ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <algorithm>
  24 #include <string>
  25 #include <stdexcept>
  26
  27 #include "expairseq.h"
  28 #include "lst.h"
  29 #include "relational.h"
  30 #include "print.h"
  31 #include "archive.h"
  32 #include "debugmsg.h"
  33 #include "utils.h"
  34
  35 #if EXPAIRSEQ_USE_HASHTAB
  36 #include <cmath>
  37 #endif // EXPAIRSEQ_USE_HASHTAB
  38
  39 namespace GiNaC {
  40
  41 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  42
  43 //////////
  44 // helper classes
  45 //////////
  46
  47 class epp_is_less
  48 {
  49 public:
  50         bool operator()(const epp &lh, const epp &rh) const
  51         {
  52                 return (*lh).is_less(*rh);
  53         }
  54 };
  55
  56 //////////
  57 // default ctor, dtor, copy ctor assignment operator and helpers
  58 //////////
  59
  60 // public
  61
  62 expairseq::expairseq(const expairseq &other)
  63 {
  64         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
  65         copy(other);
  66 }
  67
  68 const expairseq &expairseq::operator=(const expairseq &other)
  69 {
  70         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  71         if (this != &other) {
  72                 destroy(true);
  73                 copy(other);
  74         }
  75         return *this;
  76 }
  77
  78 // protected
  79
  80 /** For use by copy ctor and assignment operator. */
  81 void expairseq::copy(const expairseq &other)
  82 {
  83         inherited::copy(other);
  84         seq = other.seq;
  85         overall_coeff = other.overall_coeff;
  86 #if EXPAIRSEQ_USE_HASHTAB
  87         // copy hashtab
  88         hashtabsize = other.hashtabsize;
  89         if (hashtabsize!=0) {
  90                 hashmask = other.hashmask;
  91                 hashtab.resize(hashtabsize);
  92                 epvector::const_iterator osb = other.seq.begin();
  93                 for (unsigned i=0; i<hashtabsize; ++i) {
  94                         hashtab[i].clear();
  95                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  96                              cit!=other.hashtab[i].end(); ++cit) {
  97                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  98                         }
  99                 }
 100         } else {
 101                 hashtab.clear();
 102         }
 103 #endif // EXPAIRSEQ_USE_HASHTAB
 104 }
 105
 106 DEFAULT_DESTROY(expairseq)
 107
 108 //////////
 109 // other ctors
 110 //////////
 111
 112 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 113 {
 114         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 115         construct_from_2_ex(lh,rh);
 116         GINAC_ASSERT(is_canonical());
 117 }
 118
 119 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 120 {
 121         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 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         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 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         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 138         GINAC_ASSERT(vp!=0);
 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         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
 154         for (unsigned int i=0; true; i++) {
 155                 ex rest;
 156                 ex coeff;
 157                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 158                         seq.push_back(expair(rest, coeff));
 159                 else
 160                         break;
 161         }
 162         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 163 }
 164
 165 void expairseq::archive(archive_node &n) const
 166 {
 167         inherited::archive(n);
 168         epvector::const_iterator i = seq.begin(), iend = seq.end();
 169         while (i != iend) {
 170                 n.add_ex("rest", i->rest);
 171                 n.add_ex("coeff", i->coeff);
 172                 ++i;
 173         }
 174         n.add_ex("overall_coeff", overall_coeff);
 175 }
 176
 177 DEFAULT_UNARCHIVE(expairseq)
 178
 179 //////////
 180 // functions overriding virtual functions from base classes
 181 //////////
 182
 183 // public
 184
 185 basic *expairseq::duplicate() const
 186 {
 187         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 188         return new expairseq(*this);
 189 }
 190
 191 void expairseq::print(const print_context & c, unsigned level) const
 192 {
 193         debugmsg("expairseq print",LOGLEVEL_PRINT);
 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 ex expairseq::eval(int level) const
 321 {
 322         if ((level==1) && (flags &status_flags::evaluated))
 323                 return *this;
 324
 325         epvector *vp = evalchildren(level);
 326         if (vp==0)
 327                 return this->hold();
 328
 329         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 330 }
 331
 332 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 333 {
 334         // This differs from basic::match() because we want "a+b+c+d" to
 335         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 336
 337         if (tinfo() == pattern.bp->tinfo()) {
 338
 339                 // Check whether global wildcard (one that matches the "rest of the
 340                 // expression", like "*" above) is present
 341                 bool has_global_wildcard = false;
 342                 ex global_wildcard;
 343                 for (unsigned int i=0; i<pattern.nops(); i++) {
 344                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 345                                 has_global_wildcard = true;
 346                                 global_wildcard = pattern.op(i);
 347                                 break;
 348                         }
 349                 }
 350
 351                 // Unfortunately, this is an O(N^2) operation because we can't
 352                 // sort the pattern in a useful way...
