bgeot_sparse_tensors.cc

/*===========================================================================
 
 Copyright (C) 2000-2020 Julien Pommier
 
 This file is a part of GetFEM
 
 GetFEM  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 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 Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
 
===========================================================================*/
 
#include <bitset>
#include "gmm/gmm_blas_interface.h"
#include "getfem/bgeot_sparse_tensors.h"
 
 
namespace bgeot {
  std::ostream& operator<<(std::ostream& o, const tensor_ranges& r) {
    for (size_type i=0; i < r.size(); ++i) {
      if (i) o << "x";
      o << "[0.." << r[i] << "]"; 
    }
    return o;
  }
 
  /*
    strides:
    0 1 2 3 4 5 6 7
    ---------------
    x x   x
    x       x x
    x   x   x x x x
    x   x   x x   x
 
    => n={0,4,6,8,8}
 
    basic iterator on a set of full tensors, just used for iterating over binary masks
  */
  template<typename IT> class basic_multi_iterator {
    unsigned N;
    index_set idxnums;
    tensor_ranges ranges;
    tensor_strides strides;
    tensor_ranges cnt;
    index_set ilst2idxnums;
    std::vector<const tensor_strides*> slst;
    std::vector<IT> iter;
    std::vector<int> n;
  public:
    const tensor_ranges& getcnt() const { return cnt; }
    basic_multi_iterator() { 
      N = 0; idxnums.reserve(16); strides.reserve(64); 
      slst.reserve(16); 
      ilst2idxnums.reserve(64); iter.reserve(4);
    }
    const tensor_ranges& all_ranges() const { return ranges; }
    const index_set& all_indexes() const { return idxnums; }
    /* /!!!!!\ attention les strides ont 1 elt de plus que r et idxs (pour les tensor_masks)
       (ca intervient aussi dans prepare()) */
    void insert(const index_set& idxs, const tensor_ranges& r, const tensor_strides& s, IT it_) {
      assert(idxs.size() == r.size()); assert(s.size() == r.size()+1);
      slst.push_back(&s);
      for (unsigned int i=0; i < idxs.size(); ++i) {
        index_set::const_iterator f=std::find(idxnums.begin(), idxnums.end(), idxs[i]); 
        if (f == idxnums.end()) {
          ilst2idxnums.push_back(dim_type(idxnums.size()));
          idxnums.push_back(idxs[i]);
          ranges.push_back(r[i]);
        } else {
          ilst2idxnums.push_back(dim_type(f-idxnums.begin()));
          assert(ranges[ilst2idxnums.back()] == r[i]);
        }
      }
      iter.push_back(it_);
      N++;
    }
    void prepare() {
      unsigned c = 0;
      strides.assign(N*idxnums.size(),0);
      for (unsigned int i=0; i < N; ++i) {
        for (unsigned int j=0; j < slst[i]->size()-1; ++j) {
          stride_type s = (*slst[i])[j];
          strides[ilst2idxnums[c]*N + i] = s;
          c++;
        }
      }
      n.assign(N+1,-1);
      for (unsigned int i=0; i < idxnums.size(); ++i) {
        for (unsigned int j=0; j < N; ++j) {
          if (strides[i*N+j]) n[j+1] = i;
        }
      }
      cnt.assign(idxnums.size(),0);
    }
    /* unfortunatly these two function don't inline
       and are not optimized by the compiler 
       (when b and N are known at compile-time) (at least for gcc-3.2) */
    bool next(unsigned int b) { return next(b,N); }
    bool next(unsigned int b, unsigned int NN) {
      int i0 = n[b+1];
      while (i0 > n[b]) {
        if (++cnt[i0] < ranges[i0]) {
          for (unsigned int i=b; i < NN; ++i) {
            iter[i] += strides[i0*NN+i];
          }
          return true;
        } else {
          for (unsigned int i=b; i < NN; ++i) {
            iter[i] -= strides[i0*NN+i]*(ranges[i0]-1);
          }
          cnt[i0]=0; i0--;
        }
      }
      return false;
    }
    template<unsigned b, unsigned NN> bool qnext() { return next(b,NN); }
    IT it(unsigned int b) const { return iter[b]; }
  };
 
