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::eval(int level) const
304 if ((level==1) && (flags &status_flags::evaluated))
307 epvector *vp = evalchildren(level);
311 return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
314 ex expairseq::evalf(int level) const
316 return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
319 ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
321 ex n = thisexpairseq(normalchildren(level),overall_coeff);
322 return n.bp->basic::normal(sym_lst,repl_lst,level);
325 bool expairseq::match(const ex & pattern, lst & repl_lst) const
327 //clog << "match " << *this << " with " << pattern << ", repl_lst = " << repl_lst << endl;
328 // This differs from basic::match() because we want "a+b+c+d" to
329 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
331 if (tinfo() == pattern.bp->tinfo()) {
333 // Check whether global wildcard (one that matches the "rest of the
334 // expression", like "*" above) is present
335 bool has_global_wildcard = false;
337 for (unsigned int i=0; i<pattern.nops(); i++) {
338 if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
339 has_global_wildcard = true;
340 global_wildcard = pattern.op(i);
345 // Unfortunately, this is an O(N^2) operation because we can't
346 // sort the pattern in a useful way...
351 for (unsigned i=0; i<nops(); i++)
352 ops.push_back(op(i));
354 // Now, for every term of the pattern, look for a matching term in
355 // the expression and remove the match
356 for (unsigned i=0; i<pattern.nops(); i++) {
357 ex p = pattern.op(i);
358 if (has_global_wildcard && p.is_equal(global_wildcard))
360 exvector::iterator it = ops.begin(), itend = ops.end();
361 while (it != itend) {
362 if (it->match(p, repl_lst)) {
368 return false; // no match found
372 if (has_global_wildcard) {
374 // Assign all the remaining terms to the global wildcard (unless
375 // it has already been matched before, in which case the matches
377 epvector *vp = new epvector();
378 vp->reserve(ops.size());
379 for (unsigned i=0; i<ops.size(); i++)
380 vp->push_back(split_ex_to_pair(ops[i]));
381 ex rest = thisexpairseq(vp, default_overall_coeff());
382 for (unsigned i=0; i<repl_lst.nops(); i++) {
383 if (repl_lst.op(i).op(0).is_equal(global_wildcard))
384 return rest.is_equal(*repl_lst.op(i).op(1).bp);
386 repl_lst.append(global_wildcard == rest);
391 // No global wildcard, then the match fails if there are any
392 // unmatched terms left
396 return inherited::match(pattern, repl_lst);
399 ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
401 epvector *vp = subschildren(ls, lr, no_pattern);
403 return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
405 return basic::subs(ls, lr, no_pattern);
410 /** Implementation of ex::diff() for an expairseq.
411 * It differentiates all elements of the sequence.
413 ex expairseq::derivative(const symbol &s) const
415 return thisexpairseq(diffchildren(s),overall_coeff);
418 int expairseq::compare_same_type(const basic &other) const
420 GINAC_ASSERT(is_of_type(other, expairseq));
421 const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
425 // compare number of elements
426 if (seq.size() != o.seq.size())
427 return (seq.size()<o.seq.size()) ? -1 : 1;
429 // compare overall_coeff
430 cmpval = overall_coeff.compare(o.overall_coeff);
434 #if EXPAIRSEQ_USE_HASHTAB
435 GINAC_ASSERT(hashtabsize==o.hashtabsize);
436 if (hashtabsize==0) {
437 #endif // EXPAIRSEQ_USE_HASHTAB
438 epvector::const_iterator cit1 = seq.begin();
439 epvector::const_iterator cit2 = o.seq.begin();
440 epvector::const_iterator last1 = seq.end();
441 epvector::const_iterator last2 = o.seq.end();
443 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
444 cmpval = (*cit1).compare(*cit2);
445 if (cmpval!=0) return cmpval;
448 GINAC_ASSERT(cit1==last1);
449 GINAC_ASSERT(cit2==last2);
452 #if EXPAIRSEQ_USE_HASHTAB
455 // compare number of elements in each hashtab entry
456 for (unsigned i=0; i<hashtabsize; ++i) {
457 unsigned cursize=hashtab[i].size();
458 if (cursize != o.hashtab[i].size())
459 return (cursize < o.hashtab[i].size()) ? -1 : 1;
462 // compare individual (sorted) hashtab entries
463 for (unsigned i=0; i<hashtabsize; ++i) {
