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 <algorithm>
  24 #include <string>
  25 #include <stdexcept>
  26
  27 #include "expairseq.h"
  28 #include "lst.h"
  29 #include "relational.h"
  30 #include "print.h"
  31 #include "archive.h"
  32 #include "debugmsg.h"
  33 #include "utils.h"
  34
  35 #if EXPAIRSEQ_USE_HASHTAB
  36 #include <cmath>
  37 #endif // EXPAIRSEQ_USE_HASHTAB
  38
  39 namespace GiNaC {
  40
  41 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  42
  43 //////////
  44 // helper classes
  45 //////////
  46
  47 class epp_is_less
  48 {
  49 public:
  50         bool operator()(const epp &lh, const epp &rh) const
  51         {
  52                 return (*lh).is_less(*rh);
  53         }
  54 };
  55
  56 //////////
  57 // default ctor, dtor, copy ctor assignment operator and helpers
  58 //////////
  59
  60 // public
  61
  62 expairseq::expairseq(const expairseq &other)
  63 {
  64         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
  65         copy(other);
  66 }
  67
  68 const expairseq &expairseq::operator=(const expairseq &other)
  69 {
  70         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  71         if (this != &other) {
  72                 destroy(true);
  73                 copy(other);
  74         }
  75         return *this;
  76 }
  77
  78 // protected
  79
  80 /** For use by copy ctor and assignment operator. */
  81 void expairseq::copy(const expairseq &other)
  82 {
  83         inherited::copy(other);
  84         seq = other.seq;
  85         overall_coeff = other.overall_coeff;
  86 #if EXPAIRSEQ_USE_HASHTAB
  87         // copy hashtab
  88         hashtabsize = other.hashtabsize;
  89         if (hashtabsize!=0) {
  90                 hashmask = other.hashmask;
  91                 hashtab.resize(hashtabsize);
  92                 epvector::const_iterator osb = other.seq.begin();
  93                 for (unsigned i=0; i<hashtabsize; ++i) {
  94                         hashtab[i].clear();
  95                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  96                              cit!=other.hashtab[i].end(); ++cit) {
  97                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  98                         }
  99                 }
 100         } else {
 101                 hashtab.clear();
 102         }
 103 #endif // EXPAIRSEQ_USE_HASHTAB
 104 }
 105
 106 DEFAULT_DESTROY(expairseq)
 107
 108 //////////
 109 // other ctors
 110 //////////
 111
 112 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 113 {
 114         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 115         construct_from_2_ex(lh,rh);
 116         GINAC_ASSERT(is_canonical());
 117 }
 118
 119 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 120 {
 121         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 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         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 130         construct_from_epvector(v);
 131         GINAC_ASSERT(is_canonical());
 132 }
 133
 134 expairseq::expairseq(epvector *vp, const ex &oc)
 135   : inherited(TINFO_expairseq), overall_coeff(oc)
 136 {
 137         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 138         GINAC_ASSERT(vp!=0);
 139         construct_from_epvector(*vp);
 140         delete vp;
 141         GINAC_ASSERT(is_canonical());
 142 }
 143
 144 //////////
 145 // archiving
 146 //////////
 147
 148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 149 #if EXPAIRSEQ_USE_HASHTAB
 150         , hashtabsize(0)
 151 #endif
 152 {
 153         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
 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 bases classes
 181 //////////
 182
 183 // public
 184
 185 basic *expairseq::duplicate() const
 186 {
 187         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 188         return new expairseq(*this);
 189 }
 190
 191 void expairseq::print(const print_context & c, unsigned level) const
 192 {
 193         debugmsg("expairseq print",LOGLEVEL_PRINT);
 194
 195         if (is_of_type(c, print_tree)) {
 196
 197                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 198
 199                 c.s << std::string(level, ' ') << class_name()
 200                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 201                     << ", nops=" << nops()
 202                     << std::endl;
 203                 for (unsigned i=0; i<seq.size(); ++i) {
 204                         seq[i].rest.print(c, level + delta_indent);
 205                         seq[i].coeff.print(c, level + delta_indent);
 206                         if (i != seq.size()-1)
 207                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 208                 }
 209                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 210                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 211                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 212                         overall_coeff.print(c, level + delta_indent);
 213                 }
 214                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 215 #if EXPAIRSEQ_USE_HASHTAB
 216                 c.s << std::string(level + delta_indent,' ')
 217                     << "hashtab size " << hashtabsize << std::endl;
 218                 if (hashtabsize == 0) return;
 219 #define MAXCOUNT 5
 220                 unsigned count[MAXCOUNT+1];
 221                 for (int i=0; i<MAXCOUNT+1; ++i)
 222                         count[i] = 0;
 223                 unsigned this_bin_fill;
 224                 unsigned cum_fill_sq = 0;
 225                 unsigned cum_fill = 0;
 226                 for (unsigned i=0; i<hashtabsize; ++i) {
 227                         this_bin_fill = 0;
 228                         if (hashtab[i].size() > 0) {
 229                                 c.s << std::string(level + delta_indent, ' ')
 230                                     << "bin " << i << " with entries ";
 231                                 for (epplist::const_iterator it=hashtab[i].begin();
 232                                      it!=hashtab[i].end(); ++it) {
 233                                         c.s << *it-seq.begin() << " ";
 234                                         ++this_bin_fill;
 235                                 }
 236                                 os << std::endl;
 237                                 cum_fill += this_bin_fill;
 238                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 239                         }
 240                         if (this_bin_fill<MAXCOUNT)
 241                                 ++count[this_bin_fill];
 242                         else
 243                                 ++count[MAXCOUNT];
 244                 }
 245                 unsigned fact = 1;
 246                 double cum_prob = 0;
 247                 double lambda = (1.0*seq.size()) / hashtabsize;
 248                 for (int k=0; k<MAXCOUNT; ++k) {
 249                         if (k>0)
 250                                 fact *= k;
 251                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 252                         cum_prob += prob;
 253                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 254                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 255                             << int(prob*1000)/10.0 << ")" << std::endl;
 256                 }
 257                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 258                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 259                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 260
 261                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 262                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 263                     << std::endl;
 264                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 265                     << (1.0*cum_fill)/hashtabsize
 266                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 267 #endif // EXPAIRSEQ_USE_HASHTAB
 268
 269         } else {
 270                 c.s << "[[";
 271                 printseq(c, ',', precedence(), level);
 272                 c.s << "]]";
 273         }
 274 }
 275
 276 bool expairseq::info(unsigned inf) const
 277 {
 278         return inherited::info(inf);
 279 }
 280
 281 unsigned expairseq::nops() const
 282 {
 283         if (overall_coeff.is_equal(default_overall_coeff()))
 284                 return seq.size();
 285         else
 286                 return seq.size()+1;
 287 }
 288
 289 ex expairseq::op(int i) const
 290 {
 291         if (unsigned(i)<seq.size())
 292                 return recombine_pair_to_ex(seq[i]);
 293         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 294         return overall_coeff;
 295 }
 296
 297 ex &expairseq::let_op(int i)
 298 {
 299         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 300 }
 301
 302 ex expairseq::map(map_func f) const
 303 {
 304         epvector *v = new epvector;
 305         v->reserve(seq.size());
 306
 307         epvector::const_iterator cit = seq.begin(), last = seq.end();
 308         while (cit != last) {
 309                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 310                 cit++;
 311         }
 312
 313         return thisexpairseq(v, f(overall_coeff));
 314 }
 315
 316 ex expairseq::eval(int level) const
 317 {
 318         if ((level==1) && (flags &status_flags::evaluated))
 319                 return *this;
 320
 321         epvector *vp = evalchildren(level);
 322         if (vp==0)
 323                 return this->hold();
 324
 325         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 326 }
 327
 328 ex expairseq::evalf(int level) const
 329 {
 330         return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
 331 }
 332
 333 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 334 {
 335         ex n = thisexpairseq(normalchildren(level),overall_coeff);
 336         return n.bp->basic::normal(sym_lst,repl_lst,level);
 337 }
 338
 339 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 340 {
 341         // This differs from basic::match() because we want "a+b+c+d" to
 342         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 343
 344         if (tinfo() == pattern.bp->tinfo()) {
 345
 346                 // Check whether global wildcard (one that matches the "rest of the
 347                 // expression", like "*" above) is present
 348                 bool has_global_wildcard = false;
 349                 ex global_wildcard;
 350                 for (unsigned int i=0; i<pattern.nops(); i++) {
 351                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 352                                 has_global_wildcard = true;
 353                                 global_wildcard = pattern.op(i);
 354                                 break;
 355                         }
 356                 }
 357
 358                 // Unfortunately, this is an O(N^2) operation because we can't
 359                 // sort the pattern in a useful way...
