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
  31 namespace GiNaC {
  32
  33 #ifdef EXPAIRSEQ_USE_HASHTAB
  34 #error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
  35 #endif // def EXPAIRSEQ_USE_HASHTAB
  36
  37 //////////
  38 // helper classes
  39 //////////
  40
  41 class epp_is_less
  42 {
  43 public:
  44     bool operator()(epp const & lh, epp const & rh) const
  45     {
  46         return (*lh).is_less(*rh);
  47     }
  48 };
  49
  50 //////////
  51 // default constructor, destructor, copy constructor assignment operator and helpers
  52 //////////
  53
  54 // public
  55
  56 expairseq::expairseq(expairseq const & other)
  57 {
  58     debugmsg("expairseq copy constructor",LOGLEVEL_CONSTRUCT);
  59     copy(other);
  60 }
  61
  62 expairseq const & expairseq::operator=(expairseq const & other)
  63 {
  64     debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  65     if (this != &other) {
  66         destroy(1);
  67         copy(other);
  68     }
  69     return *this;
  70 }
  71
  72 // protected
  73
  74 void expairseq::copy(expairseq const & other)
  75 {
  76     basic::copy(other);
  77     seq=other.seq;
  78     overall_coeff=other.overall_coeff;
  79 #ifdef EXPAIRSEQ_USE_HASHTAB
  80     // copy hashtab
  81     hashtabsize=other.hashtabsize;
  82     if (hashtabsize!=0) {
  83     hashmask=other.hashmask;
  84         hashtab.resize(hashtabsize);
  85         epvector::const_iterator osb=other.seq.begin();
  86         for (unsigned i=0; i<hashtabsize; ++i) {
  87             hashtab[i].clear();
  88             for (epplist::const_iterator cit=other.hashtab[i].begin();
  89                  cit!=other.hashtab[i].end(); ++cit) {
  90                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  91             }
  92         }
  93     } else {
  94         hashtab.clear();
  95     }
  96 #endif // def EXPAIRSEQ_USE_HASHTAB
  97 }
  98
  99 //////////
 100 // other constructors
 101 //////////
 102
 103 expairseq::expairseq(ex const & lh, ex const & rh) : basic(TINFO_expairseq)
 104 {
 105     debugmsg("expairseq constructor from ex,ex",LOGLEVEL_CONSTRUCT);
 106     construct_from_2_ex(lh,rh);
 107     ASSERT(is_canonical());
 108 }
 109
 110 expairseq::expairseq(exvector const & v) : basic(TINFO_expairseq)
 111 {
 112     debugmsg("expairseq constructor from exvector",LOGLEVEL_CONSTRUCT);
 113     construct_from_exvector(v);
 114     ASSERT(is_canonical());
 115 }
 116
 117 /*
 118 expairseq::expairseq(epvector const & v, bool do_not_canonicalize) :
 119     basic(TINFO_expairseq)
 120 {
 121     debugmsg("expairseq constructor from epvector",LOGLEVEL_CONSTRUCT);
 122     if (do_not_canonicalize) {
 123         seq=v;
 124 #ifdef EXPAIRSEQ_USE_HASHTAB
 125         combine_same_terms(); // to build hashtab
 126 #endif // def EXPAIRSEQ_USE_HASHTAB
 127     } else {
 128         construct_from_epvector(v);
 129     }
 130     ASSERT(is_canonical());
 131 }
 132 */
 133
 134 expairseq::expairseq(epvector const & v, ex const & oc) :
 135     basic(TINFO_expairseq), overall_coeff(oc)
 136 {
 137     debugmsg("expairseq constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 138     construct_from_epvector(v);
 139     ASSERT(is_canonical());
 140 }
 141
 142 expairseq::expairseq(epvector * vp, ex const & oc) :
 143     basic(TINFO_expairseq), overall_coeff(oc)
 144 {
 145     debugmsg("expairseq constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 146     ASSERT(vp!=0);
 147     construct_from_epvector(*vp);
 148     delete vp;
 149     ASSERT(is_canonical());
 150 }
 151
 152 //////////
 153 // functions overriding virtual functions from bases classes
 154 //////////
 155
 156 // public
 157
 158 basic * expairseq::duplicate() const
 159 {
 160     debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 161     return new expairseq(*this);
 162 }
 163
 164 bool expairseq::info(unsigned inf) const
 165 {
 166     return basic::info(inf);
 167 }
 168
 169 int expairseq::nops() const
 170 {
 171     if (overall_coeff.is_equal(default_overall_coeff())) {
 172         return seq.size();
 173     }
 174     return seq.size()+1;
 175 }
 176
 177 ex expairseq::op(int const i) const
 178 {
 179     if (unsigned(i)<seq.size()) {
 180         return recombine_pair_to_ex(seq[i]);
 181     }
 182     ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 183     return overall_coeff;
 184 }
 185
 186 ex & expairseq::let_op(int const i)
 187 {
 188     throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 189 }
 190
 191 ex expairseq::eval(int level) const
 192 {
 193     if ((level==1)&&(flags & status_flags::evaluated)) {
 194         return *this;
 195     }
 196
 197     epvector * vp=evalchildren(level);
 198     if (vp==0) {
 199         return this->hold();
 200     }
 201
 202     return (new expairseq(vp,overall_coeff))
 203                ->setflag(status_flags::dynallocated |
 204                          status_flags::evaluated );
 205 }
 206
 207 ex expairseq::evalf(int level) const
 208 {
 209     return thisexpairseq(evalfchildren(level),overall_coeff);
 210 }
 211
 212 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 213 {
 214     ex n=thisexpairseq(normalchildren(level),overall_coeff);
 215     return n.bp->basic::normal(sym_lst,repl_lst,level);
 216 }
 217
 218 ex expairseq::subs(lst const & ls, lst const & lr) const
 219 {
 220     epvector * vp=subschildren(ls,lr);
 221     if (vp==0) {
 222         return *this;
 223     }
 224     return thisexpairseq(vp,overall_coeff);
 225 }
 226
 227 // protected
 228
 229 int expairseq::compare_same_type(basic const & other) const
 230 {
 231     ASSERT(is_of_type(other, expairseq));
 232     expairseq const & o=static_cast<expairseq const &>(const_cast<basic &>(other));
 233
 234     int cmpval;
 235
 236     // compare number of elements
 237     if (seq.size() != o.seq.size()) {
 238         return (seq.size()<o.seq.size()) ? -1 : 1;
 239     }
 240
 241     // compare overall_coeff
 242     cmpval=overall_coeff.compare(o.overall_coeff);
 243     if (cmpval!=0) return cmpval;
 244
 245     //if (seq.size()==0) return 0; // empty expairseq's are equal
 246
 247 #ifdef EXPAIRSEQ_USE_HASHTAB
 248     ASSERT(hashtabsize==o.hashtabsize);
 249     if (hashtabsize==0) {
 250 #endif // def EXPAIRSEQ_USE_HASHTAB
 251         epvector::const_iterator cit1=seq.begin();
 252         epvector::const_iterator cit2=o.seq.begin();
 253         epvector::const_iterator last1=seq.end();
