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::eval(int level) const
 303 {
 304         if ((level==1) && (flags &status_flags::evaluated))
 305                 return *this;
 306
 307         epvector *vp = evalchildren(level);
 308         if (vp==0)
 309                 return this->hold();
 310
 311         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 312 }
 313
 314 ex expairseq::evalf(int level) const
 315 {
 316         return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
 317 }
 318
 319 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 320 {
 321         ex n = thisexpairseq(normalchildren(level),overall_coeff);
 322         return n.bp->basic::normal(sym_lst,repl_lst,level);
 323 }
 324
 325 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 326 {
 327 //clog << "match " << *this << " with " << pattern << ", repl_lst = " << repl_lst << endl;
 328         // This differs from basic::match() because we want "a+b+c+d" to
 329         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 330
 331         if (tinfo() == pattern.bp->tinfo()) {
 332
 333                 // Check whether global wildcard (one that matches the "rest of the
 334                 // expression", like "*" above) is present
 335                 bool has_global_wildcard = false;
 336                 ex global_wildcard;
 337                 for (unsigned int i=0; i<pattern.nops(); i++) {
 338                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 339                                 has_global_wildcard = true;
 340                                 global_wildcard = pattern.op(i);
 341                                 break;
 342                         }
 343                 }
 344
 345                 // Unfortunately, this is an O(N^2) operation because we can't
 346                 // sort the pattern in a useful way...
 347
 348                 // Chop into terms
 349                 exvector ops;
 350                 ops.reserve(nops());
 351                 for (unsigned i=0; i<nops(); i++)
 352                         ops.push_back(op(i));
 353
 354                 // Now, for every term of the pattern, look for a matching term in
 355                 // the expression and remove the match
 356                 for (unsigned i=0; i<pattern.nops(); i++) {
 357                         ex p = pattern.op(i);
 358                         if (has_global_wildcard && p.is_equal(global_wildcard))
 359                                 continue;
 360                         exvector::iterator it = ops.begin(), itend = ops.end();
 361                         while (it != itend) {
 362                                 if (it->match(p, repl_lst)) {
 363                                         ops.erase(it);
 364                                         goto found;
 365                                 }
 366                                 it++;
 367                         }
 368                         return false; // no match found
 369 found:          ;
 370                 }
 371
 372                 if (has_global_wildcard) {
 373
 374                         // Assign all the remaining terms to the global wildcard (unless
 375                         // it has already been matched before, in which case the matches
 376                         // must be equal)
 377                         epvector *vp = new epvector();
 378                         vp->reserve(ops.size());
 379                         for (unsigned i=0; i<ops.size(); i++)
 380                                 vp->push_back(split_ex_to_pair(ops[i]));
 381                         ex rest = thisexpairseq(vp, default_overall_coeff());
 382                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 383                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 384                                         return rest.is_equal(*repl_lst.op(i).op(1).bp);
 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, bool no_pattern) const
 400 {
 401         epvector *vp = subschildren(ls, lr, no_pattern);
 402         if (vp)
 403                 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
 404         else
 405                 return basic::subs(ls, lr, no_pattern);
 406 }
 407
 408 // protected
 409
 410 /** Implementation of ex::diff() for an expairseq.
 411  *  It differentiates all elements of the sequence.
 412  *  @see ex::diff */
 413 ex expairseq::derivative(const symbol &s) const
 414 {
 415         return thisexpairseq(diffchildren(s),overall_coeff);
 416 }
 417
 418 int expairseq::compare_same_type(const basic &other) const
 419 {
 420         GINAC_ASSERT(is_of_type(other, expairseq));
 421         const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
 422
 423         int cmpval;
 424
 425         // compare number of elements
 426         if (seq.size() != o.seq.size())
 427                 return (seq.size()<o.seq.size()) ? -1 : 1;
 428
 429         // compare overall_coeff
 430         cmpval = overall_coeff.compare(o.overall_coeff);
 431         if (cmpval!=0)
 432                 return cmpval;
 433
 434 #if EXPAIRSEQ_USE_HASHTAB
 435         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 436         if (hashtabsize==0) {
 437 #endif // EXPAIRSEQ_USE_HASHTAB
 438                 epvector::const_iterator cit1 = seq.begin();
 439                 epvector::const_iterator cit2 = o.seq.begin();
 440                 epvector::const_iterator last1 = seq.end();
 441                 epvector::const_iterator last2 = o.seq.end();
 442
 443                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 444                         cmpval = (*cit1).compare(*cit2);
 445                         if (cmpval!=0) return cmpval;
 446                 }
 447
 448                 GINAC_ASSERT(cit1==last1);
 449                 GINAC_ASSERT(cit2==last2);
 450
 451                 return 0;
 452 #if EXPAIRSEQ_USE_HASHTAB
 453         }
 454
 455         // compare number of elements in each hashtab entry
 456         for (unsigned i=0; i<hashtabsize; ++i) {
 457                 unsigned cursize=hashtab[i].size();
 458                 if (cursize != o.hashtab[i].size())
 459                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 460         }
 461
 462         // compare individual (sorted) hashtab entries
 463         for (unsigned i=0; i<hashtabsize; ++i) {
 464                 unsigned sz = hashtab[i].size();
 465                 if (sz>0) {
 466                         const epplist &eppl1 = hashtab[i];
 467                         const epplist &eppl2 = o.hashtab[i];
