ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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 <iostream>
  24 #include <algorithm>
  25 #include <string>
  26 #include <stdexcept>
  27
  28 #include "expairseq.h"
  29 #include "lst.h"
  30 #include "mul.h"
  31 #include "power.h"
  32 #include "relational.h"
  33 #include "wildcard.h"
  34 #include "print.h"
  35 #include "archive.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  46
  47 //////////
  48 // helper classes
  49 //////////
  50
  51 class epp_is_less
  52 {
  53 public:
  54         bool operator()(const epp &lh, const epp &rh) const
  55         {
  56                 return (*lh).is_less(*rh);
  57         }
  58 };
  59
  60 //////////
  61 // default ctor, dtor, copy ctor, assignment operator and helpers
  62 //////////
  63
  64 // public
  65
  66 expairseq::expairseq(const expairseq &other)
  67 {
  68         copy(other);
  69 }
  70
  71 const expairseq &expairseq::operator=(const expairseq &other)
  72 {
  73         if (this != &other) {
  74                 destroy(true);
  75                 copy(other);
  76         }
  77         return *this;
  78 }
  79
  80 // protected
  81
  82 /** For use by copy ctor and assignment operator. */
  83 void expairseq::copy(const expairseq &other)
  84 {
  85         inherited::copy(other);
  86         seq = other.seq;
  87         overall_coeff = other.overall_coeff;
  88 #if EXPAIRSEQ_USE_HASHTAB
  89         // copy hashtab
  90         hashtabsize = other.hashtabsize;
  91         if (hashtabsize!=0) {
  92                 hashmask = other.hashmask;
  93                 hashtab.resize(hashtabsize);
  94                 epvector::const_iterator osb = other.seq.begin();
  95                 for (unsigned i=0; i<hashtabsize; ++i) {
  96                         hashtab[i].clear();
  97                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  98                              cit!=other.hashtab[i].end(); ++cit) {
  99                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 100                         }
 101                 }
 102         } else {
 103                 hashtab.clear();
 104         }
 105 #endif // EXPAIRSEQ_USE_HASHTAB
 106 }
 107
 108 DEFAULT_DESTROY(expairseq)
 109
 110 //////////
 111 // other ctors
 112 //////////
 113
 114 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 115 {
 116         construct_from_2_ex(lh,rh);
 117         GINAC_ASSERT(is_canonical());
 118 }
 119
 120 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 121 {
 122         construct_from_exvector(v);
 123         GINAC_ASSERT(is_canonical());
 124 }
 125
 126 expairseq::expairseq(const epvector &v, const ex &oc)
 127   : inherited(TINFO_expairseq), overall_coeff(oc)
 128 {
 129         GINAC_ASSERT(is_a<numeric>(oc));
 130         construct_from_epvector(v);
 131         GINAC_ASSERT(is_canonical());
 132 }
 133
 134 expairseq::expairseq(epvector *vp, const ex &oc)
 135   : inherited(TINFO_expairseq), overall_coeff(oc)
 136 {
 137         GINAC_ASSERT(vp!=0);
 138         GINAC_ASSERT(is_a<numeric>(oc));
 139         construct_from_epvector(*vp);
 140         delete vp;
 141         GINAC_ASSERT(is_canonical());
 142 }
 143
 144 //////////
 145 // archiving
 146 //////////
 147
 148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 149 #if EXPAIRSEQ_USE_HASHTAB
 150         , hashtabsize(0)
 151 #endif
 152 {
 153
 154         for (unsigned int i=0; true; i++) {
 155
 156         canonicalize();
 157         GINAC_ASSERT(is_canonical());
 158                 ex rest;
 159                 ex coeff;
 160                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 161                         seq.push_back(expair(rest, coeff));
 162                 else
 163                         break;
 164         }
 165         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 166 }
 167
 168 void expairseq::archive(archive_node &n) const
 169 {
 170         inherited::archive(n);
 171         epvector::const_iterator i = seq.begin(), iend = seq.end();
 172         while (i != iend) {
 173                 n.add_ex("rest", i->rest);
 174                 n.add_ex("coeff", i->coeff);
 175                 ++i;
 176         }
 177         n.add_ex("overall_coeff", overall_coeff);
 178 }
 179
 180 DEFAULT_UNARCHIVE(expairseq)
 181
 182 //////////
 183 // functions overriding virtual functions from base classes
 184 //////////
 185
 186 // public
 187
 188 basic *expairseq::duplicate() const
 189 {
 190         return new expairseq(*this);
 191 }
 192
 193 void expairseq::print(const print_context &c, unsigned level) const
 194 {
 195         if (is_of_type(c, print_tree)) {
 196
 197                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 198
 199                 c.s << std::string(level, ' ') << class_name()
 200                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 201                     << ", nops=" << nops()
 202                     << std::endl;
 203                 unsigned num = seq.size();
 204                 for (unsigned i=0; i<num; ++i) {
 205                         seq[i].rest.print(c, level + delta_indent);
 206                         seq[i].coeff.print(c, level + delta_indent);
 207                         if (i != num - 1)
 208                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 209                 }
 210                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 211                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 212                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 213                         overall_coeff.print(c, level + delta_indent);
 214                 }
 215                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 216 #if EXPAIRSEQ_USE_HASHTAB
 217                 c.s << std::string(level + delta_indent,' ')
 218                     << "hashtab size " << hashtabsize << std::endl;
 219                 if (hashtabsize == 0) return;
 220 #define MAXCOUNT 5
 221                 unsigned count[MAXCOUNT+1];
 222                 for (int i=0; i<MAXCOUNT+1; ++i)
 223                         count[i] = 0;
 224                 unsigned this_bin_fill;
 225                 unsigned cum_fill_sq = 0;
 226                 unsigned cum_fill = 0;
 227                 for (unsigned i=0; i<hashtabsize; ++i) {
 228                         this_bin_fill = 0;
 229                         if (hashtab[i].size() > 0) {
 230                                 c.s << std::string(level + delta_indent, ' ')
 231                                     << "bin " << i << " with entries ";
 232                                 for (epplist::const_iterator it=hashtab[i].begin();
 233                                      it!=hashtab[i].end(); ++it) {
 234                                         c.s << *it-seq.begin() << " ";
 235                                         ++this_bin_fill;
 236                                 }
 237                                 c.s << std::endl;
 238                                 cum_fill += this_bin_fill;
 239                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 240                         }
 241                         if (this_bin_fill<MAXCOUNT)
 242                                 ++count[this_bin_fill];
 243                         else
 244                                 ++count[MAXCOUNT];
 245                 }
 246                 unsigned fact = 1;
 247                 double cum_prob = 0;
 248                 double lambda = (1.0*seq.size()) / hashtabsize;
 249                 for (int k=0; k<MAXCOUNT; ++k) {
 250                         if (k>0)
 251                                 fact *= k;
