ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999 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 "debugmsg.h"
  30 #include "utils.h"
  31
  32 namespace GiNaC {
  33
  34 #ifdef EXPAIRSEQ_USE_HASHTAB
  35 #error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
  36 #endif // def EXPAIRSEQ_USE_HASHTAB
  37
  38 //////////
  39 // helper classes
  40 //////////
  41
  42 class epp_is_less
  43 {
  44 public:
  45     bool operator()(epp const & lh, epp const & rh) const
  46     {
  47         return (*lh).is_less(*rh);
  48     }
  49 };
  50
  51 //////////
  52 // default constructor, destructor, copy constructor assignment operator and helpers
  53 //////////
  54
  55 // public
  56
  57 expairseq::expairseq(expairseq const & other)
  58 {
  59     debugmsg("expairseq copy constructor",LOGLEVEL_CONSTRUCT);
  60     copy(other);
  61 }
  62
  63 expairseq const & expairseq::operator=(expairseq const & other)
  64 {
  65     debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  66     if (this != &other) {
  67         destroy(1);
  68         copy(other);
  69     }
  70     return *this;
  71 }
  72
  73 // protected
  74
  75 void expairseq::copy(expairseq const & other)
  76 {
  77     basic::copy(other);
  78     seq=other.seq;
  79     overall_coeff=other.overall_coeff;
  80 #ifdef EXPAIRSEQ_USE_HASHTAB
  81     // copy hashtab
  82     hashtabsize=other.hashtabsize;
  83     if (hashtabsize!=0) {
  84     hashmask=other.hashmask;
  85         hashtab.resize(hashtabsize);
  86         epvector::const_iterator osb=other.seq.begin();
  87         for (unsigned i=0; i<hashtabsize; ++i) {
  88             hashtab[i].clear();
  89             for (epplist::const_iterator cit=other.hashtab[i].begin();
  90                  cit!=other.hashtab[i].end(); ++cit) {
  91                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  92             }
  93         }
  94     } else {
  95         hashtab.clear();
  96     }
  97 #endif // def EXPAIRSEQ_USE_HASHTAB
  98 }
  99
 100 //////////
 101 // other constructors
 102 //////////
 103
 104 expairseq::expairseq(ex const & lh, ex const & rh) : basic(TINFO_expairseq)
 105 {
 106     debugmsg("expairseq constructor from ex,ex",LOGLEVEL_CONSTRUCT);
 107     construct_from_2_ex(lh,rh);
 108     GINAC_ASSERT(is_canonical());
 109 }
 110
 111 expairseq::expairseq(exvector const & v) : basic(TINFO_expairseq)
 112 {
 113     debugmsg("expairseq constructor from exvector",LOGLEVEL_CONSTRUCT);
 114     construct_from_exvector(v);
 115     GINAC_ASSERT(is_canonical());
 116 }
 117
 118 /*
 119 expairseq::expairseq(epvector const & v, bool do_not_canonicalize) :
 120     basic(TINFO_expairseq)
 121 {
 122     debugmsg("expairseq constructor from epvector",LOGLEVEL_CONSTRUCT);
 123     if (do_not_canonicalize) {
 124         seq=v;
 125 #ifdef EXPAIRSEQ_USE_HASHTAB
 126         combine_same_terms(); // to build hashtab
 127 #endif // def EXPAIRSEQ_USE_HASHTAB
 128     } else {
 129         construct_from_epvector(v);
 130     }
 131     GINAC_ASSERT(is_canonical());
 132 }
 133 */
 134
 135 expairseq::expairseq(epvector const & v, ex const & oc) :
 136     basic(TINFO_expairseq), overall_coeff(oc)
 137 {
 138     debugmsg("expairseq constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 139     construct_from_epvector(v);
 140     GINAC_ASSERT(is_canonical());
 141 }
 142
 143 expairseq::expairseq(epvector * vp, ex const & oc) :
 144     basic(TINFO_expairseq), overall_coeff(oc)
 145 {
 146     debugmsg("expairseq constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 147     GINAC_ASSERT(vp!=0);
 148     construct_from_epvector(*vp);
 149     delete vp;
 150     GINAC_ASSERT(is_canonical());
 151 }
 152
 153 //////////
 154 // functions overriding virtual functions from bases classes
 155 //////////
 156
 157 // public
 158
 159 basic * expairseq::duplicate() const
 160 {
 161     debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 162     return new expairseq(*this);
 163 }
 164
 165 bool expairseq::info(unsigned inf) const
 166 {
 167     return basic::info(inf);
 168 }
 169
 170 int expairseq::nops() const
 171 {
 172     if (overall_coeff.is_equal(default_overall_coeff())) {
 173         return seq.size();
 174     }
 175     return seq.size()+1;
 176 }
 177
 178 ex expairseq::op(int const i) const
 179 {
 180     if (unsigned(i)<seq.size()) {
 181         return recombine_pair_to_ex(seq[i]);
 182     }
 183     GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 184     return overall_coeff;
 185 }
 186
 187 ex & expairseq::let_op(int const i)
 188 {
 189     throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 190 }
 191
 192 ex expairseq::eval(int level) const
 193 {
 194     if ((level==1)&&(flags & status_flags::evaluated)) {
 195         return *this;
 196     }
 197
 198     epvector * vp=evalchildren(level);
 199     if (vp==0) {
 200         return this->hold();
 201     }
 202
 203     return (new expairseq(vp,overall_coeff))
 204                ->setflag(status_flags::dynallocated |
 205                          status_flags::evaluated );
 206 }
 207
 208 ex expairseq::evalf(int level) const
 209 {
 210     return thisexpairseq(evalfchildren(level),overall_coeff);
 211 }
 212
 213 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 214 {
 215     ex n=thisexpairseq(normalchildren(level),overall_coeff);
 216     return n.bp->basic::normal(sym_lst,repl_lst,level);
 217 }
 218
 219 ex expairseq::subs(lst const & ls, lst const & lr) const
 220 {
 221     epvector * vp=subschildren(ls,lr);
 222     if (vp==0) {
 223         return *this;
 224     }
 225     return thisexpairseq(vp,overall_coeff);
 226 }
 227
 228 // protected
 229
 230 int expairseq::compare_same_type(basic const & other) const
 231 {
 232     GINAC_ASSERT(is_of_type(other, expairseq));
 233     expairseq const & o=static_cast<expairseq const &>(const_cast<basic &>(other));
 234
 235     int cmpval;
 236
 237     // compare number of elements
 238     if (seq.size() != o.seq.size()) {
 239         return (seq.size()<o.seq.size()) ? -1 : 1;
 240     }
 241
 242     // compare overall_coeff
 243     cmpval=overall_coeff.compare(o.overall_coeff);
 244     if (cmpval!=0) return cmpval;
 245
 246     //if (seq.size()==0) return 0; // empty expairseq's are equal
 247
 248 #ifdef EXPAIRSEQ_USE_HASHTAB
 249     GINAC_ASSERT(hashtabsize==o.hashtabsize);
 250     if (hashtabsize==0) {
 251 #endif // def EXPAIRSEQ_USE_HASHTAB
 252         epvector::const_iterator cit1=seq.begin();
 253         epvector::const_iterator cit2=o.seq.begin();
 254         epvector::const_iterator last1=seq.end();