 468                         epplist::const_iterator it1 = eppl1.begin();
 469                         epplist::const_iterator it2 = eppl2.begin();
 470                         while (it1!=eppl1.end()) {
 471                                 cmpval = (*(*it1)).compare(*(*it2));
 472                                 if (cmpval!=0)
 473                                         return cmpval;
 474                                 ++it1;
 475                                 ++it2;
 476                         }
 477                 }
 478         }
 479
 480         return 0; // equal
 481 #endif // EXPAIRSEQ_USE_HASHTAB
 482 }
 483
 484 bool expairseq::is_equal_same_type(const basic &other) const
 485 {
 486         const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
 487
 488         // compare number of elements
 489         if (seq.size()!=o.seq.size())
 490                 return false;
 491
 492         // compare overall_coeff
 493         if (!overall_coeff.is_equal(o.overall_coeff))
 494                 return false;
 495
 496 #if EXPAIRSEQ_USE_HASHTAB
 497         // compare number of elements in each hashtab entry
 498         if (hashtabsize!=o.hashtabsize) {
 499                 std::cout << "this:" << std::endl;
 500                 print(print_tree(std::cout));
 501                 std::cout << "other:" << std::endl;
 502                 other.print(print_tree(std::cout));
 503         }
 504
 505         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 506
 507         if (hashtabsize==0) {
 508 #endif // EXPAIRSEQ_USE_HASHTAB
 509                 epvector::const_iterator cit1 = seq.begin();
 510                 epvector::const_iterator cit2 = o.seq.begin();
 511                 epvector::const_iterator last1 = seq.end();
 512
 513                 while (cit1!=last1) {
 514                         if (!(*cit1).is_equal(*cit2)) return false;
 515                         ++cit1;
 516                         ++cit2;
 517                 }
 518
 519                 return true;
 520 #if EXPAIRSEQ_USE_HASHTAB
 521         }
 522
 523         for (unsigned i=0; i<hashtabsize; ++i) {
 524                 if (hashtab[i].size() != o.hashtab[i].size())
 525                         return false;
 526         }
 527
 528         // compare individual sorted hashtab entries
 529         for (unsigned i=0; i<hashtabsize; ++i) {
 530                 unsigned sz = hashtab[i].size();
 531                 if (sz>0) {
 532                         const epplist &eppl1 = hashtab[i];
 533                         const epplist &eppl2 = o.hashtab[i];
 534                         epplist::const_iterator it1 = eppl1.begin();
 535                         epplist::const_iterator it2 = eppl2.begin();
 536                         while (it1!=eppl1.end()) {
 537                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 538                                 ++it1;
 539                                 ++it2;
 540                         }
 541                 }
 542         }
 543
 544         return true;
 545 #endif // EXPAIRSEQ_USE_HASHTAB
 546 }
 547
 548 unsigned expairseq::return_type(void) const
 549 {
 550         return return_types::noncommutative_composite;
 551 }
 552
 553 unsigned expairseq::calchash(void) const
 554 {
 555         unsigned v = golden_ratio_hash(tinfo());
 556         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 557 #if !EXPAIRSEQ_USE_HASHTAB
 558                 v = rotate_left_31(v); // rotation would spoil commutativity
 559 #endif // EXPAIRSEQ_USE_HASHTAB
 560                 v ^= cit->rest.gethash();
 561 #if !EXPAIRSEQ_USE_HASHTAB
 562                 v = rotate_left_31(v);
 563                 v ^= cit->coeff.gethash();
 564 #endif // EXPAIRSEQ_USE_HASHTAB
 565         }
 566
 567         v ^= overall_coeff.gethash();
 568         v &= 0x7FFFFFFFU;
 569
 570         // store calculated hash value only if object is already evaluated
 571         if (flags &status_flags::evaluated) {
 572                 setflag(status_flags::hash_calculated);
 573                 hashvalue = v;
 574         }
 575
 576         return v;
 577 }
 578
 579 ex expairseq::expand(unsigned options) const
 580 {
 581         epvector *vp = expandchildren(options);
 582         if (vp==0) {
 583                 // the terms have not changed, so it is safe to declare this expanded
 584                 setflag(status_flags::expanded);
 585                 return *this;
 586         }
 587
 588         return thisexpairseq(vp,overall_coeff);
 589 }
 590
 591 //////////
 592 // new virtual functions which can be overridden by derived classes
 593 //////////
 594
 595 // protected
 596
 597 /** Create an object of this type.
 598  *  This method works similar to a constructor.  It is useful because expairseq
 599  *  has (at least) two possible different semantics but we want to inherit
 600  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 601  *  has to create a new one of the same semantics, which cannot be done by a
 602  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 603  *  order for this trick to work a derived class must of course override this
 604  *  definition. */
 605 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 606 {
 607         return expairseq(v,oc);
 608 }
 609
 610 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 611 {
 612         return expairseq(vp,oc);
 613 }
 614
 615 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 616 {
 617         c.s << "[[";
 618         p.rest.bp->print(c, precedence());
 619         c.s << ",";
 620         p.coeff.bp->print(c, precedence());
 621         c.s << "]]";
 622 }
 623
 624 void expairseq::printseq(const print_context & c, char delim,
 625                          unsigned this_precedence,
 626                          unsigned upper_precedence) const
 627 {
 628         if (this_precedence <= upper_precedence)
 629                 c.s << "(";
 630         epvector::const_iterator it, it_last = seq.end() - 1;
 631         for (it=seq.begin(); it!=it_last; ++it) {
 632                 printpair(c, *it, this_precedence);
 633                 c.s << delim;
 634         }
 635         printpair(c, *it, this_precedence);
 636         if (!overall_coeff.is_equal(default_overall_coeff())) {
 637                 c.s << delim;
 638                 overall_coeff.print(c, this_precedence);
 639         }
 640
 641         if (this_precedence <= upper_precedence)
 642                 c.s << ")";
 643 }
 644
 645
 646 /** Form an expair from an ex, using the corresponding semantics.