464 unsigned sz = hashtab[i].size();
466 const epplist &eppl1 = hashtab[i];
467 const epplist &eppl2 = o.hashtab[i];
468 epplist::const_iterator it1 = eppl1.begin();
469 epplist::const_iterator it2 = eppl2.begin();
470 while (it1!=eppl1.end()) {
471 cmpval = (*(*it1)).compare(*(*it2));
481 #endif // EXPAIRSEQ_USE_HASHTAB
484 bool expairseq::is_equal_same_type(const basic &other) const
486 const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
488 // compare number of elements
489 if (seq.size()!=o.seq.size())
492 // compare overall_coeff
493 if (!overall_coeff.is_equal(o.overall_coeff))
496 #if EXPAIRSEQ_USE_HASHTAB
497 // compare number of elements in each hashtab entry
498 if (hashtabsize!=o.hashtabsize) {
499 std::cout << "this:" << std::endl;
500 print(print_tree(std::cout));
501 std::cout << "other:" << std::endl;
502 other.print(print_tree(std::cout));
505 GINAC_ASSERT(hashtabsize==o.hashtabsize);
507 if (hashtabsize==0) {
508 #endif // EXPAIRSEQ_USE_HASHTAB
509 epvector::const_iterator cit1 = seq.begin();
510 epvector::const_iterator cit2 = o.seq.begin();
511 epvector::const_iterator last1 = seq.end();
513 while (cit1!=last1) {
514 if (!(*cit1).is_equal(*cit2)) return false;
520 #if EXPAIRSEQ_USE_HASHTAB
523 for (unsigned i=0; i<hashtabsize; ++i) {
524 if (hashtab[i].size() != o.hashtab[i].size())
528 // compare individual sorted hashtab entries
529 for (unsigned i=0; i<hashtabsize; ++i) {
530 unsigned sz = hashtab[i].size();
532 const epplist &eppl1 = hashtab[i];
533 const epplist &eppl2 = o.hashtab[i];
534 epplist::const_iterator it1 = eppl1.begin();
535 epplist::const_iterator it2 = eppl2.begin();
536 while (it1!=eppl1.end()) {
537 if (!(*(*it1)).is_equal(*(*it2))) return false;
545 #endif // EXPAIRSEQ_USE_HASHTAB
548 unsigned expairseq::return_type(void) const
550 return return_types::noncommutative_composite;
553 unsigned expairseq::calchash(void) const
555 unsigned v = golden_ratio_hash(tinfo());
556 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
557 #if !EXPAIRSEQ_USE_HASHTAB
558 v = rotate_left_31(v); // rotation would spoil commutativity
559 #endif // EXPAIRSEQ_USE_HASHTAB
560 v ^= cit->rest.gethash();
561 #if !EXPAIRSEQ_USE_HASHTAB
562 v = rotate_left_31(v);
563 v ^= cit->coeff.gethash();
564 #endif // EXPAIRSEQ_USE_HASHTAB
567 v ^= overall_coeff.gethash();
570 // store calculated hash value only if object is already evaluated
571 if (flags &status_flags::evaluated) {
572 setflag(status_flags::hash_calculated);
579 ex expairseq::expand(unsigned options) const
581 epvector *vp = expandchildren(options);
583 // the terms have not changed, so it is safe to declare this expanded
584 setflag(status_flags::expanded);
588 return thisexpairseq(vp,overall_coeff);
592 // new virtual functions which can be overridden by derived classes
597 /** Create an object of this type.
598 * This method works similar to a constructor. It is useful because expairseq
599 * has (at least) two possible different semantics but we want to inherit
600 * methods thus avoiding code duplication. Sometimes a method in expairseq
601 * has to create a new one of the same semantics, which cannot be done by a
602 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
603 * order for this trick to work a derived class must of course override this
605 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
607 return expairseq(v,oc);
610 ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
612 return expairseq(vp,oc);
615 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
618 p.rest.bp->print(c, precedence());
620 p.coeff.bp->print(c, precedence());
624 void expairseq::printseq(const print_context & c, char delim,
625 unsigned this_precedence,
626 unsigned upper_precedence) const
628 if (this_precedence <= upper_precedence)
630 epvector::const_iterator it, it_last = seq.end() - 1;
631 for (it=seq.begin(); it!=it_last; ++it) {
632 printpair(c, *it, this_precedence);
635 printpair(c, *it, this_precedence);
636 if (!overall_coeff.is_equal(default_overall_coeff())) {
638 overall_coeff.print(c, this_precedence);
641 if (this_precedence <= upper_precedence)
646 /** Form an expair from an ex, using the corresponding semantics.
