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 "print.h"
  30 #include "archive.h"
  31 #include "debugmsg.h"
  32 #include "utils.h"
  33
  34 #if EXPAIRSEQ_USE_HASHTAB
  35 #include <cmath>
  36 #endif // EXPAIRSEQ_USE_HASHTAB
  37
  38 namespace GiNaC {
  39
  40 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  41
  42 //////////
  43 // helper classes
  44 //////////
  45
  46 class epp_is_less
  47 {
  48 public:
  49         bool operator()(const epp &lh, const epp &rh) const
  50         {
  51                 return (*lh).is_less(*rh);
  52         }
  53 };
  54
  55 //////////
  56 // default ctor, dtor, copy ctor assignment operator and helpers
  57 //////////
  58
  59 // public
  60
  61 expairseq::expairseq(const expairseq &other)
  62 {
  63         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
  64         copy(other);
  65 }
  66
  67 const expairseq &expairseq::operator=(const expairseq &other)
  68 {
  69         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  70         if (this != &other) {
  71                 destroy(true);
  72                 copy(other);
  73         }
  74         return *this;
  75 }
  76
  77 // protected
  78
  79 /** For use by copy ctor and assignment operator. */
  80 void expairseq::copy(const expairseq &other)
  81 {
  82         inherited::copy(other);
  83         seq = other.seq;
  84         overall_coeff = other.overall_coeff;
  85 #if EXPAIRSEQ_USE_HASHTAB
  86         // copy hashtab
  87         hashtabsize = other.hashtabsize;
  88         if (hashtabsize!=0) {
  89                 hashmask = other.hashmask;
  90                 hashtab.resize(hashtabsize);
  91                 epvector::const_iterator osb = other.seq.begin();
  92                 for (unsigned i=0; i<hashtabsize; ++i) {
  93                         hashtab[i].clear();
  94                         for (epplist::const_iterator cit=other.hashtab[i].begin();
  95                              cit!=other.hashtab[i].end(); ++cit) {
  96                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
  97                         }
  98                 }
  99         } else {
 100                 hashtab.clear();
 101         }
 102 #endif // EXPAIRSEQ_USE_HASHTAB
 103 }
 104
 105 DEFAULT_DESTROY(expairseq)
 106
 107 //////////
 108 // other ctors
 109 //////////
 110
 111 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 112 {
 113         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 114         construct_from_2_ex(lh,rh);
 115         GINAC_ASSERT(is_canonical());
 116 }
 117
 118 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 119 {
 120         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 121         construct_from_exvector(v);
 122         GINAC_ASSERT(is_canonical());
 123 }
 124
 125 expairseq::expairseq(const epvector &v, const ex &oc)
 126   : inherited(TINFO_expairseq), overall_coeff(oc)
 127 {
 128         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 129         construct_from_epvector(v);
 130         GINAC_ASSERT(is_canonical());
 131 }
 132
 133 expairseq::expairseq(epvector *vp, const ex &oc)
 134   : inherited(TINFO_expairseq), overall_coeff(oc)
 135 {
 136         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 137         GINAC_ASSERT(vp!=0);
 138         construct_from_epvector(*vp);
 139         delete vp;
 140         GINAC_ASSERT(is_canonical());
 141 }
 142
 143 //////////
 144 // archiving
 145 //////////
 146
 147 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 148 #if EXPAIRSEQ_USE_HASHTAB
 149         , hashtabsize(0)
 150 #endif
 151 {
 152         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
 153         for (unsigned int i=0; true; i++) {
 154                 ex rest;
 155                 ex coeff;
 156                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 157                         seq.push_back(expair(rest, coeff));
 158                 else
 159                         break;
 160         }
 161         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 162 }
 163
 164 void expairseq::archive(archive_node &n) const
 165 {
 166         inherited::archive(n);
 167         epvector::const_iterator i = seq.begin(), iend = seq.end();
 168         while (i != iend) {
 169                 n.add_ex("rest", i->rest);
 170                 n.add_ex("coeff", i->coeff);
 171                 ++i;
 172         }
 173         n.add_ex("overall_coeff", overall_coeff);
 174 }
 175
 176 DEFAULT_UNARCHIVE(expairseq)
 177
 178 //////////
 179 // functions overriding virtual functions from bases classes
 180 //////////
 181
 182 // public
 183
 184 basic *expairseq::duplicate() const
 185 {
 186         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 187         return new expairseq(*this);
 188 }
 189
 190 void expairseq::print(const print_context & c, unsigned level) const
 191 {
 192         debugmsg("expairseq print",LOGLEVEL_PRINT);
 193
 194         if (is_of_type(c, print_tree)) {
 195
 196                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 197
 198                 c.s << std::string(level, ' ') << class_name()
 199                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 200                     << ", nops=" << nops()
 201                     << std::endl;
 202                 for (unsigned i=0; i<seq.size(); ++i) {
 203                         seq[i].rest.print(c, level + delta_indent);
 204                         seq[i].coeff.print(c, level + delta_indent);
 205                         if (i != seq.size()-1)
 206                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 207                 }
 208                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 209                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 210                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 211                         overall_coeff.print(c, level + delta_indent);
 212                 }
 213                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 214 #if EXPAIRSEQ_USE_HASHTAB
 215                 c.s << std::string(level + delta_indent,' ')
 216                     << "hashtab size " << hashtabsize << std::endl;
 217                 if (hashtabsize == 0) return;
 218 #define MAXCOUNT 5
 219                 unsigned count[MAXCOUNT+1];
 220                 for (int i=0; i<MAXCOUNT+1; ++i)
 221                         count[i] = 0;
 222                 unsigned this_bin_fill;
 223                 unsigned cum_fill_sq = 0;
 224                 unsigned cum_fill = 0;
 225                 for (unsigned i=0; i<hashtabsize; ++i) {
 226                         this_bin_fill = 0;
 227                         if (hashtab[i].size() > 0) {
 228                                 c.s << std::string(level + delta_indent, ' ')
 229                                     << "bin " << i << " with entries ";
 230                                 for (epplist::const_iterator it=hashtab[i].begin();
 231                                      it!=hashtab[i].end(); ++it) {
 232                                         c.s << *it-seq.begin() << " ";
 233                                         ++this_bin_fill;
 234                                 }