 255         epvector::const_iterator last2=o.seq.end();
 256
 257         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 258             cmpval=(*cit1).compare(*cit2);
 259             if (cmpval!=0) return cmpval;
 260         }
 261
 262         GINAC_ASSERT(cit1==last1);
 263         GINAC_ASSERT(cit2==last2);
 264
 265         return 0;
 266 #ifdef EXPAIRSEQ_USE_HASHTAB
 267     }
 268
 269     // compare number of elements in each hashtab entry
 270     for (unsigned i=0; i<hashtabsize; ++i) {
 271         unsigned cursize=hashtab[i].size();
 272         if (cursize != o.hashtab[i].size()) {
 273             return (cursize < o.hashtab[i].size()) ? -1 : 1;
 274         }
 275     }
 276
 277     // compare individual (sorted) hashtab entries
 278     for (unsigned i=0; i<hashtabsize; ++i) {
 279         unsigned sz=hashtab[i].size();
 280         if (sz>0) {
 281             epplist const & eppl1=hashtab[i];
 282             epplist const & eppl2=o.hashtab[i];
 283             epplist::const_iterator it1=eppl1.begin();
 284             epplist::const_iterator it2=eppl2.begin();
 285             while (it1!=eppl1.end()) {
 286                 cmpval=(*(*it1)).compare(*(*it2));
 287                 if (cmpval!=0) return cmpval;
 288                 ++it1;
 289                 ++it2;
 290             }
 291         }
 292     }
 293
 294     return 0; // equal
 295 #endif // def EXPAIRSEQ_USE_HASHTAB
 296 }
 297
 298 bool expairseq::is_equal_same_type(basic const & other) const
 299 {
 300     expairseq const & o=dynamic_cast<expairseq const &>(const_cast<basic &>(other));
 301
 302     // compare number of elements
 303     if (seq.size() != o.seq.size()) return false;
 304
 305     // compare overall_coeff
 306     if (!overall_coeff.is_equal(o.overall_coeff)) return false;
 307
 308 #ifdef EXPAIRSEQ_USE_HASHTAB
 309     // compare number of elements in each hashtab entry
 310     if (hashtabsize!=o.hashtabsize) {
 311         cout << "this:" << endl;
 312         printtree(cout,0);
 313         cout << "other:" << endl;
 314         other.printtree(cout,0);
 315     }
 316
 317     GINAC_ASSERT(hashtabsize==o.hashtabsize);
 318
 319     if (hashtabsize==0) {
 320 #endif // def EXPAIRSEQ_USE_HASHTAB
 321         epvector::const_iterator cit1=seq.begin();
 322         epvector::const_iterator cit2=o.seq.begin();
 323         epvector::const_iterator last1=seq.end();
 324
 325         while (cit1!=last1) {
 326             if (!(*cit1).is_equal(*cit2)) return false;
 327             ++cit1;
 328             ++cit2;
 329         }
 330
 331         return true;
 332 #ifdef EXPAIRSEQ_USE_HASHTAB
 333     }
 334
 335     for (unsigned i=0; i<hashtabsize; ++i) {
 336         if (hashtab[i].size() != o.hashtab[i].size()) return false;
 337     }
 338
 339     // compare individual sorted hashtab entries
 340     for (unsigned i=0; i<hashtabsize; ++i) {
 341         unsigned sz=hashtab[i].size();
 342         if (sz>0) {
 343             epplist const & eppl1=hashtab[i];
 344             epplist const & eppl2=o.hashtab[i];
 345             epplist::const_iterator it1=eppl1.begin();
 346             epplist::const_iterator it2=eppl2.begin();
 347             while (it1!=eppl1.end()) {
 348                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 349                 ++it1;
 350                 ++it2;
 351             }
 352         }
 353     }
 354
 355     return true;
 356 #endif // def EXPAIRSEQ_USE_HASHTAB
 357 }
 358
 359 unsigned expairseq::return_type(void) const
 360 {
 361     return return_types::noncommutative_composite;
 362 }
 363
 364 unsigned expairseq::calchash(void) const
 365 {
 366     unsigned v=golden_ratio_hash(tinfo());
 367     epvector::const_iterator last=seq.end();
 368     for (epvector::const_iterator cit=seq.begin(); cit!=last; ++cit) {
 369 #ifndef EXPAIRSEQ_USE_HASHTAB
 370         v=rotate_left_31(v); // rotation would spoil commutativity
 371 #endif // ndef EXPAIRSEQ_USE_HASHTAB
 372         v ^= (*cit).rest.gethash();
 373     }
 374
 375     v ^= overall_coeff.gethash();
 376     v=v & 0x7FFFFFFFU;
 377
 378     // store calculated hash value only if object is already evaluated
 379     if (flags & status_flags::evaluated) {
 380         setflag(status_flags::hash_calculated);
 381         hashvalue=v;
 382     }
 383
 384     return v;
 385 }
 386
 387 ex expairseq::expand(unsigned options) const
 388 {
 389     epvector * vp=expandchildren(options);
 390     if (vp==0) {
 391         return *this;
 392     }
 393     return thisexpairseq(vp,overall_coeff);
 394 }
 395
 396 //////////
 397 // new virtual functions which can be overridden by derived classes
 398 //////////
 399
 400 // protected
 401
 402 ex expairseq::thisexpairseq(epvector const & v,ex const & oc) const
 403 {
 404     return expairseq(v,oc);
 405 }
 406
 407 ex expairseq::thisexpairseq(epvector * vp, ex const & oc) const
 408 {
 409     return expairseq(vp,oc);
 410 }
 411
 412 expair expairseq::split_ex_to_pair(ex const & e) const
 413 {
 414     return expair(e,exONE());
 415 }
 416
 417 expair expairseq::combine_ex_with_coeff_to_pair(ex const & e,
 418                                                 ex const & c) const
 419 {
 420     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 421
 422     return expair(e,c);
 423 }
 424
 425 expair expairseq::combine_pair_with_coeff_to_pair(expair const & p,
 426                                                   ex const & c) const
 427 {
 428     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 429     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 430
 431     return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 432 }
 433
 434 ex expairseq::recombine_pair_to_ex(expair const & p) const
 435 {
 436     return lst(p.rest,p.coeff);
 437 }
 438
 439 bool expairseq::expair_needs_further_processing(epp it)
 440 {
 441     return false;
 442 }
 443
 444 ex expairseq::default_overall_coeff(void) const
 445 {
 446     return exZERO();
 447 }
 448
 449 void expairseq::combine_overall_coeff(ex const & c)
 450 {
 451     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 452     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 453     overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 454 }
 455
 456 void expairseq::combine_overall_coeff(ex const & c1, ex const & c2)
 457 {
 458     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 459     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 460     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 461     overall_coeff = ex_to_numeric(overall_coeff).