 252                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 253                         cum_prob += prob;
 254                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 255                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 256                             << int(prob*1000)/10.0 << ")" << std::endl;
 257                 }
 258                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 259                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 260                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 261
 262                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 263                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 264                     << std::endl;
 265                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 266                     << (1.0*cum_fill)/hashtabsize
 267                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 268 #endif // EXPAIRSEQ_USE_HASHTAB
 269
 270         } else {
 271                 c.s << "[[";
 272                 printseq(c, ',', precedence(), level);
 273                 c.s << "]]";
 274         }
 275 }
 276
 277 bool expairseq::info(unsigned inf) const
 278 {
 279         return inherited::info(inf);
 280 }
 281
 282 unsigned expairseq::nops() const
 283 {
 284         if (overall_coeff.is_equal(default_overall_coeff()))
 285                 return seq.size();
 286         else
 287                 return seq.size()+1;
 288 }
 289
 290 ex expairseq::op(int i) const
 291 {
 292         if (unsigned(i)<seq.size())
 293                 return recombine_pair_to_ex(seq[i]);
 294         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 295         return overall_coeff;
 296 }
 297
 298 ex &expairseq::let_op(int i)
 299 {
 300         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 301 }
 302
 303 ex expairseq::map(map_function &f) const
 304 {
 305         epvector *v = new epvector;
 306         v->reserve(seq.size());
 307
 308         epvector::const_iterator cit = seq.begin(), last = seq.end();
 309         while (cit != last) {
 310                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 311                 ++cit;
 312         }
 313
 314         if (overall_coeff.is_equal(default_overall_coeff()))
 315                 return thisexpairseq(v, default_overall_coeff());
 316         else
 317                 return thisexpairseq(v, f(overall_coeff));
 318 }
 319
 320 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 321 ex expairseq::eval(int level) const
 322 {
 323         if ((level==1) && (flags &status_flags::evaluated))
 324                 return *this;
 325
 326         epvector *vp = evalchildren(level);
 327         if (vp==0)
 328                 return this->hold();
 329
 330         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 331 }
 332
 333 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 334 {
 335         // This differs from basic::match() because we want "a+b+c+d" to
 336         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 337
 338         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 339
 340                 // Check whether global wildcard (one that matches the "rest of the
 341                 // expression", like "*" above) is present
 342                 bool has_global_wildcard = false;
 343                 ex global_wildcard;
 344                 for (unsigned int i=0; i<pattern.nops(); i++) {
 345                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 346                                 has_global_wildcard = true;
 347                                 global_wildcard = pattern.op(i);
 348                                 break;
 349                         }
 350                 }
 351
 352                 // Unfortunately, this is an O(N^2) operation because we can't
 353                 // sort the pattern in a useful way...
 354
 355                 // Chop into terms
 356                 exvector ops;
 357                 ops.reserve(nops());
 358                 for (unsigned i=0; i<nops(); i++)
 359                         ops.push_back(op(i));
 360
 361                 // Now, for every term of the pattern, look for a matching term in
 362                 // the expression and remove the match
 363                 for (unsigned i=0; i<pattern.nops(); i++) {
 364                         ex p = pattern.op(i);
 365                         if (has_global_wildcard && p.is_equal(global_wildcard))
 366                                 continue;
 367                         exvector::iterator it = ops.begin(), itend = ops.end();
 368                         while (it != itend) {
 369                                 if (it->match(p, repl_lst)) {
 370                                         ops.erase(it);
 371                                         goto found;
 372                                 }
 373                                 ++it;
 374                         }
 375                         return false; // no match found
 376 found:          ;
 377                 }
 378
 379                 if (has_global_wildcard) {
 380
 381                         // Assign all the remaining terms to the global wildcard (unless
 382                         // it has already been matched before, in which case the matches
 383                         // must be equal)
 384                         unsigned num = ops.size();
 385                         epvector *vp = new epvector();
 386                         vp->reserve(num);
 387                         for (unsigned i=0; i<num; i++)
 388                                 vp->push_back(split_ex_to_pair(ops[i]));
 389                         ex rest = thisexpairseq(vp, default_overall_coeff());
 390                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 391                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 392                                         return rest.is_equal(repl_lst.op(i).op(1));
 393                         }
 394                         repl_lst.append(global_wildcard == rest);
 395                         return true;
 396
 397                 } else {
 398
 399                         // No global wildcard, then the match fails if there are any
 400                         // unmatched terms left
 401                         return ops.empty();
 402                 }
 403         }
 404         return inherited::match(pattern, repl_lst);
 405 }
 406
 407 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 408 {
 409         epvector *vp = subschildren(ls, lr, no_pattern);
 410         if (vp)
 411                 return ex_to<basic>(thisexpairseq(vp, overall_coeff));
 412         else
 413                 return basic::subs(ls, lr, no_pattern);
 414 }
 415
 416 // protected
 417
 418 int expairseq::compare_same_type(const basic &other) const
 419 {
 420         GINAC_ASSERT(is_a<expairseq>(other));
 421         const expairseq &o = static_cast<const expairseq &>(other);
 422
 423         int cmpval;
 424
 425         // compare number of elements
 426         if (seq.size() != o.seq.size())
 427                 return (seq.size()<o.seq.size()) ? -1 : 1;
 428
 429         // compare overall_coeff
 430         cmpval = overall_coeff.compare(o.overall_coeff);
 431         if (cmpval!=0)
 432                 return cmpval;
 433
 434 #if EXPAIRSEQ_USE_HASHTAB
 435         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 436         if (hashtabsize==0) {
 437 #endif // EXPAIRSEQ_USE_HASHTAB
 438                 epvector::const_iterator cit1 = seq.begin();
 439                 epvector::const_iterator cit2 = o.seq.begin();
 440                 epvector::const_iterator last1 = seq.end();