 235                                 os << std::endl;
 236                                 cum_fill += this_bin_fill;
 237                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 238                         }
 239                         if (this_bin_fill<MAXCOUNT)
 240                                 ++count[this_bin_fill];
 241                         else
 242                                 ++count[MAXCOUNT];
 243                 }
 244                 unsigned fact = 1;
 245                 double cum_prob = 0;
 246                 double lambda = (1.0*seq.size()) / hashtabsize;
 247                 for (int k=0; k<MAXCOUNT; ++k) {
 248                         if (k>0)
 249                                 fact *= k;
 250                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 251                         cum_prob += prob;
 252                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 253                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 254                             << int(prob*1000)/10.0 << ")" << std::endl;
 255                 }
 256                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 257                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 258                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 259
 260                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 261                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 262                     << std::endl;
 263                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 264                     << (1.0*cum_fill)/hashtabsize
 265                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 266 #endif // EXPAIRSEQ_USE_HASHTAB
 267
 268         } else {
 269                 c.s << "[[";
 270                 printseq(c, ',', precedence, level);
 271                 c.s << "]]";
 272         }
 273 }
 274
 275 bool expairseq::info(unsigned inf) const
 276 {
 277         return inherited::info(inf);
 278 }
 279
 280 unsigned expairseq::nops() const
 281 {
 282         if (overall_coeff.is_equal(default_overall_coeff()))
 283                 return seq.size();
 284         else
 285                 return seq.size()+1;
 286 }
 287
 288 ex expairseq::op(int i) const
 289 {
 290         if (unsigned(i)<seq.size())
 291                 return recombine_pair_to_ex(seq[i]);
 292         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 293         return overall_coeff;
 294 }
 295
 296 ex &expairseq::let_op(int i)
 297 {
 298         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 299 }
 300
 301 ex expairseq::eval(int level) const
 302 {
 303         if ((level==1) && (flags &status_flags::evaluated))
 304                 return *this;
 305
 306         epvector *vp = evalchildren(level);
 307         if (vp==0)
 308                 return this->hold();
 309
 310         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 311 }
 312
 313 ex expairseq::evalf(int level) const
 314 {
 315         return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
 316 }
 317
 318 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
 319 {
 320         ex n = thisexpairseq(normalchildren(level),overall_coeff);
 321         return n.bp->basic::normal(sym_lst,repl_lst,level);
 322 }
 323
 324 ex expairseq::subs(const lst &ls, const lst &lr) const
 325 {
 326         epvector *vp = subschildren(ls,lr);
 327         if (vp==0)
 328                 return inherited::subs(ls, lr);
 329
 330         return thisexpairseq(vp,overall_coeff);
 331 }
 332
 333 // protected
 334
 335 /** Implementation of ex::diff() for an expairseq.
 336  *  It differentiates all elements of the sequence.
 337  *  @see ex::diff */
 338 ex expairseq::derivative(const symbol &s) const
 339 {
 340         return thisexpairseq(diffchildren(s),overall_coeff);
 341 }
 342
 343 int expairseq::compare_same_type(const basic &other) const
 344 {
 345         GINAC_ASSERT(is_of_type(other, expairseq));
 346         const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
 347
 348         int cmpval;
 349
 350         // compare number of elements
 351         if (seq.size() != o.seq.size())
 352                 return (seq.size()<o.seq.size()) ? -1 : 1;
 353
 354         // compare overall_coeff
 355         cmpval = overall_coeff.compare(o.overall_coeff);
 356         if (cmpval!=0)
 357                 return cmpval;
 358
 359 #if EXPAIRSEQ_USE_HASHTAB
 360         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 361         if (hashtabsize==0) {
 362 #endif // EXPAIRSEQ_USE_HASHTAB
 363                 epvector::const_iterator cit1 = seq.begin();
 364                 epvector::const_iterator cit2 = o.seq.begin();
 365                 epvector::const_iterator last1 = seq.end();
 366                 epvector::const_iterator last2 = o.seq.end();
 367
 368                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 369                         cmpval = (*cit1).compare(*cit2);
 370                         if (cmpval!=0) return cmpval;
 371                 }
 372
 373                 GINAC_ASSERT(cit1==last1);
 374                 GINAC_ASSERT(cit2==last2);
 375
 376                 return 0;
 377 #if EXPAIRSEQ_USE_HASHTAB
 378         }
 379
 380         // compare number of elements in each hashtab entry
 381         for (unsigned i=0; i<hashtabsize; ++i) {
 382                 unsigned cursize=hashtab[i].size();
 383                 if (cursize != o.hashtab[i].size())
 384                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 385         }
 386
 387         // compare individual (sorted) hashtab entries
 388         for (unsigned i=0; i<hashtabsize; ++i) {
 389                 unsigned sz = hashtab[i].size();
 390                 if (sz>0) {
 391                         const epplist &eppl1 = hashtab[i];
 392                         const epplist &eppl2 = o.hashtab[i];
 393                         epplist::const_iterator it1 = eppl1.begin();
 394                         epplist::const_iterator it2 = eppl2.begin();
 395                         while (it1!=eppl1.end()) {
 396                                 cmpval = (*(*it1)).compare(*(*it2));
 397                                 if (cmpval!=0)
 398                                         return cmpval;
 399                                 ++it1;
 400                                 ++it2;
 401                         }
 402                 }
 403         }
 404
 405         return 0; // equal
 406 #endif // EXPAIRSEQ_USE_HASHTAB
 407 }
 408
 409 bool expairseq::is_equal_same_type(const basic &other) const
 410 {
 411         const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
 412
 413         // compare number of elements
 414         if (seq.size()!=o.seq.size())
 415                 return false;
 416
 417         // compare overall_coeff
 418         if (!overall_coeff.is_equal(o.overall_coeff))
 419                 return false;
 420
 421 #if EXPAIRSEQ_USE_HASHTAB
 422         // compare number of elements in each hashtab entry
 423         if (hashtabsize!=o.hashtabsize) {
 424                 std::cout << "this:" << std::endl;
 425                 print(print_tree(std::cout));
