/*
 * Normaliz
 * Copyright (C) 2007-2014  Winfried Bruns, Bogdan Ichim, Christof Soeger
 * 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 3 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, see <http://www.gnu.org/licenses/>.
 *
 * As an exception, when this program is distributed through (i) the App Store
 * by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or (iii) Google Play
 * by Google Inc., then that store may impose any digital rights management,
 * device limits and/or redistribution restrictions that are required by its
 * terms of service.
 */

#include <iomanip>

#include "libnormaliz/descent.h"
#include "libnormaliz/cone.h"
#include "libnormaliz/vector_operations.h"
#include "libnormaliz/my_omp.h"
#include "libnormaliz/sublattice_representation.h"

namespace libnormaliz {

template<typename Integer>
DescentFace<Integer>::DescentFace(){

    simplicial=false;
    coeff=0;
    tree_size=0;
}

template<typename Integer>
DescentSystem<Integer>::DescentSystem(){

    descent_steps=0;
    tree_size=0;
    nr_simplicial=0;
    system_size=0;
}

template<typename Integer>
DescentSystem<Integer>::DescentSystem(const Matrix<Integer>& Gens_given, const Matrix<Integer>& SuppHyps_given, const vector<Integer>& Grading_given){

    descent_steps=0;
    tree_size=0;
    nr_simplicial=0;
    system_size=0;
    
    Gens=Gens_given;
    SuppHyps=SuppHyps_given;
    Grading=Grading_given;
    
    nr_gens=Gens.nr_of_rows();
    nr_supphyps=SuppHyps.nr_of_rows();    
    dim=Gens.nr_of_columns();
    
    GradGens.resize(nr_gens);
    GradGens_mpz.resize(nr_gens);
    for(size_t i=0;i<nr_gens;++i){
        GradGens[i]=v_scalar_product(Grading,Gens[i]);
        convert(GradGens_mpz[i],GradGens[i]);
    }
    
    multiplicity=0;    
    
    SuppHypInd.resize(nr_supphyps);
    vector<size_t> NrFacetsContainingGen(nr_gens,0);
     
    for(size_t i=0;i<nr_supphyps;++i){
         
        INTERRUPT_COMPUTATION_BY_EXCEPTION
         
        SuppHypInd[i].resize(nr_gens);
        for(size_t j=0;j<nr_gens;++j)
            if(v_scalar_product(SuppHyps[i],Gens[j])==0){
                SuppHypInd[i][j]=true;
                NrFacetsContainingGen[j]++;
            }
    }
     
    OldNrFacetsContainingGen.resize(nr_gens,1);
    NewNrFacetsContainingGen.resize(nr_gens,0);
     
    SimplePolytope=true;
    for(size_t j=0;j<nr_gens;++j){
        if(NrFacetsContainingGen[j] > dim-1){
            SimplePolytope=false;
            break;
        }           
    }
    
    OldNrFacetsContainingGen.resize(nr_gens,1);
    /*for(size_t i=0;i<nr_gens;++i){
        for(size_t j=0;j<nr_supphyps;++j){
            if(SuppHypInd[j][i])
                OldNrFacetsContainingGen[i]++;
        }        
    }*/
    NewNrFacetsContainingGen.resize(nr_gens,0);
}

// size_t nr_large=0;
// size_t nr_rand=0;
// size_t nr_overflow=0;