 647  *  @see expairseq::recombine_pair_to_ex() */
 648 expair expairseq::split_ex_to_pair(const ex &e) const
 649 {
 650         return expair(e,_ex1());
 651 }
 652
 653
 654 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 655                                                 const ex &c) const
 656 {
 657         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 658
 659         return expair(e,c);
 660 }
 661
 662
 663 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 664                                                   const ex &c) const
 665 {
 666         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 667         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 668
 669         return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 670 }
 671
 672
 673 /** Form an ex out of an expair, using the corresponding semantics.
 674  *  @see expairseq::split_ex_to_pair() */
 675 ex expairseq::recombine_pair_to_ex(const expair &p) const
 676 {
 677         return lst(p.rest,p.coeff);
 678 }
 679
 680 bool expairseq::expair_needs_further_processing(epp it)
 681 {
 682 #if EXPAIRSEQ_USE_HASHTAB
 683         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 684 #endif // EXPAIRSEQ_USE_HASHTAB
 685         return false;
 686 }
 687
 688 ex expairseq::default_overall_coeff(void) const
 689 {
 690         return _ex0();
 691 }
 692
 693 void expairseq::combine_overall_coeff(const ex &c)
 694 {
 695         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 696         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 697         overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 698 }
 699
 700 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 701 {
 702         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 703         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 704         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 705         overall_coeff = ex_to_numeric(overall_coeff).
 706                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 707 }
 708
 709 bool expairseq::can_make_flat(const expair &p) const
 710 {
 711         return true;
 712 }
 713
 714
 715 //////////
 716 // non-virtual functions in this class
 717 //////////
 718
 719 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 720 {
 721         exvector v;
 722         v.reserve(2);
 723         v.push_back(lh);
 724         v.push_back(rh);
 725         construct_from_exvector(v);
 726 #if EXPAIRSEQ_USE_HASHTAB
 727         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 728         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 729 #endif // EXPAIRSEQ_USE_HASHTAB
 730 }
 731
 732 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 733 {
 734         if (lh.bp->tinfo()==tinfo()) {
 735                 if (rh.bp->tinfo()==tinfo()) {
 736 #if EXPAIRSEQ_USE_HASHTAB
 737                         unsigned totalsize = ex_to_expairseq(lh).seq.size() +
 738                                              ex_to_expairseq(rh).seq.size();
 739                         if (calc_hashtabsize(totalsize)!=0) {
 740                                 construct_from_2_ex_via_exvector(lh,rh);
 741                         } else {
 742 #endif // EXPAIRSEQ_USE_HASHTAB
 743                                 construct_from_2_expairseq(ex_to_expairseq(lh),
 744                                                            ex_to_expairseq(rh));
 745 #if EXPAIRSEQ_USE_HASHTAB
 746                         }
 747 #endif // EXPAIRSEQ_USE_HASHTAB
 748                         return;
 749                 } else {
 750 #if EXPAIRSEQ_USE_HASHTAB
 751                         unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
 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_expairseq_ex(ex_to_expairseq(lh), rh);
 757 #if EXPAIRSEQ_USE_HASHTAB
 758                         }
 759 #endif // EXPAIRSEQ_USE_HASHTAB
 760                         return;
 761                 }
 762         } else if (rh.bp->tinfo()==tinfo()) {
 763 #if EXPAIRSEQ_USE_HASHTAB
 764                 unsigned totalsize=ex_to_expairseq(rh).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(rh),lh);
 770 #if EXPAIRSEQ_USE_HASHTAB
 771                 }
 772 #endif // EXPAIRSEQ_USE_HASHTAB
 773                 return;
 774         }
 775
 776 #if EXPAIRSEQ_USE_HASHTAB
 777         if (calc_hashtabsize(2)!=0) {
 778                 construct_from_2_ex_via_exvector(lh,rh);
 779                 return;
 780         }
 781         hashtabsize = 0;
 782 #endif // EXPAIRSEQ_USE_HASHTAB
 783
 784         if (is_ex_exactly_of_type(lh,numeric)) {
 785                 if (is_ex_exactly_of_type(rh,numeric)) {
 786                         combine_overall_coeff(lh);
 787                         combine_overall_coeff(rh);
 788                 } else {
 789                         combine_overall_coeff(lh);
 790                         seq.push_back(split_ex_to_pair(rh));
 791                 }
 792         } else {
 793                 if (is_ex_exactly_of_type(rh,numeric)) {
 794                         combine_overall_coeff(rh);
 795                         seq.push_back(split_ex_to_pair(lh));
 796                 } else {
 797                         expair p1 = split_ex_to_pair(lh);
 798                         expair p2 = split_ex_to_pair(rh);
 799
 800                         int cmpval = p1.rest.compare(p2.rest);
 801                         if (cmpval==0) {
 802                                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 803                                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 804                                         // no further processing is necessary, since this
 805                                         // one element will usually be recombined in eval()
 806                                         seq.push_back(p1);
 807                                 }
 808                         } else {
 809                                 seq.reserve(2);
 810                                 if (cmpval<0) {
 811                                         seq.push_back(p1);
 812                                         seq.push_back(p2);
 813                                 } else {
 814                                         seq.push_back(p2);
 815                                         seq.push_back(p1);
 816                                 }
 817                         }
 818                 }
 819         }
 820 }
 821
 822 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 823                                                                                    const expairseq &s2)
 824 {
 825         combine_overall_coeff(s1.overall_coeff);
 826         combine_overall_coeff(s2.overall_coeff);
 827
 828         epvector::const_iterator first1 = s1.seq.begin();
 829         epvector::const_iterator last1 = s1.seq.end();
 830         epvector::const_iterator first2 = s2.seq.begin();
 831         epvector::const_iterator last2 = s2.seq.end();
 832
 833         seq.reserve(s1.seq.size()+s2.seq.size());
 834
 835         bool needs_further_processing=false;
 836
 837         while (first1!=last1 && first2!=last2) {
 838                 int cmpval = (*first1).rest.compare((*first2).rest);
 839                 if (cmpval==0) {
 840                         // combine terms
 841                         const numeric &newcoeff = ex_to_numeric((*first1).coeff).
