ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 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 #include <cmath>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "archive.h"
  31 #include "debugmsg.h"
  32 #include "utils.h"
  33
  34 #ifndef NO_NAMESPACE_GINAC
  35 namespace GiNaC {
  36 #endif // ndef NO_NAMESPACE_GINAC
  37
  38 #ifdef EXPAIRSEQ_USE_HASHTAB
  39 #error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
  40 #endif // def EXPAIRSEQ_USE_HASHTAB
  41
  42 GINAC_IMPLEMENT_REGISTERED_CLASS(expairseq, basic)
  43
  44 //////////
  45 // helper classes
  46 //////////
  47
  48 class epp_is_less
  49 {
  50 public:
  51     bool operator()(const epp & lh, const epp & rh) const
  52     {
  53         return (*lh).is_less(*rh);
  54     }
  55 };
  56
  57 //////////
  58 // default constructor, destructor, copy constructor assignment operator and helpers
  59 //////////
  60
  61 // public
  62
  63 expairseq::expairseq(const expairseq & other)
  64 {
  65     debugmsg("expairseq copy constructor",LOGLEVEL_CONSTRUCT);
  66     copy(other);
  67 }
  68
  69 const expairseq & expairseq::operator=(const expairseq & other)
  70 {
  71     debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  72     if (this != &other) {
  73         destroy(1);
  74         copy(other);
  75     }
  76     return *this;
  77 }
  78
  79 // protected
  80
  81 void expairseq::copy(const expairseq & other)
  82 {
  83     inherited::copy(other);
  84     seq=other.seq;
  85     overall_coeff=other.overall_coeff;
  86 #ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
 104 }
 105
 106 //////////
 107 // other constructors
 108 //////////
 109
 110 expairseq::expairseq(const ex & lh, const ex & rh) : inherited(TINFO_expairseq)
 111 {
 112     debugmsg("expairseq constructor from ex,ex",LOGLEVEL_CONSTRUCT);
 113     construct_from_2_ex(lh,rh);
 114     GINAC_ASSERT(is_canonical());
 115 }
 116
 117 expairseq::expairseq(const exvector & v) : inherited(TINFO_expairseq)
 118 {
 119     debugmsg("expairseq constructor from exvector",LOGLEVEL_CONSTRUCT);
 120     construct_from_exvector(v);
 121     GINAC_ASSERT(is_canonical());
 122 }
 123
 124 /*
 125 expairseq::expairseq(const epvector & v, bool do_not_canonicalize) :
 126     inherited(TINFO_expairseq)
 127 {
 128     debugmsg("expairseq constructor from epvector",LOGLEVEL_CONSTRUCT);
 129     if (do_not_canonicalize) {
 130         seq=v;
 131 #ifdef EXPAIRSEQ_USE_HASHTAB
 132         combine_same_terms(); // to build hashtab
 133 #endif // def EXPAIRSEQ_USE_HASHTAB
 134     } else {
 135         construct_from_epvector(v);
 136     }
 137     GINAC_ASSERT(is_canonical());
 138 }
 139 */
 140
 141 expairseq::expairseq(const epvector & v, const ex & oc) :
 142     inherited(TINFO_expairseq), overall_coeff(oc)
 143 {
 144     debugmsg("expairseq constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 145     construct_from_epvector(v);
 146     GINAC_ASSERT(is_canonical());
 147 }
 148
 149 expairseq::expairseq(epvector * vp, const ex & oc) :
 150     inherited(TINFO_expairseq), overall_coeff(oc)
 151 {
 152     debugmsg("expairseq constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 153     GINAC_ASSERT(vp!=0);
 154     construct_from_epvector(*vp);
 155     delete vp;
 156     GINAC_ASSERT(is_canonical());
 157 }
 158
 159 //////////
 160 // archiving
 161 //////////
 162
 163 /** Construct object from archive_node. */
 164 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 165 #ifdef EXPAIRSEQ_USE_HASHTAB
 166     , hashtabsize(0)
 167 #endif
 168 {
 169     debugmsg("expairseq constructor from archive_node", LOGLEVEL_CONSTRUCT);
 170     for (unsigned int i=0; true; i++) {
 171         ex rest;
 172         ex coeff;
 173         if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 174             seq.push_back(expair(rest, coeff));
 175         else
 176             break;
 177     }
 178     n.find_ex("overall_coeff", overall_coeff, sym_lst);
 179 }
 180
 181 /** Unarchive the object. */
 182 ex expairseq::unarchive(const archive_node &n, const lst &sym_lst)
 183 {
 184     return (new expairseq(n, sym_lst))->setflag(status_flags::dynallocated);
 185 }
 186
 187 /** Archive the object. */
 188 void expairseq::archive(archive_node &n) const
 189 {
 190     inherited::archive(n);
 191     epvector::const_iterator i = seq.begin(), iend = seq.end();
 192     while (i != iend) {
 193         n.add_ex("rest", i->rest);
 194         n.add_ex("coeff", i->coeff);
 195         i++;
 196     }
 197     n.add_ex("overall_coeff", overall_coeff);
 198 }
 199
 200 //////////
 201 // functions overriding virtual functions from bases classes
 202 //////////
 203
 204 // public
 205
 206 basic * expairseq::duplicate() const
 207 {
 208     debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 209     return new expairseq(*this);
 210 }
 211
 212 void expairseq::print(ostream & os, unsigned upper_precedence) const
 213 {
 214     debugmsg("expairseq print",LOGLEVEL_PRINT);
 215     os << "[[";
 216     printseq(os,',',precedence,upper_precedence);
 217     os << "]]";
 218 }
 219
 220 void expairseq::printraw(ostream & os) const
 221 {
 222     debugmsg("expairseq printraw",LOGLEVEL_PRINT);
 223
 224     os << "expairseq(";
 225     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 226         os << "(";
 227         (*cit).rest.printraw(os);
 228         os << ",";
 229         (*cit).coeff.printraw(os);
 230         os << "),";
 231     }
 232     os << ")";
 233 }
 234
 235 void expairseq::printtree(ostream & os, unsigned indent) const
 236 {
 237     debugmsg("expairseq printtree",LOGLEVEL_PRINT);
 238
 239     os << string(indent,' ') << "type=" << typeid(*this).name()
 240        << ", hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")"
 241        << ", flags=" << flags
 242        << ", nops=" << nops() << endl;
 243     for (unsigned i=0; i<seq.size(); ++i) {
 244         seq[i].rest.printtree(os,indent+delta_indent);
 245         seq[i].coeff.printtree(os,indent+delta_indent);
 246         if (i!=seq.size()-1) {
 247             os << string(indent+delta_indent,' ') << "-----" << endl;
 248         }
 249     }
 250     if (!overall_coeff.is_equal(default_overall_coeff())) {
 251         os << string(indent+delta_indent,' ') << "-----" << endl;
 252         os << string(indent+delta_indent,' ') << "overall_coeff" << endl;