 441                 epvector::const_iterator last2 = o.seq.end();
 442
 443                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 444                         cmpval = (*cit1).compare(*cit2);
 445                         if (cmpval!=0) return cmpval;
 446                 }
 447
 448                 GINAC_ASSERT(cit1==last1);
 449                 GINAC_ASSERT(cit2==last2);
 450
 451                 return 0;
 452 #if EXPAIRSEQ_USE_HASHTAB
 453         }
 454
 455         // compare number of elements in each hashtab entry
 456         for (unsigned i=0; i<hashtabsize; ++i) {
 457                 unsigned cursize=hashtab[i].size();
 458                 if (cursize != o.hashtab[i].size())
 459                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 460         }
 461
 462         // compare individual (sorted) hashtab entries
 463         for (unsigned i=0; i<hashtabsize; ++i) {
 464                 unsigned sz = hashtab[i].size();
 465                 if (sz>0) {
 466                         const epplist &eppl1 = hashtab[i];
 467                         const epplist &eppl2 = o.hashtab[i];
 468                         epplist::const_iterator it1 = eppl1.begin();
 469                         epplist::const_iterator it2 = eppl2.begin();
 470                         while (it1!=eppl1.end()) {
 471                                 cmpval = (*(*it1)).compare(*(*it2));
 472                                 if (cmpval!=0)
 473                                         return cmpval;
 474                                 ++it1;
 475                                 ++it2;
 476                         }
 477                 }
 478         }
 479
 480         return 0; // equal
 481 #endif // EXPAIRSEQ_USE_HASHTAB
 482 }
 483
 484 bool expairseq::is_equal_same_type(const basic &other) const
 485 {
 486         const expairseq &o = static_cast<const expairseq &>(other);
 487
 488         // compare number of elements
 489         if (seq.size()!=o.seq.size())
 490                 return false;
 491
 492         // compare overall_coeff
 493         if (!overall_coeff.is_equal(o.overall_coeff))
 494                 return false;
 495
 496 #if EXPAIRSEQ_USE_HASHTAB
 497         // compare number of elements in each hashtab entry
 498         if (hashtabsize!=o.hashtabsize) {
 499                 std::cout << "this:" << std::endl;
 500                 print(print_tree(std::cout));
 501                 std::cout << "other:" << std::endl;
 502                 other.print(print_tree(std::cout));
 503         }
 504
 505         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 506
 507         if (hashtabsize==0) {
 508 #endif // EXPAIRSEQ_USE_HASHTAB
 509                 epvector::const_iterator cit1 = seq.begin();
 510                 epvector::const_iterator cit2 = o.seq.begin();
 511                 epvector::const_iterator last1 = seq.end();
 512
 513                 while (cit1!=last1) {
 514                         if (!(*cit1).is_equal(*cit2)) return false;
 515                         ++cit1;
 516                         ++cit2;
 517                 }
 518
 519                 return true;
 520 #if EXPAIRSEQ_USE_HASHTAB
 521         }
 522
 523         for (unsigned i=0; i<hashtabsize; ++i) {
 524                 if (hashtab[i].size() != o.hashtab[i].size())
 525                         return false;
 526         }
 527
 528         // compare individual sorted hashtab entries
 529         for (unsigned i=0; i<hashtabsize; ++i) {
 530                 unsigned sz = hashtab[i].size();
 531                 if (sz>0) {
 532                         const epplist &eppl1 = hashtab[i];
 533                         const epplist &eppl2 = o.hashtab[i];
 534                         epplist::const_iterator it1 = eppl1.begin();
 535                         epplist::const_iterator it2 = eppl2.begin();
 536                         while (it1!=eppl1.end()) {
 537                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 538                                 ++it1;
 539                                 ++it2;
 540                         }
 541                 }
 542         }
 543
 544         return true;
 545 #endif // EXPAIRSEQ_USE_HASHTAB
 546 }
 547
 548 unsigned expairseq::return_type(void) const
 549 {
 550         return return_types::noncommutative_composite;
 551 }
 552
 553 unsigned expairseq::calchash(void) const
 554 {
 555         unsigned v = golden_ratio_hash(this->tinfo());
 556         epvector::const_iterator i = seq.begin(), end = seq.end();
 557         while (i != end) {
 558 #if !EXPAIRSEQ_USE_HASHTAB
 559                 v = rotate_left_31(v); // rotation would spoil commutativity
 560 #endif // EXPAIRSEQ_USE_HASHTAB
 561                 v ^= i->rest.gethash();
 562 #if !EXPAIRSEQ_USE_HASHTAB
 563                 v = rotate_left_31(v);
 564                 v ^= i->coeff.gethash();
 565 #endif // EXPAIRSEQ_USE_HASHTAB
 566                 ++i;
 567         }
 568
 569         v ^= overall_coeff.gethash();
 570         v &= 0x7FFFFFFFU;
 571
 572         // store calculated hash value only if object is already evaluated
 573         if (flags &status_flags::evaluated) {
 574                 setflag(status_flags::hash_calculated);
 575                 hashvalue = v;
 576         }
 577
 578         return v;
 579 }
 580
 581 ex expairseq::expand(unsigned options) const
 582 {
 583         epvector *vp = expandchildren(options);
 584         if (vp == NULL) {
 585                 // The terms have not changed, so it is safe to declare this expanded
 586                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 587         } else
 588                 return thisexpairseq(vp, overall_coeff);
 589 }
 590
 591 //////////
 592 // new virtual functions which can be overridden by derived classes
 593 //////////
 594
 595 // protected
 596
 597 /** Create an object of this type.
 598  *  This method works similar to a constructor.  It is useful because expairseq
 599  *  has (at least) two possible different semantics but we want to inherit
 600  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 601  *  has to create a new one of the same semantics, which cannot be done by a
 602  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 603  *  order for this trick to work a derived class must of course override this
 604  *  definition. */
 605 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 606 {
 607         return expairseq(v,oc);
 608 }
 609
 610 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 611 {
 612         return expairseq(vp,oc);
 613 }
 614
 615 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 616 {
 617         c.s << "[[";
 618         p.rest.print(c, precedence());
 619         c.s << ",";
 620         p.coeff.print(c, precedence());
 621         c.s << "]]";
 622 }
 623
 624 void expairseq::printseq(const print_context & c, char delim,
 625                          unsigned this_precedence,
 626                          unsigned upper_precedence) const
 627 {
 628         if (this_precedence <= upper_precedence)
 629                 c.s << "(";
 630         epvector::const_iterator it, it_last = seq.end() - 1;
 631         for (it=seq.begin(); it!=it_last; ++it) {
 632                 printpair(c, *it, this_precedence);
 633                 c.s << delim;
 634         }
 635         printpair(c, *it, this_precedence);
 636         if (!overall_coeff.is_equal(default_overall_coeff())) {
 637                 c.s << delim;
 638                 overall_coeff.print(c, this_precedence);
 639         }
 640
 641         if (this_precedence <= upper_precedence)
 642                 c.s << ")";
 643 }
 644
 645
 646 /** Form an expair from an ex, using the corresponding semantics.
