ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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 "operators.h"
  37 #include "utils.h"
  38
  39 #if EXPAIRSEQ_USE_HASHTAB
  40 #include <cmath>
  41 #endif // EXPAIRSEQ_USE_HASHTAB
  42
  43 namespace GiNaC {
  44
  45
  46 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  47
  48 //////////
  49 // helper classes
  50 //////////
  51
  52 class epp_is_less
  53 {
  54 public:
  55         bool operator()(const epp &lh, const epp &rh) const
  56         {
  57                 return (*lh).is_less(*rh);
  58         }
  59 };
  60
  61 //////////
  62 // default ctor, dtor, copy ctor, assignment operator and helpers
  63 //////////
  64
  65 // public
  66
  67 expairseq::expairseq(const expairseq &other)
  68 {
  69         copy(other);
  70 }
  71
  72 const expairseq &expairseq::operator=(const expairseq &other)
  73 {
  74         if (this != &other) {
  75                 destroy(true);
  76                 copy(other);
  77         }
  78         return *this;
  79 }
  80
  81 // protected
  82
  83 /** For use by copy ctor and assignment operator. */
  84 void expairseq::copy(const expairseq &other)
  85 {
  86         inherited::copy(other);
  87         seq = other.seq;
  88         overall_coeff = other.overall_coeff;
  89 #if EXPAIRSEQ_USE_HASHTAB
  90         // copy hashtab
  91         hashtabsize = other.hashtabsize;
  92         if (hashtabsize!=0) {
  93                 hashmask = other.hashmask;
  94                 hashtab.resize(hashtabsize);
  95                 epvector::const_iterator osb = other.seq.begin();
  96                 for (unsigned i=0; i<hashtabsize; ++i) {
  97                         hashtab[i].clear();
  98                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  99                              cit!=other.hashtab[i].end(); ++cit) {
 100                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 101                         }
 102                 }
 103         } else {
 104                 hashtab.clear();
 105         }
 106 #endif // EXPAIRSEQ_USE_HASHTAB
 107 }
 108
 109 DEFAULT_DESTROY(expairseq)
 110
 111 //////////
 112 // other ctors
 113 //////////
 114
 115 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 116 {
 117         construct_from_2_ex(lh,rh);
 118         GINAC_ASSERT(is_canonical());
 119 }
 120
 121 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 122 {
 123         construct_from_exvector(v);
 124         GINAC_ASSERT(is_canonical());
 125 }
 126
 127 expairseq::expairseq(const epvector &v, const ex &oc)
 128   : inherited(TINFO_expairseq), overall_coeff(oc)
 129 {
 130         GINAC_ASSERT(is_a<numeric>(oc));
 131         construct_from_epvector(v);
 132         GINAC_ASSERT(is_canonical());
 133 }
 134
 135 expairseq::expairseq(epvector *vp, const ex &oc)
 136   : inherited(TINFO_expairseq), overall_coeff(oc)
 137 {
 138         GINAC_ASSERT(vp!=0);
 139         GINAC_ASSERT(is_a<numeric>(oc));
 140         construct_from_epvector(*vp);
 141         delete vp;
 142         GINAC_ASSERT(is_canonical());
 143 }
 144
 145 //////////
 146 // archiving
 147 //////////
 148
 149 expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 150 #if EXPAIRSEQ_USE_HASHTAB
 151         , hashtabsize(0)
 152 #endif
 153 {
 154         for (unsigned int i=0; true; i++) {
 155                 ex rest;
 156                 ex coeff;
 157                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 158                         seq.push_back(expair(rest, coeff));
 159                 else
 160                         break;
 161         }
 162         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 163 }
 164
 165 void expairseq::archive(archive_node &n) const
 166 {
 167         inherited::archive(n);
 168         epvector::const_iterator i = seq.begin(), iend = seq.end();
 169         while (i != iend) {
 170                 n.add_ex("rest", i->rest);
 171                 n.add_ex("coeff", i->coeff);
 172                 ++i;
 173         }
 174         n.add_ex("overall_coeff", overall_coeff);
 175 }
 176
 177 DEFAULT_UNARCHIVE(expairseq)
 178
 179 //////////
 180 // functions overriding virtual functions from base classes
 181 //////////
 182
 183 // public
 184
 185 basic *expairseq::duplicate() const
 186 {
 187         return new expairseq(*this);
 188 }
 189
 190 void expairseq::print(const print_context &c, unsigned level) const
 191 {
 192         if (is_a<print_tree>(c)) {
 193
 194                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 195
 196                 c.s << std::string(level, ' ') << class_name()
 197                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 198                     << ", nops=" << nops()
 199                     << std::endl;
 200                 size_t num = seq.size();
 201                 for (size_t i=0; i<num; ++i) {
 202                         seq[i].rest.print(c, level + delta_indent);
 203                         seq[i].coeff.print(c, level + delta_indent);
 204                         if (i != num - 1)
 205                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 206                 }
 207                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 208                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 209                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 210                         overall_coeff.print(c, level + delta_indent);
 211                 }
 212                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 213 #if EXPAIRSEQ_USE_HASHTAB
 214                 c.s << std::string(level + delta_indent,' ')
 215                     << "hashtab size " << hashtabsize << std::endl;
 216                 if (hashtabsize == 0) return;
 217 #define MAXCOUNT 5
 218                 unsigned count[MAXCOUNT+1];
 219                 for (int i=0; i<MAXCOUNT+1; ++i)
 220                         count[i] = 0;
 221                 unsigned this_bin_fill;
 222                 unsigned cum_fill_sq = 0;
 223                 unsigned cum_fill = 0;
 224                 for (unsigned i=0; i<hashtabsize; ++i) {
 225                         this_bin_fill = 0;
 226                         if (hashtab[i].size() > 0) {
 227                                 c.s << std::string(level + delta_indent, ' ')
 228                                     << "bin " << i << " with entries ";
 229                                 for (epplist::const_iterator it=hashtab[i].begin();
 230                                      it!=hashtab[i].end(); ++it) {
 231                                         c.s << *it-seq.begin() << " ";
 232                                         ++this_bin_fill;
 233                                 }
 234                                 c.s << std::endl;
 235                                 cum_fill += this_bin_fill;
 236                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 237                         }
 238                         if (this_bin_fill<MAXCOUNT)
 239                                 ++count[this_bin_fill];
 240                         else
 241                                 ++count[MAXCOUNT];
 242                 }
 243                 unsigned fact = 1;
 244                 double cum_prob = 0;
