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 "mul.h"
  30 #include "power.h"
  31 #include "relational.h"
  32 #include "wildcard.h"
  33 #include "print.h"
  34 #include "archive.h"
  35 #include "debugmsg.h"
  36 #include "utils.h"
  37
  38 #if EXPAIRSEQ_USE_HASHTAB
  39 #include <cmath>
  40 #endif // EXPAIRSEQ_USE_HASHTAB
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
  46
  47 //////////
  48 // helper classes
  49 //////////
  50
  51 class epp_is_less
  52 {
  53 public:
  54         bool operator()(const epp &lh, const epp &rh) const
  55         {
  56                 return (*lh).is_less(*rh);
  57         }
  58 };
  59
  60 //////////
  61 // default ctor, dtor, copy ctor assignment operator and helpers
  62 //////////
  63
  64 // public
  65
  66 expairseq::expairseq(const expairseq &other)
  67 {
  68         debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
  69         copy(other);
  70 }
  71
  72 const expairseq &expairseq::operator=(const expairseq &other)
  73 {
  74         debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
  75         if (this != &other) {
  76                 destroy(true);
  77                 copy(other);
  78         }
  79         return *this;
  80 }
  81
  82 // protected
  83
  84 /** For use by copy ctor and assignment operator. */
  85 void expairseq::copy(const expairseq &other)
  86 {
  87         inherited::copy(other);
  88         seq = other.seq;
  89         overall_coeff = other.overall_coeff;
  90 #if EXPAIRSEQ_USE_HASHTAB
  91         // copy hashtab
  92         hashtabsize = other.hashtabsize;
  93         if (hashtabsize!=0) {
  94                 hashmask = other.hashmask;
  95                 hashtab.resize(hashtabsize);
  96                 epvector::const_iterator osb = other.seq.begin();
  97                 for (unsigned i=0; i<hashtabsize; ++i) {
  98                         hashtab[i].clear();
  99                         for (epplist::const_iterator cit=other.hashtab[i].begin();
 100                              cit!=other.hashtab[i].end(); ++cit) {
 101                                 hashtab[i].push_back(seq.begin()+((*cit)-osb));
 102                         }
 103                 }
 104         } else {
 105                 hashtab.clear();
 106         }
 107 #endif // EXPAIRSEQ_USE_HASHTAB
 108 }
 109
 110 DEFAULT_DESTROY(expairseq)
 111
 112 //////////
 113 // other ctors
 114 //////////
 115
 116 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 117 {
 118         debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 119         construct_from_2_ex(lh,rh);
 120         GINAC_ASSERT(is_canonical());
 121 }
 122
 123 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 124 {
 125         debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 126         construct_from_exvector(v);
 127         GINAC_ASSERT(is_canonical());
 128 }
 129
 130 expairseq::expairseq(const epvector &v, const ex &oc)
 131   : inherited(TINFO_expairseq), overall_coeff(oc)
 132 {
 133         debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 134         construct_from_epvector(v);
 135         GINAC_ASSERT(is_canonical());
 136 }
 137
 138 expairseq::expairseq(epvector *vp, const ex &oc)
 139   : inherited(TINFO_expairseq), overall_coeff(oc)
 140 {
 141         debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 142         GINAC_ASSERT(vp!=0);
 143         construct_from_epvector(*vp);
 144         delete vp;
 145         GINAC_ASSERT(is_canonical());
 146 }
 147
 148 //////////
 149 // archiving
 150 //////////
 151
 152 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 153 #if EXPAIRSEQ_USE_HASHTAB
 154         , hashtabsize(0)
 155 #endif
 156 {
 157         debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
 158         for (unsigned int i=0; true; i++) {
 159                 ex rest;
 160                 ex coeff;
 161                 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
 162                         seq.push_back(expair(rest, coeff));
 163                 else
 164                         break;
 165         }
 166         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 167 }
 168
 169 void expairseq::archive(archive_node &n) const
 170 {
 171         inherited::archive(n);
 172         epvector::const_iterator i = seq.begin(), iend = seq.end();
 173         while (i != iend) {
 174                 n.add_ex("rest", i->rest);
 175                 n.add_ex("coeff", i->coeff);
 176                 ++i;
 177         }
 178         n.add_ex("overall_coeff", overall_coeff);
 179 }
 180
 181 DEFAULT_UNARCHIVE(expairseq)
 182
 183 //////////
 184 // functions overriding virtual functions from base classes
 185 //////////
 186
 187 // public
 188
 189 basic *expairseq::duplicate() const
 190 {
 191         debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
 192         return new expairseq(*this);
 193 }
 194
 195 void expairseq::print(const print_context &c, unsigned level) const
 196 {
 197         debugmsg("expairseq print",LOGLEVEL_PRINT);
 198
 199         if (is_of_type(c, print_tree)) {
 200
 201                 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 202
 203                 c.s << std::string(level, ' ') << class_name()
 204                     << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 205                     << ", nops=" << nops()
 206                     << std::endl;
 207                 unsigned num = seq.size();
 208                 for (unsigned i=0; i<num; ++i) {
 209                         seq[i].rest.print(c, level + delta_indent);
 210                         seq[i].coeff.print(c, level + delta_indent);
 211                         if (i != num - 1)
 212                                 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
 213                 }
 214                 if (!overall_coeff.is_equal(default_overall_coeff())) {
 215                         c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
 216                             << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
 217                         overall_coeff.print(c, level + delta_indent);
 218                 }
 219                 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 220 #if EXPAIRSEQ_USE_HASHTAB
 221                 c.s << std::string(level + delta_indent,' ')
 222                     << "hashtab size " << hashtabsize << std::endl;
 223                 if (hashtabsize == 0) return;
 224 #define MAXCOUNT 5
 225                 unsigned count[MAXCOUNT+1];
 226                 for (int i=0; i<MAXCOUNT+1; ++i)
 227                         count[i] = 0;
 228                 unsigned this_bin_fill;
 229                 unsigned cum_fill_sq = 0;
 230                 unsigned cum_fill = 0;
 231                 for (unsigned i=0; i<hashtabsize; ++i) {
 232                         this_bin_fill = 0;
 233                         if (hashtab[i].size() > 0) {
 234                                 c.s << std::string(level + delta_indent, ' ')
 235                                     << "bin " << i << " with entries ";
 236                                 for (epplist::const_iterator it=hashtab[i].begin();
 237                                      it!=hashtab[i].end(); ++it) {
 238                                         c.s << *it-seq.begin() << " ";
 239                                         ++this_bin_fill;
 240                                 }
 241                                 c.s << std::endl;
 242                                 cum_fill += this_bin_fill;
 243                                 cum_fill_sq += this_bin_fill*this_bin_fill;
 244                         }
 245                         if (this_bin_fill<MAXCOUNT)
 246                                 ++count[this_bin_fill];
 247                         else
 248                                 ++count[MAXCOUNT];
 249                 }
 250                 unsigned fact = 1;
 251                 double cum_prob = 0;