 
  /* 
     constructeur par fusion de deux masques binaires
     (avec potentiellement une intersection non vide)
  */
  tensor_mask::tensor_mask(const tensor_mask& tm1, const tensor_mask& tm2, bool and_op) {
    assign(tm1,tm2,and_op); unset_card();
  }
#if 0
  void tensor_mask::assign(const tensor_mask& tm1, const tensor_mask& tm2, bool and_op) {
    clear(); unset_card();
    if (tm1.ndim()==0) { assign(tm2); return; }
    if (tm2.ndim()==0) { assign(tm1); return; }
    r = tm1.ranges();
    idxs = tm1.indexes();
    
    /* ce tableau va permettre de faire une boucle commune sur les
       deux masques, les dimension inutilisees etant mises a 1 pour
       ne pas gener */
    tensor_ranges global_r(std::max(tm1.max_dim(),tm2.max_dim())+1, index_type(1));
 
    for (index_type i = 0; i < tm1.indexes().size(); ++i) 
      global_r[tm1.indexes()[i]] = tm1.ranges()[i];
 
    /* detect new indices */
    for (index_type i = 0; i < tm2.indexes().size(); ++i) {
      index_set::const_iterator f=std::find(tm1.indexes().begin(), tm1.indexes().end(), tm2.indexes()[i]);
      if (f == tm1.indexes().end()) {
        assert(global_r[tm2.indexes()[i]]==1);
        global_r[tm2.indexes()[i]] = tm2.ranges()[i];
        r.push_back(tm2.ranges()[i]);
        idxs.push_back(tm2.indexes()[i]);       
      }
      else assert(global_r[tm2.indexes()[i]] = tm2.ranges()[i]);
    }
    eval_strides();
    assert(size());
    m.assign(size(),false);
    /* sans doute pas tres optimal, mais la fonction n'est pas critique .. */    
    for (tensor_ranges_loop l(global_r); !l.finished(); l.next()) {
      if (and_op) {
        if (tm1(l.cnt) && tm2(l.cnt)) m.add(pos(l.cnt));
      } else {
        if (tm1(l.cnt) || tm2(l.cnt)) m.add(pos(l.cnt));
      }
    }
    unset_card();
  }
#endif
 
 
  void tensor_mask::assign(const tensor_mask& tm1, const tensor_mask& tm2, bool and_op) {
    clear(); unset_card();
    /* check simple cases first, since this function can be called often and
       is quite expensive */
    if (tm1.ndim()==0) { assign(tm2); return; }
    if (tm2.ndim()==0) { assign(tm1); return; }
 
    /* same masks ? */
    if (tm1.indexes() == tm2.indexes() &&
        tm1.ranges() == tm2.ranges() &&
        tm1.strides() == tm2.strides()) {
      r = tm1.ranges(); idxs=tm1.indexes(); s=tm1.strides();
      assert(tm1.m.size() == tm2.m.size()); 
      m = tm1.m;
      if (and_op) {
        for (index_type i=0; i < tm2.m.size(); ++i)
          if (!tm2.m[i]) m[i] = false;
      } else {
        for (index_type i=0; i < tm2.m.size(); ++i)
          if (tm2.m[i]) m[i] = true;
      }
      return;
    }
 
    basic_multi_iterator<unsigned> bmit;
    bmit.insert(tm1.indexes(), tm1.ranges(), tm1.strides(), 0); 
    bmit.insert(tm2.indexes(), tm2.ranges(), tm2.strides(), 0); 
    r = bmit.all_ranges(); idxs = bmit.all_indexes(); eval_strides();
    assert(size());
    m.assign(size(),false);    
    bmit.insert(indexes(), ranges(), strides(), 0);
    bmit.prepare(); 
    //cout << "tm1=" << tm1 << "\ntm2=" << tm2 << endl;
    if (and_op) {
      do {
        if (tm1.m[bmit.it(0)]) {
          do {
            if (tm2.m[bmit.it(1)]) {
              m[bmit.it(2)] = 1;
            }
            //      cout << "at cnt=" << bmit.getcnt() << ", it0=" << bmit.it(0) << "=" << tm1.m[bmit.it(0)]
            //           << ", it1=" << bmit.it(1) << "=" << tm2.m[bmit.it(1)] << ", res=" << bmit.it(2) << "=" << m[bmit.it(2)] << endl;
          } while (bmit.qnext<1,3>());
        }
      } while (bmit.qnext<0,3>());
    } else {
      do {
        bool v1 = tm1.m[bmit.it(0)];
        do {
          if (v1 || (tm2.m[bmit.it(1)]))
            m[bmit.it(2)] = 1;
        } while (bmit.qnext<1,3>());
      } while (bmit.qnext<0,3>());
    }
    //    cout << "output: " << *this << endl;
  }
 