 245                 double lambda = (1.0*seq.size()) / hashtabsize;
 246                 for (int k=0; k<MAXCOUNT; ++k) {
 247                         if (k>0)
 248                                 fact *= k;
 249                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 250                         cum_prob += prob;
 251                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 252                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 253                             << int(prob*1000)/10.0 << ")" << std::endl;
 254                 }
 255                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 256                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 257                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 258
 259                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 260                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 261                     << std::endl;
 262                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 263                     << (1.0*cum_fill)/hashtabsize
 264                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 265 #endif // EXPAIRSEQ_USE_HASHTAB
 266
 267         } else {
 268                 c.s << "[[";
 269                 printseq(c, ',', precedence(), level);
 270                 c.s << "]]";
 271         }
 272 }
 273
 274 bool expairseq::info(unsigned inf) const
 275 {
 276         return inherited::info(inf);
 277 }
 278
 279 size_t expairseq::nops() const
 280 {
 281         if (overall_coeff.is_equal(default_overall_coeff()))
 282                 return seq.size();
 283         else
 284                 return seq.size()+1;
 285 }
 286
 287 ex expairseq::op(size_t i) const
 288 {
 289         if (i < seq.size())
 290                 return recombine_pair_to_ex(seq[i]);
 291         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 292         return overall_coeff;
 293 }
 294
 295 ex expairseq::map(map_function &f) const
 296 {
 297         epvector *v = new epvector;
 298         v->reserve(seq.size());
 299
 300         epvector::const_iterator cit = seq.begin(), last = seq.end();
 301         while (cit != last) {
 302                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 303                 ++cit;
 304         }
 305
 306         if (overall_coeff.is_equal(default_overall_coeff()))
 307                 return thisexpairseq(v, default_overall_coeff());
 308         else
 309                 return thisexpairseq(v, f(overall_coeff));
 310 }
 311
 312 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 313 ex expairseq::eval(int level) const
 314 {
 315         if ((level==1) && (flags &status_flags::evaluated))
 316                 return *this;
 317
 318         epvector *vp = evalchildren(level);
 319         if (vp==0)
 320                 return this->hold();
 321
 322         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 323 }
 324
 325 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 326 {
 327         // This differs from basic::match() because we want "a+b+c+d" to
 328         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 329
 330         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 331
 332                 // Check whether global wildcard (one that matches the "rest of the
 333                 // expression", like "*" above) is present
 334                 bool has_global_wildcard = false;
 335                 ex global_wildcard;
 336                 for (size_t i=0; i<pattern.nops(); i++) {
 337                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 338                                 has_global_wildcard = true;
 339                                 global_wildcard = pattern.op(i);
 340                                 break;
 341                         }
 342                 }
 343
 344                 // Unfortunately, this is an O(N^2) operation because we can't
 345                 // sort the pattern in a useful way...
 346
 347                 // Chop into terms
 348                 exvector ops;
 349                 ops.reserve(nops());
 350                 for (size_t i=0; i<nops(); i++)
 351                         ops.push_back(op(i));
 352
 353                 // Now, for every term of the pattern, look for a matching term in
 354                 // the expression and remove the match
 355                 for (size_t i=0; i<pattern.nops(); i++) {
 356                         ex p = pattern.op(i);
 357                         if (has_global_wildcard && p.is_equal(global_wildcard))
 358                                 continue;
 359                         exvector::iterator it = ops.begin(), itend = ops.end();
 360                         while (it != itend) {
 361                                 if (it->match(p, repl_lst)) {
 362                                         ops.erase(it);
 363                                         goto found;
 364                                 }
 365                                 ++it;
 366                         }
 367                         return false; // no match found
 368 found:          ;
 369                 }
 370
 371                 if (has_global_wildcard) {
 372
 373                         // Assign all the remaining terms to the global wildcard (unless
 374                         // it has already been matched before, in which case the matches
 375                         // must be equal)
 376                         size_t num = ops.size();
 377                         epvector *vp = new epvector();
 378                         vp->reserve(num);
 379                         for (size_t i=0; i<num; i++)
 380                                 vp->push_back(split_ex_to_pair(ops[i]));
 381                         ex rest = thisexpairseq(vp, default_overall_coeff());
 382                         for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
 383                                 if (it->op(0).is_equal(global_wildcard))
 384                                         return rest.is_equal(it->op(1));
 385                         }
 386                         repl_lst.append(global_wildcard == rest);
 387                         return true;
 388
 389                 } else {
 390
 391                         // No global wildcard, then the match fails if there are any
 392                         // unmatched terms left
 393                         return ops.empty();
 394                 }
 395         }
 396         return inherited::match(pattern, repl_lst);
 397 }
 398
 399 ex expairseq::subs(const lst &ls, const lst &lr, unsigned options) const
 400 {
 401         epvector *vp = subschildren(ls, lr, options);
 402         if (vp)
 403                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 404         else if ((options & subs_options::subs_algebraic) && is_exactly_a<mul>(*this))
 405                 return static_cast<const mul *>(this)->algebraic_subs_mul(ls, lr, options);
 406         else
 407                 return basic::subs(ls, lr, options);
 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();
 551         const epvector::const_iterator end = seq.end();
 552         while (i != end) {
 553                 v ^= i->rest.gethash();
 554 #if !EXPAIRSEQ_USE_HASHTAB
 555                 // rotation spoils commutativity!