 252                 double lambda = (1.0*seq.size()) / hashtabsize;
 253                 for (int k=0; k<MAXCOUNT; ++k) {
 254                         if (k>0)
 255                                 fact *= k;
 256                         double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
 257                         cum_prob += prob;
 258                         c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
 259                             << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
 260                             << int(prob*1000)/10.0 << ")" << std::endl;
 261                 }
 262                 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
 263                     << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
 264                     << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
 265
 266                 c.s << std::string(level + delta_indent, ' ') << "variance: "
 267                     << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
 268                     << std::endl;
 269                 c.s << std::string(level + delta_indent, ' ') << "average fill: "
 270                     << (1.0*cum_fill)/hashtabsize
 271                     << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 272 #endif // EXPAIRSEQ_USE_HASHTAB
 273
 274         } else {
 275                 c.s << "[[";
 276                 printseq(c, ',', precedence(), level);
 277                 c.s << "]]";
 278         }
 279 }
 280
 281 bool expairseq::info(unsigned inf) const
 282 {
 283         return inherited::info(inf);
 284 }
 285
 286 unsigned expairseq::nops() const
 287 {
 288         if (overall_coeff.is_equal(default_overall_coeff()))
 289                 return seq.size();
 290         else
 291                 return seq.size()+1;
 292 }
 293
 294 ex expairseq::op(int i) const
 295 {
 296         if (unsigned(i)<seq.size())
 297                 return recombine_pair_to_ex(seq[i]);
 298         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 299         return overall_coeff;
 300 }
 301
 302 ex &expairseq::let_op(int i)
 303 {
 304         throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
 305 }
 306
 307 ex expairseq::map(map_function &f) const
 308 {
 309         epvector *v = new epvector;
 310         v->reserve(seq.size());
 311
 312         epvector::const_iterator cit = seq.begin(), last = seq.end();
 313         while (cit != last) {
 314                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 315                 ++cit;
 316         }
 317
 318         if (overall_coeff.is_equal(default_overall_coeff()))
 319                 return thisexpairseq(v, default_overall_coeff());
 320         else
 321                 return thisexpairseq(v, f(overall_coeff));
 322 }
 323
 324 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 325 ex expairseq::eval(int level) const
 326 {
 327         if ((level==1) && (flags &status_flags::evaluated))
 328                 return *this;
 329
 330         epvector *vp = evalchildren(level);
 331         if (vp==0)
 332                 return this->hold();
 333
 334         return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 335 }
 336
 337 bool expairseq::match(const ex & pattern, lst & repl_lst) const
 338 {
 339         // This differs from basic::match() because we want "a+b+c+d" to
 340         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 341
 342         if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 343
 344                 // Check whether global wildcard (one that matches the "rest of the
 345                 // expression", like "*" above) is present
 346                 bool has_global_wildcard = false;
 347                 ex global_wildcard;
 348                 for (unsigned int i=0; i<pattern.nops(); i++) {
 349                         if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
 350                                 has_global_wildcard = true;
 351                                 global_wildcard = pattern.op(i);
 352                                 break;
 353                         }
 354                 }
 355
 356                 // Unfortunately, this is an O(N^2) operation because we can't
 357                 // sort the pattern in a useful way...
 358
 359                 // Chop into terms
 360                 exvector ops;
 361                 ops.reserve(nops());
 362                 for (unsigned i=0; i<nops(); i++)
 363                         ops.push_back(op(i));
 364
 365                 // Now, for every term of the pattern, look for a matching term in
 366                 // the expression and remove the match
 367                 for (unsigned i=0; i<pattern.nops(); i++) {
 368                         ex p = pattern.op(i);
 369                         if (has_global_wildcard && p.is_equal(global_wildcard))
 370                                 continue;
 371                         exvector::iterator it = ops.begin(), itend = ops.end();
 372                         while (it != itend) {
 373                                 if (it->match(p, repl_lst)) {
 374                                         ops.erase(it);
 375                                         goto found;
 376                                 }
 377                                 ++it;
 378                         }
 379                         return false; // no match found
 380 found:          ;
 381                 }
 382
 383                 if (has_global_wildcard) {
 384
 385                         // Assign all the remaining terms to the global wildcard (unless
 386                         // it has already been matched before, in which case the matches
 387                         // must be equal)
 388                         unsigned num = ops.size();
 389                         epvector *vp = new epvector();
 390                         vp->reserve(num);
 391                         for (unsigned i=0; i<num; i++)
 392                                 vp->push_back(split_ex_to_pair(ops[i]));
 393                         ex rest = thisexpairseq(vp, default_overall_coeff());
 394                         for (unsigned i=0; i<repl_lst.nops(); i++) {
 395                                 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
 396                                         return rest.is_equal(repl_lst.op(i).op(1));
 397                         }
 398                         repl_lst.append(global_wildcard == rest);
 399                         return true;
 400
 401                 } else {
 402
 403                         // No global wildcard, then the match fails if there are any
 404                         // unmatched terms left
 405                         return ops.empty();
 406                 }
 407         }
 408         return inherited::match(pattern, repl_lst);
 409 }
 410
 411 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 412 {
 413         epvector *vp = subschildren(ls, lr, no_pattern);
 414         if (vp)
 415                 return ex_to<basic>(thisexpairseq(vp, overall_coeff)).basic::subs(ls, lr, no_pattern);
 416         else
 417                 return basic::subs(ls, lr, no_pattern);
 418 }
 419
 420 // protected
 421
 422 int expairseq::compare_same_type(const basic &other) const
 423 {
 424         GINAC_ASSERT(is_a<expairseq>(other));
 425         const expairseq &o = static_cast<const expairseq &>(other);
 426
 427         int cmpval;
 428
 429         // compare number of elements
 430         if (seq.size() != o.seq.size())
 431                 return (seq.size()<o.seq.size()) ? -1 : 1;
 432
 433         // compare overall_coeff
 434         cmpval = overall_coeff.compare(o.overall_coeff);
 435         if (cmpval!=0)
 436                 return cmpval;
 437
 438 #if EXPAIRSEQ_USE_HASHTAB
 439         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 440         if (hashtabsize==0) {
 441 #endif // EXPAIRSEQ_USE_HASHTAB