 360
 361                 // Chop into terms
 362                 exvector ops;
 363                 ops.reserve(nops());
 364                 for (unsigned i=0; i<nops(); i++)
 365                         ops.push_back(op(i));
 366
 367                 // Now, for every term of the pattern, look for a matching term in
 368                 // the expression and remove the match
 369                 for (unsigned i=0; i<pattern.nops(); i++) {
 370                         ex p = pattern.op(i);
 371                         if (has_global_wildcard && p.is_equal(global_wildcard))
 372                                 continue;
 373                         exvector::iterator it = ops.begin(), itend = ops.end();
 374                         while (it != itend) {
 375                                 if (it->match(p, repl_lst)) {
 376                                         ops.erase(it);
 377                                         goto found;
 378                                 }
 379                                 it++;
 380                         }
 381                         return false; // no match found
 382 found:          ;
 383                 }
 384
 385                 if (has_global_wildcard) {
 386
 387                         // Assign all the remaining terms to the global wildcard (unless
 388                         // it has already been matched before, in which case the matches
 389                         // must be equal)
 390                         epvector *vp = new epvector();
 391                         vp->reserve(ops.size());
 392                         for (unsigned i=0; i<ops.size(); i++)
 393                                 vp->push_back(split_ex_to_pair(ops[i]));
 394                         ex rest = thisexpairseq(vp, default_overall_coeff());
 395                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 396                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 397                                         return rest.is_equal(*repl_lst.op(i).op(1).bp);
 398                         }
 399                         repl_lst.append(global_wildcard == rest);
 400                         return true;
 401
 402                 } else {
 403
 404                         // No global wildcard, then the match fails if there are any
 405                         // unmatched terms left
 406                         return ops.empty();
 407                 }
 408         }
 409         return inherited::match(pattern, repl_lst);
 410 }
 411
 412 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 413 {
 414         epvector *vp = subschildren(ls, lr, no_pattern);
 415         if (vp)
 416                 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
 417         else
 418                 return basic::subs(ls, lr, no_pattern);
 419 }
 420
 421 // protected
 422
 423 /** Implementation of ex::diff() for an expairseq.
 424  *  It differentiates all elements of the sequence.
 425  *  @see ex::diff */
 426 ex expairseq::derivative(const symbol &s) const
 427 {
 428         return thisexpairseq(diffchildren(s),overall_coeff);
 429 }
 430
 431 int expairseq::compare_same_type(const basic &other) const
 432 {
 433         GINAC_ASSERT(is_of_type(other, expairseq));
 434         const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
 435
 436         int cmpval;
 437
 438         // compare number of elements
 439         if (seq.size() != o.seq.size())
 440                 return (seq.size()<o.seq.size()) ? -1 : 1;
 441
 442         // compare overall_coeff
 443         cmpval = overall_coeff.compare(o.overall_coeff);
 444         if (cmpval!=0)
 445                 return cmpval;
 446
 447 #if EXPAIRSEQ_USE_HASHTAB
 448         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 449         if (hashtabsize==0) {
 450 #endif // EXPAIRSEQ_USE_HASHTAB
 451                 epvector::const_iterator cit1 = seq.begin();
 452                 epvector::const_iterator cit2 = o.seq.begin();
 453                 epvector::const_iterator last1 = seq.end();
 454                 epvector::const_iterator last2 = o.seq.end();
 455
 456                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 457                         cmpval = (*cit1).compare(*cit2);
 458                         if (cmpval!=0) return cmpval;
 459                 }
 460
 461                 GINAC_ASSERT(cit1==last1);
 462                 GINAC_ASSERT(cit2==last2);
 463
 464                 return 0;
 465 #if EXPAIRSEQ_USE_HASHTAB
 466         }
 467
 468         // compare number of elements in each hashtab entry
 469         for (unsigned i=0; i<hashtabsize; ++i) {
 470                 unsigned cursize=hashtab[i].size();
 471                 if (cursize != o.hashtab[i].size())
 472                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 473         }
 474
 475         // compare individual (sorted) hashtab entries
 476         for (unsigned i=0; i<hashtabsize; ++i) {
 477                 unsigned sz = hashtab[i].size();
 478                 if (sz>0) {
 479                         const epplist &eppl1 = hashtab[i];
 480                         const epplist &eppl2 = o.hashtab[i];
 481                         epplist::const_iterator it1 = eppl1.begin();
 482                         epplist::const_iterator it2 = eppl2.begin();
 483                         while (it1!=eppl1.end()) {
 484                                 cmpval = (*(*it1)).compare(*(*it2));
 485                                 if (cmpval!=0)
 486                                         return cmpval;
 487                                 ++it1;
 488                                 ++it2;
 489                         }
 490                 }
 491         }
 492
 493         return 0; // equal
 494 #endif // EXPAIRSEQ_USE_HASHTAB
 495 }
 496
 497 bool expairseq::is_equal_same_type(const basic &other) const
 498 {
 499         const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
 500
 501         // compare number of elements
 502         if (seq.size()!=o.seq.size())
 503                 return false;
 504
 505         // compare overall_coeff
 506         if (!overall_coeff.is_equal(o.overall_coeff))
 507                 return false;
 508
 509 #if EXPAIRSEQ_USE_HASHTAB
 510         // compare number of elements in each hashtab entry
 511         if (hashtabsize!=o.hashtabsize) {
 512                 std::cout << "this:" << std::endl;
 513                 print(print_tree(std::cout));
 514                 std::cout << "other:" << std::endl;
 515                 other.print(print_tree(std::cout));
 516         }
 517
 518         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 519
 520         if (hashtabsize==0) {
 521 #endif // EXPAIRSEQ_USE_HASHTAB
 522                 epvector::const_iterator cit1 = seq.begin();
 523                 epvector::const_iterator cit2 = o.seq.begin();