// long nr_sat=0;
// long nr_not_sat=0;

template<typename Integer>
void  DescentFace<Integer>::compute(DescentSystem<Integer>& FF, size_t dim,
                 const boost::dynamic_bitset<>& own_facets, vector<key_t>& mother_key,
                 vector<boost::dynamic_bitset<> >& opposite_facets,
                 vector<key_t>& CuttingFacet, vector<Integer>& heights,
                 key_t& selected_gen){
    
    long omp_start_level=omp_get_level();
    
    mother_key.clear();
    
    size_t nr_supphyps=FF.nr_supphyps;
    size_t nr_gens=FF.nr_gens;
    
    size_t d=dim;    
    
    boost::dynamic_bitset<> GensInd(nr_gens);
    GensInd.set();
    // vector<key_t> own_facets_key;
    for(size_t i=0;i<nr_supphyps;++i){ // find Gens in this
        if(own_facets[i]==true){ 
            GensInd= GensInd & FF.SuppHypInd[i];
        }
    }
    
    for(size_t i=0;i<nr_gens;++i)
        if(GensInd[i])
            mother_key.push_back(i);
    
    Matrix<Integer> Gens_this;
    
    if(mother_key.size()>3*dim){
        try{
            size_t nr_selected=3*dim;
            vector<key_t> selection;
            key_t j;
            size_t rk=0;
            while(rk<dim && nr_selected <= mother_key.size()){
                selection.resize(nr_selected);
                for(size_t i=0;i<nr_selected;++i){
                    j=rand() % mother_key.size();
                    selection[i]=mother_key[j];
                }
                Gens_this=FF.Gens.submatrix(selection);
                rk=Gens_this.row_echelon();
                nr_selected*=2;
            }
            if(rk<dim){
                Gens_this=FF.Gens.submatrix(mother_key);
                Gens_this.row_echelon();
            }
        }
        catch(const ArithmeticException& e) {
            Gens_this=FF.Gens.submatrix(mother_key);
            Gens_this.row_echelon();
        }
    }
    else{
        Gens_this=FF.Gens.submatrix(mother_key);
        Gens_this.row_echelon();
    }
    
    bool must_saturate=false;
    
    for(size_t i=0;i<Gens_this.nr_of_rows();++i){
        for(size_t j=i;j<FF.dim;++j){
            if(Gens_this[i][j]==0)
                continue;
            if(Gens_this[i][j]!=1 && Gens_this[i][j]!=-1){
                must_saturate=true;
            }
            break;
        }
        if(must_saturate)
            break;
    }
    
    /* if(must_saturate)
        nr_sat++;
    else
        nr_not_sat++; */
    
    Sublattice_Representation<Integer> Sublatt_this;
    if(must_saturate) 
        Sublatt_this=Sublattice_Representation<Integer>(Gens_this,true,false); //  take saturation, no LLL
        
    if(mother_key.size()==dim){ // *this is simplicial        
        simplicial=true;
        Integer det;
        if(!must_saturate){
            det=1;
        }
        else{
            Matrix<Integer> Embedded_Gens=Sublatt_this.to_sublattice(Gens_this);
            det=Embedded_Gens.vol();
        }
        mpz_class mpz_det=convertTo<mpz_class>(det);
        // cout << "Vol " << mpz_det << endl;
        mpq_class multiplicity=mpz_det;
        multiplicity*=coeff;
        mpz_class GradDen=1;
        for(size_t i=0;i<Gens_this.nr_of_rows();++i)
            // GradDen*=convertTo<mpz_class>(FF.GradGens[mother_key[i]]);
            GradDen*=FF.GradGens_mpz[mother_key[i]];
        multiplicity/=GradDen;
        
        #pragma omp critical(ADD_MULT)
        FF.multiplicity+=multiplicity;
        #pragma omp atomic
        FF.nr_simplicial++;
        #pragma omp atomic
        FF.tree_size+=tree_size;
        return;

    }   
    
    // Now we find the potential facets of *this.

    boost::dynamic_bitset<> facet_ind(mother_key.size()); // lists Gens
    map<boost::dynamic_bitset<>, boost::dynamic_bitset<> > FacetInds; // potential facets
    map<boost::dynamic_bitset<>, key_t > CutOutBy; // the facet citting it out
    
    map<boost::dynamic_bitset<>, vector<key_t> > SimpKeys; // generator keys for simplicial facets
    map<boost::dynamic_bitset<>, vector<bool> > SimpInds; // generator indices for simplicial facets (if less memory needed)
    
    bool ind_better_than_keys = (dim*64 > FF.nr_gens);

    for(size_t i=0;i<nr_supphyps;++i){
        if(own_facets[i]==true) // contains *this
            continue;
        