 254         epvector::const_iterator last2=o.seq.end();
 255
 256         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 257             cmpval=(*cit1).compare(*cit2);
 258             if (cmpval!=0) return cmpval;
 259         }
 260
 261         ASSERT(cit1==last1);
 262         ASSERT(cit2==last2);
 263
 264         return 0;
 265 #ifdef EXPAIRSEQ_USE_HASHTAB
 266     }
 267
 268     // compare number of elements in each hashtab entry
 269     for (unsigned i=0; i<hashtabsize; ++i) {
 270         unsigned cursize=hashtab[i].size();
 271         if (cursize != o.hashtab[i].size()) {
 272             return (cursize < o.hashtab[i].size()) ? -1 : 1;
 273         }
 274     }
 275
 276     // compare individual (sorted) hashtab entries
 277     for (unsigned i=0; i<hashtabsize; ++i) {
 278         unsigned sz=hashtab[i].size();
 279         if (sz>0) {
 280             epplist const & eppl1=hashtab[i];
 281             epplist const & eppl2=o.hashtab[i];
 282             epplist::const_iterator it1=eppl1.begin();
 283             epplist::const_iterator it2=eppl2.begin();
 284             while (it1!=eppl1.end()) {
 285                 cmpval=(*(*it1)).compare(*(*it2));
 286                 if (cmpval!=0) return cmpval;
 287                 ++it1;
 288                 ++it2;
 289             }
 290         }
 291     }
 292
 293     return 0; // equal
 294 #endif // def EXPAIRSEQ_USE_HASHTAB
 295 }
 296
 297 bool expairseq::is_equal_same_type(basic const & other) const
 298 {
 299     expairseq const & o=dynamic_cast<expairseq const &>(const_cast<basic &>(other));
 300
 301     // compare number of elements
 302     if (seq.size() != o.seq.size()) return false;
 303
 304     // compare overall_coeff
 305     if (!overall_coeff.is_equal(o.overall_coeff)) return false;
 306
 307 #ifdef EXPAIRSEQ_USE_HASHTAB
 308     // compare number of elements in each hashtab entry
 309     if (hashtabsize!=o.hashtabsize) {
 310         cout << "this:" << endl;
 311         printtree(cout,0);
 312         cout << "other:" << endl;
 313         other.printtree(cout,0);
 314     }
 315
 316     ASSERT(hashtabsize==o.hashtabsize);
 317
 318     if (hashtabsize==0) {
 319 #endif // def EXPAIRSEQ_USE_HASHTAB
 320         epvector::const_iterator cit1=seq.begin();
 321         epvector::const_iterator cit2=o.seq.begin();
 322         epvector::const_iterator last1=seq.end();
 323
 324         while (cit1!=last1) {
 325             if (!(*cit1).is_equal(*cit2)) return false;
 326             ++cit1;
 327             ++cit2;
 328         }
 329
 330         return true;
 331 #ifdef EXPAIRSEQ_USE_HASHTAB
 332     }
 333
 334     for (unsigned i=0; i<hashtabsize; ++i) {
 335         if (hashtab[i].size() != o.hashtab[i].size()) return false;
 336     }
 337
 338     // compare individual sorted hashtab entries
 339     for (unsigned i=0; i<hashtabsize; ++i) {
 340         unsigned sz=hashtab[i].size();
 341         if (sz>0) {
 342             epplist const & eppl1=hashtab[i];
 343             epplist const & eppl2=o.hashtab[i];
 344             epplist::const_iterator it1=eppl1.begin();
 345             epplist::const_iterator it2=eppl2.begin();
 346             while (it1!=eppl1.end()) {
 347                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 348                 ++it1;
 349                 ++it2;
 350             }
 351         }
 352     }
 353
 354     return true;
 355 #endif // def EXPAIRSEQ_USE_HASHTAB
 356 }
 357
 358 unsigned expairseq::return_type(void) const
 359 {
 360     return return_types::noncommutative_composite;
 361 }
 362
 363 unsigned expairseq::calchash(void) const
 364 {
 365     unsigned v=golden_ratio_hash(tinfo());
 366     epvector::const_iterator last=seq.end();
 367     for (epvector::const_iterator cit=seq.begin(); cit!=last; ++cit) {
 368 #ifndef EXPAIRSEQ_USE_HASHTAB
 369         v=rotate_left_31(v); // rotation would spoil commutativity
 370 #endif // ndef EXPAIRSEQ_USE_HASHTAB
 371         v ^= (*cit).rest.gethash();
 372     }
 373
 374     v ^= overall_coeff.gethash();
 375     v=v & 0x7FFFFFFFU;
 376
 377     // store calculated hash value only if object is already evaluated
 378     if (flags & status_flags::evaluated) {
 379         setflag(status_flags::hash_calculated);
 380         hashvalue=v;
 381     }
 382
 383     return v;
 384 }
 385
 386 ex expairseq::expand(unsigned options) const
 387 {
 388     epvector * vp=expandchildren(options);
 389     if (vp==0) {
 390         return *this;
 391     }
 392     return thisexpairseq(vp,overall_coeff);
 393 }
 394
 395 //////////
 396 // new virtual functions which can be overridden by derived classes
 397 //////////
 398
 399 // protected
 400
 401 ex expairseq::thisexpairseq(epvector const & v,ex const & oc) const
 402 {
 403     return expairseq(v,oc);
 404 }
 405
 406 ex expairseq::thisexpairseq(epvector * vp, ex const & oc) const
 407 {
 408     return expairseq(vp,oc);
 409 }
 410
 411 expair expairseq::split_ex_to_pair(ex const & e) const
 412 {
 413     return expair(e,exONE());
 414 }
 415
 416 expair expairseq::combine_ex_with_coeff_to_pair(ex const & e,
 417                                                 ex const & c) const
 418 {
 419     ASSERT(is_ex_exactly_of_type(c,numeric));
 420
 421     return expair(e,c);
 422 }
 423
 424 expair expairseq::combine_pair_with_coeff_to_pair(expair const & p,
 425                                                   ex const & c) const
 426 {
 427     ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 428     ASSERT(is_ex_exactly_of_type(c,numeric));
 429
 430     return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 431 }
 432
 433 ex expairseq::recombine_pair_to_ex(expair const & p) const
 434 {
 435     return lst(p.rest,p.coeff);
 436 }
 437
 438 bool expairseq::expair_needs_further_processing(epp it)
 439 {
 440     return false;
 441 }
 442
 443 ex expairseq::default_overall_coeff(void) const
 444 {
 445     return exZERO();
 446 }
 447
 448 void expairseq::combine_overall_coeff(ex const & c)
 449 {
 450     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 451     ASSERT(is_ex_exactly_of_type(c,numeric));
 452     overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 453 }
 454
 455 void expairseq::combine_overall_coeff(ex const & c1, ex const & c2)
 456 {
 457     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 458     ASSERT(is_ex_exactly_of_type(c1,numeric));
 459     ASSERT(is_ex_exactly_of_type(c2,numeric));
 460     overall_coeff = ex_to_numeric(overall_coeff).