 524                 epvector::const_iterator last1 = seq.end();
 525
 526                 while (cit1!=last1) {
 527                         if (!(*cit1).is_equal(*cit2)) return false;
 528                         ++cit1;
 529                         ++cit2;
 530                 }
 531
 532                 return true;
 533 #if EXPAIRSEQ_USE_HASHTAB
 534         }
 535
 536         for (unsigned i=0; i<hashtabsize; ++i) {
 537                 if (hashtab[i].size() != o.hashtab[i].size())
 538                         return false;
 539         }
 540
 541         // compare individual sorted hashtab entries
 542         for (unsigned i=0; i<hashtabsize; ++i) {
 543                 unsigned sz = hashtab[i].size();
 544                 if (sz>0) {
 545                         const epplist &eppl1 = hashtab[i];
 546                         const epplist &eppl2 = o.hashtab[i];
 547                         epplist::const_iterator it1 = eppl1.begin();
 548                         epplist::const_iterator it2 = eppl2.begin();
 549                         while (it1!=eppl1.end()) {
 550                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 551                                 ++it1;
 552                                 ++it2;
 553                         }
 554                 }
 555         }
 556
 557         return true;
 558 #endif // EXPAIRSEQ_USE_HASHTAB
 559 }
 560
 561 unsigned expairseq::return_type(void) const
 562 {
 563         return return_types::noncommutative_composite;
 564 }
 565
 566 unsigned expairseq::calchash(void) const
 567 {
 568         unsigned v = golden_ratio_hash(tinfo());
 569         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 570 #if !EXPAIRSEQ_USE_HASHTAB
 571                 v = rotate_left_31(v); // rotation would spoil commutativity
 572 #endif // EXPAIRSEQ_USE_HASHTAB
 573                 v ^= cit->rest.gethash();
 574 #if !EXPAIRSEQ_USE_HASHTAB
 575                 v = rotate_left_31(v);
 576                 v ^= cit->coeff.gethash();
 577 #endif // EXPAIRSEQ_USE_HASHTAB
 578         }
 579
 580         v ^= overall_coeff.gethash();
 581         v &= 0x7FFFFFFFU;
 582
 583         // store calculated hash value only if object is already evaluated
 584         if (flags &status_flags::evaluated) {
 585                 setflag(status_flags::hash_calculated);
 586                 hashvalue = v;
 587         }
 588
 589         return v;
 590 }
 591
 592 ex expairseq::expand(unsigned options) const
 593 {
 594         epvector *vp = expandchildren(options);
 595         if (vp==0) {
 596                 // the terms have not changed, so it is safe to declare this expanded
 597                 setflag(status_flags::expanded);
 598                 return *this;
 599         }
 600
 601         return thisexpairseq(vp,overall_coeff);
 602 }
 603
 604 //////////
 605 // new virtual functions which can be overridden by derived classes
 606 //////////
 607
 608 // protected
 609
 610 /** Create an object of this type.
 611  *  This method works similar to a constructor.  It is useful because expairseq
 612  *  has (at least) two possible different semantics but we want to inherit
 613  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 614  *  has to create a new one of the same semantics, which cannot be done by a
 615  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 616  *  order for this trick to work a derived class must of course override this
 617  *  definition. */
 618 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 619 {
 620         return expairseq(v,oc);
 621 }
 622
 623 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 624 {
 625         return expairseq(vp,oc);
 626 }
 627
 628 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 629 {
 630         c.s << "[[";
 631         p.rest.bp->print(c, precedence());
 632         c.s << ",";
 633         p.coeff.bp->print(c, precedence());
 634         c.s << "]]";
 635 }
 636
 637 void expairseq::printseq(const print_context & c, char delim,
 638                          unsigned this_precedence,
 639                          unsigned upper_precedence) const
 640 {
 641         if (this_precedence <= upper_precedence)
 642                 c.s << "(";
 643         epvector::const_iterator it, it_last = seq.end() - 1;
 644         for (it=seq.begin(); it!=it_last; ++it) {
 645                 printpair(c, *it, this_precedence);
 646                 c.s << delim;
 647         }
 648         printpair(c, *it, this_precedence);
 649         if (!overall_coeff.is_equal(default_overall_coeff())) {
 650                 c.s << delim;
 651                 overall_coeff.print(c, this_precedence);
 652         }
 653
 654         if (this_precedence <= upper_precedence)
 655                 c.s << ")";
 656 }
 657
 658
 659 /** Form an expair from an ex, using the corresponding semantics.
 660  *  @see expairseq::recombine_pair_to_ex() */
 661 expair expairseq::split_ex_to_pair(const ex &e) const
 662 {
 663         return expair(e,_ex1());
 664 }
 665
 666
 667 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 668                                                 const ex &c) const
 669 {
 670         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 671
 672         return expair(e,c);
 673 }
 674
 675
 676 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 677                                                   const ex &c) const
 678 {
 679         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 680         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 681
 682         return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 683 }
 684
 685
 686 /** Form an ex out of an expair, using the corresponding semantics.
 687  *  @see expairseq::split_ex_to_pair() */
 688 ex expairseq::recombine_pair_to_ex(const expair &p) const
 689 {
 690         return lst(p.rest,p.coeff);
 691 }
 692
 693 bool expairseq::expair_needs_further_processing(epp it)
 694 {
 695 #if EXPAIRSEQ_USE_HASHTAB
 696         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 697 #endif // EXPAIRSEQ_USE_HASHTAB
 698         return false;
 699 }
 700
 701 ex expairseq::default_overall_coeff(void) const
 702 {
 703         return _ex0();
 704 }
 705
 706 void expairseq::combine_overall_coeff(const ex &c)
 707 {
 708         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 709         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 710         overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 711 }
 712
 713 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 714 {
 715         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 716         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 717         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 718         overall_coeff = ex_to_numeric(overall_coeff).