 
  /* construit un masque forme du produit cartesien de plusieurs masques (disjoints)
     /!\ aucune verif sur la validite des arguments */
  tensor_mask::tensor_mask(const std::vector<const tensor_mask*>& tm) { 
    assign(tm); 
  }
#if 0
  // REMPLACE PAR LA FONCTION SUIVANTE
  void tensor_mask::assign(const std::vector<const tensor_mask*> & tm) {
    index_set mask_start; unset_card();
    clear();
    r.reserve(255); idxs.reserve(255); mask_start.reserve(255);
    for (dim_type i=0; i < tm.size(); ++i) {
      mask_start.push_back(r.size());
      for (dim_type j=0; j < tm[i]->ndim(); ++j) { 
        r.push_back(tm[i]->ranges()[j]);
        idxs.push_back(tm[i]->indexes()[j]);
      }
    }
    eval_strides(); assert(size());
    m.assign(size(),false);
    for (tensor_ranges_loop l(r); !l.finished(); l.next()) {
      bool is_in = true;
      for (dim_type i=0; is_in && i < tm.size(); ++i) {
        index_type s_ = 0; 
        for (dim_type j=0; j < tm[i]->ndim(); ++j) 
          s_ += l.cnt[j+mask_start[i]]*tm[i]->strides()[j];
        if (!tm[i]->m[s_]) is_in = false;
      }
      if (is_in) m.add(lpos(l.cnt));
    }
  }
#endif
  // PRODUIT CARTESIEN DE MASQUES BINAIRES DISJOINTS
  void tensor_mask::assign(const std::vector<const tensor_mask*> & tm) {
    unset_card();
    if (tm.size() == 0) { clear(); return; }
    if (tm.size() == 1) { assign(*tm[0]); return; }
    clear();
    basic_multi_iterator<unsigned> bmit;
    for (dim_type i=0; i < tm.size(); ++i)
      bmit.insert(tm[i]->indexes(), tm[i]->ranges(), tm[i]->strides(), 0);
    r = bmit.all_ranges(); idxs = bmit.all_indexes(); eval_strides();
    assert(size());
    m.assign(size(), false);
    bmit.insert(indexes(), ranges(), strides(), 0);
    bmit.prepare(); 
    unsigned N = unsigned(tm.size());
    bool finished = false;
    while (!finished) {
      bool is_in = true;
      unsigned int b;
      for (b=0; b < N; ++b) {
        if (!tm[b]->m[bmit.it(b)]) {
          is_in = false; break;
        }
      }
      if (is_in) { m[bmit.it(N)] = 1; b = N-1; }
      while (!finished && !bmit.next(b)) { if (b == 0) finished = true; b--; }
    }
  }
 
  void tensor_mask::unpack_strides(const tensor_strides& packed, tensor_strides& unpacked) const {
    if (packed.size() != card()) 
      assert(packed.size()==card());
    unpacked.assign(size(),INT_MIN);
    index_type i=0;
    for (tensor_ranges_loop l(r); !l.finished(); l.next()) {
      if (m[lpos(l.cnt)]) unpacked[lpos(l.cnt)] = packed[i++];
    }
  }
 
  void tensor_mask::check_assertions() const {
    GMM_ASSERT3(r.size() == idxs.size(), "");
    GMM_ASSERT3(s.size() == idxs.size()+1, "");
    GMM_ASSERT3(m.size() == size(), "");
    dal::bit_vector bv;
    for (dim_type i=0; i < idxs.size(); ++i) {
      GMM_ASSERT3(!bv.is_in(i), "");
      bv.add(i);
    }
  }
 
  tensor_mask::tensor_mask(const std::vector<const tensor_mask*> tm1, const std::vector<const tensor_mask*> tm2, bool and_op) {
    assign(tensor_mask(tm1), tensor_mask(tm2), and_op);
  }
 
  void tensor_ref::set_sub_tensor(const tensor_ref& tr, const tensor_shape& sub) {
    assign_shape(sub);
    /* fusionne sub et tr.shape */
    merge(tr);
    