 353
 354                 // Chop into terms
 355                 exvector ops;
 356                 ops.reserve(nops());
 357                 for (unsigned i=0; i<nops(); i++)
 358                         ops.push_back(op(i));
 359
 360                 // Now, for every term of the pattern, look for a matching term in
 361                 // the expression and remove the match
 362                 for (unsigned i=0; i<pattern.nops(); i++) {
 363                         ex p = pattern.op(i);
 364                         if (has_global_wildcard && p.is_equal(global_wildcard))
 365                                 continue;
 366                         exvector::iterator it = ops.begin(), itend = ops.end();
 367                         while (it != itend) {
 368                                 if (it->match(p, repl_lst)) {
 369                                         ops.erase(it);
 370                                         goto found;
 371                                 }
 372                                 ++it;
 373                         }
 374                         return false; // no match found
 375 found:          ;
 376                 }
 377
 378                 if (has_global_wildcard) {
 379
 380                         // Assign all the remaining terms to the global wildcard (unless
 381                         // it has already been matched before, in which case the matches
 382                         // must be equal)
 383                         unsigned num = ops.size();
 384                         epvector *vp = new epvector();
 385                         vp->reserve(num);
 386                         for (unsigned i=0; i<num; i++)
 387                                 vp->push_back(split_ex_to_pair(ops[i]));
 388                         ex rest = thisexpairseq(vp, default_overall_coeff());
 389                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 390                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 391                                         return rest.is_equal(*repl_lst.op(i).op(1).bp);
 392                         }
 393                         repl_lst.append(global_wildcard == rest);
 394                         return true;
 395
 396                 } else {
 397
 398                         // No global wildcard, then the match fails if there are any
 399                         // unmatched terms left
 400                         return ops.empty();
 401                 }
 402         }
 403         return inherited::match(pattern, repl_lst);
 404 }
 405
 406 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 407 {
 408         epvector *vp = subschildren(ls, lr, no_pattern);
 409         if (vp)
 410                 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
 411         else
 412                 return basic::subs(ls, lr, no_pattern);
 413 }
 414
 415 // protected
 416
 417 int expairseq::compare_same_type(const basic &other) const
 418 {
 419         GINAC_ASSERT(is_of_type(other, expairseq));
 420         const expairseq &o = static_cast<const expairseq &>(other);
 421
 422         int cmpval;
 423
 424         // compare number of elements
 425         if (seq.size() != o.seq.size())
 426                 return (seq.size()<o.seq.size()) ? -1 : 1;
 427
 428         // compare overall_coeff
 429         cmpval = overall_coeff.compare(o.overall_coeff);
 430         if (cmpval!=0)
 431                 return cmpval;
 432
 433 #if EXPAIRSEQ_USE_HASHTAB
 434         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 435         if (hashtabsize==0) {
 436 #endif // EXPAIRSEQ_USE_HASHTAB
 437                 epvector::const_iterator cit1 = seq.begin();
 438                 epvector::const_iterator cit2 = o.seq.begin();
 439                 epvector::const_iterator last1 = seq.end();
 440                 epvector::const_iterator last2 = o.seq.end();
 441
 442                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 443                         cmpval = (*cit1).compare(*cit2);
 444                         if (cmpval!=0) return cmpval;
 445                 }
 446
 447                 GINAC_ASSERT(cit1==last1);
 448                 GINAC_ASSERT(cit2==last2);
 449
 450                 return 0;
 451 #if EXPAIRSEQ_USE_HASHTAB
 452         }
 453
 454         // compare number of elements in each hashtab entry
 455         for (unsigned i=0; i<hashtabsize; ++i) {
 456                 unsigned cursize=hashtab[i].size();
 457                 if (cursize != o.hashtab[i].size())
 458                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 459         }
 460
 461         // compare individual (sorted) hashtab entries
 462         for (unsigned i=0; i<hashtabsize; ++i) {
 463                 unsigned sz = hashtab[i].size();
 464                 if (sz>0) {
 465                         const epplist &eppl1 = hashtab[i];
 466                         const epplist &eppl2 = o.hashtab[i];
 467                         epplist::const_iterator it1 = eppl1.begin();
 468                         epplist::const_iterator it2 = eppl2.begin();
 469                         while (it1!=eppl1.end()) {
 470                                 cmpval = (*(*it1)).compare(*(*it2));
 471                                 if (cmpval!=0)
 472                                         return cmpval;
 473                                 ++it1;
 474                                 ++it2;
 475                         }
 476                 }
 477         }
 478
 479         return 0; // equal
 480 #endif // EXPAIRSEQ_USE_HASHTAB
 481 }
 482
 483 bool expairseq::is_equal_same_type(const basic &other) const
 484 {
 485         const expairseq &o = static_cast<const expairseq &>(other);
 486
 487         // compare number of elements
 488         if (seq.size()!=o.seq.size())
 489                 return false;
 490
 491         // compare overall_coeff
 492         if (!overall_coeff.is_equal(o.overall_coeff))
 493                 return false;
 494
 495 #if EXPAIRSEQ_USE_HASHTAB
 496         // compare number of elements in each hashtab entry
 497         if (hashtabsize!=o.hashtabsize) {
 498                 std::cout << "this:" << std::endl;
 499                 print(print_tree(std::cout));
 500                 std::cout << "other:" << std::endl;
 501                 other.print(print_tree(std::cout));
 502         }
 503
 504         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 505
 506         if (hashtabsize==0) {
 507 #endif // EXPAIRSEQ_USE_HASHTAB
 508                 epvector::const_iterator cit1 = seq.begin();
 509                 epvector::const_iterator cit2 = o.seq.begin();
 510                 epvector::const_iterator last1 = seq.end();
 511
 512                 while (cit1!=last1) {
 513                         if (!(*cit1).is_equal(*cit2)) return false;
 514                         ++cit1;
 515                         ++cit2;
 516                 }
 517
 518                 return true;
 519 #if EXPAIRSEQ_USE_HASHTAB
 520         }
 521
 522         for (unsigned i=0; i<hashtabsize; ++i) {
 523                 if (hashtab[i].size() != o.hashtab[i].size())
 524                         return false;
 525         }
 526
 527         // compare individual sorted hashtab entries
 528         for (unsigned i=0; i<hashtabsize; ++i) {
 529                 unsigned sz = hashtab[i].size();
 530                 if (sz>0) {
 531                         const epplist &eppl1 = hashtab[i];
 532                         const epplist &eppl2 = o.hashtab[i];
 533                         epplist::const_iterator it1 = eppl1.begin();
 534                         epplist::const_iterator it2 = eppl2.begin();
 535                         while (it1!=eppl1.end()) {
 536                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 537                                 ++it1;
 538                                 ++it2;
 539                         }
 540                 }
 541         }
 542
 543         return true;
 544 #endif // EXPAIRSEQ_USE_HASHTAB
 545 }
 546
 547 unsigned expairseq::return_type(void) const
 548 {
 549         return return_types::noncommutative_composite;
 550 }
 551
 552 unsigned expairseq::calchash(void) const
 553 {
 554         unsigned v = golden_ratio_hash(tinfo());
 555         epvector::const_iterator i = seq.begin(), end = seq.end();
 556         while (i != end) {
 557 #if !EXPAIRSEQ_USE_HASHTAB
 558                 v = rotate_left_31(v); // rotation would spoil commutativity
 559 #endif // EXPAIRSEQ_USE_HASHTAB
 560                 v ^= i->rest.gethash();
 561 #if !EXPAIRSEQ_USE_HASHTAB
 562                 v = rotate_left_31(v);
 563                 v ^= i->coeff.gethash();
 564 #endif // EXPAIRSEQ_USE_HASHTAB
 565                 ++i;
 566         }
 567
 568         v ^= overall_coeff.gethash();
 569         v &= 0x7FFFFFFFU;
 570
 571         // store calculated hash value only if object is already evaluated
 572         if (flags &status_flags::evaluated) {
 573                 setflag(status_flags::hash_calculated);
 574                 hashvalue = v;
 575         }
 576
 577         return v;
 578 }
 579
 580 ex expairseq::expand(unsigned options) const
 581 {
 582         epvector *vp = expandchildren(options);
 583         if (vp == NULL) {
 584                 // The terms have not changed, so it is safe to declare this expanded
 585                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 586         } else
 587                 return thisexpairseq(vp, overall_coeff);
 588 }
 589
 590 //////////
 591 // new virtual functions which can be overridden by derived classes
 592 //////////
 593
 594 // protected
 595
 596 /** Create an object of this type.