        // we can identify the facet(*this) uniquely only via the Gens in it
        vector<libnormaliz::key_t> facet_key;
        for(size_t k=0;k<mother_key.size();++k){
            if(FF.SuppHypInd[i][mother_key[k]]==true)
                facet_key.push_back(k);            
        }
        if(facet_key.size() < d-1) // can't be a facet(*this)
            continue;
        
        
        // now we make facet_ind
        facet_ind.reset();
        for(size_t jj=0;jj<facet_key.size();++jj)
            facet_ind[facet_key[jj]]=true;
        
        // next we check whether we have the intersection already
        // not necessary for simple polytopes and in top dimension
        // Note: if P is simple, F is a face opf P and H a support hyperplave of P,
        // then F\cap H is either empty or a facet of F. Moreover H is eniquely determined
        // by F\cap H. This will again be used below.
        if(d<FF.dim && !FF.SimplePolytope){
            if(FacetInds.find(facet_ind)!=FacetInds.end()){ // already found, we need it only once
                if(facet_key.size()>d-1)
                    FacetInds[facet_ind][i]=true;
                   // but in the nonsimplicial case we must add SuppHyps[i] to the facets(C) containing 
                   // the current facet(*this)
                continue;            
            }
        }

        // now we have a new potential facet
        if(facet_key.size()==d-1){ // simplicial or not a facet
            FacetInds[facet_ind]=boost::dynamic_bitset<>(0); // don't need support hyperplanes 
            CutOutBy[facet_ind]=FF.nr_supphyps+1; // signalizes "simplicial facet"
            if(ind_better_than_keys){
                vector<bool> gen_ind(FF.nr_gens);
                for(size_t k=0;k<facet_key.size();++k)
                    gen_ind[mother_key[facet_key[k]]]=1;
                SimpInds[facet_ind]=gen_ind;                
            }
            else{
                vector<key_t> trans_key; // translate back to FF
                for(size_t k=0;k<facet_key.size();++k)
                    trans_key.push_back(mother_key[facet_key[k]]);
                SimpKeys[facet_ind]=trans_key; // helps to pick the submatrix of its generators
            }
        }
        else{
            FacetInds[facet_ind]=own_facets;
            FacetInds[facet_ind][i]=true;  //plus the facet cutting out facet_ind
            CutOutBy[facet_ind]=i; // memorize the facet that cuts it out           
        }
    }

    // if we don't have the coordinate transformation and there is a simplicial facet, we must make it
    if(!must_saturate && (SimpKeys.size()>0 || SimpInds.size()>0))
        Sublatt_this=Sublattice_Representation<Integer>(Gens_this,true,false); //  take saturation, no LLL
    
    if(d<FF.dim && !FF.SimplePolytope){
        auto G=FacetInds.end();
        for(--G;G!=FacetInds.begin();--G){
            for(auto F=FacetInds.begin();F!=G;){
                if(F->first.is_subset_of(G->first))
                    F=FacetInds.erase(F);
                else
                    ++F;                
            }
        }
    } 
    
    // At this point we know the facets of *this.
    // The map FacetInds assigns the set of containing SuppHyps to the facet_ind(Gens).
    // The set of containing SuppHyps is a unique signature as well.