    /* reserve l'espace pour les strides */
    strides_.resize(masks().size());
    for (dim_type i = 0; i < strides_.size(); ++i)
      strides_[i].resize(mask(i).card());
    
    pbase_ = tr.pbase_; base_shift_ = tr.base_shift();
    
    /*    
    cout << "\n  -> entree dans set_sub_tensor: " << endl 
         << "tr.shape=" << (tensor_shape&)(tr) << endl
         << "     sub=" << sub << endl;
    */
    /* pre-calcul rapide des strides sur tr, pour chacun de ses masques */
    std::vector<tensor_strides> trstrides_unpacked(tr.masks().size());
    for (dim_type im = 0; im < tr.masks().size(); ++im) {
      tr.mask(im).check_assertions();
      tr.mask(im).unpack_strides(tr.strides()[im], trstrides_unpacked[im]);
    }
    
    
    /* on parcours chaque masque (merge) */
    for (dim_type im = 0; im < masks().size(); ++im) {
      const tensor_mask& m = masks()[im];
      /* par construction, tous les masques de tr sont inclus (ou egaux)
         dans un masque de l'objet courant 
         
         on construit donc la liste des masques de tr qui sont inclus dans m
      */
      std::vector<dim_type> trmasks; trmasks.reserve(tr.masks().size());
      for (dim_type i=0; i < m.indexes().size(); ++i) {
        if (tr.index_is_valid(m.indexes()[i])) {        /* l'index n'est pas forcement valide pour tr !*/
          dim_type im2 = tr.index_to_mask_num(m.indexes()[i]);
          if (std::find(trmasks.begin(), trmasks.end(), im2)==trmasks.end()) trmasks.push_back(im2);
        }
      }
      
      tensor_ranges gcnt(tr.ndim(),0);
      stride_type stcnt = 0;
 
      for (tensor_ranges_loop l(m.ranges()); !l.finished(); l.next()) {
        /* recopie les indice de la boucle dans les indices globaux */
        for (dim_type i=0; i < m.ranges().size(); ++i) gcnt[m.indexes()[i]] = l.index(i);
        
        bool in_m = m(gcnt);
        bool in_trm = true;
        stride_type tr_s = 0;
        
        /* verifie si l'element est bien marque non nul dans les masques de tr
             et met a jour le stride */
        for (dim_type i=0; i < trmasks.size(); ++i) { 
          const tensor_mask &mm = tr.mask(trmasks[i]);
 
          //cout << "  mm=" << mm << endl << "gcnt=" << gcnt << endl;
          if (mm(gcnt)) {
            tr_s += trstrides_unpacked[trmasks[i]][mm.pos(gcnt)];
            assert(trstrides_unpacked[trmasks[i]][mm.pos(gcnt)]>=0); // --- DEBUG --- 
          } else { in_trm = false; break; }
        }
          /* verifie que m est un sous-ensemble des masques de trmasks */
        if (in_m) assert(in_trm);
        if (!in_trm) assert(!in_m);
        /* recopie le stride si l'element est non nul dans m */
        if (in_m) {
          //      cout << "ajout du " << stcnt << "eme elt @ stride=" << tr_s << endl;
            strides_[im][stcnt++] = tr_s;
        }
      }
      
      /* verif que yapa bug */
      assert(stcnt == stride_type(m.card()));
      }
    ensure_0_stride(); /* c'est plus propre comme ca */
  }
 
  /* slices a tensor_ref, at dimension 'dim', position 'islice'
     ... not straightforward for sparse tensors !
  */
  tensor_ref::tensor_ref(const tensor_ref& tr, tensor_mask::Slice slice) {
    set_sub_tensor(tr, tr.slice_shape(slice));
 
    /* shift the base according to the old stride */
    ensure_0_stride();
    
