/** @file expairseq.cpp
*
* Implementation of sequences of expression pairs. */
/*
* GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <iostream>
#include <algorithm>
#include <string>
#include <stdexcept>
#include "expairseq.h"
#include "lst.h"
#include "mul.h"
#include "power.h"
#include "relational.h"
#include "wildcard.h"
#include "archive.h"
#include "operators.h"
#include "utils.h"
#if EXPAIRSEQ_USE_HASHTAB
#include <cmath>
#endif // EXPAIRSEQ_USE_HASHTAB
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
print_func<print_context>(&expairseq::do_print).
print_func<print_tree>(&expairseq::do_print_tree))
//////////
// helper classes
//////////
class epp_is_less
{
public:
bool operator()(const epp &lh, const epp &rh) const
{
return (*lh).is_less(*rh);
}
};
//////////
// default constructor
//////////
// public
expairseq::expairseq() : inherited(TINFO_expairseq)
#if EXPAIRSEQ_USE_HASHTAB
, hashtabsize(0)
#endif // EXPAIRSEQ_USE_HASHTAB
{}
// protected
#if 0
/** For use by copy ctor and assignment operator. */
void expairseq::copy(const expairseq &other)
{
seq = other.seq;
overall_coeff = other.overall_coeff;
#if EXPAIRSEQ_USE_HASHTAB
// copy hashtab
hashtabsize = other.hashtabsize;
if (hashtabsize!=0) {
hashmask = other.hashmask;
hashtab.resize(hashtabsize);
epvector::const_iterator osb = other.seq.begin();
for (unsigned i=0; i<hashtabsize; ++i) {
hashtab[i].clear();
for (epplist::const_iterator cit=other.hashtab[i].begin();
cit!=other.hashtab[i].end(); ++cit) {
hashtab[i].push_back(seq.begin()+((*cit)-osb));
}
}
} else {
hashtab.clear();
}
#endif // EXPAIRSEQ_USE_HASHTAB
}
#endif
//////////
// other constructors
//////////
expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
{
construct_from_2_ex(lh,rh);
GINAC_ASSERT(is_canonical());
}
expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
{
construct_from_exvector(v);
GINAC_ASSERT(is_canonical());
}
expairseq::expairseq(const epvector &v, const ex &oc)
: inherited(TINFO_expairseq), overall_coeff(oc)
{
GINAC_ASSERT(is_a<numeric>(oc));
construct_from_epvector(v);
GINAC_ASSERT(is_canonical());
}
expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
: inherited(TINFO_expairseq), overall_coeff(oc)
{
GINAC_ASSERT(vp.get()!=0);
GINAC_ASSERT(is_a<numeric>(oc));
construct_from_epvector(*vp);
GINAC_ASSERT(is_canonical());
}
//////////
// archiving
//////////
expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
#if EXPAIRSEQ_USE_HASHTAB
, hashtabsize(0)
#endif
{
for (unsigned int i=0; true; i++) {
ex rest;
ex coeff;
if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
seq.push_back(expair(rest, coeff));
else
break;
}
n.find_ex("overall_coeff", overall_coeff, sym_lst);
canonicalize();
GINAC_ASSERT(is_canonical());
}
void expairseq::archive(archive_node &n) const
{
inherited::archive(n);
epvector::const_iterator i = seq.begin(), iend = seq.end();
while (i != iend) {
n.add_ex("rest", i->rest);
n.add_ex("coeff", i->coeff);
++i;
}
n.add_ex("overall_coeff", overall_coeff);
}
DEFAULT_UNARCHIVE(expairseq)
//////////
// functions overriding virtual functions from base classes
//////////
// public
void expairseq::do_print(const print_context & c, unsigned level) const
{
c.s << "[[";
printseq(c, ',', precedence(), level);
c.s << "]]";
}
void expairseq::do_print_tree(const print_tree & c, unsigned level) const
{
c.s << std::string(level, ' ') << class_name() << " @" << this
<< std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
<< ", nops=" << nops()
<< std::endl;
size_t num = seq.size();
for (size_t i=0; i<num; ++i) {
seq[i].rest.print(c, level + c.delta_indent);
seq[i].coeff.print(c, level + c.delta_indent);
if (i != num - 1)
c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
}
if (!overall_coeff.is_equal(default_overall_coeff())) {
c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
<< std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
overall_coeff.print(c, level + c.delta_indent);
}
c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
#if EXPAIRSEQ_USE_HASHTAB
c.s << std::string(level + c.delta_indent,' ')
<< "hashtab size " << hashtabsize << std::endl;
if (hashtabsize == 0) return;
#define MAXCOUNT 5
unsigned count[MAXCOUNT+1];
for (int i=0; i<MAXCOUNT+1; ++i)
count[i] = 0;
unsigned this_bin_fill;
unsigned cum_fill_sq = 0;
unsigned cum_fill = 0;
for (unsigned i=0; i<hashtabsize; ++i) {
this_bin_fill = 0;
if (hashtab[i].size() > 0) {
c.s << std::string(level + c.delta_indent, ' ')
<< "bin " << i << " with entries ";
for (epplist::const_iterator it=hashtab[i].begin();
it!=hashtab[i].end(); ++it) {
c.s << *it-seq.begin() << " ";
++this_bin_fill;
}
c.s << std::endl;
cum_fill += this_bin_fill;
cum_fill_sq += this_bin_fill*this_bin_fill;
}
if (this_bin_fill<MAXCOUNT)
++count[this_bin_fill];