647 * @see expairseq::recombine_pair_to_ex() */
648 expair expairseq::split_ex_to_pair(const ex &e) const
650 return expair(e,_ex1());
654 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
657 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
663 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
666 GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
667 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
669 return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
673 /** Form an ex out of an expair, using the corresponding semantics.
674 * @see expairseq::split_ex_to_pair() */
675 ex expairseq::recombine_pair_to_ex(const expair &p) const
677 return lst(p.rest,p.coeff);
680 bool expairseq::expair_needs_further_processing(epp it)
682 #if EXPAIRSEQ_USE_HASHTAB
683 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
684 #endif // EXPAIRSEQ_USE_HASHTAB
688 ex expairseq::default_overall_coeff(void) const
693 void expairseq::combine_overall_coeff(const ex &c)
695 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
696 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
697 overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
700 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
702 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
703 GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
704 GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
705 overall_coeff = ex_to_numeric(overall_coeff).
706 add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
709 bool expairseq::can_make_flat(const expair &p) const
716 // non-virtual functions in this class
719 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
725 construct_from_exvector(v);
726 #if EXPAIRSEQ_USE_HASHTAB
727 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
728 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
729 #endif // EXPAIRSEQ_USE_HASHTAB
732 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
734 if (lh.bp->tinfo()==tinfo()) {
735 if (rh.bp->tinfo()==tinfo()) {
736 #if EXPAIRSEQ_USE_HASHTAB
737 unsigned totalsize = ex_to_expairseq(lh).seq.size() +
738 ex_to_expairseq(rh).seq.size();
739 if (calc_hashtabsize(totalsize)!=0) {
740 construct_from_2_ex_via_exvector(lh,rh);
742 #endif // EXPAIRSEQ_USE_HASHTAB
743 construct_from_2_expairseq(ex_to_expairseq(lh),
744 ex_to_expairseq(rh));
745 #if EXPAIRSEQ_USE_HASHTAB
747 #endif // EXPAIRSEQ_USE_HASHTAB
750 #if EXPAIRSEQ_USE_HASHTAB
751 unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
752 if (calc_hashtabsize(totalsize)!=0) {
753 construct_from_2_ex_via_exvector(lh, rh);
755 #endif // EXPAIRSEQ_USE_HASHTAB
756 construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
757 #if EXPAIRSEQ_USE_HASHTAB
759 #endif // EXPAIRSEQ_USE_HASHTAB
762 } else if (rh.bp->tinfo()==tinfo()) {
763 #if EXPAIRSEQ_USE_HASHTAB
764 unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
765 if (calc_hashtabsize(totalsize)!=0) {
766 construct_from_2_ex_via_exvector(lh,rh);
768 #endif // EXPAIRSEQ_USE_HASHTAB
769 construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
770 #if EXPAIRSEQ_USE_HASHTAB
772 #endif // EXPAIRSEQ_USE_HASHTAB
776 #if EXPAIRSEQ_USE_HASHTAB
777 if (calc_hashtabsize(2)!=0) {
778 construct_from_2_ex_via_exvector(lh,rh);
782 #endif // EXPAIRSEQ_USE_HASHTAB
784 if (is_ex_exactly_of_type(lh,numeric)) {
785 if (is_ex_exactly_of_type(rh,numeric)) {
786 combine_overall_coeff(lh);
787 combine_overall_coeff(rh);
789 combine_overall_coeff(lh);
790 seq.push_back(split_ex_to_pair(rh));
793 if (is_ex_exactly_of_type(rh,numeric)) {
794 combine_overall_coeff(rh);
795 seq.push_back(split_ex_to_pair(lh));
797 expair p1 = split_ex_to_pair(lh);
798 expair p2 = split_ex_to_pair(rh);
800 int cmpval = p1.rest.compare(p2.rest);
802 p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
803 if (!ex_to_numeric(p1.coeff).is_zero()) {
804 // no further processing is necessary, since this
805 // one element will usually be recombined in eval()
822 void expairseq::construct_from_2_expairseq(const expairseq &s1,
825 combine_overall_coeff(s1.overall_coeff);
826 combine_overall_coeff(s2.overall_coeff);
828 epvector::const_iterator first1 = s1.seq.begin();
829 epvector::const_iterator last1 = s1.seq.end();
830 epvector::const_iterator first2 = s2.seq.begin();
831 epvector::const_iterator last2 = s2.seq.end();
833 seq.reserve(s1.seq.size()+s2.seq.size());
835 bool needs_further_processing=false;
837 while (first1!=last1 && first2!=last2) {
838 int cmpval = (*first1).rest.compare((*first2).rest);
841 const numeric &newcoeff = ex_to_numeric((*first1).coeff).