 647  *  @see expairseq::recombine_pair_to_ex() */
 648 expair expairseq::split_ex_to_pair(const ex &e) const
 649 {
 650         return expair(e,_ex1);
 651 }
 652
 653
 654 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 655                                                 const ex &c) const
 656 {
 657         GINAC_ASSERT(is_exactly_a<numeric>(c));
 658
 659         return expair(e,c);
 660 }
 661
 662
 663 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 664                                                   const ex &c) const
 665 {
 666         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 667         GINAC_ASSERT(is_exactly_a<numeric>(c));
 668
 669         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 670 }
 671
 672
 673 /** Form an ex out of an expair, using the corresponding semantics.
 674  *  @see expairseq::split_ex_to_pair() */
 675 ex expairseq::recombine_pair_to_ex(const expair &p) const
 676 {
 677         return lst(p.rest,p.coeff);
 678 }
 679
 680 bool expairseq::expair_needs_further_processing(epp it)
 681 {
 682 #if EXPAIRSEQ_USE_HASHTAB
 683         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 684 #endif // EXPAIRSEQ_USE_HASHTAB
 685         return false;
 686 }
 687
 688 ex expairseq::default_overall_coeff(void) const
 689 {
 690         return _ex0;
 691 }
 692
 693 void expairseq::combine_overall_coeff(const ex &c)
 694 {
 695         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 696         GINAC_ASSERT(is_exactly_a<numeric>(c));
 697         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 698 }
 699
 700 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 701 {
 702         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 703         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 704         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 705         overall_coeff = ex_to<numeric>(overall_coeff).
 706                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 707 }
 708
 709 bool expairseq::can_make_flat(const expair &p) const
 710 {
 711         return true;
 712 }
 713
 714
 715 //////////
 716 // non-virtual functions in this class
 717 //////////
 718
 719 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 720 {
 721         exvector v;
 722         v.reserve(2);
 723         v.push_back(lh);
 724         v.push_back(rh);
 725         construct_from_exvector(v);
 726 #if EXPAIRSEQ_USE_HASHTAB
 727         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 728         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 729 #endif // EXPAIRSEQ_USE_HASHTAB
 730 }
 731
 732 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 733 {
 734         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 735                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 736 #if EXPAIRSEQ_USE_HASHTAB
 737                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 738                                              ex_to<expairseq>(rh).seq.size();
 739                         if (calc_hashtabsize(totalsize)!=0) {
 740                                 construct_from_2_ex_via_exvector(lh,rh);
 741                         } else {
 742 #endif // EXPAIRSEQ_USE_HASHTAB
 743                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 744                                                            ex_to<expairseq>(rh));
 745 #if EXPAIRSEQ_USE_HASHTAB
 746                         }
 747 #endif // EXPAIRSEQ_USE_HASHTAB
 748                         return;
 749                 } else {
 750 #if EXPAIRSEQ_USE_HASHTAB
 751                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 752                         if (calc_hashtabsize(totalsize)!=0) {
 753                                 construct_from_2_ex_via_exvector(lh, rh);
 754                         } else {
 755 #endif // EXPAIRSEQ_USE_HASHTAB
 756                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 757 #if EXPAIRSEQ_USE_HASHTAB
 758                         }
 759 #endif // EXPAIRSEQ_USE_HASHTAB
 760                         return;
 761                 }
 762         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 763 #if EXPAIRSEQ_USE_HASHTAB
 764                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 765                 if (calc_hashtabsize(totalsize)!=0) {
 766                         construct_from_2_ex_via_exvector(lh,rh);
 767                 } else {
 768 #endif // EXPAIRSEQ_USE_HASHTAB
 769                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 770 #if EXPAIRSEQ_USE_HASHTAB
 771                 }
 772 #endif // EXPAIRSEQ_USE_HASHTAB
 773                 return;
 774         }
 775
 776 #if EXPAIRSEQ_USE_HASHTAB
 777         if (calc_hashtabsize(2)!=0) {
 778                 construct_from_2_ex_via_exvector(lh,rh);
 779                 return;
 780         }
 781         hashtabsize = 0;
 782 #endif // EXPAIRSEQ_USE_HASHTAB
 783
 784         if (is_ex_exactly_of_type(lh,numeric)) {
 785                 if (is_ex_exactly_of_type(rh,numeric)) {
 786                         combine_overall_coeff(lh);
 787                         combine_overall_coeff(rh);
 788                 } else {
 789                         combine_overall_coeff(lh);
 790                         seq.push_back(split_ex_to_pair(rh));
 791                 }
 792         } else {
 793                 if (is_ex_exactly_of_type(rh,numeric)) {
 794                         combine_overall_coeff(rh);
 795                         seq.push_back(split_ex_to_pair(lh));
 796                 } else {
 797                         expair p1 = split_ex_to_pair(lh);
 798                         expair p2 = split_ex_to_pair(rh);
 799
 800                         int cmpval = p1.rest.compare(p2.rest);
 801                         if (cmpval==0) {
 802                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 803                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 804                                         // no further processing is necessary, since this
 805                                         // one element will usually be recombined in eval()
 806                                         seq.push_back(p1);
 807                                 }
 808                         } else {
 809                                 seq.reserve(2);
 810                                 if (cmpval<0) {
 811                                         seq.push_back(p1);
 812                                         seq.push_back(p2);
 813                                 } else {
 814                                         seq.push_back(p2);
 815                                         seq.push_back(p1);
 816                                 }
 817                         }
 818                 }
 819         }
 820 }
 821
 822 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 823                                                                                    const expairseq &s2)
 824 {
 825         combine_overall_coeff(s1.overall_coeff);
 826         combine_overall_coeff(s2.overall_coeff);
 827
 828         epvector::const_iterator first1 = s1.seq.begin();
 829         epvector::const_iterator last1 = s1.seq.end();
 830         epvector::const_iterator first2 = s2.seq.begin();