 597  *  This method works similar to a constructor.  It is useful because expairseq
 598  *  has (at least) two possible different semantics but we want to inherit
 599  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 600  *  has to create a new one of the same semantics, which cannot be done by a
 601  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 602  *  order for this trick to work a derived class must of course override this
 603  *  definition. */
 604 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 605 {
 606         return expairseq(v,oc);
 607 }
 608
 609 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 610 {
 611         return expairseq(vp,oc);
 612 }
 613
 614 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 615 {
 616         c.s << "[[";
 617         p.rest.bp->print(c, precedence());
 618         c.s << ",";
 619         p.coeff.bp->print(c, precedence());
 620         c.s << "]]";
 621 }
 622
 623 void expairseq::printseq(const print_context & c, char delim,
 624                          unsigned this_precedence,
 625                          unsigned upper_precedence) const
 626 {
 627         if (this_precedence <= upper_precedence)
 628                 c.s << "(";
 629         epvector::const_iterator it, it_last = seq.end() - 1;
 630         for (it=seq.begin(); it!=it_last; ++it) {
 631                 printpair(c, *it, this_precedence);
 632                 c.s << delim;
 633         }
 634         printpair(c, *it, this_precedence);
 635         if (!overall_coeff.is_equal(default_overall_coeff())) {
 636                 c.s << delim;
 637                 overall_coeff.print(c, this_precedence);
 638         }
 639
 640         if (this_precedence <= upper_precedence)
 641                 c.s << ")";
 642 }
 643
 644
 645 /** Form an expair from an ex, using the corresponding semantics.
 646  *  @see expairseq::recombine_pair_to_ex() */
 647 expair expairseq::split_ex_to_pair(const ex &e) const
 648 {
 649         return expair(e,_ex1());
 650 }
 651
 652
 653 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 654                                                 const ex &c) const
 655 {
 656         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 657
 658         return expair(e,c);
 659 }
 660
 661
 662 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 663                                                   const ex &c) const
 664 {
 665         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 666         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 667
 668         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 669 }
 670
 671
 672 /** Form an ex out of an expair, using the corresponding semantics.
 673  *  @see expairseq::split_ex_to_pair() */
 674 ex expairseq::recombine_pair_to_ex(const expair &p) const
 675 {
 676         return lst(p.rest,p.coeff);
 677 }
 678
 679 bool expairseq::expair_needs_further_processing(epp it)
 680 {
 681 #if EXPAIRSEQ_USE_HASHTAB
 682         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 683 #endif // EXPAIRSEQ_USE_HASHTAB
 684         return false;
 685 }
 686
 687 ex expairseq::default_overall_coeff(void) const
 688 {
 689         return _ex0();
 690 }
 691
 692 void expairseq::combine_overall_coeff(const ex &c)
 693 {
 694         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 695         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 696         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 697 }
 698
 699 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 700 {
 701         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 702         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 703         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 704         overall_coeff = ex_to<numeric>(overall_coeff).