 556                 v = rotate_left(v);
 557                 v ^= i->coeff.gethash();
 558 #endif // !EXPAIRSEQ_USE_HASHTAB
 559                 ++i;
 560         }
 561
 562         v ^= overall_coeff.gethash();
 563
 564         // store calculated hash value only if object is already evaluated
 565         if (flags &status_flags::evaluated) {
 566                 setflag(status_flags::hash_calculated);
 567                 hashvalue = v;
 568         }
 569
 570         return v;
 571 }
 572
 573 ex expairseq::expand(unsigned options) const
 574 {
 575         epvector *vp = expandchildren(options);
 576         if (vp == NULL) {
 577                 // The terms have not changed, so it is safe to declare this expanded
 578                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 579         } else
 580                 return thisexpairseq(vp, overall_coeff);
 581 }
 582
 583 //////////
 584 // new virtual functions which can be overridden by derived classes
 585 //////////
 586
 587 // protected
 588
 589 /** Create an object of this type.
 590  *  This method works similar to a constructor.  It is useful because expairseq
 591  *  has (at least) two possible different semantics but we want to inherit
 592  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 593  *  has to create a new one of the same semantics, which cannot be done by a
 594  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 595  *  order for this trick to work a derived class must of course override this
 596  *  definition. */
 597 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 598 {
 599         return expairseq(v,oc);
 600 }
 601
 602 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 603 {
 604         return expairseq(vp,oc);
 605 }
 606
 607 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 608 {
 609         c.s << "[[";
 610         p.rest.print(c, precedence());
 611         c.s << ",";
 612         p.coeff.print(c, precedence());
 613         c.s << "]]";
 614 }
 615
 616 void expairseq::printseq(const print_context & c, char delim,
 617                          unsigned this_precedence,
 618                          unsigned upper_precedence) const
 619 {
 620         if (this_precedence <= upper_precedence)
 621                 c.s << "(";
 622         epvector::const_iterator it, it_last = seq.end() - 1;
 623         for (it=seq.begin(); it!=it_last; ++it) {
 624                 printpair(c, *it, this_precedence);
 625                 c.s << delim;
 626         }
 627         printpair(c, *it, this_precedence);
 628         if (!overall_coeff.is_equal(default_overall_coeff())) {
 629                 c.s << delim;
 630                 overall_coeff.print(c, this_precedence);
 631         }
 632
 633         if (this_precedence <= upper_precedence)
 634                 c.s << ")";
 635 }
 636
 637
 638 /** Form an expair from an ex, using the corresponding semantics.
 639  *  @see expairseq::recombine_pair_to_ex() */
 640 expair expairseq::split_ex_to_pair(const ex &e) const
 641 {
 642         return expair(e,_ex1);
 643 }
 644
 645
 646 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 647                                                 const ex &c) const
 648 {
 649         GINAC_ASSERT(is_exactly_a<numeric>(c));
 650
 651         return expair(e,c);
 652 }
 653
 654
 655 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 656                                                   const ex &c) const
 657 {
 658         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 659         GINAC_ASSERT(is_exactly_a<numeric>(c));
 660
 661         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 662 }
 663
 664
 665 /** Form an ex out of an expair, using the corresponding semantics.
 666  *  @see expairseq::split_ex_to_pair() */
 667 ex expairseq::recombine_pair_to_ex(const expair &p) const
 668 {
 669         return lst(p.rest,p.coeff);
 670 }
 671
 672 bool expairseq::expair_needs_further_processing(epp it)
 673 {
 674 #if EXPAIRSEQ_USE_HASHTAB
 675         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 676 #endif // EXPAIRSEQ_USE_HASHTAB
 677         return false;
 678 }
 679
 680 ex expairseq::default_overall_coeff(void) const
 681 {
 682         return _ex0;
 683 }
 684
 685 void expairseq::combine_overall_coeff(const ex &c)
 686 {
 687         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 688         GINAC_ASSERT(is_exactly_a<numeric>(c));
 689         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 690 }
 691
 692 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 693 {
 694         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 695         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 696         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 697         overall_coeff = ex_to<numeric>(overall_coeff).