 719                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 720 }
 721
 722 bool expairseq::can_make_flat(const expair &p) const
 723 {
 724         return true;
 725 }
 726
 727
 728 //////////
 729 // non-virtual functions in this class
 730 //////////
 731
 732 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 733 {
 734         exvector v;
 735         v.reserve(2);
 736         v.push_back(lh);
 737         v.push_back(rh);
 738         construct_from_exvector(v);
 739 #if EXPAIRSEQ_USE_HASHTAB
 740         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 741         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 742 #endif // EXPAIRSEQ_USE_HASHTAB
 743 }
 744
 745 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 746 {
 747         if (lh.bp->tinfo()==tinfo()) {
 748                 if (rh.bp->tinfo()==tinfo()) {
 749 #if EXPAIRSEQ_USE_HASHTAB
 750                         unsigned totalsize = ex_to_expairseq(lh).seq.size() +
 751                                              ex_to_expairseq(rh).seq.size();
 752                         if (calc_hashtabsize(totalsize)!=0) {
 753                                 construct_from_2_ex_via_exvector(lh,rh);
 754                         } else {
 755 #endif // EXPAIRSEQ_USE_HASHTAB
 756                                 construct_from_2_expairseq(ex_to_expairseq(lh),
 757                                                            ex_to_expairseq(rh));
 758 #if EXPAIRSEQ_USE_HASHTAB
 759                         }
 760 #endif // EXPAIRSEQ_USE_HASHTAB
 761                         return;
 762                 } else {
 763 #if EXPAIRSEQ_USE_HASHTAB
 764                         unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
 765                         if (calc_hashtabsize(totalsize)!=0) {
 766                                 construct_from_2_ex_via_exvector(lh, rh);
 767                         } else {
 768 #endif // EXPAIRSEQ_USE_HASHTAB
 769                                 construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
 770 #if EXPAIRSEQ_USE_HASHTAB
 771                         }
 772 #endif // EXPAIRSEQ_USE_HASHTAB
 773                         return;
 774                 }
 775         } else if (rh.bp->tinfo()==tinfo()) {
 776 #if EXPAIRSEQ_USE_HASHTAB
 777                 unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 778                 if (calc_hashtabsize(totalsize)!=0) {
 779                         construct_from_2_ex_via_exvector(lh,rh);
 780                 } else {
 781 #endif // EXPAIRSEQ_USE_HASHTAB
 782                         construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 783 #if EXPAIRSEQ_USE_HASHTAB
 784                 }
 785 #endif // EXPAIRSEQ_USE_HASHTAB
 786                 return;
 787         }
 788
 789 #if EXPAIRSEQ_USE_HASHTAB
 790         if (calc_hashtabsize(2)!=0) {
 791                 construct_from_2_ex_via_exvector(lh,rh);
 792                 return;
 793         }
 794         hashtabsize = 0;
 795 #endif // EXPAIRSEQ_USE_HASHTAB
 796
 797         if (is_ex_exactly_of_type(lh,numeric)) {
 798                 if (is_ex_exactly_of_type(rh,numeric)) {
 799                         combine_overall_coeff(lh);
 800                         combine_overall_coeff(rh);
 801                 } else {
 802                         combine_overall_coeff(lh);
 803                         seq.push_back(split_ex_to_pair(rh));
 804                 }
 805         } else {
 806                 if (is_ex_exactly_of_type(rh,numeric)) {
 807                         combine_overall_coeff(rh);
 808                         seq.push_back(split_ex_to_pair(lh));
 809                 } else {
 810                         expair p1 = split_ex_to_pair(lh);
 811                         expair p2 = split_ex_to_pair(rh);
 812
 813                         int cmpval = p1.rest.compare(p2.rest);
 814                         if (cmpval==0) {
 815                                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 816                                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 817                                         // no further processing is necessary, since this
 818                                         // one element will usually be recombined in eval()
 819                                         seq.push_back(p1);
 820                                 }
 821                         } else {
 822                                 seq.reserve(2);
 823                                 if (cmpval<0) {
 824                                         seq.push_back(p1);
 825                                         seq.push_back(p2);
 826                                 } else {
 827                                         seq.push_back(p2);
 828                                         seq.push_back(p1);
 829                                 }
 830                         }
 831                 }
 832         }
 833 }
 834
 835 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 836                                                                                    const expairseq &s2)
 837 {
 838         combine_overall_coeff(s1.overall_coeff);
 839         combine_overall_coeff(s2.overall_coeff);
 840
 841         epvector::const_iterator first1 = s1.seq.begin();
 842         epvector::const_iterator last1 = s1.seq.end();
 843         epvector::const_iterator first2 = s2.seq.begin();
 844         epvector::const_iterator last2 = s2.seq.end();
 845
 846         seq.reserve(s1.seq.size()+s2.seq.size());
 847
 848         bool needs_further_processing=false;
 849
 850         while (first1!=last1 && first2!=last2) {
 851                 int cmpval = (*first1).rest.compare((*first2).rest);
 852                 if (cmpval==0) {
 853                         // combine terms
 854                         const numeric &newcoeff = ex_to_numeric((*first1).coeff).
 855                                                    add(ex_to_numeric((*first2).coeff));
 856                         if (!newcoeff.is_zero()) {
 857                                 seq.push_back(expair((*first1).rest,newcoeff));
 858                                 if (expair_needs_further_processing(seq.end()-1)) {
 859                                         needs_further_processing = true;
 860                                 }
 861                         }
 862                         ++first1;
 863                         ++first2;
 864                 } else if (cmpval<0) {
 865                         seq.push_back(*first1);
 866                         ++first1;
 867                 } else {
 868                         seq.push_back(*first2);
 869                         ++first2;
 870                 }
 871         }
 872
 873         while (first1!=last1) {
 874                 seq.push_back(*first1);
 875                 ++first1;
 876         }
 877         while (first2!=last2) {
 878                 seq.push_back(*first2);
 879                 ++first2;
 880         }
 881
 882         if (needs_further_processing) {
 883                 epvector v = seq;
 884                 seq.clear();
 885                 construct_from_epvector(v);
 886         }
 887 }
 888
 889 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 890                                                                                         const ex &e)
 891 {
 892         combine_overall_coeff(s.overall_coeff);
 893         if (is_ex_exactly_of_type(e,numeric)) {
 894                 combine_overall_coeff(e);
 895                 seq = s.seq;
 896                 return;
 897         }
 898
 899         epvector::const_iterator first = s.seq.begin();
 900         epvector::const_iterator last = s.seq.end();
 901         expair p = split_ex_to_pair(e);
 902
 903         seq.reserve(s.seq.size()+1);
 904         bool p_pushed = false;
 905
 906         bool needs_further_processing=false;
 907
 908         // merge p into s.seq
 909         while (first!=last) {
 910                 int cmpval=(*first).rest.compare(p.rest);
 911                 if (cmpval==0) {
 912                         // combine terms
 913                         const numeric &newcoeff = ex_to_numeric((*first).coeff).