 426                 std::cout << "other:" << std::endl;
 427                 other.print(print_tree(std::cout));
 428         }
 429
 430         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 431
 432         if (hashtabsize==0) {
 433 #endif // EXPAIRSEQ_USE_HASHTAB
 434                 epvector::const_iterator cit1 = seq.begin();
 435                 epvector::const_iterator cit2 = o.seq.begin();
 436                 epvector::const_iterator last1 = seq.end();
 437
 438                 while (cit1!=last1) {
 439                         if (!(*cit1).is_equal(*cit2)) return false;
 440                         ++cit1;
 441                         ++cit2;
 442                 }
 443
 444                 return true;
 445 #if EXPAIRSEQ_USE_HASHTAB
 446         }
 447
 448         for (unsigned i=0; i<hashtabsize; ++i) {
 449                 if (hashtab[i].size() != o.hashtab[i].size())
 450                         return false;
 451         }
 452
 453         // compare individual sorted hashtab entries
 454         for (unsigned i=0; i<hashtabsize; ++i) {
 455                 unsigned sz = hashtab[i].size();
 456                 if (sz>0) {
 457                         const epplist &eppl1 = hashtab[i];
 458                         const epplist &eppl2 = o.hashtab[i];
 459                         epplist::const_iterator it1 = eppl1.begin();
 460                         epplist::const_iterator it2 = eppl2.begin();
 461                         while (it1!=eppl1.end()) {
 462                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 463                                 ++it1;
 464                                 ++it2;
 465                         }
 466                 }
 467         }
 468
 469         return true;
 470 #endif // EXPAIRSEQ_USE_HASHTAB
 471 }
 472
 473 unsigned expairseq::return_type(void) const
 474 {
 475         return return_types::noncommutative_composite;
 476 }
 477
 478 unsigned expairseq::calchash(void) const
 479 {
 480         unsigned v = golden_ratio_hash(tinfo());
 481         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 482 #if !EXPAIRSEQ_USE_HASHTAB
 483                 v = rotate_left_31(v); // rotation would spoil commutativity
 484 #endif // EXPAIRSEQ_USE_HASHTAB
 485                 v ^= cit->rest.gethash();
 486 #if !EXPAIRSEQ_USE_HASHTAB
 487                 v = rotate_left_31(v);
 488                 v ^= cit->coeff.gethash();
 489 #endif // EXPAIRSEQ_USE_HASHTAB
 490         }
 491
 492         v ^= overall_coeff.gethash();
 493         v &= 0x7FFFFFFFU;
 494
 495         // store calculated hash value only if object is already evaluated
 496         if (flags &status_flags::evaluated) {
 497                 setflag(status_flags::hash_calculated);
 498                 hashvalue = v;
 499         }
 500
 501         return v;
 502 }
 503
 504 ex expairseq::expand(unsigned options) const
 505 {
 506         epvector *vp = expandchildren(options);
 507         if (vp==0) {
 508                 // the terms have not changed, so it is safe to declare this expanded
 509                 setflag(status_flags::expanded);
 510                 return *this;
 511         }
 512
 513         return thisexpairseq(vp,overall_coeff);
 514 }
 515
 516 //////////
 517 // new virtual functions which can be overridden by derived classes
 518 //////////
 519
 520 // protected
 521
 522 /** Create an object of this type.
 523  *  This method works similar to a constructor.  It is useful because expairseq
 524  *  has (at least) two possible different semantics but we want to inherit
 525  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 526  *  has to create a new one of the same semantics, which cannot be done by a
 527  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 528  *  order for this trick to work a derived class must of course override this
 529  *  definition. */
 530 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 531 {
 532         return expairseq(v,oc);
 533 }
 534
 535 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 536 {
 537         return expairseq(vp,oc);
 538 }
 539
 540 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 541 {
 542         c.s << "[[";
 543         p.rest.bp->print(c, precedence);
 544         c.s << ",";
 545         p.coeff.bp->print(c, precedence);
 546         c.s << "]]";
 547 }
 548
 549 void expairseq::printseq(const print_context & c, char delim,
 550                          unsigned this_precedence,
 551                          unsigned upper_precedence) const
 552 {
 553         if (this_precedence <= upper_precedence)
 554                 c.s << "(";
 555         epvector::const_iterator it, it_last = seq.end() - 1;
 556         for (it=seq.begin(); it!=it_last; ++it) {
 557                 printpair(c, *it, this_precedence);
 558                 c.s << delim;
 559         }
 560         printpair(c, *it, this_precedence);
 561         if (!overall_coeff.is_equal(default_overall_coeff())) {
 562                 c.s << delim;
 563                 overall_coeff.print(c, this_precedence);
 564         }
 565
 566         if (this_precedence <= upper_precedence)
 567                 c.s << ")";
 568 }
 569
 570
 571 /** Form an expair from an ex, using the corresponding semantics.
 572  *  @see expairseq::recombine_pair_to_ex() */
 573 expair expairseq::split_ex_to_pair(const ex &e) const
 574 {
 575         return expair(e,_ex1());
 576 }
 577
 578
 579 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 580                                                 const ex &c) const
 581 {
 582         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 583
 584         return expair(e,c);
 585 }
 586
 587
 588 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 589                                                   const ex &c) const
 590 {
 591         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 592         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 593
 594         return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 595 }
 596
 597
 598 /** Form an ex out of an expair, using the corresponding semantics.
 599  *  @see expairseq::split_ex_to_pair() */
 600 ex expairseq::recombine_pair_to_ex(const expair &p) const
 601 {
 602         return lst(p.rest,p.coeff);
 603 }
 604
 605 bool expairseq::expair_needs_further_processing(epp it)
 606 {
 607 #if EXPAIRSEQ_USE_HASHTAB
 608         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 609 #endif // EXPAIRSEQ_USE_HASHTAB
 610         return false;
 611 }
 612
 613 ex expairseq::default_overall_coeff(void) const
 614 {
 615         return _ex0();
 616 }
 617
 618 void expairseq::combine_overall_coeff(const ex &c)
 619 {
 620         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 621         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 622         overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
 623 }
 624
 625 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 626 {
 627         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 628         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 629         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 630         overall_coeff = ex_to_numeric(overall_coeff).
