ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
   4  *
   5  *  This program is free software; you can redistribute it and/or modify
   6  *  it under the terms of the GNU General Public License as published by
   7  *  the Free Software Foundation; either version 2 of the License, or
   8  *  (at your option) any later version.
   9  *
  10  *  This program is distributed in the hope that it will be useful,
  11  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13  *  GNU General Public License for more details.
  14  *
  15  *  You should have received a copy of the GNU General Public License
  16  *  along with this program; if not, write to the Free Software
  17  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  18  */
  19
  20 #include <algorithm>
  21 #include <string>
  22 #include <stdexcept>
  23
  24 #include "expairseq.h"
  25 #include "lst.h"
  26
  27 #ifdef EXPAIRSEQ_USE_HASHTAB
  28 #error "!!!!!!!!TODO: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
  29 #endif // def EXPAIRSEQ_USE_HASHTAB
  30
  31 //////////
  32 // helper classes
  33 //////////
  34
  35 class epp_is_less
  36 {
  37 public:
  38     bool operator()(epp const & lh, epp const & rh) const
  39     {
  40         return (*lh).is_less(*rh);
  41     }
  42 };
  43
  44 //////////
  45 // default constructor, destructor, copy constructor assignment operator and helpers
  46 //////////
  47
  48 // public
  49
  50 expairseq::expairseq(expairseq const & other)
  51 {
  52     debugmsg("expairseq copy constructor",LOGLEVEL_CONSTRUCT);
  53     copy(other);
  54 }
  55
  56 expairseq const & expairseq::operator=(expairseq const & other)
  57 {
  58     debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  59     if (this != &other) {
  60         destroy(1);
  61         copy(other);
  62     }
  63     return *this;
  64 }
  65
  66 // protected
  67
  68 void expairseq::copy(expairseq const & other)
  69 {
  70     basic::copy(other);
  71     seq=other.seq;
  72     overall_coeff=other.overall_coeff;
  73 #ifdef EXPAIRSEQ_USE_HASHTAB
  74     // copy hashtab
  75     hashtabsize=other.hashtabsize;
  76     if (hashtabsize!=0) {
  77     hashmask=other.hashmask;
  78         hashtab.resize(hashtabsize);
  79         epvector::const_iterator osb=other.seq.begin();
  80         for (unsigned i=0; i<hashtabsize; ++i) {
  81             hashtab[i].clear();
  82             for (epplist::const_iterator cit=other.hashtab[i].begin();
  83                  cit!=other.hashtab[i].end(); ++cit) {
  84                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  85             }
  86         }
  87     } else {
  88         hashtab.clear();
  89     }
  90 #endif // def EXPAIRSEQ_USE_HASHTAB
  91 }
  92
  93 //////////
  94 // other constructors
  95 //////////
  96
  97 expairseq::expairseq(ex const & lh, ex const & rh) : basic(TINFO_expairseq)
  98 {
  99     debugmsg("expairseq constructor from ex,ex",LOGLEVEL_CONSTRUCT);
 100     construct_from_2_ex(lh,rh);
 101     ASSERT(is_canonical());
 102 }
 103
 104 expairseq::expairseq(exvector const & v) : basic(TINFO_expairseq)
 105 {
 106     debugmsg("expairseq constructor from exvector",LOGLEVEL_CONSTRUCT);
 107     construct_from_exvector(v);
 108     ASSERT(is_canonical());
 109 }
 110
 111 /*
 112 expairseq::expairseq(epvector const & v, bool do_not_canonicalize) :
 113     basic(TINFO_expairseq)
 114 {
 115     debugmsg("expairseq constructor from epvector",LOGLEVEL_CONSTRUCT);
 116     if (do_not_canonicalize) {
 117         seq=v;
 118 #ifdef EXPAIRSEQ_USE_HASHTAB
 119         combine_same_terms(); // to build hashtab
 120 #endif // def EXPAIRSEQ_USE_HASHTAB
 121     } else {
 122         construct_from_epvector(v);
 123     }
 124     ASSERT(is_canonical());
 125 }
 126 */
 127
 128 expairseq::expairseq(epvector const & v, ex const & oc) :
 129     basic(TINFO_expairseq), overall_coeff(oc)
 130 {
 131     debugmsg("expairseq constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 132     construct_from_epvector(v);
 133     ASSERT(is_canonical());
 134 }
 135
 136 expairseq::expairseq(epvector * vp, ex const & oc) :
 137     basic(TINFO_expairseq), overall_coeff(oc)
 138 {
 139     debugmsg("expairseq constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 140     ASSERT(vp!=0);
 141     construct_from_epvector(*vp);
 142     delete vp;
 143     ASSERT(is_canonical());
 144 }
 145
 146 //////////
 147 // functions overriding virtual functions from bases classes
 148 //////////
 149
 150 // public
 151
 152 basic * expairseq::duplicate() const
 153 {
 154     debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 155     return new expairseq(*this);
 156 }
 157
 158 bool expairseq::info(unsigned inf) const
 159 {
 160     return basic::info(inf);
 161 }
 162
 163 int expairseq::nops() const
 164 {
 165     if (overall_coeff.is_equal(default_overall_coeff())) {
 166         return seq.size();
 167     }
 168     return seq.size()+1;
 169 }
 170
 171 ex expairseq::op(int const i) const
 172 {
 173     if (unsigned(i)<seq.size()) {
 174         return recombine_pair_to_ex(seq[i]);
 175     }
 176     ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 177     return overall_coeff;
 178 }
 179
 180 ex & expairseq::let_op(int const i)
 181 {
 182     throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 183 }
 184
 185 ex expairseq::eval(int level) const
 186 {
 187     if ((level==1)&&(flags & status_flags::evaluated)) {
 188         return *this;
 189     }
 190
 191     epvector * vp=evalchildren(level);
 192     if (vp==0) {
 193         return this->hold();
 194     }
 195
 196     return (new expairseq(vp,overall_coeff))
 197                ->setflag(status_flags::dynallocated |
 198                          status_flags::evaluated );
 199 }
 200
 201 ex expairseq::evalf(int level) const
 202 {
 203     return thisexpairseq(evalfchildren(level),overall_coeff);
 204 }
 205
 206 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 207 {
 208     ex n=thisexpairseq(normalchildren(level),overall_coeff);
 209     return n.bp->basic::normal(sym_lst,repl_lst,level);
 210 }
 211
 212 ex expairseq::subs(lst const & ls, lst const & lr) const
 213 {
 214     epvector * vp=subschildren(ls,lr);
 215     if (vp==0) {
 216         return *this;
 217     }
 218     return thisexpairseq(vp,overall_coeff);
 219 }
 220
 221 // protected
 222
 223 int expairseq::compare_same_type(basic const & other) const
 224 {
 225     ASSERT(is_of_type(other, expairseq));
 226     expairseq const & o=static_cast<expairseq const &>(const_cast<basic &>(other));
 227
 228     int cmpval;
 229
 230     // compare number of elements
 231     if (seq.size() != o.seq.size()) {
 232         return (seq.size()<o.seq.size()) ? -1 : 1;
 233     }
 234
 235     // compare overall_coeff
 236     cmpval=overall_coeff.compare(o.overall_coeff);
 237     if (cmpval!=0) return cmpval;
 238