    /* create a mask m2 with one less dimension than m1 */
    const tensor_mask& m1(index_to_mask(slice.dim));
    dim_type mdim = index_to_mask_dim(slice.dim);
    if (m1.ndim() > 1) { 
      tensor_ranges r(m1.ranges()); r.erase(r.begin()+mdim);
      index_set idx(m1.indexes()); idx.erase(idx.begin()+mdim);
      tensor_mask m2(r,idx);
      index_type pos1 = 0, pos2 = 0;
      for (tensor_ranges_loop l(m1.ranges()); !l.finished(); l.next()) {
        if (l.index(mdim) == slice.i0) {
          m2.set_mask_val(pos2++, m1(pos1));
        } else assert(m1(pos1) == 0);
        pos1++;
      }
      
      
      /* replace the old mask by the new one */
      assert(index_to_mask_num(slice.dim) < masks().size());
      masks()[index_to_mask_num(slice.dim)] = m2;
    } else {
      /* simply remove the mask since it only contained the dimension 'dim' */
      remove_mask(index_to_mask_num(slice.dim));
    }
    /* shift all indexes greater than dim */
    shift_dim_num_ge(slice.dim,-1);
    set_ndim_noclean(dim_type(ndim()-1));
    update_idx2mask();
  }
 
  
  struct compare_packed_range {
    const std::vector<packed_range_info>& pri;
    std::vector<stride_type> mean_inc;
    compare_packed_range(const std::vector<packed_range_info>& pri_) : pri(pri_) {}
    bool operator()(dim_type a, dim_type b) {
      if (pri[a].n < pri[b].n) return true;
      else if (pri[a].n > pri[b].n) return false;
      else { /* c'est la que ca devient interessant */
        if (pri[a].mean_increm > pri[b].mean_increm) return true;
      }
      return false;      
    }
  };
 
  void multi_tensor_iterator::init(std::vector<tensor_ref> trtab, bool with_index_values) {
    N = index_type(trtab.size());
    index_type N_packed_idx = 0;
 
    /* non null elements across all tensors */
      
    tensor_shape ts(trtab[0]);
    for (dim_type i=1; i < trtab.size(); ++i)
      ts.merge(trtab[i]);
    
    
    /* apply the mask to all tensors, 
       updating strides according to it */
    for (dim_type i = 0; i < N; ++i) {
      tensor_ref tmp = trtab[i];
      trtab[i].set_sub_tensor(tmp,ts);
    }
 
    /* find significant indexes (ie remove indexes who only address 1 element) */
    dal::bit_vector packed_idx; packed_idx.sup(0,ts.ndim());
    for (index_type mi=0; mi < ts.masks().size(); ++mi) {
      if (ts.masks()[mi].card() != 1) {
        packed_idx.add(mi);
        N_packed_idx++;
      } else {
        /* sanity check (TODO: s'assurer que sub_tensor_ref appelle bien ensure_0_stride) */
        for (dim_type j=0; j < N; ++j) {
          if (trtab[j].strides()[mi].size() != 0) {
            assert(trtab[j].strides()[mi].size() == 1);
            assert(trtab[j].strides()[mi][0] == 0);
          }
        }
      }
    }
 
    pr.resize(N_packed_idx);
    pri.resize(N_packed_idx);
 
    /* evaluation of "ranks" per indice */
 
    index_type pmi = 0;
    for (dim_type mi = 0; mi < ts.masks().size(); ++mi) {
      if (packed_idx[mi]) {
        dim_type n;
        pri[pmi].original_masknum = mi;
        pri[pmi].range = ts.masks()[mi].card();
        for (n = 0; n < N; n++)
          if (trtab[n].index_is_valid(mi)) break;
        pri[pmi].n = n; pr[pmi].n = n;
        pmi++;
      }
    }
 
    /* sort the packed_range_info according to the "ranks" */
    std::sort(pri.begin(), pri.end());
 
 
    /* eval bloc ranks */      
    bloc_rank.resize(N+1); bloc_rank[0] = 0;
    bloc_nelt.resize(N+1); bloc_nelt[0] = 0;
    for (index_type i=1; i <= N; ++i) {
      bloc_rank[i] = bloc_rank[i-1];
      while (bloc_rank[i] < pri.size() && pri[bloc_rank[i]].n == i-1) bloc_rank[i]++;
      bloc_nelt[i] = bloc_rank[i] - bloc_rank[i-1];
    }
 