 253         overall_coeff.printtree(os,indent+delta_indent);
 254     }
 255     os << string(indent+delta_indent,' ') << "=====" << endl;
 256 #ifdef EXPAIRSEQ_USE_HASHTAB
 257     os << string(indent+delta_indent,' ')
 258        << "hashtab size " << hashtabsize << endl;
 259     if (hashtabsize==0) return;
 260 #define MAXCOUNT 5
 261     unsigned count[MAXCOUNT+1];
 262     for (int i=0; i<MAXCOUNT+1; ++i) count[i]=0;
 263     unsigned this_bin_fill;
 264     unsigned cum_fill_sq = 0;
 265     unsigned cum_fill = 0;
 266     for (unsigned i=0; i<hashtabsize; ++i) {
 267         this_bin_fill=0;
 268         if (hashtab[i].size()>0) {
 269             os << string(indent+delta_indent,' ')
 270                << "bin " << i << " with entries ";
 271             for (epplist::const_iterator it=hashtab[i].begin();
 272                  it!=hashtab[i].end(); ++it) {
 273                 os << *it-seq.begin() << " ";
 274                 this_bin_fill++;
 275             }
 276             os << endl;
 277             cum_fill += this_bin_fill;
 278             cum_fill_sq += this_bin_fill*this_bin_fill;
 279         }
 280         if (this_bin_fill<MAXCOUNT) {
 281             ++count[this_bin_fill];
 282         } else {
 283             ++count[MAXCOUNT];
 284         }
 285     }
 286     unsigned fact = 1;
 287     double cum_prob = 0;
 288     double lambda = (1.0*seq.size())/hashtabsize;
 289     for (int k=0; k<MAXCOUNT; ++k) {
 290         if (k>0) fact *= k;
 291         double prob = pow(lambda,k)/fact*exp(-lambda);
 292         cum_prob += prob;
 293         os << string(indent+delta_indent,' ') << "bins with " << k << " entries: "
 294            << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 295            << int(prob*1000)/10.0 << ")" << endl;
 296     }
 297     os << string(indent+delta_indent,' ') << "bins with more entries: "
 298        << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 299        << int((1-cum_prob)*1000)/10.0 << ")" << endl;
 300
 301     os << string(indent+delta_indent,' ') << "variance: "
 302        << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 303        << endl;
 304     os << string(indent+delta_indent,' ') << "average fill: "
 305        << (1.0*cum_fill)/hashtabsize
 306        << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << endl;
 307 #endif // def EXPAIRSEQ_USE_HASHTAB
 308 }
 309
 310 bool expairseq::info(unsigned inf) const
 311 {
 312     return inherited::info(inf);
 313 }
 314
 315 unsigned expairseq::nops() const
 316 {
 317     if (overall_coeff.is_equal(default_overall_coeff())) {
 318         return seq.size();
 319     }
 320     return seq.size()+1;
 321 }
 322
 323 ex expairseq::op(int i) const
 324 {
 325     if (unsigned(i)<seq.size()) {
 326         return recombine_pair_to_ex(seq[i]);
 327     }
 328     GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 329     return overall_coeff;
 330 }
 331
 332 ex & expairseq::let_op(int i)
 333 {
 334     throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 335 }
 336
 337 ex expairseq::eval(int level) const
 338 {
 339     if ((level==1)&&(flags & status_flags::evaluated)) {
 340         return *this;
 341     }
 342
 343     epvector * vp=evalchildren(level);
 344     if (vp==0) {
 345         return this->hold();
 346     }
 347
 348     return (new expairseq(vp,overall_coeff))
 349                ->setflag(status_flags::dynallocated |
 350                          status_flags::evaluated );
 351 }
 352
 353 ex expairseq::evalf(int level) const
 354 {
 355     return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
 356 }
 357
 358 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 359 {
 360     ex n = thisexpairseq(normalchildren(level),overall_coeff);
 361     return n.bp->basic::normal(sym_lst,repl_lst,level);
 362 }
 363
 364 ex expairseq::subs(const lst & ls, const lst & lr) const
 365 {
 366     epvector * vp=subschildren(ls,lr);
 367     if (vp==0) {
 368         return *this;
 369     }
 370     return thisexpairseq(vp,overall_coeff);
 371 }
 372
 373 // protected
 374
 375 /** Implementation of ex::diff() for an expairseq. It differentiates all elements of the
 376  *  sequence.
 377  *  @see ex::diff */
 378 ex expairseq::derivative(const symbol & s) const
 379 {
 380     return thisexpairseq(diffchildren(s),overall_coeff);
 381 }
 382
 383 int expairseq::compare_same_type(const basic & other) const
 384 {
 385     GINAC_ASSERT(is_of_type(other, expairseq));
 386     const expairseq & o = static_cast<const expairseq &>(const_cast<basic &>(other));
 387
 388     int cmpval;
 389
 390     // compare number of elements
 391     if (seq.size() != o.seq.size()) {
 392         return (seq.size()<o.seq.size()) ? -1 : 1;
 393     }
 394
 395     // compare overall_coeff
 396     cmpval = overall_coeff.compare(o.overall_coeff);
 397     if (cmpval!=0) return cmpval;
 398
 399     //if (seq.size()==0) return 0; // empty expairseq's are equal
 400
 401 #ifdef EXPAIRSEQ_USE_HASHTAB
 402     GINAC_ASSERT(hashtabsize==o.hashtabsize);
 403     if (hashtabsize==0) {
 404 #endif // def EXPAIRSEQ_USE_HASHTAB
 405         epvector::const_iterator cit1 = seq.begin();
 406         epvector::const_iterator cit2 = o.seq.begin();
 407         epvector::const_iterator last1 = seq.end();
 408         epvector::const_iterator last2 = o.seq.end();
 409
 410         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 411             cmpval = (*cit1).compare(*cit2);
 412             if (cmpval!=0) return cmpval;
 413         }
 414
 415         GINAC_ASSERT(cit1==last1);
 416         GINAC_ASSERT(cit2==last2);
 417
 418         return 0;
 419 #ifdef EXPAIRSEQ_USE_HASHTAB
 420     }
 421
 422     // compare number of elements in each hashtab entry
 423     for (unsigned i=0; i<hashtabsize; ++i) {
 424         unsigned cursize=hashtab[i].size();
 425         if (cursize != o.hashtab[i].size()) {
 426             return (cursize < o.hashtab[i].size()) ? -1 : 1;
 427         }
 428     }
 429
 430     // compare individual (sorted) hashtab entries
 431     for (unsigned i=0; i<hashtabsize; ++i) {
 432         unsigned sz=hashtab[i].size();
 433         if (sz>0) {
 434             const epplist & eppl1=hashtab[i];
 435             const epplist & eppl2=o.hashtab[i];
 436             epplist::const_iterator it1=eppl1.begin();
 437             epplist::const_iterator it2=eppl2.begin();