 239     //if (seq.size()==0) return 0; // empty expairseq's are equal
 240
 241 #ifdef EXPAIRSEQ_USE_HASHTAB
 242     ASSERT(hashtabsize==o.hashtabsize);
 243     if (hashtabsize==0) {
 244 #endif // def EXPAIRSEQ_USE_HASHTAB
 245         epvector::const_iterator cit1=seq.begin();
 246         epvector::const_iterator cit2=o.seq.begin();
 247         epvector::const_iterator last1=seq.end();
 248         epvector::const_iterator last2=o.seq.end();
 249
 250         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 251             cmpval=(*cit1).compare(*cit2);
 252             if (cmpval!=0) return cmpval;
 253         }
 254
 255         ASSERT(cit1==last1);
 256         ASSERT(cit2==last2);
 257
 258         return 0;
 259 #ifdef EXPAIRSEQ_USE_HASHTAB
 260     }
 261
 262     // compare number of elements in each hashtab entry
 263     for (unsigned i=0; i<hashtabsize; ++i) {
 264         unsigned cursize=hashtab[i].size();
 265         if (cursize != o.hashtab[i].size()) {
 266             return (cursize < o.hashtab[i].size()) ? -1 : 1;
 267         }
 268     }
 269
 270     // compare individual (sorted) hashtab entries
 271     for (unsigned i=0; i<hashtabsize; ++i) {
 272         unsigned sz=hashtab[i].size();
 273         if (sz>0) {
 274             epplist const & eppl1=hashtab[i];
 275             epplist const & eppl2=o.hashtab[i];
 276             epplist::const_iterator it1=eppl1.begin();
 277             epplist::const_iterator it2=eppl2.begin();
 278             while (it1!=eppl1.end()) {
 279                 cmpval=(*(*it1)).compare(*(*it2));
 280                 if (cmpval!=0) return cmpval;
 281                 ++it1;
 282                 ++it2;
 283             }
 284         }
 285     }
 286
 287     return 0; // equal
 288 #endif // def EXPAIRSEQ_USE_HASHTAB
 289 }
 290
 291 bool expairseq::is_equal_same_type(basic const & other) const
 292 {
 293     expairseq const & o=dynamic_cast<expairseq const &>(const_cast<basic &>(other));
 294
 295     // compare number of elements
 296     if (seq.size() != o.seq.size()) return false;
 297
 298     // compare overall_coeff
 299     if (!overall_coeff.is_equal(o.overall_coeff)) return false;
 300
 301 #ifdef EXPAIRSEQ_USE_HASHTAB
 302     // compare number of elements in each hashtab entry
 303     if (hashtabsize!=o.hashtabsize) {
 304         cout << "this:" << endl;
 305         printtree(cout,0);
 306         cout << "other:" << endl;
 307         other.printtree(cout,0);
 308     }
 309
 310     ASSERT(hashtabsize==o.hashtabsize);
 311
 312     if (hashtabsize==0) {
 313 #endif // def EXPAIRSEQ_USE_HASHTAB
 314         epvector::const_iterator cit1=seq.begin();
 315         epvector::const_iterator cit2=o.seq.begin();
 316         epvector::const_iterator last1=seq.end();
 317
 318         while (cit1!=last1) {
 319             if (!(*cit1).is_equal(*cit2)) return false;
 320             ++cit1;
 321             ++cit2;
 322         }
 323
 324         return true;
 325 #ifdef EXPAIRSEQ_USE_HASHTAB
 326     }
 327
 328     for (unsigned i=0; i<hashtabsize; ++i) {
 329         if (hashtab[i].size() != o.hashtab[i].size()) return false;
 330     }
 331
 332     // compare individual sorted hashtab entries
 333     for (unsigned i=0; i<hashtabsize; ++i) {
 334         unsigned sz=hashtab[i].size();
 335         if (sz>0) {
 336             epplist const & eppl1=hashtab[i];
 337             epplist const & eppl2=o.hashtab[i];
 338             epplist::const_iterator it1=eppl1.begin();
 339             epplist::const_iterator it2=eppl2.begin();
 340             while (it1!=eppl1.end()) {
 341                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 342                 ++it1;
 343                 ++it2;
 344             }
 345         }
 346     }
 347
 348     return true;
 349 #endif // def EXPAIRSEQ_USE_HASHTAB
 350 }
 351
 352 unsigned expairseq::return_type(void) const
 353 {
 354     return return_types::noncommutative_composite;
 355 }
 356
 357 unsigned expairseq::calchash(void) const
 358 {
 359     unsigned v=golden_ratio_hash(tinfo());
 360     epvector::const_iterator last=seq.end();
 361     for (epvector::const_iterator cit=seq.begin(); cit!=last; ++cit) {
 362 #ifndef EXPAIRSEQ_USE_HASHTAB
 363         v=rotate_left_31(v); // rotation would spoil commutativity
 364 #endif // ndef EXPAIRSEQ_USE_HASHTAB
 365         v ^= (*cit).rest.gethash();
 366     }
 367
 368     v ^= overall_coeff.gethash();
 369     v=v & 0x7FFFFFFFU;
 370
 371     // store calculated hash value only if object is already evaluated
 372     if (flags & status_flags::evaluated) {
 373         setflag(status_flags::hash_calculated);
 374         hashvalue=v;
 375     }
 376
 377     return v;
 378 }
 379
 380 ex expairseq::expand(unsigned options) const
 381 {
 382     epvector * vp=expandchildren(options);
 383     if (vp==0) {
 384         return *this;
 385     }
 386     return thisexpairseq(vp,overall_coeff);
 387 }
 388
 389 //////////
 390 // new virtual functions which can be overridden by derived classes
 391 //////////
 392
 393 // protected
 394
 395 ex expairseq::thisexpairseq(epvector const & v,ex const & oc) const
 396 {
 397     return expairseq(v,oc);
 398 }
 399
 400 ex expairseq::thisexpairseq(epvector * vp, ex const & oc) const
 401 {
 402     return expairseq(vp,oc);
 403 }
 404
 405 expair expairseq::split_ex_to_pair(ex const & e) const
 406 {
 407     return expair(e,exONE());
 408 }
 409
 410 expair expairseq::combine_ex_with_coeff_to_pair(ex const & e,
 411                                                 ex const & c) const
 412 {
 413     ASSERT(is_ex_exactly_of_type(c,numeric));
 414
 415     return expair(e,c);
 416 }
 417
 418 expair expairseq::combine_pair_with_coeff_to_pair(expair const & p,
 419                                                   ex const & c) const
 420 {
 421     ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 422     ASSERT(is_ex_exactly_of_type(c,numeric));
 423
 424     return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 425 }
 426
 427 ex expairseq::recombine_pair_to_ex(expair const & p) const
 428 {
 429     return lst(p.rest,p.coeff);
 430 }
 431
 432 bool expairseq::expair_needs_further_processing(epp it)
 433 {
 434     return false;
 435 }
 436
 437 ex expairseq::default_overall_coeff(void) const
 438 {
 439     return exZERO();
 440 }
 441
 442 void expairseq::combine_overall_coeff(ex const & c)
 443 {
 444     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 445     ASSERT(is_ex_exactly_of_type(c,numeric));
 446     overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 447 }
 448
 449 void expairseq::combine_overall_coeff(ex const & c1, ex const & c2)
 450 {
 451     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 452     ASSERT(is_ex_exactly_of_type(c1,numeric));
 453     ASSERT(is_ex_exactly_of_type(c2,numeric));
 454     overall_coeff = ex_to_numeric(overall_coeff).