842 add(ex_to_numeric((*first2).coeff));
843 if (!newcoeff.is_zero()) {
844 seq.push_back(expair((*first1).rest,newcoeff));
845 if (expair_needs_further_processing(seq.end()-1)) {
846 needs_further_processing = true;
851 } else if (cmpval<0) {
852 seq.push_back(*first1);
855 seq.push_back(*first2);
860 while (first1!=last1) {
861 seq.push_back(*first1);
864 while (first2!=last2) {
865 seq.push_back(*first2);
869 if (needs_further_processing) {
872 construct_from_epvector(v);
876 void expairseq::construct_from_expairseq_ex(const expairseq &s,
879 combine_overall_coeff(s.overall_coeff);
880 if (is_ex_exactly_of_type(e,numeric)) {
881 combine_overall_coeff(e);
886 epvector::const_iterator first = s.seq.begin();
887 epvector::const_iterator last = s.seq.end();
888 expair p = split_ex_to_pair(e);
890 seq.reserve(s.seq.size()+1);
891 bool p_pushed = false;
893 bool needs_further_processing=false;
895 // merge p into s.seq
896 while (first!=last) {
897 int cmpval=(*first).rest.compare(p.rest);
900 const numeric &newcoeff = ex_to_numeric((*first).coeff).
901 add(ex_to_numeric(p.coeff));
902 if (!newcoeff.is_zero()) {
903 seq.push_back(expair((*first).rest,newcoeff));
904 if (expair_needs_further_processing(seq.end()-1)) {
905 needs_further_processing = true;
911 } else if (cmpval<0) {
912 seq.push_back(*first);
922 // while loop exited because p was pushed, now push rest of s.seq
923 while (first!=last) {
924 seq.push_back(*first);
928 // while loop exited because s.seq was pushed, now push p
932 if (needs_further_processing) {
935 construct_from_epvector(v);
939 void expairseq::construct_from_exvector(const exvector &v)
941 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
942 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
943 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
944 // (same for (+,*) -> (*,^)
947 #if EXPAIRSEQ_USE_HASHTAB
948 combine_same_terms();
951 combine_same_terms_sorted_seq();
952 #endif // EXPAIRSEQ_USE_HASHTAB
956 void expairseq::construct_from_epvector(const epvector &v)
958 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
959 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
960 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
961 // (same for (+,*) -> (*,^)
964 #if EXPAIRSEQ_USE_HASHTAB
965 combine_same_terms();
968 combine_same_terms_sorted_seq();
969 #endif // EXPAIRSEQ_USE_HASHTAB
973 /** Combine this expairseq with argument exvector.
974 * It cares for associativity as well as for special handling of numerics. */
975 void expairseq::make_flat(const exvector &v)
977 exvector::const_iterator cit;
979 // count number of operands which are of same expairseq derived type
980 // and their cumulative number of operands
985 while (cit!=v.end()) {
986 if (cit->bp->tinfo()==this->tinfo()) {
988 noperands += ex_to_expairseq(*cit).seq.size();
993 // reserve seq and coeffseq which will hold all operands
994 seq.reserve(v.size()+noperands-nexpairseqs);
996 // copy elements and split off numerical part
998 while (cit!=v.end()) {
999 if (cit->bp->tinfo()==this->tinfo()) {
1000 const expairseq &subseqref = ex_to_expairseq(*cit);
1001 combine_overall_coeff(subseqref.overall_coeff);
1002 epvector::const_iterator cit_s = subseqref.seq.begin();
1003 while (cit_s!=subseqref.seq.end()) {
1004 seq.push_back(*cit_s);
1008 if (is_ex_exactly_of_type(*cit,numeric))
1009 combine_overall_coeff(*cit);
1011 seq.push_back(split_ex_to_pair(*cit));
1019 /** Combine this expairseq with argument epvector.