 842                                                    add(ex_to_numeric((*first2).coeff));
 843                         if (!newcoeff.is_zero()) {
 844                                 seq.push_back(expair((*first1).rest,newcoeff));
 845                                 if (expair_needs_further_processing(seq.end()-1)) {
 846                                         needs_further_processing = true;
 847                                 }
 848                         }
 849                         ++first1;
 850                         ++first2;
 851                 } else if (cmpval<0) {
 852                         seq.push_back(*first1);
 853                         ++first1;
 854                 } else {
 855                         seq.push_back(*first2);
 856                         ++first2;
 857                 }
 858         }
 859
 860         while (first1!=last1) {
 861                 seq.push_back(*first1);
 862                 ++first1;
 863         }
 864         while (first2!=last2) {
 865                 seq.push_back(*first2);
 866                 ++first2;
 867         }
 868
 869         if (needs_further_processing) {
 870                 epvector v = seq;
 871                 seq.clear();
 872                 construct_from_epvector(v);
 873         }
 874 }
 875
 876 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 877                                                                                         const ex &e)
 878 {
 879         combine_overall_coeff(s.overall_coeff);
 880         if (is_ex_exactly_of_type(e,numeric)) {
 881                 combine_overall_coeff(e);
 882                 seq = s.seq;
 883                 return;
 884         }
 885
 886         epvector::const_iterator first = s.seq.begin();
 887         epvector::const_iterator last = s.seq.end();
 888         expair p = split_ex_to_pair(e);
 889
 890         seq.reserve(s.seq.size()+1);
 891         bool p_pushed = false;
 892
 893         bool needs_further_processing=false;
 894
 895         // merge p into s.seq
 896         while (first!=last) {
 897                 int cmpval=(*first).rest.compare(p.rest);
 898                 if (cmpval==0) {
 899                         // combine terms
 900                         const numeric &newcoeff = ex_to_numeric((*first).coeff).
 901                                                    add(ex_to_numeric(p.coeff));
 902                         if (!newcoeff.is_zero()) {
 903                                 seq.push_back(expair((*first).rest,newcoeff));
 904                                 if (expair_needs_further_processing(seq.end()-1)) {
 905                                         needs_further_processing = true;
 906                                 }
 907                         }
 908                         ++first;
 909                         p_pushed = true;
 910                         break;
 911                 } else if (cmpval<0) {
 912                         seq.push_back(*first);
 913                         ++first;
 914                 } else {
 915                         seq.push_back(p);
 916                         p_pushed = true;
 917                         break;
 918                 }
 919         }
 920
 921         if (p_pushed) {
 922                 // while loop exited because p was pushed, now push rest of s.seq
 923                 while (first!=last) {
 924                         seq.push_back(*first);
 925                         ++first;
 926                 }
 927         } else {
 928                 // while loop exited because s.seq was pushed, now push p
 929                 seq.push_back(p);
 930         }
 931
 932         if (needs_further_processing) {
 933                 epvector v = seq;
 934                 seq.clear();
 935                 construct_from_epvector(v);
 936         }
 937 }
 938
 939 void expairseq::construct_from_exvector(const exvector &v)
 940 {
 941         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 942         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 943         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 944         //                  (same for (+,*) -> (*,^)
 945
 946         make_flat(v);
 947 #if EXPAIRSEQ_USE_HASHTAB
 948         combine_same_terms();
 949 #else
 950         canonicalize();
 951         combine_same_terms_sorted_seq();
 952 #endif // EXPAIRSEQ_USE_HASHTAB
 953         return;
 954 }
 955
 956 void expairseq::construct_from_epvector(const epvector &v)
 957 {
 958         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 959         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 960         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 961         //                  (same for (+,*) -> (*,^)
 962
 963         make_flat(v);
 964 #if EXPAIRSEQ_USE_HASHTAB
 965         combine_same_terms();
 966 #else
 967         canonicalize();
 968         combine_same_terms_sorted_seq();
 969 #endif // EXPAIRSEQ_USE_HASHTAB
 970         return;
 971 }
 972
 973 /** Combine this expairseq with argument exvector.
 974  *  It cares for associativity as well as for special handling of numerics. */
 975 void expairseq::make_flat(const exvector &v)
 976 {
 977         exvector::const_iterator cit;
 978
 979         // count number of operands which are of same expairseq derived type
 980         // and their cumulative number of operands
 981         int nexpairseqs = 0;
 982         int noperands = 0;
 983
 984         cit = v.begin();
 985         while (cit!=v.end()) {
 986                 if (cit->bp->tinfo()==this->tinfo()) {
 987                         ++nexpairseqs;
 988                         noperands += ex_to_expairseq(*cit).seq.size();
 989                 }
 990                 ++cit;
 991         }
 992
 993         // reserve seq and coeffseq which will hold all operands
 994         seq.reserve(v.size()+noperands-nexpairseqs);
 995
 996         // copy elements and split off numerical part
 997         cit = v.begin();
 998         while (cit!=v.end()) {
 999                 if (cit->bp->tinfo()==this->tinfo()) {
1000                         const expairseq &subseqref = ex_to_expairseq(*cit);
1001                         combine_overall_coeff(subseqref.overall_coeff);
1002                         epvector::const_iterator cit_s = subseqref.seq.begin();
1003                         while (cit_s!=subseqref.seq.end()) {
1004                                 seq.push_back(*cit_s);
1005                                 ++cit_s;
1006                         }
1007                 } else {
1008                         if (is_ex_exactly_of_type(*cit,numeric))
1009                                 combine_overall_coeff(*cit);
1010                         else
1011                                 seq.push_back(split_ex_to_pair(*cit));
1012                 }
1013                 ++cit;
1014         }
1015
1016         return;
1017 }
1018
1019 /** Combine this expairseq with argument epvector.