 455                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 456 }
 457
 458 bool expairseq::can_make_flat(expair const & p) const
 459 {
 460     return true;
 461 }
 462
 463
 464 //////////
 465 // non-virtual functions in this class
 466 //////////
 467
 468 void expairseq::construct_from_2_ex_via_exvector(ex const & lh, ex const & rh)
 469 {
 470     exvector v;
 471     v.reserve(2);
 472     v.push_back(lh);
 473     v.push_back(rh);
 474     construct_from_exvector(v);
 475 #ifdef EXPAIRSEQ_USE_HASHTAB
 476     ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 477     ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 478 #endif // def EXPAIRSEQ_USE_HASHTAB
 479 }
 480
 481 void expairseq::construct_from_2_ex(ex const & lh, ex const & rh)
 482 {
 483     if (lh.bp->tinfo()==tinfo()) {
 484        if (rh.bp->tinfo()==tinfo()) {
 485 #ifdef EXPAIRSEQ_USE_HASHTAB
 486            unsigned totalsize=ex_to_expairseq(lh).seq.size()+
 487                               ex_to_expairseq(rh).seq.size();
 488            if (calc_hashtabsize(totalsize)!=0) {
 489                construct_from_2_ex_via_exvector(lh,rh);
 490            } else {
 491 #endif // def EXPAIRSEQ_USE_HASHTAB
 492                construct_from_2_expairseq(ex_to_expairseq(lh),
 493                                           ex_to_expairseq(rh));
 494 #ifdef EXPAIRSEQ_USE_HASHTAB
 495            }
 496 #endif // def EXPAIRSEQ_USE_HASHTAB
 497            return;
 498        } else {
 499 #ifdef EXPAIRSEQ_USE_HASHTAB
 500            unsigned totalsize=ex_to_expairseq(lh).seq.size()+1;
 501            if (calc_hashtabsize(totalsize)!=0) {
 502                construct_from_2_ex_via_exvector(lh,rh);
 503            } else {
 504 #endif // def EXPAIRSEQ_USE_HASHTAB
 505                construct_from_expairseq_ex(ex_to_expairseq(lh),rh);
 506 #ifdef EXPAIRSEQ_USE_HASHTAB
 507            }
 508 #endif // def EXPAIRSEQ_USE_HASHTAB
 509            return;
 510        }
 511     } else if (rh.bp->tinfo()==tinfo()) {
 512 #ifdef EXPAIRSEQ_USE_HASHTAB
 513         unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 514         if (calc_hashtabsize(totalsize)!=0) {
 515             construct_from_2_ex_via_exvector(lh,rh);
 516         } else {
 517 #endif // def EXPAIRSEQ_USE_HASHTAB
 518             construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 519 #ifdef EXPAIRSEQ_USE_HASHTAB
 520         }
 521 #endif // def EXPAIRSEQ_USE_HASHTAB
 522         return;
 523     }
 524
 525 #ifdef EXPAIRSEQ_USE_HASHTAB
 526     if (calc_hashtabsize(2)!=0) {
 527         construct_from_2_ex_via_exvector(lh,rh);
 528         return;
 529     }
 530     hashtabsize=0;
 531 #endif // def EXPAIRSEQ_USE_HASHTAB
 532
 533     if (is_ex_exactly_of_type(lh,numeric)) {
 534         if (is_ex_exactly_of_type(rh,numeric)) {
 535             combine_overall_coeff(lh);
 536             combine_overall_coeff(rh);
 537         } else {
 538             combine_overall_coeff(lh);
 539             seq.push_back(split_ex_to_pair(rh));
 540         }
 541     } else {
 542         if (is_ex_exactly_of_type(rh,numeric)) {
 543             combine_overall_coeff(rh);
 544             seq.push_back(split_ex_to_pair(lh));
 545         } else {
 546             expair p1=split_ex_to_pair(lh);
 547             expair p2=split_ex_to_pair(rh);
 548
 549             int cmpval=p1.rest.compare(p2.rest);
 550             if (cmpval==0) {
 551                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 552                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 553                     // no further processing is necessary, since this
 554                     // one element will usually be recombined in eval()
 555                     seq.push_back(p1);
 556                 }
 557             } else {
 558                 seq.reserve(2);
 559                 if (cmpval<0) {
 560                     seq.push_back(p1);
 561                     seq.push_back(p2);
 562                 } else {
 563                     seq.push_back(p2);
 564                     seq.push_back(p1);
 565                 }
 566             }
 567         }
 568     }
 569 }
 570
 571 void expairseq::construct_from_2_expairseq(expairseq const & s1,
 572                                            expairseq const & s2)
 573 {
 574     combine_overall_coeff(s1.overall_coeff);
 575     combine_overall_coeff(s2.overall_coeff);
 576
 577     epvector::const_iterator first1=s1.seq.begin();
 578     epvector::const_iterator last1=s1.seq.end();
 579     epvector::const_iterator first2=s2.seq.begin();
 580     epvector::const_iterator last2=s2.seq.end();
 581
 582     seq.reserve(s1.seq.size()+s2.seq.size());
 583
 584     bool needs_further_processing=false;
 585
 586     while (first1!=last1 && first2!=last2) {
 587         int cmpval=(*first1).rest.compare((*first2).rest);
 588         if (cmpval==0) {
 589             // combine terms
 590             numeric const & newcoeff=ex_to_numeric((*first1).coeff).