 462                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 463 }
 464
 465 bool expairseq::can_make_flat(expair const & p) const
 466 {
 467     return true;
 468 }
 469
 470
 471 //////////
 472 // non-virtual functions in this class
 473 //////////
 474
 475 void expairseq::construct_from_2_ex_via_exvector(ex const & lh, ex const & rh)
 476 {
 477     exvector v;
 478     v.reserve(2);
 479     v.push_back(lh);
 480     v.push_back(rh);
 481     construct_from_exvector(v);
 482 #ifdef EXPAIRSEQ_USE_HASHTAB
 483     GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 484     GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 485 #endif // def EXPAIRSEQ_USE_HASHTAB
 486 }
 487
 488 void expairseq::construct_from_2_ex(ex const & lh, ex const & rh)
 489 {
 490     if (lh.bp->tinfo()==tinfo()) {
 491        if (rh.bp->tinfo()==tinfo()) {
 492 #ifdef EXPAIRSEQ_USE_HASHTAB
 493            unsigned totalsize=ex_to_expairseq(lh).seq.size()+
 494                               ex_to_expairseq(rh).seq.size();
 495            if (calc_hashtabsize(totalsize)!=0) {
 496                construct_from_2_ex_via_exvector(lh,rh);
 497            } else {
 498 #endif // def EXPAIRSEQ_USE_HASHTAB
 499                construct_from_2_expairseq(ex_to_expairseq(lh),
 500                                           ex_to_expairseq(rh));
 501 #ifdef EXPAIRSEQ_USE_HASHTAB
 502            }
 503 #endif // def EXPAIRSEQ_USE_HASHTAB
 504            return;
 505        } else {
 506 #ifdef EXPAIRSEQ_USE_HASHTAB
 507            unsigned totalsize=ex_to_expairseq(lh).seq.size()+1;
 508            if (calc_hashtabsize(totalsize)!=0) {
 509                construct_from_2_ex_via_exvector(lh,rh);
 510            } else {
 511 #endif // def EXPAIRSEQ_USE_HASHTAB
 512                construct_from_expairseq_ex(ex_to_expairseq(lh),rh);
 513 #ifdef EXPAIRSEQ_USE_HASHTAB
 514            }
 515 #endif // def EXPAIRSEQ_USE_HASHTAB
 516            return;
 517        }
 518     } else if (rh.bp->tinfo()==tinfo()) {
 519 #ifdef EXPAIRSEQ_USE_HASHTAB
 520         unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 521         if (calc_hashtabsize(totalsize)!=0) {
 522             construct_from_2_ex_via_exvector(lh,rh);
 523         } else {
 524 #endif // def EXPAIRSEQ_USE_HASHTAB
 525             construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 526 #ifdef EXPAIRSEQ_USE_HASHTAB
 527         }
 528 #endif // def EXPAIRSEQ_USE_HASHTAB
 529         return;
 530     }
 531
 532 #ifdef EXPAIRSEQ_USE_HASHTAB
 533     if (calc_hashtabsize(2)!=0) {
 534         construct_from_2_ex_via_exvector(lh,rh);
 535         return;
 536     }
 537     hashtabsize=0;
 538 #endif // def EXPAIRSEQ_USE_HASHTAB
 539
 540     if (is_ex_exactly_of_type(lh,numeric)) {
 541         if (is_ex_exactly_of_type(rh,numeric)) {
 542             combine_overall_coeff(lh);
 543             combine_overall_coeff(rh);
 544         } else {
 545             combine_overall_coeff(lh);
 546             seq.push_back(split_ex_to_pair(rh));
 547         }
 548     } else {
 549         if (is_ex_exactly_of_type(rh,numeric)) {
 550             combine_overall_coeff(rh);
 551             seq.push_back(split_ex_to_pair(lh));
 552         } else {
 553             expair p1=split_ex_to_pair(lh);
 554             expair p2=split_ex_to_pair(rh);
 555
 556             int cmpval=p1.rest.compare(p2.rest);
 557             if (cmpval==0) {
 558                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 559                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 560                     // no further processing is necessary, since this
 561                     // one element will usually be recombined in eval()
 562                     seq.push_back(p1);
 563                 }
 564             } else {
 565                 seq.reserve(2);
 566                 if (cmpval<0) {
 567                     seq.push_back(p1);
 568                     seq.push_back(p2);
 569                 } else {
 570                     seq.push_back(p2);
 571                     seq.push_back(p1);
 572                 }
 573             }
 574         }
 575     }
 576 }
 577
 578 void expairseq::construct_from_2_expairseq(expairseq const & s1,
 579                                            expairseq const & s2)
 580 {
 581     combine_overall_coeff(s1.overall_coeff);
 582     combine_overall_coeff(s2.overall_coeff);
 583
 584     epvector::const_iterator first1=s1.seq.begin();
 585     epvector::const_iterator last1=s1.seq.end();
 586     epvector::const_iterator first2=s2.seq.begin();
 587     epvector::const_iterator last2=s2.seq.end();
 588
 589     seq.reserve(s1.seq.size()+s2.seq.size());
 590
 591     bool needs_further_processing=false;
 592
 593     while (first1!=last1 && first2!=last2) {
 594         int cmpval=(*first1).rest.compare((*first2).rest);
 595         if (cmpval==0) {
 596             // combine terms
 597             numeric const & newcoeff=ex_to_numeric((*first1).coeff).