 438             while (it1!=eppl1.end()) {
 439                 cmpval=(*(*it1)).compare(*(*it2));
 440                 if (cmpval!=0) return cmpval;
 441                 ++it1;
 442                 ++it2;
 443             }
 444         }
 445     }
 446
 447     return 0; // equal
 448 #endif // def EXPAIRSEQ_USE_HASHTAB
 449 }
 450
 451 bool expairseq::is_equal_same_type(const basic & other) const
 452 {
 453     const expairseq & o=dynamic_cast<const expairseq &>(const_cast<basic &>(other));
 454
 455     // compare number of elements
 456     if (seq.size() != o.seq.size()) return false;
 457
 458     // compare overall_coeff
 459     if (!overall_coeff.is_equal(o.overall_coeff)) return false;
 460
 461 #ifdef EXPAIRSEQ_USE_HASHTAB
 462     // compare number of elements in each hashtab entry
 463     if (hashtabsize!=o.hashtabsize) {
 464         cout << "this:" << endl;
 465         printtree(cout,0);
 466         cout << "other:" << endl;
 467         other.printtree(cout,0);
 468     }
 469
 470     GINAC_ASSERT(hashtabsize==o.hashtabsize);
 471
 472     if (hashtabsize==0) {
 473 #endif // def EXPAIRSEQ_USE_HASHTAB
 474         epvector::const_iterator cit1=seq.begin();
 475         epvector::const_iterator cit2=o.seq.begin();
 476         epvector::const_iterator last1=seq.end();
 477
 478         while (cit1!=last1) {
 479             if (!(*cit1).is_equal(*cit2)) return false;
 480             ++cit1;
 481             ++cit2;
 482         }
 483
 484         return true;
 485 #ifdef EXPAIRSEQ_USE_HASHTAB
 486     }
 487
 488     for (unsigned i=0; i<hashtabsize; ++i) {
 489         if (hashtab[i].size() != o.hashtab[i].size()) return false;
 490     }
 491
 492     // compare individual sorted hashtab entries
 493     for (unsigned i=0; i<hashtabsize; ++i) {
 494         unsigned sz=hashtab[i].size();
 495         if (sz>0) {
 496             const epplist & eppl1=hashtab[i];
 497             const epplist & eppl2=o.hashtab[i];
 498             epplist::const_iterator it1=eppl1.begin();
 499             epplist::const_iterator it2=eppl2.begin();
 500             while (it1!=eppl1.end()) {
 501                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 502                 ++it1;
 503                 ++it2;
 504             }
 505         }
 506     }
 507
 508     return true;
 509 #endif // def EXPAIRSEQ_USE_HASHTAB
 510 }
 511
 512 unsigned expairseq::return_type(void) const
 513 {
 514     return return_types::noncommutative_composite;
 515 }
 516
 517 unsigned expairseq::calchash(void) const
 518 {
 519     unsigned v=golden_ratio_hash(tinfo());
 520     epvector::const_iterator last=seq.end();
 521     for (epvector::const_iterator cit=seq.begin(); cit!=last; ++cit) {
 522 #ifndef EXPAIRSEQ_USE_HASHTAB
 523         v=rotate_left_31(v); // rotation would spoil commutativity
 524 #endif // ndef EXPAIRSEQ_USE_HASHTAB
 525         v ^= (*cit).rest.gethash();
 526     }
 527
 528     v ^= overall_coeff.gethash();
 529     v=v & 0x7FFFFFFFU;
 530
 531     // store calculated hash value only if object is already evaluated
 532     if (flags & status_flags::evaluated) {
 533         setflag(status_flags::hash_calculated);
 534         hashvalue=v;
 535     }
 536
 537     return v;
 538 }
 539
 540 ex expairseq::expand(unsigned options) const
 541 {
 542     epvector * vp=expandchildren(options);
 543     if (vp==0) {
 544         return *this;
 545     }
 546     return thisexpairseq(vp,overall_coeff);
 547 }
 548
 549 //////////
 550 // new virtual functions which can be overridden by derived classes
 551 //////////
 552
 553 // protected
 554
 555 ex expairseq::thisexpairseq(const epvector & v,const ex & oc) const
 556 {
 557     return expairseq(v,oc);
 558 }
 559
 560 ex expairseq::thisexpairseq(epvector * vp, const ex & oc) const
 561 {
 562     return expairseq(vp,oc);
 563 }
 564
 565 void expairseq::printpair(ostream & os, const expair & p, unsigned upper_precedence) const
 566 {
 567     os << "[[";
 568     p.rest.bp->print(os,precedence);
 569     os << ",";
 570     p.coeff.bp->print(os,precedence);
 571     os << "]]";
 572 }
 573
 574 void expairseq::printseq(ostream & os, char delim, unsigned this_precedence,
 575                          unsigned upper_precedence) const
 576 {
 577     if (this_precedence<=upper_precedence) os << "(";
 578     epvector::const_iterator it,it_last;
 579     it_last=seq.end();
 580     --it_last;
 581     for (it=seq.begin(); it!=it_last; ++it) {
 582         printpair(os,*it,this_precedence);
 583         os << delim;
 584     }
 585     printpair(os,*it,this_precedence);
 586     if (!overall_coeff.is_equal(default_overall_coeff())) {
 587         os << delim << overall_coeff;
 588     }
 589     if (this_precedence<=upper_precedence) os << ")";
 590 }
 591
 592 expair expairseq::split_ex_to_pair(const ex & e) const
 593 {
 594     return expair(e,_ex1());
 595 }
 596
 597 expair expairseq::combine_ex_with_coeff_to_pair(const ex & e,
 598                                                 const ex & c) const
 599 {
 600     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 601
 602     return expair(e,c);
 603 }
 604
 605 expair expairseq::combine_pair_with_coeff_to_pair(const expair & p,
 606                                                   const ex & c) const
 607 {
 608     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 609     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 610
 611     return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 612 }
 613
 614 ex expairseq::recombine_pair_to_ex(const expair & p) const
 615 {
 616     return lst(p.rest,p.coeff);
 617 }
 618
 619 bool expairseq::expair_needs_further_processing(epp it)
 620 {
 621     return false;
 622 }
 623
 624 ex expairseq::default_overall_coeff(void) const
 625 {
 626     return _ex0();
 627 }
 628
 629 void expairseq::combine_overall_coeff(const ex & c)
 630 {
 631     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 632     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 633     overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 634 }
 635
 636 void expairseq::combine_overall_coeff(const ex & c1, const ex & c2)
 637 {
 638     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 639     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 640     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 641     overall_coeff = ex_to_numeric(overall_coeff).