1020 * It cares for associativity as well as for special handling of numerics. */
1021 void expairseq::make_flat(const epvector &v)
1023 epvector::const_iterator cit;
1025 // count number of operands which are of same expairseq derived type
1026 // and their cumulative number of operands
1027 int nexpairseqs = 0;
1031 while (cit!=v.end()) {
1032 if (cit->rest.bp->tinfo()==this->tinfo()) {
1034 noperands += ex_to_expairseq((*cit).rest).seq.size();
1039 // reserve seq and coeffseq which will hold all operands
1040 seq.reserve(v.size()+noperands-nexpairseqs);
1042 // copy elements and split off numerical part
1044 while (cit!=v.end()) {
1045 if (cit->rest.bp->tinfo()==this->tinfo() &&
1046 this->can_make_flat(*cit)) {
1047 const expairseq &subseqref = ex_to_expairseq((*cit).rest);
1048 combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
1049 ex_to_numeric((*cit).coeff));
1050 epvector::const_iterator cit_s = subseqref.seq.begin();
1051 while (cit_s!=subseqref.seq.end()) {
1052 seq.push_back(expair((*cit_s).rest,
1053 ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
1054 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1059 if (cit->is_canonical_numeric())
1060 combine_overall_coeff(cit->rest);
1062 seq.push_back(*cit);
1069 /** Brings this expairseq into a sorted (canonical) form. */
1070 void expairseq::canonicalize(void)
1073 sort(seq.begin(),seq.end(),expair_is_less());
1078 /** Compact a presorted expairseq by combining all matching expairs to one
1079 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1081 void expairseq::combine_same_terms_sorted_seq(void)
1083 bool needs_further_processing = false;
1086 epvector::iterator itin1 = seq.begin();
1087 epvector::iterator itin2 = itin1+1;
1088 epvector::iterator itout = itin1;
1089 epvector::iterator last = seq.end();
1090 // must_copy will be set to true the first time some combination is
1091 // possible from then on the sequence has changed and must be compacted
1092 bool must_copy = false;
1093 while (itin2!=last) {
1094 if ((*itin1).rest.compare((*itin2).rest)==0) {
1095 (*itin1).coeff = ex_to_numeric((*itin1).coeff).
1096 add_dyn(ex_to_numeric((*itin2).coeff));
1097 if (expair_needs_further_processing(itin1))
1098 needs_further_processing = true;
1101 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1110 if (!ex_to_numeric((*itin1).coeff).is_zero()) {
1116 seq.erase(itout,last);
1119 if (needs_further_processing) {
1122 construct_from_epvector(v);
1127 #if EXPAIRSEQ_USE_HASHTAB
1129 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1132 unsigned nearest_power_of_2 = 1 << log2(sz);
1133 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1134 // size = nearest_power_of_2*hashtabfactor;
1135 size = nearest_power_of_2/hashtabfactor;
1136 if (size<minhashtabsize)
1138 GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
1139 // hashtabsize must be a power of 2
1140 GINAC_ASSERT((1U << log2(size))==size);
1144 unsigned expairseq::calc_hashindex(const ex &e) const
1146 // calculate hashindex
1147 unsigned hash = e.gethash();
1149 if (is_a_numeric_hash(hash)) {
1150 hashindex = hashmask;
1152 hashindex = hash &hashmask;
1153 // last hashtab entry is reserved for numerics
1154 if (hashindex==hashmask) hashindex = 0;
1156 GINAC_ASSERT(hashindex>=0);
1157 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1161 void expairseq::shrink_hashtab(void)
1163 unsigned new_hashtabsize;
1164 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1165 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1166 if (new_hashtabsize==0) {
1173 // shrink by a factor of 2
1174 unsigned half_hashtabsize = hashtabsize/2;
1175 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1176 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1177 // special treatment for numeric hashes
1178 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1179 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1180 hashtab.resize(half_hashtabsize);
1181 hashtabsize = half_hashtabsize;
