1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
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.
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.
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
27 #include "expairseq.h"
29 #include "relational.h"
35 #if EXPAIRSEQ_USE_HASHTAB
37 #endif // EXPAIRSEQ_USE_HASHTAB
41 GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
50 bool operator()(const epp &lh, const epp &rh) const
52 return (*lh).is_less(*rh);
57 // default ctor, dtor, copy ctor assignment operator and helpers
62 expairseq::expairseq(const expairseq &other)
64 debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
68 const expairseq &expairseq::operator=(const expairseq &other)
70 debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
80 /** For use by copy ctor and assignment operator. */
81 void expairseq::copy(const expairseq &other)
83 inherited::copy(other);
85 overall_coeff = other.overall_coeff;
86 #if EXPAIRSEQ_USE_HASHTAB
88 hashtabsize = other.hashtabsize;
90 hashmask = other.hashmask;
91 hashtab.resize(hashtabsize);
92 epvector::const_iterator osb = other.seq.begin();
93 for (unsigned i=0; i<hashtabsize; ++i) {
95 for (epplist::const_iterator cit=other.hashtab[i].begin();
96 cit!=other.hashtab[i].end(); ++cit) {
97 hashtab[i].push_back(seq.begin()+((*cit)-osb));
103 #endif // EXPAIRSEQ_USE_HASHTAB
106 DEFAULT_DESTROY(expairseq)
112 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
114 debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
115 construct_from_2_ex(lh,rh);
116 GINAC_ASSERT(is_canonical());
119 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
121 debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
122 construct_from_exvector(v);
123 GINAC_ASSERT(is_canonical());
126 expairseq::expairseq(const epvector &v, const ex &oc)
127 : inherited(TINFO_expairseq), overall_coeff(oc)
129 debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
130 construct_from_epvector(v);
131 GINAC_ASSERT(is_canonical());
134 expairseq::expairseq(epvector *vp, const ex &oc)
135 : inherited(TINFO_expairseq), overall_coeff(oc)
137 debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
139 construct_from_epvector(*vp);
141 GINAC_ASSERT(is_canonical());
148 expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
149 #if EXPAIRSEQ_USE_HASHTAB
153 debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
154 for (unsigned int i=0; true; i++) {
157 if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
158 seq.push_back(expair(rest, coeff));
162 n.find_ex("overall_coeff", overall_coeff, sym_lst);
165 void expairseq::archive(archive_node &n) const
167 inherited::archive(n);
168 epvector::const_iterator i = seq.begin(), iend = seq.end();
170 n.add_ex("rest", i->rest);
171 n.add_ex("coeff", i->coeff);
174 n.add_ex("overall_coeff", overall_coeff);
177 DEFAULT_UNARCHIVE(expairseq)
180 // functions overriding virtual functions from bases classes
185 basic *expairseq::duplicate() const
187 debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
188 return new expairseq(*this);
191 void expairseq::print(const print_context & c, unsigned level) const
193 debugmsg("expairseq print",LOGLEVEL_PRINT);
195 if (is_of_type(c, print_tree)) {
197 unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
199 c.s << std::string(level, ' ') << class_name()
200 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
201 << ", nops=" << nops()
203 for (unsigned i=0; i<seq.size(); ++i) {
204 seq[i].rest.print(c, level + delta_indent);
205 seq[i].coeff.print(c, level + delta_indent);
206 if (i != seq.size()-1)
207 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
209 if (!overall_coeff.is_equal(default_overall_coeff())) {
210 c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
211 << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
212 overall_coeff.print(c, level + delta_indent);
214 c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
215 #if EXPAIRSEQ_USE_HASHTAB
216 c.s << std::string(level + delta_indent,' ')
217 << "hashtab size " << hashtabsize << std::endl;
218 if (hashtabsize == 0) return;
220 unsigned count[MAXCOUNT+1];
221 for (int i=0; i<MAXCOUNT+1; ++i)
223 unsigned this_bin_fill;
224 unsigned cum_fill_sq = 0;
225 unsigned cum_fill = 0;
226 for (unsigned i=0; i<hashtabsize; ++i) {
228 if (hashtab[i].size() > 0) {
229 c.s << std::string(level + delta_indent, ' ')
230 << "bin " << i << " with entries ";
231 for (epplist::const_iterator it=hashtab[i].begin();
232 it!=hashtab[i].end(); ++it) {
233 c.s << *it-seq.begin() << " ";
237 cum_fill += this_bin_fill;
238 cum_fill_sq += this_bin_fill*this_bin_fill;
240 if (this_bin_fill<MAXCOUNT)
241 ++count[this_bin_fill];
247 double lambda = (1.0*seq.size()) / hashtabsize;
248 for (int k=0; k<MAXCOUNT; ++k) {
251 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
253 c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