 914                                                    add(ex_to_numeric(p.coeff));
 915                         if (!newcoeff.is_zero()) {
 916                                 seq.push_back(expair((*first).rest,newcoeff));
 917                                 if (expair_needs_further_processing(seq.end()-1)) {
 918                                         needs_further_processing = true;
 919                                 }
 920                         }
 921                         ++first;
 922                         p_pushed = true;
 923                         break;
 924                 } else if (cmpval<0) {
 925                         seq.push_back(*first);
 926                         ++first;
 927                 } else {
 928                         seq.push_back(p);
 929                         p_pushed = true;
 930                         break;
 931                 }
 932         }
 933
 934         if (p_pushed) {
 935                 // while loop exited because p was pushed, now push rest of s.seq
 936                 while (first!=last) {
 937                         seq.push_back(*first);
 938                         ++first;
 939                 }
 940         } else {
 941                 // while loop exited because s.seq was pushed, now push p
 942                 seq.push_back(p);
 943         }
 944
 945         if (needs_further_processing) {
 946                 epvector v = seq;
 947                 seq.clear();
 948                 construct_from_epvector(v);
 949         }
 950 }
 951
 952 void expairseq::construct_from_exvector(const exvector &v)
 953 {
 954         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 955         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 956         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 957         //                  (same for (+,*) -> (*,^)
 958
 959         make_flat(v);
 960 #if EXPAIRSEQ_USE_HASHTAB
 961         combine_same_terms();
 962 #else
 963         canonicalize();
 964         combine_same_terms_sorted_seq();
 965 #endif // EXPAIRSEQ_USE_HASHTAB
 966         return;
 967 }
 968
 969 void expairseq::construct_from_epvector(const epvector &v)
 970 {
 971         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 972         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 973         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 974         //                  (same for (+,*) -> (*,^)
 975
 976         make_flat(v);
 977 #if EXPAIRSEQ_USE_HASHTAB
 978         combine_same_terms();
 979 #else
 980         canonicalize();
 981         combine_same_terms_sorted_seq();
 982 #endif // EXPAIRSEQ_USE_HASHTAB
 983         return;
 984 }
 985
 986 /** Combine this expairseq with argument exvector.
 987  *  It cares for associativity as well as for special handling of numerics. */
 988 void expairseq::make_flat(const exvector &v)
 989 {
 990         exvector::const_iterator cit;
 991
 992         // count number of operands which are of same expairseq derived type
 993         // and their cumulative number of operands
 994         int nexpairseqs = 0;
 995         int noperands = 0;
 996
 997         cit = v.begin();
 998         while (cit!=v.end()) {
 999                 if (cit->bp->tinfo()==this->tinfo()) {
1000                         ++nexpairseqs;
1001                         noperands += ex_to_expairseq(*cit).seq.size();
1002                 }
1003                 ++cit;
1004         }
1005
1006         // reserve seq and coeffseq which will hold all operands
1007         seq.reserve(v.size()+noperands-nexpairseqs);
1008
1009         // copy elements and split off numerical part
1010         cit = v.begin();
1011         while (cit!=v.end()) {
1012                 if (cit->bp->tinfo()==this->tinfo()) {
1013                         const expairseq &subseqref = ex_to_expairseq(*cit);
1014                         combine_overall_coeff(subseqref.overall_coeff);
1015                         epvector::const_iterator cit_s = subseqref.seq.begin();
1016                         while (cit_s!=subseqref.seq.end()) {
1017                                 seq.push_back(*cit_s);
1018                                 ++cit_s;
1019                         }
1020                 } else {
1021                         if (is_ex_exactly_of_type(*cit,numeric))
1022                                 combine_overall_coeff(*cit);
1023                         else
1024                                 seq.push_back(split_ex_to_pair(*cit));
1025                 }
1026                 ++cit;
1027         }
1028
1029         return;
1030 }
1031
1032 /** Combine this expairseq with argument epvector.
1033  *  It cares for associativity as well as for special handling of numerics. */
1034 void expairseq::make_flat(const epvector &v)
1035 {
1036         epvector::const_iterator cit;
1037
1038         // count number of operands which are of same expairseq derived type
1039         // and their cumulative number of operands
1040         int nexpairseqs = 0;
1041         int noperands = 0;
1042
1043         cit = v.begin();
1044         while (cit!=v.end()) {
1045                 if (cit->rest.bp->tinfo()==this->tinfo()) {
1046                         ++nexpairseqs;
1047                         noperands += ex_to_expairseq((*cit).rest).seq.size();
1048                 }
1049                 ++cit;
1050         }
1051
1052         // reserve seq and coeffseq which will hold all operands
1053         seq.reserve(v.size()+noperands-nexpairseqs);
1054
1055         // copy elements and split off numerical part
1056         cit = v.begin();
1057         while (cit!=v.end()) {
1058                 if (cit->rest.bp->tinfo()==this->tinfo() &&
1059                     this->can_make_flat(*cit)) {
1060                         const expairseq &subseqref = ex_to_expairseq((*cit).rest);
1061                         combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
1062                                                             ex_to_numeric((*cit).coeff));
1063                         epvector::const_iterator cit_s = subseqref.seq.begin();
1064                         while (cit_s!=subseqref.seq.end()) {
1065                                 seq.push_back(expair((*cit_s).rest,
1066                                                      ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
1067                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1068                                 //                                              (*cit).coeff));
1069                                 ++cit_s;
1070                         }
1071                 } else {
1072                         if (cit->is_canonical_numeric())
1073                                 combine_overall_coeff(cit->rest);
1074                         else
1075                                 seq.push_back(*cit);
1076                 }
1077                 ++cit;
1078         }
1079         return;
1080 }
1081
1082 /** Brings this expairseq into a sorted (canonical) form. */
1083 void expairseq::canonicalize(void)
1084 {
1085         // canonicalize
1086         sort(seq.begin(),seq.end(),expair_is_less());
1087         return;
1088 }
1089
1090
1091 /** Compact a presorted expairseq by combining all matching expairs to one
1092  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1093  *  instance. */
1094 void expairseq::combine_same_terms_sorted_seq(void)
1095 {
1096         bool needs_further_processing = false;
1097
1098         if (seq.size()>1) {
1099                 epvector::iterator itin1 = seq.begin();
1100                 epvector::iterator itin2 = itin1+1;
1101                 epvector::iterator itout = itin1;
1102                 epvector::iterator last = seq.end();
1103                 // must_copy will be set to true the first time some combination is
1104                 // possible from then on the sequence has changed and must be compacted
1105                 bool must_copy = false;
1106                 while (itin2!=last) {
1107                         if ((*itin1).rest.compare((*itin2).rest)==0) {
1108                                 (*itin1).coeff = ex_to_numeric((*itin1).coeff).