1182 hashmask = hashtabsize-1;
1186 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1189 return; // nothing to do
1191 // calculate hashindex of element to be deleted
1192 unsigned hashindex = calc_hashindex((*element).rest);
1194 // find it in hashtab and remove it
1195 epplist &eppl = hashtab[hashindex];
1196 epplist::iterator epplit = eppl.begin();
1197 bool erased = false;
1198 while (epplit!=eppl.end()) {
1199 if (*epplit == element) {
1208 cout << "tried to erase " << element-seq.begin() << std::endl;
1209 cout << "size " << seq.end()-seq.begin() << std::endl;
1211 unsigned hashindex = calc_hashindex((*element).rest);
1212 epplist &eppl = hashtab[hashindex];
1213 epplist::iterator epplit=eppl.begin();
1215 while (epplit!=eppl.end()) {
1216 if (*epplit == element) {
1223 GINAC_ASSERT(erased);
1225 GINAC_ASSERT(erased);
1228 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1229 epvector::iterator newpos)
1231 GINAC_ASSERT(hashtabsize!=0);
1233 // calculate hashindex of element which was moved
1234 unsigned hashindex=calc_hashindex((*newpos).rest);
1236 // find it in hashtab and modify it
1237 epplist &eppl = hashtab[hashindex];
1238 epplist::iterator epplit = eppl.begin();
1239 while (epplit!=eppl.end()) {
1240 if (*epplit == oldpos) {
1246 GINAC_ASSERT(epplit!=eppl.end());
1249 void expairseq::sorted_insert(epplist &eppl, epp elem)
1251 epplist::iterator current = eppl.begin();
1252 while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
1255 eppl.insert(current,elem);
1258 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1259 epvector::iterator &last_non_zero,
1260 std::vector<bool> &touched,
1261 unsigned &number_of_zeroes)
1263 epp current=seq.begin();
1265 while (current!=first_numeric) {
1266 if (is_ex_exactly_of_type((*current).rest,numeric)) {
1268 iter_swap(current,first_numeric);
1270 // calculate hashindex
1271 unsigned currenthashindex = calc_hashindex((*current).rest);
1273 // test if there is already a matching expair in the hashtab-list
1274 epplist &eppl=hashtab[currenthashindex];
1275 epplist::iterator epplit = eppl.begin();
1276 while (epplit!=eppl.end()) {
1277 if ((*current).rest.is_equal((*(*epplit)).rest))
1281 if (epplit==eppl.end()) {
1282 // no matching expair found, append this to end of list
1283 sorted_insert(eppl,current);
1286 // epplit points to a matching expair, combine it with current
1287 (*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
1288 add_dyn(ex_to_numeric((*current).coeff));
1290 // move obsolete current expair to end by swapping with last_non_zero element
1291 // if this was a numeric, it is swapped with the expair before first_numeric
1292 iter_swap(current,last_non_zero);
1294 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1297 // test if combined term has coeff 0 and can be removed is done later
1298 touched[(*epplit)-seq.begin()]=true;
1304 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1305 epvector::iterator &last_non_zero,
1306 std::vector<bool> &touched,
1307 unsigned &number_of_zeroes)
1309 // move terms with coeff 0 to end and remove them from hashtab
1310 // check only those elements which have been touched
1311 epp current = seq.begin();
1313 while (current!=first_numeric) {
1317 } else if (!ex_to_numeric((*current).coeff).is_zero()) {
1321 remove_hashtab_entry(current);
1323 // move element to the end, unless it is already at the end
1324 if (current!=last_non_zero) {
1325 iter_swap(current,last_non_zero);
1327 bool numeric_swapped=first_numeric!=last_non_zero;
1328 if (numeric_swapped) iter_swap(first_numeric,current);
1329 epvector::iterator changed_entry;
1331 if (numeric_swapped)
1332 changed_entry = first_numeric;
1334 changed_entry = last_non_zero;
1339 if (first_numeric!=current) {
1341 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1342 move_hashtab_entry(changed_entry,current);
1343 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1352 GINAC_ASSERT(i==current-seq.begin());
1355 /** True if one of the coeffs vanishes, otherwise false.