254 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
255 << int(prob*1000)/10.0 << ")" << std::endl;
257 c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
258 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
259 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
261 c.s << std::string(level + delta_indent, ' ') << "variance: "
262 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
264 c.s << std::string(level + delta_indent, ' ') << "average fill: "
265 << (1.0*cum_fill)/hashtabsize
266 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
267 #endif // EXPAIRSEQ_USE_HASHTAB
271 printseq(c, ',', precedence(), level);
276 bool expairseq::info(unsigned inf) const
278 return inherited::info(inf);
281 unsigned expairseq::nops() const
283 if (overall_coeff.is_equal(default_overall_coeff()))
289 ex expairseq::op(int i) const
291 if (unsigned(i)<seq.size())
292 return recombine_pair_to_ex(seq[i]);
293 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
294 return overall_coeff;
297 ex &expairseq::let_op(int i)
299 throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
302 ex expairseq::map(map_function & f) const
304 epvector *v = new epvector;
305 v->reserve(seq.size());
307 epvector::const_iterator cit = seq.begin(), last = seq.end();
308 while (cit != last) {
309 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
313 return thisexpairseq(v, f(overall_coeff));
316 ex expairseq::eval(int level) const
318 if ((level==1) && (flags &status_flags::evaluated))
321 epvector *vp = evalchildren(level);
325 return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
328 bool expairseq::match(const ex & pattern, lst & repl_lst) const
330 // This differs from basic::match() because we want "a+b+c+d" to
331 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
333 if (tinfo() == pattern.bp->tinfo()) {
335 // Check whether global wildcard (one that matches the "rest of the
336 // expression", like "*" above) is present
337 bool has_global_wildcard = false;
339 for (unsigned int i=0; i<pattern.nops(); i++) {
340 if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
341 has_global_wildcard = true;
342 global_wildcard = pattern.op(i);
347 // Unfortunately, this is an O(N^2) operation because we can't
348 // sort the pattern in a useful way...
353 for (unsigned i=0; i<nops(); i++)
354 ops.push_back(op(i));
356 // Now, for every term of the pattern, look for a matching term in
357 // the expression and remove the match
358 for (unsigned i=0; i<pattern.nops(); i++) {
359 ex p = pattern.op(i);
360 if (has_global_wildcard && p.is_equal(global_wildcard))
362 exvector::iterator it = ops.begin(), itend = ops.end();
363 while (it != itend) {
364 if (it->match(p, repl_lst)) {
370 return false; // no match found
374 if (has_global_wildcard) {
376 // Assign all the remaining terms to the global wildcard (unless
377 // it has already been matched before, in which case the matches
379 epvector *vp = new epvector();
380 vp->reserve(ops.size());
381 for (unsigned i=0; i<ops.size(); i++)
382 vp->push_back(split_ex_to_pair(ops[i]));
383 ex rest = thisexpairseq(vp, default_overall_coeff());
384 for (unsigned i=0; i<repl_lst.nops(); i++) {
385 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
386 return rest.is_equal(*repl_lst.op(i).op(1).bp);
388 repl_lst.append(global_wildcard == rest);
393 // No global wildcard, then the match fails if there are any
394 // unmatched terms left
398 return inherited::match(pattern, repl_lst);
401 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
403 epvector *vp = subschildren(ls, lr, no_pattern);
405 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
407 return basic::subs(ls, lr, no_pattern);
412 int expairseq::compare_same_type(const basic &other) const
414 GINAC_ASSERT(is_of_type(other, expairseq));
415 const expairseq &o = static_cast<const expairseq &>(other);
419 // compare number of elements
420 if (seq.size() != o.seq.size())
421 return (seq.size()<o.seq.size()) ? -1 : 1;
423 // compare overall_coeff
424 cmpval = overall_coeff.compare(o.overall_coeff);
428 #if EXPAIRSEQ_USE_HASHTAB
429 GINAC_ASSERT(hashtabsize==o.hashtabsize);
430 if (hashtabsize==0) {
431 #endif // EXPAIRSEQ_USE_HASHTAB
432 epvector::const_iterator cit1 = seq.begin();
433 epvector::const_iterator cit2 = o.seq.begin();
434 epvector::const_iterator last1 = seq.end();
435 epvector::const_iterator last2 = o.seq.end();
437 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
438 cmpval = (*cit1).compare(*cit2);
439 if (cmpval!=0) return cmpval;
442 GINAC_ASSERT(cit1==last1);
443 GINAC_ASSERT(cit2==last2);
446 #if EXPAIRSEQ_USE_HASHTAB
449 // compare number of elements in each hashtab entry
450 for (unsigned i=0; i<hashtabsize; ++i) {
451 unsigned cursize=hashtab[i].size();
452 if (cursize != o.hashtab[i].size())
453 return (cursize < o.hashtab[i].size()) ? -1 : 1;