 442                 epvector::const_iterator cit1 = seq.begin();
 443                 epvector::const_iterator cit2 = o.seq.begin();
 444                 epvector::const_iterator last1 = seq.end();
 445                 epvector::const_iterator last2 = o.seq.end();
 446
 447                 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 448                         cmpval = (*cit1).compare(*cit2);
 449                         if (cmpval!=0) return cmpval;
 450                 }
 451
 452                 GINAC_ASSERT(cit1==last1);
 453                 GINAC_ASSERT(cit2==last2);
 454
 455                 return 0;
 456 #if EXPAIRSEQ_USE_HASHTAB
 457         }
 458
 459         // compare number of elements in each hashtab entry
 460         for (unsigned i=0; i<hashtabsize; ++i) {
 461                 unsigned cursize=hashtab[i].size();
 462                 if (cursize != o.hashtab[i].size())
 463                         return (cursize < o.hashtab[i].size()) ? -1 : 1;
 464         }
 465
 466         // compare individual (sorted) hashtab entries
 467         for (unsigned i=0; i<hashtabsize; ++i) {
 468                 unsigned sz = hashtab[i].size();
 469                 if (sz>0) {
 470                         const epplist &eppl1 = hashtab[i];
 471                         const epplist &eppl2 = o.hashtab[i];
 472                         epplist::const_iterator it1 = eppl1.begin();
 473                         epplist::const_iterator it2 = eppl2.begin();
 474                         while (it1!=eppl1.end()) {
 475                                 cmpval = (*(*it1)).compare(*(*it2));
 476                                 if (cmpval!=0)
 477                                         return cmpval;
 478                                 ++it1;
 479                                 ++it2;
 480                         }
 481                 }
 482         }
 483
 484         return 0; // equal
 485 #endif // EXPAIRSEQ_USE_HASHTAB
 486 }
 487
 488 bool expairseq::is_equal_same_type(const basic &other) const
 489 {
 490         const expairseq &o = static_cast<const expairseq &>(other);
 491
 492         // compare number of elements
 493         if (seq.size()!=o.seq.size())
 494                 return false;
 495
 496         // compare overall_coeff
 497         if (!overall_coeff.is_equal(o.overall_coeff))
 498                 return false;
 499
 500 #if EXPAIRSEQ_USE_HASHTAB
 501         // compare number of elements in each hashtab entry
 502         if (hashtabsize!=o.hashtabsize) {
 503                 std::cout << "this:" << std::endl;
 504                 print(print_tree(std::cout));
 505                 std::cout << "other:" << std::endl;
 506                 other.print(print_tree(std::cout));
 507         }
 508
 509         GINAC_ASSERT(hashtabsize==o.hashtabsize);
 510
 511         if (hashtabsize==0) {
 512 #endif // EXPAIRSEQ_USE_HASHTAB
 513                 epvector::const_iterator cit1 = seq.begin();
 514                 epvector::const_iterator cit2 = o.seq.begin();
 515                 epvector::const_iterator last1 = seq.end();
 516
 517                 while (cit1!=last1) {
 518                         if (!(*cit1).is_equal(*cit2)) return false;
 519                         ++cit1;
 520                         ++cit2;
 521                 }
 522
 523                 return true;
 524 #if EXPAIRSEQ_USE_HASHTAB
 525         }
 526
 527         for (unsigned i=0; i<hashtabsize; ++i) {
 528                 if (hashtab[i].size() != o.hashtab[i].size())
 529                         return false;
 530         }
 531
 532         // compare individual sorted hashtab entries
 533         for (unsigned i=0; i<hashtabsize; ++i) {
 534                 unsigned sz = hashtab[i].size();
 535                 if (sz>0) {
 536                         const epplist &eppl1 = hashtab[i];
 537                         const epplist &eppl2 = o.hashtab[i];
 538                         epplist::const_iterator it1 = eppl1.begin();
 539                         epplist::const_iterator it2 = eppl2.begin();
 540                         while (it1!=eppl1.end()) {
 541                                 if (!(*(*it1)).is_equal(*(*it2))) return false;
 542                                 ++it1;
 543                                 ++it2;
 544                         }
 545                 }
 546         }
 547
 548         return true;
 549 #endif // EXPAIRSEQ_USE_HASHTAB
 550 }
 551
 552 unsigned expairseq::return_type(void) const
 553 {
 554         return return_types::noncommutative_composite;
 555 }
 556
 557 unsigned expairseq::calchash(void) const
 558 {
 559         unsigned v = golden_ratio_hash(this->tinfo());
 560         epvector::const_iterator i = seq.begin(), end = seq.end();
 561         while (i != end) {
 562 #if !EXPAIRSEQ_USE_HASHTAB
 563                 v = rotate_left_31(v); // rotation would spoil commutativity
 564 #endif // EXPAIRSEQ_USE_HASHTAB
 565                 v ^= i->rest.gethash();
 566 #if !EXPAIRSEQ_USE_HASHTAB
 567                 v = rotate_left_31(v);
 568                 v ^= i->coeff.gethash();
 569 #endif // EXPAIRSEQ_USE_HASHTAB
 570                 ++i;
 571         }
 572
 573         v ^= overall_coeff.gethash();
 574         v &= 0x7FFFFFFFU;
 575
 576         // store calculated hash value only if object is already evaluated
 577         if (flags &status_flags::evaluated) {
 578                 setflag(status_flags::hash_calculated);
 579                 hashvalue = v;
 580         }
 581
 582         return v;
 583 }
 584
 585 ex expairseq::expand(unsigned options) const
 586 {
 587         epvector *vp = expandchildren(options);
 588         if (vp == NULL) {
 589                 // The terms have not changed, so it is safe to declare this expanded
 590                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 591         } else
 592                 return thisexpairseq(vp, overall_coeff);
 593 }
 594
 595 //////////
 596 // new virtual functions which can be overridden by derived classes
 597 //////////
 598
 599 // protected
 600
 601 /** Create an object of this type.
 602  *  This method works similar to a constructor.  It is useful because expairseq
 603  *  has (at least) two possible different semantics but we want to inherit
 604  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 605  *  has to create a new one of the same semantics, which cannot be done by a
 606  *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
 607  *  order for this trick to work a derived class must of course override this
 608  *  definition. */
 609 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 610 {
 611         return expairseq(v,oc);
 612 }
 613
 614 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
 615 {
 616         return expairseq(vp,oc);
 617 }
 618
 619 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 620 {
 621         c.s << "[[";
 622         p.rest.print(c, precedence());
 623         c.s << ",";
 624         p.coeff.print(c, precedence());
 625         c.s << "]]";
 626 }
 627
 628 void expairseq::printseq(const print_context & c, char delim,
 629                          unsigned this_precedence,
 630                          unsigned upper_precedence) const
 631 {
 632         if (this_precedence <= upper_precedence)
 633                 c.s << "(";
 634         epvector::const_iterator it, it_last = seq.end() - 1;
 635         for (it=seq.begin(); it!=it_last; ++it) {
 636                 printpair(c, *it, this_precedence);
 637                 c.s << delim;
 638         }
 639         printpair(c, *it, this_precedence);
 640         if (!overall_coeff.is_equal(default_overall_coeff())) {
 641                 c.s << delim;
 642                 overall_coeff.print(c, this_precedence);
 643         }
 644
 645         if (this_precedence <= upper_precedence)
 646                 c.s << ")";
 647 }
 648
 649
 650 /** Form an expair from an ex, using the corresponding semantics.