 598                                      add(ex_to_numeric((*first2).coeff));
 599             if (!newcoeff.is_zero()) {
 600                 seq.push_back(expair((*first1).rest,newcoeff));
 601                 if (expair_needs_further_processing(seq.end()-1)) {
 602                     needs_further_processing = true;
 603                 }
 604             }
 605             ++first1;
 606             ++first2;
 607         } else if (cmpval<0) {
 608             seq.push_back(*first1);
 609             ++first1;
 610         } else {
 611             seq.push_back(*first2);
 612             ++first2;
 613         }
 614     }
 615
 616     while (first1!=last1) {
 617         seq.push_back(*first1);
 618         ++first1;
 619     }
 620     while (first2!=last2) {
 621         seq.push_back(*first2);
 622         ++first2;
 623     }
 624
 625     if (needs_further_processing) {
 626         epvector v=seq;
 627         seq.clear();
 628         construct_from_epvector(v);
 629     }
 630 }
 631
 632 void expairseq::construct_from_expairseq_ex(expairseq const & s,
 633                                             ex const & e)
 634 {
 635     combine_overall_coeff(s.overall_coeff);
 636     if (is_ex_exactly_of_type(e,numeric)) {
 637         combine_overall_coeff(e);
 638         seq=s.seq;
 639         return;
 640     }
 641
 642     epvector::const_iterator first=s.seq.begin();
 643     epvector::const_iterator last=s.seq.end();
 644     expair p=split_ex_to_pair(e);
 645
 646     seq.reserve(s.seq.size()+1);
 647     bool p_pushed=0;
 648
 649     bool needs_further_processing=false;
 650
 651     // merge p into s.seq
 652     while (first!=last) {
 653         int cmpval=(*first).rest.compare(p.rest);
 654         if (cmpval==0) {
 655             // combine terms
 656             numeric const & newcoeff=ex_to_numeric((*first).coeff).
 657                                      add(ex_to_numeric(p.coeff));
 658             if (!newcoeff.is_zero()) {
 659                 seq.push_back(expair((*first).rest,newcoeff));
 660                 if (expair_needs_further_processing(seq.end()-1)) {
 661                     needs_further_processing = true;
 662                 }
 663             }
 664             ++first;
 665             p_pushed=1;
 666             break;
 667         } else if (cmpval<0) {
 668             seq.push_back(*first);
 669             ++first;
 670         } else {
 671             seq.push_back(p);
 672             p_pushed=1;
 673             break;
 674         }
 675     }
 676
 677     if (p_pushed) {
 678         // while loop exited because p was pushed, now push rest of s.seq
 679         while (first!=last) {
 680             seq.push_back(*first);
 681             ++first;
 682         }
 683     } else {
 684         // while loop exited because s.seq was pushed, now push p
 685         seq.push_back(p);
 686     }
 687
 688     if (needs_further_processing) {
 689         epvector v=seq;
 690         seq.clear();
 691         construct_from_epvector(v);
 692     }
 693 }
 694
 695 void expairseq::construct_from_exvector(exvector const & v)
 696 {
 697     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 698     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 699     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 700     //                  (same for (+,*) -> (*,^)
 701
 702     make_flat(v);
 703 #ifdef EXPAIRSEQ_USE_HASHTAB
 704     combine_same_terms();
 705 #else
 706     canonicalize();
 707     combine_same_terms_sorted_seq();
 708 #endif // def EXPAIRSEQ_USE_HASHTAB
 709 }
 710
 711 void expairseq::construct_from_epvector(epvector const & v)
 712 {
 713     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 714     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 715     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 716     //                  (same for (+,*) -> (*,^)
 717
 718     make_flat(v);
 719 #ifdef EXPAIRSEQ_USE_HASHTAB
 720     combine_same_terms();
 721 #else
 722     canonicalize();
 723     combine_same_terms_sorted_seq();
 724 #endif // def EXPAIRSEQ_USE_HASHTAB
 725 }
 726
 727 #include <iostream>
 728
 729 void expairseq::make_flat(exvector const & v)
 730 {
 731     exvector::const_iterator cit, citend = v.end();
 732
 733     // count number of operands which are of same expairseq derived type
 734     // and their cumulative number of operands
 735     int nexpairseqs=0;
 736     int noperands=0;
 737     cit=v.begin();
 738     while (cit!=citend) {
 739         if (cit->bp->tinfo()==tinfo()) {
 740             nexpairseqs++;
 741             noperands+=ex_to_expairseq(*cit).seq.size();
 742         }
 743         ++cit;
 744     }
 745
 746     // reserve seq and coeffseq which will hold all operands
 747     seq.reserve(v.size()+noperands-nexpairseqs);
 748
 749     // copy elements and split off numerical part
 750     cit=v.begin();
 751     while (cit!=citend) {
 752         if (cit->bp->tinfo()==tinfo()) {
 753             expairseq const & subseqref=ex_to_expairseq(*cit);
 754             combine_overall_coeff(subseqref.overall_coeff);
 755             epvector::const_iterator cit_s=subseqref.seq.begin();
 756             while (cit_s!=subseqref.seq.end()) {
 757                 seq.push_back(*cit_s);
 758                 ++cit_s;
 759             }
 760         } else {
 761             if (is_ex_exactly_of_type(*cit,numeric)) {
 762                 combine_overall_coeff(*cit);
 763             } else {
 764                 seq.push_back(split_ex_to_pair(*cit));
 765             }
 766         }
 767         ++cit;
 768     }
 769
 770     /*
 771     cout << "after make flat" << endl;
 772     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 773         (*cit).printraw(cout);
 774     }
 775     cout << endl;
 776     cout.flush();
 777     */
 778 }
 779
 780 void expairseq::make_flat(epvector const & v)
 781 {
 782     epvector::const_iterator cit, citend = v.end();
 783