1356 * This would be an invariant violation, so this should only be used for
1357 * debugging purposes. */
1358 bool expairseq::has_coeff_0(void) const
1360 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
1361 if ((*cit).coeff.is_zero())
1367 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1368 epvector::const_iterator last_non_zero)
1370 if (first_numeric==seq.end()) return; // no numerics
1372 epvector::iterator current = first_numeric;
1373 epvector::const_iterator last = last_non_zero+1;
1374 while (current!=last) {
1375 sorted_insert(hashtab[hashmask],current);
1380 void expairseq::combine_same_terms(void)
1382 // combine same terms, drop term with coeff 0, move numerics to end
1384 // calculate size of hashtab
1385 hashtabsize = calc_hashtabsize(seq.size());
1387 // hashtabsize is a power of 2
1388 hashmask = hashtabsize-1;
1392 hashtab.resize(hashtabsize);
1394 if (hashtabsize==0) {
1396 combine_same_terms_sorted_seq();
1397 GINAC_ASSERT(!has_coeff_0());
1401 // iterate through seq, move numerics to end,
1402 // fill hashtab and combine same terms
1403 epvector::iterator first_numeric = seq.end();
1404 epvector::iterator last_non_zero = seq.end()-1;
1406 std::vector<bool> touched;
1407 touched.reserve(seq.size());
1408 for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
1410 unsigned number_of_zeroes = 0;
1412 GINAC_ASSERT(!has_coeff_0());
1413 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1415 cout << "in combine:" << std::endl;
1417 cout << "size=" << seq.end() - seq.begin() << std::endl;
1418 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1419 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1420 for (unsigned i=0; i<seq.size(); ++i) {
1421 if (touched[i]) cout << i << " is touched" << std::endl;
1423 cout << "end in combine" << std::endl;
1426 // there should not be any terms with coeff 0 from the beginning,
1427 // so it should be safe to skip this step
1428 if (number_of_zeroes!=0) {
1429 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1431 cout << "in combine after drop:" << std::endl;
1433 cout << "size=" << seq.end() - seq.begin() << std::endl;
1434 cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
1435 cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
1436 for (unsigned i=0; i<seq.size(); ++i) {
1437 if (touched[i]) cout << i << " is touched" << std::endl;
1439 cout << "end in combine after drop" << std::endl;
1443 add_numerics_to_hashtab(first_numeric,last_non_zero);
1445 // pop zero elements
1446 for (unsigned i=0; i<number_of_zeroes; ++i) {
1450 // shrink hashtabsize to calculated value
1451 GINAC_ASSERT(!has_coeff_0());
1455 GINAC_ASSERT(!has_coeff_0());
1458 #endif // EXPAIRSEQ_USE_HASHTAB
1460 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1461 * debugging or in assertions since being sorted is an invariance. */
1462 bool expairseq::is_canonical() const
1464 if (seq.size() <= 1)
1467 #if EXPAIRSEQ_USE_HASHTAB
1468 if (hashtabsize > 0) return 1; // not canoncalized
1469 #endif // EXPAIRSEQ_USE_HASHTAB
1471 epvector::const_iterator it = seq.begin();
1472 epvector::const_iterator it_last = it;
1473 for (++it; it!=seq.end(); it_last=it, ++it) {
1474 if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
1475 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1476 !is_ex_exactly_of_type((*it).rest,numeric)) {
1477 // double test makes it easier to set a breakpoint...
1478 if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
1479 !is_ex_exactly_of_type((*it).rest,numeric)) {
1480 printpair(std::clog, *it_last, 0);
1482 printpair(std::clog, *it, 0);
1484 std::clog << "pair1:" << std::endl;
1485 (*it_last).rest.print(print_tree(std::clog));
1486 (*it_last).coeff.print(print_tree(std::clog));
1487 std::clog << "pair2:" << std::endl;
1488 (*it).rest.print(print_tree(std::clog));
1489 (*it).coeff.print(print_tree(std::clog));
1499 /** Member-wise expand the expairs in this sequence.