1109                                                  add_dyn(ex_to_numeric((*itin2).coeff));
1110                                 if (expair_needs_further_processing(itin1))
1111                                         needs_further_processing = true;
1112                                 must_copy = true;
1113                         } else {
1114                                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1115                                         if (must_copy)
1116                                                 *itout = *itin1;
1117                                         ++itout;
1118                                 }
1119                                 itin1 = itin2;
1120                         }
1121                         ++itin2;
1122                 }
1123                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1124                         if (must_copy)
1125                                 *itout = *itin1;
1126                         ++itout;
1127                 }
1128                 if (itout!=last)
1129                         seq.erase(itout,last);
1130         }
1131
1132         if (needs_further_processing) {
1133                 epvector v = seq;
1134                 seq.clear();
1135                 construct_from_epvector(v);
1136         }
1137         return;
1138 }
1139
1140 #if EXPAIRSEQ_USE_HASHTAB
1141
1142 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1143 {
1144         unsigned size;
1145         unsigned nearest_power_of_2 = 1 << log2(sz);
1146         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1147         //  size = nearest_power_of_2*hashtabfactor;
1148         size = nearest_power_of_2/hashtabfactor;
1149         if (size<minhashtabsize)
1150                 return 0;
1151         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1152         // hashtabsize must be a power of 2
1153         GINAC_ASSERT((1U << log2(size))==size);
1154         return size;
1155 }
1156
1157 unsigned expairseq::calc_hashindex(const ex &e) const
1158 {
1159         // calculate hashindex
1160         unsigned hash = e.gethash();
1161         unsigned hashindex;
1162         if (is_a_numeric_hash(hash)) {
1163                 hashindex = hashmask;
1164         } else {
1165                 hashindex = hash &hashmask;
1166                 // last hashtab entry is reserved for numerics
1167                 if (hashindex==hashmask) hashindex = 0;
1168         }
1169         GINAC_ASSERT(hashindex>=0);
1170         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1171         return hashindex;
1172 }
1173
1174 void expairseq::shrink_hashtab(void)
1175 {
1176         unsigned new_hashtabsize;
1177         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1178                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1179                 if (new_hashtabsize==0) {
1180                         hashtab.clear();
1181                         hashtabsize = 0;
1182                         canonicalize();
1183                         return;
1184                 }
1185
1186                 // shrink by a factor of 2
1187                 unsigned half_hashtabsize = hashtabsize/2;
1188                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1189                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1190                 // special treatment for numeric hashes
1191                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1192                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1193                 hashtab.resize(half_hashtabsize);
1194                 hashtabsize = half_hashtabsize;
1195                 hashmask = hashtabsize-1;
1196         }
1197 }
1198
1199 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1200 {
1201         if (hashtabsize==0)
1202                 return; // nothing to do
1203
1204         // calculate hashindex of element to be deleted
1205         unsigned hashindex = calc_hashindex((*element).rest);
1206
1207         // find it in hashtab and remove it
1208         epplist &eppl = hashtab[hashindex];
1209         epplist::iterator epplit = eppl.begin();
1210         bool erased = false;
1211         while (epplit!=eppl.end()) {
1212                 if (*epplit == element) {
1213                         eppl.erase(epplit);
1214                         erased = true;
1215                         break;
1216                 }
1217                 ++epplit;
1218         }
1219         if (!erased) {
1220                 printtree(cout,0);
1221                 cout << "tried to erase " << element-seq.begin() << std::endl;
1222                 cout << "size " << seq.end()-seq.begin() << std::endl;
1223
1224                 unsigned hashindex = calc_hashindex((*element).rest);
1225                 epplist &eppl = hashtab[hashindex];
1226                 epplist::iterator epplit=eppl.begin();
1227                 bool erased=false;
1228                 while (epplit!=eppl.end()) {
1229                         if (*epplit == element) {
1230                                 eppl.erase(epplit);
1231                                 erased = true;
1232                                 break;
1233                         }
1234                         ++epplit;
1235                 }
1236                 GINAC_ASSERT(erased);
1237         }
1238         GINAC_ASSERT(erased);
1239 }
1240
1241 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1242                                    epvector::iterator newpos)
1243 {
1244         GINAC_ASSERT(hashtabsize!=0);
1245
1246         // calculate hashindex of element which was moved
1247         unsigned hashindex=calc_hashindex((*newpos).rest);
1248
1249         // find it in hashtab and modify it
1250         epplist &eppl = hashtab[hashindex];
1251         epplist::iterator epplit = eppl.begin();
1252         while (epplit!=eppl.end()) {
1253                 if (*epplit == oldpos) {
1254                         *epplit = newpos;
1255                         break;
1256                 }
1257                 ++epplit;
1258         }
1259         GINAC_ASSERT(epplit!=eppl.end());
1260 }
1261
1262 void expairseq::sorted_insert(epplist &eppl, epp elem)
1263 {
1264         epplist::iterator current = eppl.begin();
1265         while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1266                 ++current;
1267         }
1268         eppl.insert(current,elem);
1269 }
1270
1271 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1272                                           epvector::iterator &last_non_zero,
1273                                           std::vector<bool> &touched,
1274                                           unsigned &number_of_zeroes)
1275 {
1276         epp current=seq.begin();
1277
1278         while (current!=first_numeric) {
1279                 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1280                         --first_numeric;
1281                         iter_swap(current,first_numeric);
1282                 } else {
1283                         // calculate hashindex
1284                         unsigned currenthashindex = calc_hashindex((*current).rest);
1285
1286                         // test if there is already a matching expair in the hashtab-list
1287                         epplist &eppl=hashtab[currenthashindex];
1288                         epplist::iterator epplit = eppl.begin();
1289                         while (epplit!=eppl.end()) {
1290                                 if ((*current).rest.is_equal((*(*epplit)).rest))
1291                                         break;
1292                                 ++epplit;
1293                         }
1294                         if (epplit==eppl.end()) {
1295                                 // no matching expair found, append this to end of list
1296                                 sorted_insert(eppl,current);
1297                                 ++current;
1298                         } else {
1299                                 // epplit points to a matching expair, combine it with current
1300                                 (*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
1301                                                      add_dyn(ex_to_numeric((*current).coeff));
1302
1303                                 // move obsolete current expair to end by swapping with last_non_zero element
1304                                 // if this was a numeric, it is swapped with the expair before first_numeric
1305                                 iter_swap(current,last_non_zero);
1306                                 --first_numeric;
1307                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1308                                 --last_non_zero;
1309                                 ++number_of_zeroes;
1310                                 // test if combined term has coeff 0 and can be removed is done later
1311                                 touched[(*epplit)-seq.begin()]=true;
1312                         }
1313                 }
1314         }
1315 }
1316
1317 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1318                                    epvector::iterator &last_non_zero,
1319                                    std::vector<bool> &touched,
1320                                    unsigned &number_of_zeroes)
1321 {
1322         // move terms with coeff 0 to end and remove them from hashtab
1323         // check only those elements which have been touched
1324         epp current = seq.begin();
1325         unsigned i = 0;
1326         while (current!=first_numeric) {
1327                 if (!touched[i]) {
1328                         ++current;
1329                         ++i;
1330                 } else if (!ex_to_numeric((*current).coeff).is_zero()) {
1331                         ++current;
1332                         ++i;
1333                 } else {
1334                         remove_hashtab_entry(current);
1335
1336                         // move element to the end, unless it is already at the end
1337                         if (current!=last_non_zero) {
1338                                 iter_swap(current,last_non_zero);
1339                                 --first_numeric;
1340                                 bool numeric_swapped=first_numeric!=last_non_zero;
1341                                 if (numeric_swapped) iter_swap(first_numeric,current);
1342                                 epvector::iterator changed_entry;
1343
1344                                 if (numeric_swapped)
1345                                         changed_entry = first_numeric;
1346                                 else
1347                                         changed_entry = last_non_zero;
1348
1349                                 --last_non_zero;
1350                                 ++number_of_zeroes;
1351
1352                                 if (first_numeric!=current) {
1353
1354                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1355                                         move_hashtab_entry(changed_entry,current);
1356                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1357                                 }
1358                         } else {
1359                                 --first_numeric;
1360                                 --last_non_zero;
1361                                 ++number_of_zeroes;
1362                         }
1363                 }
1364         }
1365         GINAC_ASSERT(i==current-seq.begin());
1366 }
1367
1368 /** True if one of the coeffs vanishes, otherwise false.