    // Now we want to find the generator with the lrast number opf opposite facets(*this)    
    vector<size_t> count_in_facets(mother_key.size());
    #pragma omp parallel for
    for(size_t i=0;i<mother_key.size();++i){
        size_t k=i;
        for(auto F=FacetInds.begin();F!=FacetInds.end();++F)
            if((F->first)[k]==true )
                count_in_facets[k]++;        
    }
        
    size_t m=count_in_facets[0]; // we must have at least one facet (actually 3, since dim 2 is simplicial)
    libnormaliz::key_t m_ind=0;
        
    for(size_t i=1;i<count_in_facets.size();++i){
        if(count_in_facets[i]>m){
            m=count_in_facets[i];
            m_ind=i;
            continue;
        }
        if(count_in_facets[i]==m && FF.OldNrFacetsContainingGen[mother_key[i]]<FF.OldNrFacetsContainingGen[mother_key[m_ind]]){
            m_ind=i;        
        }        
    }
        
    selected_gen=mother_key[m_ind]; // this is the selected generator
    vector<Integer> embedded_selected_gen;
    if(must_saturate)
        embedded_selected_gen=Sublatt_this.to_sublattice(FF.Gens[selected_gen]);
    
    // now we must find the facets opposite to thge selected generator
    
    vector<Integer> embedded_supphyp;
    Integer ht;
    
    opposite_facets.clear();
    heights.clear();
    CuttingFacet.clear();
    
    auto G=FacetInds.begin();    
    for(;G!=FacetInds.end();++G){
        
        INTERRUPT_COMPUTATION_BY_EXCEPTION
                    
       if((G->first)[m_ind]==false && CutOutBy[G->first]!=FF.nr_supphyps+1){ // is opposite and not simplicial
            opposite_facets.push_back(G->second);
            if(must_saturate){
                embedded_supphyp=Sublatt_this.to_sublattice_dual(FF.SuppHyps[CutOutBy[G->first]]);
                ht=v_scalar_product(embedded_selected_gen,embedded_supphyp);
            }
            else{
                embedded_supphyp=Gens_this.MxV(FF.SuppHyps[CutOutBy[G->first]]);
                Integer den=v_make_prime(embedded_supphyp);
                ht=v_scalar_product(FF.Gens[selected_gen],FF.SuppHyps[CutOutBy[G->first]])/den;;                
            }
            // cout <<  ht << endl;
            heights.push_back(ht);
            CuttingFacet.push_back(CutOutBy[G->first]);
       }       
    }
    
    if(SimpKeys.size()>0 || SimpInds.size()>0){
        
        G=FacetInds.begin();
        size_t loop_length=FacetInds.size();
        size_t fpos=0;
        bool skip_remaining = false;
        vector<mpq_class> thread_mult(omp_get_max_threads(),0);
        Matrix<Integer> Embedded_Gens(d,d);
        Matrix<Integer> Gens_this(d,FF.dim);

    std::exception_ptr tmp_exception;
        
        #pragma omp parallel for firstprivate(G,fpos,Embedded_Gens,Gens_this)
        for(size_t ff=0;ff<loop_length;++ff){
        
            if (skip_remaining)
                continue;
            for(; ff > fpos; ++fpos, ++G) ;
            for(; ff < fpos; --fpos, --G) ;
            
            int tn;
            if(omp_get_level()==omp_start_level)
                tn=0;
            else    
                tn = omp_get_ancestor_thread_num(omp_start_level+1);
            
