs,
1561  *    or NULL pointer if no members were changed. */
1562 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1563 {
1564         GINAC_ASSERT(ls.nops()==lr.nops());
1565
1566         // The substitution is "complex" when any of the objects to be substituted
1567         // is a product or power. In this case we have to recombine the pairs
1568         // because the numeric coefficients may be part of the search pattern.
1569         bool complex_subs = false;
1570         for (unsigned i=0; i<ls.nops(); ++i)
1571                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1572                         complex_subs = true;
1573                         break;
1574                 }
1575
1576         if (complex_subs) {
1577
1578                 // Substitute in the recombined pairs
1579                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1580                 while (cit != last) {
1581
1582                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1583                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1584                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1585
1586                                 // Something changed, copy seq, subs and return it
1587                                 epvector *s = new epvector;
1588                                 s->reserve(seq.size());
1589
1590                                 // Copy parts of seq which are known not to have changed
1591                                 s->insert(s->begin(), seq.begin(), cit);
1592
1593                                 // Copy first changed element
1594                                 s->push_back(split_ex_to_pair(subsed_ex));
1595                                 ++cit;
1596
1597                                 // Copy rest
1598                                 while (cit != last) {
1599                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1600                                         ++cit;
1601                                 }
1602                                 return s;
1603                         }
1604
1605                         ++cit;
1606                 }
1607
1608         } else {
1609
1610                 // Substitute only in the "rest" part of the pairs
1611                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1612                 while (cit != last) {
1613
1614                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1615                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1616
1617                                 // Something changed, copy seq, subs and return it
1618                                 epvector *s = new epvector;
1619                                 s->reserve(seq.size());
1620
1621                                 // Copy parts of seq which are known not to have changed
1622                                 s->insert(s->begin(), seq.begin(), cit);
1623
1624                                 // Copy first changed element
1625                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1626                                 ++cit;
1627
1628                                 // Copy rest
1629                                 while (cit != last) {
1630                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1631                                                                                    cit->coeff));
1632                                         ++cit;
1633                                 }
1634                                 return s;
1635                         }
1636
1637                         ++cit;
1638                 }
1639         }
1640
1641         // Nothing has changed
1642         return NULL;
1643 }
1644
1645 //////////
1646 // static member variables
1647 //////////
1648
1649 #if EXPAIRSEQ_USE_HASHTAB
1650 unsigned expairseq::maxhashtabsize = 0x4000000U;
1651 unsigned expairseq::minhashtabsize = 0x1000U;
1652 unsigned expairseq::hashtabfactor = 1;
1653 #endif // EXPAIRSEQ_USE_HASHTAB
1654
1655 } // namespace GiNaC