456 // compare individual (sorted) hashtab entries
457 for (unsigned i=0; i<hashtabsize; ++i) {
458 unsigned sz = hashtab[i].size();
460 const epplist &eppl1 = hashtab[i];
461 const epplist &eppl2 = o.hashtab[i];
462 epplist::const_iterator it1 = eppl1.begin();
463 epplist::const_iterator it2 = eppl2.begin();
464 while (it1!=eppl1.end()) {
465 cmpval = (*(*it1)).compare(*(*it2));
475 #endif // EXPAIRSEQ_USE_HASHTAB
478 bool expairseq::is_equal_same_type(const basic &other) const
480 const expairseq &o = static_cast<const expairseq &>(other);
482 // compare number of elements
483 if (seq.size()!=o.seq.size())
486 // compare overall_coeff
487 if (!overall_coeff.is_equal(o.overall_coeff))
490 #if EXPAIRSEQ_USE_HASHTAB
491 // compare number of elements in each hashtab entry
492 if (hashtabsize!=o.hashtabsize) {
493 std::cout << "this:" << std::endl;
494 print(print_tree(std::cout));
495 std::cout << "other:" << std::endl;
496 other.print(print_tree(std::cout));
499 GINAC_ASSERT(hashtabsize==o.hashtabsize);
501 if (hashtabsize==0) {
502 #endif // EXPAIRSEQ_USE_HASHTAB
503 epvector::const_iterator cit1 = seq.begin();
504 epvector::const_iterator cit2 = o.seq.begin();
505 epvector::const_iterator last1 = seq.end();
507 while (cit1!=last1) {
508 if (!(*cit1).is_equal(*cit2)) return false;
514 #if EXPAIRSEQ_USE_HASHTAB
517 for (unsigned i=0; i<hashtabsize; ++i) {
518 if (hashtab[i].size() != o.hashtab[i].size())
522 // compare individual sorted hashtab entries
523 for (unsigned i=0; i<hashtabsize; ++i) {
524 unsigned sz = hashtab[i].size();
526 const epplist &eppl1 = hashtab[i];
527 const epplist &eppl2 = o.hashtab[i];
528 epplist::const_iterator it1 = eppl1.begin();
529 epplist::const_iterator it2 = eppl2.begin();
530 while (it1!=eppl1.end()) {
531 if (!(*(*it1)).is_equal(*(*it2))) return false;
539 #endif // EXPAIRSEQ_USE_HASHTAB
542 unsigned expairseq::return_type(void) const
544 return return_types::noncommutative_composite;
547 unsigned expairseq::calchash(void) const
549 unsigned v = golden_ratio_hash(tinfo());
550 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
551 #if !EXPAIRSEQ_USE_HASHTAB
552 v = rotate_left_31(v); // rotation would spoil commutativity
553 #endif // EXPAIRSEQ_USE_HASHTAB
554 v ^= cit->rest.gethash();
555 #if !EXPAIRSEQ_USE_HASHTAB
556 v = rotate_left_31(v);
557 v ^= cit->coeff.gethash();
558 #endif // EXPAIRSEQ_USE_HASHTAB
561 v ^= overall_coeff.gethash();
564 // store calculated hash value only if object is already evaluated
565 if (flags &status_flags::evaluated) {
566 setflag(status_flags::hash_calculated);
573 ex expairseq::expand(unsigned options) const
575 epvector *vp = expandchildren(options);
577 // The terms have not changed, so it is safe to declare this expanded
578 return this->setflag(status_flags::expanded);
580 return thisexpairseq(vp, overall_coeff);
584 // new virtual functions which can be overridden by derived classes
589 /** Create an object of this type.
590 * This method works similar to a constructor. It is useful because expairseq
591 * has (at least) two possible different semantics but we want to inherit
592 * methods thus avoiding code duplication. Sometimes a method in expairseq
593 * has to create a new one of the same semantics, which cannot be done by a
594 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
595 * order for this trick to work a derived class must of course override this
597 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
599 return expairseq(v,oc);
602 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
604 return expairseq(vp,oc);
607 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
610 p.rest.bp->print(c, precedence());
612 p.coeff.bp->print(c, precedence());
616 void expairseq::printseq(const print_context & c, char delim,
617 unsigned this_precedence,
618 unsigned upper_precedence) const
620 if (this_precedence <= upper_precedence)
622 epvector::const_iterator it, it_last = seq.end() - 1;
623 for (it=seq.begin(); it!=it_last; ++it) {
624 printpair(c, *it, this_precedence);
627 printpair(c, *it, this_precedence);
628 if (!overall_coeff.is_equal(default_overall_coeff())) {
630 overall_coeff.print(c, this_precedence);
633 if (this_precedence <= upper_precedence)
638 /** Form an expair from an ex, using the corresponding semantics.
639 * @see expairseq::recombine_pair_to_ex() */
640 expair expairseq::split_ex_to_pair(const ex &e) const
642 return expair(e,_ex1());
646 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
649 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
655 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
658 GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
659 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
661 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
665 /** Form an ex out of an expair, using the corresponding semantics.