 831         epvector::const_iterator last2 = s2.seq.end();
 832
 833         seq.reserve(s1.seq.size()+s2.seq.size());
 834
 835         bool needs_further_processing=false;
 836
 837         while (first1!=last1 && first2!=last2) {
 838                 int cmpval = (*first1).rest.compare((*first2).rest);
 839                 if (cmpval==0) {
 840                         // combine terms
 841                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 842                                                    add(ex_to<numeric>(first2->coeff));
 843                         if (!newcoeff.is_zero()) {
 844                                 seq.push_back(expair(first1->rest,newcoeff));
 845                                 if (expair_needs_further_processing(seq.end()-1)) {
 846                                         needs_further_processing = true;
 847                                 }
 848                         }
 849                         ++first1;
 850                         ++first2;
 851                 } else if (cmpval<0) {
 852                         seq.push_back(*first1);
 853                         ++first1;
 854                 } else {
 855                         seq.push_back(*first2);
 856                         ++first2;
 857                 }
 858         }
 859
 860         while (first1!=last1) {
 861                 seq.push_back(*first1);
 862                 ++first1;
 863         }
 864         while (first2!=last2) {
 865                 seq.push_back(*first2);
 866                 ++first2;
 867         }
 868
 869         if (needs_further_processing) {
 870                 epvector v = seq;
 871                 seq.clear();
 872                 construct_from_epvector(v);
 873         }
 874 }
 875
 876 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 877                                                                                         const ex &e)
 878 {
 879         combine_overall_coeff(s.overall_coeff);
 880         if (is_ex_exactly_of_type(e,numeric)) {
 881                 combine_overall_coeff(e);
 882                 seq = s.seq;
 883                 return;
 884         }
 885
 886         epvector::const_iterator first = s.seq.begin();
 887         epvector::const_iterator last = s.seq.end();
 888         expair p = split_ex_to_pair(e);
 889
 890         seq.reserve(s.seq.size()+1);
 891         bool p_pushed = false;
 892
 893         bool needs_further_processing=false;
 894
 895         // merge p into s.seq
 896         while (first!=last) {
 897                 int cmpval = (*first).rest.compare(p.rest);
 898                 if (cmpval==0) {
 899                         // combine terms
 900                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 901                                                    add(ex_to<numeric>(p.coeff));
 902                         if (!newcoeff.is_zero()) {
 903                                 seq.push_back(expair(first->rest,newcoeff));
 904                                 if (expair_needs_further_processing(seq.end()-1))
 905                                         needs_further_processing = true;
 906                         }
 907                         ++first;
 908                         p_pushed = true;
 909                         break;
 910                 } else if (cmpval<0) {
 911                         seq.push_back(*first);
 912                         ++first;
 913                 } else {
 914                         seq.push_back(p);
 915                         p_pushed = true;
 916                         break;
 917                 }
 918         }
 919
 920         if (p_pushed) {
 921                 // while loop exited because p was pushed, now push rest of s.seq
 922                 while (first!=last) {
 923                         seq.push_back(*first);
 924                         ++first;
 925                 }
 926         } else {
 927                 // while loop exited because s.seq was pushed, now push p
 928                 seq.push_back(p);
 929         }
 930
 931         if (needs_further_processing) {
 932                 epvector v = seq;
 933                 seq.clear();
 934                 construct_from_epvector(v);
 935         }
 936 }
 937
 938 void expairseq::construct_from_exvector(const exvector &v)
 939 {
 940         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 941         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 942         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 943         //                  (same for (+,*) -> (*,^)
 944
 945         make_flat(v);
 946 #if EXPAIRSEQ_USE_HASHTAB
 947         combine_same_terms();
 948 #else
 949         canonicalize();
 950         combine_same_terms_sorted_seq();
 951 #endif // EXPAIRSEQ_USE_HASHTAB
 952 }
 953
 954 void expairseq::construct_from_epvector(const epvector &v)
 955 {
 956         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 957         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 958         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 959         //                  (same for (+,*) -> (*,^)
 960
 961         make_flat(v);
 962 #if EXPAIRSEQ_USE_HASHTAB
 963         combine_same_terms();
 964 #else
 965         canonicalize();
 966         combine_same_terms_sorted_seq();
 967 #endif // EXPAIRSEQ_USE_HASHTAB
 968 }
 969
 970 /** Combine this expairseq with argument exvector.
 971  *  It cares for associativity as well as for special handling of numerics. */
 972 void expairseq::make_flat(const exvector &v)
 973 {
 974         exvector::const_iterator cit;
 975
 976         // count number of operands which are of same expairseq derived type
 977         // and their cumulative number of operands
 978         int nexpairseqs = 0;
 979         int noperands = 0;
 980
 981         cit = v.begin();
 982         while (cit!=v.end()) {
 983                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 984                         ++nexpairseqs;
 985                         noperands += ex_to<expairseq>(*cit).seq.size();
 986                 }
 987                 ++cit;
 988         }
 989
 990         // reserve seq and coeffseq which will hold all operands
 991         seq.reserve(v.size()+noperands-nexpairseqs);
 992
 993         // copy elements and split off numerical part
 994         cit = v.begin();
 995         while (cit!=v.end()) {
 996                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 997                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 998                         combine_overall_coeff(subseqref.overall_coeff);
 999                         epvector::const_iterator cit_s = subseqref.seq.begin();
1000                         while (cit_s!=subseqref.seq.end()) {
1001                                 seq.push_back(*cit_s);
1002                                 ++cit_s;
1003                         }
1004                 } else {
1005                         if (is_ex_exactly_of_type(*cit,numeric))
1006                                 combine_overall_coeff(*cit);
1007                         else
1008                                 seq.push_back(split_ex_to_pair(*cit));
1009                 }
1010                 ++cit;
1011         }
1012 }
1013
1014 /** Combine this expairseq with argument epvector.