 784     // count number of operands which are of same expairseq derived type
 785     // and their cumulative number of operands
 786     int nexpairseqs=0;
 787     int noperands=0;
 788     cit=v.begin();
 789     while (cit!=citend) {
 790         if (cit->rest.bp->tinfo()==tinfo()) {
 791             nexpairseqs++;
 792             noperands+=ex_to_expairseq((*cit).rest).seq.size();
 793         }
 794         ++cit;
 795     }
 796
 797     // reserve seq and coeffseq which will hold all operands
 798     seq.reserve(v.size()+noperands-nexpairseqs);
 799
 800     // copy elements and split off numerical part
 801     cit=v.begin();
 802     while (cit!=citend) {
 803         if ((cit->rest.bp->tinfo()==tinfo())&&can_make_flat(*cit)) {
 804             expairseq const & subseqref=ex_to_expairseq((*cit).rest);
 805             combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 806                                   ex_to_numeric((*cit).coeff));
 807             epvector::const_iterator cit_s=subseqref.seq.begin();
 808             while (cit_s!=subseqref.seq.end()) {
 809                 seq.push_back(expair((*cit_s).rest,
 810                               ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
 811                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 812                 //                                              (*cit).coeff));
 813                 ++cit_s;
 814             }
 815         } else {
 816             if ((*cit).is_numeric_with_coeff_1()) {
 817                 combine_overall_coeff((*cit).rest);
 818             //if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 819             //    combine_overall_coeff(recombine_pair_to_ex(*cit));
 820             } else {
 821                 seq.push_back(*cit);
 822             }
 823         }
 824         ++cit;
 825     }
 826 }
 827
 828 epvector * expairseq::bubblesort(epvector::iterator itbegin, epvector::iterator itend)
 829 {
 830     unsigned n=itend-itbegin;
 831
 832     epvector * sp=new epvector;
 833     sp->reserve(n);
 834
 835     epvector::iterator last=itend-1;
 836     for (epvector::iterator it1=itbegin; it1!=last; ++it1) {
 837         for (epvector::iterator it2=it1+1; it2!=itend; ++it2) {
 838             if ((*it2).rest.compare((*it1).rest)<0) {
 839                 iter_swap(it1,it2);
 840             }
 841         }
 842         sp->push_back(*it1);
 843     }
 844     sp->push_back(*last);
 845     return sp;
 846 }
 847
 848 epvector * expairseq::mergesort(epvector::iterator itbegin, epvector::iterator itend)
 849 {
 850     unsigned n=itend-itbegin;
 851     /*
 852     if (n==1) {
 853         epvector * sp=new epvector;
 854         sp->push_back(*itbegin);
 855         return sp;
 856     }
 857     */
 858     if (n<16) return bubblesort(itbegin, itend);
 859     unsigned m=n/2;
 860
 861     epvector * s1p=mergesort(itbegin, itbegin+m);
 862     epvector * s2p=mergesort(itbegin+m, itend);
 863
 864     epvector * sp=new epvector;
 865     sp->reserve(s1p->size()+s2p->size());
 866
 867     epvector::iterator first1=s1p->begin();
 868     epvector::iterator last1=s1p->end();
 869
 870     epvector::iterator first2=s2p->begin();
 871     epvector::iterator last2=s2p->end();
 872
 873     while (first1 != last1 && first2 != last2) {
 874         if ((*first1).rest.compare((*first2).rest)<0) {
 875             sp->push_back(*first1);
 876             ++first1;
 877         } else {
 878             sp->push_back(*first2);
 879             ++first2;
 880         }
 881     }
 882
 883     if (first1 != last1) {
 884         while (first1 != last1) {
 885             sp->push_back(*first1);
 886             ++first1;
 887         }
 888     } else {
 889         while (first2 != last2) {
 890             sp->push_back(*first2);
 891             ++first2;
 892         }
 893     }
 894
 895     delete s1p;
 896     delete s2p;
 897
 898     return sp;
 899 }
 900
 901
 902 void expairseq::canonicalize(void)
 903 {
 904     // canonicalize
 905     sort(seq.begin(),seq.end(),expair_is_less());
 906     /*
 907     sort(seq.begin(),seq.end(),expair_is_less_old());
 908     if (seq.size()>1) {
 909         if (is_ex_exactly_of_type((*(seq.begin())).rest,numeric)) {
 910             sort(seq.begin(),seq.end(),expair_is_less());
 911         } else {
 912             epvector::iterator last_numeric=seq.end();
 913             do {
 914                 last_numeric--;
 915             } while (is_ex_exactly_of_type((*last_numeric).rest,numeric));
 916             last_numeric++;
 917             sort(last_numeric,seq.end(),expair_is_less());
 918         }
 919     }
 920     */
 921
 922     /*
 923     epvector * sorted_seqp=mergesort(seq.begin(),seq.end());
 924     epvector::iterator last=sorted_seqp->end();
 925     epvector::iterator it2=seq.begin();
 926     for (epvector::iterator it1=sorted_seqp->begin(); it1!=last; ++it1, ++it2) {
 927         iter_swap(it1,it2);
 928     }
 929     delete sorted_seqp;
 930     */
 931
 932     /*
 933     cout << "after canonicalize" << endl;
 934     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 935         (*cit).printraw(cout);
 936     }
 937     cout << endl;
 938     cout.flush();
 939     */
 940 }
 941
 942 void expairseq::combine_same_terms_sorted_seq(void)
 943 {
 944     bool needs_further_processing=false;
 945
 946     // combine same terms, drop term with coeff 0
 947     if (seq.size()>1) {
 948         epvector::iterator itin1=seq.begin();
 949         epvector::iterator itin2=itin1+1;
 950         epvector::iterator itout=itin1;
 951         epvector::iterator last=seq.end();
 952         // must_copy will be set to true the first time some combination is possible
 953         // from then on the sequence has changed and must be compacted
 954         bool must_copy=false;
 955         while (itin2!=last) {
 956             if ((*itin1).rest.compare((*itin2).rest)==0) {
 957                 (*itin1).coeff=ex_to_numeric((*itin1).coeff).