666 * @see expairseq::split_ex_to_pair() */
667 ex expairseq::recombine_pair_to_ex(const expair &p) const
669 return lst(p.rest,p.coeff);
672 bool expairseq::expair_needs_further_processing(epp it)
674 #if EXPAIRSEQ_USE_HASHTAB
675 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
676 #endif // EXPAIRSEQ_USE_HASHTAB
680 ex expairseq::default_overall_coeff(void) const
685 void expairseq::combine_overall_coeff(const ex &c)
687 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
688 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
689 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
692 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
694 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
695 GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
696 GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
697 overall_coeff = ex_to<numeric>(overall_coeff).
698 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
701 bool expairseq::can_make_flat(const expair &p) const
708 // non-virtual functions in this class
711 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
717 construct_from_exvector(v);
718 #if EXPAIRSEQ_USE_HASHTAB
719 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
720 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
721 #endif // EXPAIRSEQ_USE_HASHTAB
724 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
726 if (lh.bp->tinfo()==tinfo()) {
727 if (rh.bp->tinfo()==tinfo()) {
728 #if EXPAIRSEQ_USE_HASHTAB
729 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
730 ex_to<expairseq>(rh).seq.size();
731 if (calc_hashtabsize(totalsize)!=0) {
732 construct_from_2_ex_via_exvector(lh,rh);
734 #endif // EXPAIRSEQ_USE_HASHTAB
735 construct_from_2_expairseq(ex_to<expairseq>(lh),
736 ex_to<expairseq>(rh));
737 #if EXPAIRSEQ_USE_HASHTAB
739 #endif // EXPAIRSEQ_USE_HASHTAB
742 #if EXPAIRSEQ_USE_HASHTAB
743 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
744 if (calc_hashtabsize(totalsize)!=0) {
745 construct_from_2_ex_via_exvector(lh, rh);
747 #endif // EXPAIRSEQ_USE_HASHTAB
748 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
749 #if EXPAIRSEQ_USE_HASHTAB
751 #endif // EXPAIRSEQ_USE_HASHTAB
754 } else if (rh.bp->tinfo()==tinfo()) {
755 #if EXPAIRSEQ_USE_HASHTAB
756 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
757 if (calc_hashtabsize(totalsize)!=0) {
758 construct_from_2_ex_via_exvector(lh,rh);
760 #endif // EXPAIRSEQ_USE_HASHTAB
761 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
762 #if EXPAIRSEQ_USE_HASHTAB
764 #endif // EXPAIRSEQ_USE_HASHTAB
768 #if EXPAIRSEQ_USE_HASHTAB
769 if (calc_hashtabsize(2)!=0) {
770 construct_from_2_ex_via_exvector(lh,rh);
774 #endif // EXPAIRSEQ_USE_HASHTAB
776 if (is_ex_exactly_of_type(lh,numeric)) {
777 if (is_ex_exactly_of_type(rh,numeric)) {
778 combine_overall_coeff(lh);
779 combine_overall_coeff(rh);
781 combine_overall_coeff(lh);
782 seq.push_back(split_ex_to_pair(rh));
785 if (is_ex_exactly_of_type(rh,numeric)) {
786 combine_overall_coeff(rh);
787 seq.push_back(split_ex_to_pair(lh));
789 expair p1 = split_ex_to_pair(lh);
790 expair p2 = split_ex_to_pair(rh);
792 int cmpval = p1.rest.compare(p2.rest);
794 p1.coeff=ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
795 if (!ex_to<numeric>(p1.coeff).is_zero()) {
796 // no further processing is necessary, since this
797 // one element will usually be recombined in eval()
814 void expairseq::construct_from_2_expairseq(const expairseq &s1,
817 combine_overall_coeff(s1.overall_coeff);
818 combine_overall_coeff(s2.overall_coeff);
820 epvector::const_iterator first1 = s1.seq.begin();
821 epvector::const_iterator last1 = s1.seq.end();
822 epvector::const_iterator first2 = s2.seq.begin();
823 epvector::const_iterator last2 = s2.seq.end();
825 seq.reserve(s1.seq.size()+s2.seq.size());
827 bool needs_further_processing=false;
829 while (first1!=last1 && first2!=last2) {
830 int cmpval = (*first1).rest.compare((*first2).rest);
833 const numeric &newcoeff = ex_to<numeric>((*first1).coeff).