 705                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 706 }
 707
 708 bool expairseq::can_make_flat(const expair &p) const
 709 {
 710         return true;
 711 }
 712
 713
 714 //////////
 715 // non-virtual functions in this class
 716 //////////
 717
 718 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 719 {
 720         exvector v;
 721         v.reserve(2);
 722         v.push_back(lh);
 723         v.push_back(rh);
 724         construct_from_exvector(v);
 725 #if EXPAIRSEQ_USE_HASHTAB
 726         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 727         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 728 #endif // EXPAIRSEQ_USE_HASHTAB
 729 }
 730
 731 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 732 {
 733         if (lh.bp->tinfo()==tinfo()) {
 734                 if (rh.bp->tinfo()==tinfo()) {
 735 #if EXPAIRSEQ_USE_HASHTAB
 736                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 737                                              ex_to<expairseq>(rh).seq.size();
 738                         if (calc_hashtabsize(totalsize)!=0) {
 739                                 construct_from_2_ex_via_exvector(lh,rh);
 740                         } else {
 741 #endif // EXPAIRSEQ_USE_HASHTAB
 742                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 743                                                            ex_to<expairseq>(rh));
 744 #if EXPAIRSEQ_USE_HASHTAB
 745                         }
 746 #endif // EXPAIRSEQ_USE_HASHTAB
 747                         return;
 748                 } else {
 749 #if EXPAIRSEQ_USE_HASHTAB
 750                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 751                         if (calc_hashtabsize(totalsize)!=0) {
 752                                 construct_from_2_ex_via_exvector(lh, rh);
 753                         } else {
 754 #endif // EXPAIRSEQ_USE_HASHTAB
 755                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 756 #if EXPAIRSEQ_USE_HASHTAB
 757                         }
 758 #endif // EXPAIRSEQ_USE_HASHTAB
 759                         return;
 760                 }
 761         } else if (rh.bp->tinfo()==tinfo()) {
 762 #if EXPAIRSEQ_USE_HASHTAB
 763                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 764                 if (calc_hashtabsize(totalsize)!=0) {
 765                         construct_from_2_ex_via_exvector(lh,rh);
 766                 } else {
 767 #endif // EXPAIRSEQ_USE_HASHTAB
 768                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 769 #if EXPAIRSEQ_USE_HASHTAB
 770                 }
 771 #endif // EXPAIRSEQ_USE_HASHTAB
 772                 return;
 773         }
 774
 775 #if EXPAIRSEQ_USE_HASHTAB
 776         if (calc_hashtabsize(2)!=0) {
 777                 construct_from_2_ex_via_exvector(lh,rh);
 778                 return;
 779         }
 780         hashtabsize = 0;
 781 #endif // EXPAIRSEQ_USE_HASHTAB
 782
 783         if (is_ex_exactly_of_type(lh,numeric)) {
 784                 if (is_ex_exactly_of_type(rh,numeric)) {
 785                         combine_overall_coeff(lh);
 786                         combine_overall_coeff(rh);
 787                 } else {
 788                         combine_overall_coeff(lh);
 789                         seq.push_back(split_ex_to_pair(rh));
 790                 }
 791         } else {
 792                 if (is_ex_exactly_of_type(rh,numeric)) {
 793                         combine_overall_coeff(rh);
 794                         seq.push_back(split_ex_to_pair(lh));
 795                 } else {
 796                         expair p1 = split_ex_to_pair(lh);
 797                         expair p2 = split_ex_to_pair(rh);
 798
 799                         int cmpval = p1.rest.compare(p2.rest);
 800                         if (cmpval==0) {
 801                                 p1.coeff=ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 802                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 803                                         // no further processing is necessary, since this
 804                                         // one element will usually be recombined in eval()
 805                                         seq.push_back(p1);
 806                                 }
 807                         } else {
 808                                 seq.reserve(2);
 809                                 if (cmpval<0) {
 810                                         seq.push_back(p1);
 811                                         seq.push_back(p2);
 812                                 } else {
 813                                         seq.push_back(p2);
 814                                         seq.push_back(p1);
 815                                 }
 816                         }
 817                 }
 818         }
 819 }
 820
 821 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 822                                                                                    const expairseq &s2)
 823 {
 824         combine_overall_coeff(s1.overall_coeff);
 825         combine_overall_coeff(s2.overall_coeff);
 826
 827         epvector::const_iterator first1 = s1.seq.begin();
 828         epvector::const_iterator last1 = s1.seq.end();
 829         epvector::const_iterator first2 = s2.seq.begin();
 830         epvector::const_iterator last2 = s2.seq.end();
 831
 832         seq.reserve(s1.seq.size()+s2.seq.size());
 833
 834         bool needs_further_processing=false;
 835
 836         while (first1!=last1 && first2!=last2) {
 837                 int cmpval = (*first1).rest.compare((*first2).rest);
 838                 if (cmpval==0) {
 839                         // combine terms
 840                         const numeric &newcoeff = ex_to<numeric>((*first1).coeff).
 841                                                    add(ex_to<numeric>((*first2).coeff));
 842                         if (!newcoeff.is_zero()) {
 843                                 seq.push_back(expair((*first1).rest,newcoeff));
 844                                 if (expair_needs_further_processing(seq.end()-1)) {
 845                                         needs_further_processing = true;
 846                                 }
 847                         }
 848                         ++first1;
 849                         ++first2;
 850                 } else if (cmpval<0) {
 851                         seq.push_back(*first1);
 852                         ++first1;
 853                 } else {
 854                         seq.push_back(*first2);
 855                         ++first2;
 856                 }
 857         }
 858
 859         while (first1!=last1) {
 860                 seq.push_back(*first1);
 861                 ++first1;
 862         }
 863         while (first2!=last2) {
 864                 seq.push_back(*first2);
 865                 ++first2;
 866         }
 867
 868         if (needs_further_processing) {
 869                 epvector v = seq;
 870                 seq.clear();
 871                 construct_from_epvector(v);
 872         }
 873 }
 874
 875 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 876                                                                                         const ex &e)
 877 {
 878         combine_overall_coeff(s.overall_coeff);
 879         if (is_ex_exactly_of_type(e,numeric)) {
 880                 combine_overall_coeff(e);
 881                 seq = s.seq;
 882                 return;
 883         }
 884
 885         epvector::const_iterator first = s.seq.begin();
 886         epvector::const_iterator last = s.seq.end();
 887         expair p = split_ex_to_pair(e);
 888
 889         seq.reserve(s.seq.size()+1);
 890         bool p_pushed = false;
 891
 892         bool needs_further_processing=false;
 893
 894         // merge p into s.seq
 895         while (first!=last) {
 896                 int cmpval = (*first).rest.compare(p.rest);
 897                 if (cmpval==0) {
 898                         // combine terms
 899                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 900                                                    add(ex_to<numeric>(p.coeff));
 901                         if (!newcoeff.is_zero()) {
 902                                 seq.push_back(expair(first->rest,newcoeff));
 903                                 if (expair_needs_further_processing(seq.end()-1))
 904                                         needs_further_processing = true;
 905                         }
 906                         ++first;
 907                         p_pushed = true;
 908                         break;
 909                 } else if (cmpval<0) {
 910                         seq.push_back(*first);
 911                         ++first;
 912                 } else {
 913                         seq.push_back(p);
 914                         p_pushed = true;
 915                         break;
 916                 }
 917         }
 918
 919         if (p_pushed) {
 920                 // while loop exited because p was pushed, now push rest of s.seq
 921                 while (first!=last) {
 922                         seq.push_back(*first);
 923                         ++first;
 924                 }
 925         } else {
 926                 // while loop exited because s.seq was pushed, now push p
 927                 seq.push_back(p);
 928         }
 929
 930         if (needs_further_processing) {
 931                 epvector v = seq;
 932                 seq.clear();
 933                 construct_from_epvector(v);
 934         }
 935 }
 936
 937 void expairseq::construct_from_exvector(const exvector &v)
 938 {
 939         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 940         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 941         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 942         //                  (same for (+,*) -> (*,^)
 943
 944         make_flat(v);
 945 #if EXPAIRSEQ_USE_HASHTAB
 946         combine_same_terms();
 947 #else
 948         canonicalize();
 949         combine_same_terms_sorted_seq();
 950 #endif // EXPAIRSEQ_USE_HASHTAB
 951 }
 952
 953 void expairseq::construct_from_epvector(const epvector &v)
 954 {
 955         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 956         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 957         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 958         //                  (same for (+,*) -> (*,^)
 959
 960         make_flat(v);
 961 #if EXPAIRSEQ_USE_HASHTAB
 962         combine_same_terms();
 963 #else
 964         canonicalize();
 965         combine_same_terms_sorted_seq();
 966 #endif // EXPAIRSEQ_USE_HASHTAB
 967 }
 968
 969 /** Combine this expairseq with argument exvector.