 461                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 462 }
 463
 464 bool expairseq::can_make_flat(expair const & p) const
 465 {
 466     return true;
 467 }
 468
 469
 470 //////////
 471 // non-virtual functions in this class
 472 //////////
 473
 474 void expairseq::construct_from_2_ex_via_exvector(ex const & lh, ex const & rh)
 475 {
 476     exvector v;
 477     v.reserve(2);
 478     v.push_back(lh);
 479     v.push_back(rh);
 480     construct_from_exvector(v);
 481 #ifdef EXPAIRSEQ_USE_HASHTAB
 482     ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 483     ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 484 #endif // def EXPAIRSEQ_USE_HASHTAB
 485 }
 486
 487 void expairseq::construct_from_2_ex(ex const & lh, ex const & rh)
 488 {
 489     if (lh.bp->tinfo()==tinfo()) {
 490        if (rh.bp->tinfo()==tinfo()) {
 491 #ifdef EXPAIRSEQ_USE_HASHTAB
 492            unsigned totalsize=ex_to_expairseq(lh).seq.size()+
 493                               ex_to_expairseq(rh).seq.size();
 494            if (calc_hashtabsize(totalsize)!=0) {
 495                construct_from_2_ex_via_exvector(lh,rh);
 496            } else {
 497 #endif // def EXPAIRSEQ_USE_HASHTAB
 498                construct_from_2_expairseq(ex_to_expairseq(lh),
 499                                           ex_to_expairseq(rh));
 500 #ifdef EXPAIRSEQ_USE_HASHTAB
 501            }
 502 #endif // def EXPAIRSEQ_USE_HASHTAB
 503            return;
 504        } else {
 505 #ifdef EXPAIRSEQ_USE_HASHTAB
 506            unsigned totalsize=ex_to_expairseq(lh).seq.size()+1;
 507            if (calc_hashtabsize(totalsize)!=0) {
 508                construct_from_2_ex_via_exvector(lh,rh);
 509            } else {
 510 #endif // def EXPAIRSEQ_USE_HASHTAB
 511                construct_from_expairseq_ex(ex_to_expairseq(lh),rh);
 512 #ifdef EXPAIRSEQ_USE_HASHTAB
 513            }
 514 #endif // def EXPAIRSEQ_USE_HASHTAB
 515            return;
 516        }
 517     } else if (rh.bp->tinfo()==tinfo()) {
 518 #ifdef EXPAIRSEQ_USE_HASHTAB
 519         unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 520         if (calc_hashtabsize(totalsize)!=0) {
 521             construct_from_2_ex_via_exvector(lh,rh);
 522         } else {
 523 #endif // def EXPAIRSEQ_USE_HASHTAB
 524             construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 525 #ifdef EXPAIRSEQ_USE_HASHTAB
 526         }
 527 #endif // def EXPAIRSEQ_USE_HASHTAB
 528         return;
 529     }
 530
 531 #ifdef EXPAIRSEQ_USE_HASHTAB
 532     if (calc_hashtabsize(2)!=0) {
 533         construct_from_2_ex_via_exvector(lh,rh);
 534         return;
 535     }
 536     hashtabsize=0;
 537 #endif // def EXPAIRSEQ_USE_HASHTAB
 538
 539     if (is_ex_exactly_of_type(lh,numeric)) {
 540         if (is_ex_exactly_of_type(rh,numeric)) {
 541             combine_overall_coeff(lh);
 542             combine_overall_coeff(rh);
 543         } else {
 544             combine_overall_coeff(lh);
 545             seq.push_back(split_ex_to_pair(rh));
 546         }
 547     } else {
 548         if (is_ex_exactly_of_type(rh,numeric)) {
 549             combine_overall_coeff(rh);
 550             seq.push_back(split_ex_to_pair(lh));
 551         } else {
 552             expair p1=split_ex_to_pair(lh);
 553             expair p2=split_ex_to_pair(rh);
 554
 555             int cmpval=p1.rest.compare(p2.rest);
 556             if (cmpval==0) {
 557                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 558                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 559                     // no further processing is necessary, since this
 560                     // one element will usually be recombined in eval()
 561                     seq.push_back(p1);
 562                 }
 563             } else {
 564                 seq.reserve(2);
 565                 if (cmpval<0) {
 566                     seq.push_back(p1);
 567                     seq.push_back(p2);
 568                 } else {
 569                     seq.push_back(p2);
 570                     seq.push_back(p1);
 571                 }
 572             }
 573         }
 574     }
 575 }
 576
 577 void expairseq::construct_from_2_expairseq(expairseq const & s1,
 578                                            expairseq const & s2)
 579 {
 580     combine_overall_coeff(s1.overall_coeff);
 581     combine_overall_coeff(s2.overall_coeff);
 582
 583     epvector::const_iterator first1=s1.seq.begin();
 584     epvector::const_iterator last1=s1.seq.end();
 585     epvector::const_iterator first2=s2.seq.begin();
 586     epvector::const_iterator last2=s2.seq.end();
 587
 588     seq.reserve(s1.seq.size()+s2.seq.size());
 589
 590     bool needs_further_processing=false;
 591
 592     while (first1!=last1 && first2!=last2) {
 593         int cmpval=(*first1).rest.compare((*first2).rest);
 594         if (cmpval==0) {
 595             // combine terms
 596             numeric const & newcoeff=ex_to_numeric((*first1).coeff).