834 add(ex_to<numeric>((*first2).coeff));
835 if (!newcoeff.is_zero()) {
836 seq.push_back(expair((*first1).rest,newcoeff));
837 if (expair_needs_further_processing(seq.end()-1)) {
838 needs_further_processing = true;
843 } else if (cmpval<0) {
844 seq.push_back(*first1);
847 seq.push_back(*first2);
852 while (first1!=last1) {
853 seq.push_back(*first1);
856 while (first2!=last2) {
857 seq.push_back(*first2);
861 if (needs_further_processing) {
864 construct_from_epvector(v);
868 void expairseq::construct_from_expairseq_ex(const expairseq &s,
871 combine_overall_coeff(s.overall_coeff);
872 if (is_ex_exactly_of_type(e,numeric)) {
873 combine_overall_coeff(e);
878 epvector::const_iterator first = s.seq.begin();
879 epvector::const_iterator last = s.seq.end();
880 expair p = split_ex_to_pair(e);
882 seq.reserve(s.seq.size()+1);
883 bool p_pushed = false;
885 bool needs_further_processing=false;
887 // merge p into s.seq
888 while (first!=last) {
889 int cmpval=(*first).rest.compare(p.rest);
892 const numeric &newcoeff = ex_to<numeric>((*first).coeff).
893 add(ex_to<numeric>(p.coeff));
894 if (!newcoeff.is_zero()) {
895 seq.push_back(expair((*first).rest,newcoeff));
896 if (expair_needs_further_processing(seq.end()-1)) {
897 needs_further_processing = true;
903 } else if (cmpval<0) {
904 seq.push_back(*first);
914 // while loop exited because p was pushed, now push rest of s.seq
915 while (first!=last) {
916 seq.push_back(*first);
920 // while loop exited because s.seq was pushed, now push p
924 if (needs_further_processing) {
927 construct_from_epvector(v);
931 void expairseq::construct_from_exvector(const exvector &v)
933 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
934 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
935 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
936 // (same for (+,*) -> (*,^)
939 #if EXPAIRSEQ_USE_HASHTAB
940 combine_same_terms();
943 combine_same_terms_sorted_seq();
944 #endif // EXPAIRSEQ_USE_HASHTAB
948 void expairseq::construct_from_epvector(const epvector &v)
950 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
951 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
952 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
953 // (same for (+,*) -> (*,^)
956 #if EXPAIRSEQ_USE_HASHTAB
957 combine_same_terms();
960 combine_same_terms_sorted_seq();
961 #endif // EXPAIRSEQ_USE_HASHTAB
965 /** Combine this expairseq with argument exvector.
966 * It cares for associativity as well as for special handling of numerics. */
967 void expairseq::make_flat(const exvector &v)
969 exvector::const_iterator cit;
971 // count number of operands which are of same expairseq derived type
972 // and their cumulative number of operands
977 while (cit!=v.end()) {
978 if (cit->bp->tinfo()==this->tinfo()) {
980 noperands += ex_to<expairseq>(*cit).seq.size();
985 // reserve seq and coeffseq which will hold all operands
986 seq.reserve(v.size()+noperands-nexpairseqs);
988 // copy elements and split off numerical part
990 while (cit!=v.end()) {
991 if (cit->bp->tinfo()==this->tinfo()) {
992 const expairseq &subseqref = ex_to<expairseq>(*cit);
993 combine_overall_coeff(subseqref.overall_coeff);
994 epvector::const_iterator cit_s = subseqref.seq.begin();
995 while (cit_s!=subseqref.seq.end()) {
996 seq.push_back(*cit_s);
1000 if (is_ex_exactly_of_type(*cit,numeric))
1001 combine_overall_coeff(*cit);
1003 seq.push_back(split_ex_to_pair(*cit));
1011 /** Combine this expairseq with argument epvector.
1012 * It cares for associativity as well as for special handling of numerics. */
1013 void expairseq::make_flat(const epvector &v)
1015 epvector::const_iterator cit;
1017 // count number of operands which are of same expairseq derived type
1018 // and their cumulative number of operands
1019 int nexpairseqs = 0;
1023 while (cit!=v.end()) {
1024 if (cit->rest.bp->tinfo()==this->tinfo()) {
1026 noperands += ex_to<expairseq>((*cit).rest).seq.size();
1031 // reserve seq and coeffseq which will hold all operands
1032 seq.reserve(v.size()+noperands-nexpairseqs);
1034 // copy elements and split off numerical part
1036 while (cit!=v.end()) {
1037 if (cit->rest.bp->tinfo()==this->tinfo() &&
1038 this->can_make_flat(*cit)) {
1039 const expairseq &subseqref = ex_to<expairseq>((*cit).rest);
1040 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1041 ex_to<numeric>((*cit).coeff));
1042 epvector::const_iterator cit_s = subseqref.seq.begin();
1043 while (cit_s!=subseqref.seq.end()) {
1044 seq.push_back(expair((*cit_s).rest,
1045 ex_to<numeric>((*cit_s).coeff).mul_dyn(ex_to<numeric>((*cit).coeff))));
1046 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1051 if (cit->is_canonical_numeric())
1052 combine_overall_coeff(cit->rest);
1054 seq.push_back(*cit);
1061 /** Brings this expairseq into a sorted (canonical) form. */
1062 void expairseq::canonicalize(void)
1065 sort(seq.begin(),seq.end(),expair_is_less());
1070 /** Compact a presorted expairseq by combining all matching expairs to one
1071 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1073 void expairseq::combine_same_terms_sorted_seq(void)
1075 bool needs_further_processing = false;
1078 epvector::iterator itin1 = seq.begin();
1079 epvector::iterator itin2 = itin1+1;
1080 epvector::iterator itout = itin1;
1081 epvector::iterator last = seq.end();
1082 // must_copy will be set to true the first time some combination is
1083 // possible from then on the sequence has changed and must be compacted
1084 bool must_copy = false;
1085 while (itin2!=last) {
1086 if ((*itin1).rest.compare((*itin2).rest)==0) {
1087 (*itin1).coeff = ex_to<numeric>((*itin1).coeff).