1015  *  It cares for associativity as well as for special handling of numerics. */
1016 void expairseq::make_flat(const epvector &v)
1017 {
1018         epvector::const_iterator cit;
1019
1020         // count number of operands which are of same expairseq derived type
1021         // and their cumulative number of operands
1022         int nexpairseqs = 0;
1023         int noperands = 0;
1024
1025         cit = v.begin();
1026         while (cit!=v.end()) {
1027                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1028                         ++nexpairseqs;
1029                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1030                 }
1031                 ++cit;
1032         }
1033
1034         // reserve seq and coeffseq which will hold all operands
1035         seq.reserve(v.size()+noperands-nexpairseqs);
1036
1037         // copy elements and split off numerical part
1038         cit = v.begin();
1039         while (cit!=v.end()) {
1040                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1041                     this->can_make_flat(*cit)) {
1042                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1043                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1044                                                             ex_to<numeric>(cit->coeff));
1045                         epvector::const_iterator cit_s = subseqref.seq.begin();
1046                         while (cit_s!=subseqref.seq.end()) {
1047                                 seq.push_back(expair(cit_s->rest,
1048                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1049                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1050                                 //                                              (*cit).coeff));
1051                                 ++cit_s;
1052                         }
1053                 } else {
1054                         if (cit->is_canonical_numeric())
1055                                 combine_overall_coeff(cit->rest);
1056                         else
1057                                 seq.push_back(*cit);
1058                 }
1059                 ++cit;
1060         }
1061 }
1062
1063 /** Brings this expairseq into a sorted (canonical) form. */
1064 void expairseq::canonicalize(void)
1065 {
1066         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1067 }
1068
1069
1070 /** Compact a presorted expairseq by combining all matching expairs to one
1071  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1072  *  instance. */
1073 void expairseq::combine_same_terms_sorted_seq(void)
1074 {
1075         if (seq.size()<2)
1076                 return;
1077
1078         bool needs_further_processing = false;
1079
1080         epvector::iterator itin1 = seq.begin();
1081         epvector::iterator itin2 = itin1+1;
1082         epvector::iterator itout = itin1;
1083         epvector::iterator last = seq.end();
1084         // must_copy will be set to true the first time some combination is
1085         // possible from then on the sequence has changed and must be compacted
1086         bool must_copy = false;
1087         while (itin2!=last) {
1088                 if (itin1->rest.compare(itin2->rest)==0) {
1089                         itin1->coeff = ex_to<numeric>(itin1->coeff).
1090                                        add_dyn(ex_to<numeric>(itin2->coeff));
1091                         if (expair_needs_further_processing(itin1))
1092                                 needs_further_processing = true;
1093                         must_copy = true;
1094                 } else {
1095                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1096                                 if (must_copy)
1097                                         *itout = *itin1;
1098                                 ++itout;
1099                         }
1100                         itin1 = itin2;
1101                 }
1102                 ++itin2;
1103         }
1104         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1105                 if (must_copy)
1106                         *itout = *itin1;
1107                 ++itout;
1108         }
1109         if (itout!=last)
1110                 seq.erase(itout,last);
1111
1112         if (needs_further_processing) {
1113                 epvector v = seq;
1114                 seq.clear();
1115                 construct_from_epvector(v);
1116         }
1117 }
1118
1119 #if EXPAIRSEQ_USE_HASHTAB
1120
1121 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1122 {
1123         unsigned size;
1124         unsigned nearest_power_of_2 = 1 << log2(sz);
1125         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1126         //  size = nearest_power_of_2*hashtabfactor;
1127         size = nearest_power_of_2/hashtabfactor;
1128         if (size<minhashtabsize)
1129                 return 0;
1130         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1131         // hashtabsize must be a power of 2
1132         GINAC_ASSERT((1U << log2(size))==size);
1133         return size;
1134 }
1135
1136 unsigned expairseq::calc_hashindex(const ex &e) const
1137 {
1138         // calculate hashindex
1139         unsigned hash = e.gethash();
1140         unsigned hashindex;
1141         if (is_a_numeric_hash(hash)) {
1142                 hashindex = hashmask;
1143         } else {
1144                 hashindex = hash &hashmask;
1145                 // last hashtab entry is reserved for numerics
1146                 if (hashindex==hashmask) hashindex = 0;
1147         }
1148         GINAC_ASSERT(hashindex>=0);
1149         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1150         return hashindex;
1151 }
1152
1153 void expairseq::shrink_hashtab(void)
1154 {
1155         unsigned new_hashtabsize;
1156         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1157                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1158                 if (new_hashtabsize==0) {
1159                         hashtab.clear();
1160                         hashtabsize = 0;
1161                         canonicalize();
1162                         return;
1163                 }
1164
1165                 // shrink by a factor of 2
1166                 unsigned half_hashtabsize = hashtabsize/2;
1167                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1168                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1169                 // special treatment for numeric hashes
1170                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1171                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1172                 hashtab.resize(half_hashtabsize);
1173                 hashtabsize = half_hashtabsize;
1174                 hashmask = hashtabsize-1;
1175         }
1176 }
1177
1178 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1179 {
1180         if (hashtabsize==0)
1181                 return; // nothing to do
1182
1183         // calculate hashindex of element to be deleted
1184         unsigned hashindex = calc_hashindex((*element).rest);
1185
1186         // find it in hashtab and remove it
1187         epplist &eppl = hashtab[hashindex];
1188         epplist::iterator epplit = eppl.begin();
1189         bool erased = false;
1190         while (epplit!=eppl.end()) {
1191                 if (*epplit == element) {
1192                         eppl.erase(epplit);
1193                         erased = true;
1194                         break;
1195                 }
1196                 ++epplit;
1197         }
1198         if (!erased) {
1199                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1200                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1201
1202                 unsigned hashindex = calc_hashindex(element->rest);
1203                 epplist &eppl = hashtab[hashindex];
1204                 epplist::iterator epplit = eppl.begin();
1205                 bool erased = false;
1206                 while (epplit!=eppl.end()) {
1207                         if (*epplit == element) {
1208                                 eppl.erase(epplit);
1209                                 erased = true;
1210                                 break;
1211                         }
1212                         ++epplit;
1213                 }
1214                 GINAC_ASSERT(erased);
1215         }
1216         GINAC_ASSERT(erased);
1217 }
1218
1219 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1220                                    epvector::iterator newpos)
1221 {
1222         GINAC_ASSERT(hashtabsize!=0);
1223
1224         // calculate hashindex of element which was moved
1225         unsigned hashindex=calc_hashindex((*newpos).rest);
1226
1227         // find it in hashtab and modify it
1228         epplist &eppl = hashtab[hashindex];
1229         epplist::iterator epplit = eppl.begin();
1230         while (epplit!=eppl.end()) {
1231                 if (*epplit == oldpos) {
1232                         *epplit = newpos;
1233                         break;
1234                 }
1235                 ++epplit;
1236         }