 591                                      add(ex_to_numeric((*first2).coeff));
 592             if (!newcoeff.is_zero()) {
 593                 seq.push_back(expair((*first1).rest,newcoeff));
 594                 if (expair_needs_further_processing(seq.end()-1)) {
 595                     needs_further_processing = true;
 596                 }
 597             }
 598             ++first1;
 599             ++first2;
 600         } else if (cmpval<0) {
 601             seq.push_back(*first1);
 602             ++first1;
 603         } else {
 604             seq.push_back(*first2);
 605             ++first2;
 606         }
 607     }
 608
 609     while (first1!=last1) {
 610         seq.push_back(*first1);
 611         ++first1;
 612     }
 613     while (first2!=last2) {
 614         seq.push_back(*first2);
 615         ++first2;
 616     }
 617
 618     if (needs_further_processing) {
 619         epvector v=seq;
 620         seq.clear();
 621         construct_from_epvector(v);
 622     }
 623 }
 624
 625 void expairseq::construct_from_expairseq_ex(expairseq const & s,
 626                                             ex const & e)
 627 {
 628     combine_overall_coeff(s.overall_coeff);
 629     if (is_ex_exactly_of_type(e,numeric)) {
 630         combine_overall_coeff(e);
 631         seq=s.seq;
 632         return;
 633     }
 634
 635     epvector::const_iterator first=s.seq.begin();
 636     epvector::const_iterator last=s.seq.end();
 637     expair p=split_ex_to_pair(e);
 638
 639     seq.reserve(s.seq.size()+1);
 640     bool p_pushed=0;
 641
 642     bool needs_further_processing=false;
 643
 644     // merge p into s.seq
 645     while (first!=last) {
 646         int cmpval=(*first).rest.compare(p.rest);
 647         if (cmpval==0) {
 648             // combine terms
 649             numeric const & newcoeff=ex_to_numeric((*first).coeff).
 650                                      add(ex_to_numeric(p.coeff));
 651             if (!newcoeff.is_zero()) {
 652                 seq.push_back(expair((*first).rest,newcoeff));
 653                 if (expair_needs_further_processing(seq.end()-1)) {
 654                     needs_further_processing = true;
 655                 }
 656             }
 657             ++first;
 658             p_pushed=1;
 659             break;
 660         } else if (cmpval<0) {
 661             seq.push_back(*first);
 662             ++first;
 663         } else {
 664             seq.push_back(p);
 665             p_pushed=1;
 666             break;
 667         }
 668     }
 669
 670     if (p_pushed) {
 671         // while loop exited because p was pushed, now push rest of s.seq
 672         while (first!=last) {
 673             seq.push_back(*first);
 674             ++first;
 675         }
 676     } else {
 677         // while loop exited because s.seq was pushed, now push p
 678         seq.push_back(p);
 679     }
 680
 681     if (needs_further_processing) {
 682         epvector v=seq;
 683         seq.clear();
 684         construct_from_epvector(v);
 685     }
 686 }
 687
 688 void expairseq::construct_from_exvector(exvector const & v)
 689 {
 690     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 691     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 692     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 693     //                  (same for (+,*) -> (*,^)
 694
 695     make_flat(v);
 696 #ifdef EXPAIRSEQ_USE_HASHTAB
 697     combine_same_terms();
 698 #else
 699     canonicalize();
 700     combine_same_terms_sorted_seq();
 701 #endif // def EXPAIRSEQ_USE_HASHTAB
 702 }
 703
 704 void expairseq::construct_from_epvector(epvector const & v)
 705 {
 706     // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 707     //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 708     //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 709     //                  (same for (+,*) -> (*,^)
 710
 711     make_flat(v);
 712 #ifdef EXPAIRSEQ_USE_HASHTAB
 713     combine_same_terms();
 714 #else
 715     canonicalize();
 716     combine_same_terms_sorted_seq();
 717 #endif // def EXPAIRSEQ_USE_HASHTAB
 718 }
 719
 720 #include <iostream>
 721
 722 void expairseq::make_flat(exvector const & v)
 723 {
 724     exvector::const_iterator cit, citend = v.end();
 725
 726     // count number of operands which are of same expairseq derived type
 727     // and their cumulative number of operands
 728     int nexpairseqs=0;
 729     int noperands=0;
 730     cit=v.begin();
 731     while (cit!=citend) {
 732         if (cit->bp->tinfo()==tinfo()) {
 733             nexpairseqs++;
 734             noperands+=ex_to_expairseq(*cit).seq.size();
 735         }
 736         ++cit;
 737     }
 738
 739     // reserve seq and coeffseq which will hold all operands
 740     seq.reserve(v.size()+noperands-nexpairseqs);
 741
 742     // copy elements and split off numerical part
 743     cit=v.begin();
 744     while (cit!=citend) {
 745         if (cit->bp->tinfo()==tinfo()) {
 746             expairseq const & subseqref=ex_to_expairseq(*cit);
 747             combine_overall_coeff(subseqref.overall_coeff);
 748             epvector::const_iterator cit_s=subseqref.seq.begin();
 749             while (cit_s!=subseqref.seq.end()) {
 750                 seq.push_back(*cit_s);
 751                 ++cit_s;
 752             }
 753         } else {
 754             if (is_ex_exactly_of_type(*cit,numeric)) {
 755                 combine_overall_coeff(*cit);
 756             } else {
 757                 seq.push_back(split_ex_to_pair(*cit));
 758             }
 759         }
 760         ++cit;
 761     }
 762
 763     /*
 764     cout << "after make flat" << endl;
 765     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 766         (*cit).printraw(cout);
 767     }
 768     cout << endl;
 769     cout.flush();
 770     */
 771 }
 772
 773 void expairseq::make_flat(epvector const & v)
 774 {
 775     epvector::const_iterator cit, citend = v.end();
 776