 642                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 643 }
 644
 645 bool expairseq::can_make_flat(const expair & p) const
 646 {
 647     return true;
 648 }
 649
 650
 651 //////////
 652 // non-virtual functions in this class
 653 //////////
 654
 655 void expairseq::construct_from_2_ex_via_exvector(const ex & lh, const ex & rh)
 656 {
 657     exvector v;
 658     v.reserve(2);
 659     v.push_back(lh);
 660     v.push_back(rh);
 661     construct_from_exvector(v);
 662 #ifdef EXPAIRSEQ_USE_HASHTAB
 663     GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 664     GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 665 #endif // def EXPAIRSEQ_USE_HASHTAB
 666 }
 667
 668 void expairseq::construct_from_2_ex(const ex & lh, const ex & rh)
 669 {
 670     if (lh.bp->tinfo()==tinfo()) {
 671        if (rh.bp->tinfo()==tinfo()) {
 672 #ifdef EXPAIRSEQ_USE_HASHTAB
 673            unsigned totalsize=ex_to_expairseq(lh).seq.size()+
 674                               ex_to_expairseq(rh).seq.size();
 675            if (calc_hashtabsize(totalsize)!=0) {
 676                construct_from_2_ex_via_exvector(lh,rh);
 677            } else {
 678 #endif // def EXPAIRSEQ_USE_HASHTAB
 679                construct_from_2_expairseq(ex_to_expairseq(lh),
 680                                           ex_to_expairseq(rh));
 681 #ifdef EXPAIRSEQ_USE_HASHTAB
 682            }
 683 #endif // def EXPAIRSEQ_USE_HASHTAB
 684            return;
 685        } else {
 686 #ifdef EXPAIRSEQ_USE_HASHTAB
 687            unsigned totalsize=ex_to_expairseq(lh).seq.size()+1;
 688            if (calc_hashtabsize(totalsize)!=0) {
 689                construct_from_2_ex_via_exvector(lh,rh);
 690            } else {
 691 #endif // def EXPAIRSEQ_USE_HASHTAB
 692                construct_from_expairseq_ex(ex_to_expairseq(lh),rh);
 693 #ifdef EXPAIRSEQ_USE_HASHTAB
 694            }
 695 #endif // def EXPAIRSEQ_USE_HASHTAB
 696            return;
 697        }
 698     } else if (rh.bp->tinfo()==tinfo()) {
 699 #ifdef EXPAIRSEQ_USE_HASHTAB
 700         unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 701         if (calc_hashtabsize(totalsize)!=0) {
 702             construct_from_2_ex_via_exvector(lh,rh);
 703         } else {
 704 #endif // def EXPAIRSEQ_USE_HASHTAB
 705             construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 706 #ifdef EXPAIRSEQ_USE_HASHTAB
 707         }
 708 #endif // def EXPAIRSEQ_USE_HASHTAB
 709         return;
 710     }
 711
 712 #ifdef EXPAIRSEQ_USE_HASHTAB
 713     if (calc_hashtabsize(2)!=0) {
 714         construct_from_2_ex_via_exvector(lh,rh);
 715         return;
 716     }
 717     hashtabsize=0;
 718 #endif // def EXPAIRSEQ_USE_HASHTAB
 719
 720     if (is_ex_exactly_of_type(lh,numeric)) {
 721         if (is_ex_exactly_of_type(rh,numeric)) {
 722             combine_overall_coeff(lh);
 723             combine_overall_coeff(rh);
 724         } else {
 725             combine_overall_coeff(lh);
 726             seq.push_back(split_ex_to_pair(rh));
 727         }
 728     } else {
 729         if (is_ex_exactly_of_type(rh,numeric)) {
 730             combine_overall_coeff(rh);
 731             seq.push_back(split_ex_to_pair(lh));
 732         } else {
 733             expair p1=split_ex_to_pair(lh);
 734             expair p2=split_ex_to_pair(rh);
 735
 736             int cmpval=p1.rest.compare(p2.rest);
 737             if (cmpval==0) {
 738                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 739                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 740                     // no further processing is necessary, since this
 741                     // one element will usually be recombined in eval()
 742                     seq.push_back(p1);
 743                 }
 744             } else {
 745                 seq.reserve(2);
 746                 if (cmpval<0) {
 747                     seq.push_back(p1);
 748                     seq.push_back(p2);
 749                 } else {
 750                     seq.push_back(p2);
 751                     seq.push_back(p1);
 752                 }
 753             }
 754         }
 755     }
 756 }
 757
 758 void expairseq::construct_from_2_expairseq(const expairseq & s1,
 759                                            const expairseq & s2)
 760 {
 761     combine_overall_coeff(s1.overall_coeff);
 762     combine_overall_coeff(s2.overall_coeff);
 763
 764     epvector::const_iterator first1=s1.seq.begin();
 765     epvector::const_iterator last1=s1.seq.end();
 766     epvector::const_iterator first2=s2.seq.begin();
 767     epvector::const_iterator last2=s2.seq.end();
 768
 769     seq.reserve(s1.seq.size()+s2.seq.size());
 770
 771     bool needs_further_processing=false;
 772
 773     while (first1!=last1 && first2!=last2) {
 774         int cmpval=(*first1).rest.compare((*first2).rest);
 775         if (cmpval==0) {
 776             // combine terms
 777             const numeric & newcoeff=ex_to_numeric((*first1).coeff).
 778                                      add(ex_to_numeric((*first2).coeff));
 779             if (!newcoeff.is_zero()) {
 780                 seq.push_back(expair((*first1).rest,newcoeff));
 781                 if (expair_needs_further_processing(seq.end()-1)) {
 782                     needs_further_processing = true;
 783                 }
 784             }
 785             ++first1;
 786             ++first2;
 787         } else if (cmpval<0) {
 788             seq.push_back(*first1);
 789             ++first1;
 790         } else {
 791             seq.push_back(*first2);
 792             ++first2;
 793         }
 794     }
 795
 796     while (first1!=last1) {
 797         seq.push_back(*first1);
 798         ++first1;
 799     }
 800     while (first2!=last2) {
 801         seq.push_back(*first2);
 802         ++first2;
 803     }
 804
 805     if (needs_further_processing) {
 806         epvector v=seq;
 807         seq.clear();
 808         construct_from_epvector(v);
 809     }
 810 }
 811
 812 void expairseq::construct_from_expairseq_ex(const expairseq & s,
 813                                             const ex & e)
 814 {
 815     combine_overall_coeff(s.overall_coeff);
 816     if (is_ex_exactly_of_type(e,numeric)) {
 817         combine_overall_coeff(e);
 818         seq=s.seq;
 819         return;
 820     }
 821
 822     epvector::const_iterator first=s.seq.begin();
 823     epvector::const_iterator last=s.seq.end();
 824     expair p=split_ex_to_pair(e);
 825
 826     seq.reserve(s.seq.size()+1);
 827     bool p_pushed=0;
 828
 829     bool needs_further_processing=false;
 830
 831     // merge p into s.seq
 832     while (first!=last) {
 833         int cmpval=(*first).rest.compare(p.rest);
 834         if (cmpval==0) {
 835             // combine terms
 836             const numeric & newcoeff=ex_to_numeric((*first).coeff).