1020  *  It cares for associativity as well as for special handling of numerics. */
1021 void expairseq::make_flat(const epvector &v)
1022 {
1023         epvector::const_iterator cit;
1024
1025         // count number of operands which are of same expairseq derived type
1026         // and their cumulative number of operands
1027         int nexpairseqs = 0;
1028         int noperands = 0;
1029
1030         cit = v.begin();
1031         while (cit!=v.end()) {
1032                 if (cit->rest.bp->tinfo()==this->tinfo()) {
1033                         ++nexpairseqs;
1034                         noperands += ex_to_expairseq((*cit).rest).seq.size();
1035                 }
1036                 ++cit;
1037         }
1038
1039         // reserve seq and coeffseq which will hold all operands
1040         seq.reserve(v.size()+noperands-nexpairseqs);
1041
1042         // copy elements and split off numerical part
1043         cit = v.begin();
1044         while (cit!=v.end()) {
1045                 if (cit->rest.bp->tinfo()==this->tinfo() &&
1046                     this->can_make_flat(*cit)) {
1047                         const expairseq &subseqref = ex_to_expairseq((*cit).rest);
1048                         combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
1049                                                             ex_to_numeric((*cit).coeff));
1050                         epvector::const_iterator cit_s = subseqref.seq.begin();
1051                         while (cit_s!=subseqref.seq.end()) {
1052                                 seq.push_back(expair((*cit_s).rest,
1053                                                      ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
1054                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1055                                 //                                              (*cit).coeff));
1056                                 ++cit_s;
1057                         }
1058                 } else {
1059                         if (cit->is_canonical_numeric())
1060                                 combine_overall_coeff(cit->rest);
1061                         else
1062                                 seq.push_back(*cit);
1063                 }
1064                 ++cit;
1065         }
1066         return;
1067 }
1068
1069 /** Brings this expairseq into a sorted (canonical) form. */
1070 void expairseq::canonicalize(void)
1071 {
1072         // canonicalize
1073         sort(seq.begin(),seq.end(),expair_is_less());
1074         return;
1075 }
1076
1077
1078 /** Compact a presorted expairseq by combining all matching expairs to one
1079  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1080  *  instance. */
1081 void expairseq::combine_same_terms_sorted_seq(void)
1082 {
1083         bool needs_further_processing = false;
1084
1085         if (seq.size()>1) {
1086                 epvector::iterator itin1 = seq.begin();
1087                 epvector::iterator itin2 = itin1+1;
1088                 epvector::iterator itout = itin1;
1089                 epvector::iterator last = seq.end();
1090                 // must_copy will be set to true the first time some combination is
1091                 // possible from then on the sequence has changed and must be compacted
1092                 bool must_copy = false;
1093                 while (itin2!=last) {
1094                         if ((*itin1).rest.compare((*itin2).rest)==0) {
1095                                 (*itin1).coeff = ex_to_numeric((*itin1).coeff).
1096                                                  add_dyn(ex_to_numeric((*itin2).coeff));
1097                                 if (expair_needs_further_processing(itin1))
1098                                         needs_further_processing = true;
1099                                 must_copy = true;
1100                         } else {
1101                                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1102                                         if (must_copy)
1103                                                 *itout = *itin1;
1104                                         ++itout;
1105                                 }
1106                                 itin1 = itin2;
1107                         }
1108                         ++itin2;
1109                 }
1110                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1111                         if (must_copy)
1112                                 *itout = *itin1;
1113                         ++itout;
1114                 }
1115                 if (itout!=last)
1116                         seq.erase(itout,last);
1117         }
1118
1119         if (needs_further_processing) {
1120                 epvector v = seq;
1121                 seq.clear();
1122                 construct_from_epvector(v);
1123         }
1124         return;
1125 }
1126
1127 #if EXPAIRSEQ_USE_HASHTAB
1128
1129 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1130 {
1131         unsigned size;
1132         unsigned nearest_power_of_2 = 1 << log2(sz);
1133         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1134         //  size = nearest_power_of_2*hashtabfactor;
1135         size = nearest_power_of_2/hashtabfactor;
1136         if (size<minhashtabsize)
1137                 return 0;
1138         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1139         // hashtabsize must be a power of 2
1140         GINAC_ASSERT((1U << log2(size))==size);
1141         return size;
1142 }
1143
1144 unsigned expairseq::calc_hashindex(const ex &e) const
1145 {
1146         // calculate hashindex
1147         unsigned hash = e.gethash();
1148         unsigned hashindex;
1149         if (is_a_numeric_hash(hash)) {
1150                 hashindex = hashmask;
1151         } else {
1152                 hashindex = hash &hashmask;
1153                 // last hashtab entry is reserved for numerics
1154                 if (hashindex==hashmask) hashindex = 0;
1155         }
1156         GINAC_ASSERT(hashindex>=0);
1157         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1158         return hashindex;
1159 }
1160
1161 void expairseq::shrink_hashtab(void)
1162 {
1163         unsigned new_hashtabsize;
1164         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1165                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1166                 if (new_hashtabsize==0) {
1167                         hashtab.clear();
1168                         hashtabsize = 0;
1169                         canonicalize();
1170                         return;
1171                 }
1172
1173                 // shrink by a factor of 2
1174                 unsigned half_hashtabsize = hashtabsize/2;
1175                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1176                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1177                 // special treatment for numeric hashes
1178                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1179                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1180                 hashtab.resize(half_hashtabsize);
1181                 hashtabsize = half_hashtabsize;
1182                 hashmask = hashtabsize-1;
1183         }
1184 }
1185
1186 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1187 {
1188         if (hashtabsize==0)
1189                 return; // nothing to do
1190
1191         // calculate hashindex of element to be deleted
1192         unsigned hashindex = calc_hashindex((*element).rest);
1193
1194         // find it in hashtab and remove it