1369  *  This would be an invariant violation, so this should only be used for
1370  *  debugging purposes. */
1371 bool expairseq::has_coeff_0(void) const
1372 {
1373         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1374                 if ((*cit).coeff.is_zero())
1375                         return true;
1376         }
1377         return false;
1378 }
1379
1380 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1381                                                                                 epvector::const_iterator last_non_zero)
1382 {
1383         if (first_numeric==seq.end()) return; // no numerics
1384
1385         epvector::iterator current = first_numeric;
1386         epvector::const_iterator last = last_non_zero+1;
1387         while (current!=last) {
1388                 sorted_insert(hashtab[hashmask],current);
1389                 ++current;
1390         }
1391 }
1392
1393 void expairseq::combine_same_terms(void)
1394 {
1395         // combine same terms, drop term with coeff 0, move numerics to end
1396
1397         // calculate size of hashtab
1398         hashtabsize = calc_hashtabsize(seq.size());
1399
1400         // hashtabsize is a power of 2
1401         hashmask = hashtabsize-1;
1402
1403         // allocate hashtab
1404         hashtab.clear();
1405         hashtab.resize(hashtabsize);
1406
1407         if (hashtabsize==0) {
1408                 canonicalize();
1409                 combine_same_terms_sorted_seq();
1410                 GINAC_ASSERT(!has_coeff_0());
1411                 return;
1412         }
1413
1414         // iterate through seq, move numerics to end,
1415         // fill hashtab and combine same terms
1416         epvector::iterator first_numeric = seq.end();
1417         epvector::iterator last_non_zero = seq.end()-1;
1418
1419         std::vector<bool> touched;
1420         touched.reserve(seq.size());
1421         for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1422
1423         unsigned number_of_zeroes = 0;
1424
1425         GINAC_ASSERT(!has_coeff_0());
1426         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1427         /*
1428         cout << "in combine:" << std::endl;
1429         printtree(cout,0);
1430         cout << "size=" << seq.end() - seq.begin() << std::endl;
1431         cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1432         cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1433         for (unsigned i=0; i<seq.size(); ++i) {
1434                 if (touched[i]) cout << i << " is touched" << std::endl;
1435         }
1436         cout << "end in combine" << std::endl;
1437         */
1438
1439         // there should not be any terms with coeff 0 from the beginning,
1440         // so it should be safe to skip this step
1441         if (number_of_zeroes!=0) {
1442                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1443                 /*
1444                 cout << "in combine after drop:" << std::endl;
1445                 printtree(cout,0);
1446                 cout << "size=" << seq.end() - seq.begin() << std::endl;
1447                 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1448                 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1449                 for (unsigned i=0; i<seq.size(); ++i) {
1450                         if (touched[i]) cout << i << " is touched" << std::endl;
1451                 }
1452                 cout << "end in combine after drop" << std::endl;
1453                 */
1454         }
1455
1456         add_numerics_to_hashtab(first_numeric,last_non_zero);
1457
1458         // pop zero elements
1459         for (unsigned i=0; i<number_of_zeroes; ++i) {
1460                 seq.pop_back();
1461         }
1462
1463         // shrink hashtabsize to calculated value
1464         GINAC_ASSERT(!has_coeff_0());
1465
1466         shrink_hashtab();
1467
1468         GINAC_ASSERT(!has_coeff_0());
1469 }
1470
1471 #endif // EXPAIRSEQ_USE_HASHTAB
1472
1473 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1474  *  debugging or in assertions since being sorted is an invariance. */
1475 bool expairseq::is_canonical() const
1476 {
1477         if (seq.size() <= 1)
1478                 return 1;
1479
1480 #if EXPAIRSEQ_USE_HASHTAB
1481         if (hashtabsize > 0) return 1; // not canoncalized
1482 #endif // EXPAIRSEQ_USE_HASHTAB
1483
1484         epvector::const_iterator it = seq.begin();
1485         epvector::const_iterator it_last = it;
1486         for (++it; it!=seq.end(); it_last=it, ++it) {
1487                 if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
1488                         if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1489                                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1490                                 // double test makes it easier to set a breakpoint...
1491                                 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1492                                         !is_ex_exactly_of_type((*it).rest,numeric)) {
1493                                         printpair(std::clog, *it_last, 0);
1494                                         std::clog << ">";
1495                                         printpair(std::clog, *it, 0);
1496                                         std::clog << "\n";
1497                                         std::clog << "pair1:" << std::endl;
1498                                         (*it_last).rest.print(print_tree(std::clog));
1499                                         (*it_last).coeff.print(print_tree(std::clog));
1500                                         std::clog << "pair2:" << std::endl;
1501                                         (*it).rest.print(print_tree(std::clog));
1502                                         (*it).coeff.print(print_tree(std::clog));
1503                                         return 0;
1504                                 }
1505                         }
1506                 }
1507         }
1508         return 1;
1509 }
1510
1511
1512 /** Member-wise expand the expairs in this sequence.