 958                                add_dyn(ex_to_numeric((*itin2).coeff));
 959                 if (expair_needs_further_processing(itin1)) {
 960                     needs_further_processing = true;
 961                 }
 962                 must_copy=true;
 963             } else {
 964                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 965                     if (must_copy) {
 966                         *itout=*itin1;
 967                     }
 968                     ++itout;
 969                 }
 970                 itin1=itin2;
 971             }
 972             ++itin2;
 973         }
 974         if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 975             if (must_copy) {
 976                 *itout=*itin1;
 977             }
 978             ++itout;
 979         }
 980         if (itout!=last) {
 981             seq.erase(itout,last);
 982         }
 983     }
 984
 985     /*
 986     cout << "after combine" << endl;
 987     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 988         (*cit).printraw(cout);
 989     }
 990     cout << endl;
 991     cout.flush();
 992     */
 993
 994     if (needs_further_processing) {
 995         epvector v=seq;
 996         seq.clear();
 997         construct_from_epvector(v);
 998     }
 999 }
1000
1001 #ifdef EXPAIRSEQ_USE_HASHTAB
1002
1003 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1004 {
1005     unsigned size;
1006     unsigned nearest_power_of_2 = 1 << log2(sz);
1007     //    if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1008     //  size=nearest_power_of_2*hashtabfactor;
1009     size=nearest_power_of_2/hashtabfactor;
1010     if (size<minhashtabsize) return 0;
1011     GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1012     // hashtabsize must be a power of 2
1013     GINAC_ASSERT((1U << log2(size))==size);
1014     return size;
1015 }
1016
1017 unsigned expairseq::calc_hashindex(ex const & e) const
1018 {
1019     // calculate hashindex
1020     unsigned hash=e.gethash();
1021     unsigned hashindex;
1022     if (is_a_numeric_hash(hash)) {
1023         hashindex=hashmask;
1024     } else {
1025         hashindex=hash & hashmask;
1026         // last hashtab entry is reserved for numerics
1027         if (hashindex==hashmask) hashindex=0;
1028     }
1029     GINAC_ASSERT(hashindex>=0);
1030     GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1031     return hashindex;
1032 }
1033
1034 void expairseq::shrink_hashtab(void)
1035 {
1036     unsigned new_hashtabsize;
1037     while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1038         GINAC_ASSERT(new_hashtabsize<hashtabsize);
1039         if (new_hashtabsize==0) {
1040             hashtab.clear();
1041             hashtabsize=0;
1042             canonicalize();
1043             return;
1044         }
1045
1046         // shrink by a factor of 2
1047         unsigned half_hashtabsize=hashtabsize/2;
1048         for (unsigned i=0; i<half_hashtabsize-1; ++i) {
1049             hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1050         }
1051         // special treatment for numeric hashes
1052         hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1053         hashtab[half_hashtabsize-1]=hashtab[hashtabsize-1];
1054         hashtab.resize(half_hashtabsize);
1055         hashtabsize=half_hashtabsize;
1056         hashmask=hashtabsize-1;
1057     }
1058 }
1059
1060 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1061 {
1062     if (hashtabsize==0) return; // nothing to do
1063
1064     // calculate hashindex of element to be deleted
1065     unsigned hashindex=calc_hashindex((*element).rest);
1066
1067     // find it in hashtab and remove it
1068     epplist & eppl=hashtab[hashindex];
1069     epplist::iterator epplit=eppl.begin();
1070     bool erased=false;
1071     while (epplit!=eppl.end()) {
1072         if (*epplit == element) {
1073             eppl.erase(epplit);
1074             erased=true;
1075             break;
1076         }
1077         ++epplit;
1078     }
1079     if (!erased) {
1080         printtree(cout,0);
1081         cout << "tried to erase " << element-seq.begin() << endl;
1082         cout << "size " << seq.end()-seq.begin() << endl;
1083
1084         unsigned hashindex=calc_hashindex((*element).rest);
1085         epplist & eppl=hashtab[hashindex];
1086         epplist::iterator epplit=eppl.begin();
1087         bool erased=false;
1088         while (epplit!=eppl.end()) {
1089             if (*epplit == element) {
1090                 eppl.erase(epplit);
1091                 erased=true;
1092                 break;
1093             }
1094             ++epplit;
1095         }
1096         GINAC_ASSERT(erased);
1097     }
1098     GINAC_ASSERT(erased);
1099 }
1100
1101 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1102                                    epvector::iterator newpos)
1103 {
1104     GINAC_ASSERT(hashtabsize!=0);
1105
1106     // calculate hashindex of element which was moved
1107     unsigned hashindex=calc_hashindex((*newpos).rest);
1108
1109     // find it in hashtab and modify it
1110     epplist & eppl=hashtab[hashindex];
1111     epplist::iterator epplit=eppl.begin();
1112     while (epplit!=eppl.end()) {
1113         if (*epplit == oldpos) {
1114             *epplit=newpos;
1115             break;
1116         }
1117         ++epplit;
1118     }
1119     GINAC_ASSERT(epplit!=eppl.end());
1120 }
1121
1122 void expairseq::sorted_insert(epplist & eppl, epp elem)
1123 {
1124     epplist::iterator current=eppl.begin();
1125     while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1126         ++current;
1127     }
1128     eppl.insert(current,elem);
1129 }
1130
1131 void expairseq::build_hashtab_and_combine(epvector::iterator & first_numeric,
1132                                           epvector::iterator & last_non_zero,
1133                                           vector<bool> & touched,
1134                                           unsigned & number_of_zeroes)
1135 {
1136     epp current=seq.begin();
1137
1138     while (current!=first_numeric) {
1139         if (is_ex_exactly_of_type((*current).rest,numeric)) {
1140             --first_numeric;
1141             iter_swap(current,first_numeric);
1142         } else {
1143             // calculate hashindex
1144             unsigned currenthashindex=calc_hashindex((*current).rest);
1145
1146             // test if there is already a matching expair in the hashtab-list
1147             epplist & eppl=hashtab[currenthashindex];
1148             epplist::iterator epplit=eppl.begin();
1149             while (epplit!=eppl.end()) {
1150                 if ((*current).rest.is_equal((*(*epplit)).rest)) break;
1151                 ++epplit;
1152             }
1153             if (epplit==eppl.end()) {
1154                 // no matching expair found, append this to end of list
1155                 sorted_insert(eppl,current);
1156                 ++current;
1157             } else {
1158                 // epplit points to a matching expair, combine it with current
1159                 (*(*epplit)).coeff=ex_to_numeric((*(*epplit)).coeff).