 698                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 699 }
 700
 701 bool expairseq::can_make_flat(const expair &p) const
 702 {
 703         return true;
 704 }
 705
 706
 707 //////////
 708 // non-virtual functions in this class
 709 //////////
 710
 711 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 712 {
 713         exvector v;
 714         v.reserve(2);
 715         v.push_back(lh);
 716         v.push_back(rh);
 717         construct_from_exvector(v);
 718 #if EXPAIRSEQ_USE_HASHTAB
 719         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 720         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 721 #endif // EXPAIRSEQ_USE_HASHTAB
 722 }
 723
 724 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 725 {
 726         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 727                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 728 #if EXPAIRSEQ_USE_HASHTAB
 729                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 730                                              ex_to<expairseq>(rh).seq.size();
 731                         if (calc_hashtabsize(totalsize)!=0) {
 732                                 construct_from_2_ex_via_exvector(lh,rh);
 733                         } else {
 734 #endif // EXPAIRSEQ_USE_HASHTAB
 735                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 736                                                            ex_to<expairseq>(rh));
 737 #if EXPAIRSEQ_USE_HASHTAB
 738                         }
 739 #endif // EXPAIRSEQ_USE_HASHTAB
 740                         return;
 741                 } else {
 742 #if EXPAIRSEQ_USE_HASHTAB
 743                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 744                         if (calc_hashtabsize(totalsize)!=0) {
 745                                 construct_from_2_ex_via_exvector(lh, rh);
 746                         } else {
 747 #endif // EXPAIRSEQ_USE_HASHTAB
 748                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 749 #if EXPAIRSEQ_USE_HASHTAB
 750                         }
 751 #endif // EXPAIRSEQ_USE_HASHTAB
 752                         return;
 753                 }
 754         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 755 #if EXPAIRSEQ_USE_HASHTAB
 756                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 757                 if (calc_hashtabsize(totalsize)!=0) {
 758                         construct_from_2_ex_via_exvector(lh,rh);
 759                 } else {
 760 #endif // EXPAIRSEQ_USE_HASHTAB
 761                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 762 #if EXPAIRSEQ_USE_HASHTAB
 763                 }
 764 #endif // EXPAIRSEQ_USE_HASHTAB
 765                 return;
 766         }
 767
 768 #if EXPAIRSEQ_USE_HASHTAB
 769         if (calc_hashtabsize(2)!=0) {
 770                 construct_from_2_ex_via_exvector(lh,rh);
 771                 return;
 772         }
 773         hashtabsize = 0;
 774 #endif // EXPAIRSEQ_USE_HASHTAB
 775
 776         if (is_exactly_a<numeric>(lh)) {
 777                 if (is_exactly_a<numeric>(rh)) {
 778                         combine_overall_coeff(lh);
 779                         combine_overall_coeff(rh);
 780                 } else {
 781                         combine_overall_coeff(lh);
 782                         seq.push_back(split_ex_to_pair(rh));
 783                 }
 784         } else {
 785                 if (is_exactly_a<numeric>(rh)) {
 786                         combine_overall_coeff(rh);
 787                         seq.push_back(split_ex_to_pair(lh));
 788                 } else {
 789                         expair p1 = split_ex_to_pair(lh);
 790                         expair p2 = split_ex_to_pair(rh);
 791
 792                         int cmpval = p1.rest.compare(p2.rest);
 793                         if (cmpval==0) {
 794                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 795                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 796                                         // no further processing is necessary, since this
 797                                         // one element will usually be recombined in eval()
 798                                         seq.push_back(p1);
 799                                 }
 800                         } else {
 801                                 seq.reserve(2);
 802                                 if (cmpval<0) {
 803                                         seq.push_back(p1);
 804                                         seq.push_back(p2);
 805                                 } else {
 806                                         seq.push_back(p2);
 807                                         seq.push_back(p1);
 808                                 }
 809                         }
 810                 }
 811         }
 812 }
 813
 814 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 815                                                                                    const expairseq &s2)
 816 {
 817         combine_overall_coeff(s1.overall_coeff);
 818         combine_overall_coeff(s2.overall_coeff);
 819
 820         epvector::const_iterator first1 = s1.seq.begin();
 821         epvector::const_iterator last1 = s1.seq.end();
 822         epvector::const_iterator first2 = s2.seq.begin();
 823         epvector::const_iterator last2 = s2.seq.end();
 824
 825         seq.reserve(s1.seq.size()+s2.seq.size());
 826
 827         bool needs_further_processing=false;
 828
 829         while (first1!=last1 && first2!=last2) {
 830                 int cmpval = (*first1).rest.compare((*first2).rest);
 831                 if (cmpval==0) {
 832                         // combine terms
 833                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 834                                                    add(ex_to<numeric>(first2->coeff));
 835                         if (!newcoeff.is_zero()) {
 836                                 seq.push_back(expair(first1->rest,newcoeff));
 837                                 if (expair_needs_further_processing(seq.end()-1)) {
 838                                         needs_further_processing = true;
 839                                 }
 840                         }
 841                         ++first1;
 842                         ++first2;
 843                 } else if (cmpval<0) {
 844                         seq.push_back(*first1);
 845                         ++first1;
 846                 } else {
 847                         seq.push_back(*first2);
 848                         ++first2;
 849                 }
 850         }
 851
 852         while (first1!=last1) {
 853                 seq.push_back(*first1);
 854                 ++first1;
 855         }
 856         while (first2!=last2) {
 857                 seq.push_back(*first2);
 858                 ++first2;
 859         }
 860
 861         if (needs_further_processing) {
 862                 epvector v = seq;
 863                 seq.clear();
 864                 construct_from_epvector(v);
 865         }
 866 }
 867
 868 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 869                                                                                         const ex &e)
 870 {
 871         combine_overall_coeff(s.overall_coeff);
 872         if (is_exactly_a<numeric>(e)) {
 873                 combine_overall_coeff(e);
 874                 seq = s.seq;
 875                 return;
 876         }
 877
 878         epvector::const_iterator first = s.seq.begin();
 879         epvector::const_iterator last = s.seq.end();
 880         expair p = split_ex_to_pair(e);
 881
 882         seq.reserve(s.seq.size()+1);
 883         bool p_pushed = false;
 884
 885         bool needs_further_processing=false;
 886
 887         // merge p into s.seq
 888         while (first!=last) {
 889                 int cmpval = (*first).rest.compare(p.rest);
 890                 if (cmpval==0) {
 891                         // combine terms
 892                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 893                                                    add(ex_to<numeric>(p.coeff));
 894                         if (!newcoeff.is_zero()) {
 895                                 seq.push_back(expair(first->rest,newcoeff));
 896                                 if (expair_needs_further_processing(seq.end()-1))
 897                                         needs_further_processing = true;
 898                         }
 899                         ++first;
 900                         p_pushed = true;