 631                         add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
 632 }
 633
 634 bool expairseq::can_make_flat(const expair &p) const
 635 {
 636         return true;
 637 }
 638
 639
 640 //////////
 641 // non-virtual functions in this class
 642 //////////
 643
 644 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 645 {
 646         exvector v;
 647         v.reserve(2);
 648         v.push_back(lh);
 649         v.push_back(rh);
 650         construct_from_exvector(v);
 651 #if EXPAIRSEQ_USE_HASHTAB
 652         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 653         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 654 #endif // EXPAIRSEQ_USE_HASHTAB
 655 }
 656
 657 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 658 {
 659         if (lh.bp->tinfo()==tinfo()) {
 660                 if (rh.bp->tinfo()==tinfo()) {
 661 #if EXPAIRSEQ_USE_HASHTAB
 662                         unsigned totalsize = ex_to_expairseq(lh).seq.size() +
 663                                              ex_to_expairseq(rh).seq.size();
 664                         if (calc_hashtabsize(totalsize)!=0) {
 665                                 construct_from_2_ex_via_exvector(lh,rh);
 666                         } else {
 667 #endif // EXPAIRSEQ_USE_HASHTAB
 668                                 construct_from_2_expairseq(ex_to_expairseq(lh),
 669                                                            ex_to_expairseq(rh));
 670 #if EXPAIRSEQ_USE_HASHTAB
 671                         }
 672 #endif // EXPAIRSEQ_USE_HASHTAB
 673                         return;
 674                 } else {
 675 #if EXPAIRSEQ_USE_HASHTAB
 676                         unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
 677                         if (calc_hashtabsize(totalsize)!=0) {
 678                                 construct_from_2_ex_via_exvector(lh, rh);
 679                         } else {
 680 #endif // EXPAIRSEQ_USE_HASHTAB
 681                                 construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
 682 #if EXPAIRSEQ_USE_HASHTAB
 683                         }
 684 #endif // EXPAIRSEQ_USE_HASHTAB
 685                         return;
 686                 }
 687         } else if (rh.bp->tinfo()==tinfo()) {
 688 #if EXPAIRSEQ_USE_HASHTAB
 689                 unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
 690                 if (calc_hashtabsize(totalsize)!=0) {
 691                         construct_from_2_ex_via_exvector(lh,rh);
 692                 } else {
 693 #endif // EXPAIRSEQ_USE_HASHTAB
 694                         construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
 695 #if EXPAIRSEQ_USE_HASHTAB
 696                 }
 697 #endif // EXPAIRSEQ_USE_HASHTAB
 698                 return;
 699         }
 700
 701 #if EXPAIRSEQ_USE_HASHTAB
 702         if (calc_hashtabsize(2)!=0) {
 703                 construct_from_2_ex_via_exvector(lh,rh);
 704                 return;
 705         }
 706         hashtabsize = 0;
 707 #endif // EXPAIRSEQ_USE_HASHTAB
 708
 709         if (is_ex_exactly_of_type(lh,numeric)) {
 710                 if (is_ex_exactly_of_type(rh,numeric)) {
 711                         combine_overall_coeff(lh);
 712                         combine_overall_coeff(rh);
 713                 } else {
 714                         combine_overall_coeff(lh);
 715                         seq.push_back(split_ex_to_pair(rh));
 716                 }
 717         } else {
 718                 if (is_ex_exactly_of_type(rh,numeric)) {
 719                         combine_overall_coeff(rh);
 720                         seq.push_back(split_ex_to_pair(lh));
 721                 } else {
 722                         expair p1 = split_ex_to_pair(lh);
 723                         expair p2 = split_ex_to_pair(rh);
 724
 725                         int cmpval = p1.rest.compare(p2.rest);
 726                         if (cmpval==0) {
 727                                 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
 728                                 if (!ex_to_numeric(p1.coeff).is_zero()) {
 729                                         // no further processing is necessary, since this
 730                                         // one element will usually be recombined in eval()
 731                                         seq.push_back(p1);
 732                                 }
 733                         } else {
 734                                 seq.reserve(2);
 735                                 if (cmpval<0) {
 736                                         seq.push_back(p1);
 737                                         seq.push_back(p2);
 738                                 } else {
 739                                         seq.push_back(p2);
 740                                         seq.push_back(p1);
 741                                 }
 742                         }
 743                 }
 744         }
 745 }
 746
 747 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 748                                                                                    const expairseq &s2)
 749 {
 750         combine_overall_coeff(s1.overall_coeff);
 751         combine_overall_coeff(s2.overall_coeff);
 752
 753         epvector::const_iterator first1 = s1.seq.begin();
 754         epvector::const_iterator last1 = s1.seq.end();
 755         epvector::const_iterator first2 = s2.seq.begin();
 756         epvector::const_iterator last2 = s2.seq.end();
 757
 758         seq.reserve(s1.seq.size()+s2.seq.size());
 759
 760         bool needs_further_processing=false;
 761
 762         while (first1!=last1 && first2!=last2) {
 763                 int cmpval = (*first1).rest.compare((*first2).rest);
 764                 if (cmpval==0) {
 765                         // combine terms
 766                         const numeric &newcoeff = ex_to_numeric((*first1).coeff).
 767                                                    add(ex_to_numeric((*first2).coeff));
 768                         if (!newcoeff.is_zero()) {
 769                                 seq.push_back(expair((*first1).rest,newcoeff));
 770                                 if (expair_needs_further_processing(seq.end()-1)) {
 771                                         needs_further_processing = true;
 772                                 }
 773                         }
 774                         ++first1;
 775                         ++first2;
 776                 } else if (cmpval<0) {
 777                         seq.push_back(*first1);
 778                         ++first1;
 779                 } else {
 780                         seq.push_back(*first2);
 781                         ++first2;
 782                 }
 783         }
 784
 785         while (first1!=last1) {
 786                 seq.push_back(*first1);
 787                 ++first1;
 788         }
 789         while (first2!=last2) {
 790                 seq.push_back(*first2);
 791                 ++first2;
 792         }
 793
 794         if (needs_further_processing) {
 795                 epvector v = seq;
 796                 seq.clear();
 797                 construct_from_epvector(v);
 798         }
 799 }
 800
 801 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 802                                                                                         const ex &e)
 803 {
 804         combine_overall_coeff(s.overall_coeff);
 805         if (is_ex_exactly_of_type(e,numeric)) {
 806                 combine_overall_coeff(e);
 807                 seq = s.seq;
 808                 return;
 809         }
 810
 811         epvector::const_iterator first = s.seq.begin();
 812         epvector::const_iterator last = s.seq.end();
 813         expair p = split_ex_to_pair(e);
 814
 815         seq.reserve(s.seq.size()+1);
 816         bool p_pushed = false;
 817
 818         bool needs_further_processing=false;
 819
 820         // merge p into s.seq
 821         while (first!=last) {
 822                 int cmpval=(*first).rest.compare(p.rest);
 823                 if (cmpval==0) {
 824                         // combine terms
 825                         const numeric &newcoeff = ex_to_numeric((*first).coeff).