 837                                      add(ex_to_numeric(p.coeff));
 838             if (!newcoeff.is_zero()) {
 839                 seq.push_back(expair((*first).rest,newcoeff));
 840                 if (expair_needs_further_processing(seq.end()-1)) {
 841                     needs_further_processing = true;
 842                 }
 843             }
 844             ++first;
 845             p_pushed=1;
 846             break;
 847         } else if (cmpval<0) {
 848             seq.push_back(*first);
 849             ++first;
 850         } else {
 851             seq.push_back(p);
 852             p_pushed=1;
 853             break;
 854         }
 855     }
 856
 857     if (p_pushed) {
 858         // while loop exited because p was pushed, now push rest of s.seq
 859         while (first!=last) {
 860             seq.push_back(*first);
 861             ++first;
 862         }
 863     } else {
 864         // while loop exited because s.seq was pushed, now push p
 865         seq.push_back(p);
 866     }
 867
 868     if (needs_further_processing) {
 869         epvector v=seq;
 870         seq.clear();
 871         construct_from_epvector(v);
 872     }
 873 }
 874
 875 void expairseq::construct_from_exvector(const exvector & v)
 876 {
 877     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 878     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 879     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 880     //                  (same for (+,*) -> (*,^)
 881
 882     make_flat(v);
 883 #ifdef EXPAIRSEQ_USE_HASHTAB
 884     combine_same_terms();
 885 #else
 886     canonicalize();
 887     combine_same_terms_sorted_seq();
 888 #endif // def EXPAIRSEQ_USE_HASHTAB
 889 }
 890
 891 void expairseq::construct_from_epvector(const epvector & v)
 892 {
 893     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 894     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 895     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 896     //                  (same for (+,*) -> (*,^)
 897
 898     make_flat(v);
 899 #ifdef EXPAIRSEQ_USE_HASHTAB
 900     combine_same_terms();
 901 #else
 902     canonicalize();
 903     combine_same_terms_sorted_seq();
 904 #endif // def EXPAIRSEQ_USE_HASHTAB
 905 }
 906
 907 #include <iostream>
 908
 909 void expairseq::make_flat(const exvector & v)
 910 {
 911     exvector::const_iterator cit, citend = v.end();
 912
 913     // count number of operands which are of same expairseq derived type
 914     // and their cumulative number of operands
 915     int nexpairseqs=0;
 916     int noperands=0;
 917     cit=v.begin();
 918     while (cit!=citend) {
 919         if (cit->bp->tinfo()==tinfo()) {
 920             nexpairseqs++;
 921             noperands+=ex_to_expairseq(*cit).seq.size();
 922         }
 923         ++cit;
 924     }
 925
 926     // reserve seq and coeffseq which will hold all operands
 927     seq.reserve(v.size()+noperands-nexpairseqs);
 928
 929     // copy elements and split off numerical part
 930     cit=v.begin();
 931     while (cit!=citend) {
 932         if (cit->bp->tinfo()==tinfo()) {
 933             const expairseq & subseqref=ex_to_expairseq(*cit);
 934             combine_overall_coeff(subseqref.overall_coeff);
 935             epvector::const_iterator cit_s=subseqref.seq.begin();
 936             while (cit_s!=subseqref.seq.end()) {
 937                 seq.push_back(*cit_s);
 938                 ++cit_s;
 939             }
 940         } else {
 941             if (is_ex_exactly_of_type(*cit,numeric)) {
 942                 combine_overall_coeff(*cit);
 943             } else {
 944                 seq.push_back(split_ex_to_pair(*cit));
 945             }
 946         }
 947         ++cit;
 948     }
 949
 950     /*
 951     cout << "after make flat" << endl;
 952     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 953         (*cit).printraw(cout);
 954     }
 955     cout << endl;
 956     */
 957 }
 958
 959 void expairseq::make_flat(const epvector & v)
 960 {
 961     epvector::const_iterator cit, citend = v.end();
 962
 963     // count number of operands which are of same expairseq derived type
 964     // and their cumulative number of operands
 965     int nexpairseqs=0;
 966     int noperands=0;
 967
 968     cit = v.begin();
 969     while (cit!=citend) {
 970         if (cit->rest.bp->tinfo()==tinfo()) {
 971             nexpairseqs++;
 972             noperands += ex_to_expairseq((*cit).rest).seq.size();
 973         }
 974         ++cit;
 975     }
 976
 977     // reserve seq and coeffseq which will hold all operands
 978     seq.reserve(v.size()+noperands-nexpairseqs);
 979
 980     // copy elements and split off numerical part
 981     cit = v.begin();
 982     while (cit!=citend) {
 983         if ((cit->rest.bp->tinfo()==tinfo())&&can_make_flat(*cit)) {
 984             const expairseq & subseqref=ex_to_expairseq((*cit).rest);
 985             combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 986                                   ex_to_numeric((*cit).coeff));
 987             epvector::const_iterator cit_s=subseqref.seq.begin();
 988             while (cit_s!=subseqref.seq.end()) {
 989                 seq.push_back(expair((*cit_s).rest,
 990                               ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
 991                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 992                 //                                              (*cit).coeff));
 993                 ++cit_s;
 994             }
 995         } else {
 996             if ((*cit).is_numeric_with_coeff_1()) {
 997                 combine_overall_coeff((*cit).rest);
 998             //if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 999             //    combine_overall_coeff(recombine_pair_to_ex(*cit));
1000             } else {
1001                 seq.push_back(*cit);
1002             }
1003         }
1004         ++cit;
1005     }
1006 }
1007
1008 epvector * expairseq::bubblesort(epvector::iterator itbegin, epvector::iterator itend)
1009 {
1010     unsigned n=itend-itbegin;
1011
1012     epvector * sp=new epvector;
1013     sp->reserve(n);
1014
1015     epvector::iterator last=itend-1;
1016     for (epvector::iterator it1=itbegin; it1!=last; ++it1) {
1017         for (epvector::iterator it2=it1+1; it2!=itend; ++it2) {
1018             if ((*it2).rest.compare((*it1).rest)<0) {
1019                 iter_swap(it1,it2);
1020             }
1021         }
1022         sp->push_back(*it1);
1023     }
1024     sp->push_back(*last);
1025     return sp;
1026 }
1027
1028 epvector * expairseq::mergesort(epvector::iterator itbegin, epvector::iterator itend)
1029 {
1030     unsigned n=itend-itbegin;
1031     /*
1032     if (n==1) {
1033         epvector * sp=new epvector;
1034         sp->push_back(*itbegin);
1035         return sp;
1036     }
1037     */
1038     if (n<16) return bubblesort(itbegin, itend);
1039     unsigned m=n/2;
1040
1041     epvector * s1p=mergesort(itbegin, itbegin+m);
1042     epvector * s2p=mergesort(itbegin+m, itend);
1043
1044     epvector * sp=new epvector;
1045     sp->reserve(s1p->size()+s2p->size());
1046
1047     epvector::iterator first1=s1p->begin();
1048     epvector::iterator last1=s1p->end();
1049
1050     epvector::iterator first2=s2p->begin();
1051     epvector::iterator last2=s2p->end();
1052
1053     while (first1 != last1 && first2 != last2) {
1054         if ((*first1).rest.compare((*first2).rest)<0) {
1055             sp->push_back(*first1);
1056             ++first1;
1057         } else {
1058             sp->push_back(*first2);
1059             ++first2;
1060         }
1061     }
1062
1063     if (first1 != last1) {
1064         while (first1 != last1) {
1065             sp->push_back(*first1);
1066             ++first1;
1067         }
1068     } else {
1069         while (first2 != last2) {
1070             sp->push_back(*first2);
1071             ++first2;
1072         }
1073     }
1074
1075     delete s1p;
1076     delete s2p;
1077
1078     return sp;
1079 }
1080
1081
1082 void expairseq::canonicalize(void)
1083 {
1084     // canonicalize
1085     sort(seq.begin(),seq.end(),expair_is_less());
1086     /*
1087     sort(seq.begin(),seq.end(),expair_is_less_old());
1088     if (seq.size()>1) {
1089         if (is_ex_exactly_of_type((*(seq.begin())).rest,numeric)) {
1090             sort(seq.begin(),seq.end(),expair_is_less());
1091         } else {
1092             epvector::iterator last_numeric=seq.end();
1093             do {
1094                 last_numeric--;
1095             } while (is_ex_exactly_of_type((*last_numeric).rest,numeric));
1096             last_numeric++;
1097             sort(last_numeric,seq.end(),expair_is_less());
1098         }
1099     }
1100     */
1101
1102     /*
1103     epvector * sorted_seqp=mergesort(seq.begin(),seq.end());
1104     epvector::iterator last=sorted_seqp->end();
1105     epvector::iterator it2=seq.begin();
1106     for (epvector::iterator it1=sorted_seqp->begin(); it1!=last; ++it1, ++it2) {
1107         iter_swap(it1,it2);
1108     }
1109     delete sorted_seqp;
1110     */
1111
1112     /*
1113     cout << "after canonicalize" << endl;
1114     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1115         (*cit).printraw(cout);
1116     }
1117     cout << endl;
1118     cout.flush();
1119     */
1120 }
1121
1122 void expairseq::combine_same_terms_sorted_seq(void)
1123 {
1124     bool needs_further_processing=false;
1125
1126     // combine same terms, drop term with coeff 0
1127     if (seq.size()>1) {
1128         epvector::iterator itin1=seq.begin();
1129         epvector::iterator itin2=itin1+1;
1130         epvector::iterator itout=itin1;
1131         epvector::iterator last=seq.end();
1132         // must_copy will be set to true the first time some combination is possible
1133         // from then on the sequence has changed and must be compacted
1134         bool must_copy=false;
1135         while (itin2!=last) {
1136             if ((*itin1).rest.compare((*itin2).rest)==0) {
1137                 (*itin1).coeff=ex_to_numeric((*itin1).coeff).