 970  *  It cares for associativity as well as for special handling of numerics. */
 971 void expairseq::make_flat(const exvector &v)
 972 {
 973         exvector::const_iterator cit;
 974
 975         // count number of operands which are of same expairseq derived type
 976         // and their cumulative number of operands
 977         int nexpairseqs = 0;
 978         int noperands = 0;
 979
 980         cit = v.begin();
 981         while (cit!=v.end()) {
 982                 if (cit->bp->tinfo()==this->tinfo()) {
 983                         ++nexpairseqs;
 984                         noperands += ex_to<expairseq>(*cit).seq.size();
 985                 }
 986                 ++cit;
 987         }
 988
 989         // reserve seq and coeffseq which will hold all operands
 990         seq.reserve(v.size()+noperands-nexpairseqs);
 991
 992         // copy elements and split off numerical part
 993         cit = v.begin();
 994         while (cit!=v.end()) {
 995                 if (cit->bp->tinfo()==this->tinfo()) {
 996                         const expairseq &subseqref = ex_to<expairseq>(*cit);
 997                         combine_overall_coeff(subseqref.overall_coeff);
 998                         epvector::const_iterator cit_s = subseqref.seq.begin();
 999                         while (cit_s!=subseqref.seq.end()) {
1000                                 seq.push_back(*cit_s);
1001                                 ++cit_s;
1002                         }
1003                 } else {
1004                         if (is_ex_exactly_of_type(*cit,numeric))
1005                                 combine_overall_coeff(*cit);
1006                         else
1007                                 seq.push_back(split_ex_to_pair(*cit));
1008                 }
1009                 ++cit;
1010         }
1011 }
1012
1013 /** Combine this expairseq with argument epvector.
1014  *  It cares for associativity as well as for special handling of numerics. */
1015 void expairseq::make_flat(const epvector &v)
1016 {
1017         epvector::const_iterator cit;
1018
1019         // count number of operands which are of same expairseq derived type
1020         // and their cumulative number of operands
1021         int nexpairseqs = 0;
1022         int noperands = 0;
1023
1024         cit = v.begin();
1025         while (cit!=v.end()) {
1026                 if (cit->rest.bp->tinfo()==this->tinfo()) {
1027                         ++nexpairseqs;
1028                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1029                 }
1030                 ++cit;
1031         }
1032
1033         // reserve seq and coeffseq which will hold all operands
1034         seq.reserve(v.size()+noperands-nexpairseqs);
1035
1036         // copy elements and split off numerical part
1037         cit = v.begin();
1038         while (cit!=v.end()) {
1039                 if (cit->rest.bp->tinfo()==this->tinfo() &&
1040                     this->can_make_flat(*cit)) {
1041                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1042                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1043                                                             ex_to<numeric>(cit->coeff));
1044                         epvector::const_iterator cit_s = subseqref.seq.begin();
1045                         while (cit_s!=subseqref.seq.end()) {
1046                                 seq.push_back(expair(cit_s->rest,
1047                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1048                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1049                                 //                                              (*cit).coeff));
1050                                 ++cit_s;
1051                         }
1052                 } else {
1053                         if (cit->is_canonical_numeric())
1054                                 combine_overall_coeff(cit->rest);
1055                         else
1056                                 seq.push_back(*cit);
1057                 }
1058                 ++cit;
1059         }
1060 }
1061
1062 /** Brings this expairseq into a sorted (canonical) form. */
1063 void expairseq::canonicalize(void)
1064 {
1065         sort(seq.begin(), seq.end(), expair_is_less());
1066 }
1067
1068
1069 /** Compact a presorted expairseq by combining all matching expairs to one
1070  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1071  *  instance. */
1072 void expairseq::combine_same_terms_sorted_seq(void)
1073 {
1074         bool needs_further_processing = false;
1075
1076         if (seq.size()>1) {
1077                 epvector::iterator itin1 = seq.begin();
1078                 epvector::iterator itin2 = itin1+1;
1079                 epvector::iterator itout = itin1;
1080                 epvector::iterator last = seq.end();
1081                 // must_copy will be set to true the first time some combination is
1082                 // possible from then on the sequence has changed and must be compacted
1083                 bool must_copy = false;
1084                 while (itin2!=last) {
1085                         if (itin1->rest.compare(itin2->rest)==0) {
1086                                 itin1->coeff = ex_to<numeric>(itin1->coeff).