 597                                      add(ex_to_numeric((*first2).coeff));
 598             if (!newcoeff.is_zero()) {
 599                 seq.push_back(expair((*first1).rest,newcoeff));
 600                 if (expair_needs_further_processing(seq.end()-1)) {
 601                     needs_further_processing = true;
 602                 }
 603             }
 604             ++first1;
 605             ++first2;
 606         } else if (cmpval<0) {
 607             seq.push_back(*first1);
 608             ++first1;
 609         } else {
 610             seq.push_back(*first2);
 611             ++first2;
 612         }
 613     }
 614
 615     while (first1!=last1) {
 616         seq.push_back(*first1);
 617         ++first1;
 618     }
 619     while (first2!=last2) {
 620         seq.push_back(*first2);
 621         ++first2;
 622     }
 623
 624     if (needs_further_processing) {
 625         epvector v=seq;
 626         seq.clear();
 627         construct_from_epvector(v);
 628     }
 629 }
 630
 631 void expairseq::construct_from_expairseq_ex(expairseq const & s,
 632                                             ex const & e)
 633 {
 634     combine_overall_coeff(s.overall_coeff);
 635     if (is_ex_exactly_of_type(e,numeric)) {
 636         combine_overall_coeff(e);
 637         seq=s.seq;
 638         return;
 639     }
 640
 641     epvector::const_iterator first=s.seq.begin();
 642     epvector::const_iterator last=s.seq.end();
 643     expair p=split_ex_to_pair(e);
 644
 645     seq.reserve(s.seq.size()+1);
 646     bool p_pushed=0;
 647
 648     bool needs_further_processing=false;
 649
 650     // merge p into s.seq
 651     while (first!=last) {
 652         int cmpval=(*first).rest.compare(p.rest);
 653         if (cmpval==0) {
 654             // combine terms
 655             numeric const & newcoeff=ex_to_numeric((*first).coeff).
 656                                      add(ex_to_numeric(p.coeff));
 657             if (!newcoeff.is_zero()) {
 658                 seq.push_back(expair((*first).rest,newcoeff));
 659                 if (expair_needs_further_processing(seq.end()-1)) {
 660                     needs_further_processing = true;
 661                 }
 662             }
 663             ++first;
 664             p_pushed=1;
 665             break;
 666         } else if (cmpval<0) {
 667             seq.push_back(*first);
 668             ++first;
 669         } else {
 670             seq.push_back(p);
 671             p_pushed=1;
 672             break;
 673         }
 674     }
 675
 676     if (p_pushed) {
 677         // while loop exited because p was pushed, now push rest of s.seq
 678         while (first!=last) {
 679             seq.push_back(*first);
 680             ++first;
 681         }
 682     } else {
 683         // while loop exited because s.seq was pushed, now push p
 684         seq.push_back(p);
 685     }
 686
 687     if (needs_further_processing) {
 688         epvector v=seq;
 689         seq.clear();
 690         construct_from_epvector(v);
 691     }
 692 }
 693
 694 void expairseq::construct_from_exvector(exvector const & v)
 695 {
 696     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 697     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 698     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 699     //                  (same for (+,*) -> (*,^)
 700
 701     make_flat(v);
 702 #ifdef EXPAIRSEQ_USE_HASHTAB
 703     combine_same_terms();
 704 #else
 705     canonicalize();
 706     combine_same_terms_sorted_seq();
 707 #endif // def EXPAIRSEQ_USE_HASHTAB
 708 }
 709
 710 void expairseq::construct_from_epvector(epvector const & v)
 711 {
 712     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 713     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 714     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 715     //                  (same for (+,*) -> (*,^)
 716
 717     make_flat(v);
 718 #ifdef EXPAIRSEQ_USE_HASHTAB
 719     combine_same_terms();
 720 #else
 721     canonicalize();
 722     combine_same_terms_sorted_seq();
 723 #endif // def EXPAIRSEQ_USE_HASHTAB
 724 }
 725
 726 #include <iostream>
 727
 728 void expairseq::make_flat(exvector const & v)
 729 {
 730     exvector::const_iterator cit, citend = v.end();
 731
 732     // count number of operands which are of same expairseq derived type
 733     // and their cumulative number of operands
 734     int nexpairseqs=0;
 735     int noperands=0;
 736     cit=v.begin();
 737     while (cit!=citend) {
 738         if (cit->bp->tinfo()==tinfo()) {
 739             nexpairseqs++;
 740             noperands+=ex_to_expairseq(*cit).seq.size();
 741         }
 742         ++cit;
 743     }
 744
 745     // reserve seq and coeffseq which will hold all operands
 746     seq.reserve(v.size()+noperands-nexpairseqs);
 747
 748     // copy elements and split off numerical part
 749     cit=v.begin();
 750     while (cit!=citend) {
 751         if (cit->bp->tinfo()==tinfo()) {
 752             expairseq const & subseqref=ex_to_expairseq(*cit);
 753             combine_overall_coeff(subseqref.overall_coeff);
 754             epvector::const_iterator cit_s=subseqref.seq.begin();
 755             while (cit_s!=subseqref.seq.end()) {
 756                 seq.push_back(*cit_s);
 757                 ++cit_s;
 758             }
 759         } else {
 760             if (is_ex_exactly_of_type(*cit,numeric)) {
 761                 combine_overall_coeff(*cit);
 762             } else {
 763                 seq.push_back(split_ex_to_pair(*cit));
 764             }
 765         }
 766         ++cit;
 767     }
 768
 769     /*
 770     cout << "after make flat" << endl;
 771     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 772         (*cit).printraw(cout);
 773     }
 774     cout << endl;
 775     cout.flush();
 776     */
 777 }
 778
 779 void expairseq::make_flat(epvector const & v)
 780 {
 781     epvector::const_iterator cit, citend = v.end();
 782