 651  *  @see expairseq::recombine_pair_to_ex() */
 652 expair expairseq::split_ex_to_pair(const ex &e) const
 653 {
 654         return expair(e,_ex1());
 655 }
 656
 657
 658 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 659                                                 const ex &c) const
 660 {
 661         GINAC_ASSERT(is_exactly_a<numeric>(c));
 662
 663         return expair(e,c);
 664 }
 665
 666
 667 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 668                                                   const ex &c) const
 669 {
 670         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 671         GINAC_ASSERT(is_exactly_a<numeric>(c));
 672
 673         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 674 }
 675
 676
 677 /** Form an ex out of an expair, using the corresponding semantics.
 678  *  @see expairseq::split_ex_to_pair() */
 679 ex expairseq::recombine_pair_to_ex(const expair &p) const
 680 {
 681         return lst(p.rest,p.coeff);
 682 }
 683
 684 bool expairseq::expair_needs_further_processing(epp it)
 685 {
 686 #if EXPAIRSEQ_USE_HASHTAB
 687         //#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
 688 #endif // EXPAIRSEQ_USE_HASHTAB
 689         return false;
 690 }
 691
 692 ex expairseq::default_overall_coeff(void) const
 693 {
 694         return _ex0();
 695 }
 696
 697 void expairseq::combine_overall_coeff(const ex &c)
 698 {
 699         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 700         GINAC_ASSERT(is_exactly_a<numeric>(c));
 701         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 702 }
 703
 704 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 705 {
 706         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 707         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 708         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 709         overall_coeff = ex_to<numeric>(overall_coeff).
 710                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 711 }
 712
 713 bool expairseq::can_make_flat(const expair &p) const
 714 {
 715         return true;
 716 }
 717
 718
 719 //////////
 720 // non-virtual functions in this class
 721 //////////
 722
 723 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 724 {
 725         exvector v;
 726         v.reserve(2);
 727         v.push_back(lh);
 728         v.push_back(rh);
 729         construct_from_exvector(v);
 730 #if EXPAIRSEQ_USE_HASHTAB
 731         GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
 732         GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
 733 #endif // EXPAIRSEQ_USE_HASHTAB
 734 }
 735
 736 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 737 {
 738         if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
 739                 if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 740 #if EXPAIRSEQ_USE_HASHTAB
 741                         unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
 742                                              ex_to<expairseq>(rh).seq.size();
 743                         if (calc_hashtabsize(totalsize)!=0) {
 744                                 construct_from_2_ex_via_exvector(lh,rh);
 745                         } else {
 746 #endif // EXPAIRSEQ_USE_HASHTAB
 747                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 748                                                            ex_to<expairseq>(rh));
 749 #if EXPAIRSEQ_USE_HASHTAB
 750                         }
 751 #endif // EXPAIRSEQ_USE_HASHTAB
 752                         return;
 753                 } else {
 754 #if EXPAIRSEQ_USE_HASHTAB
 755                         unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
 756                         if (calc_hashtabsize(totalsize)!=0) {
 757                                 construct_from_2_ex_via_exvector(lh, rh);
 758                         } else {
 759 #endif // EXPAIRSEQ_USE_HASHTAB
 760                                 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 761 #if EXPAIRSEQ_USE_HASHTAB
 762                         }
 763 #endif // EXPAIRSEQ_USE_HASHTAB
 764                         return;
 765                 }
 766         } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 767 #if EXPAIRSEQ_USE_HASHTAB
 768                 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
 769                 if (calc_hashtabsize(totalsize)!=0) {
 770                         construct_from_2_ex_via_exvector(lh,rh);
 771                 } else {
 772 #endif // EXPAIRSEQ_USE_HASHTAB
 773                         construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 774 #if EXPAIRSEQ_USE_HASHTAB
 775                 }
 776 #endif // EXPAIRSEQ_USE_HASHTAB
 777                 return;
 778         }
 779
 780 #if EXPAIRSEQ_USE_HASHTAB
 781         if (calc_hashtabsize(2)!=0) {
 782                 construct_from_2_ex_via_exvector(lh,rh);
 783                 return;
 784         }
 785         hashtabsize = 0;
 786 #endif // EXPAIRSEQ_USE_HASHTAB
 787
 788         if (is_ex_exactly_of_type(lh,numeric)) {
 789                 if (is_ex_exactly_of_type(rh,numeric)) {
 790                         combine_overall_coeff(lh);
 791                         combine_overall_coeff(rh);
 792                 } else {
 793                         combine_overall_coeff(lh);
 794                         seq.push_back(split_ex_to_pair(rh));
 795                 }
 796         } else {
 797                 if (is_ex_exactly_of_type(rh,numeric)) {
 798                         combine_overall_coeff(rh);
 799                         seq.push_back(split_ex_to_pair(lh));
 800                 } else {
 801                         expair p1 = split_ex_to_pair(lh);
 802                         expair p2 = split_ex_to_pair(rh);
 803
 804                         int cmpval = p1.rest.compare(p2.rest);
 805                         if (cmpval==0) {
 806                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 807                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 808                                         // no further processing is necessary, since this
 809                                         // one element will usually be recombined in eval()
 810                                         seq.push_back(p1);
 811                                 }
 812                         } else {
 813                                 seq.reserve(2);
 814                                 if (cmpval<0) {
 815                                         seq.push_back(p1);
 816                                         seq.push_back(p2);
 817                                 } else {
 818                                         seq.push_back(p2);
 819                                         seq.push_back(p1);
 820                                 }
 821                         }
 822                 }
 823         }
 824 }
 825
 826 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 827                                                                                    const expairseq &s2)
 828 {
 829         combine_overall_coeff(s1.overall_coeff);
 830         combine_overall_coeff(s2.overall_coeff);
 831
 832         epvector::const_iterator first1 = s1.seq.begin();
 833         epvector::const_iterator last1 = s1.seq.end();
 834         epvector::const_iterator first2 = s2.seq.begin();