1138                                add_dyn(ex_to_numeric((*itin2).coeff));
1139                 if (expair_needs_further_processing(itin1)) {
1140                     needs_further_processing = true;
1141                 }
1142                 must_copy=true;
1143             } else {
1144                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1145                     if (must_copy) {
1146                         *itout=*itin1;
1147                     }
1148                     ++itout;
1149                 }
1150                 itin1=itin2;
1151             }
1152             ++itin2;
1153         }
1154         if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1155             if (must_copy) {
1156                 *itout=*itin1;
1157             }
1158             ++itout;
1159         }
1160         if (itout!=last) {
1161             seq.erase(itout,last);
1162         }
1163     }
1164
1165     /*
1166     cout << "after combine" << endl;
1167     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1168         (*cit).printraw(cout);
1169     }
1170     cout << endl;
1171     cout.flush();
1172     */
1173
1174     if (needs_further_processing) {
1175         epvector v=seq;
1176         seq.clear();
1177         construct_from_epvector(v);
1178     }
1179 }
1180
1181 #ifdef EXPAIRSEQ_USE_HASHTAB
1182
1183 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1184 {
1185     unsigned size;
1186     unsigned nearest_power_of_2 = 1 << log2(sz);
1187     //    if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1188     //  size=nearest_power_of_2*hashtabfactor;
1189     size=nearest_power_of_2/hashtabfactor;
1190     if (size<minhashtabsize) return 0;
1191     GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1192     // hashtabsize must be a power of 2
1193     GINAC_ASSERT((1U << log2(size))==size);
1194     return size;
1195 }
1196
1197 unsigned expairseq::calc_hashindex(const ex & e) const
1198 {
1199     // calculate hashindex
1200     unsigned hash=e.gethash();
1201     unsigned hashindex;
1202     if (is_a_numeric_hash(hash)) {
1203         hashindex=hashmask;
1204     } else {
1205         hashindex=hash & hashmask;
1206         // last hashtab entry is reserved for numerics
1207         if (hashindex==hashmask) hashindex=0;
1208     }
1209     GINAC_ASSERT(hashindex>=0);
1210     GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1211     return hashindex;
1212 }
1213
1214 void expairseq::shrink_hashtab(void)
1215 {
1216     unsigned new_hashtabsize;
1217     while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1218         GINAC_ASSERT(new_hashtabsize<hashtabsize);
1219         if (new_hashtabsize==0) {
1220             hashtab.clear();
1221             hashtabsize=0;
1222             canonicalize();
1223             return;
1224         }
1225
1226         // shrink by a factor of 2
1227         unsigned half_hashtabsize=hashtabsize/2;
1228         for (unsigned i=0; i<half_hashtabsize-1; ++i) {
1229             hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1230         }
1231         // special treatment for numeric hashes
1232         hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1233         hashtab[half_hashtabsize-1]=hashtab[hashtabsize-1];
1234         hashtab.resize(half_hashtabsize);
1235         hashtabsize=half_hashtabsize;
1236         hashmask=hashtabsize-1;
1237     }
1238 }
1239
1240 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1241 {
1242     if (hashtabsize==0) return; // nothing to do
1243
1244     // calculate hashindex of element to be deleted
1245     unsigned hashindex=calc_hashindex((*element).rest);
1246
1247     // find it in hashtab and remove it
1248     epplist & eppl=hashtab[hashindex];
1249     epplist::iterator epplit=eppl.begin();
1250     bool erased=false;
1251     while (epplit!=eppl.end()) {
1252         if (*epplit == element) {
1253             eppl.erase(epplit);
1254             erased=true;
1255             break;
1256         }
1257         ++epplit;
1258     }
1259     if (!erased) {
1260         printtree(cout,0);
1261         cout << "tried to erase " << element-seq.begin() << endl;
1262         cout << "size " << seq.end()-seq.begin() << endl;
1263
1264         unsigned hashindex=calc_hashindex((*element).rest);
1265         epplist & eppl=hashtab[hashindex];
1266         epplist::iterator epplit=eppl.begin();
1267         bool erased=false;
1268         while (epplit!=eppl.end()) {
1269             if (*epplit == element) {
1270                 eppl.erase(epplit);
1271                 erased=true;
1272                 break;
1273             }
1274             ++epplit;
1275         }
1276         GINAC_ASSERT(erased);
1277     }
1278     GINAC_ASSERT(erased);
1279 }
1280
1281 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1282                                    epvector::iterator newpos)
1283 {
1284     GINAC_ASSERT(hashtabsize!=0);
1285
1286     // calculate hashindex of element which was moved
1287     unsigned hashindex=calc_hashindex((*newpos).rest);
1288
1289     // find it in hashtab and modify it
1290     epplist & eppl=hashtab[hashindex];
1291     epplist::iterator epplit=eppl.begin();
1292     while (epplit!=eppl.end()) {
1293         if (*epplit == oldpos) {
1294             *epplit=newpos;
1295             break;
1296         }
1297         ++epplit;
1298     }
1299     GINAC_ASSERT(epplit!=eppl.end());
1300 }
1301
1302 void expairseq::sorted_insert(epplist & eppl, epp elem)
1303 {
1304     epplist::iterator current=eppl.begin();
1305     while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1306         ++current;
1307     }
1308     eppl.insert(current,elem);
1309 }
1310
1311 void expairseq::build_hashtab_and_combine(epvector::iterator & first_numeric,
1312                                           epvector::iterator & last_non_zero,
1313                                           vector<bool> & touched,
1314                                           unsigned & number_of_zeroes)
1315 {
1316     epp current=seq.begin();
1317
1318     while (current!=first_numeric) {
1319         if (is_ex_exactly_of_type((*current).rest,numeric)) {
1320             --first_numeric;
1321             iter_swap(current,first_numeric);
1322         } else {
1323             // calculate hashindex
1324             unsigned currenthashindex=calc_hashindex((*current).rest);
1325
1326             // test if there is already a matching expair in the hashtab-list
1327             epplist & eppl=hashtab[currenthashindex];
1328             epplist::iterator epplit=eppl.begin();
1329             while (epplit!=eppl.end()) {
1330                 if ((*current).rest.is_equal((*(*epplit)).rest)) break;
1331                 ++epplit;
1332             }
1333             if (epplit==eppl.end()) {
1334                 // no matching expair found, append this to end of list
1335                 sorted_insert(eppl,current);
1336                 ++current;
1337             } else {
1338                 // epplit points to a matching expair, combine it with current
1339                 (*(*epplit)).coeff=ex_to_numeric((*(*epplit)).coeff).