1513  *
1514  *  @see expairseq::expand()
1515  *  @return pointer to epvector containing expanded pairs or zero pointer,
1516  *  if no members were changed. */
1517 epvector * expairseq::expandchildren(unsigned options) const
1518 {
1519         epvector::const_iterator last = seq.end();
1520         epvector::const_iterator cit = seq.begin();
1521         while (cit!=last) {
1522                 const ex &expanded_ex = (*cit).rest.expand(options);
1523                 if (!are_ex_trivially_equal((*cit).rest,expanded_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(expanded_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.expand(options),
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 evaluate the expairs in this sequence.
1555  *
1556  *  @see expairseq::eval()
1557  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1558  *  if no members were changed. */
1559 epvector * expairseq::evalchildren(int level) const
1560 {
1561         // returns a NULL pointer if nothing had to be evaluated
1562         // returns a pointer to a newly created epvector otherwise
1563         // (which has to be deleted somewhere else)
1564
1565         if (level==1)
1566                 return 0;
1567
1568         if (level == -max_recursion_level)
1569                 throw(std::runtime_error("max recursion level reached"));
1570
1571         --level;
1572         epvector::const_iterator last=seq.end();
1573         epvector::const_iterator cit=seq.begin();
1574         while (cit!=last) {
1575                 const ex &evaled_ex = (*cit).rest.eval(level);
1576                 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1577
1578                         // something changed, copy seq, eval and return it
1579                         epvector *s = new epvector;
1580                         s->reserve(seq.size());
1581
1582                         // copy parts of seq which are known not to have changed
1583                         epvector::const_iterator cit2=seq.begin();
1584                         while (cit2!=cit) {
1585                                 s->push_back(*cit2);
1586                                 ++cit2;
1587                         }
1588                         // copy first changed element
1589                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1590                                                                    (*cit2).coeff));
1591                         ++cit2;
1592                         // copy rest
1593                         while (cit2!=last) {
1594                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1595                                                                            (*cit2).coeff));
1596                                 ++cit2;
1597                         }
1598                         return s;
1599                 }
1600                 ++cit;
1601         }
1602
1603         return 0; // signalling nothing has changed
1604 }
1605
1606
1607 /** Member-wise evaluate numerically all expairs in this sequence.
1608  *
1609  *  @see expairseq::evalf()
1610  *  @return epvector with all entries evaluated numerically. */
1611 epvector expairseq::evalfchildren(int level) const
1612 {
1613         if (level==1)
1614                 return seq;
1615
1616         if (level==-max_recursion_level)
1617                 throw(std::runtime_error("max recursion level reached"));
1618
1619         epvector s;
1620         s.reserve(seq.size());
1621
1622         --level;
1623         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1624                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1625                                                           (*it).coeff.evalf(level)));
1626         }
1627         return s;
1628 }
1629
1630
1631 /** Member-wise normalize all expairs in this sequence.
1632  *
1633  *  @see expairseq::normal()
1634  *  @return epvector with all entries normalized. */
1635 epvector expairseq::normalchildren(int level) const
1636 {
1637         if (level==1)
1638                 return seq;
1639
1640         if (level==-max_recursion_level)
1641                 throw(std::runtime_error("max recursion level reached"));
1642
1643         epvector s;
1644         s.reserve(seq.size());
1645
1646         --level;
1647         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1648                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1649                                                           (*it).coeff));
1650         }
1651         return s;
1652 }
1653
1654
1655 /** Member-wise differentiate all expairs in this sequence.
1656  *
1657  *  @see expairseq::diff()
1658  *  @return epvector with all entries differentiated. */
1659 epvector expairseq::diffchildren(const symbol &y) const
1660 {
1661         epvector s;
1662         s.reserve(seq.size());
1663
1664         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1665                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1666                                                           (*it).coeff));
1667         }
1668         return s;
1669 }
1670
1671
1672 /** Member-wise substitute in this sequence.
1673  *
1674  *  @see expairseq::subs()
1675  *  @return pointer to epvector containing pairs after application of subs,
1676  *    or NULL pointer if no members were changed. */
1677 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1678 {
1679         GINAC_ASSERT(ls.nops()==lr.nops());
1680
1681         // The substitution is "complex" when any of the objects to be substituted
1682         // is a product or power. In this case we have to recombine the pairs
1683         // because the numeric coefficients may be part of the search pattern.
1684         bool complex_subs = false;
1685         for (unsigned i=0; i<ls.nops(); i++)
1686                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1687                         complex_subs = true;
1688                         break;
1689                 }
1690
1691         if (complex_subs) {
1692
1693                 // Substitute in the recombined pairs
1694                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1695                 while (cit != last) {
1696
1697                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1698                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1699                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1700
1701                                 // Something changed, copy seq, subs and return it
1702                                 epvector *s = new epvector;
1703                                 s->reserve(seq.size());
1704
1705                                 // Copy parts of seq which are known not to have changed
1706                                 s->insert(s->begin(), seq.begin(), cit);
1707
1708                                 // Copy first changed element
1709                                 s->push_back(split_ex_to_pair(subsed_ex));
1710                                 ++cit;
1711
1712                                 // Copy rest
1713                                 while (cit != last) {
1714                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1715                                         ++cit;
1716                                 }
1717                                 return s;
1718                         }
1719
1720                         ++cit;
1721                 }
1722
1723         } else {
1724
1725                 // Substitute only in the "rest" part of the pairs
1726                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1727                 while (cit != last) {
1728
1729                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1730                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1731
1732                                 // Something changed, copy seq, subs and return it
1733                                 epvector *s = new epvector;
1734                                 s->reserve(seq.size());
1735
1736                                 // Copy parts of seq which are known not to have changed
1737                                 s->insert(s->begin(), seq.begin(), cit);
1738
1739                                 // Copy first changed element
1740                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1741                                 ++cit;
1742
1743                                 // Copy rest
1744                                 while (cit != last) {
1745                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1746                                                                                    cit->coeff));
1747                                         ++cit;
1748                                 }
1749                                 return s;
1750                         }
1751
1752                         ++cit;
1753                 }
1754         }
1755
1756         // Nothing has changed
1757         return NULL;
1758 }
1759
1760 //////////
1761 // static member variables
1762 //////////
1763
1764 #if EXPAIRSEQ_USE_HASHTAB
1765 unsigned expairseq::maxhashtabsize = 0x4000000U;
1766 unsigned expairseq::minhashtabsize = 0x1000U;
1767 unsigned expairseq::hashtabfactor = 1;
1768 #endif // EXPAIRSEQ_USE_HASHTAB
1769
1770 } // namespace GiNaC