else
++count[MAXCOUNT];
}
unsigned fact = 1;
double cum_prob = 0;
double lambda = (1.0*seq.size()) / hashtabsize;
for (int k=0; k<MAXCOUNT; ++k) {
if (k>0)
fact *= k;
double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
cum_prob += prob;
c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
<< int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
<< int(prob*1000)/10.0 << ")" << std::endl;
}
c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
<< int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
<< int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
c.s << std::string(level + c.delta_indent, ' ') << "variance: "
<< 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
<< std::endl;
c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
<< (1.0*cum_fill)/hashtabsize
<< " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
#endif // EXPAIRSEQ_USE_HASHTAB
}
bool expairseq::info(unsigned inf) const
{
if (inf == info_flags::expanded)
return (flags & status_flags::expanded);
return inherited::info(inf);
}
size_t expairseq::nops() const
{
if (overall_coeff.is_equal(default_overall_coeff()))
return seq.size();
else
return seq.size()+1;
}
ex expairseq::op(size_t i) const
{
if (i < seq.size())
return recombine_pair_to_ex(seq[i]);
GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
return overall_coeff;
}
ex expairseq::map(map_function &f) const
{
std::auto_ptr<epvector> v(new epvector);
v->reserve(seq.size()+1);
epvector::const_iterator cit = seq.begin(), last = seq.end();
while (cit != last) {
v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
++cit;
}
if (overall_coeff.is_equal(default_overall_coeff()))
return thisexpairseq(v, default_overall_coeff());
else {
ex newcoeff = f(overall_coeff);
if(is_a<numeric>(newcoeff))
return thisexpairseq(v, newcoeff);
else {
v->push_back(split_ex_to_pair(newcoeff));
return thisexpairseq(v, default_overall_coeff());
}
}
}
/** Perform coefficient-wise automatic term rewriting rules in this class. */
ex expairseq::eval(int level) const
{
if ((level==1) && (flags &status_flags::evaluated))
return *this;
std::auto_ptr<epvector> vp = evalchildren(level);
if (vp.get() == 0)
return this->hold();
return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
epvector* conjugateepvector(const epvector&epv)
{
epvector *newepv = 0;
for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
if(newepv) {
newepv->push_back(i->conjugate());
continue;
}
expair x = i->conjugate();
if (x.is_equal(*i)) {
continue;
}
newepv = new epvector;
newepv->reserve(epv.size());
for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
newepv->push_back(*j);
}
newepv->push_back(x);
}
return newepv;
}
ex expairseq::conjugate() const
{
epvector* newepv = conjugateepvector(seq);
ex x = overall_coeff.conjugate();
if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
return *this;
}
ex result = thisexpairseq(newepv ? *newepv : seq, x);
if (newepv) {
delete newepv;
}
return result;
}
bool expairseq::match(const ex & pattern, lst & repl_lst) const
{
// This differs from basic::match() because we want "a+b+c+d" to
// match "d+*+b" with "*" being "a+c", and we want to honor commutativity
if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
// Check whether global wildcard (one that matches the "rest of the
// expression", like "*" above) is present
bool has_global_wildcard = false;
ex global_wildcard;
for (size_t i=0; i<pattern.nops(); i++) {
if (is_exactly_a<wildcard>(pattern.op(i))) {
has_global_wildcard = true;
global_wildcard = pattern.op(i);
break;
}
}
// Unfortunately, this is an O(N^2) operation because we can't
// sort the pattern in a useful way...
// Chop into terms
exvector ops;
ops.reserve(nops());
for (size_t i=0; i<nops(); i++)
ops.push_back(op(i));
// Now, for every term of the pattern, look for a matching term in
// the expression and remove the match
for (size_t i=0; i<pattern.nops(); i++) {
ex p = pattern.op(i);
if (has_global_wildcard && p.is_equal(global_wildcard))
continue;
exvector::iterator it = ops.begin(), itend = ops.end();
while (it != itend) {
lst::const_iterator last_el = repl_lst.end();
--last_el;
if (it->match(p, repl_lst)) {
ops.erase(it);
goto found;
}
while(true) {
lst::const_iterator next_el = last_el;
++next_el;
if(next_el == repl_lst.end())
break;
else
repl_lst.remove_last();
}
++it;
}
return false; // no match found
found: ;
}
if (has_global_wildcard) {
// Assign all the remaining terms to the global wildcard (unless
// it has already been matched before, in which case the matches
// must be equal)
size_t num = ops.size();
std::auto_ptr<epvector> vp(new epvector);
vp->reserve(num);
for (size_t i=0; i<num; i++)
vp->push_back(split_ex_to_pair(ops[i]));
ex rest = thisexpairseq(vp, default_overall_coeff());