 777     // count number of operands which are of same expairseq derived type
 778     // and their cumulative number of operands
 779     int nexpairseqs=0;
 780     int noperands=0;
 781     cit=v.begin();
 782     while (cit!=citend) {
 783         if (cit->rest.bp->tinfo()==tinfo()) {
 784             nexpairseqs++;
 785             noperands+=ex_to_expairseq((*cit).rest).seq.size();
 786         }
 787         ++cit;
 788     }
 789
 790     // reserve seq and coeffseq which will hold all operands
 791     seq.reserve(v.size()+noperands-nexpairseqs);
 792
 793     // copy elements and split off numerical part
 794     cit=v.begin();
 795     while (cit!=citend) {
 796         if ((cit->rest.bp->tinfo()==tinfo())&&can_make_flat(*cit)) {
 797             expairseq const & subseqref=ex_to_expairseq((*cit).rest);
 798             combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 799                                   ex_to_numeric((*cit).coeff));
 800             epvector::const_iterator cit_s=subseqref.seq.begin();
 801             while (cit_s!=subseqref.seq.end()) {
 802                 seq.push_back(expair((*cit_s).rest,
 803                               ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
 804                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 805                 //                                              (*cit).coeff));
 806                 ++cit_s;
 807             }
 808         } else {
 809             if ((*cit).is_numeric_with_coeff_1()) {
 810                 combine_overall_coeff((*cit).rest);
 811             //if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 812             //    combine_overall_coeff(recombine_pair_to_ex(*cit));
 813             } else {
 814                 seq.push_back(*cit);
 815             }
 816         }
 817         ++cit;
 818     }
 819 }
 820
 821 epvector * expairseq::bubblesort(epvector::iterator itbegin, epvector::iterator itend)
 822 {
 823     unsigned n=itend-itbegin;
 824
 825     epvector * sp=new epvector;
 826     sp->reserve(n);
 827
 828     epvector::iterator last=itend-1;
 829     for (epvector::iterator it1=itbegin; it1!=last; ++it1) {
 830         for (epvector::iterator it2=it1+1; it2!=itend; ++it2) {
 831             if ((*it2).rest.compare((*it1).rest)<0) {
 832                 iter_swap(it1,it2);
 833             }
 834         }
 835         sp->push_back(*it1);
 836     }
 837     sp->push_back(*last);
 838     return sp;
 839 }
 840
 841 epvector * expairseq::mergesort(epvector::iterator itbegin, epvector::iterator itend)
 842 {
 843     unsigned n=itend-itbegin;
 844     /*
 845     if (n==1) {
 846         epvector * sp=new epvector;
 847         sp->push_back(*itbegin);
 848         return sp;
 849     }
 850     */
 851     if (n<16) return bubblesort(itbegin, itend);
 852     unsigned m=n/2;
 853
 854     epvector * s1p=mergesort(itbegin, itbegin+m);
 855     epvector * s2p=mergesort(itbegin+m, itend);
 856
 857     epvector * sp=new epvector;
 858     sp->reserve(s1p->size()+s2p->size());
 859
 860     epvector::iterator first1=s1p->begin();
 861     epvector::iterator last1=s1p->end();
 862
 863     epvector::iterator first2=s2p->begin();
 864     epvector::iterator last2=s2p->end();
 865
 866     while (first1 != last1 && first2 != last2) {
 867         if ((*first1).rest.compare((*first2).rest)<0) {
 868             sp->push_back(*first1);
 869             ++first1;
 870         } else {
 871             sp->push_back(*first2);
 872             ++first2;
 873         }
 874     }
 875
 876     if (first1 != last1) {
 877         while (first1 != last1) {
 878             sp->push_back(*first1);
 879             ++first1;
 880         }
 881     } else {
 882         while (first2 != last2) {
 883             sp->push_back(*first2);
 884             ++first2;
 885         }
 886     }
 887
 888     delete s1p;
 889     delete s2p;
 890
 891     return sp;
 892 }
 893
 894
 895 void expairseq::canonicalize(void)
 896 {
 897     // canonicalize
 898     sort(seq.begin(),seq.end(),expair_is_less());
 899     /*
 900     sort(seq.begin(),seq.end(),expair_is_less_old());
 901     if (seq.size()>1) {
 902         if (is_ex_exactly_of_type((*(seq.begin())).rest,numeric)) {
 903             sort(seq.begin(),seq.end(),expair_is_less());
 904         } else {
 905             epvector::iterator last_numeric=seq.end();
 906             do {
 907                 last_numeric--;
 908             } while (is_ex_exactly_of_type((*last_numeric).rest,numeric));
 909             last_numeric++;
 910             sort(last_numeric,seq.end(),expair_is_less());
 911         }
 912     }
 913     */
 914
 915     /*
 916     epvector * sorted_seqp=mergesort(seq.begin(),seq.end());
 917     epvector::iterator last=sorted_seqp->end();
 918     epvector::iterator it2=seq.begin();
 919     for (epvector::iterator it1=sorted_seqp->begin(); it1!=last; ++it1, ++it2) {
 920         iter_swap(it1,it2);
 921     }
 922     delete sorted_seqp;
 923     */
 924
 925     /*
 926     cout << "after canonicalize" << endl;
 927     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 928         (*cit).printraw(cout);
 929     }
 930     cout << endl;
 931     cout.flush();
 932     */
 933 }
 934
 935 void expairseq::combine_same_terms_sorted_seq(void)
 936 {
 937     bool needs_further_processing=false;
 938
 939     // combine same terms, drop term with coeff 0
 940     if (seq.size()>1) {
 941         epvector::iterator itin1=seq.begin();
 942         epvector::iterator itin2=itin1+1;
 943         epvector::iterator itout=itin1;
 944         epvector::iterator last=seq.end();
 945         // must_copy will be set to true the first time some combination is possible
 946         // from then on the sequence has changed and must be compacted
 947         bool must_copy=false;
 948         while (itin2!=last) {
 949             if ((*itin1).rest.compare((*itin2).rest)==0) {
 950                 (*itin1).coeff=ex_to_numeric((*itin1).coeff).