 826                                                    add(ex_to_numeric(p.coeff));
 827                         if (!newcoeff.is_zero()) {
 828                                 seq.push_back(expair((*first).rest,newcoeff));
 829                                 if (expair_needs_further_processing(seq.end()-1)) {
 830                                         needs_further_processing = true;
 831                                 }
 832                         }
 833                         ++first;
 834                         p_pushed = true;
 835                         break;
 836                 } else if (cmpval<0) {
 837                         seq.push_back(*first);
 838                         ++first;
 839                 } else {
 840                         seq.push_back(p);
 841                         p_pushed = true;
 842                         break;
 843                 }
 844         }
 845
 846         if (p_pushed) {
 847                 // while loop exited because p was pushed, now push rest of s.seq
 848                 while (first!=last) {
 849                         seq.push_back(*first);
 850                         ++first;
 851                 }
 852         } else {
 853                 // while loop exited because s.seq was pushed, now push p
 854                 seq.push_back(p);
 855         }
 856
 857         if (needs_further_processing) {
 858                 epvector v = seq;
 859                 seq.clear();
 860                 construct_from_epvector(v);
 861         }
 862 }
 863
 864 void expairseq::construct_from_exvector(const exvector &v)
 865 {
 866         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 867         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 868         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 869         //                  (same for (+,*) -> (*,^)
 870
 871         make_flat(v);
 872 #if EXPAIRSEQ_USE_HASHTAB
 873         combine_same_terms();
 874 #else
 875         canonicalize();
 876         combine_same_terms_sorted_seq();
 877 #endif // EXPAIRSEQ_USE_HASHTAB
 878         return;
 879 }
 880
 881 void expairseq::construct_from_epvector(const epvector &v)
 882 {
 883         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 884         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 885         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 886         //                  (same for (+,*) -> (*,^)
 887
 888         make_flat(v);
 889 #if EXPAIRSEQ_USE_HASHTAB
 890         combine_same_terms();
 891 #else
 892         canonicalize();
 893         combine_same_terms_sorted_seq();
 894 #endif // EXPAIRSEQ_USE_HASHTAB
 895         return;
 896 }
 897
 898 /** Combine this expairseq with argument exvector.
 899  *  It cares for associativity as well as for special handling of numerics. */
 900 void expairseq::make_flat(const exvector &v)
 901 {
 902         exvector::const_iterator cit;
 903
 904         // count number of operands which are of same expairseq derived type
 905         // and their cumulative number of operands
 906         int nexpairseqs = 0;
 907         int noperands = 0;
 908
 909         cit = v.begin();
 910         while (cit!=v.end()) {
 911                 if (cit->bp->tinfo()==this->tinfo()) {
 912                         ++nexpairseqs;
 913                         noperands += ex_to_expairseq(*cit).seq.size();
 914                 }
 915                 ++cit;
 916         }
 917
 918         // reserve seq and coeffseq which will hold all operands
 919         seq.reserve(v.size()+noperands-nexpairseqs);
 920
 921         // copy elements and split off numerical part
 922         cit = v.begin();
 923         while (cit!=v.end()) {
 924                 if (cit->bp->tinfo()==this->tinfo()) {
 925                         const expairseq &subseqref = ex_to_expairseq(*cit);
 926                         combine_overall_coeff(subseqref.overall_coeff);
 927                         epvector::const_iterator cit_s = subseqref.seq.begin();
 928                         while (cit_s!=subseqref.seq.end()) {
 929                                 seq.push_back(*cit_s);
 930                                 ++cit_s;
 931                         }
 932                 } else {
 933                         if (is_ex_exactly_of_type(*cit,numeric))
 934                                 combine_overall_coeff(*cit);
 935                         else
 936                                 seq.push_back(split_ex_to_pair(*cit));
 937                 }
 938                 ++cit;
 939         }
 940
 941         return;
 942 }
 943
 944 /** Combine this expairseq with argument epvector.
 945  *  It cares for associativity as well as for special handling of numerics. */
 946 void expairseq::make_flat(const epvector &v)
 947 {
 948         epvector::const_iterator cit;
 949
 950         // count number of operands which are of same expairseq derived type
 951         // and their cumulative number of operands
 952         int nexpairseqs = 0;
 953         int noperands = 0;
 954
 955         cit = v.begin();
 956         while (cit!=v.end()) {
 957                 if (cit->rest.bp->tinfo()==this->tinfo()) {
 958                         ++nexpairseqs;
 959                         noperands += ex_to_expairseq((*cit).rest).seq.size();
 960                 }
 961                 ++cit;
 962         }
 963
 964         // reserve seq and coeffseq which will hold all operands
 965         seq.reserve(v.size()+noperands-nexpairseqs);
 966
 967         // copy elements and split off numerical part
 968         cit = v.begin();
 969         while (cit!=v.end()) {
 970                 if (cit->rest.bp->tinfo()==this->tinfo() &&
 971                     this->can_make_flat(*cit)) {
 972                         const expairseq &subseqref = ex_to_expairseq((*cit).rest);
 973                         combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
 974                                                             ex_to_numeric((*cit).coeff));
 975                         epvector::const_iterator cit_s = subseqref.seq.begin();
 976                         while (cit_s!=subseqref.seq.end()) {
 977                                 seq.push_back(expair((*cit_s).rest,
 978                                                      ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
 979                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 980                                 //                                              (*cit).coeff));
 981                                 ++cit_s;
 982                         }
 983                 } else {
 984                         if (cit->is_canonical_numeric())
 985                                 combine_overall_coeff(cit->rest);
 986                         else
 987                                 seq.push_back(*cit);
 988                 }
 989                 ++cit;
 990         }
 991         return;
 992 }
 993
 994
 995 /** Brings this expairseq into a sorted (canonical) form. */
 996 void expairseq::canonicalize(void)
 997 {
 998         // canonicalize
 999         sort(seq.begin(),seq.end(),expair_is_less());
1000         return;
1001 }
1002
1003
1004 /** Compact a presorted expairseq by combining all matching expairs to one
1005  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1006  *  instance. */
1007 void expairseq::combine_same_terms_sorted_seq(void)
1008 {
1009         bool needs_further_processing = false;
1010
1011         if (seq.size()>1) {
1012                 epvector::iterator itin1 = seq.begin();
1013                 epvector::iterator itin2 = itin1+1;
1014                 epvector::iterator itout = itin1;
1015                 epvector::iterator last = seq.end();
1016                 // must_copy will be set to true the first time some combination is
1017                 // possible from then on the sequence has changed and must be compacted
1018                 bool must_copy = false;
1019                 while (itin2!=last) {
1020                         if ((*itin1).rest.compare((*itin2).rest)==0) {
1021                                 (*itin1).coeff = ex_to_numeric((*itin1).coeff).