for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
if (it->op(0).is_equal(global_wildcard))
return rest.is_equal(it->op(1));
}
repl_lst.append(global_wildcard == rest);
return true;
} else {
// No global wildcard, then the match fails if there are any
// unmatched terms left
return ops.empty();
}
}
return inherited::match(pattern, repl_lst);
}
ex expairseq::subs(const exmap & m, unsigned options) const
{
std::auto_ptr<epvector> vp = subschildren(m, options);
if (vp.get())
return ex_to<basic>(thisexpairseq(vp, overall_coeff));
else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
else
return subs_one_level(m, options);
}
// protected
int expairseq::compare_same_type(const basic &other) const
{
GINAC_ASSERT(is_a<expairseq>(other));
const expairseq &o = static_cast<const expairseq &>(other);
int cmpval;
// compare number of elements
if (seq.size() != o.seq.size())
return (seq.size()<o.seq.size()) ? -1 : 1;
// compare overall_coeff
cmpval = overall_coeff.compare(o.overall_coeff);
if (cmpval!=0)
return cmpval;
#if EXPAIRSEQ_USE_HASHTAB
GINAC_ASSERT(hashtabsize==o.hashtabsize);
if (hashtabsize==0) {
#endif // EXPAIRSEQ_USE_HASHTAB
epvector::const_iterator cit1 = seq.begin();
epvector::const_iterator cit2 = o.seq.begin();
epvector::const_iterator last1 = seq.end();
epvector::const_iterator last2 = o.seq.end();
for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
cmpval = (*cit1).compare(*cit2);
if (cmpval!=0) return cmpval;
}
GINAC_ASSERT(cit1==last1);
GINAC_ASSERT(cit2==last2);
return 0;
#if EXPAIRSEQ_USE_HASHTAB
}
// compare number of elements in each hashtab entry
for (unsigned i=0; i<hashtabsize; ++i) {
unsigned cursize=hashtab[i].size();
if (cursize != o.hashtab[i].size())
return (cursize < o.hashtab[i].size()) ? -1 : 1;
}
// compare individual (sorted) hashtab entries
for (unsigned i=0; i<hashtabsize; ++i) {
unsigned sz = hashtab[i].size();
if (sz>0) {
const epplist &eppl1 = hashtab[i];
const epplist &eppl2 = o.hashtab[i];
epplist::const_iterator it1 = eppl1.begin();
epplist::const_iterator it2 = eppl2.begin();
while (it1!=eppl1.end()) {
cmpval = (*(*it1)).compare(*(*it2));
if (cmpval!=0)
return cmpval;
++it1;
++it2;
}
}
}
return 0; // equal
#endif // EXPAIRSEQ_USE_HASHTAB
}
bool expairseq::is_equal_same_type(const basic &other) const
{
const expairseq &o = static_cast<const expairseq &>(other);
// compare number of elements
if (seq.size()!=o.seq.size())
return false;
// compare overall_coeff
if (!overall_coeff.is_equal(o.overall_coeff))
return false;
#if EXPAIRSEQ_USE_HASHTAB
// compare number of elements in each hashtab entry
if (hashtabsize!=o.hashtabsize) {
std::cout << "this:" << std::endl;
print(print_tree(std::cout));
std::cout << "other:" << std::endl;
other.print(print_tree(std::cout));
}
GINAC_ASSERT(hashtabsize==o.hashtabsize);
if (hashtabsize==0) {
#endif // EXPAIRSEQ_USE_HASHTAB
epvector::const_iterator cit1 = seq.begin();
epvector::const_iterator cit2 = o.seq.begin();
epvector::const_iterator last1 = seq.end();
while (cit1!=last1) {
if (!(*cit1).is_equal(*cit2)) return false;
++cit1;
++cit2;
}
return true;
#if EXPAIRSEQ_USE_HASHTAB
}
for (unsigned i=0; i<hashtabsize; ++i) {
if (hashtab[i].size() != o.hashtab[i].size())
return false;
}
// compare individual sorted hashtab entries
for (unsigned i=0; i<hashtabsize; ++i) {
unsigned sz = hashtab[i].size();
if (sz>0) {
const epplist &eppl1 = hashtab[i];
const epplist &eppl2 = o.hashtab[i];
epplist::const_iterator it1 = eppl1.begin();
epplist::const_iterator it2 = eppl2.begin();
while (it1!=eppl1.end()) {
if (!(*(*it1)).is_equal(*(*it2))) return false;
++it1;
++it2;
}
}
}
return true;
#endif // EXPAIRSEQ_USE_HASHTAB
}
unsigned expairseq::return_type() const
{
return return_types::noncommutative_composite;
}
unsigned expairseq::calchash() const
{
unsigned v = golden_ratio_hash(this->tinfo());
epvector::const_iterator i = seq.begin();
const epvector::const_iterator end = seq.end();
while (i != end) {
v ^= i->rest.gethash();
#if !EXPAIRSEQ_USE_HASHTAB
// rotation spoils commutativity!
v = rotate_left(v);
v ^= i->coeff.gethash();
#endif // !EXPAIRSEQ_USE_HASHTAB
++i;
}
v ^= overall_coeff.gethash();
// store calculated hash value only if object is already evaluated
if (flags &status_flags::evaluated) {
setflag(status_flags::hash_calculated);
hashvalue = v;
}
return v;
}
ex expairseq::expand(unsigned options) const
{
std::auto_ptr<epvector> vp = expandchildren(options);
if (vp.get())
return thisexpairseq(vp, overall_coeff);
else {
// The terms have not changed, so it is safe to declare this expanded
return (options == 0) ? setflag(status_flags::expanded) : *this;
}
}
//////////
// new virtual functions which can be overridden by derived classes
//////////
// protected
/** Create an object of this type.