 783     // count number of operands which are of same expairseq derived type
 784     // and their cumulative number of operands
 785     int nexpairseqs=0;
 786     int noperands=0;
 787     cit=v.begin();
 788     while (cit!=citend) {
 789         if (cit->rest.bp->tinfo()==tinfo()) {
 790             nexpairseqs++;
 791             noperands+=ex_to_expairseq((*cit).rest).seq.size();
 792         }
 793         ++cit;
 794     }
 795
 796     // reserve seq and coeffseq which will hold all operands
 797     seq.reserve(v.size()+noperands-nexpairseqs);
 798
 799     // copy elements and split off numerical part
 800     cit=v.begin();
 801     while (cit!=citend) {
 802         if ((cit->rest.bp->tinfo()==tinfo())&&can_make_flat(*cit)) {
 803             expairseq const & subseqref=ex_to_expairseq((*cit).rest);
 804             combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 805                                   ex_to_numeric((*cit).coeff));
 806             epvector::const_iterator cit_s=subseqref.seq.begin();
 807             while (cit_s!=subseqref.seq.end()) {
 808                 seq.push_back(expair((*cit_s).rest,
 809                               ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
 810                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 811                 //                                              (*cit).coeff));
 812                 ++cit_s;
 813             }
 814         } else {
 815             if ((*cit).is_numeric_with_coeff_1()) {
 816                 combine_overall_coeff((*cit).rest);
 817             //if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 818             //    combine_overall_coeff(recombine_pair_to_ex(*cit));
 819             } else {
 820                 seq.push_back(*cit);
 821             }
 822         }
 823         ++cit;
 824     }
 825 }
 826
 827 epvector * expairseq::bubblesort(epvector::iterator itbegin, epvector::iterator itend)
 828 {
 829     unsigned n=itend-itbegin;
 830
 831     epvector * sp=new epvector;
 832     sp->reserve(n);
 833
 834     epvector::iterator last=itend-1;
 835     for (epvector::iterator it1=itbegin; it1!=last; ++it1) {
 836         for (epvector::iterator it2=it1+1; it2!=itend; ++it2) {
 837             if ((*it2).rest.compare((*it1).rest)<0) {
 838                 iter_swap(it1,it2);
 839             }
 840         }
 841         sp->push_back(*it1);
 842     }
 843     sp->push_back(*last);
 844     return sp;
 845 }
 846
 847 epvector * expairseq::mergesort(epvector::iterator itbegin, epvector::iterator itend)
 848 {
 849     unsigned n=itend-itbegin;
 850     /*
 851     if (n==1) {
 852         epvector * sp=new epvector;
 853         sp->push_back(*itbegin);
 854         return sp;
 855     }
 856     */
 857     if (n<16) return bubblesort(itbegin, itend);
 858     unsigned m=n/2;
 859
 860     epvector * s1p=mergesort(itbegin, itbegin+m);
 861     epvector * s2p=mergesort(itbegin+m, itend);
 862
 863     epvector * sp=new epvector;
 864     sp->reserve(s1p->size()+s2p->size());
 865
 866     epvector::iterator first1=s1p->begin();
 867     epvector::iterator last1=s1p->end();
 868
 869     epvector::iterator first2=s2p->begin();
 870     epvector::iterator last2=s2p->end();
 871
 872     while (first1 != last1 && first2 != last2) {
 873         if ((*first1).rest.compare((*first2).rest)<0) {
 874             sp->push_back(*first1);
 875             ++first1;
 876         } else {
 877             sp->push_back(*first2);
 878             ++first2;
 879         }
 880     }
 881
 882     if (first1 != last1) {
 883         while (first1 != last1) {
 884             sp->push_back(*first1);
 885             ++first1;
 886         }
 887     } else {
 888         while (first2 != last2) {
 889             sp->push_back(*first2);
 890             ++first2;
 891         }
 892     }
 893
 894     delete s1p;
 895     delete s2p;
 896
 897     return sp;
 898 }
 899
 900
 901 void expairseq::canonicalize(void)
 902 {
 903     // canonicalize
 904     sort(seq.begin(),seq.end(),expair_is_less());
 905     /*
 906     sort(seq.begin(),seq.end(),expair_is_less_old());
 907     if (seq.size()>1) {
 908         if (is_ex_exactly_of_type((*(seq.begin())).rest,numeric)) {
 909             sort(seq.begin(),seq.end(),expair_is_less());
 910         } else {
 911             epvector::iterator last_numeric=seq.end();
 912             do {
 913                 last_numeric--;
 914             } while (is_ex_exactly_of_type((*last_numeric).rest,numeric));
 915             last_numeric++;
 916             sort(last_numeric,seq.end(),expair_is_less());
 917         }
 918     }
 919     */
 920
 921     /*
 922     epvector * sorted_seqp=mergesort(seq.begin(),seq.end());
 923     epvector::iterator last=sorted_seqp->end();
 924     epvector::iterator it2=seq.begin();
 925     for (epvector::iterator it1=sorted_seqp->begin(); it1!=last; ++it1, ++it2) {
 926         iter_swap(it1,it2);
 927     }
 928     delete sorted_seqp;
 929     */
 930
 931     /*
 932     cout << "after canonicalize" << endl;
 933     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 934         (*cit).printraw(cout);
 935     }
 936     cout << endl;
 937     cout.flush();
 938     */
 939 }
 940
 941 void expairseq::combine_same_terms_sorted_seq(void)
 942 {
 943     bool needs_further_processing=false;
 944
 945     // combine same terms, drop term with coeff 0
 946     if (seq.size()>1) {
 947         epvector::iterator itin1=seq.begin();
 948         epvector::iterator itin2=itin1+1;
 949         epvector::iterator itout=itin1;
 950         epvector::iterator last=seq.end();
 951         // must_copy will be set to true the first time some combination is possible
 952         // from then on the sequence has changed and must be compacted
 953         bool must_copy=false;
 954         while (itin2!=last) {
 955             if ((*itin1).rest.compare((*itin2).rest)==0) {
 956                 (*itin1).coeff=ex_to_numeric((*itin1).coeff).