 951                                add_dyn(ex_to_numeric((*itin2).coeff));
 952                 if (expair_needs_further_processing(itin1)) {
 953                     needs_further_processing = true;
 954                 }
 955                 must_copy=true;
 956             } else {
 957                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 958                     if (must_copy) {
 959                         *itout=*itin1;
 960                     }
 961                     ++itout;
 962                 }
 963                 itin1=itin2;
 964             }
 965             ++itin2;
 966         }
 967         if (!ex_to_numeric((*itin1).coeff).is_zero()) {
 968             if (must_copy) {
 969                 *itout=*itin1;
 970             }
 971             ++itout;
 972         }
 973         if (itout!=last) {
 974             seq.erase(itout,last);
 975         }
 976     }
 977
 978     /*
 979     cout << "after combine" << endl;
 980     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 981         (*cit).printraw(cout);
 982     }
 983     cout << endl;
 984     cout.flush();
 985     */
 986
 987     if (needs_further_processing) {
 988         epvector v=seq;
 989         seq.clear();
 990         construct_from_epvector(v);
 991     }
 992 }
 993
 994 #ifdef EXPAIRSEQ_USE_HASHTAB
 995
 996 unsigned expairseq::calc_hashtabsize(unsigned sz) const
 997 {
 998     unsigned size;
 999     unsigned nearest_power_of_2 = 1 << log2(sz);
1000     //    if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1001     //  size=nearest_power_of_2*hashtabfactor;
1002     size=nearest_power_of_2/hashtabfactor;
1003     if (size<minhashtabsize) return 0;
1004     ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1005     // hashtabsize must be a power of 2
1006     ASSERT((1U << log2(size))==size);
1007     return size;
1008 }
1009
1010 unsigned expairseq::calc_hashindex(ex const & e) const
1011 {
1012     // calculate hashindex
1013     unsigned hash=e.gethash();
1014     unsigned hashindex;
1015     if (is_a_numeric_hash(hash)) {
1016         hashindex=hashmask;
1017     } else {
1018         hashindex=hash & hashmask;
1019         // last hashtab entry is reserved for numerics
1020         if (hashindex==hashmask) hashindex=0;
1021     }
1022     ASSERT(hashindex>=0);
1023     ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1024     return hashindex;
1025 }
1026
1027 void expairseq::shrink_hashtab(void)
1028 {
1029     unsigned new_hashtabsize;
1030     while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1031         ASSERT(new_hashtabsize<hashtabsize);
1032         if (new_hashtabsize==0) {
1033             hashtab.clear();
1034             hashtabsize=0;
1035             canonicalize();
1036             return;
1037         }
1038
1039         // shrink by a factor of 2
1040         unsigned half_hashtabsize=hashtabsize/2;
1041         for (unsigned i=0; i<half_hashtabsize-1; ++i) {
1042             hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1043         }
1044         // special treatment for numeric hashes
1045         hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1046         hashtab[half_hashtabsize-1]=hashtab[hashtabsize-1];
1047         hashtab.resize(half_hashtabsize);
1048         hashtabsize=half_hashtabsize;
1049         hashmask=hashtabsize-1;
1050     }
1051 }
1052
1053 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1054 {
1055     if (hashtabsize==0) return; // nothing to do
1056
1057     // calculate hashindex of element to be deleted
1058     unsigned hashindex=calc_hashindex((*element).rest);
1059
1060     // find it in hashtab and remove it
1061     epplist & eppl=hashtab[hashindex];
1062     epplist::iterator epplit=eppl.begin();
1063     bool erased=false;
1064     while (epplit!=eppl.end()) {
1065         if (*epplit == element) {
1066             eppl.erase(epplit);
1067             erased=true;
1068             break;
1069         }
1070         ++epplit;
1071     }
1072     if (!erased) {
1073         printtree(cout,0);
1074         cout << "tried to erase " << element-seq.begin() << endl;
1075         cout << "size " << seq.end()-seq.begin() << endl;
1076
1077         unsigned hashindex=calc_hashindex((*element).rest);
1078         epplist & eppl=hashtab[hashindex];
1079         epplist::iterator epplit=eppl.begin();
1080         bool erased=false;
1081         while (epplit!=eppl.end()) {
1082             if (*epplit == element) {
1083                 eppl.erase(epplit);
1084                 erased=true;
1085                 break;
1086             }
1087             ++epplit;
1088         }
1089         ASSERT(erased);
1090     }
1091     ASSERT(erased);
1092 }
1093
1094 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1095                                    epvector::iterator newpos)
1096 {
1097     ASSERT(hashtabsize!=0);
1098
1099     // calculate hashindex of element which was moved
1100     unsigned hashindex=calc_hashindex((*newpos).rest);
1101
1102     // find it in hashtab and modify it
1103     epplist & eppl=hashtab[hashindex];
1104     epplist::iterator epplit=eppl.begin();
1105     while (epplit!=eppl.end()) {
1106         if (*epplit == oldpos) {
1107             *epplit=newpos;
1108             break;
1109         }
1110         ++epplit;
1111     }
1112     ASSERT(epplit!=eppl.end());
1113 }
1114
1115 void expairseq::sorted_insert(epplist & eppl, epp elem)
1116 {
1117     epplist::iterator current=eppl.begin();
1118     while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1119         ++current;
1120     }
1121     eppl.insert(current,elem);
1122 }
1123
1124 void expairseq::build_hashtab_and_combine(epvector::iterator & first_numeric,
1125                                           epvector::iterator & last_non_zero,
1126                                           vector<bool> & touched,
1127                                           unsigned & number_of_zeroes)
1128 {
1129     epp current=seq.begin();
1130
1131     while (current!=first_numeric) {
1132         if (is_ex_exactly_of_type((*current).rest,numeric)) {
1133             --first_numeric;
1134             iter_swap(current,first_numeric);
1135         } else {
1136             // calculate hashindex
1137             unsigned currenthashindex=calc_hashindex((*current).rest);
1138
1139             // test if there is already a matching expair in the hashtab-list
1140             epplist & eppl=hashtab[currenthashindex];
1141             epplist::iterator epplit=eppl.begin();
1142             while (epplit!=eppl.end()) {
1143                 if ((*current).rest.is_equal((*(*epplit)).rest)) break;
1144                 ++epplit;
1145             }
1146             if (epplit==eppl.end()) {
1147                 // no matching expair found, append this to end of list
1148                 sorted_insert(eppl,current);
1149                 ++current;
1150             } else {
1151                 // epplit points to a matching expair, combine it with current
1152                 (*(*epplit)).coeff=ex_to_numeric((*(*epplit)).coeff).