1160                                    add_dyn(ex_to_numeric((*current).coeff));
1161
1162                 // move obsolete current expair to end by swapping with last_non_zero element
1163                 // if this was a numeric, it is swapped with the expair before first_numeric
1164                 iter_swap(current,last_non_zero);
1165                 --first_numeric;
1166                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1167                 --last_non_zero;
1168                 ++number_of_zeroes;
1169                 // test if combined term has coeff 0 and can be removed is done later
1170                 touched[(*epplit)-seq.begin()]=true;
1171             }
1172         }
1173     }
1174 }
1175
1176 void expairseq::drop_coeff_0_terms(epvector::iterator & first_numeric,
1177                                    epvector::iterator & last_non_zero,
1178                                    vector<bool> & touched,
1179                                    unsigned & number_of_zeroes)
1180 {
1181     // move terms with coeff 0 to end and remove them from hashtab
1182     // check only those elements which have been touched
1183     epp current=seq.begin();
1184     unsigned i=0;
1185     while (current!=first_numeric) {
1186         if (!touched[i]) {
1187             ++current;
1188             ++i;
1189         } else if (!ex_to_numeric((*current).coeff).is_equal(numZERO())) {
1190             ++current;
1191             ++i;
1192         } else {
1193             remove_hashtab_entry(current);
1194
1195             // move element to the end, unless it is already at the end
1196             if (current!=last_non_zero) {
1197                 iter_swap(current,last_non_zero);
1198                 --first_numeric;
1199                 bool numeric_swapped=first_numeric!=last_non_zero;
1200                 if (numeric_swapped) iter_swap(first_numeric,current);
1201                 epvector::iterator changed_entry;
1202
1203                 if (numeric_swapped) {
1204                     changed_entry=first_numeric;
1205                 } else {
1206                     changed_entry=last_non_zero;
1207                 }
1208
1209                 --last_non_zero;
1210                 ++number_of_zeroes;
1211
1212                 if (first_numeric!=current) {
1213
1214                     // change entry in hashtab which referred to first_numeric or last_non_zero to current
1215                     move_hashtab_entry(changed_entry,current);
1216                     touched[current-seq.begin()]=touched[changed_entry-seq.begin()];
1217                 }
1218             } else {
1219                 --first_numeric;
1220                 --last_non_zero;
1221                 ++number_of_zeroes;
1222             }
1223         }
1224     }
1225     GINAC_ASSERT(i==current-seq.begin());
1226 }
1227
1228 bool expairseq::has_coeff_0(void) const
1229 {
1230     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1231         if ((*cit).coeff.is_equal(exZERO())) {
1232             return true;
1233         }
1234     }
1235     return false;
1236 }
1237
1238 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1239                                         epvector::const_iterator last_non_zero)
1240 {
1241     if (first_numeric==seq.end()) return; // no numerics
1242
1243     epvector::iterator current=first_numeric;
1244     epvector::const_iterator last=last_non_zero+1;
1245     while (current!=last) {
1246         sorted_insert(hashtab[hashmask],current);
1247         ++current;
1248     }
1249 }
1250
1251 void expairseq::combine_same_terms(void)
1252 {
1253     // combine same terms, drop term with coeff 0, move numerics to end
1254
1255     // calculate size of hashtab
1256     hashtabsize=calc_hashtabsize(seq.size());
1257
1258     // hashtabsize is a power of 2
1259     hashmask=hashtabsize-1;
1260
1261     // allocate hashtab
1262     hashtab.clear();
1263     hashtab.resize(hashtabsize);
1264
1265     if (hashtabsize==0) {
1266         canonicalize();
1267         combine_same_terms_sorted_seq();
1268         GINAC_ASSERT(!has_coeff_0());
1269         return;
1270     }
1271
1272     // iterate through seq, move numerics to end,
1273     // fill hashtab and combine same terms
1274     epvector::iterator first_numeric=seq.end();
1275     epvector::iterator last_non_zero=seq.end()-1;
1276
1277     vector<bool> touched;
1278     touched.reserve(seq.size());
1279     for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1280
1281     unsigned number_of_zeroes=0;
1282
1283     GINAC_ASSERT(!has_coeff_0());
1284     build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1285     /*
1286     cout << "in combine:" << endl;
1287     printtree(cout,0);
1288     cout << "size=" << seq.end() - seq.begin() << endl;
1289     cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1290     cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1291     for (unsigned i=0; i<seq.size(); ++i) {
1292         if (touched[i]) cout << i << " is touched" << endl;
1293     }
1294     cout << "end in combine" << endl;
1295     */
1296
1297     // there should not be any terms with coeff 0 from the beginning,
1298     // so it should be safe to skip this step
1299     if (number_of_zeroes!=0) {
1300         drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1301         /*
1302         cout << "in combine after drop:" << endl;
1303         printtree(cout,0);
1304         cout << "size=" << seq.end() - seq.begin() << endl;
1305         cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1306         cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1307         for (unsigned i=0; i<seq.size(); ++i) {
1308             if (touched[i]) cout << i << " is touched" << endl;
1309         }
1310         cout << "end in combine after drop" << endl;
1311         */
1312     }
1313
1314     add_numerics_to_hashtab(first_numeric,last_non_zero);
1315
1316     // pop zero elements
1317     for (unsigned i=0; i<number_of_zeroes; ++i) {
1318         seq.pop_back();
1319     }
1320
1321     // shrink hashtabsize to calculated value
1322     GINAC_ASSERT(!has_coeff_0());
1323
1324     shrink_hashtab();
1325
1326     GINAC_ASSERT(!has_coeff_0());
1327 }
1328
1329 #endif // def EXPAIRSEQ_USE_HASHTAB
1330
1331 bool expairseq::is_canonical() const
1332 {
1333     if (seq.size()<=1) return 1;
1334
1335 #ifdef EXPAIRSEQ_USE_HASHTAB
1336     if (hashtabsize>0) return 1; // not canoncalized
1337 #endif // def EXPAIRSEQ_USE_HASHTAB
1338
1339     epvector::const_iterator it=seq.begin();
1340     epvector::const_iterator it_last=it;
1341     for (++it; it!=seq.end(); it_last=it, ++it) {
1342         if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
1343             if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1344                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1345                 // double test makes it easier to set a breakpoint...