1088 add_dyn(ex_to<numeric>((*itin2).coeff));
1089 if (expair_needs_further_processing(itin1))
1090 needs_further_processing = true;
1093 if (!ex_to<numeric>((*itin1).coeff).is_zero()) {
1102 if (!ex_to<numeric>((*itin1).coeff).is_zero()) {
1108 seq.erase(itout,last);
1111 if (needs_further_processing) {
1114 construct_from_epvector(v);
1119 #if EXPAIRSEQ_USE_HASHTAB
1121 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1124 unsigned nearest_power_of_2 = 1 << log2(sz);
1125 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1126 // size = nearest_power_of_2*hashtabfactor;
1127 size = nearest_power_of_2/hashtabfactor;
1128 if (size<minhashtabsize)
1130 GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1131 // hashtabsize must be a power of 2
1132 GINAC_ASSERT((1U << log2(size))==size);
1136 unsigned expairseq::calc_hashindex(const ex &e) const
1138 // calculate hashindex
1139 unsigned hash = e.gethash();
1141 if (is_a_numeric_hash(hash)) {
1142 hashindex = hashmask;
1144 hashindex = hash &hashmask;
1145 // last hashtab entry is reserved for numerics
1146 if (hashindex==hashmask) hashindex = 0;
1148 GINAC_ASSERT(hashindex>=0);
1149 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1153 void expairseq::shrink_hashtab(void)
1155 unsigned new_hashtabsize;
1156 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1157 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1158 if (new_hashtabsize==0) {
1165 // shrink by a factor of 2
1166 unsigned half_hashtabsize = hashtabsize/2;
1167 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1168 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1169 // special treatment for numeric hashes
1170 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1171 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1172 hashtab.resize(half_hashtabsize);
1173 hashtabsize = half_hashtabsize;
1174 hashmask = hashtabsize-1;
1178 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1181 return; // nothing to do
1183 // calculate hashindex of element to be deleted
1184 unsigned hashindex = calc_hashindex((*element).rest);
1186 // find it in hashtab and remove it
1187 epplist &eppl = hashtab[hashindex];
1188 epplist::iterator epplit = eppl.begin();
1189 bool erased = false;
1190 while (epplit!=eppl.end()) {
1191 if (*epplit == element) {
1200 cout << "tried to erase " << element-seq.begin() << std::endl;
1201 cout << "size " << seq.end()-seq.begin() << std::endl;
1203 unsigned hashindex = calc_hashindex((*element).rest);
1204 epplist &eppl = hashtab[hashindex];
1205 epplist::iterator epplit=eppl.begin();
1207 while (epplit!=eppl.end()) {
1208 if (*epplit == element) {
1215 GINAC_ASSERT(erased);
1217 GINAC_ASSERT(erased);
1220 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1221 epvector::iterator newpos)
1223 GINAC_ASSERT(hashtabsize!=0);
1225 // calculate hashindex of element which was moved
1226 unsigned hashindex=calc_hashindex((*newpos).rest);
1228 // find it in hashtab and modify it
1229 epplist &eppl = hashtab[hashindex];
1230 epplist::iterator epplit = eppl.begin();
1231 while (epplit!=eppl.end()) {
1232 if (*epplit == oldpos) {
1238 GINAC_ASSERT(epplit!=eppl.end());
1241 void expairseq::sorted_insert(epplist &eppl, epp elem)
1243 epplist::iterator current = eppl.begin();
1244 while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1247 eppl.insert(current,elem);
1250 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1251 epvector::iterator &last_non_zero,
1252 std::vector<bool> &touched,
1253 unsigned &number_of_zeroes)
1255 epp current=seq.begin();
1257 while (current!=first_numeric) {
1258 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1260 iter_swap(current,first_numeric);
1262 // calculate hashindex
1263 unsigned currenthashindex = calc_hashindex((*current).rest);
1265 // test if there is already a matching expair in the hashtab-list
1266 epplist &eppl=hashtab[currenthashindex];
1267 epplist::iterator epplit = eppl.begin();
1268 while (epplit!=eppl.end()) {
1269 if ((*current).rest.is_equal((*(*epplit)).rest))
1273 if (epplit==eppl.end()) {
1274 // no matching expair found, append this to end of list
1275 sorted_insert(eppl,current);
1278 // epplit points to a matching expair, combine it with current
1279 (*(*epplit)).coeff = ex_to<numeric>((*(*epplit)).coeff).