 901                         break;
 902                 } else if (cmpval<0) {
 903                         seq.push_back(*first);
 904                         ++first;
 905                 } else {
 906                         seq.push_back(p);
 907                         p_pushed = true;
 908                         break;
 909                 }
 910         }
 911
 912         if (p_pushed) {
 913                 // while loop exited because p was pushed, now push rest of s.seq
 914                 while (first!=last) {
 915                         seq.push_back(*first);
 916                         ++first;
 917                 }
 918         } else {
 919                 // while loop exited because s.seq was pushed, now push p
 920                 seq.push_back(p);
 921         }
 922
 923         if (needs_further_processing) {
 924                 epvector v = seq;
 925                 seq.clear();
 926                 construct_from_epvector(v);
 927         }
 928 }
 929
 930 void expairseq::construct_from_exvector(const exvector &v)
 931 {
 932         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 933         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 934         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 935         //                  (same for (+,*) -> (*,^)
 936
 937         make_flat(v);
 938 #if EXPAIRSEQ_USE_HASHTAB
 939         combine_same_terms();
 940 #else
 941         canonicalize();
 942         combine_same_terms_sorted_seq();
 943 #endif // EXPAIRSEQ_USE_HASHTAB
 944 }
 945
 946 void expairseq::construct_from_epvector(const epvector &v)
 947 {
 948         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 949         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 950         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 951         //                  (same for (+,*) -> (*,^)
 952
 953         make_flat(v);
 954 #if EXPAIRSEQ_USE_HASHTAB
 955         combine_same_terms();
 956 #else
 957         canonicalize();
 958         combine_same_terms_sorted_seq();
 959 #endif // EXPAIRSEQ_USE_HASHTAB
 960 }
 961
 962 /** Combine this expairseq with argument exvector.
 963  *  It cares for associativity as well as for special handling of numerics. */
 964 void expairseq::make_flat(const exvector &v)
 965 {
 966         exvector::const_iterator cit;
 967
 968         // count number of operands which are of same expairseq derived type
 969         // and their cumulative number of operands
 970         int nexpairseqs = 0;
 971         int noperands = 0;
 972
 973         cit = v.begin();
 974         while (cit!=v.end()) {
 975                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 976                         ++nexpairseqs;
 977                         noperands += ex_to<expairseq>(*cit).seq.size();
 978                 }
 979                 ++cit;
 980         }
 981
 982         // reserve seq and coeffseq which will hold all operands
 983         seq.reserve(v.size()+noperands-nexpairseqs);
 984
 985         // copy elements and split off numerical part
 986         cit = v.begin();
 987         while (cit!=v.end()) {
 988                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 989                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 990                         combine_overall_coeff(subseqref.overall_coeff);
 991                         epvector::const_iterator cit_s = subseqref.seq.begin();
 992                         while (cit_s!=subseqref.seq.end()) {
 993                                 seq.push_back(*cit_s);
 994                                 ++cit_s;
 995                         }
 996                 } else {
 997                         if (is_exactly_a<numeric>(*cit))
 998                                 combine_overall_coeff(*cit);
 999                         else
1000                                 seq.push_back(split_ex_to_pair(*cit));
1001                 }
1002                 ++cit;
1003         }
1004 }
1005
1006 /** Combine this expairseq with argument epvector.
1007  *  It cares for associativity as well as for special handling of numerics. */
1008 void expairseq::make_flat(const epvector &v)
1009 {
1010         epvector::const_iterator cit;
1011
1012         // count number of operands which are of same expairseq derived type
1013         // and their cumulative number of operands
1014         int nexpairseqs = 0;
1015         int noperands = 0;
1016
1017         cit = v.begin();
1018         while (cit!=v.end()) {
1019                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1020                         ++nexpairseqs;
1021                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1022                 }
1023                 ++cit;
1024         }
1025
1026         // reserve seq and coeffseq which will hold all operands
1027         seq.reserve(v.size()+noperands-nexpairseqs);
1028
1029         // copy elements and split off numerical part
1030         cit = v.begin();
1031         while (cit!=v.end()) {
1032                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1033                     this->can_make_flat(*cit)) {
1034                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1035                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1036                                                             ex_to<numeric>(cit->coeff));
1037                         epvector::const_iterator cit_s = subseqref.seq.begin();
1038                         while (cit_s!=subseqref.seq.end()) {
1039                                 seq.push_back(expair(cit_s->rest,
1040                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1041                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1042                                 //                                              (*cit).coeff));
1043                                 ++cit_s;
1044                         }
1045                 } else {
1046                         if (cit->is_canonical_numeric())
1047                                 combine_overall_coeff(cit->rest);
1048                         else
1049                                 seq.push_back(*cit);
1050                 }
1051                 ++cit;
1052         }
1053 }
1054
1055 /** Brings this expairseq into a sorted (canonical) form. */
1056 void expairseq::canonicalize(void)
1057 {
1058         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1059 }
1060
1061
1062 /** Compact a presorted expairseq by combining all matching expairs to one
1063  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1064  *  instance. */
1065 void expairseq::combine_same_terms_sorted_seq(void)
1066 {
1067         if (seq.size()<2)
1068                 return;
1069
1070         bool needs_further_processing = false;
1071
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         if (needs_further_processing) {
1105                 epvector v = seq;
1106                 seq.clear();
1107                 construct_from_epvector(v);
1108         }
1109 }
1110
1111 #if EXPAIRSEQ_USE_HASHTAB
1112
1113 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1114 {
1115         unsigned size;
1116         unsigned nearest_power_of_2 = 1 << log2(sz);
1117         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1118         //  size = nearest_power_of_2*hashtabfactor;
1119         size = nearest_power_of_2/hashtabfactor;
1120         if (size<minhashtabsize)
1121                 return 0;
1122
1123         // hashtabsize must be a power of 2
1124         GINAC_ASSERT((1U << log2(size))==size);
1125         return size;
1126 }
1127
1128 unsigned expairseq::calc_hashindex(const ex &e) const
1129 {
1130         // calculate hashindex
1131         unsigned hashindex;
1132         if (is_a<numeric>(e)) {
1133                 hashindex = hashmask;
1134         } else {
1135                 hashindex = e.gethash() & hashmask;
1136                 // last hashtab entry is reserved for numerics
1137                 if (hashindex==hashmask) hashindex = 0;
1138         }
1139         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1140         return hashindex;
1141 }
1142
1143 void expairseq::shrink_hashtab(void)
1144 {
1145         unsigned new_hashtabsize;
1146         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1147                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1148                 if (new_hashtabsize==0) {
1149                         hashtab.clear();
1150                         hashtabsize = 0;