1022                                                  add_dyn(ex_to_numeric((*itin2).coeff));
1023                                 if (expair_needs_further_processing(itin1))
1024                                         needs_further_processing = true;
1025                                 must_copy = true;
1026                         } else {
1027                                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1028                                         if (must_copy)
1029                                                 *itout = *itin1;
1030                                         ++itout;
1031                                 }
1032                                 itin1 = itin2;
1033                         }
1034                         ++itin2;
1035                 }
1036                 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1037                         if (must_copy)
1038                                 *itout = *itin1;
1039                         ++itout;
1040                 }
1041                 if (itout!=last)
1042                         seq.erase(itout,last);
1043         }
1044
1045         if (needs_further_processing) {
1046                 epvector v = seq;
1047                 seq.clear();
1048                 construct_from_epvector(v);
1049         }
1050         return;
1051 }
1052
1053 #if EXPAIRSEQ_USE_HASHTAB
1054
1055 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1056 {
1057         unsigned size;
1058         unsigned nearest_power_of_2 = 1 << log2(sz);
1059         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1060         //  size = nearest_power_of_2*hashtabfactor;
1061         size = nearest_power_of_2/hashtabfactor;
1062         if (size<minhashtabsize)
1063                 return 0;
1064         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1065         // hashtabsize must be a power of 2
1066         GINAC_ASSERT((1U << log2(size))==size);
1067         return size;
1068 }
1069
1070 unsigned expairseq::calc_hashindex(const ex &e) const
1071 {
1072         // calculate hashindex
1073         unsigned hash = e.gethash();
1074         unsigned hashindex;
1075         if (is_a_numeric_hash(hash)) {
1076                 hashindex = hashmask;
1077         } else {
1078                 hashindex = hash &hashmask;
1079                 // last hashtab entry is reserved for numerics
1080                 if (hashindex==hashmask) hashindex = 0;
1081         }
1082         GINAC_ASSERT(hashindex>=0);
1083         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1084         return hashindex;
1085 }
1086
1087 void expairseq::shrink_hashtab(void)
1088 {
1089         unsigned new_hashtabsize;
1090         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1091                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1092                 if (new_hashtabsize==0) {
1093                         hashtab.clear();
1094                         hashtabsize = 0;
1095                         canonicalize();
1096                         return;
1097                 }
1098
1099                 // shrink by a factor of 2
1100                 unsigned half_hashtabsize = hashtabsize/2;
1101                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1102                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1103                 // special treatment for numeric hashes
1104                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1105                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1106                 hashtab.resize(half_hashtabsize);
1107                 hashtabsize = half_hashtabsize;
1108                 hashmask = hashtabsize-1;
1109         }
1110 }
1111
1112 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1113 {
1114         if (hashtabsize==0)
1115                 return; // nothing to do
1116
1117         // calculate hashindex of element to be deleted
1118         unsigned hashindex = calc_hashindex((*element).rest);
1119
1120         // find it in hashtab and remove it
1121         epplist &eppl = hashtab[hashindex];
1122         epplist::iterator epplit = eppl.begin();
1123         bool erased = false;
1124         while (epplit!=eppl.end()) {
1125                 if (*epplit == element) {
1126                         eppl.erase(epplit);
1127                         erased = true;
1128                         break;
1129                 }
1130                 ++epplit;
1131         }
1132         if (!erased) {
1133                 printtree(cout,0);
1134                 cout << "tried to erase " << element-seq.begin() << std::endl;
1135                 cout << "size " << seq.end()-seq.begin() << std::endl;
1136
1137                 unsigned hashindex = calc_hashindex((*element).rest);
1138                 epplist &eppl = hashtab[hashindex];
1139                 epplist::iterator epplit=eppl.begin();
1140                 bool erased=false;
1141                 while (epplit!=eppl.end()) {
1142                         if (*epplit == element) {
1143                                 eppl.erase(epplit);
1144                                 erased = true;
1145                                 break;
1146                         }
1147                         ++epplit;
1148                 }
1149                 GINAC_ASSERT(erased);
1150         }
1151         GINAC_ASSERT(erased);
1152 }
1153
1154 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1155                                    epvector::iterator newpos)
1156 {
1157         GINAC_ASSERT(hashtabsize!=0);
1158
1159         // calculate hashindex of element which was moved
1160         unsigned hashindex=calc_hashindex((*newpos).rest);
1161
1162         // find it in hashtab and modify it
1163         epplist &eppl = hashtab[hashindex];
1164         epplist::iterator epplit = eppl.begin();
1165         while (epplit!=eppl.end()) {
1166                 if (*epplit == oldpos) {
1167                         *epplit = newpos;
1168                         break;
1169                 }
1170                 ++epplit;
1171         }
1172         GINAC_ASSERT(epplit!=eppl.end());
1173 }
1174
1175 void expairseq::sorted_insert(epplist &eppl, epp elem)
1176 {
1177         epplist::iterator current = eppl.begin();
1178         while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1179                 ++current;
1180         }
1181         eppl.insert(current,elem);
1182 }
1183
1184 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1185                                           epvector::iterator &last_non_zero,
1186                                           std::vector<bool> &touched,
1187                                           unsigned &number_of_zeroes)
1188 {
1189         epp current=seq.begin();
1190
1191         while (current!=first_numeric) {
1192                 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1193                         --first_numeric;
1194                         iter_swap(current,first_numeric);
1195                 } else {
1196                         // calculate hashindex
1197                         unsigned currenthashindex = calc_hashindex((*current).rest);
1198
1199                         // test if there is already a matching expair in the hashtab-list
1200                         epplist &eppl=hashtab[currenthashindex];
1201                         epplist::iterator epplit = eppl.begin();
1202                         while (epplit!=eppl.end()) {
1203                                 if ((*current).rest.is_equal((*(*epplit)).rest))
1204                                         break;
1205                                 ++epplit;
1206                         }
1207                         if (epplit==eppl.end()) {
1208                                 // no matching expair found, append this to end of list
1209                                 sorted_insert(eppl,current);
1210                                 ++current;
1211                         } else {
1212                                 // epplit points to a matching expair, combine it with current
1213                                 (*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
1214                                                      add_dyn(ex_to_numeric((*current).coeff));
1215
1216                                 // move obsolete current expair to end by swapping with last_non_zero element
1217                                 // if this was a numeric, it is swapped with the expair before first_numeric
1218                                 iter_swap(current,last_non_zero);
1219                                 --first_numeric;
1220                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1221                                 --last_non_zero;
1222                                 ++number_of_zeroes;
1223                                 // test if combined term has coeff 0 and can be removed is done later
1224                                 touched[(*epplit)-seq.begin()]=true;
1225                         }
1226                 }
1227         }
1228 }
1229
1230 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1231                                    epvector::iterator &last_non_zero,
1232                                    std::vector<bool> &touched,
1233                                    unsigned &number_of_zeroes)
1234 {
1235         // move terms with coeff 0 to end and remove them from hashtab
1236         // check only those elements which have been touched
1237         epp current = seq.begin();
1238         unsigned i = 0;
1239         while (current!=first_numeric) {
1240                 if (!touched[i]) {
1241                         ++current;
1242                         ++i;
1243                 } else if (!ex_to_numeric((*current).coeff).is_zero()) {
1244                         ++current;
1245                         ++i;
1246                 } else {
1247                         remove_hashtab_entry(current);
1248
1249                         // move element to the end, unless it is already at the end
1250                         if (current!=last_non_zero) {
1251                                 iter_swap(current,last_non_zero);
1252                                 --first_numeric;
1253                                 bool numeric_swapped=first_numeric!=last_non_zero;
1254                                 if (numeric_swapped) iter_swap(first_numeric,current);
1255                                 epvector::iterator changed_entry;
1256
1257                                 if (numeric_swapped)
1258                                         changed_entry = first_numeric;
1259                                 else
1260                                         changed_entry = last_non_zero;
1261
1262                                 --last_non_zero;
1263                                 ++number_of_zeroes;
1264
1265                                 if (first_numeric!=current) {
1266
1267                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1268                                         move_hashtab_entry(changed_entry,current);
1269                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1270                                 }
1271                         } else {
1272                                 --first_numeric;
1273                                 --last_non_zero;
1274                                 ++number_of_zeroes;
1275                         }
1276                 }
1277         }
1278         GINAC_ASSERT(i==current-seq.begin());
1279 }
1280
1281 /** True if one of the coeffs vanishes, otherwise false.