1340                                    add_dyn(ex_to_numeric((*current).coeff));
1341
1342                 // move obsolete current expair to end by swapping with last_non_zero element
1343                 // if this was a numeric, it is swapped with the expair before first_numeric
1344                 iter_swap(current,last_non_zero);
1345                 --first_numeric;
1346                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1347                 --last_non_zero;
1348                 ++number_of_zeroes;
1349                 // test if combined term has coeff 0 and can be removed is done later
1350                 touched[(*epplit)-seq.begin()]=true;
1351             }
1352         }
1353     }
1354 }
1355
1356 void expairseq::drop_coeff_0_terms(epvector::iterator & first_numeric,
1357                                    epvector::iterator & last_non_zero,
1358                                    vector<bool> & touched,
1359                                    unsigned & number_of_zeroes)
1360 {
1361     // move terms with coeff 0 to end and remove them from hashtab
1362     // check only those elements which have been touched
1363     epp current=seq.begin();
1364     unsigned i=0;
1365     while (current!=first_numeric) {
1366         if (!touched[i]) {
1367             ++current;
1368             ++i;
1369         } else if (!ex_to_numeric((*current).coeff).is_equal(_num0())) {
1370             ++current;
1371             ++i;
1372         } else {
1373             remove_hashtab_entry(current);
1374
1375             // move element to the end, unless it is already at the end
1376             if (current!=last_non_zero) {
1377                 iter_swap(current,last_non_zero);
1378                 --first_numeric;
1379                 bool numeric_swapped=first_numeric!=last_non_zero;
1380                 if (numeric_swapped) iter_swap(first_numeric,current);
1381                 epvector::iterator changed_entry;
1382
1383                 if (numeric_swapped) {
1384                     changed_entry=first_numeric;
1385                 } else {
1386                     changed_entry=last_non_zero;
1387                 }
1388
1389                 --last_non_zero;
1390                 ++number_of_zeroes;
1391
1392                 if (first_numeric!=current) {
1393
1394                     // change entry in hashtab which referred to first_numeric or last_non_zero to current
1395                     move_hashtab_entry(changed_entry,current);
1396                     touched[current-seq.begin()]=touched[changed_entry-seq.begin()];
1397                 }
1398             } else {
1399                 --first_numeric;
1400                 --last_non_zero;
1401                 ++number_of_zeroes;
1402             }
1403         }
1404     }
1405     GINAC_ASSERT(i==current-seq.begin());
1406 }
1407
1408 bool expairseq::has_coeff_0(void) const
1409 {
1410     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1411         if ((*cit).coeff.is_equal(_ex0())) {
1412             return true;
1413         }
1414     }
1415     return false;
1416 }
1417
1418 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1419                                         epvector::const_iterator last_non_zero)
1420 {
1421     if (first_numeric==seq.end()) return; // no numerics
1422
1423     epvector::iterator current=first_numeric;
1424     epvector::const_iterator last=last_non_zero+1;
1425     while (current!=last) {
1426         sorted_insert(hashtab[hashmask],current);
1427         ++current;
1428     }
1429 }
1430
1431 void expairseq::combine_same_terms(void)
1432 {
1433     // combine same terms, drop term with coeff 0, move numerics to end
1434
1435     // calculate size of hashtab
1436     hashtabsize=calc_hashtabsize(seq.size());
1437
1438     // hashtabsize is a power of 2
1439     hashmask=hashtabsize-1;
1440
1441     // allocate hashtab
1442     hashtab.clear();
1443     hashtab.resize(hashtabsize);
1444
1445     if (hashtabsize==0) {
1446         canonicalize();
1447         combine_same_terms_sorted_seq();
1448         GINAC_ASSERT(!has_coeff_0());
1449         return;
1450     }
1451
1452     // iterate through seq, move numerics to end,
1453     // fill hashtab and combine same terms
1454     epvector::iterator first_numeric=seq.end();
1455     epvector::iterator last_non_zero=seq.end()-1;
1456
1457     vector<bool> touched;
1458     touched.reserve(seq.size());
1459     for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1460
1461     unsigned number_of_zeroes=0;
1462
1463     GINAC_ASSERT(!has_coeff_0());
1464     build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1465     /*
1466     cout << "in combine:" << endl;
1467     printtree(cout,0);
1468     cout << "size=" << seq.end() - seq.begin() << endl;
1469     cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1470     cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1471     for (unsigned i=0; i<seq.size(); ++i) {
1472         if (touched[i]) cout << i << " is touched" << endl;
1473     }
1474     cout << "end in combine" << endl;
1475     */
1476
1477     // there should not be any terms with coeff 0 from the beginning,
1478     // so it should be safe to skip this step
1479     if (number_of_zeroes!=0) {
1480         drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1481         /*
1482         cout << "in combine after drop:" << endl;
1483         printtree(cout,0);
1484         cout << "size=" << seq.end() - seq.begin() << endl;
1485         cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1486         cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1487         for (unsigned i=0; i<seq.size(); ++i) {
1488             if (touched[i]) cout << i << " is touched" << endl;
1489         }
1490         cout << "end in combine after drop" << endl;
1491         */
1492     }
1493
1494     add_numerics_to_hashtab(first_numeric,last_non_zero);
1495
1496     // pop zero elements
1497     for (unsigned i=0; i<number_of_zeroes; ++i) {
1498         seq.pop_back();
1499     }
1500
1501     // shrink hashtabsize to calculated value
1502     GINAC_ASSERT(!has_coeff_0());
1503
1504     shrink_hashtab();
1505
1506     GINAC_ASSERT(!has_coeff_0());
1507 }
1508
1509 #endif // def EXPAIRSEQ_USE_HASHTAB
1510
1511 bool expairseq::is_canonical() const
1512 {
1513     if (seq.size()<=1) return 1;
1514
1515 #ifdef EXPAIRSEQ_USE_HASHTAB
1516     if (hashtabsize>0) return 1; // not canoncalized
1517 #endif // def EXPAIRSEQ_USE_HASHTAB
1518
1519     epvector::const_iterator it = seq.begin();
1520     epvector::const_iterator it_last = it;
1521     for (++it; it!=seq.end(); it_last=it, ++it) {
1522         if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
1523             if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1524                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1525                 // double test makes it easier to set a breakpoint...