 835         epvector::const_iterator last2 = s2.seq.end();
 836
 837         seq.reserve(s1.seq.size()+s2.seq.size());
 838
 839         bool needs_further_processing=false;
 840
 841         while (first1!=last1 && first2!=last2) {
 842                 int cmpval = (*first1).rest.compare((*first2).rest);
 843                 if (cmpval==0) {
 844                         // combine terms
 845                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 846                                                    add(ex_to<numeric>(first2->coeff));
 847                         if (!newcoeff.is_zero()) {
 848                                 seq.push_back(expair(first1->rest,newcoeff));
 849                                 if (expair_needs_further_processing(seq.end()-1)) {
 850                                         needs_further_processing = true;
 851                                 }
 852                         }
 853                         ++first1;
 854                         ++first2;
 855                 } else if (cmpval<0) {
 856                         seq.push_back(*first1);
 857                         ++first1;
 858                 } else {
 859                         seq.push_back(*first2);
 860                         ++first2;
 861                 }
 862         }
 863
 864         while (first1!=last1) {
 865                 seq.push_back(*first1);
 866                 ++first1;
 867         }
 868         while (first2!=last2) {
 869                 seq.push_back(*first2);
 870                 ++first2;
 871         }
 872
 873         if (needs_further_processing) {
 874                 epvector v = seq;
 875                 seq.clear();
 876                 construct_from_epvector(v);
 877         }
 878 }
 879
 880 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 881                                                                                         const ex &e)
 882 {
 883         combine_overall_coeff(s.overall_coeff);
 884         if (is_ex_exactly_of_type(e,numeric)) {
 885                 combine_overall_coeff(e);
 886                 seq = s.seq;
 887                 return;
 888         }
 889
 890         epvector::const_iterator first = s.seq.begin();
 891         epvector::const_iterator last = s.seq.end();
 892         expair p = split_ex_to_pair(e);
 893
 894         seq.reserve(s.seq.size()+1);
 895         bool p_pushed = false;
 896
 897         bool needs_further_processing=false;
 898
 899         // merge p into s.seq
 900         while (first!=last) {
 901                 int cmpval = (*first).rest.compare(p.rest);
 902                 if (cmpval==0) {
 903                         // combine terms
 904                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 905                                                    add(ex_to<numeric>(p.coeff));
 906                         if (!newcoeff.is_zero()) {
 907                                 seq.push_back(expair(first->rest,newcoeff));
 908                                 if (expair_needs_further_processing(seq.end()-1))
 909                                         needs_further_processing = true;
 910                         }
 911                         ++first;
 912                         p_pushed = true;
 913                         break;
 914                 } else if (cmpval<0) {
 915                         seq.push_back(*first);
 916                         ++first;
 917                 } else {
 918                         seq.push_back(p);
 919                         p_pushed = true;
 920                         break;
 921                 }
 922         }
 923
 924         if (p_pushed) {
 925                 // while loop exited because p was pushed, now push rest of s.seq
 926                 while (first!=last) {
 927                         seq.push_back(*first);
 928                         ++first;
 929                 }
 930         } else {
 931                 // while loop exited because s.seq was pushed, now push p
 932                 seq.push_back(p);
 933         }
 934
 935         if (needs_further_processing) {
 936                 epvector v = seq;
 937                 seq.clear();
 938                 construct_from_epvector(v);
 939         }
 940 }
 941
 942 void expairseq::construct_from_exvector(const exvector &v)
 943 {
 944         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 945         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 946         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 947         //                  (same for (+,*) -> (*,^)
 948
 949         make_flat(v);
 950 #if EXPAIRSEQ_USE_HASHTAB
 951         combine_same_terms();
 952 #else
 953         canonicalize();
 954         combine_same_terms_sorted_seq();
 955 #endif // EXPAIRSEQ_USE_HASHTAB
 956 }
 957
 958 void expairseq::construct_from_epvector(const epvector &v)
 959 {
 960         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 961         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 962         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
 963         //                  (same for (+,*) -> (*,^)
 964
 965         make_flat(v);
 966 #if EXPAIRSEQ_USE_HASHTAB
 967         combine_same_terms();
 968 #else
 969         canonicalize();
 970         combine_same_terms_sorted_seq();
 971 #endif // EXPAIRSEQ_USE_HASHTAB
 972 }
 973
 974 /** Combine this expairseq with argument exvector.
 975  *  It cares for associativity as well as for special handling of numerics. */
 976 void expairseq::make_flat(const exvector &v)
 977 {
 978         exvector::const_iterator cit;
 979
 980         // count number of operands which are of same expairseq derived type
 981         // and their cumulative number of operands
 982         int nexpairseqs = 0;
 983         int noperands = 0;
 984
 985         cit = v.begin();
 986         while (cit!=v.end()) {
 987                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
 988                         ++nexpairseqs;
 989                         noperands += ex_to<expairseq>(*cit).seq.size();
 990                 }
 991                 ++cit;
 992         }
 993
 994         // reserve seq and coeffseq which will hold all operands
 995         seq.reserve(v.size()+noperands-nexpairseqs);
 996
 997         // copy elements and split off numerical part
 998         cit = v.begin();
 999         while (cit!=v.end()) {
1000                 if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
1001                         const expairseq &subseqref = ex_to<expairseq>(*cit);
1002                         combine_overall_coeff(subseqref.overall_coeff);
1003                         epvector::const_iterator cit_s = subseqref.seq.begin();
1004                         while (cit_s!=subseqref.seq.end()) {
1005                                 seq.push_back(*cit_s);
1006                                 ++cit_s;
1007                         }
1008                 } else {
1009                         if (is_ex_exactly_of_type(*cit,numeric))
1010                                 combine_overall_coeff(*cit);
1011                         else
1012                                 seq.push_back(split_ex_to_pair(*cit));
1013                 }
1014                 ++cit;
1015         }
1016 }
1017
1018 /** Combine this expairseq with argument epvector.