* This method works similar to a constructor. It is useful because expairseq
* has (at least) two possible different semantics but we want to inherit
* methods thus avoiding code duplication. Sometimes a method in expairseq
* has to create a new one of the same semantics, which cannot be done by a
* ctor because the name (add, mul,...) is unknown on the expaiseq level. In
* order for this trick to work a derived class must of course override this
* definition. */
ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
{
return expairseq(v, oc);
}
ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
{
return expairseq(vp, oc);
}
void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
{
c.s << "[[";
p.rest.print(c, precedence());
c.s << ",";
p.coeff.print(c, precedence());
c.s << "]]";
}
void expairseq::printseq(const print_context & c, char delim,
unsigned this_precedence,
unsigned upper_precedence) const
{
if (this_precedence <= upper_precedence)
c.s << "(";
epvector::const_iterator it, it_last = seq.end() - 1;
for (it=seq.begin(); it!=it_last; ++it) {
printpair(c, *it, this_precedence);
c.s << delim;
}
printpair(c, *it, this_precedence);
if (!overall_coeff.is_equal(default_overall_coeff())) {
c.s << delim;
overall_coeff.print(c, this_precedence);
}
if (this_precedence <= upper_precedence)
c.s << ")";
}
/** Form an expair from an ex, using the corresponding semantics.
* @see expairseq::recombine_pair_to_ex() */
expair expairseq::split_ex_to_pair(const ex &e) const
{
return expair(e,_ex1);
}
expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
const ex &c) const
{
GINAC_ASSERT(is_exactly_a<numeric>(c));
return expair(e,c);
}
expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
const ex &c) const
{
GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
GINAC_ASSERT(is_exactly_a<numeric>(c));
return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
}
/** Form an ex out of an expair, using the corresponding semantics.
* @see expairseq::split_ex_to_pair() */
ex expairseq::recombine_pair_to_ex(const expair &p) const
{
return lst(p.rest,p.coeff);
}
bool expairseq::expair_needs_further_processing(epp it)
{
#if EXPAIRSEQ_USE_HASHTAB
//# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
#endif // EXPAIRSEQ_USE_HASHTAB
return false;
}
ex expairseq::default_overall_coeff() const
{
return _ex0;
}
void expairseq::combine_overall_coeff(const ex &c)
{
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
GINAC_ASSERT(is_exactly_a<numeric>(c));
overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
}
void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
{
GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
GINAC_ASSERT(is_exactly_a<numeric>(c1));
GINAC_ASSERT(is_exactly_a<numeric>(c2));
overall_coeff = ex_to<numeric>(overall_coeff).
add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
}
bool expairseq::can_make_flat(const expair &p) const
{
return true;
}
//////////
// non-virtual functions in this class
//////////
void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
{
exvector v;
v.reserve(2);
v.push_back(lh);
v.push_back(rh);
construct_from_exvector(v);
#if EXPAIRSEQ_USE_HASHTAB
GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
#endif // EXPAIRSEQ_USE_HASHTAB
}
void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
{
if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
#if EXPAIRSEQ_USE_HASHTAB
unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
ex_to<expairseq>(rh).seq.size();
if (calc_hashtabsize(totalsize)!=0) {
construct_from_2_ex_via_exvector(lh,rh);
} else {
#endif // EXPAIRSEQ_USE_HASHTAB
construct_from_2_expairseq(ex_to<expairseq>(lh),
ex_to<expairseq>(rh));
#if EXPAIRSEQ_USE_HASHTAB
}
#endif // EXPAIRSEQ_USE_HASHTAB
return;
} else {
#if EXPAIRSEQ_USE_HASHTAB
unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
if (calc_hashtabsize(totalsize)!=0) {
construct_from_2_ex_via_exvector(lh, rh);
} else {
#endif // EXPAIRSEQ_USE_HASHTAB
construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
#if EXPAIRSEQ_USE_HASHTAB
}
#endif // EXPAIRSEQ_USE_HASHTAB
return;
}
} else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
#if EXPAIRSEQ_USE_HASHTAB
unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
if (calc_hashtabsize(totalsize)!=0) {
construct_from_2_ex_via_exvector(lh,rh);
} else {
#endif // EXPAIRSEQ_USE_HASHTAB
construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
#if EXPAIRSEQ_USE_HASHTAB
}
#endif // EXPAIRSEQ_USE_HASHTAB
return;
}
#if EXPAIRSEQ_USE_HASHTAB
if (calc_hashtabsize(2)!=0) {
construct_from_2_ex_via_exvector(lh,rh);
return;
}
hashtabsize = 0;
#endif // EXPAIRSEQ_USE_HASHTAB
if (is_exactly_a<numeric>(lh)) {
if (is_exactly_a<numeric>(rh)) {
combine_overall_coeff(lh);
combine_overall_coeff(rh);
} else {
combine_overall_coeff(lh);
seq.push_back(split_ex_to_pair(rh));
}
} else {
if (is_exactly_a<numeric>(rh)) {
combine_overall_coeff(rh);
seq.push_back(split_ex_to_pair(lh));
} else {
expair p1 = split_ex_to_pair(lh);
expair p2 = split_ex_to_pair(rh);
int cmpval = p1.rest.compare(p2.rest);
if (cmpval==0) {
p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
if (!ex_to<numeric>(p1.coeff).is_zero()) {
// no further processing is necessary, since this
// one element will usually be recombined in eval()
seq.push_back(p1);
}
} else {
seq.reserve(2);
if (cmpval<0) {
seq.push_back(p1);
seq.push_back(p2);
} else {
seq.push_back(p2);
seq.push_back(p1);
}
}
}
}
}
void expairseq::construct_from_2_expairseq(const expairseq &s1,
const expairseq &s2)
{
combine_overall_coeff(s1.overall_coeff);
combine_overall_coeff(s2.overall_coeff);
epvector::const_iterator first1 = s1.seq.begin();
epvector::const_iterator last1 = s1.seq.end();
epvector::const_iterator first2 = s2.seq.begin();
epvector::const_iterator last2 = s2.seq.end();
seq.reserve(s1.seq.size()+s2.seq.size());
bool needs_further_processing=false;
while (first1!=last1 && first2!=last2) {
int cmpval = (*first1).rest.compare((*first2).rest);
if (cmpval==0) {
// combine terms
const numeric &newcoeff = ex_to<numeric>(first1->coeff).