 957                                add_dyn(ex_to_numeric((*itin2).coeff));
 958                 if (expair_needs_further_processing(itin1)) {
 959                     needs_further_processing = true;
 960                 }
 961                 must_copy=true;
 962             } else {
 963                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 964                     if (must_copy) {
 965                         *itout=*itin1;
 966                     }
 967                     ++itout;
 968                 }
 969                 itin1=itin2;
 970             }
 971             ++itin2;
 972         }
 973         if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 974             if (must_copy) {
 975                 *itout=*itin1;
 976             }
 977             ++itout;
 978         }
 979         if (itout!=last) {
 980             seq.erase(itout,last);
 981         }
 982     }
 983
 984     /*
 985     cout << "after combine" << endl;
 986     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 987         (*cit).printraw(cout);
 988     }
 989     cout << endl;
 990     cout.flush();
 991     */
 992
 993     if (needs_further_processing) {
 994         epvector v=seq;
 995         seq.clear();
 996         construct_from_epvector(v);
 997     }
 998 }
 999
1000 #ifdef EXPAIRSEQ_USE_HASHTAB
1001
1002 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1003 {
1004     unsigned size;
1005     unsigned nearest_power_of_2 = 1 << log2(sz);
1006     //    if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1007     //  size=nearest_power_of_2*hashtabfactor;
1008     size=nearest_power_of_2/hashtabfactor;
1009     if (size<minhashtabsize) return 0;
1010     ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1011     // hashtabsize must be a power of 2
1012     ASSERT((1U << log2(size))==size);
1013     return size;
1014 }
1015
1016 unsigned expairseq::calc_hashindex(ex const & e) const
1017 {
1018     // calculate hashindex
1019     unsigned hash=e.gethash();
1020     unsigned hashindex;
1021     if (is_a_numeric_hash(hash)) {
1022         hashindex=hashmask;
1023     } else {
1024         hashindex=hash & hashmask;
1025         // last hashtab entry is reserved for numerics
1026         if (hashindex==hashmask) hashindex=0;
1027     }
1028     ASSERT(hashindex>=0);
1029     ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1030     return hashindex;
1031 }
1032
1033 void expairseq::shrink_hashtab(void)
1034 {
1035     unsigned new_hashtabsize;
1036     while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1037         ASSERT(new_hashtabsize<hashtabsize);
1038         if (new_hashtabsize==0) {
1039             hashtab.clear();
1040             hashtabsize=0;
1041             canonicalize();
1042             return;
1043         }
1044
1045         // shrink by a factor of 2
1046         unsigned half_hashtabsize=hashtabsize/2;
1047         for (unsigned i=0; i<half_hashtabsize-1; ++i) {
1048             hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1049         }
1050         // special treatment for numeric hashes
1051         hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1052         hashtab[half_hashtabsize-1]=hashtab[hashtabsize-1];
1053         hashtab.resize(half_hashtabsize);
1054         hashtabsize=half_hashtabsize;
1055         hashmask=hashtabsize-1;
1056     }
1057 }
1058
1059 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1060 {
1061     if (hashtabsize==0) return; // nothing to do
1062
1063     // calculate hashindex of element to be deleted
1064     unsigned hashindex=calc_hashindex((*element).rest);
1065
1066     // find it in hashtab and remove it
1067     epplist & eppl=hashtab[hashindex];
1068     epplist::iterator epplit=eppl.begin();
1069     bool erased=false;
1070     while (epplit!=eppl.end()) {
1071         if (*epplit == element) {
1072             eppl.erase(epplit);
1073             erased=true;
1074             break;
1075         }
1076         ++epplit;
1077     }
1078     if (!erased) {
1079         printtree(cout,0);
1080         cout << "tried to erase " << element-seq.begin() << endl;
1081         cout << "size " << seq.end()-seq.begin() << endl;
1082
1083         unsigned hashindex=calc_hashindex((*element).rest);
1084         epplist & eppl=hashtab[hashindex];
1085         epplist::iterator epplit=eppl.begin();
1086         bool erased=false;
1087         while (epplit!=eppl.end()) {
1088             if (*epplit == element) {
1089                 eppl.erase(epplit);
1090                 erased=true;
1091                 break;
1092             }
1093             ++epplit;
1094         }
1095         ASSERT(erased);
1096     }
1097     ASSERT(erased);
1098 }
1099
1100 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1101                                    epvector::iterator newpos)
1102 {
1103     ASSERT(hashtabsize!=0);
1104
1105     // calculate hashindex of element which was moved
1106     unsigned hashindex=calc_hashindex((*newpos).rest);
1107
1108     // find it in hashtab and modify it
1109     epplist & eppl=hashtab[hashindex];
1110     epplist::iterator epplit=eppl.begin();
1111     while (epplit!=eppl.end()) {
1112         if (*epplit == oldpos) {
1113             *epplit=newpos;
1114             break;
1115         }
1116         ++epplit;
1117     }
1118     ASSERT(epplit!=eppl.end());
1119 }
1120
1121 void expairseq::sorted_insert(epplist & eppl, epp elem)
1122 {
1123     epplist::iterator current=eppl.begin();
1124     while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1125         ++current;
1126     }
1127     eppl.insert(current,elem);
1128 }
1129
1130 void expairseq::build_hashtab_and_combine(epvector::iterator & first_numeric,
1131                                           epvector::iterator & last_non_zero,
1132                                           vector<bool> & touched,
1133                                           unsigned & number_of_zeroes)
1134 {
1135     epp current=seq.begin();
1136
1137     while (current!=first_numeric) {
1138         if (is_ex_exactly_of_type((*current).rest,numeric)) {
1139             --first_numeric;
1140             iter_swap(current,first_numeric);
1141         } else {
1142             // calculate hashindex
1143             unsigned currenthashindex=calc_hashindex((*current).rest);
1144
1145             // test if there is already a matching expair in the hashtab-list
1146             epplist & eppl=hashtab[currenthashindex];
1147             epplist::iterator epplit=eppl.begin();
1148             while (epplit!=eppl.end()) {
1149                 if ((*current).rest.is_equal((*(*epplit)).rest)) break;
1150                 ++epplit;
1151             }
1152             if (epplit==eppl.end()) {
1153                 // no matching expair found, append this to end of list
1154                 sorted_insert(eppl,current);
1155                 ++current;
1156             } else {
1157                 // epplit points to a matching expair, combine it with current
1158                 (*(*epplit)).coeff=ex_to_numeric((*(*epplit)).coeff).