1019  *  It cares for associativity as well as for special handling of numerics. */
1020 void expairseq::make_flat(const epvector &v)
1021 {
1022         epvector::const_iterator cit;
1023
1024         // count number of operands which are of same expairseq derived type
1025         // and their cumulative number of operands
1026         int nexpairseqs = 0;
1027         int noperands = 0;
1028
1029         cit = v.begin();
1030         while (cit!=v.end()) {
1031                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
1032                         ++nexpairseqs;
1033                         noperands += ex_to<expairseq>(cit->rest).seq.size();
1034                 }
1035                 ++cit;
1036         }
1037
1038         // reserve seq and coeffseq which will hold all operands
1039         seq.reserve(v.size()+noperands-nexpairseqs);
1040
1041         // copy elements and split off numerical part
1042         cit = v.begin();
1043         while (cit!=v.end()) {
1044                 if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
1045                     this->can_make_flat(*cit)) {
1046                         const expairseq &subseqref = ex_to<expairseq>(cit->rest);
1047                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1048                                                             ex_to<numeric>(cit->coeff));
1049                         epvector::const_iterator cit_s = subseqref.seq.begin();
1050                         while (cit_s!=subseqref.seq.end()) {
1051                                 seq.push_back(expair(cit_s->rest,
1052                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1053                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1054                                 //                                              (*cit).coeff));
1055                                 ++cit_s;
1056                         }
1057                 } else {
1058                         if (cit->is_canonical_numeric())
1059                                 combine_overall_coeff(cit->rest);
1060                         else
1061                                 seq.push_back(*cit);
1062                 }
1063                 ++cit;
1064         }
1065 }
1066
1067 /** Brings this expairseq into a sorted (canonical) form. */
1068 void expairseq::canonicalize(void)
1069 {
1070         sort(seq.begin(), seq.end(), expair_is_less());
1071 }
1072
1073
1074 /** Compact a presorted expairseq by combining all matching expairs to one
1075  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1076  *  instance. */
1077 void expairseq::combine_same_terms_sorted_seq(void)
1078 {
1079         bool needs_further_processing = false;
1080
1081         if (seq.size()>1) {
1082                 epvector::iterator itin1 = seq.begin();
1083                 epvector::iterator itin2 = itin1+1;
1084                 epvector::iterator itout = itin1;
1085                 epvector::iterator last = seq.end();
1086                 // must_copy will be set to true the first time some combination is
1087                 // possible from then on the sequence has changed and must be compacted
1088                 bool must_copy = false;
1089                 while (itin2!=last) {
1090                         if (itin1->rest.compare(itin2->rest)==0) {
1091                                 itin1->coeff = ex_to<numeric>(itin1->coeff).
1092                                                add_dyn(ex_to<numeric>(itin2->coeff));
1093                                 if (expair_needs_further_processing(itin1))
1094                                         needs_further_processing = true;
1095                                 must_copy = true;
1096                         } else {
1097                                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1098                                         if (must_copy)
1099                                                 *itout = *itin1;
1100                                         ++itout;
1101                                 }
1102                                 itin1 = itin2;
1103                         }
1104                         ++itin2;
1105                 }
1106                 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1107                         if (must_copy)
1108                                 *itout = *itin1;
1109                         ++itout;
1110                 }
1111                 if (itout!=last)
1112                         seq.erase(itout,last);
1113         }
1114
1115         if (needs_further_processing) {
1116                 epvector v = seq;
1117                 seq.clear();
1118                 construct_from_epvector(v);
1119         }
1120 }
1121
1122 #if EXPAIRSEQ_USE_HASHTAB
1123
1124 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1125 {
1126         unsigned size;
1127         unsigned nearest_power_of_2 = 1 << log2(sz);
1128         // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1129         //  size = nearest_power_of_2*hashtabfactor;
1130         size = nearest_power_of_2/hashtabfactor;
1131         if (size<minhashtabsize)
1132                 return 0;
1133         GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1134         // hashtabsize must be a power of 2
1135         GINAC_ASSERT((1U << log2(size))==size);
1136         return size;
1137 }
1138
1139 unsigned expairseq::calc_hashindex(const ex &e) const
1140 {
1141         // calculate hashindex
1142         unsigned hash = e.gethash();
1143         unsigned hashindex;
1144         if (is_a_numeric_hash(hash)) {
1145                 hashindex = hashmask;
1146         } else {
1147                 hashindex = hash &hashmask;
1148                 // last hashtab entry is reserved for numerics
1149                 if (hashindex==hashmask) hashindex = 0;
1150         }
1151         GINAC_ASSERT(hashindex>=0);
1152         GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1153         return hashindex;
1154 }
1155
1156 void expairseq::shrink_hashtab(void)
1157 {
1158         unsigned new_hashtabsize;
1159         while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1160                 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1161                 if (new_hashtabsize==0) {
1162                         hashtab.clear();
1163                         hashtabsize = 0;
1164                         canonicalize();
1165                         return;
1166                 }
1167
1168                 // shrink by a factor of 2
1169                 unsigned half_hashtabsize = hashtabsize/2;
1170                 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1171                         hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1172                 // special treatment for numeric hashes
1173                 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1174                 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1175                 hashtab.resize(half_hashtabsize);
1176                 hashtabsize = half_hashtabsize;
1177                 hashmask = hashtabsize-1;
1178         }
1179 }
1180
1181 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1182 {
1183         if (hashtabsize==0)
1184                 return; // nothing to do
1185
1186         // calculate hashindex of element to be deleted
1187         unsigned hashindex = calc_hashindex((*element).rest);
1188
1189         // find it in hashtab and remove it
1190         epplist &eppl = hashtab[hashindex];
1191         epplist::iterator epplit = eppl.begin();
1192         bool erased = false;
1193         while (epplit!=eppl.end()) {
1194                 if (*epplit == element) {
1195                         eppl.erase(epplit);
1196                         erased = true;
1197                         break;
1198                 }
1199                 ++epplit;
1200         }
1201         if (!erased) {
1202                 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1203                 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1204
1205                 unsigned hashindex = calc_hashindex(element->rest);
1206                 epplist &eppl = hashtab[hashindex];
1207                 epplist::iterator epplit = eppl.begin();
1208                 bool erased = false;
1209                 while (epplit!=eppl.end()) {
1210                         if (*epplit == element) {
1211                                 eppl.erase(epplit);
1212                                 erased = true;
1213                                 break;
1214                         }
1215                         ++epplit;
1216                 }
1217                 GINAC_ASSERT(erased);
1218         }
1219         GINAC_ASSERT(erased);
1220 }
1221
1222 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1223                                    epvector::iterator newpos)
1224 {
1225         GINAC_ASSERT(hashtabsize!=0);
1226
1227         // calculate hashindex of element which was moved
1228         unsigned hashindex=calc_hashindex((*newpos).rest);
1229
1230         // find it in hashtab and modify it
1231         epplist &eppl = hashtab[hashindex];
1232         epplist::iterator epplit = eppl.begin();
1233         while (epplit!=eppl.end()) {
1234                 if (*epplit == oldpos) {
1235                         *epplit = newpos;
1236                         break;
1237                 }