1526                 if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1527                     !is_ex_exactly_of_type((*it).rest,numeric)) {
1528                     printpair(cout,*it_last,0);
1529                     cout << ">";
1530                     printpair(cout,*it,0);
1531                     cout << "\n";
1532                     cout << "pair1:" << endl;
1533                     (*it_last).rest.printtree(cout);
1534                     (*it_last).coeff.printtree(cout);
1535                     cout << "pair2:" << endl;
1536                     (*it).rest.printtree(cout);
1537                     (*it).coeff.printtree(cout);
1538                     return 0;
1539                 }
1540             }
1541         }
1542     }
1543     return 1;
1544 }
1545
1546 epvector * expairseq::expandchildren(unsigned options) const
1547 {
1548     epvector::const_iterator last=seq.end();
1549     epvector::const_iterator cit=seq.begin();
1550     while (cit!=last) {
1551         const ex & expanded_ex=(*cit).rest.expand(options);
1552         if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1553
1554             // something changed, copy seq, eval and return it
1555             epvector *s=new epvector;
1556             s->reserve(seq.size());
1557
1558             // copy parts of seq which are known not to have changed
1559             epvector::const_iterator cit2 = seq.begin();
1560             while (cit2!=cit) {
1561                 s->push_back(*cit2);
1562                 ++cit2;
1563             }
1564             // copy first changed element
1565             s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1566                                                        (*cit2).coeff));
1567             ++cit2;
1568             // copy rest
1569             while (cit2!=last) {
1570                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1571                                                            (*cit2).coeff));
1572                 ++cit2;
1573             }
1574             return s;
1575         }
1576         ++cit;
1577     }
1578
1579     return 0; // nothing has changed
1580 }
1581
1582 epvector * expairseq::evalchildren(int level) const
1583 {
1584     // returns a NULL pointer if nothing had to be evaluated
1585     // returns a pointer to a newly created epvector otherwise
1586     // (which has to be deleted somewhere else)
1587
1588     if (level==1) {
1589         return 0;
1590     }
1591     if (level == -max_recursion_level) {
1592         throw(std::runtime_error("max recursion level reached"));
1593     }
1594
1595     --level;
1596     epvector::const_iterator last=seq.end();
1597     epvector::const_iterator cit=seq.begin();
1598     while (cit!=last) {
1599         const ex & evaled_ex=(*cit).rest.eval(level);
1600         if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1601
1602             // something changed, copy seq, eval and return it
1603             epvector *s = new epvector;
1604             s->reserve(seq.size());
1605
1606             // copy parts of seq which are known not to have changed
1607             epvector::const_iterator cit2=seq.begin();
1608             while (cit2!=cit) {
1609                 s->push_back(*cit2);
1610                 ++cit2;
1611             }
1612             // copy first changed element
1613             s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1614                                                        (*cit2).coeff));
1615             ++cit2;
1616             // copy rest
1617             while (cit2!=last) {
1618                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1619                                                            (*cit2).coeff));
1620                 ++cit2;
1621             }
1622             return s;
1623         }
1624         ++cit;
1625     }
1626
1627     return 0; // nothing has changed
1628 }
1629
1630 epvector expairseq::evalfchildren(int level) const
1631 {
1632     if (level==1)
1633         return seq;
1634
1635     if (level==-max_recursion_level)
1636         throw(std::runtime_error("max recursion level reached"));
1637
1638     epvector s;
1639     s.reserve(seq.size());
1640
1641     --level;
1642     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1643         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1644                                                   (*it).coeff.evalf(level)));
1645     }
1646     return s;
1647 }
1648
1649 epvector expairseq::normalchildren(int level) const
1650 {
1651     if (level==1)
1652         return seq;
1653
1654     if (level == -max_recursion_level)
1655         throw(std::runtime_error("max recursion level reached"));
1656
1657     epvector s;
1658     s.reserve(seq.size());
1659
1660     --level;
1661     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1662         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1663                                                   (*it).coeff));
1664     }
1665     return s;
1666 }
1667
1668 epvector expairseq::diffchildren(const symbol & y) const
1669 {
1670     epvector s;
1671     s.reserve(seq.size());
1672
1673     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1674         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1675                                                   (*it).coeff));
1676     }
1677     return s;
1678 }
1679
1680 epvector * expairseq::subschildren(const lst & ls, const lst & lr) const
1681 {
1682     // returns a NULL pointer if nothing had to be substituted
1683     // returns a pointer to a newly created epvector otherwise
1684     // (which has to be deleted somewhere else)
1685     GINAC_ASSERT(ls.nops()==lr.nops());
1686
1687     epvector::const_iterator last=seq.end();
1688     epvector::const_iterator cit=seq.begin();
1689     while (cit!=last) {
1690         const ex & subsed_ex=(*cit).rest.subs(ls,lr);
1691         if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1692
1693             // something changed, copy seq, subs and return it
1694             epvector *s=new epvector;
1695             s->reserve(seq.size());
1696
1697             // copy parts of seq which are known not to have changed
1698             epvector::const_iterator cit2=seq.begin();
1699             while (cit2!=cit) {
1700                 s->push_back(*cit2);
1701                 ++cit2;
1702             }
1703             // copy first changed element
1704             s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1705                                                        (*cit2).coeff));
1706             ++cit2;
1707             // copy rest
1708             while (cit2!=last) {
1709                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
1710                                                            (*cit2).coeff));
1711                 ++cit2;
1712             }
1713             return s;
1714         }
1715         ++cit;
1716     }
1717
1718     return 0; // nothing has changed
1719 }
1720
1721 //////////
1722 // static member variables
1723 //////////
1724
1725 // protected
1726
1727 unsigned expairseq::precedence=10;
1728
1729 #ifdef EXPAIRSEQ_USE_HASHTAB
1730 unsigned expairseq::maxhashtabsize=0x4000000U;
1731 unsigned expairseq::minhashtabsize=0x1000U;
1732 unsigned expairseq::hashtabfactor=1;
1733 #endif // def EXPAIRSEQ_USE_HASHTAB
1734
1735 //////////
1736 // global constants
1737 //////////
1738
1739 const expairseq some_expairseq;
1740 const type_info & typeid_expairseq=typeid(some_expairseq);
1741
1742 #ifndef NO_NAMESPACE_GINAC
1743 } // namespace GiNaC
1744 #endif // ndef NO_NAMESPACE_GINAC