1195         epplist &eppl = hashtab[hashindex];
1196         epplist::iterator epplit = eppl.begin();
1197         bool erased = false;
1198         while (epplit!=eppl.end()) {
1199                 if (*epplit == element) {
1200                         eppl.erase(epplit);
1201                         erased = true;
1202                         break;
1203                 }
1204                 ++epplit;
1205         }
1206         if (!erased) {
1207                 printtree(cout,0);
1208                 cout << "tried to erase " << element-seq.begin() << std::endl;
1209                 cout << "size " << seq.end()-seq.begin() << std::endl;
1210
1211                 unsigned hashindex = calc_hashindex((*element).rest);
1212                 epplist &eppl = hashtab[hashindex];
1213                 epplist::iterator epplit=eppl.begin();
1214                 bool erased=false;
1215                 while (epplit!=eppl.end()) {
1216                         if (*epplit == element) {
1217                                 eppl.erase(epplit);
1218                                 erased = true;
1219                                 break;
1220                         }
1221                         ++epplit;
1222                 }
1223                 GINAC_ASSERT(erased);
1224         }
1225         GINAC_ASSERT(erased);
1226 }
1227
1228 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1229                                    epvector::iterator newpos)
1230 {
1231         GINAC_ASSERT(hashtabsize!=0);
1232
1233         // calculate hashindex of element which was moved
1234         unsigned hashindex=calc_hashindex((*newpos).rest);
1235
1236         // find it in hashtab and modify it
1237         epplist &eppl = hashtab[hashindex];
1238         epplist::iterator epplit = eppl.begin();
1239         while (epplit!=eppl.end()) {
1240                 if (*epplit == oldpos) {
1241                         *epplit = newpos;
1242                         break;
1243                 }
1244                 ++epplit;
1245         }
1246         GINAC_ASSERT(epplit!=eppl.end());
1247 }
1248
1249 void expairseq::sorted_insert(epplist &eppl, epp elem)
1250 {
1251         epplist::iterator current = eppl.begin();
1252         while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1253                 ++current;
1254         }
1255         eppl.insert(current,elem);
1256 }
1257
1258 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1259                                           epvector::iterator &last_non_zero,
1260                                           std::vector<bool> &touched,
1261                                           unsigned &number_of_zeroes)
1262 {
1263         epp current=seq.begin();
1264
1265         while (current!=first_numeric) {
1266                 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1267                         --first_numeric;
1268                         iter_swap(current,first_numeric);
1269                 } else {
1270                         // calculate hashindex
1271                         unsigned currenthashindex = calc_hashindex((*current).rest);
1272
1273                         // test if there is already a matching expair in the hashtab-list
1274                         epplist &eppl=hashtab[currenthashindex];
1275                         epplist::iterator epplit = eppl.begin();
1276                         while (epplit!=eppl.end()) {
1277                                 if ((*current).rest.is_equal((*(*epplit)).rest))
1278                                         break;
1279                                 ++epplit;
1280                         }
1281                         if (epplit==eppl.end()) {
1282                                 // no matching expair found, append this to end of list
1283                                 sorted_insert(eppl,current);
1284                                 ++current;
1285                         } else {
1286                                 // epplit points to a matching expair, combine it with current
1287                                 (*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
1288                                                      add_dyn(ex_to_numeric((*current).coeff));
1289
1290                                 // move obsolete current expair to end by swapping with last_non_zero element
1291                                 // if this was a numeric, it is swapped with the expair before first_numeric
1292                                 iter_swap(current,last_non_zero);
1293                                 --first_numeric;
1294                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1295                                 --last_non_zero;
1296                                 ++number_of_zeroes;
1297                                 // test if combined term has coeff 0 and can be removed is done later
1298                                 touched[(*epplit)-seq.begin()]=true;
1299                         }
1300                 }
1301         }
1302 }
1303
1304 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1305                                    epvector::iterator &last_non_zero,
1306                                    std::vector<bool> &touched,
1307                                    unsigned &number_of_zeroes)
1308 {
1309         // move terms with coeff 0 to end and remove them from hashtab
1310         // check only those elements which have been touched
1311         epp current = seq.begin();
1312         unsigned i = 0;
1313         while (current!=first_numeric) {
1314                 if (!touched[i]) {
1315                         ++current;
1316                         ++i;
1317                 } else if (!ex_to_numeric((*current).coeff).is_zero()) {
1318                         ++current;
1319                         ++i;
1320                 } else {
1321                         remove_hashtab_entry(current);
1322
1323                         // move element to the end, unless it is already at the end
1324                         if (current!=last_non_zero) {
1325                                 iter_swap(current,last_non_zero);
1326                                 --first_numeric;
1327                                 bool numeric_swapped=first_numeric!=last_non_zero;
1328                                 if (numeric_swapped) iter_swap(first_numeric,current);
1329                                 epvector::iterator changed_entry;
1330
1331                                 if (numeric_swapped)
1332                                         changed_entry = first_numeric;
1333                                 else
1334                                         changed_entry = last_non_zero;
1335
1336                                 --last_non_zero;
1337                                 ++number_of_zeroes;
1338
1339                                 if (first_numeric!=current) {
1340
1341                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1342                                         move_hashtab_entry(changed_entry,current);
1343                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1344                                 }
1345                         } else {
1346                                 --first_numeric;
1347                                 --last_non_zero;
1348                                 ++number_of_zeroes;
1349                         }
1350                 }
1351         }
1352         GINAC_ASSERT(i==current-seq.begin());
1353 }
1354
1355 /** True if one of the coeffs vanishes, otherwise false.