    /* "package" the strides in structure pri */
    for (pmi = 0; pmi < pri.size(); ++pmi) {
      index_type mi = pri[pmi].original_masknum;
      pri[pmi].mean_increm = 0;
      pri[pmi].inc.assign(pri[pmi].range*(N-pri[pmi].n), 0);
      pri[pmi].have_regular_strides.reset();
      pri[pmi].have_regular_strides = std::bitset<32>((1 << N)-1);
      for (dim_type n=pri[pmi].n; n < N; ++n) {
        index_type pos0 = (n - pri[pmi].n);
        for (index_type i = 0; i < pri[pmi].range; ++i) {
          index_type pos = i * (N-pri[pmi].n) + pos0;
          if (i != pri[pmi].range-1) {
            stride_type increm = trtab[n].strides()[mi][i+1] - trtab[n].strides()[mi][i];
            pri[pmi].inc[pos]      = increm;
            if (pri[pmi].inc[pos] != pri[pmi].inc[pos0]) 
              pri[pmi].have_regular_strides[n] = false;
            pri[pmi].mean_increm += increm;
          } else { pri[pmi].inc[pos] = -trtab[n].strides()[mi][i]; }
        }
      }
      if (pri[pmi].n!=N)
        pri[pmi].mean_increm /= ((N-pri[pmi].n)*(pri[pmi].range-1));
    }
 
    /* optimize them w/r to mean strides (without modifying the "ranks") */
    index_set pr_reorder(pri.size());
    for (pmi = 0; pmi < pri.size(); ++pmi) {
      pr_reorder[pmi]=dim_type(pmi);
    }
    std::sort(pr_reorder.begin(), pr_reorder.end(), compare_packed_range(pri));
    {
      std::vector<packed_range> tmppr(pr);
      std::vector<packed_range_info> tmppri(pri);
      for (dim_type i =0; i < pri.size(); ++i) {
        pr[i]  = tmppr [pr_reorder[i]];
        pri[i] = tmppri[pr_reorder[i]];
      }
    }
 
    /* setup data necessary to get back (quite quickly) the index values while iterating */
    if (with_index_values) {
      idxval.resize(ts.ndim());
 
      for (dim_type i=0; i < ts.ndim(); ++i) {
        idxval[i].ppinc = NULL; idxval[i].pposbase = NULL; idxval[i].pos_ = 0;
      }
 
      for (index_type mi = 0; mi < ts.masks().size(); ++mi) {
        tensor_strides v;
        pmi = index_type(-1);
        for (dim_type i=0; i < pr.size(); ++i)
          if (pri[i].original_masknum == mi) pmi = i;
 
        if (pmi != index_type(-1)) {
          ts.masks()[mi].gen_mask_pos(pri[pmi].mask_pos);
        } else { /* not very nice .. */
          ts.masks()[mi].gen_mask_pos(v); assert(v.size()==1);
        }
        for (dim_type i=0; i < ts.masks()[mi].indexes().size(); ++i) {
          dim_type ii = ts.masks()[mi].indexes()[i];
          idxval[ii].cnt_num = dim_type(pmi); //packed_idx[mi] ? pmi : dim_type(-1);
          idxval[ii].pos_ = (pmi != index_type(-1)) ? 0 : v[0];
          idxval[ii].mod = ts.masks()[mi].strides()[i+1];
          idxval[ii].div = ts.masks()[mi].strides()[i];
        }
      }
    }
 
    /* check for opportunities to vectorize the loops with the mti 
       (assuming regular strides etc.)
     */
    vectorized_strides_.resize(N); vectorized_size_ = 0;
    std::fill(vectorized_strides_.begin(), vectorized_strides_.end(), 0);
    vectorized_pr_dim = index_type(pri.size());
    for (vectorized_pr_dim = index_type(pri.size()-1); vectorized_pr_dim != index_type(-1); vectorized_pr_dim--) {
      std::vector<packed_range_info>::const_iterator pp = pri.begin() + vectorized_pr_dim;
      if (vectorized_pr_dim == pri.size()-1) {
        if (pp->have_regular_strides.count() == N) vectorized_size_ = pp->range;
        for (dim_type n=pp->n; n < N; ++n) {
          GMM_ASSERT3(n < pp->inc.size(), ""); // expected failure here with "empty" tensors, see tests/test_assembly.cc, testbug() function.
          vectorized_strides_[n] = pp->inc[n]; 
        }
      } else {
        if (pp->have_regular_strides.count() != N) break;
        bool still_ok = true;
        for (dim_type n=pp->n; n < N; ++n) {
          if (stride_type(vectorized_strides_[n]*vectorized_size_) != pp->inc[n]) still_ok = false;
        }
        if (still_ok) {
          vectorized_size_ *= pp->range;
        } else break;
      }
    }
 