add(ex_to<numeric>(first2->coeff));
if (!newcoeff.is_zero()) {
seq.push_back(expair(first1->rest,newcoeff));
if (expair_needs_further_processing(seq.end()-1)) {
needs_further_processing = true;
}
}
++first1;
++first2;
} else if (cmpval<0) {
seq.push_back(*first1);
++first1;
} else {
seq.push_back(*first2);
++first2;
}
}
while (first1!=last1) {
seq.push_back(*first1);
++first1;
}
while (first2!=last2) {
seq.push_back(*first2);
++first2;
}
if (needs_further_processing) {
epvector v = seq;
seq.clear();
construct_from_epvector(v);
}
}
void expairseq::construct_from_expairseq_ex(const expairseq &s,
const ex &e)
{
combine_overall_coeff(s.overall_coeff);
if (is_exactly_a<numeric>(e)) {
combine_overall_coeff(e);
seq = s.seq;
return;
}
epvector::const_iterator first = s.seq.begin();
epvector::const_iterator last = s.seq.end();
expair p = split_ex_to_pair(e);
seq.reserve(s.seq.size()+1);
bool p_pushed = false;
bool needs_further_processing=false;
// merge p into s.seq
while (first!=last) {
int cmpval = (*first).rest.compare(p.rest);
if (cmpval==0) {
// combine terms
const numeric &newcoeff = ex_to<numeric>(first->coeff).
add(ex_to<numeric>(p.coeff));
if (!newcoeff.is_zero()) {
seq.push_back(expair(first->rest,newcoeff));
if (expair_needs_further_processing(seq.end()-1))
needs_further_processing = true;
}
++first;
p_pushed = true;
break;
} else if (cmpval<0) {
seq.push_back(*first);
++first;
} else {
seq.push_back(p);
p_pushed = true;
break;
}
}
if (p_pushed) {
// while loop exited because p was pushed, now push rest of s.seq
while (first!=last) {
seq.push_back(*first);
++first;
}
} else {
// while loop exited because s.seq was pushed, now push p
seq.push_back(p);
}
if (needs_further_processing) {
epvector v = seq;
seq.clear();
construct_from_epvector(v);
}
}
void expairseq::construct_from_exvector(const exvector &v)
{
// simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
// +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
// +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
// (same for (+,*) -> (*,^)
make_flat(v);
#if EXPAIRSEQ_USE_HASHTAB
combine_same_terms();
#else
canonicalize();
combine_same_terms_sorted_seq();
#endif // EXPAIRSEQ_USE_HASHTAB
}
void expairseq::construct_from_epvector(const epvector &v)
{
// simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
// +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
// +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
// (same for (+,*) -> (*,^)
make_flat(v);
#if EXPAIRSEQ_USE_HASHTAB
combine_same_terms();
#else
canonicalize();
combine_same_terms_sorted_seq();
#endif // EXPAIRSEQ_USE_HASHTAB
}
/** Combine this expairseq with argument exvector.
* It cares for associativity as well as for special handling of numerics. */
void expairseq::make_flat(const exvector &v)
{
exvector::const_iterator cit;
// count number of operands which are of same expairseq derived type
// and their cumulative number of operands
int nexpairseqs = 0;
int noperands = 0;
cit = v.begin();
while (cit!=v.end()) {
if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
++nexpairseqs;
noperands += ex_to<expairseq>(*cit).seq.size();
}
++cit;
}
// reserve seq and coeffseq which will hold all operands
seq.reserve(v.size()+noperands-nexpairseqs);
// copy elements and split off numerical part
cit = v.begin();
while (cit!=v.end()) {
if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
const expairseq &subseqref = ex_to<expairseq>(*cit);
combine_overall_coeff(subseqref.overall_coeff);
epvector::const_iterator cit_s = subseqref.seq.begin();
while (cit_s!=subseqref.seq.end()) {
seq.push_back(*cit_s);
++cit_s;
}
} else {
if (is_exactly_a<numeric>(*cit))
combine_overall_coeff(*cit);
else
seq.push_back(split_ex_to_pair(*cit));
}
++cit;
}
}
/** Combine this expairseq with argument epvector.