1151                         canonicalize();
1152                         return;
1153                 }
1154
1155                 // shrink by a factor of 2
1156                 unsigned half_hashtabsize = hashtabsize/2;
1157                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1158                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1159                 // special treatment for numeric hashes
1160                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1161                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1162                 hashtab.resize(half_hashtabsize);
1163                 hashtabsize = half_hashtabsize;
1164                 hashmask = hashtabsize-1;
1165         }
1166 }
1167
1168 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1169 {
1170         if (hashtabsize==0)
1171                 return; // nothing to do
1172
1173         // calculate hashindex of element to be deleted
1174         unsigned hashindex = calc_hashindex((*element).rest);
1175
1176         // find it in hashtab and remove it
1177         epplist &eppl = hashtab[hashindex];
1178         epplist::iterator epplit = eppl.begin();
1179         bool erased = false;
1180         while (epplit!=eppl.end()) {
1181                 if (*epplit == element) {
1182                         eppl.erase(epplit);
1183                         erased = true;
1184                         break;
1185                 }
1186                 ++epplit;
1187         }
1188         if (!erased) {
1189                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1190                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1191
1192                 unsigned hashindex = calc_hashindex(element->rest);
1193                 epplist &eppl = hashtab[hashindex];
1194                 epplist::iterator epplit = eppl.begin();
1195                 bool erased = false;
1196                 while (epplit!=eppl.end()) {
1197                         if (*epplit == element) {
1198                                 eppl.erase(epplit);
1199                                 erased = true;
1200                                 break;
1201                         }
1202                         ++epplit;
1203                 }
1204                 GINAC_ASSERT(erased);
1205         }
1206         GINAC_ASSERT(erased);
1207 }
1208
1209 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1210                                    epvector::iterator newpos)
1211 {
1212         GINAC_ASSERT(hashtabsize!=0);
1213
1214         // calculate hashindex of element which was moved
1215         unsigned hashindex=calc_hashindex((*newpos).rest);
1216
1217         // find it in hashtab and modify it
1218         epplist &eppl = hashtab[hashindex];
1219         epplist::iterator epplit = eppl.begin();
1220         while (epplit!=eppl.end()) {
1221                 if (*epplit == oldpos) {
1222                         *epplit = newpos;
1223                         break;
1224                 }
1225                 ++epplit;
1226         }
1227         GINAC_ASSERT(epplit!=eppl.end());
1228 }
1229
1230 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1231 {
1232         epplist::const_iterator current = eppl.begin();
1233         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1234                 ++current;
1235         }
1236         eppl.insert(current,elem);
1237 }
1238
1239 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1240                                           epvector::iterator &last_non_zero,
1241                                           std::vector<bool> &touched,
1242                                           unsigned &number_of_zeroes)
1243 {
1244         epp current = seq.begin();
1245
1246         while (current!=first_numeric) {
1247                 if (is_exactly_a<numeric>(current->rest)) {
1248                         --first_numeric;
1249                         iter_swap(current,first_numeric);
1250                 } else {
1251                         // calculate hashindex
1252                         unsigned currenthashindex = calc_hashindex(current->rest);
1253
1254                         // test if there is already a matching expair in the hashtab-list
1255                         epplist &eppl=hashtab[currenthashindex];
1256                         epplist::iterator epplit = eppl.begin();
1257                         while (epplit!=eppl.end()) {
1258                                 if (current->rest.is_equal((*epplit)->rest))
1259                                         break;
1260                                 ++epplit;
1261                         }
1262                         if (epplit==eppl.end()) {
1263                                 // no matching expair found, append this to end of list
1264                                 sorted_insert(eppl,current);
1265                                 ++current;
1266                         } else {
1267                                 // epplit points to a matching expair, combine it with current
1268                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1269                                                    add_dyn(ex_to<numeric>(current->coeff));
1270
1271                                 // move obsolete current expair to end by swapping with last_non_zero element
1272                                 // if this was a numeric, it is swapped with the expair before first_numeric
1273                                 iter_swap(current,last_non_zero);
1274                                 --first_numeric;
1275                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1276                                 --last_non_zero;
1277                                 ++number_of_zeroes;
1278                                 // test if combined term has coeff 0 and can be removed is done later
1279                                 touched[(*epplit)-seq.begin()] = true;
1280                         }
1281                 }
1282         }
1283 }
1284
1285 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1286                                    epvector::iterator &last_non_zero,
1287                                    std::vector<bool> &touched,
1288                                    unsigned &number_of_zeroes)
1289 {
1290         // move terms with coeff 0 to end and remove them from hashtab
1291         // check only those elements which have been touched
1292         epp current = seq.begin();
1293         size_t i = 0;
1294         while (current!=first_numeric) {
1295                 if (!touched[i]) {
1296                         ++current;
1297                         ++i;
1298                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1299                         ++current;
1300                         ++i;
1301                 } else {
1302                         remove_hashtab_entry(current);
1303
1304                         // move element to the end, unless it is already at the end
1305                         if (current!=last_non_zero) {
1306                                 iter_swap(current,last_non_zero);
1307                                 --first_numeric;
1308                                 bool numeric_swapped = first_numeric!=last_non_zero;
1309                                 if (numeric_swapped)
1310                                         iter_swap(first_numeric,current);
1311                                 epvector::iterator changed_entry;
1312
1313                                 if (numeric_swapped)
1314                                         changed_entry = first_numeric;
1315                                 else
1316                                         changed_entry = last_non_zero;
1317
1318                                 --last_non_zero;
1319                                 ++number_of_zeroes;
1320
1321                                 if (first_numeric!=current) {
1322
1323                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1324                                         move_hashtab_entry(changed_entry,current);
1325                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1326                                 }
1327                         } else {
1328                                 --first_numeric;
1329                                 --last_non_zero;
1330                                 ++number_of_zeroes;
1331                         }
1332                 }
1333         }
1334         GINAC_ASSERT(i==current-seq.begin());
1335 }
1336
1337 /** True if one of the coeffs vanishes, otherwise false.