1282  *  This would be an invariant violation, so this should only be used for
1283  *  debugging purposes. */
1284 bool expairseq::has_coeff_0(void) const
1285 {
1286         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1287                 if ((*cit).coeff.is_zero())
1288                         return true;
1289         }
1290         return false;
1291 }
1292
1293 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1294                                                                                 epvector::const_iterator last_non_zero)
1295 {
1296         if (first_numeric==seq.end()) return; // no numerics
1297
1298         epvector::iterator current = first_numeric;
1299         epvector::const_iterator last = last_non_zero+1;
1300         while (current!=last) {
1301                 sorted_insert(hashtab[hashmask],current);
1302                 ++current;
1303         }
1304 }
1305
1306 void expairseq::combine_same_terms(void)
1307 {
1308         // combine same terms, drop term with coeff 0, move numerics to end
1309
1310         // calculate size of hashtab
1311         hashtabsize = calc_hashtabsize(seq.size());
1312
1313         // hashtabsize is a power of 2
1314         hashmask = hashtabsize-1;
1315
1316         // allocate hashtab
1317         hashtab.clear();
1318         hashtab.resize(hashtabsize);
1319
1320         if (hashtabsize==0) {
1321                 canonicalize();
1322                 combine_same_terms_sorted_seq();
1323                 GINAC_ASSERT(!has_coeff_0());
1324                 return;
1325         }
1326
1327         // iterate through seq, move numerics to end,
1328         // fill hashtab and combine same terms
1329         epvector::iterator first_numeric = seq.end();
1330         epvector::iterator last_non_zero = seq.end()-1;
1331
1332         std::vector<bool> touched;
1333         touched.reserve(seq.size());
1334         for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1335
1336         unsigned number_of_zeroes = 0;
1337
1338         GINAC_ASSERT(!has_coeff_0());
1339         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1340         /*
1341         cout << "in combine:" << std::endl;
1342         printtree(cout,0);
1343         cout << "size=" << seq.end() - seq.begin() << std::endl;
1344         cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1345         cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1346         for (unsigned i=0; i<seq.size(); ++i) {
1347                 if (touched[i]) cout << i << " is touched" << std::endl;
1348         }
1349         cout << "end in combine" << std::endl;
1350         */
1351
1352         // there should not be any terms with coeff 0 from the beginning,
1353         // so it should be safe to skip this step
1354         if (number_of_zeroes!=0) {
1355                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1356                 /*
1357                 cout << "in combine after drop:" << std::endl;
1358                 printtree(cout,0);
1359                 cout << "size=" << seq.end() - seq.begin() << std::endl;
1360                 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1361                 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1362                 for (unsigned i=0; i<seq.size(); ++i) {
1363                         if (touched[i]) cout << i << " is touched" << std::endl;
1364                 }
1365                 cout << "end in combine after drop" << std::endl;
1366                 */
1367         }
1368
1369         add_numerics_to_hashtab(first_numeric,last_non_zero);
1370
1371         // pop zero elements
1372         for (unsigned i=0; i<number_of_zeroes; ++i) {
1373                 seq.pop_back();
1374         }
1375
1376         // shrink hashtabsize to calculated value
1377         GINAC_ASSERT(!has_coeff_0());
1378
1379         shrink_hashtab();
1380
1381         GINAC_ASSERT(!has_coeff_0());
1382 }
1383
1384 #endif // EXPAIRSEQ_USE_HASHTAB
1385
1386 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1387  *  debugging or in assertions since being sorted is an invariance. */
1388 bool expairseq::is_canonical() const
1389 {
1390         if (seq.size() <= 1)
1391                 return 1;
1392
1393 #if EXPAIRSEQ_USE_HASHTAB
1394         if (hashtabsize > 0) return 1; // not canoncalized
1395 #endif // EXPAIRSEQ_USE_HASHTAB
1396
1397         epvector::const_iterator it = seq.begin();
1398         epvector::const_iterator it_last = it;
1399         for (++it; it!=seq.end(); it_last=it, ++it) {
1400                 if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
1401                         if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1402                                 !is_ex_exactly_of_type((*it).rest,numeric)) {
1403                                 // double test makes it easier to set a breakpoint...
1404                                 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1405                                         !is_ex_exactly_of_type((*it).rest,numeric)) {
1406                                         printpair(std::clog, *it_last, 0);
1407                                         std::clog << ">";
1408                                         printpair(std::clog, *it, 0);
1409                                         std::clog << "\n";
1410                                         std::clog << "pair1:" << std::endl;
1411                                         (*it_last).rest.print(print_tree(std::clog));
1412                                         (*it_last).coeff.print(print_tree(std::clog));
1413                                         std::clog << "pair2:" << std::endl;
1414                                         (*it).rest.print(print_tree(std::clog));
1415                                         (*it).coeff.print(print_tree(std::clog));
1416                                         return 0;
1417                                 }
1418                         }
1419                 }
1420         }
1421         return 1;
1422 }
1423
1424
1425 /** Member-wise expand the expairs in this sequence.