    it.resize(N); pit0.resize(N); itbase.resize(N);
    for (dim_type n=0; n < N; ++n) {
      pit0[n]=trtab[n].pbase();
      itbase[n]=trtab[n].base_shift();
    }
    rewind();
  }
 
  void multi_tensor_iterator::print() const {
    cout << "MTI(N=" << N << "): "; 
    for (dim_type i=0; i < pr.size(); ++i) 
      cout << "  pri[" << int(i) << "]: n=" << int(pri[i].n) 
           << ", range=" << pri[i].range << ", mean_increm=" 
           << pri[i].mean_increm << ", regular = " << pri[i].have_regular_strides 
           << ", inc=" << vref(pri[i].inc) << "\n";
    cout << "bloc_rank: " << vref(bloc_rank) << ", bloc_nelt: " << vref(bloc_nelt) << "\n";    
    cout << "vectorized_size : " << vectorized_size_ << ", strides = " << vref(vectorized_strides_) << ", pr_dim=" << vectorized_pr_dim << "\n";
  }
 
  void tensor_reduction::insert(const tensor_ref& tr_, const std::string& s) {
    tensor_shape ts(tr_); 
    diag_shape(ts,s);
    trtab.push_back(tref_or_reduction(tensor_ref(tr_, ts), s));
    //cout << "reduction.insert('" << s << "')\n";
    //cout << "Reduction: INSERT tr(ndim=" << int(tr_.ndim()) << ", s='" << s << "')\n";
    //cout << "Content: " << tr_ << endl;
    //cout << "shape: " << (tensor_shape&)tr_ << endl;
  }
  
  void tensor_reduction::insert(const tref_or_reduction& t, const std::string& s) {
    if (!t.is_reduction()) {
      insert(t.tr(),s);
    } else {
      trtab.push_back(t); trtab.back().ridx = s;
      //cout << "reduction.insert_reduction('" << s << "')\n";
      //cout << "Reduction: INSERT REDUCTION tr(ndim=" << int(t.tr().ndim()) << ", s='" << s << "')\n";   
    }
  }
 
  /* ensure that  r(i,i).t(j,:,j,j,k,o) 
     becomes      r(i,A).t(j,:,B,C,k,o)
     and updates reduction_chars accordingly
  */
  void tensor_reduction::update_reduction_chars() {
    reduction_chars.clear();
    for (trtab_iterator it = trtab.begin(); it != trtab.end(); ++it) {
      assert(it->ridx.size() == it->tr().ndim());
      for (unsigned i =0; i < it->ridx.size(); ++i) {
        if (it->ridx[i] != ' ' &&
            reduction_chars.find(it->ridx[i]) == std::string::npos)
          reduction_chars.push_back(it->ridx[i]);
      }
    }
    /* for each tensor, if a diagonal reduction inside the tensor is used,
       the mask of the tensor has been 'and'-ed with a diagonal mask
       and a second 'virtual' reduction index is used */    
    for (trtab_iterator it = trtab.begin(); it != trtab.end(); ++it) {
      it->gdim.resize(it->ridx.size());
      for (unsigned i =0; i < it->ridx.size(); ++i) {
        char c = it->ridx[i];
        if (c != ' ' && it->ridx.find(c) != i) { 
          for (c = 'A'; c <= 'Z'; ++c)
            if (reduction_chars.find(c) == std::string::npos) break;
          it->ridx[i] = c;
          reduction_chars.push_back(it->ridx[i]);
        }
      }
    }
  }
 
  /* 
     initialize 'reduced_range' and it->rdim 
  */
  void tensor_reduction::pre_prepare() {
    for (trtab_iterator it = trtab.begin(); it != trtab.end(); ++it) {
      assert(it->ridx.size() == it->tr().ndim());
      it->rdim.resize(it->ridx.size());
      //cout << " rix = '" << it->ridx << "'\n";
      for (dim_type i =0; i < it->ridx.size(); ++i) {
        if (it->ridx[i] == ' ') {
          reduced_range.push_back(it->tr().dim(i));
          it->rdim[i] = dim_type(reduced_range.size()-1);
        } else it->rdim[i] = dim_type(-1);
      }
    }
  }
 