1280 add_dyn(ex_to<numeric>((*current).coeff));
1282 // move obsolete current expair to end by swapping with last_non_zero element
1283 // if this was a numeric, it is swapped with the expair before first_numeric
1284 iter_swap(current,last_non_zero);
1286 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1289 // test if combined term has coeff 0 and can be removed is done later
1290 touched[(*epplit)-seq.begin()]=true;
1296 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1297 epvector::iterator &last_non_zero,
1298 std::vector<bool> &touched,
1299 unsigned &number_of_zeroes)
1301 // move terms with coeff 0 to end and remove them from hashtab
1302 // check only those elements which have been touched
1303 epp current = seq.begin();
1305 while (current!=first_numeric) {
1309 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1313 remove_hashtab_entry(current);
1315 // move element to the end, unless it is already at the end
1316 if (current!=last_non_zero) {
1317 iter_swap(current,last_non_zero);
1319 bool numeric_swapped=first_numeric!=last_non_zero;
1320 if (numeric_swapped) iter_swap(first_numeric,current);
1321 epvector::iterator changed_entry;
1323 if (numeric_swapped)
1324 changed_entry = first_numeric;
1326 changed_entry = last_non_zero;
1331 if (first_numeric!=current) {
1333 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1334 move_hashtab_entry(changed_entry,current);
1335 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1344 GINAC_ASSERT(i==current-seq.begin());
1347 /** True if one of the coeffs vanishes, otherwise false.
1348 * This would be an invariant violation, so this should only be used for
1349 * debugging purposes. */
1350 bool expairseq::has_coeff_0(void) const
1352 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1353 if ((*cit).coeff.is_zero())
1359 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1360 epvector::const_iterator last_non_zero)
1362 if (first_numeric==seq.end()) return; // no numerics
1364 epvector::iterator current = first_numeric;
1365 epvector::const_iterator last = last_non_zero+1;
1366 while (current!=last) {
1367 sorted_insert(hashtab[hashmask],current);
1372 void expairseq::combine_same_terms(void)
1374 // combine same terms, drop term with coeff 0, move numerics to end
1376 // calculate size of hashtab
1377 hashtabsize = calc_hashtabsize(seq.size());
1379 // hashtabsize is a power of 2
1380 hashmask = hashtabsize-1;
1384 hashtab.resize(hashtabsize);
1386 if (hashtabsize==0) {
1388 combine_same_terms_sorted_seq();
1389 GINAC_ASSERT(!has_coeff_0());
1393 // iterate through seq, move numerics to end,
1394 // fill hashtab and combine same terms
1395 epvector::iterator first_numeric = seq.end();
1396 epvector::iterator last_non_zero = seq.end()-1;
1398 std::vector<bool> touched;
1399 touched.reserve(seq.size());
1400 for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1402 unsigned number_of_zeroes = 0;
1404 GINAC_ASSERT(!has_coeff_0());
1405 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1407 cout << "in combine:" << std::endl;
1409 cout << "size=" << seq.end() - seq.begin() << std::endl;
1410 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1411 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1412 for (unsigned i=0; i<seq.size(); ++i) {
1413 if (touched[i]) cout << i << " is touched" << std::endl;
1415 cout << "end in combine" << std::endl;
1418 // there should not be any terms with coeff 0 from the beginning,
1419 // so it should be safe to skip this step
1420 if (number_of_zeroes!=0) {
1421 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1423 cout << "in combine after drop:" << std::endl;
1425 cout << "size=" << seq.end() - seq.begin() << std::endl;
1426 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1427 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1428 for (unsigned i=0; i<seq.size(); ++i) {
1429 if (touched[i]) cout << i << " is touched" << std::endl;
1431 cout << "end in combine after drop" << std::endl;
1435 add_numerics_to_hashtab(first_numeric,last_non_zero);
1437 // pop zero elements
1438 for (unsigned i=0; i<number_of_zeroes; ++i) {
1442 // shrink hashtabsize to calculated value
1443 GINAC_ASSERT(!has_coeff_0());
1447 GINAC_ASSERT(!has_coeff_0());
1450 #endif // EXPAIRSEQ_USE_HASHTAB
1452 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1453 * debugging or in assertions since being sorted is an invariance. */
1454 bool expairseq::is_canonical() const
1456 if (seq.size() <= 1)
1459 #if EXPAIRSEQ_USE_HASHTAB
1460 if (hashtabsize > 0) return 1; // not canoncalized
1461 #endif // EXPAIRSEQ_USE_HASHTAB
1463 epvector::const_iterator it = seq.begin();
1464 epvector::const_iterator it_last = it;
1465 for (++it; it!=seq.end(); it_last=it, ++it) {
1466 if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
1467 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1468 !is_ex_exactly_of_type((*it).rest,numeric)) {
1469 // double test makes it easier to set a breakpoint...