1153                                    add_dyn(ex_to_numeric((*current).coeff));
1154
1155                 // move obsolete current expair to end by swapping with last_non_zero element
1156                 // if this was a numeric, it is swapped with the expair before first_numeric
1157                 iter_swap(current,last_non_zero);
1158                 --first_numeric;
1159                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1160                 --last_non_zero;
1161                 ++number_of_zeroes;
1162                 // test if combined term has coeff 0 and can be removed is done later
1163                 touched[(*epplit)-seq.begin()]=true;
1164             }
1165         }
1166     }
1167 }
1168
1169 void expairseq::drop_coeff_0_terms(epvector::iterator & first_numeric,
1170                                    epvector::iterator & last_non_zero,
1171                                    vector<bool> & touched,
1172                                    unsigned & number_of_zeroes)
1173 {
1174     // move terms with coeff 0 to end and remove them from hashtab
1175     // check only those elements which have been touched
1176     epp current=seq.begin();
1177     unsigned i=0;
1178     while (current!=first_numeric) {
1179         if (!touched[i]) {
1180             ++current;
1181             ++i;
1182         } else if (!ex_to_numeric((*current).coeff).is_equal(numZERO())) {
1183             ++current;
1184             ++i;
1185         } else {
1186             remove_hashtab_entry(current);
1187
1188             // move element to the end, unless it is already at the end
1189             if (current!=last_non_zero) {
1190                 iter_swap(current,last_non_zero);
1191                 --first_numeric;
1192                 bool numeric_swapped=first_numeric!=last_non_zero;
1193                 if (numeric_swapped) iter_swap(first_numeric,current);
1194                 epvector::iterator changed_entry;
1195
1196                 if (numeric_swapped) {
1197                     changed_entry=first_numeric;
1198                 } else {
1199                     changed_entry=last_non_zero;
1200                 }
1201
1202                 --last_non_zero;
1203                 ++number_of_zeroes;
1204
1205                 if (first_numeric!=current) {
1206
1207                     // change entry in hashtab which referred to first_numeric or last_non_zero to current
1208                     move_hashtab_entry(changed_entry,current);
1209                     touched[current-seq.begin()]=touched[changed_entry-seq.begin()];
1210                 }
1211             } else {
1212                 --first_numeric;
1213                 --last_non_zero;
1214                 ++number_of_zeroes;
1215             }
1216         }
1217     }
1218     ASSERT(i==current-seq.begin());
1219 }
1220
1221 bool expairseq::has_coeff_0(void) const
1222 {
1223     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1224         if ((*cit).coeff.is_equal(exZERO())) {
1225             return true;
1226         }
1227     }
1228     return false;
1229 }
1230
1231 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1232                                         epvector::const_iterator last_non_zero)
1233 {
1234     if (first_numeric==seq.end()) return; // no numerics
1235
1236     epvector::iterator current=first_numeric;
1237     epvector::const_iterator last=last_non_zero+1;
1238     while (current!=last) {
1239         sorted_insert(hashtab[hashmask],current);
1240         ++current;
1241     }
1242 }
1243
1244 void expairseq::combine_same_terms(void)
1245 {
1246     // combine same terms, drop term with coeff 0, move numerics to end
1247
1248     // calculate size of hashtab
1249     hashtabsize=calc_hashtabsize(seq.size());
1250
1251     // hashtabsize is a power of 2
1252     hashmask=hashtabsize-1;
1253
1254     // allocate hashtab
1255     hashtab.clear();
1256     hashtab.resize(hashtabsize);
1257
1258     if (hashtabsize==0) {
1259         canonicalize();
1260         combine_same_terms_sorted_seq();
1261         ASSERT(!has_coeff_0());
1262         return;
1263     }
1264
1265     // iterate through seq, move numerics to end,
1266     // fill hashtab and combine same terms
1267     epvector::iterator first_numeric=seq.end();
1268     epvector::iterator last_non_zero=seq.end()-1;
1269
1270     vector<bool> touched;
1271     touched.reserve(seq.size());
1272     for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1273
1274     unsigned number_of_zeroes=0;
1275
1276     ASSERT(!has_coeff_0());
1277     build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1278     /*
1279     cout << "in combine:" << endl;
1280     printtree(cout,0);
1281     cout << "size=" << seq.end() - seq.begin() << endl;
1282     cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1283     cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1284     for (unsigned i=0; i<seq.size(); ++i) {
1285         if (touched[i]) cout << i << " is touched" << endl;
1286     }
1287     cout << "end in combine" << endl;
1288     */
1289
1290     // there should not be any terms with coeff 0 from the beginning,
1291     // so it should be safe to skip this step
1292     if (number_of_zeroes!=0) {
1293         drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1294         /*
1295         cout << "in combine after drop:" << endl;
1296         printtree(cout,0);
1297         cout << "size=" << seq.end() - seq.begin() << endl;
1298         cout << "first_numeric=" << first_numeric - seq.begin() << endl;
1299         cout << "last_non_zero=" << last_non_zero - seq.begin() << endl;
1300         for (unsigned i=0; i<seq.size(); ++i) {
1301             if (touched[i]) cout << i << " is touched" << endl;
1302         }
1303         cout << "end in combine after drop" << endl;
1304         */
1305     }
1306
1307     add_numerics_to_hashtab(first_numeric,last_non_zero);
1308
1309     // pop zero elements
1310     for (unsigned i=0; i<number_of_zeroes; ++i) {
1311         seq.pop_back();
1312     }
1313
1314     // shrink hashtabsize to calculated value
1315     ASSERT(!has_coeff_0());
1316
1317     shrink_hashtab();
1318
1319     ASSERT(!has_coeff_0());
1320 }
1321
1322 #endif // def EXPAIRSEQ_USE_HASHTAB
1323
1324 bool expairseq::is_canonical() const
1325 {
1326     if (seq.size()<=1) return 1;
1327
1328 #ifdef EXPAIRSEQ_USE_HASHTAB
1329     if (hashtabsize>0) return 1; // not canoncalized
1330 #endif // def EXPAIRSEQ_USE_HASHTAB
1331
1332     epvector::const_iterator it=seq.begin();
1333     epvector::const_iterator it_last=it;
1334     for (++it; it!=seq.end(); it_last=it, ++it) {
1335         if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
1336             if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1337                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1338                 // double test makes it easier to set a breakpoint...
