expairseq.cpp

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/*
 *  GiNaC Copyright (C) 1999-2011 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 "expairseq.h"
#include "lst.h"
#include "add.h"
#include "mul.h"
#include "power.h"
#include "relational.h"
#include "wildcard.h"
#include "archive.h"
#include "operators.h"
#include "utils.h"
#include "hash_seed.h"
#include "indexed.h"

#include <algorithm>
#if EXPAIRSEQ_USE_HASHTAB
#include <cmath>
#endif // EXPAIRSEQ_USE_HASHTAB
#include <iostream>
#include <iterator>
#include <stdexcept>
#include <string>

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() 
#if EXPAIRSEQ_USE_HASHTAB
    : hashtabsize(0)
#endif // EXPAIRSEQ_USE_HASHTAB
{}

// protected

#if 0

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)
{
    construct_from_2_ex(lh,rh);
    GINAC_ASSERT(is_canonical());
}

expairseq::expairseq(const exvector &v)
{
    construct_from_exvector(v);
    GINAC_ASSERT(is_canonical());
}

expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
  :  overall_coeff(oc)
{
    GINAC_ASSERT(is_a<numeric>(oc));
    construct_from_epvector(v, do_index_renaming);
    GINAC_ASSERT(is_canonical());
}

expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
  :  overall_coeff(oc)
{
    GINAC_ASSERT(vp.get()!=0);
    GINAC_ASSERT(is_a<numeric>(oc));
    construct_from_epvector(*vp, do_index_renaming);
    GINAC_ASSERT(is_canonical());
}

// archiving

void expairseq::read_archive(const archive_node &n, lst &sym_lst) 
{
    inherited::read_archive(n, sym_lst);
    archive_node::archive_node_cit first = n.find_first("rest");
    archive_node::archive_node_cit last = n.find_last("coeff");
    ++last;
    seq.reserve((last-first)/2);

    for (archive_node::archive_node_cit loc = first; loc < last;) {
        ex rest;
        ex coeff;
        n.find_ex_by_loc(loc++, rest, sym_lst);
        n.find_ex_by_loc(loc++, coeff, sym_lst);
        seq.push_back(expair(rest, coeff));
    }

    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);
}


// 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
{
    switch(inf) {
        case info_flags::expanded:
            return (flags & status_flags::expanded);
        case info_flags::has_indices: {
            if (flags & status_flags::has_indices)
                return true;
            else if (flags & status_flags::has_no_indices)
                return false;
            for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
                if (i->rest.info(info_flags::has_indices)) {
                    this->setflag(status_flags::has_indices);
                    this->clearflag(status_flags::has_no_indices);
                    return true;
                }
            }
            this->clearflag(status_flags::has_indices);
            this->setflag(status_flags::has_no_indices);
            return false;
        }
    }
    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(), true);
    else {
        ex newcoeff = f(overall_coeff);
        if(is_a<numeric>(newcoeff))
            return thisexpairseq(v, newcoeff, true);
        else {
            v->push_back(split_ex_to_pair(newcoeff));
            return thisexpairseq(v, default_overall_coeff(), true);
        }
    }
}

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);
    delete newepv;
    return result;
}

bool expairseq::match(const ex & pattern, exmap & 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 (typeid(*this) == typeid(ex_to<basic>(pattern))) {

        // 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) {
                if (it->match(p, repl_lst)) {
                    ops.erase(it);
                    goto found;
                }
                ++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 (exmap::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
                if (it->first.is_equal(global_wildcard))
                    return rest.is_equal(it->second);
            }
            repl_lst[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, (options & subs_options::no_index_renaming) == 0));
    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 = make_hash_seed(typeid(*this));
    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

ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
{
    return expairseq(v, oc, do_index_renaming);
}

ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
{
    return expairseq(vp, oc, do_index_renaming);
}

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 << ")";
}


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)));
}


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 (typeid(ex_to<basic>(lh)) == typeid(*this)) {
        if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
#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
                if (is_a<mul>(lh) && lh.info(info_flags::has_indices) && 
                    rh.info(info_flags::has_indices)) {
                    ex newrh=rename_dummy_indices_uniquely(lh, rh);
                    construct_from_2_expairseq(ex_to<expairseq>(lh),
                                               ex_to<expairseq>(newrh));
                }
                else
                    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 (typeid(ex_to<basic>(rh)) == typeid(*this)) {
#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, bool do_index_renaming)
{
    // 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, do_index_renaming);
#if EXPAIRSEQ_USE_HASHTAB
    combine_same_terms();
#else
    canonicalize();
    combine_same_terms_sorted_seq();
#endif // EXPAIRSEQ_USE_HASHTAB
}

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;
    bool do_idx_rename = false;
    
    cit = v.begin();
    while (cit!=v.end()) {
        if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
            ++nexpairseqs;
            noperands += ex_to<expairseq>(*cit).seq.size();
        }
        if (is_a<mul>(*this) && (!do_idx_rename) &&
                cit->info(info_flags::has_indices))
            do_idx_rename = true;
        ++cit;
    }
    
    // reserve seq and coeffseq which will hold all operands
    seq.reserve(v.size()+noperands-nexpairseqs);
    
    // copy elements and split off numerical part
    make_flat_inserter mf(v, do_idx_rename);
    cit = v.begin();
    while (cit!=v.end()) {
        if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
            ex newfactor = mf.handle_factor(*cit, _ex1);
            const expairseq &subseqref = ex_to<expairseq>(newfactor);
            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 {
                ex newfactor = mf.handle_factor(*cit, _ex1);
                seq.push_back(split_ex_to_pair(newfactor));
            }
        }
        ++cit;
    }
}

void expairseq::make_flat(const epvector &v, bool do_index_renaming)
{
    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;
    bool really_need_rename_inds = false;
    
    cit = v.begin();
    while (cit!=v.end()) {
        if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
            ++nexpairseqs;
            noperands += ex_to<expairseq>(cit->rest).seq.size();
        }
        if ((!really_need_rename_inds) && is_a<mul>(*this) &&
                cit->rest.info(info_flags::has_indices))
            really_need_rename_inds = true;
        ++cit;
    }
    do_index_renaming = do_index_renaming && really_need_rename_inds;
    
    // reserve seq and coeffseq which will hold all operands
    seq.reserve(v.size()+noperands-nexpairseqs);
    make_flat_inserter mf(v, do_index_renaming);
    
    // copy elements and split off numerical part
    cit = v.begin();
    while (cit!=v.end()) {
        if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
            this->can_make_flat(*cit)) {
            ex newrest = mf.handle_factor(cit->rest, cit->coeff);
            const expairseq &subseqref = ex_to<expairseq>(newrest);
            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(mf.handle_factor(cit->rest, _ex1));
            else {
                ex rest = cit->rest;
                ex newrest = mf.handle_factor(rest, cit->coeff);
                if (are_ex_trivially_equal(newrest, rest))
                    seq.push_back(*cit);
                else
                    seq.push_back(expair(newrest, cit->coeff));
            }
        }
        ++cit;
    }
}

void expairseq::canonicalize()
{
    std::sort(seq.begin(), seq.end(), expair_rest_is_less());
}


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());
}

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

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;
}


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
}


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
}

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