1238                 ++epplit;
1239         }
1240         GINAC_ASSERT(epplit!=eppl.end());
1241 }
1242
1243 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1244 {
1245         epplist::const_iterator current = eppl.begin();
1246         while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1247                 ++current;
1248         }
1249         eppl.insert(current,elem);
1250 }
1251
1252 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1253                                           epvector::iterator &last_non_zero,
1254                                           std::vector<bool> &touched,
1255                                           unsigned &number_of_zeroes)
1256 {
1257         epp current = seq.begin();
1258
1259         while (current!=first_numeric) {
1260                 if (is_ex_exactly_of_type(current->rest,numeric)) {
1261                         --first_numeric;
1262                         iter_swap(current,first_numeric);
1263                 } else {
1264                         // calculate hashindex
1265                         unsigned currenthashindex = calc_hashindex(current->rest);
1266
1267                         // test if there is already a matching expair in the hashtab-list
1268                         epplist &eppl=hashtab[currenthashindex];
1269                         epplist::iterator epplit = eppl.begin();
1270                         while (epplit!=eppl.end()) {
1271                                 if (current->rest.is_equal((*epplit)->rest))
1272                                         break;
1273                                 ++epplit;
1274                         }
1275                         if (epplit==eppl.end()) {
1276                                 // no matching expair found, append this to end of list
1277                                 sorted_insert(eppl,current);
1278                                 ++current;
1279                         } else {
1280                                 // epplit points to a matching expair, combine it with current
1281                                 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1282                                                    add_dyn(ex_to<numeric>(current->coeff));
1283
1284                                 // move obsolete current expair to end by swapping with last_non_zero element
1285                                 // if this was a numeric, it is swapped with the expair before first_numeric
1286                                 iter_swap(current,last_non_zero);
1287                                 --first_numeric;
1288                                 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1289                                 --last_non_zero;
1290                                 ++number_of_zeroes;
1291                                 // test if combined term has coeff 0 and can be removed is done later
1292                                 touched[(*epplit)-seq.begin()] = true;
1293                         }
1294                 }
1295         }
1296 }
1297
1298 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1299                                    epvector::iterator &last_non_zero,
1300                                    std::vector<bool> &touched,
1301                                    unsigned &number_of_zeroes)
1302 {
1303         // move terms with coeff 0 to end and remove them from hashtab
1304         // check only those elements which have been touched
1305         epp current = seq.begin();
1306         unsigned i = 0;
1307         while (current!=first_numeric) {
1308                 if (!touched[i]) {
1309                         ++current;
1310                         ++i;
1311                 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1312                         ++current;
1313                         ++i;
1314                 } else {
1315                         remove_hashtab_entry(current);
1316
1317                         // move element to the end, unless it is already at the end
1318                         if (current!=last_non_zero) {
1319                                 iter_swap(current,last_non_zero);
1320                                 --first_numeric;
1321                                 bool numeric_swapped = first_numeric!=last_non_zero;
1322                                 if (numeric_swapped)
1323                                         iter_swap(first_numeric,current);
1324                                 epvector::iterator changed_entry;
1325
1326                                 if (numeric_swapped)
1327                                         changed_entry = first_numeric;
1328                                 else
1329                                         changed_entry = last_non_zero;
1330
1331                                 --last_non_zero;
1332                                 ++number_of_zeroes;
1333
1334                                 if (first_numeric!=current) {
1335
1336                                         // change entry in hashtab which referred to first_numeric or last_non_zero to current
1337                                         move_hashtab_entry(changed_entry,current);
1338                                         touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1339                                 }
1340                         } else {
1341                                 --first_numeric;
1342                                 --last_non_zero;
1343                                 ++number_of_zeroes;
1344                         }
1345                 }
1346         }
1347         GINAC_ASSERT(i==current-seq.begin());
1348 }
1349
1350 /** True if one of the coeffs vanishes, otherwise false.
1351  *  This would be an invariant violation, so this should only be used for
1352  *  debugging purposes. */
1353 bool expairseq::has_coeff_0(void) const
1354 {
1355         epvector::const_iterator i = seq.begin(), end = seq.end();
1356         while (i != end) {
1357                 if (i->coeff.is_zero())
1358                         return true;
1359                 ++i;
1360         }
1361         return false;
1362 }
1363
1364 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1365                                                                                 epvector::const_iterator last_non_zero)
1366 {
1367         if (first_numeric == seq.end()) return; // no numerics
1368
1369         epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1370         while (current != last) {
1371                 sorted_insert(hashtab[hashmask], current);
1372                 ++current;
1373         }
1374 }
1375
1376 void expairseq::combine_same_terms(void)
1377 {
1378         // combine same terms, drop term with coeff 0, move numerics to end
1379
1380         // calculate size of hashtab
1381         hashtabsize = calc_hashtabsize(seq.size());
1382
1383         // hashtabsize is a power of 2
1384         hashmask = hashtabsize-1;
1385
1386         // allocate hashtab
1387         hashtab.clear();
1388         hashtab.resize(hashtabsize);
1389
1390         if (hashtabsize==0) {
1391                 canonicalize();
1392                 combine_same_terms_sorted_seq();
1393                 GINAC_ASSERT(!has_coeff_0());
1394                 return;
1395         }
1396
1397         // iterate through seq, move numerics to end,
1398         // fill hashtab and combine same terms
1399         epvector::iterator first_numeric = seq.end();
1400         epvector::iterator last_non_zero = seq.end()-1;
1401
1402         unsigned num = seq.size();
1403         std::vector<bool> touched(num);
1404
1405         unsigned number_of_zeroes = 0;
1406
1407         GINAC_ASSERT(!has_coeff_0());
1408         build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1409
1410         // there should not be any terms with coeff 0 from the beginning,
1411         // so it should be safe to skip this step
1412         if (number_of_zeroes!=0) {
1413                 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1414         }
1415
1416         add_numerics_to_hashtab(first_numeric,last_non_zero);
1417
1418         // pop zero elements
1419         for (unsigned i=0; i<number_of_zeroes; ++i) {
1420                 seq.pop_back();
1421         }
1422
1423         // shrink hashtabsize to calculated value
1424         GINAC_ASSERT(!has_coeff_0());
1425
1426         shrink_hashtab();
1427
1428         GINAC_ASSERT(!has_coeff_0());
1429 }
1430
1431 #endif // EXPAIRSEQ_USE_HASHTAB
1432
1433 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1434  *  debugging or in assertions since being sorted is an invariance. */
1435 bool expairseq::is_canonical() const
1436 {
1437         if (seq.size() <= 1)
1438                 return 1;
1439
1440 #if EXPAIRSEQ_USE_HASHTAB
1441         if (hashtabsize > 0) return 1; // not canoncalized
1442 #endif // EXPAIRSEQ_USE_HASHTAB
1443
1444         epvector::const_iterator it = seq.begin(), itend = seq.end();
1445         epvector::const_iterator it_last = it;
1446         for (++it; it!=itend; it_last=it, ++it) {
1447                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1448                         if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1449                                 !is_ex_exactly_of_type(it->rest,numeric)) {
1450                                 // double test makes it easier to set a breakpoint...