1470 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1471 !is_ex_exactly_of_type((*it).rest,numeric)) {
1472 printpair(std::clog, *it_last, 0);
1474 printpair(std::clog, *it, 0);
1476 std::clog << "pair1:" << std::endl;
1477 (*it_last).rest.print(print_tree(std::clog));
1478 (*it_last).coeff.print(print_tree(std::clog));
1479 std::clog << "pair2:" << std::endl;
1480 (*it).rest.print(print_tree(std::clog));
1481 (*it).coeff.print(print_tree(std::clog));
1491 /** Member-wise expand the expairs in this sequence.
1493 * @see expairseq::expand()
1494 * @return pointer to epvector containing expanded pairs or zero pointer,
1495 * if no members were changed. */
1496 epvector * expairseq::expandchildren(unsigned options) const
1498 epvector::const_iterator last = seq.end();
1499 epvector::const_iterator cit = seq.begin();
1501 const ex &expanded_ex = (*cit).rest.expand(options);
1502 if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1504 // something changed, copy seq, eval and return it
1505 epvector *s = new epvector;
1506 s->reserve(seq.size());
1508 // copy parts of seq which are known not to have changed
1509 epvector::const_iterator cit2 = seq.begin();
1511 s->push_back(*cit2);
1514 // copy first changed element
1515 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1519 while (cit2!=last) {
1520 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1529 return 0; // signalling nothing has changed
1533 /** Member-wise evaluate the expairs in this sequence.
1535 * @see expairseq::eval()
1536 * @return pointer to epvector containing evaluated pairs or zero pointer,
1537 * if no members were changed. */
1538 epvector * expairseq::evalchildren(int level) const
1540 // returns a NULL pointer if nothing had to be evaluated
1541 // returns a pointer to a newly created epvector otherwise
1542 // (which has to be deleted somewhere else)
1547 if (level == -max_recursion_level)
1548 throw(std::runtime_error("max recursion level reached"));
1551 epvector::const_iterator last=seq.end();
1552 epvector::const_iterator cit=seq.begin();
1554 const ex &evaled_ex = (*cit).rest.eval(level);
1555 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1557 // something changed, copy seq, eval and return it
1558 epvector *s = new epvector;
1559 s->reserve(seq.size());
1561 // copy parts of seq which are known not to have changed
1562 epvector::const_iterator cit2=seq.begin();
1564 s->push_back(*cit2);
1567 // copy first changed element
1568 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1572 while (cit2!=last) {
1573 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1582 return 0; // signalling nothing has changed
1586 /** Member-wise substitute in this sequence.
1588 * @see expairseq::subs()
1589 * @return pointer to epvector containing pairs after application of subs,
1590 * or NULL pointer if no members were changed. */
1591 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1593 GINAC_ASSERT(ls.nops()==lr.nops());
1595 // The substitution is "complex" when any of the objects to be substituted
1596 // is a product or power. In this case we have to recombine the pairs
1597 // because the numeric coefficients may be part of the search pattern.
1598 bool complex_subs = false;
1599 for (unsigned i=0; i<ls.nops(); i++)
1600 if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
1601 complex_subs = true;
1607 // Substitute in the recombined pairs
1608 epvector::const_iterator cit = seq.begin(), last = seq.end();
1609 while (cit != last) {
1611 const ex &orig_ex = recombine_pair_to_ex(*cit);
1612 const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
1613 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1615 // Something changed, copy seq, subs and return it
1616 epvector *s = new epvector;
1617 s->reserve(seq.size());
1619 // Copy parts of seq which are known not to have changed
1620 s->insert(s->begin(), seq.begin(), cit);
1622 // Copy first changed element
1623 s->push_back(split_ex_to_pair(subsed_ex));
1627 while (cit != last) {
1628 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
1639 // Substitute only in the "rest" part of the pairs
1640 epvector::const_iterator cit = seq.begin(), last = seq.end();
1641 while (cit != last) {
1643 const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
1644 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1646 // Something changed, copy seq, subs and return it
1647 epvector *s = new epvector;
1648 s->reserve(seq.size());
1650 // Copy parts of seq which are known not to have changed
1651 s->insert(s->begin(), seq.begin(), cit);
1653 // Copy first changed element
1654 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1658 while (cit != last) {
1659 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
1670 // Nothing has changed
1675 // static member variables
1678 #if EXPAIRSEQ_USE_HASHTAB
1679 unsigned expairseq::maxhashtabsize = 0x4000000U;
1680 unsigned expairseq::minhashtabsize = 0x1000U;
1681 unsigned expairseq::hashtabfactor = 1;
1682 #endif // EXPAIRSEQ_USE_HASHTAB
1684 } // namespace GiNaC