1087                                                add_dyn(ex_to<numeric>(itin2->coeff));
1088                                 if (expair_needs_further_processing(itin1))
1089                                         needs_further_processing = true;
1090                                 must_copy = true;
1091                         } else {
1092                                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1093                                         if (must_copy)
1094                                                 *itout = *itin1;
1095                                         ++itout;
1096                                 }
1097                                 itin1 = itin2;
1098                         }
1099                         ++itin2;
1100                 }
1101                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1102                         if (must_copy)
1103                                 *itout = *itin1;
1104                         ++itout;
1105                 }
1106                 if (itout!=last)
1107                         seq.erase(itout,last);
1108         }
1109
1110         if (needs_further_processing) {
1111                 epvector v = seq;
1112                 seq.clear();
1113                 construct_from_epvector(v);
1114         }
1115 }
1116
1117 #if EXPAIRSEQ_USE_HASHTAB
1118
1119 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1120 {
1121         unsigned size;
1122         unsigned nearest_power_of_2 = 1 << log2(sz);
1123         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1124         //  size = nearest_power_of_2*hashtabfactor;
1125         size = nearest_power_of_2/hashtabfactor;
1126         if (size<minhashtabsize)
1127                 return 0;
1128         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1129         // hashtabsize must be a power of 2
1130         GINAC_ASSERT((1U << log2(size))==size);
1131         return size;
1132 }
1133
1134 unsigned expairseq::calc_hashindex(const ex &e) const
1135 {
1136         // calculate hashindex
1137         unsigned hash = e.gethash();
1138         unsigned hashindex;
1139         if (is_a_numeric_hash(hash)) {
1140                 hashindex = hashmask;
1141         } else {
1142                 hashindex = hash &hashmask;
1143                 // last hashtab entry is reserved for numerics
1144                 if (hashindex==hashmask) hashindex = 0;
1145         }
1146         GINAC_ASSERT(hashindex>=0);
1147         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1148         return hashindex;
1149 }
1150
1151 void expairseq::shrink_hashtab(void)
1152 {
1153         unsigned new_hashtabsize;
1154         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1155                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1156                 if (new_hashtabsize==0) {
1157                         hashtab.clear();
1158                         hashtabsize = 0;
1159                         canonicalize();
1160                         return;
1161                 }
1162
1163                 // shrink by a factor of 2
1164                 unsigned half_hashtabsize = hashtabsize/2;
1165                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1166                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1167                 // special treatment for numeric hashes
1168                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1169                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1170                 hashtab.resize(half_hashtabsize);
1171                 hashtabsize = half_hashtabsize;
1172                 hashmask = hashtabsize-1;
1173         }
1174 }
1175
1176 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1177 {
1178         if (hashtabsize==0)
1179                 return; // nothing to do
1180
1181         // calculate hashindex of element to be deleted
1182         unsigned hashindex = calc_hashindex((*element).rest);
1183
1184         // find it in hashtab and remove it
1185         epplist &eppl = hashtab[hashindex];
1186         epplist::iterator epplit = eppl.begin();
1187         bool erased = false;
1188         while (epplit!=eppl.end()) {
1189                 if (*epplit == element) {
1190                         eppl.erase(epplit);
1191                         erased = true;
1192                         break;
1193                 }
1194                 ++epplit;
1195         }
1196         if (!erased) {
1197                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1198                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1199
1200                 unsigned hashindex = calc_hashindex(element->rest);
1201                 epplist &eppl = hashtab[hashindex];
1202                 epplist::iterator epplit = eppl.begin();
1203                 bool erased = false;
1204                 while (epplit!=eppl.end()) {
1205                         if (*epplit == element) {
1206                                 eppl.erase(epplit);
1207                                 erased = true;
1208                                 break;
1209                         }
1210                         ++epplit;
1211                 }
1212                 GINAC_ASSERT(erased);
1213         }
1214         GINAC_ASSERT(erased);
1215 }
1216
1217 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1218                                    epvector::iterator newpos)
1219 {
1220         GINAC_ASSERT(hashtabsize!=0);
1221
1222         // calculate hashindex of element which was moved
1223         unsigned hashindex=calc_hashindex((*newpos).rest);
1224
1225         // find it in hashtab and modify it
1226         epplist &eppl = hashtab[hashindex];
1227         epplist::iterator epplit = eppl.begin();
1228         while (epplit!=eppl.end()) {
1229                 if (*epplit == oldpos) {
1230                         *epplit = newpos;
1231                         break;
1232                 }
1233                 ++epplit;
1234         }
1235         GINAC_ASSERT(epplit!=eppl.end());
1236 }
1237
1238 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1239 {
1240         epplist::const_iterator current = eppl.begin();
1241         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1242                 ++current;
1243         }
1244         eppl.insert(current,elem);
1245 }
1246
1247 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1248                                           epvector::iterator &last_non_zero,
1249                                           std::vector<bool> &touched,
1250                                           unsigned &number_of_zeroes)
1251 {
1252         epp current = seq.begin();
1253
1254         while (current!=first_numeric) {
1255                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1256                         --first_numeric;
1257                         iter_swap(current,first_numeric);
1258                 } else {
1259                         // calculate hashindex
1260                         unsigned currenthashindex = calc_hashindex(current->rest);
1261
1262                         // test if there is already a matching expair in the hashtab-list
1263                         epplist &eppl=hashtab[currenthashindex];
1264                         epplist::iterator epplit = eppl.begin();
1265                         while (epplit!=eppl.end()) {
1266                                 if (current->rest.is_equal((*epplit)->rest))
1267                                         break;
1268                                 ++epplit;
1269                         }
1270                         if (epplit==eppl.end()) {
1271                                 // no matching expair found, append this to end of list
1272                                 sorted_insert(eppl,current);
1273                                 ++current;
1274                         } else {
1275                                 // epplit points to a matching expair, combine it with current
1276                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1277                                                    add_dyn(ex_to<numeric>(current->coeff));
1278