1451                                 if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
1452                                         !is_ex_exactly_of_type(it->rest,numeric)) {
1453                                         printpair(std::clog, *it_last, 0);
1454                                         std::clog << ">";
1455                                         printpair(std::clog, *it, 0);
1456                                         std::clog << "\n";
1457                                         std::clog << "pair1:" << std::endl;
1458                                         it_last->rest.print(print_tree(std::clog));
1459                                         it_last->coeff.print(print_tree(std::clog));
1460                                         std::clog << "pair2:" << std::endl;
1461                                         it->rest.print(print_tree(std::clog));
1462                                         it->coeff.print(print_tree(std::clog));
1463                                         return 0;
1464                                 }
1465                         }
1466                 }
1467         }
1468         return 1;
1469 }
1470
1471
1472 /** Member-wise expand the expairs in this sequence.
1473  *
1474  *  @see expairseq::expand()
1475  *  @return pointer to epvector containing expanded pairs or zero pointer,
1476  *  if no members were changed. */
1477 epvector * expairseq::expandchildren(unsigned options) const
1478 {
1479         epvector::const_iterator last = seq.end();
1480         epvector::const_iterator cit = seq.begin();
1481         while (cit!=last) {
1482                 const ex &expanded_ex = cit->rest.expand(options);
1483                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1484
1485                         // something changed, copy seq, eval and return it
1486                         epvector *s = new epvector;
1487                         s->reserve(seq.size());
1488
1489                         // copy parts of seq which are known not to have changed
1490                         epvector::const_iterator cit2 = seq.begin();
1491                         while (cit2!=cit) {
1492                                 s->push_back(*cit2);
1493                                 ++cit2;
1494                         }
1495                         // copy first changed element
1496                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1497                                                                    cit2->coeff));
1498                         ++cit2;
1499                         // copy rest
1500                         while (cit2!=last) {
1501                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1502                                                                            cit2->coeff));
1503                                 ++cit2;
1504                         }
1505                         return s;
1506                 }
1507                 ++cit;
1508         }
1509
1510         return 0; // signalling nothing has changed
1511 }
1512
1513
1514 /** Member-wise evaluate the expairs in this sequence.
1515  *
1516  *  @see expairseq::eval()
1517  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1518  *  if no members were changed. */
1519 epvector * expairseq::evalchildren(int level) const
1520 {
1521         // returns a NULL pointer if nothing had to be evaluated
1522         // returns a pointer to a newly created epvector otherwise
1523         // (which has to be deleted somewhere else)
1524
1525         if (level==1)
1526                 return 0;
1527
1528         if (level == -max_recursion_level)
1529                 throw(std::runtime_error("max recursion level reached"));
1530
1531         --level;
1532         epvector::const_iterator last = seq.end();
1533         epvector::const_iterator cit = seq.begin();
1534         while (cit!=last) {
1535                 const ex &evaled_ex = cit->rest.eval(level);
1536                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1537
1538                         // something changed, copy seq, eval and return it
1539                         epvector *s = new epvector;
1540                         s->reserve(seq.size());
1541
1542                         // copy parts of seq which are known not to have changed
1543                         epvector::const_iterator cit2=seq.begin();
1544                         while (cit2!=cit) {
1545                                 s->push_back(*cit2);
1546                                 ++cit2;
1547                         }
1548                         // copy first changed element
1549                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1550                                                                    cit2->coeff));
1551                         ++cit2;
1552                         // copy rest
1553                         while (cit2!=last) {
1554                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1555                                                                            cit2->coeff));
1556                                 ++cit2;
1557                         }
1558                         return s;
1559                 }
1560                 ++cit;
1561         }
1562
1563         return 0; // signalling nothing has changed
1564 }
1565
1566
1567 /** Member-wise substitute in this sequence.
1568  *
1569  *  @see expairseq::subs()
1570  *  @return pointer to epvector containing pairs after application of subs,
1571  *    or NULL pointer if no members were changed. */
1572 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1573 {
1574         GINAC_ASSERT(ls.nops()==lr.nops());
1575
1576         // The substitution is "complex" when any of the objects to be substituted
1577         // is a product or power. In this case we have to recombine the pairs
1578         // because the numeric coefficients may be part of the search pattern.
1579         bool complex_subs = false;
1580         for (unsigned i=0; i<ls.nops(); ++i)
1581                 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1582                         complex_subs = true;
1583                         break;
1584                 }
1585
1586         if (complex_subs) {
1587
1588                 // Substitute in the recombined pairs
1589                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1590                 while (cit != last) {
1591
1592                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1593                         const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1594                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1595
1596                                 // Something changed, copy seq, subs and return it
1597                                 epvector *s = new epvector;
1598                                 s->reserve(seq.size());
1599
1600                                 // Copy parts of seq which are known not to have changed
1601                                 s->insert(s->begin(), seq.begin(), cit);
1602
1603                                 // Copy first changed element
1604                                 s->push_back(split_ex_to_pair(subsed_ex));
1605                                 ++cit;
1606
1607                                 // Copy rest
1608                                 while (cit != last) {
1609                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1610                                         ++cit;
1611                                 }
1612                                 return s;
1613                         }
1614
1615                         ++cit;
1616                 }
1617
1618         } else {
1619
1620                 // Substitute only in the "rest" part of the pairs
1621                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1622                 while (cit != last) {
1623
1624                         const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1625                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1626
1627                                 // Something changed, copy seq, subs and return it
1628                                 epvector *s = new epvector;
1629                                 s->reserve(seq.size());
1630
1631                                 // Copy parts of seq which are known not to have changed
1632                                 s->insert(s->begin(), seq.begin(), cit);
1633
1634                                 // Copy first changed element
1635                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1636                                 ++cit;
1637
1638                                 // Copy rest
1639                                 while (cit != last) {
1640                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1641                                                                                    cit->coeff));
1642                                         ++cit;
1643                                 }
1644                                 return s;
1645                         }
1646
1647                         ++cit;
1648                 }
1649         }
1650
1651         // Nothing has changed
1652         return NULL;
1653 }
1654
1655 //////////
1656 // static member variables
1657 //////////
1658
1659 #if EXPAIRSEQ_USE_HASHTAB
1660 unsigned expairseq::maxhashtabsize = 0x4000000U;
1661 unsigned expairseq::minhashtabsize = 0x1000U;
1662 unsigned expairseq::hashtabfactor = 1;
1663 #endif // EXPAIRSEQ_USE_HASHTAB
1664
1665 } // namespace GiNaC