* It cares for associativity as well as for special handling of numerics. */
void expairseq::make_flat(const epvector &v)
{
epvector::const_iterator cit;
// count number of operands which are of same expairseq derived type
// and their cumulative number of operands
int nexpairseqs = 0;
int noperands = 0;
cit = v.begin();
while (cit!=v.end()) {
if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
++nexpairseqs;
noperands += ex_to<expairseq>(cit->rest).seq.size();
}
++cit;
}
// reserve seq and coeffseq which will hold all operands
seq.reserve(v.size()+noperands-nexpairseqs);
// copy elements and split off numerical part
cit = v.begin();
while (cit!=v.end()) {
if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
this->can_make_flat(*cit)) {
const expairseq &subseqref = ex_to<expairseq>(cit->rest);
combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
ex_to<numeric>(cit->coeff));
epvector::const_iterator cit_s = subseqref.seq.begin();
while (cit_s!=subseqref.seq.end()) {
seq.push_back(expair(cit_s->rest,
ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
//seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
// (*cit).coeff));
++cit_s;
}
} else {
if (cit->is_canonical_numeric())
combine_overall_coeff(cit->rest);
else
seq.push_back(*cit);
}
++cit;
}
}
/** Brings this expairseq into a sorted (canonical) form. */
void expairseq::canonicalize()
{
std::sort(seq.begin(), seq.end(), expair_rest_is_less());
}
/** Compact a presorted expairseq by combining all matching expairs to one
* each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
* instance. */
void expairseq::combine_same_terms_sorted_seq()
{
if (seq.size()<2)
return;
bool needs_further_processing = false;
epvector::iterator itin1 = seq.begin();
epvector::iterator itin2 = itin1+1;
epvector::iterator itout = itin1;
epvector::iterator last = seq.end();
// must_copy will be set to true the first time some combination is
// possible from then on the sequence has changed and must be compacted
bool must_copy = false;
while (itin2!=last) {
if (itin1->rest.compare(itin2->rest)==0) {
itin1->coeff = ex_to<numeric>(itin1->coeff).
add_dyn(ex_to<numeric>(itin2->coeff));
if (expair_needs_further_processing(itin1))
needs_further_processing = true;
must_copy = true;
} else {
if (!ex_to<numeric>(itin1->coeff).is_zero()) {
if (must_copy)
*itout = *itin1;
++itout;
}
itin1 = itin2;
}
++itin2;
}
if (!ex_to<numeric>(itin1->coeff).is_zero()) {
if (must_copy)
*itout = *itin1;
++itout;
}
if (itout!=last)
seq.erase(itout,last);
if (needs_further_processing) {
epvector v = seq;
seq.clear();
construct_from_epvector(v);
}
}
#if EXPAIRSEQ_USE_HASHTAB
unsigned expairseq::calc_hashtabsize(unsigned sz) const
{
unsigned size;
unsigned nearest_power_of_2 = 1 << log2(sz);
// if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
// size = nearest_power_of_2*hashtabfactor;
size = nearest_power_of_2/hashtabfactor;
if (size<minhashtabsize)
return 0;
// hashtabsize must be a power of 2
GINAC_ASSERT((1U << log2(size))==size);
return size;
}
unsigned expairseq::calc_hashindex(const ex &e) const
{
// calculate hashindex
unsigned hashindex;
if (is_a<numeric>(e)) {
hashindex = hashmask;
} else {
hashindex = e.gethash() & hashmask;
// last hashtab entry is reserved for numerics
if (hashindex==hashmask) hashindex = 0;
}
GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
return hashindex;
}
void expairseq::shrink_hashtab()
{
unsigned new_hashtabsize;
while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
GINAC_ASSERT(new_hashtabsize<hashtabsize);
if (new_hashtabsize==0) {
hashtab.clear();
hashtabsize = 0;
canonicalize();
return;
}
// shrink by a factor of 2
unsigned half_hashtabsize = hashtabsize/2;
for (unsigned i=0; i<half_hashtabsize-1; ++i)
hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
// special treatment for numeric hashes
hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
hashtab.resize(half_hashtabsize);
hashtabsize = half_hashtabsize;
hashmask = hashtabsize-1;
}
}
void expairseq::remove_hashtab_entry(epvector::const_iterator element)
{
if (hashtabsize==0)
return; // nothing to do
// calculate hashindex of element to be deleted
unsigned hashindex = calc_hashindex((*element).rest);
// find it in hashtab and remove it
epplist &eppl = hashtab[hashindex];
epplist::iterator epplit = eppl.begin();
bool erased = false;
while (epplit!=eppl.end()) {
if (*epplit == element) {
eppl.erase(epplit);
erased = true;
break;
}
++epplit;
}
if (!erased) {
std::cout << "tried to erase " << element-seq.begin() << std::endl;
std::cout << "size " << seq.end()-seq.begin() << std::endl;
unsigned hashindex = calc_hashindex(element->rest);
epplist &eppl = hashtab[hashindex];
epplist::iterator epplit = eppl.begin();
bool erased = false;
while (epplit!=eppl.end()) {
if (*epplit == element) {
eppl.erase(epplit);
erased = true;
break;
}
++epplit;
}
GINAC_ASSERT(erased);
}
GINAC_ASSERT(erased);
}
void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
epvector::iterator newpos)
{
GINAC_ASSERT(hashtabsize!=0);
// calculate hashindex of element which was moved
unsigned hashindex=calc_hashindex((*newpos).rest);
// find it in hashtab and modify it
epplist &eppl = hashtab[hashindex];
epplist::iterator epplit = eppl.begin();
while (epplit!=eppl.end()) {
if (*epplit == oldpos) {
*epplit = newpos;
break;
}
++epplit;
}