           try {
 
            INTERRUPT_COMPUTATION_BY_EXCEPTION
                        
            if((G->first)[m_ind]==false && CutOutBy[G->first]==FF.nr_supphyps+1){ // is opposite and simplicial
                if(ind_better_than_keys)
                    Gens_this=FF.Gens.submatrix(SimpInds[G->first]);
                else
                    Gens_this=FF.Gens.submatrix(SimpKeys[G->first]);
                Gens_this.append(FF.Gens[selected_gen]);
                Integer det;
                if(Sublatt_this.IsIdentity())
                    det=Gens_this.vol();
                else{
                    Embedded_Gens=Sublatt_this.to_sublattice(Gens_this);
                    det=Embedded_Gens.vol();
                }
                mpz_class mpz_det=convertTo<mpz_class>(det);
                mpq_class multiplicity=mpz_det;
                if(ind_better_than_keys){
                    for(size_t i=0;i<FF.nr_gens;++i)
                        if(SimpInds[G->first][i] &&  FF.GradGens[i]>1)
                            multiplicity/=FF.GradGens_mpz[i];
                }
                else{
                    for(size_t i=0;i<Gens_this.nr_of_rows()-1;++i)
                        if(FF.GradGens[SimpKeys[G->first][i]]>1)
                            multiplicity/=FF.GradGens_mpz[SimpKeys[G->first][i]];
                }
                if(FF.GradGens[selected_gen]>1)
                    multiplicity/=FF.GradGens_mpz[selected_gen];
                // #pragma omp critical(ADD_MULT)
                // FF.multiplicity+=multiplicity*coeff;
                thread_mult[tn]+=multiplicity;
                #pragma omp atomic
                FF.nr_simplicial++;
                #pragma omp atomic
                FF.tree_size+=tree_size;
            }
            
           } catch(const std::exception& ) {
               tmp_exception = std::current_exception();
               skip_remaining = true;
               #pragma omp flush(skip_remaining)
           }
            
        }
        
        if (!(tmp_exception == 0)) std::rethrow_exception(tmp_exception);

        mpq_class local_multiplicity=0;
        for(size_t j=0;j<thread_mult.size();++j)
            local_multiplicity+=thread_mult[j];
        #pragma omp critical(ADD_MULT)
        FF.multiplicity+=local_multiplicity*coeff;                   
    }
}

template<typename Integer>
void DescentSystem<Integer>::compute(){
    
    if(verbose){
        if(SimplePolytope)
            verboseOutput() << "Polytope is simple" << endl;
        else
            verboseOutput() << "Polytope is not simple" << endl;        
    }
    
    const size_t ReportBound=400;
    const size_t MaxBlocksize=1000000;
    
    boost::dynamic_bitset<> empty(nr_supphyps);
    DescentFace<Integer> top;
    OldFaces[empty]=top;
    OldFaces[empty].coeff=1;
    OldFaces[empty].tree_size=1;
    long d=(long) dim;
    
    while(!OldFaces.empty()){
        
        size_t nr_F=OldFaces.size();
        system_size+=nr_F;
        if(verbose)
            verboseOutput() << "Descent from dim " << d << ", size " << nr_F << endl;
        
        bool in_blocks=false;
        if(nr_F>MaxBlocksize)
            in_blocks=true;
        if(in_blocks && verbose)
            verboseOutput() << "processing in blocks" << endl;
        
        size_t nr_remaining=nr_F;
        
        size_t nr_block=0;
        
        while(nr_remaining>0){
        
        nr_block++;
            
        size_t block_size=min((long) MaxBlocksize, (long) nr_remaining);
        
        auto F=OldFaces.begin();
        
        size_t kkpos=0;
        bool skip_remaining=false;
        
        const long VERBOSE_STEPS = 50;
        long step_x_size = block_size-VERBOSE_STEPS;
        size_t total=block_size;
        
        if(in_blocks && verbose)
            verboseOutput() << nr_block << ": " << flush;
        
        vector<key_t> mother_key;
        mother_key.reserve(nr_gens);
        vector<boost::dynamic_bitset<> > opposite_facets;
        opposite_facets.reserve(nr_supphyps);
        vector<key_t> CuttingFacet;
        CuttingFacet.reserve(nr_supphyps);
        vector<Integer> heights;
        heights.reserve(nr_supphyps);
        key_t selected_gen=0;
        
    std::exception_ptr tmp_exception;
        #pragma omp parallel for firstprivate(kkpos,F,mother_key,opposite_facets,CuttingFacet,heights,selected_gen) schedule(dynamic) if(block_size>1)
        for(size_t kk=0;kk< block_size;++kk){
            
            if(skip_remaining)
                continue;
            
            if(verbose && block_size>=ReportBound){
                #pragma omp critical(VERBOSE)
                while ((long)(kk*VERBOSE_STEPS) >= step_x_size) {
                    step_x_size += total;
                    verboseOutput() << "." <<flush;
                }
            }
            
        try {
 
            INTERRUPT_COMPUTATION_BY_EXCEPTION
            
            for(;kk > kkpos; kkpos++, F++) ;
            for(;kk < kkpos; kkpos--, F--) ;
            