1501 * @see expairseq::expand()
1502 * @return pointer to epvector containing expanded pairs or zero pointer,
1503 * if no members were changed. */
1504 epvector * expairseq::expandchildren(unsigned options) const
1506 epvector::const_iterator last = seq.end();
1507 epvector::const_iterator cit = seq.begin();
1509 const ex &expanded_ex = (*cit).rest.expand(options);
1510 if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
1512 // something changed, copy seq, eval and return it
1513 epvector *s = new epvector;
1514 s->reserve(seq.size());
1516 // copy parts of seq which are known not to have changed
1517 epvector::const_iterator cit2 = seq.begin();
1519 s->push_back(*cit2);
1522 // copy first changed element
1523 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1527 while (cit2!=last) {
1528 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
1537 return 0; // signalling nothing has changed
1541 /** Member-wise evaluate the expairs in this sequence.
1543 * @see expairseq::eval()
1544 * @return pointer to epvector containing evaluated pairs or zero pointer,
1545 * if no members were changed. */
1546 epvector * expairseq::evalchildren(int level) const
1548 // returns a NULL pointer if nothing had to be evaluated
1549 // returns a pointer to a newly created epvector otherwise
1550 // (which has to be deleted somewhere else)
1555 if (level == -max_recursion_level)
1556 throw(std::runtime_error("max recursion level reached"));
1559 epvector::const_iterator last=seq.end();
1560 epvector::const_iterator cit=seq.begin();
1562 const ex &evaled_ex = (*cit).rest.eval(level);
1563 if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
1565 // something changed, copy seq, eval and return it
1566 epvector *s = new epvector;
1567 s->reserve(seq.size());
1569 // copy parts of seq which are known not to have changed
1570 epvector::const_iterator cit2=seq.begin();
1572 s->push_back(*cit2);
1575 // copy first changed element
1576 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1580 while (cit2!=last) {
1581 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
1590 return 0; // signalling nothing has changed
1594 /** Member-wise evaluate numerically all expairs in this sequence.
1596 * @see expairseq::evalf()
1597 * @return epvector with all entries evaluated numerically. */
1598 epvector expairseq::evalfchildren(int level) const
1603 if (level==-max_recursion_level)
1604 throw(std::runtime_error("max recursion level reached"));
1607 s.reserve(seq.size());
1610 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1611 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
1612 (*it).coeff.evalf(level)));
1618 /** Member-wise normalize all expairs in this sequence.
1620 * @see expairseq::normal()
1621 * @return epvector with all entries normalized. */
1622 epvector expairseq::normalchildren(int level) const
1627 if (level==-max_recursion_level)
1628 throw(std::runtime_error("max recursion level reached"));
1631 s.reserve(seq.size());
1634 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1635 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
1642 /** Member-wise differentiate all expairs in this sequence.
1644 * @see expairseq::diff()
1645 * @return epvector with all entries differentiated. */
1646 epvector expairseq::diffchildren(const symbol &y) const
1649 s.reserve(seq.size());
1651 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
1652 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
1659 /** Member-wise substitute in this sequence.
1661 * @see expairseq::subs()
1662 * @return pointer to epvector containing pairs after application of subs or zero
1663 * pointer, if no members were changed. */
1664 epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
1666 // returns a NULL pointer if nothing had to be substituted
1667 // returns a pointer to a newly created epvector otherwise
1668 // (which has to be deleted somewhere else)
1669 GINAC_ASSERT(ls.nops()==lr.nops());
1671 epvector::const_iterator last = seq.end();
1672 epvector::const_iterator cit = seq.begin();
1674 const ex &subsed_ex=(*cit).rest.subs(ls,lr,no_pattern);
1675 if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
1677 // something changed, copy seq, subs and return it
1678 epvector *s = new epvector;
1679 s->reserve(seq.size());
1681 // copy parts of seq which are known not to have changed
1682 epvector::const_iterator cit2 = seq.begin();
1684 s->push_back(*cit2);
1687 // copy first changed element
1688 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
1692 while (cit2!=last) {
1693 s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr,no_pattern),
1702 return 0; // signalling nothing has changed
1706 // static member variables
1709 #if EXPAIRSEQ_USE_HASHTAB
1710 unsigned expairseq::maxhashtabsize = 0x4000000U;
1711 unsigned expairseq::minhashtabsize = 0x1000U;
1712 unsigned expairseq::hashtabfactor = 1;
1713 #endif // EXPAIRSEQ_USE_HASHTAB
1715 } // namespace GiNaC