1426  *
1427  *  @see expairseq::expand()
1428  *  @return pointer to epvector containing expanded pairs or zero pointer,
1429  *  if no members were changed. */
1430 epvector * expairseq::expandchildren(unsigned options) const
1431 {
1432         epvector::const_iterator last = seq.end();
1433         epvector::const_iterator cit = seq.begin();
1434         while (cit!=last) {
1435                 const ex &expanded_ex = (*cit).rest.expand(options);
1436                 if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1437
1438                         // something changed, copy seq, eval and return it
1439                         epvector *s = new epvector;
1440                         s->reserve(seq.size());
1441
1442                         // copy parts of seq which are known not to have changed
1443                         epvector::const_iterator cit2 = seq.begin();
1444                         while (cit2!=cit) {
1445                                 s->push_back(*cit2);
1446                                 ++cit2;
1447                         }
1448                         // copy first changed element
1449                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1450                                                                    (*cit2).coeff));
1451                         ++cit2;
1452                         // copy rest
1453                         while (cit2!=last) {
1454                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1455                                                                            (*cit2).coeff));
1456                                 ++cit2;
1457                         }
1458                         return s;
1459                 }
1460                 ++cit;
1461         }
1462
1463         return 0; // signalling nothing has changed
1464 }
1465
1466
1467 /** Member-wise evaluate the expairs in this sequence.
1468  *
1469  *  @see expairseq::eval()
1470  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1471  *  if no members were changed. */
1472 epvector * expairseq::evalchildren(int level) const
1473 {
1474         // returns a NULL pointer if nothing had to be evaluated
1475         // returns a pointer to a newly created epvector otherwise
1476         // (which has to be deleted somewhere else)
1477
1478         if (level==1)
1479                 return 0;
1480
1481         if (level == -max_recursion_level)
1482                 throw(std::runtime_error("max recursion level reached"));
1483
1484         --level;
1485         epvector::const_iterator last=seq.end();
1486         epvector::const_iterator cit=seq.begin();
1487         while (cit!=last) {
1488                 const ex &evaled_ex = (*cit).rest.eval(level);
1489                 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1490
1491                         // something changed, copy seq, eval and return it
1492                         epvector *s = new epvector;
1493                         s->reserve(seq.size());
1494
1495                         // copy parts of seq which are known not to have changed
1496                         epvector::const_iterator cit2=seq.begin();
1497                         while (cit2!=cit) {
1498                                 s->push_back(*cit2);
1499                                 ++cit2;
1500                         }
1501                         // copy first changed element
1502                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1503                                                                    (*cit2).coeff));
1504                         ++cit2;
1505                         // copy rest
1506                         while (cit2!=last) {
1507                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1508                                                                            (*cit2).coeff));
1509                                 ++cit2;
1510                         }
1511                         return s;
1512                 }
1513                 ++cit;
1514         }
1515
1516         return 0; // signalling nothing has changed
1517 }
1518
1519
1520 /** Member-wise evaluate numerically all expairs in this sequence.
1521  *
1522  *  @see expairseq::evalf()
1523  *  @return epvector with all entries evaluated numerically. */
1524 epvector expairseq::evalfchildren(int level) const
1525 {
1526         if (level==1)
1527                 return seq;
1528
1529         if (level==-max_recursion_level)
1530                 throw(std::runtime_error("max recursion level reached"));
1531
1532         epvector s;
1533         s.reserve(seq.size());
1534
1535         --level;
1536         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1537                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1538                                                           (*it).coeff.evalf(level)));
1539         }
1540         return s;
1541 }
1542
1543
1544 /** Member-wise normalize all expairs in this sequence.
1545  *
1546  *  @see expairseq::normal()
1547  *  @return epvector with all entries normalized. */
1548 epvector expairseq::normalchildren(int level) const
1549 {
1550         if (level==1)
1551                 return seq;
1552
1553         if (level==-max_recursion_level)
1554                 throw(std::runtime_error("max recursion level reached"));
1555
1556         epvector s;
1557         s.reserve(seq.size());
1558
1559         --level;
1560         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1561                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1562                                                           (*it).coeff));
1563         }
1564         return s;
1565 }
1566
1567
1568 /** Member-wise differentiate all expairs in this sequence.
1569  *
1570  *  @see expairseq::diff()
1571  *  @return epvector with all entries differentiated. */
1572 epvector expairseq::diffchildren(const symbol &y) const
1573 {
1574         epvector s;
1575         s.reserve(seq.size());
1576
1577         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1578                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1579                                                           (*it).coeff));
1580         }
1581         return s;
1582 }
1583
1584
1585 /** Member-wise substitute in this sequence.
1586  *
1587  *  @see expairseq::subs()
1588  *  @return pointer to epvector containing pairs after application of subs or zero
1589  *  pointer, if no members were changed. */
1590 epvector * expairseq::subschildren(const lst &ls, const lst &lr) const
1591 {
1592         // returns a NULL pointer if nothing had to be substituted
1593         // returns a pointer to a newly created epvector otherwise
1594         // (which has to be deleted somewhere else)
1595         GINAC_ASSERT(ls.nops()==lr.nops());
1596
1597         epvector::const_iterator last = seq.end();
1598         epvector::const_iterator cit = seq.begin();
1599         while (cit!=last) {
1600                 const ex &subsed_ex=(*cit).rest.subs(ls,lr);
1601                 if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1602
1603                         // something changed, copy seq, subs and return it
1604                         epvector *s = new epvector;
1605                         s->reserve(seq.size());
1606
1607                         // copy parts of seq which are known not to have changed
1608                         epvector::const_iterator cit2 = seq.begin();
1609                         while (cit2!=cit) {
1610                                 s->push_back(*cit2);
1611                                 ++cit2;
1612                         }
1613                         // copy first changed element
1614                         s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1615                                                                    (*cit2).coeff));
1616                         ++cit2;
1617                         // copy rest
1618                         while (cit2!=last) {
1619                                 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
1620                                                                            (*cit2).coeff));
1621                                 ++cit2;
1622                         }
1623                         return s;
1624                 }
1625                 ++cit;
1626         }
1627
1628         return 0; // signalling nothing has changed
1629 }
1630
1631 //////////
1632 // static member variables
1633 //////////
1634
1635 // protected
1636
1637 unsigned expairseq::precedence = 10;
1638
1639 #if EXPAIRSEQ_USE_HASHTAB
1640 unsigned expairseq::maxhashtabsize = 0x4000000U;
1641 unsigned expairseq::minhashtabsize = 0x1000U;
1642 unsigned expairseq::hashtabfactor = 1;
1643 #endif // EXPAIRSEQ_USE_HASHTAB
1644
1645 } // namespace GiNaC