1237         GINAC_ASSERT(epplit!=eppl.end());
1238 }
1239
1240 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1241 {
1242         epplist::const_iterator current = eppl.begin();
1243         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1244                 ++current;
1245         }
1246         eppl.insert(current,elem);
1247 }
1248
1249 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1250                                           epvector::iterator &last_non_zero,
1251                                           std::vector<bool> &touched,
1252                                           unsigned &number_of_zeroes)
1253 {
1254         epp current = seq.begin();
1255
1256         while (current!=first_numeric) {
1257                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1258                         --first_numeric;
1259                         iter_swap(current,first_numeric);
1260                 } else {
1261                         // calculate hashindex
1262                         unsigned currenthashindex = calc_hashindex(current->rest);
1263
1264                         // test if there is already a matching expair in the hashtab-list
1265                         epplist &eppl=hashtab[currenthashindex];
1266                         epplist::iterator epplit = eppl.begin();
1267                         while (epplit!=eppl.end()) {
1268                                 if (current->rest.is_equal((*epplit)->rest))
1269                                         break;
1270                                 ++epplit;
1271                         }
1272                         if (epplit==eppl.end()) {
1273                                 // no matching expair found, append this to end of list
1274                                 sorted_insert(eppl,current);
1275                                 ++current;
1276                         } else {
1277                                 // epplit points to a matching expair, combine it with current
1278                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1279                                                    add_dyn(ex_to<numeric>(current->coeff));
1280
1281                                 // move obsolete current expair to end by swapping with last_non_zero element
1282                                 // if this was a numeric, it is swapped with the expair before first_numeric
1283                                 iter_swap(current,last_non_zero);
1284                                 --first_numeric;
1285                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1286                                 --last_non_zero;
1287                                 ++number_of_zeroes;
1288                                 // test if combined term has coeff 0 and can be removed is done later
1289                                 touched[(*epplit)-seq.begin()] = true;
1290                         }
1291                 }
1292         }
1293 }
1294
1295 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1296                                    epvector::iterator &last_non_zero,
1297                                    std::vector<bool> &touched,
1298                                    unsigned &number_of_zeroes)
1299 {
1300         // move terms with coeff 0 to end and remove them from hashtab
1301         // check only those elements which have been touched
1302         epp current = seq.begin();
1303         unsigned i = 0;
1304         while (current!=first_numeric) {
1305                 if (!touched[i]) {
1306                         ++current;
1307                         ++i;
1308                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1309                         ++current;
1310                         ++i;
1311                 } else {
1312                         remove_hashtab_entry(current);
1313
1314                         // move element to the end, unless it is already at the end
1315                         if (current!=last_non_zero) {
1316                                 iter_swap(current,last_non_zero);
1317                                 --first_numeric;
1318                                 bool numeric_swapped = first_numeric!=last_non_zero;
1319                                 if (numeric_swapped)
1320                                         iter_swap(first_numeric,current);
1321                                 epvector::iterator changed_entry;
1322
1323                                 if (numeric_swapped)
1324                                         changed_entry = first_numeric;
1325                                 else
1326                                         changed_entry = last_non_zero;
1327
1328                                 --last_non_zero;
1329                                 ++number_of_zeroes;
1330
1331                                 if (first_numeric!=current) {
1332
1333                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1334                                         move_hashtab_entry(changed_entry,current);
1335                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1336                                 }
1337                         } else {
1338                                 --first_numeric;
1339                                 --last_non_zero;
1340                                 ++number_of_zeroes;
1341                         }
1342                 }
1343         }
1344         GINAC_ASSERT(i==current-seq.begin());
1345 }
1346
1347 /** True if one of the coeffs vanishes, otherwise false.
1348  *  This would be an invariant violation, so this should only be used for
1349  *  debugging purposes. */
1350 bool expairseq::has_coeff_0(void) const
1351 {
1352         epvector::const_iterator i = seq.begin(), end = seq.end();
1353         while (i != end) {
1354                 if (i->coeff.is_zero())
1355                         return true;
1356                 ++i;
1357         }
1358         return false;
1359 }
1360
1361 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1362                                                                                 epvector::const_iterator last_non_zero)
1363 {
1364         if (first_numeric == seq.end()) return; // no numerics
1365
1366         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1367         while (current != last) {
1368                 sorted_insert(hashtab[hashmask], current);
1369                 ++current;
1370         }
1371 }
1372
1373 void expairseq::combine_same_terms(void)
1374 {
1375         // combine same terms, drop term with coeff 0, move numerics to end
1376
1377         // calculate size of hashtab
1378         hashtabsize = calc_hashtabsize(seq.size());
1379
1380         // hashtabsize is a power of 2
1381         hashmask = hashtabsize-1;
1382
1383         // allocate hashtab
1384         hashtab.clear();
1385         hashtab.resize(hashtabsize);
1386
1387         if (hashtabsize==0) {
1388                 canonicalize();
1389                 combine_same_terms_sorted_seq();
1390                 GINAC_ASSERT(!has_coeff_0());
1391                 return;
1392         }
1393
1394         // iterate through seq, move numerics to end,
1395         // fill hashtab and combine same terms
1396         epvector::iterator first_numeric = seq.end();
1397         epvector::iterator last_non_zero = seq.end()-1;
1398
1399         unsigned num = seq.size();
1400         std::vector<bool> touched(num);
1401
1402         unsigned number_of_zeroes = 0;
1403
1404         GINAC_ASSERT(!has_coeff_0());
1405         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1406
1407         // there should not be any terms with coeff 0 from the beginning,
1408         // so it should be safe to skip this step
1409         if (number_of_zeroes!=0) {
1410                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1411         }
1412
1413         add_numerics_to_hashtab(first_numeric,last_non_zero);
1414
1415         // pop zero elements
1416         for (unsigned i=0; i<number_of_zeroes; ++i) {
1417                 seq.pop_back();
1418         }
1419
1420         // shrink hashtabsize to calculated value
1421         GINAC_ASSERT(!has_coeff_0());
1422
1423         shrink_hashtab();
1424
1425         GINAC_ASSERT(!has_coeff_0());
1426 }
1427
1428 #endif // EXPAIRSEQ_USE_HASHTAB
1429
1430 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1431  *  debugging or in assertions since being sorted is an invariance. */
1432 bool expairseq::is_canonical() const
1433 {
1434         if (seq.size() <= 1)
1435                 return 1;
1436
1437 #if EXPAIRSEQ_USE_HASHTAB
1438         if (hashtabsize > 0) return 1; // not canoncalized
1439 #endif // EXPAIRSEQ_USE_HASHTAB
1440
1441         epvector::const_iterator it = seq.begin(), itend = seq.end();
1442         epvector::const_iterator it_last = it;
1443         for (++it; it!=itend; it_last=it, ++it) {
1444                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1445                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1446                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1447                                 // double test makes it easier to set a breakpoint...