1356  *  This would be an invariant violation, so this should only be used for
1357  *  debugging purposes. */
1358 bool expairseq::has_coeff_0(void) const
1359 {
1360         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1361                 if ((*cit).coeff.is_zero())
1362                         return true;
1363         }
1364         return false;
1365 }
1366
1367 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1368                                                                                 epvector::const_iterator last_non_zero)
1369 {
1370         if (first_numeric==seq.end()) return; // no numerics
1371
1372         epvector::iterator current = first_numeric;
1373         epvector::const_iterator last = last_non_zero+1;
1374         while (current!=last) {
1375                 sorted_insert(hashtab[hashmask],current);
1376                 ++current;
1377         }
1378 }
1379
1380 void expairseq::combine_same_terms(void)
1381 {
1382         // combine same terms, drop term with coeff 0, move numerics to end
1383
1384         // calculate size of hashtab
1385         hashtabsize = calc_hashtabsize(seq.size());
1386
1387         // hashtabsize is a power of 2
1388         hashmask = hashtabsize-1;
1389
1390         // allocate hashtab
1391         hashtab.clear();
1392         hashtab.resize(hashtabsize);
1393
1394         if (hashtabsize==0) {
1395                 canonicalize();
1396                 combine_same_terms_sorted_seq();
1397                 GINAC_ASSERT(!has_coeff_0());
1398                 return;
1399         }
1400
1401         // iterate through seq, move numerics to end,
1402         // fill hashtab and combine same terms
1403         epvector::iterator first_numeric = seq.end();
1404         epvector::iterator last_non_zero = seq.end()-1;
1405
1406         std::vector<bool> touched;
1407         touched.reserve(seq.size());
1408         for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1409
1410         unsigned number_of_zeroes = 0;
1411
1412         GINAC_ASSERT(!has_coeff_0());
1413         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1414         /*
1415         cout << "in combine:" << std::endl;
1416         printtree(cout,0);
1417         cout << "size=" << seq.end() - seq.begin() << std::endl;
1418         cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1419         cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1420         for (unsigned i=0; i<seq.size(); ++i) {
1421                 if (touched[i]) cout << i << " is touched" << std::endl;
1422         }
1423         cout << "end in combine" << std::endl;
1424         */
1425
1426         // there should not be any terms with coeff 0 from the beginning,
1427         // so it should be safe to skip this step
1428         if (number_of_zeroes!=0) {
1429                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1430                 /*
1431                 cout << "in combine after drop:" << std::endl;
1432                 printtree(cout,0);
1433                 cout << "size=" << seq.end() - seq.begin() << std::endl;
1434                 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1435                 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1436                 for (unsigned i=0; i<seq.size(); ++i) {
1437                         if (touched[i]) cout << i << " is touched" << std::endl;
1438                 }
1439                 cout << "end in combine after drop" << std::endl;
1440                 */
1441         }
1442
1443         add_numerics_to_hashtab(first_numeric,last_non_zero);
1444
1445         // pop zero elements
1446         for (unsigned i=0; i<number_of_zeroes; ++i) {
1447                 seq.pop_back();
1448         }
1449
1450         // shrink hashtabsize to calculated value
1451         GINAC_ASSERT(!has_coeff_0());
1452
1453         shrink_hashtab();
1454
1455         GINAC_ASSERT(!has_coeff_0());
1456 }
1457
1458 #endif // EXPAIRSEQ_USE_HASHTAB
1459
1460 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1461  *  debugging or in assertions since being sorted is an invariance. */
1462 bool expairseq::is_canonical() const
1463 {
1464         if (seq.size() <= 1)
1465                 return 1;
1466
1467 #if EXPAIRSEQ_USE_HASHTAB
1468         if (hashtabsize > 0) return 1; // not canoncalized
1469 #endif // EXPAIRSEQ_USE_HASHTAB
1470
1471         epvector::const_iterator it = seq.begin();
1472         epvector::const_iterator it_last = it;
1473         for (++it; it!=seq.end(); it_last=it, ++it) {
1474                 if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
1475                         if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1476                                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1477                                 // double test makes it easier to set a breakpoint...
1478                                 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1479                                         !is_ex_exactly_of_type((*it).rest,numeric)) {
1480                                         printpair(std::clog, *it_last, 0);
1481                                         std::clog << ">";
1482                                         printpair(std::clog, *it, 0);
1483                                         std::clog << "\n";
1484                                         std::clog << "pair1:" << std::endl;
1485                                         (*it_last).rest.print(print_tree(std::clog));
1486                                         (*it_last).coeff.print(print_tree(std::clog));
1487                                         std::clog << "pair2:" << std::endl;
1488                                         (*it).rest.print(print_tree(std::clog));
1489                                         (*it).coeff.print(print_tree(std::clog));
1490                                         return 0;
1491                                 }
1492                         }
1493                 }
1494         }
1495         return 1;
1496 }
1497
1498
1499 /** Member-wise expand the expairs in this sequence.
1500  *
1501  *  @see expairseq::expand()
1502  *  @return pointer to epvector containing expanded pairs or zero pointer,
1503  *  if no members were changed. */
1504 epvector * expairseq::expandchildren(unsigned options) const
1505 {
1506         epvector::const_iterator last = seq.end();
1507         epvector::const_iterator cit = seq.begin();
1508         while (cit!=last) {
1509                 const ex &expanded_ex = (*cit).rest.expand(options);
1510                 if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1511
1512                         // something changed, copy seq, eval and return it
1513                         epvector *s = new epvector;
1514                         s->reserve(seq.size());
1515
1516                         // copy parts of seq which are known not to have changed
1517                         epvector::const_iterator cit2 = seq.begin();
1518                         while (cit2!=cit) {
1519                                 s->push_back(*cit2);
1520                                 ++cit2;
1521                         }
1522                         // copy first changed element
1523                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1524                                                                    (*cit2).coeff));
1525                         ++cit2;
1526                         // copy rest
1527                         while (cit2!=last) {
1528                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1529                                                                            (*cit2).coeff));
1530                                 ++cit2;
1531                         }
1532                         return s;
1533                 }
1534                 ++cit;
1535         }
1536
1537         return 0; // signalling nothing has changed
1538 }
1539
1540
1541 /** Member-wise evaluate the expairs in this sequence.