1339                 if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
1340                     !is_ex_exactly_of_type((*it).rest,numeric)) {
1341                     printpair(cout,*it_last,0);
1342                     cout << ">";
1343                     printpair(cout,*it,0);
1344                     cout << "\n";
1345                     cout << "pair1:" << endl;
1346                     (*it_last).rest.printtree(cout);
1347                     (*it_last).coeff.printtree(cout);
1348                     cout << "pair2:" << endl;
1349                     (*it).rest.printtree(cout);
1350                     (*it).coeff.printtree(cout);
1351                     return 0;
1352                 }
1353             }
1354         }
1355     }
1356     return 1;
1357 }
1358
1359 epvector * expairseq::expandchildren(unsigned options) const
1360 {
1361     epvector::const_iterator last=seq.end();
1362     epvector::const_iterator cit=seq.begin();
1363     while (cit!=last) {
1364         ex const & expanded_ex=(*cit).rest.expand(options);
1365         if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1366
1367             // something changed, copy seq, eval and return it
1368             epvector *s=new epvector;
1369             s->reserve(seq.size());
1370
1371             // copy parts of seq which are known not to have changed
1372             epvector::const_iterator cit2=seq.begin();
1373             while (cit2!=cit) {
1374                 s->push_back(*cit2);
1375                 ++cit2;
1376             }
1377             // copy first changed element
1378             s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1379                                                        (*cit2).coeff));
1380             ++cit2;
1381             // copy rest
1382             while (cit2!=last) {
1383                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1384                                                            (*cit2).coeff));
1385                 ++cit2;
1386             }
1387             return s;
1388         }
1389         ++cit;
1390     }
1391
1392     return 0; // nothing has changed
1393 }
1394
1395 epvector * expairseq::evalchildren(int level) const
1396 {
1397     // returns a NULL pointer if nothing had to be evaluated
1398     // returns a pointer to a newly created epvector otherwise
1399     // (which has to be deleted somewhere else)
1400
1401     if (level==1) {
1402         return 0;
1403     }
1404     if (level == -max_recursion_level) {
1405         throw(std::runtime_error("max recursion level reached"));
1406     }
1407
1408     --level;
1409     epvector::const_iterator last=seq.end();
1410     epvector::const_iterator cit=seq.begin();
1411     while (cit!=last) {
1412         ex const & evaled_ex=(*cit).rest.eval(level);
1413         if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1414
1415             // something changed, copy seq, eval and return it
1416             epvector *s=new epvector;
1417             s->reserve(seq.size());
1418
1419             // copy parts of seq which are known not to have changed
1420             epvector::const_iterator cit2=seq.begin();
1421             while (cit2!=cit) {
1422                 s->push_back(*cit2);
1423                 ++cit2;
1424             }
1425             // copy first changed element
1426             s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1427                                                        (*cit2).coeff));
1428             ++cit2;
1429             // copy rest
1430             while (cit2!=last) {
1431                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1432                                                            (*cit2).coeff));
1433                 ++cit2;
1434             }
1435             return s;
1436         }
1437         ++cit;
1438     }
1439
1440     return 0; // nothing has changed
1441 }
1442
1443 epvector expairseq::evalfchildren(int level) const
1444 {
1445     epvector s;
1446     s.reserve(seq.size());
1447
1448     if (level==1) {
1449         return seq;
1450     }
1451     if (level == -max_recursion_level) {
1452         throw(std::runtime_error("max recursion level reached"));
1453     }
1454     --level;
1455     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1456         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1457                                                   (*it).coeff));
1458     }
1459     return s;
1460 }
1461
1462 epvector expairseq::normalchildren(int level) const
1463 {
1464     epvector s;
1465     s.reserve(seq.size());
1466
1467     if (level==1) {
1468         return seq;
1469     }
1470     if (level == -max_recursion_level) {
1471         throw(std::runtime_error("max recursion level reached"));
1472     }
1473     --level;
1474     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1475         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1476                                                   (*it).coeff));
1477     }
1478     return s;
1479 }
1480
1481 epvector expairseq::diffchildren(symbol const & y) const
1482 {
1483     epvector s;
1484     s.reserve(seq.size());
1485
1486     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1487         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1488                                                   (*it).coeff));
1489     }
1490     return s;
1491 }
1492
1493 epvector * expairseq::subschildren(lst const & ls, lst const & lr) const
1494 {
1495     // returns a NULL pointer if nothing had to be substituted
1496     // returns a pointer to a newly created epvector otherwise
1497     // (which has to be deleted somewhere else)
1498
1499     epvector::const_iterator last=seq.end();
1500     epvector::const_iterator cit=seq.begin();
1501     while (cit!=last) {
1502         ex const & subsed_ex=(*cit).rest.subs(ls,lr);
1503         if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1504
1505             // something changed, copy seq, subs and return it
1506             epvector *s=new epvector;
1507             s->reserve(seq.size());
1508
1509             // copy parts of seq which are known not to have changed
1510             epvector::const_iterator cit2=seq.begin();
1511             while (cit2!=cit) {
1512                 s->push_back(*cit2);
1513                 ++cit2;
1514             }
1515             // copy first changed element
1516             s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1517                                                        (*cit2).coeff));
1518             ++cit2;
1519             // copy rest
1520             while (cit2!=last) {
1521                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
1522                                                            (*cit2).coeff));
1523                 ++cit2;
1524             }
1525             return s;
1526         }
1527         ++cit;
1528     }
1529
1530     return 0; // nothing has changed
1531 }
1532
1533 /*
1534 epvector expairseq::subschildren(lst const & ls, lst const & lr) const
1535 {
1536     epvector s;
1537     s.reserve(seq.size());
1538
1539     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1540         s.push_back(split_ex_to_pair((*it).rest.subs(ls,lr),(*it).coeff));
1541     }
1542     return s;
1543 }
1544 */
1545
1546 /*
1547 void expairseq::sort(epviter first, epviter last, expair_is_less comp)
1548 {
1549     if (first != last) {
1550         introsort_loop(first, last, lg(last - first) * 2, comp);
1551         __final_insertion_sort(first, last, comp);
1552     }
1553 }
1554
1555 ptrdiff_t expairseq::lg(ptrdiff_t n)
1556 {
1557     ptrdiff_t k;
1558     for (k = 0; n > 1; n >>= 1) ++k;
1559     return k;
1560 }
1561
1562 void expairseq::introsort_loop(epviter first, epviter last,
1563                                ptrdiff_t depth_limit, expair_is_less comp)
1564 {
1565     while (last - first > stl_threshold) {
1566         if (depth_limit == 0) {
1567             partial_sort(first, last, last, comp);
1568             return;
1569         }
1570         --depth_limit;
1571         epviter cut = unguarded_partition(first, last,
1572                       expair(__median(*first, *(first + (last - first)/2),
1573                       *(last - 1), comp)), comp);
1574         introsort_loop(cut, last, depth_limit, comp);
1575         last = cut;
1576     }
1577 }
1578
1579 epviter expairseq::unguarded_partition(epviter first, epviter last,
1580                                        expair pivot, expair_is_less comp)
1581 {
1582     while (1) {
1583         while (comp(*first, pivot)) ++first;
1584         --last;
1585         while (comp(pivot, *last)) --last;
1586         if (!(first < last)) return first;
1587         iter_swap(first, last);
1588         ++first;
1589     }
1590 }
1591
1592 void expairseq::partial_sort(epviter first, epviter middle, epviter last,
1593                              expair_is_less comp) {
1594   make_heap(first, middle, comp);
1595   for (RandomAccessIterator i = middle; i < last; ++i)
1596     if (comp(*i, *first))
1597       __pop_heap(first, middle, i, T(*i), comp, distance_type(first));
1598   sort_heap(first, middle, comp);
1599 }
1600 */
1601
1602 //////////
1603 // static member variables
1604 //////////
1605
1606 // protected
1607
1608 unsigned expairseq::precedence=10;
1609
1610 #ifdef EXPAIRSEQ_USE_HASHTAB
1611 unsigned expairseq::maxhashtabsize=0x4000000U;
1612 unsigned expairseq::minhashtabsize=0x1000U;
1613 unsigned expairseq::hashtabfactor=1;
1614 #endif // def EXPAIRSEQ_USE_HASHTAB
1615
1616 //////////
1617 // global constants
1618 //////////
1619
1620 const expairseq some_expairseq;
1621 type_info const & typeid_expairseq=typeid(some_expairseq);
1622