            F->second.compute(*this, d, F->first, mother_key,opposite_facets,CuttingFacet,heights,selected_gen);
            if(F->second.simplicial)
                continue;
            
            auto G=opposite_facets.begin();
            // mpz_class deg_mpz=convertTo<mpz_class>(GradGens[selected_gen]);
            // mpq_class divided_coeff=(F->second).coeff/deg_mpz;
            mpq_class divided_coeff=(F->second).coeff/GradGens_mpz[selected_gen];
            size_t j=0;
            for(;G!=opposite_facets.end();++G){
               auto H=NewFaces.begin();
               bool inserted=false;
               #pragma omp critical(INSERT)
               { 
               H=NewFaces.find(*G);
               if(H==NewFaces.end()){
                    H=NewFaces.insert(NewFaces.begin(),make_pair(*G,DescentFace<Integer>()));
                    inserted=true;
               }
               }
               if(inserted){
                    for(size_t i=0;i<mother_key.size();++i)
                        if (SuppHypInd[CuttingFacet[j]][mother_key[i]])
                            #pragma omp atomic
                            NewNrFacetsContainingGen[mother_key[i]]++;
               }
               mpq_class dc=divided_coeff*convertTo<mpz_class>(heights[j]);
               #pragma omp critical(ADD_COEFF)
               {
               (H->second).coeff+=dc;
               (H->second).tree_size+=(F->second).tree_size;
               }
               ++j;
               descent_steps++;
            }
            
            } catch(const std::exception& ) {
                tmp_exception = std::current_exception();
                skip_remaining = true;
                #pragma omp flush(skip_remaining)
            }
        } // parallel for kk
        
        if(verbose && block_size>=ReportBound)
            verboseOutput() << endl;
        
        if (!(tmp_exception == 0)) std::rethrow_exception(tmp_exception);

        for(size_t i=0;i<block_size;++i)
            OldFaces.erase(OldFaces.begin());
        
        nr_remaining-=block_size;
        
        } // while nr_remaining >0
        
        OldFaces.swap(NewFaces);
        NewFaces.clear();
        
        OldNrFacetsContainingGen.swap(NewNrFacetsContainingGen);
        for(size_t i=0;i<nr_gens;++i)
            NewNrFacetsContainingGen[i]=0;
        
        d--;
        
    }    // while
    
    if(verbose){
        verboseOutput() << "Mult " << multiplicity << endl;
        verboseOutput() << "Mult (float) " << std::setprecision(12) << mpq_to_nmz_float(multiplicity) << endl;
        verboseOutput() << "Full tree size (modulo 2^64)" << tree_size << endl;
        verboseOutput() << "Number of descent steps " << descent_steps << endl;
        verboseOutput() << "Determinants computed " << nr_simplicial << endl;
        verboseOutput() << "Number of faces in descent system " << system_size << endl;
    } 
    
    // cout << nr_sat << " " << nr_not_sat << endl;
}
    


template<typename Integer>
bool DescentSystem<Integer>::set_verbose(bool onoff){
    bool old_verbose=verbose;
    verbose=onoff;
    return old_verbose;
}

template<typename Integer>
mpq_class DescentSystem<Integer>::getMultiplicity(){
    return multiplicity;
}


template class DescentFace<long>;
template class DescentFace<long long>;
template class DescentFace<mpz_class>;

template class DescentSystem<long>;
template class DescentSystem<long long>;
template class DescentSystem<mpz_class>;

} // namespace