1542  *
1543  *  @see expairseq::eval()
1544  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1545  *  if no members were changed. */
1546 epvector * expairseq::evalchildren(int level) const
1547 {
1548         // returns a NULL pointer if nothing had to be evaluated
1549         // returns a pointer to a newly created epvector otherwise
1550         // (which has to be deleted somewhere else)
1551
1552         if (level==1)
1553                 return 0;
1554
1555         if (level == -max_recursion_level)
1556                 throw(std::runtime_error("max recursion level reached"));
1557
1558         --level;
1559         epvector::const_iterator last=seq.end();
1560         epvector::const_iterator cit=seq.begin();
1561         while (cit!=last) {
1562                 const ex &evaled_ex = (*cit).rest.eval(level);
1563                 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1564
1565                         // something changed, copy seq, eval and return it
1566                         epvector *s = new epvector;
1567                         s->reserve(seq.size());
1568
1569                         // copy parts of seq which are known not to have changed
1570                         epvector::const_iterator cit2=seq.begin();
1571                         while (cit2!=cit) {
1572                                 s->push_back(*cit2);
1573                                 ++cit2;
1574                         }
1575                         // copy first changed element
1576                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1577                                                                    (*cit2).coeff));
1578                         ++cit2;
1579                         // copy rest
1580                         while (cit2!=last) {
1581                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1582                                                                            (*cit2).coeff));
1583                                 ++cit2;
1584                         }
1585                         return s;
1586                 }
1587                 ++cit;
1588         }
1589
1590         return 0; // signalling nothing has changed
1591 }
1592
1593
1594 /** Member-wise evaluate numerically all expairs in this sequence.
1595  *
1596  *  @see expairseq::evalf()
1597  *  @return epvector with all entries evaluated numerically. */
1598 epvector expairseq::evalfchildren(int level) const
1599 {
1600         if (level==1)
1601                 return seq;
1602
1603         if (level==-max_recursion_level)
1604                 throw(std::runtime_error("max recursion level reached"));
1605
1606         epvector s;
1607         s.reserve(seq.size());
1608
1609         --level;
1610         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1611                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1612                                                           (*it).coeff.evalf(level)));
1613         }
1614         return s;
1615 }
1616
1617
1618 /** Member-wise normalize all expairs in this sequence.
1619  *
1620  *  @see expairseq::normal()
1621  *  @return epvector with all entries normalized. */
1622 epvector expairseq::normalchildren(int level) const
1623 {
1624         if (level==1)
1625                 return seq;
1626
1627         if (level==-max_recursion_level)
1628                 throw(std::runtime_error("max recursion level reached"));
1629
1630         epvector s;
1631         s.reserve(seq.size());
1632
1633         --level;
1634         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1635                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1636                                                           (*it).coeff));
1637         }
1638         return s;
1639 }
1640
1641
1642 /** Member-wise differentiate all expairs in this sequence.
1643  *
1644  *  @see expairseq::diff()
1645  *  @return epvector with all entries differentiated. */
1646 epvector expairseq::diffchildren(const symbol &y) const
1647 {
1648         epvector s;
1649         s.reserve(seq.size());
1650
1651         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1652                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1653                                                           (*it).coeff));
1654         }
1655         return s;
1656 }
1657
1658
1659 /** Member-wise substitute in this sequence.
1660  *
1661  *  @see expairseq::subs()
1662  *  @return pointer to epvector containing pairs after application of subs or zero
1663  *  pointer, if no members were changed. */
1664 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1665 {
1666         // returns a NULL pointer if nothing had to be substituted
1667         // returns a pointer to a newly created epvector otherwise
1668         // (which has to be deleted somewhere else)
1669         GINAC_ASSERT(ls.nops()==lr.nops());
1670
1671         epvector::const_iterator last = seq.end();
1672         epvector::const_iterator cit = seq.begin();
1673         while (cit!=last) {
1674                 const ex &subsed_ex=(*cit).rest.subs(ls,lr,no_pattern);
1675                 if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1676
1677                         // something changed, copy seq, subs and return it
1678                         epvector *s = new epvector;
1679                         s->reserve(seq.size());
1680
1681                         // copy parts of seq which are known not to have changed
1682                         epvector::const_iterator cit2 = seq.begin();
1683                         while (cit2!=cit) {
1684                                 s->push_back(*cit2);
1685                                 ++cit2;
1686                         }
1687                         // copy first changed element
1688                         s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1689                                                                    (*cit2).coeff));
1690                         ++cit2;
1691                         // copy rest
1692                         while (cit2!=last) {
1693                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr,no_pattern),
1694                                                                            (*cit2).coeff));
1695                                 ++cit2;
1696                         }
1697                         return s;
1698                 }
1699                 ++cit;
1700         }
1701
1702         return 0; // signalling nothing has changed
1703 }
1704
1705 //////////
1706 // static member variables
1707 //////////
1708
1709 #if EXPAIRSEQ_USE_HASHTAB
1710 unsigned expairseq::maxhashtabsize = 0x4000000U;
1711 unsigned expairseq::minhashtabsize = 0x1000U;
1712 unsigned expairseq::hashtabfactor = 1;
1713 #endif // EXPAIRSEQ_USE_HASHTAB
1714
1715 } // namespace GiNaC