GINAC_ASSERT(epplit!=eppl.end());
}
void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
{
epplist::const_iterator current = eppl.begin();
while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
++current;
}
eppl.insert(current,elem);
}
void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
epvector::iterator &last_non_zero,
std::vector<bool> &touched,
unsigned &number_of_zeroes)
{
epp current = seq.begin();
while (current!=first_numeric) {
if (is_exactly_a<numeric>(current->rest)) {
--first_numeric;
iter_swap(current,first_numeric);
} else {
// calculate hashindex
unsigned currenthashindex = calc_hashindex(current->rest);
// test if there is already a matching expair in the hashtab-list
epplist &eppl=hashtab[currenthashindex];
epplist::iterator epplit = eppl.begin();
while (epplit!=eppl.end()) {
if (current->rest.is_equal((*epplit)->rest))
break;
++epplit;
}
if (epplit==eppl.end()) {
// no matching expair found, append this to end of list
sorted_insert(eppl,current);
++current;
} else {
// epplit points to a matching expair, combine it with current
(*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
add_dyn(ex_to<numeric>(current->coeff));
// move obsolete current expair to end by swapping with last_non_zero element
// if this was a numeric, it is swapped with the expair before first_numeric
iter_swap(current,last_non_zero);
--first_numeric;
if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
--last_non_zero;
++number_of_zeroes;
// test if combined term has coeff 0 and can be removed is done later
touched[(*epplit)-seq.begin()] = true;
}
}
}
}
void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
epvector::iterator &last_non_zero,
std::vector<bool> &touched,
unsigned &number_of_zeroes)
{
// move terms with coeff 0 to end and remove them from hashtab
// check only those elements which have been touched
epp current = seq.begin();
size_t i = 0;
while (current!=first_numeric) {
if (!touched[i]) {
++current;
++i;
} else if (!ex_to<numeric>((*current).coeff).is_zero()) {
++current;
++i;
} else {
remove_hashtab_entry(current);
// move element to the end, unless it is already at the end
if (current!=last_non_zero) {
iter_swap(current,last_non_zero);
--first_numeric;
bool numeric_swapped = first_numeric!=last_non_zero;
if (numeric_swapped)
iter_swap(first_numeric,current);
epvector::iterator changed_entry;
if (numeric_swapped)
changed_entry = first_numeric;
else
changed_entry = last_non_zero;
--last_non_zero;
++number_of_zeroes;
if (first_numeric!=current) {
// change entry in hashtab which referred to first_numeric or last_non_zero to current
move_hashtab_entry(changed_entry,current);
touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
}
} else {
--first_numeric;
--last_non_zero;
++number_of_zeroes;
}
}
}
GINAC_ASSERT(i==current-seq.begin());
}
/** True if one of the coeffs vanishes, otherwise false.
* This would be an invariant violation, so this should only be used for
* debugging purposes. */
bool expairseq::has_coeff_0() const
{
epvector::const_iterator i = seq.begin(), end = seq.end();
while (i != end) {
if (i->coeff.is_zero())
return true;
++i;
}
return false;
}
void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
epvector::const_iterator last_non_zero)
{
if (first_numeric == seq.end()) return; // no numerics
epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
while (current != last) {
sorted_insert(hashtab[hashmask], current);
++current;
}
}
void expairseq::combine_same_terms()
{
// combine same terms, drop term with coeff 0, move numerics to end
// calculate size of hashtab
hashtabsize = calc_hashtabsize(seq.size());
// hashtabsize is a power of 2
hashmask = hashtabsize-1;
// allocate hashtab
hashtab.clear();
hashtab.resize(hashtabsize);
if (hashtabsize==0) {
canonicalize();
combine_same_terms_sorted_seq();
GINAC_ASSERT(!has_coeff_0());
return;
}
// iterate through seq, move numerics to end,
// fill hashtab and combine same terms
epvector::iterator first_numeric = seq.end();
epvector::iterator last_non_zero = seq.end()-1;
size_t num = seq.size();
std::vector<bool> touched(num);
unsigned number_of_zeroes = 0;
GINAC_ASSERT(!has_coeff_0());
build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
// there should not be any terms with coeff 0 from the beginning,
// so it should be safe to skip this step
if (number_of_zeroes!=0) {
drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
}
add_numerics_to_hashtab(first_numeric,last_non_zero);
// pop zero elements
for (unsigned i=0; i<number_of_zeroes; ++i) {
seq.pop_back();
}
// shrink hashtabsize to calculated value
GINAC_ASSERT(!has_coeff_0());
shrink_hashtab();
GINAC_ASSERT(!has_coeff_0());
}
#endif // EXPAIRSEQ_USE_HASHTAB
/** Check if this expairseq is in sorted (canonical) form. Useful mainly for
* debugging or in assertions since being sorted is an invariance. */
bool expairseq::is_canonical() const
{
if (seq.size() <= 1)
return 1;
#if EXPAIRSEQ_USE_HASHTAB
if (hashtabsize > 0) return 1; // not canoncalized
#endif // EXPAIRSEQ_USE_HASHTAB
epvector::const_iterator it = seq.begin(), itend = seq.end();
epvector::const_iterator it_last = it;
for (++it; it!=itend; it_last=it, ++it) {
if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
if (!is_exactly_a<numeric>(it_last->rest) ||
!is_exactly_a<numeric>(it->rest)) {
// double test makes it easier to set a breakpoint...