1338  *  This would be an invariant violation, so this should only be used for
1339  *  debugging purposes. */
1340 bool expairseq::has_coeff_0(void) const
1341 {
1342         epvector::const_iterator i = seq.begin(), end = seq.end();
1343         while (i != end) {
1344                 if (i->coeff.is_zero())
1345                         return true;
1346                 ++i;
1347         }
1348         return false;
1349 }
1350
1351 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1352                                                                                 epvector::const_iterator last_non_zero)
1353 {
1354         if (first_numeric == seq.end()) return; // no numerics
1355
1356         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1357         while (current != last) {
1358                 sorted_insert(hashtab[hashmask], current);
1359                 ++current;
1360         }
1361 }
1362
1363 void expairseq::combine_same_terms(void)
1364 {
1365         // combine same terms, drop term with coeff 0, move numerics to end
1366
1367         // calculate size of hashtab
1368         hashtabsize = calc_hashtabsize(seq.size());
1369
1370         // hashtabsize is a power of 2
1371         hashmask = hashtabsize-1;
1372
1373         // allocate hashtab
1374         hashtab.clear();
1375         hashtab.resize(hashtabsize);
1376
1377         if (hashtabsize==0) {
1378                 canonicalize();
1379                 combine_same_terms_sorted_seq();
1380                 GINAC_ASSERT(!has_coeff_0());
1381                 return;
1382         }
1383
1384         // iterate through seq, move numerics to end,
1385         // fill hashtab and combine same terms
1386         epvector::iterator first_numeric = seq.end();
1387         epvector::iterator last_non_zero = seq.end()-1;
1388
1389         size_t num = seq.size();
1390         std::vector<bool> touched(num);
1391
1392         unsigned number_of_zeroes = 0;
1393
1394         GINAC_ASSERT(!has_coeff_0());
1395         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1396
1397         // there should not be any terms with coeff 0 from the beginning,
1398         // so it should be safe to skip this step
1399         if (number_of_zeroes!=0) {
1400                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1401         }
1402
1403         add_numerics_to_hashtab(first_numeric,last_non_zero);
1404
1405         // pop zero elements
1406         for (unsigned i=0; i<number_of_zeroes; ++i) {
1407                 seq.pop_back();
1408         }
1409
1410         // shrink hashtabsize to calculated value
1411         GINAC_ASSERT(!has_coeff_0());
1412
1413         shrink_hashtab();
1414
1415         GINAC_ASSERT(!has_coeff_0());
1416 }
1417
1418 #endif // EXPAIRSEQ_USE_HASHTAB
1419
1420 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1421  *  debugging or in assertions since being sorted is an invariance. */
1422 bool expairseq::is_canonical() const
1423 {
1424         if (seq.size() <= 1)
1425                 return 1;
1426
1427 #if EXPAIRSEQ_USE_HASHTAB
1428         if (hashtabsize > 0) return 1; // not canoncalized
1429 #endif // EXPAIRSEQ_USE_HASHTAB
1430
1431         epvector::const_iterator it = seq.begin(), itend = seq.end();
1432         epvector::const_iterator it_last = it;
1433         for (++it; it!=itend; it_last=it, ++it) {
1434                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1435                         if (!is_exactly_a<numeric>(it_last->rest) ||
1436                                 !is_exactly_a<numeric>(it->rest)) {
1437                                 // double test makes it easier to set a breakpoint...
1438                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1439                                         !is_exactly_a<numeric>(it->rest)) {
1440                                         printpair(std::clog, *it_last, 0);
1441                                         std::clog << ">";
1442                                         printpair(std::clog, *it, 0);
1443                                         std::clog << "\n";
1444                                         std::clog << "pair1:" << std::endl;
1445                                         it_last->rest.print(print_tree(std::clog));
1446                                         it_last->coeff.print(print_tree(std::clog));
1447                                         std::clog << "pair2:" << std::endl;
1448                                         it->rest.print(print_tree(std::clog));
1449                                         it->coeff.print(print_tree(std::clog));
1450                                         return 0;
1451                                 }
1452                         }
1453                 }
1454         }
1455         return 1;
1456 }
1457
1458
1459 /** Member-wise expand the expairs in this sequence.