1279                                 // move obsolete current expair to end by swapping with last_non_zero element
1280                                 // if this was a numeric, it is swapped with the expair before first_numeric
1281                                 iter_swap(current,last_non_zero);
1282                                 --first_numeric;
1283                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1284                                 --last_non_zero;
1285                                 ++number_of_zeroes;
1286                                 // test if combined term has coeff 0 and can be removed is done later
1287                                 touched[(*epplit)-seq.begin()] = true;
1288                         }
1289                 }
1290         }
1291 }
1292
1293 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1294                                    epvector::iterator &last_non_zero,
1295                                    std::vector<bool> &touched,
1296                                    unsigned &number_of_zeroes)
1297 {
1298         // move terms with coeff 0 to end and remove them from hashtab
1299         // check only those elements which have been touched
1300         epp current = seq.begin();
1301         unsigned i = 0;
1302         while (current!=first_numeric) {
1303                 if (!touched[i]) {
1304                         ++current;
1305                         ++i;
1306                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1307                         ++current;
1308                         ++i;
1309                 } else {
1310                         remove_hashtab_entry(current);
1311
1312                         // move element to the end, unless it is already at the end
1313                         if (current!=last_non_zero) {
1314                                 iter_swap(current,last_non_zero);
1315                                 --first_numeric;
1316                                 bool numeric_swapped = first_numeric!=last_non_zero;
1317                                 if (numeric_swapped)
1318                                         iter_swap(first_numeric,current);
1319                                 epvector::iterator changed_entry;
1320
1321                                 if (numeric_swapped)
1322                                         changed_entry = first_numeric;
1323                                 else
1324                                         changed_entry = last_non_zero;
1325
1326                                 --last_non_zero;
1327                                 ++number_of_zeroes;
1328
1329                                 if (first_numeric!=current) {
1330
1331                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1332                                         move_hashtab_entry(changed_entry,current);
1333                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1334                                 }
1335                         } else {
1336                                 --first_numeric;
1337                                 --last_non_zero;
1338                                 ++number_of_zeroes;
1339                         }
1340                 }
1341         }
1342         GINAC_ASSERT(i==current-seq.begin());
1343 }
1344
1345 /** True if one of the coeffs vanishes, otherwise false.
1346  *  This would be an invariant violation, so this should only be used for
1347  *  debugging purposes. */
1348 bool expairseq::has_coeff_0(void) const
1349 {
1350         epvector::const_iterator i = seq.begin(), end = seq.end();
1351         while (i != end) {
1352                 if (i->coeff.is_zero())
1353                         return true;
1354                 ++i;
1355         }
1356         return false;
1357 }
1358
1359 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1360                                                                                 epvector::const_iterator last_non_zero)
1361 {
1362         if (first_numeric == seq.end()) return; // no numerics
1363
1364         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1365         while (current != last) {
1366                 sorted_insert(hashtab[hashmask], current);
1367                 ++current;
1368         }
1369 }
1370
1371 void expairseq::combine_same_terms(void)
1372 {
1373         // combine same terms, drop term with coeff 0, move numerics to end
1374
1375         // calculate size of hashtab
1376         hashtabsize = calc_hashtabsize(seq.size());
1377
1378         // hashtabsize is a power of 2
1379         hashmask = hashtabsize-1;
1380
1381         // allocate hashtab
1382         hashtab.clear();
1383         hashtab.resize(hashtabsize);
1384
1385         if (hashtabsize==0) {
1386                 canonicalize();
1387                 combine_same_terms_sorted_seq();
1388                 GINAC_ASSERT(!has_coeff_0());
1389                 return;
1390         }
1391
1392         // iterate through seq, move numerics to end,
1393         // fill hashtab and combine same terms
1394         epvector::iterator first_numeric = seq.end();
1395         epvector::iterator last_non_zero = seq.end()-1;
1396
1397         unsigned num = seq.size();
1398         std::vector<bool> touched(num);
1399
1400         unsigned number_of_zeroes = 0;
1401
1402         GINAC_ASSERT(!has_coeff_0());
1403         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1404
1405         // there should not be any terms with coeff 0 from the beginning,
1406         // so it should be safe to skip this step
1407         if (number_of_zeroes!=0) {
1408                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1409         }
1410
1411         add_numerics_to_hashtab(first_numeric,last_non_zero);
1412
1413         // pop zero elements
1414         for (unsigned i=0; i<number_of_zeroes; ++i) {
1415                 seq.pop_back();
1416         }
1417
1418         // shrink hashtabsize to calculated value
1419         GINAC_ASSERT(!has_coeff_0());
1420
1421         shrink_hashtab();
1422
1423         GINAC_ASSERT(!has_coeff_0());
1424 }
1425
1426 #endif // EXPAIRSEQ_USE_HASHTAB
1427
1428 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1429  *  debugging or in assertions since being sorted is an invariance. */
1430 bool expairseq::is_canonical() const
1431 {
1432         if (seq.size() <= 1)
1433                 return 1;
1434
1435 #if EXPAIRSEQ_USE_HASHTAB
1436         if (hashtabsize > 0) return 1; // not canoncalized
1437 #endif // EXPAIRSEQ_USE_HASHTAB
1438
1439         epvector::const_iterator it = seq.begin(), itend = seq.end();
1440         epvector::const_iterator it_last = it;
1441         for (++it; it!=itend; it_last=it, ++it) {
1442                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1443                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1444                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1445                                 // double test makes it easier to set a breakpoint...
1446                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1447                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1448                                         printpair(std::clog, *it_last, 0);
1449                                         std::clog << ">";
1450                                         printpair(std::clog, *it, 0);
1451                                         std::clog << "\n";
1452                                         std::clog << "pair1:" << std::endl;
1453                                         it_last->rest.print(print_tree(std::clog));
1454                                         it_last->coeff.print(print_tree(std::clog));
1455                                         std::clog << "pair2:" << std::endl;
1456                                         it->rest.print(print_tree(std::clog));
1457                                         it->coeff.print(print_tree(std::clog));
1458                                         return 0;
1459                                 }
1460                         }
1461                 }
1462         }
1463         return 1;
1464 }
1465
1466
1467 /** Member-wise expand the expairs in this sequence.