1346                 if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1347                     !is_ex_exactly_of_type((*it).rest,numeric)) {
1348                     printpair(cout,*it_last,0);
1349                     cout << ">";
1350                     printpair(cout,*it,0);
1351                     cout << "\n";
1352                     cout << "pair1:" << endl;
1353                     (*it_last).rest.printtree(cout);
1354                     (*it_last).coeff.printtree(cout);
1355                     cout << "pair2:" << endl;
1356                     (*it).rest.printtree(cout);
1357                     (*it).coeff.printtree(cout);
1358                     return 0;
1359                 }
1360             }
1361         }
1362     }
1363     return 1;
1364 }
1365
1366 epvector * expairseq::expandchildren(unsigned options) const
1367 {
1368     epvector::const_iterator last=seq.end();
1369     epvector::const_iterator cit=seq.begin();
1370     while (cit!=last) {
1371         ex const & expanded_ex=(*cit).rest.expand(options);
1372         if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1373
1374             // something changed, copy seq, eval and return it
1375             epvector *s=new epvector;
1376             s->reserve(seq.size());
1377
1378             // copy parts of seq which are known not to have changed
1379             epvector::const_iterator cit2=seq.begin();
1380             while (cit2!=cit) {
1381                 s->push_back(*cit2);
1382                 ++cit2;
1383             }
1384             // copy first changed element
1385             s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1386                                                        (*cit2).coeff));
1387             ++cit2;
1388             // copy rest
1389             while (cit2!=last) {
1390                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1391                                                            (*cit2).coeff));
1392                 ++cit2;
1393             }
1394             return s;
1395         }
1396         ++cit;
1397     }
1398
1399     return 0; // nothing has changed
1400 }
1401
1402 epvector * expairseq::evalchildren(int level) const
1403 {
1404     // returns a NULL pointer if nothing had to be evaluated
1405     // returns a pointer to a newly created epvector otherwise
1406     // (which has to be deleted somewhere else)
1407
1408     if (level==1) {
1409         return 0;
1410     }
1411     if (level == -max_recursion_level) {
1412         throw(std::runtime_error("max recursion level reached"));
1413     }
1414
1415     --level;
1416     epvector::const_iterator last=seq.end();
1417     epvector::const_iterator cit=seq.begin();
1418     while (cit!=last) {
1419         ex const & evaled_ex=(*cit).rest.eval(level);
1420         if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1421
1422             // something changed, copy seq, eval and return it
1423             epvector *s=new epvector;
1424             s->reserve(seq.size());
1425
1426             // copy parts of seq which are known not to have changed
1427             epvector::const_iterator cit2=seq.begin();
1428             while (cit2!=cit) {
1429                 s->push_back(*cit2);
1430                 ++cit2;
1431             }
1432             // copy first changed element
1433             s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1434                                                        (*cit2).coeff));
1435             ++cit2;
1436             // copy rest
1437             while (cit2!=last) {
1438                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1439                                                            (*cit2).coeff));
1440                 ++cit2;
1441             }
1442             return s;
1443         }
1444         ++cit;
1445     }
1446
1447     return 0; // nothing has changed
1448 }
1449
1450 epvector expairseq::evalfchildren(int level) const
1451 {
1452     epvector s;
1453     s.reserve(seq.size());
1454
1455     if (level==1) {
1456         return seq;
1457     }
1458     if (level == -max_recursion_level) {
1459         throw(std::runtime_error("max recursion level reached"));
1460     }
1461     --level;
1462     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1463         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1464                                                   (*it).coeff));
1465     }
1466     return s;
1467 }
1468
1469 epvector expairseq::normalchildren(int level) const
1470 {
1471     epvector s;
1472     s.reserve(seq.size());
1473
1474     if (level==1) {
1475         return seq;
1476     }
1477     if (level == -max_recursion_level) {
1478         throw(std::runtime_error("max recursion level reached"));
1479     }
1480     --level;
1481     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1482         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1483                                                   (*it).coeff));
1484     }
1485     return s;
1486 }
1487
1488 epvector expairseq::diffchildren(symbol const & y) const
1489 {
1490     epvector s;
1491     s.reserve(seq.size());
1492
1493     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1494         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1495                                                   (*it).coeff));
1496     }
1497     return s;
1498 }
1499
1500 epvector * expairseq::subschildren(lst const & ls, lst const & lr) const
1501 {
1502     // returns a NULL pointer if nothing had to be substituted
1503     // returns a pointer to a newly created epvector otherwise
1504     // (which has to be deleted somewhere else)
1505
1506     epvector::const_iterator last=seq.end();
1507     epvector::const_iterator cit=seq.begin();
1508     while (cit!=last) {
1509         ex const & subsed_ex=(*cit).rest.subs(ls,lr);
1510         if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1511
1512             // something changed, copy seq, subs 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(subsed_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.subs(ls,lr),
1529                                                            (*cit2).coeff));
1530                 ++cit2;
1531             }
1532             return s;
1533         }
1534         ++cit;
1535     }
1536
1537     return 0; // nothing has changed
1538 }
1539
1540 /*
1541 epvector expairseq::subschildren(lst const & ls, lst const & lr) const
1542 {
1543     epvector s;
1544     s.reserve(seq.size());
1545
1546     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1547         s.push_back(split_ex_to_pair((*it).rest.subs(ls,lr),(*it).coeff));
1548     }
1549     return s;
1550 }
1551 */
1552
1553 /*
1554 void expairseq::sort(epviter first, epviter last, expair_is_less comp)
1555 {
1556     if (first != last) {
1557         introsort_loop(first, last, lg(last - first) * 2, comp);
1558         __final_insertion_sort(first, last, comp);
1559     }
1560 }
1561
1562 ptrdiff_t expairseq::lg(ptrdiff_t n)
1563 {
1564     ptrdiff_t k;
1565     for (k = 0; n > 1; n >>= 1) ++k;
1566     return k;
1567 }
1568
1569 void expairseq::introsort_loop(epviter first, epviter last,
1570                                ptrdiff_t depth_limit, expair_is_less comp)
1571 {
1572     while (last - first > stl_threshold) {
1573         if (depth_limit == 0) {
1574             partial_sort(first, last, last, comp);
1575             return;
1576         }
1577         --depth_limit;
1578         epviter cut = unguarded_partition(first, last,
1579                       expair(__median(*first, *(first + (last - first)/2),
1580                       *(last - 1), comp)), comp);
1581         introsort_loop(cut, last, depth_limit, comp);
1582         last = cut;
1583     }
1584 }
1585
1586 epviter expairseq::unguarded_partition(epviter first, epviter last,
1587                                        expair pivot, expair_is_less comp)
1588 {
1589     while (1) {
1590         while (comp(*first, pivot)) ++first;
1591         --last;
1592         while (comp(pivot, *last)) --last;
1593         if (!(first < last)) return first;
1594         iter_swap(first, last);
1595         ++first;
1596     }
1597 }
1598
1599 void expairseq::partial_sort(epviter first, epviter middle, epviter last,
1600                              expair_is_less comp) {
1601   make_heap(first, middle, comp);
1602   for (RandomAccessIterator i = middle; i < last; ++i)
1603     if (comp(*i, *first))
1604       __pop_heap(first, middle, i, T(*i), comp, distance_type(first));
1605   sort_heap(first, middle, comp);
1606 }
1607 */
1608
1609 //////////
1610 // static member variables
1611 //////////
1612
1613 // protected
1614
1615 unsigned expairseq::precedence=10;
1616
1617 #ifdef EXPAIRSEQ_USE_HASHTAB
1618 unsigned expairseq::maxhashtabsize=0x4000000U;
1619 unsigned expairseq::minhashtabsize=0x1000U;
1620 unsigned expairseq::hashtabfactor=1;
1621 #endif // def EXPAIRSEQ_USE_HASHTAB
1622
1623 //////////
1624 // global constants
1625 //////////
1626
1627 const expairseq some_expairseq;
1628 type_info const & typeid_expairseq=typeid(some_expairseq);
1629
1630 } // namespace GiNaC