1448                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1449                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1450                                         printpair(std::clog, *it_last, 0);
1451                                         std::clog << ">";
1452                                         printpair(std::clog, *it, 0);
1453                                         std::clog << "\n";
1454                                         std::clog << "pair1:" << std::endl;
1455                                         it_last->rest.print(print_tree(std::clog));
1456                                         it_last->coeff.print(print_tree(std::clog));
1457                                         std::clog << "pair2:" << std::endl;
1458                                         it->rest.print(print_tree(std::clog));
1459                                         it->coeff.print(print_tree(std::clog));
1460                                         return 0;
1461                                 }
1462                         }
1463                 }
1464         }
1465         return 1;
1466 }
1467
1468
1469 /** Member-wise expand the expairs in this sequence.
1470  *
1471  *  @see expairseq::expand()
1472  *  @return pointer to epvector containing expanded pairs or zero pointer,
1473  *  if no members were changed. */
1474 epvector * expairseq::expandchildren(unsigned options) const
1475 {
1476         const epvector::const_iterator last = seq.end();
1477         epvector::const_iterator cit = seq.begin();
1478         while (cit!=last) {
1479                 const ex &expanded_ex = cit->rest.expand(options);
1480                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1481
1482                         // something changed, copy seq, eval and return it
1483                         epvector *s = new epvector;
1484                         s->reserve(seq.size());
1485
1486                         // copy parts of seq which are known not to have changed
1487                         epvector::const_iterator cit2 = seq.begin();
1488                         while (cit2!=cit) {
1489                                 s->push_back(*cit2);
1490                                 ++cit2;
1491                         }
1492                         // copy first changed element
1493                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1494                                                                    cit2->coeff));
1495                         ++cit2;
1496                         // copy rest
1497                         while (cit2!=last) {
1498                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1499                                                                            cit2->coeff));
1500                                 ++cit2;
1501                         }
1502                         return s;
1503                 }
1504                 ++cit;
1505         }
1506
1507         return 0; // signalling nothing has changed
1508 }
1509
1510
1511 /** Member-wise evaluate the expairs in this sequence.
1512  *
1513  *  @see expairseq::eval()
1514  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1515  *  if no members were changed. */
1516 epvector * expairseq::evalchildren(int level) const
1517 {
1518         // returns a NULL pointer if nothing had to be evaluated
1519         // returns a pointer to a newly created epvector otherwise
1520         // (which has to be deleted somewhere else)
1521
1522         if (level==1)
1523                 return 0;
1524
1525         if (level == -max_recursion_level)
1526                 throw(std::runtime_error("max recursion level reached"));
1527
1528         --level;
1529         epvector::const_iterator last = seq.end();
1530         epvector::const_iterator cit = seq.begin();
1531         while (cit!=last) {
1532                 const ex &evaled_ex = cit->rest.eval(level);
1533                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1534
1535                         // something changed, copy seq, eval and return it
1536                         epvector *s = new epvector;
1537                         s->reserve(seq.size());
1538
1539                         // copy parts of seq which are known not to have changed
1540                         epvector::const_iterator cit2=seq.begin();
1541                         while (cit2!=cit) {
1542                                 s->push_back(*cit2);
1543                                 ++cit2;
1544                         }
1545                         // copy first changed element
1546                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1547                                                                    cit2->coeff));
1548                         ++cit2;
1549                         // copy rest
1550                         while (cit2!=last) {
1551                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1552                                                                            cit2->coeff));
1553                                 ++cit2;
1554                         }
1555                         return s;
1556                 }
1557                 ++cit;
1558         }
1559
1560         return 0; // signalling nothing has changed
1561 }
1562
1563
1564 /** Member-wise substitute in this sequence.
1565  *
1566  *  @see expairseq::subs()
1567  *  @return pointer to epvector containing pairs after application of subs,
1568  *    or NULL pointer if no members were changed. */
1569 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1570 {
1571         GINAC_ASSERT(ls.nops()==lr.nops());
1572
1573         // The substitution is "complex" when any of the objects to be substituted
1574         // is a product or power. In this case we have to recombine the pairs
1575         // because the numeric coefficients may be part of the search pattern.
1576         bool complex_subs = false;
1577         for (unsigned i=0; i<ls.nops(); ++i)
1578                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1579                         complex_subs = true;
1580                         break;
1581                 }
1582
1583         if (complex_subs) {
1584
1585                 // Substitute in the recombined pairs
1586                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1587                 while (cit != last) {
1588
1589                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1590                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1591                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1592
1593                                 // Something changed, copy seq, subs and return it
1594                                 epvector *s = new epvector;
1595                                 s->reserve(seq.size());
1596
1597                                 // Copy parts of seq which are known not to have changed
1598                                 s->insert(s->begin(), seq.begin(), cit);
1599
1600                                 // Copy first changed element
1601                                 s->push_back(split_ex_to_pair(subsed_ex));
1602                                 ++cit;
1603
1604                                 // Copy rest
1605                                 while (cit != last) {
1606                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1607                                         ++cit;
1608                                 }
1609                                 return s;
1610                         }
1611
1612                         ++cit;
1613                 }
1614
1615         } else {
1616
1617                 // Substitute only in the "rest" part of the pairs
1618                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1619                 while (cit != last) {
1620
1621                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1622                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1623
1624                                 // Something changed, copy seq, subs and return it
1625                                 epvector *s = new epvector;
1626                                 s->reserve(seq.size());
1627
1628                                 // Copy parts of seq which are known not to have changed
1629                                 s->insert(s->begin(), seq.begin(), cit);
1630
1631                                 // Copy first changed element
1632                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1633                                 ++cit;
1634
1635                                 // Copy rest
1636                                 while (cit != last) {
1637                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1638                                                                                    cit->coeff));
1639                                         ++cit;
1640                                 }
1641                                 return s;
1642                         }
1643
1644                         ++cit;
1645                 }
1646         }
1647
1648         // Nothing has changed
1649         return NULL;
1650 }
1651
1652 //////////
1653 // static member variables
1654 //////////
1655
1656 #if EXPAIRSEQ_USE_HASHTAB
1657 unsigned expairseq::maxhashtabsize = 0x4000000U;
1658 unsigned expairseq::minhashtabsize = 0x1000U;
1659 unsigned expairseq::hashtabfactor = 1;
1660 #endif // EXPAIRSEQ_USE_HASHTAB
1661
1662 } // namespace GiNaC