1468  *
1469  *  @see expairseq::expand()
1470  *  @return pointer to epvector containing expanded pairs or zero pointer,
1471  *  if no members were changed. */
1472 epvector * expairseq::expandchildren(unsigned options) const
1473 {
1474         epvector::const_iterator last = seq.end();
1475         epvector::const_iterator cit = seq.begin();
1476         while (cit!=last) {
1477                 const ex &expanded_ex = cit->rest.expand(options);
1478                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1479
1480                         // something changed, copy seq, eval and return it
1481                         epvector *s = new epvector;
1482                         s->reserve(seq.size());
1483
1484                         // copy parts of seq which are known not to have changed
1485                         epvector::const_iterator cit2 = seq.begin();
1486                         while (cit2!=cit) {
1487                                 s->push_back(*cit2);
1488                                 ++cit2;
1489                         }
1490                         // copy first changed element
1491                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1492                                                                    cit2->coeff));
1493                         ++cit2;
1494                         // copy rest
1495                         while (cit2!=last) {
1496                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1497                                                                            cit2->coeff));
1498                                 ++cit2;
1499                         }
1500                         return s;
1501                 }
1502                 ++cit;
1503         }
1504
1505         return 0; // signalling nothing has changed
1506 }
1507
1508
1509 /** Member-wise evaluate the expairs in this sequence.
1510  *
1511  *  @see expairseq::eval()
1512  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1513  *  if no members were changed. */
1514 epvector * expairseq::evalchildren(int level) const
1515 {
1516         // returns a NULL pointer if nothing had to be evaluated
1517         // returns a pointer to a newly created epvector otherwise
1518         // (which has to be deleted somewhere else)
1519
1520         if (level==1)
1521                 return 0;
1522
1523         if (level == -max_recursion_level)
1524                 throw(std::runtime_error("max recursion level reached"));
1525
1526         --level;
1527         epvector::const_iterator last = seq.end();
1528         epvector::const_iterator cit = seq.begin();
1529         while (cit!=last) {
1530                 const ex &evaled_ex = cit->rest.eval(level);
1531                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1532
1533                         // something changed, copy seq, eval and return it
1534                         epvector *s = new epvector;
1535                         s->reserve(seq.size());
1536
1537                         // copy parts of seq which are known not to have changed
1538                         epvector::const_iterator cit2=seq.begin();
1539                         while (cit2!=cit) {
1540                                 s->push_back(*cit2);
1541                                 ++cit2;
1542                         }
1543                         // copy first changed element
1544                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1545                                                                    cit2->coeff));
1546                         ++cit2;
1547                         // copy rest
1548                         while (cit2!=last) {
1549                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1550                                                                            cit2->coeff));
1551                                 ++cit2;
1552                         }
1553                         return s;
1554                 }
1555                 ++cit;
1556         }
1557
1558         return 0; // signalling nothing has changed
1559 }
1560
1561
1562 /** Member-wise substitute in this sequence.
1563  *
1564  *  @see expairseq::subs()
1565  *  @return pointer to epvector containing pairs after application of subs,
1566  *    or NULL pointer if no members were changed. */
1567 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1568 {
1569         GINAC_ASSERT(ls.nops()==lr.nops());
1570
1571         // The substitution is "complex" when any of the objects to be substituted
1572         // is a product or power. In this case we have to recombine the pairs
1573         // because the numeric coefficients may be part of the search pattern.
1574         bool complex_subs = false;
1575         for (unsigned i=0; i<ls.nops(); ++i)
1576                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1577                         complex_subs = true;
1578                         break;
1579                 }
1580
1581         if (complex_subs) {
1582
1583                 // Substitute in the recombined pairs
1584                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1585                 while (cit != last) {
1586
1587                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1588                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1589                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1590
1591                                 // Something changed, copy seq, subs and return it
1592                                 epvector *s = new epvector;
1593                                 s->reserve(seq.size());
1594
1595                                 // Copy parts of seq which are known not to have changed
1596                                 s->insert(s->begin(), seq.begin(), cit);
1597
1598                                 // Copy first changed element
1599                                 s->push_back(split_ex_to_pair(subsed_ex));
1600                                 ++cit;
1601
1602                                 // Copy rest
1603                                 while (cit != last) {
1604                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1605                                         ++cit;
1606                                 }
1607                                 return s;
1608                         }
1609
1610                         ++cit;
1611                 }
1612
1613         } else {
1614
1615                 // Substitute only in the "rest" part of the pairs
1616                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1617                 while (cit != last) {
1618
1619                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1620                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1621
1622                                 // Something changed, copy seq, subs and return it
1623                                 epvector *s = new epvector;
1624                                 s->reserve(seq.size());
1625
1626                                 // Copy parts of seq which are known not to have changed
1627                                 s->insert(s->begin(), seq.begin(), cit);
1628
1629                                 // Copy first changed element
1630                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1631                                 ++cit;
1632
1633                                 // Copy rest
1634                                 while (cit != last) {
1635                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1636                                                                                    cit->coeff));
1637                                         ++cit;
1638                                 }
1639                                 return s;
1640                         }
1641
1642                         ++cit;
1643                 }
1644         }
1645
1646         // Nothing has changed
1647         return NULL;
1648 }
1649
1650 //////////
1651 // static member variables
1652 //////////
1653
1654 #if EXPAIRSEQ_USE_HASHTAB
1655 unsigned expairseq::maxhashtabsize = 0x4000000U;
1656 unsigned expairseq::minhashtabsize = 0x1000U;
1657 unsigned expairseq::hashtabfactor = 1;
1658 #endif // EXPAIRSEQ_USE_HASHTAB
1659
1660 } // namespace GiNaC