1159                                    add_dyn(ex_to_numeric((*current).coeff));
1160
1161                 // move obsolete current expair to end by swapping with last_non_zero element
1162                 // if this was a numeric, it is swapped with the expair before first_numeric
1163                 iter_swap(current,last_non_zero);
1164                 --first_numeric;
1165                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1166                 --last_non_zero;
1167                 ++number_of_zeroes;
1168                 // test if combined term has coeff 0 and can be removed is done later
1169                 touched[(*epplit)-seq.begin()]=true;
1170             }
1171         }
1172     }
1173 }
1174
1175 void expairseq::drop_coeff_0_terms(epvector::iterator & first_numeric,
1176                                    epvector::iterator & last_non_zero,
1177                                    vector<bool> & touched,
1178                                    unsigned & number_of_zeroes)
1179 {
1180     // move terms with coeff 0 to end and remove them from hashtab
1181     // check only those elements which have been touched
1182     epp current=seq.begin();
1183     unsigned i=0;
1184     while (current!=first_numeric) {
1185         if (!touched[i]) {
1186             ++current;
1187             ++i;
1188         } else if (!ex_to_numeric((*current).coeff).is_equal(numZERO())) {
1189             ++current;
1190             ++i;
1191         } else {
1192             remove_hashtab_entry(current);
1193
1194             // move element to the end, unless it is already at the end
1195             if (current!=last_non_zero) {
1196                 iter_swap(current,last_non_zero);
1197                 --first_numeric;
1198                 bool numeric_swapped=first_numeric!=last_non_zero;
1199                 if (numeric_swapped) iter_swap(first_numeric,current);
1200                 epvector::iterator changed_entry;
1201
1202                 if (numeric_swapped) {
1203                     changed_entry=first_numeric;
1204                 } else {
1205                     changed_entry=last_non_zero;
1206                 }
1207
1208                 --last_non_zero;
1209                 ++number_of_zeroes;
1210
1211                 if (first_numeric!=current) {
1212
1213                     // change entry in hashtab which referred to first_numeric or last_non_zero to current
1214                     move_hashtab_entry(changed_entry,current);
1215                     touched[current-seq.begin()]=touched[changed_entry-seq.begin()];
1216                 }
1217             } else {
1218                 --first_numeric;
1219                 --last_non_zero;
1220                 ++number_of_zeroes;
1221             }
1222         }
1223     }
1224     ASSERT(i==current-seq.begin());
1225 }
1226
1227 bool expairseq::has_coeff_0(void) const
1228 {
1229     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1230         if ((*cit).coeff.is_equal(exZERO())) {
1231             return true;
1232         }
1233     }
1234     return false;
1235 }
1236
1237 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1238                                         epvector::const_iterator last_non_zero)
1239 {
1240     if (first_numeric==seq.end()) return; // no numerics
1241
1242     epvector::iterator current=first_numeric;
1243     epvector::const_iterator last=last_non_zero+1;
1244     while (current!=last) {
1245         sorted_insert(hashtab[hashmask],current);
1246         ++current;
1247     }
1248 }
1249
1250 void expairseq::combine_same_terms(void)
1251 {
1252     // combine same terms, drop term with coeff 0, move numerics to end
1253
1254     // calculate size of hashtab
1255     hashtabsize=calc_hashtabsize(seq.size());
1256
1257     // hashtabsize is a power of 2
1258     hashmask=hashtabsize-1;
1259
1260     // allocate hashtab
1261     hashtab.clear();
1262     hashtab.resize(hashtabsize);
1263
1264     if (hashtabsize==0) {
1265         canonicalize();
1266         combine_same_terms_sorted_seq();
1267         ASSERT(!has_coeff_0());
1268         return;
1269     }
1270
1271     // iterate through seq, move numerics to end,
1272     // fill hashtab and combine same terms
1273     epvector::iterator first_numeric=seq.end();
1274     epvector::iterator last_non_zero=seq.end()-1;
1275
1276     vector<bool> touched;
1277     touched.reserve(seq.size());
1278     for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1279
1280     unsigned number_of_zeroes=0;
1281
1282     ASSERT(!has_coeff_0());
1283     build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1284     /*
1285     cout << "in combine:" << endl;
1286     printtree(cout,0);
1287     cout << "size=" << seq.end() - seq.begin() << endl;
1288     cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1289     cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1290     for (unsigned i=0; i<seq.size(); ++i) {
1291         if (touched[i]) cout << i << " is touched" << endl;
1292     }
1293     cout << "end in combine" << endl;
1294     */
1295
1296     // there should not be any terms with coeff 0 from the beginning,
1297     // so it should be safe to skip this step
1298     if (number_of_zeroes!=0) {
1299         drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1300         /*
1301         cout << "in combine after drop:" << endl;
1302         printtree(cout,0);
1303         cout << "size=" << seq.end() - seq.begin() << endl;
1304         cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1305         cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1306         for (unsigned i=0; i<seq.size(); ++i) {
1307             if (touched[i]) cout << i << " is touched" << endl;
1308         }
1309         cout << "end in combine after drop" << endl;
1310         */
1311     }
1312
1313     add_numerics_to_hashtab(first_numeric,last_non_zero);
1314
1315     // pop zero elements
1316     for (unsigned i=0; i<number_of_zeroes; ++i) {
1317         seq.pop_back();
1318     }
1319
1320     // shrink hashtabsize to calculated value
1321     ASSERT(!has_coeff_0());
1322
1323     shrink_hashtab();
1324
1325     ASSERT(!has_coeff_0());
1326 }
1327
1328 #endif // def EXPAIRSEQ_USE_HASHTAB
1329
1330 bool expairseq::is_canonical() const
1331 {
1332     if (seq.size()<=1) return 1;
1333
1334 #ifdef EXPAIRSEQ_USE_HASHTAB
1335     if (hashtabsize>0) return 1; // not canoncalized
1336 #endif // def EXPAIRSEQ_USE_HASHTAB
1337
1338     epvector::const_iterator it=seq.begin();
1339     epvector::const_iterator it_last=it;
1340     for (++it; it!=seq.end(); it_last=it, ++it) {
1341         if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
1342             if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1343                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1344                 // double test makes it easier to set a breakpoint...