if (!is_exactly_a<numeric>(it_last->rest) ||
!is_exactly_a<numeric>(it->rest)) {
printpair(std::clog, *it_last, 0);
std::clog << ">";
printpair(std::clog, *it, 0);
std::clog << "\n";
std::clog << "pair1:" << std::endl;
it_last->rest.print(print_tree(std::clog));
it_last->coeff.print(print_tree(std::clog));
std::clog << "pair2:" << std::endl;
it->rest.print(print_tree(std::clog));
it->coeff.print(print_tree(std::clog));
return 0;
}
}
}
}
return 1;
}
/** Member-wise expand the expairs in this sequence.
*
* @see expairseq::expand()
* @return pointer to epvector containing expanded pairs or zero pointer,
* if no members were changed. */
std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
{
const epvector::const_iterator last = seq.end();
epvector::const_iterator cit = seq.begin();
while (cit!=last) {
const ex &expanded_ex = cit->rest.expand(options);
if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
// something changed, copy seq, eval and return it
std::auto_ptr<epvector> s(new epvector);
s->reserve(seq.size());
// copy parts of seq which are known not to have changed
epvector::const_iterator cit2 = seq.begin();
while (cit2!=cit) {
s->push_back(*cit2);
++cit2;
}
// copy first changed element
s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
cit2->coeff));
++cit2;
// copy rest
while (cit2!=last) {
s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
cit2->coeff));
++cit2;
}
return s;
}
++cit;
}
return std::auto_ptr<epvector>(0); // signalling nothing has changed
}
/** Member-wise evaluate the expairs in this sequence.
*
* @see expairseq::eval()
* @return pointer to epvector containing evaluated pairs or zero pointer,
* if no members were changed. */
std::auto_ptr<epvector> expairseq::evalchildren(int level) const
{
// returns a NULL pointer if nothing had to be evaluated
// returns a pointer to a newly created epvector otherwise
// (which has to be deleted somewhere else)
if (level==1)
return std::auto_ptr<epvector>(0);
if (level == -max_recursion_level)
throw(std::runtime_error("max recursion level reached"));
--level;
epvector::const_iterator last = seq.end();
epvector::const_iterator cit = seq.begin();
while (cit!=last) {
const ex &evaled_ex = cit->rest.eval(level);
if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
// something changed, copy seq, eval and return it
std::auto_ptr<epvector> s(new epvector);
s->reserve(seq.size());
// copy parts of seq which are known not to have changed
epvector::const_iterator cit2=seq.begin();
while (cit2!=cit) {
s->push_back(*cit2);
++cit2;
}
// copy first changed element
s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
cit2->coeff));
++cit2;
// copy rest
while (cit2!=last) {
s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
cit2->coeff));
++cit2;
}
return s;
}
++cit;
}
return std::auto_ptr<epvector>(0); // signalling nothing has changed
}
/** Member-wise substitute in this sequence.
*
* @see expairseq::subs()
* @return pointer to epvector containing pairs after application of subs,
* or NULL pointer if no members were changed. */
std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
{
// When any of the objects to be substituted is a product or power
// we have to recombine the pairs because the numeric coefficients may
// be part of the search pattern.
if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
// Search the list of substitutions and cache our findings
for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
options |= subs_options::pattern_is_product;
break;
}
}
if (!(options & subs_options::pattern_is_product))
options |= subs_options::pattern_is_not_product;
}
if (options & subs_options::pattern_is_product) {
// Substitute in the recombined pairs
epvector::const_iterator cit = seq.begin(), last = seq.end();
while (cit != last) {
const ex &orig_ex = recombine_pair_to_ex(*cit);
const ex &subsed_ex = orig_ex.subs(m, options);
if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
// Something changed, copy seq, subs and return it
std::auto_ptr<epvector> s(new epvector);
s->reserve(seq.size());
// Copy parts of seq which are known not to have changed
s->insert(s->begin(), seq.begin(), cit);
// Copy first changed element
s->push_back(split_ex_to_pair(subsed_ex));
++cit;
// Copy rest
while (cit != last) {
s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
++cit;
}
return s;
}
++cit;
}
} else {
// Substitute only in the "rest" part of the pairs
epvector::const_iterator cit = seq.begin(), last = seq.end();
while (cit != last) {
const ex &subsed_ex = cit->rest.subs(m, options);
if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
// Something changed, copy seq, subs and return it
std::auto_ptr<epvector> s(new epvector);
s->reserve(seq.size());
// Copy parts of seq which are known not to have changed
s->insert(s->begin(), seq.begin(), cit);
// Copy first changed element
s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
++cit;
// Copy rest
while (cit != last) {
s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options),
cit->coeff));
++cit;
}
return s;
}
++cit;
}
}
// Nothing has changed
return std::auto_ptr<epvector>(0);
}
//////////
// static member variables
//////////
#if EXPAIRSEQ_USE_HASHTAB
unsigned expairseq::maxhashtabsize = 0x4000000U;
unsigned expairseq::minhashtabsize = 0x1000U;
unsigned expairseq::hashtabfactor = 1;
#endif // EXPAIRSEQ_USE_HASHTAB
} // namespace GiNaC
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