1460  *
1461  *  @see expairseq::expand()
1462  *  @return pointer to epvector containing expanded pairs or zero pointer,
1463  *  if no members were changed. */
1464 epvector * expairseq::expandchildren(unsigned options) const
1465 {
1466         const epvector::const_iterator last = seq.end();
1467         epvector::const_iterator cit = seq.begin();
1468         while (cit!=last) {
1469                 const ex &expanded_ex = cit->rest.expand(options);
1470                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1471
1472                         // something changed, copy seq, eval and return it
1473                         epvector *s = new epvector;
1474                         s->reserve(seq.size());
1475
1476                         // copy parts of seq which are known not to have changed
1477                         epvector::const_iterator cit2 = seq.begin();
1478                         while (cit2!=cit) {
1479                                 s->push_back(*cit2);
1480                                 ++cit2;
1481                         }
1482                         // copy first changed element
1483                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1484                                                                    cit2->coeff));
1485                         ++cit2;
1486                         // copy rest
1487                         while (cit2!=last) {
1488                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1489                                                                            cit2->coeff));
1490                                 ++cit2;
1491                         }
1492                         return s;
1493                 }
1494                 ++cit;
1495         }
1496
1497         return 0; // signalling nothing has changed
1498 }
1499
1500
1501 /** Member-wise evaluate the expairs in this sequence.
1502  *
1503  *  @see expairseq::eval()
1504  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1505  *  if no members were changed. */
1506 epvector * expairseq::evalchildren(int level) const
1507 {
1508         // returns a NULL pointer if nothing had to be evaluated
1509         // returns a pointer to a newly created epvector otherwise
1510         // (which has to be deleted somewhere else)
1511
1512         if (level==1)
1513                 return 0;
1514
1515         if (level == -max_recursion_level)
1516                 throw(std::runtime_error("max recursion level reached"));
1517
1518         --level;
1519         epvector::const_iterator last = seq.end();
1520         epvector::const_iterator cit = seq.begin();
1521         while (cit!=last) {
1522                 const ex &evaled_ex = cit->rest.eval(level);
1523                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1524
1525                         // something changed, copy seq, eval and return it
1526                         epvector *s = new epvector;
1527                         s->reserve(seq.size());
1528
1529                         // copy parts of seq which are known not to have changed
1530                         epvector::const_iterator cit2=seq.begin();
1531                         while (cit2!=cit) {
1532                                 s->push_back(*cit2);
1533                                 ++cit2;
1534                         }
1535                         // copy first changed element
1536                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1537                                                                    cit2->coeff));
1538                         ++cit2;
1539                         // copy rest
1540                         while (cit2!=last) {
1541                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1542                                                                            cit2->coeff));
1543                                 ++cit2;
1544                         }
1545                         return s;
1546                 }
1547                 ++cit;
1548         }
1549
1550         return 0; // signalling nothing has changed
1551 }
1552
1553
1554 /** Member-wise substitute in this sequence.
1555  *
1556  *  @see expairseq::subs()
1557  *  @return pointer to epvector containing pairs after application of subs,
1558  *    or NULL pointer if no members were changed. */
1559 epvector * expairseq::subschildren(const lst &ls, const lst &lr, unsigned options) const
1560 {
1561         GINAC_ASSERT(ls.nops()==lr.nops());
1562
1563         // The substitution is "complex" when any of the objects to be substituted
1564         // is a product or power. In this case we have to recombine the pairs
1565         // because the numeric coefficients may be part of the search pattern.
1566         bool complex_subs = false;
1567         for (lst::const_iterator it = ls.begin(); it != ls.end(); ++it) {
1568                 if (is_exactly_a<mul>(*it) || is_exactly_a<power>(*it)) {
1569                         complex_subs = true;
1570                         break;
1571                 }
1572         }
1573
1574         if (complex_subs) {
1575
1576                 // Substitute in the recombined pairs
1577                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1578                 while (cit != last) {
1579
1580                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1581                         const ex &subsed_ex = orig_ex.subs(ls, lr, options);
1582                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1583
1584                                 // Something changed, copy seq, subs and return it
1585                                 epvector *s = new epvector;
1586                                 s->reserve(seq.size());
1587
1588                                 // Copy parts of seq which are known not to have changed
1589                                 s->insert(s->begin(), seq.begin(), cit);
1590
1591                                 // Copy first changed element
1592                                 s->push_back(split_ex_to_pair(subsed_ex));
1593                                 ++cit;
1594
1595                                 // Copy rest
1596                                 while (cit != last) {
1597                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, options)));
1598                                         ++cit;
1599                                 }
1600                                 return s;
1601                         }
1602
1603                         ++cit;
1604                 }
1605
1606         } else {
1607
1608                 // Substitute only in the "rest" part of the pairs
1609                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1610                 while (cit != last) {
1611
1612                         const ex &subsed_ex = cit->rest.subs(ls, lr, options);
1613                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1614
1615                                 // Something changed, copy seq, subs and return it
1616                                 epvector *s = new epvector;
1617                                 s->reserve(seq.size());
1618
1619                                 // Copy parts of seq which are known not to have changed
1620                                 s->insert(s->begin(), seq.begin(), cit);
1621
1622                                 // Copy first changed element
1623                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1624                                 ++cit;
1625
1626                                 // Copy rest
1627                                 while (cit != last) {
1628                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, options),
1629                                                                                    cit->coeff));
1630                                         ++cit;
1631                                 }
1632                                 return s;
1633                         }
1634
1635                         ++cit;
1636                 }
1637         }
1638
1639         // Nothing has changed
1640         return NULL;
1641 }
1642
1643 //////////
1644 // static member variables
1645 //////////
1646
1647 #if EXPAIRSEQ_USE_HASHTAB
1648 unsigned expairseq::maxhashtabsize = 0x4000000U;
1649 unsigned expairseq::minhashtabsize = 0x1000U;
1650 unsigned expairseq::hashtabfactor = 1;
1651 #endif // EXPAIRSEQ_USE_HASHTAB
1652
1653 } // namespace GiNaC