1345                 if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1346                     !is_ex_exactly_of_type((*it).rest,numeric)) {
1347                     printpair(cout,*it_last,0);
1348                     cout << ">";
1349                     printpair(cout,*it,0);
1350                     cout << "\n";
1351                     cout << "pair1:" << endl;
1352                     (*it_last).rest.printtree(cout);
1353                     (*it_last).coeff.printtree(cout);
1354                     cout << "pair2:" << endl;
1355                     (*it).rest.printtree(cout);
1356                     (*it).coeff.printtree(cout);
1357                     return 0;
1358                 }
1359             }
1360         }
1361     }
1362     return 1;
1363 }
1364
1365 epvector * expairseq::expandchildren(unsigned options) const
1366 {
1367     epvector::const_iterator last=seq.end();
1368     epvector::const_iterator cit=seq.begin();
1369     while (cit!=last) {
1370         ex const & expanded_ex=(*cit).rest.expand(options);
1371         if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1372
1373             // something changed, copy seq, eval and return it
1374             epvector *s=new epvector;
1375             s->reserve(seq.size());
1376
1377             // copy parts of seq which are known not to have changed
1378             epvector::const_iterator cit2=seq.begin();
1379             while (cit2!=cit) {
1380                 s->push_back(*cit2);
1381                 ++cit2;
1382             }
1383             // copy first changed element
1384             s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1385                                                        (*cit2).coeff));
1386             ++cit2;
1387             // copy rest
1388             while (cit2!=last) {
1389                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1390                                                            (*cit2).coeff));
1391                 ++cit2;
1392             }
1393             return s;
1394         }
1395         ++cit;
1396     }
1397
1398     return 0; // nothing has changed
1399 }
1400
1401 epvector * expairseq::evalchildren(int level) const
1402 {
1403     // returns a NULL pointer if nothing had to be evaluated
1404     // returns a pointer to a newly created epvector otherwise
1405     // (which has to be deleted somewhere else)
1406
1407     if (level==1) {
1408         return 0;
1409     }
1410     if (level == -max_recursion_level) {
1411         throw(std::runtime_error("max recursion level reached"));
1412     }
1413
1414     --level;
1415     epvector::const_iterator last=seq.end();
1416     epvector::const_iterator cit=seq.begin();
1417     while (cit!=last) {
1418         ex const & evaled_ex=(*cit).rest.eval(level);
1419         if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1420
1421             // something changed, copy seq, eval and return it
1422             epvector *s=new epvector;
1423             s->reserve(seq.size());
1424
1425             // copy parts of seq which are known not to have changed
1426             epvector::const_iterator cit2=seq.begin();
1427             while (cit2!=cit) {
1428                 s->push_back(*cit2);
1429                 ++cit2;
1430             }
1431             // copy first changed element
1432             s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1433                                                        (*cit2).coeff));
1434             ++cit2;
1435             // copy rest
1436             while (cit2!=last) {
1437                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1438                                                            (*cit2).coeff));
1439                 ++cit2;
1440             }
1441             return s;
1442         }
1443         ++cit;
1444     }
1445
1446     return 0; // nothing has changed
1447 }
1448
1449 epvector expairseq::evalfchildren(int level) const
1450 {
1451     epvector s;
1452     s.reserve(seq.size());
1453
1454     if (level==1) {
1455         return seq;
1456     }
1457     if (level == -max_recursion_level) {
1458         throw(std::runtime_error("max recursion level reached"));
1459     }
1460     --level;
1461     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1462         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1463                                                   (*it).coeff));
1464     }
1465     return s;
1466 }
1467
1468 epvector expairseq::normalchildren(int level) const
1469 {
1470     epvector s;
1471     s.reserve(seq.size());
1472
1473     if (level==1) {
1474         return seq;
1475     }
1476     if (level == -max_recursion_level) {
1477         throw(std::runtime_error("max recursion level reached"));
1478     }
1479     --level;
1480     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1481         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1482                                                   (*it).coeff));
1483     }
1484     return s;
1485 }
1486
1487 epvector expairseq::diffchildren(symbol const & y) const
1488 {
1489     epvector s;
1490     s.reserve(seq.size());
1491
1492     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1493         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1494                                                   (*it).coeff));
1495     }
1496     return s;
1497 }
1498
1499 epvector * expairseq::subschildren(lst const & ls, lst const & lr) const
1500 {
1501     // returns a NULL pointer if nothing had to be substituted
1502     // returns a pointer to a newly created epvector otherwise
1503     // (which has to be deleted somewhere else)
1504
1505     epvector::const_iterator last=seq.end();
1506     epvector::const_iterator cit=seq.begin();
1507     while (cit!=last) {
1508         ex const & subsed_ex=(*cit).rest.subs(ls,lr);
1509         if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1510
1511             // something changed, copy seq, subs and return it
1512             epvector *s=new epvector;
1513             s->reserve(seq.size());
1514
1515             // copy parts of seq which are known not to have changed
1516             epvector::const_iterator cit2=seq.begin();
1517             while (cit2!=cit) {
1518                 s->push_back(*cit2);
1519                 ++cit2;
1520             }
1521             // copy first changed element
1522             s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1523                                                        (*cit2).coeff));
1524             ++cit2;
1525             // copy rest
1526             while (cit2!=last) {
1527                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
1528                                                            (*cit2).coeff));
1529                 ++cit2;
1530             }
1531             return s;
1532         }
1533         ++cit;
1534     }
1535
1536     return 0; // nothing has changed
1537 }
1538
1539 /*
1540 epvector expairseq::subschildren(lst const & ls, lst const & lr) const
1541 {
1542     epvector s;
1543     s.reserve(seq.size());
1544
1545     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1546         s.push_back(split_ex_to_pair((*it).rest.subs(ls,lr),(*it).coeff));
1547     }
1548     return s;
1549 }
1550 */
1551
1552 /*
1553 void expairseq::sort(epviter first, epviter last, expair_is_less comp)
1554 {
1555     if (first != last) {
1556         introsort_loop(first, last, lg(last - first) * 2, comp);
1557         __final_insertion_sort(first, last, comp);
1558     }
1559 }
1560
1561 ptrdiff_t expairseq::lg(ptrdiff_t n)
1562 {
1563     ptrdiff_t k;
1564     for (k = 0; n > 1; n >>= 1) ++k;
1565     return k;
1566 }
1567
1568 void expairseq::introsort_loop(epviter first, epviter last,
1569                                ptrdiff_t depth_limit, expair_is_less comp)
1570 {
1571     while (last - first > stl_threshold) {
1572         if (depth_limit == 0) {
1573             partial_sort(first, last, last, comp);
1574             return;
1575         }
1576         --depth_limit;
1577         epviter cut = unguarded_partition(first, last,
1578                       expair(__median(*first, *(first + (last - first)/2),
1579                       *(last - 1), comp)), comp);
1580         introsort_loop(cut, last, depth_limit, comp);
1581         last = cut;
1582     }
1583 }
1584
1585 epviter expairseq::unguarded_partition(epviter first, epviter last,
1586                                        expair pivot, expair_is_less comp)
1587 {
1588     while (1) {
1589         while (comp(*first, pivot)) ++first;
1590         --last;
1591         while (comp(pivot, *last)) --last;
1592         if (!(first < last)) return first;
1593         iter_swap(first, last);
1594         ++first;
1595     }
1596 }
1597
1598 void expairseq::partial_sort(epviter first, epviter middle, epviter last,
1599                              expair_is_less comp) {
1600   make_heap(first, middle, comp);
1601   for (RandomAccessIterator i = middle; i < last; ++i)
1602     if (comp(*i, *first))
1603       __pop_heap(first, middle, i, T(*i), comp, distance_type(first));
1604   sort_heap(first, middle, comp);
1605 }
1606 */
1607
1608 //////////
1609 // static member variables
1610 //////////
1611
1612 // protected
1613
1614 unsigned expairseq::precedence=10;
1615
1616 #ifdef EXPAIRSEQ_USE_HASHTAB
1617 unsigned expairseq::maxhashtabsize=0x4000000U;
1618 unsigned expairseq::minhashtabsize=0x1000U;
1619 unsigned expairseq::hashtabfactor=1;
1620 #endif // def EXPAIRSEQ_USE_HASHTAB
1621
1622 //////////
1623 // global constants
1624 //////////
1625
1626 const expairseq some_expairseq;
1627 type_info const & typeid_expairseq=typeid(some_expairseq);
1628
1629 } // namespace GiNaC