  /* look for a possible sub-reduction on a subset of the tensors.
     returns the subset, and the list of concerned reduction indexes */
  size_type tensor_reduction::find_best_sub_reduction(dal::bit_vector &best_lst, std::string &best_idxset) {
    dal::bit_vector lst;
    std::string idxset;
    best_lst.clear(); best_idxset.clear();
 
    update_reduction_chars();
 
    //cout << "find_best_reduction: reduction_chars='" << reduction_chars << "'\n";
    GMM_ASSERT2(trtab.size() <= 32, "wow it was assumed that nobody would "
                "ever need a reduction on more than 32 tensors..");
 
    std::vector<std::bitset<32> > idx_occurences(reduction_chars.size());
 
    for (unsigned ir=0; ir < reduction_chars.size(); ++ir) {
      char c = reduction_chars[ir];
      for (unsigned tnum=0; tnum < trtab.size(); ++tnum)
        idx_occurences[ir][tnum] = (trtab[tnum].ridx.find(c) != std::string::npos); 
      //cout << "find_best_reduction: idx_occurences[" << ir << "] = " << idx_occurences[ir] << "\n";
    }
    size_type best_redsz = 100000000;
    for (unsigned ir=0; ir < reduction_chars.size(); ++ir) {
      lst.clear(); lst.add(ir);
      idxset.resize(0); idxset.push_back(reduction_chars[ir]);
      /* add other possible reductions */
      for (unsigned ir2=0; ir2 < reduction_chars.size(); ++ir2) {
        if (ir2 != ir) {
          if ((idx_occurences[ir2] | idx_occurences[ir]) == idx_occurences[ir]) {
            lst.add(ir2);
            idxset.push_back(reduction_chars[ir2]);
          }
        }
      }
      /* evaluate the cost */
      size_type redsz = 1;
      for (unsigned tnum=0; tnum < trtab.size(); ++tnum) {
        if (!idx_occurences[ir][tnum]) continue;
        std::bitset<int(32)> once((int)reduction_chars.size());
        for (dim_type i=0; i < trtab[tnum].tr().ndim(); ++i) {
          bool ignore = false;
          for (dal::bv_visitor j(lst); !j.finished(); ++j) {
            if (trtab[tnum].ridx[i] == reduction_chars[(size_t)j]) {
              if (once[j]) ignore = true; else once[j] = true;
            }
          }
          if (!ignore)
            redsz *= trtab[tnum].tr().dim(i);
        }
      }
      //cout << "   test " << reduction_chars[ir] << ": lst=" << lst << ", redsz=" << redsz << "\n";
      if (redsz < best_redsz) {
        best_redsz = redsz;
        best_lst.clear();
        for (unsigned i=0; i < trtab.size(); ++i)
          if (idx_occurences[ir][i]) best_lst.add(i);
        best_idxset = idxset;
      }
    }
    /*cout << "find_best_reduction: lst = " << best_lst << " [nt=" 
         << trtab.size() << "], idx_set='" << best_idxset 
         << "', redsz=" << best_redsz << "\n";
    */
    return best_redsz;
  }
 
  void tensor_reduction::make_sub_reductions() {
    dal::bit_vector bv; std::string red;
    int iter = 1;
    do {
      find_best_sub_reduction(bv,red);
      if (bv.card() < trtab.size() && red.size()) {
        //cout << "making sub reduction\n";
        auto sub = std::make_shared<tensor_reduction>();
        std::vector<dim_type> new_rdim; new_rdim.reserve(16);
        std::string new_reduction;
        for (dal::bv_visitor tnum(bv); !tnum.finished(); ++tnum) {
          tref_or_reduction &t = trtab[tnum];
          std::string re = t.ridx; t.ridx.clear();
          for (unsigned i = 0; i < re.size(); ++i) {
            bool reduced = false;
            char c = re[i];
            if (c != ' ') {
              if (red.find(re[i]) == std::string::npos)  c = ' ';
              else reduced = true; 
            }
            if (!reduced) { 
              t.ridx.push_back(re[i]);
              new_rdim.push_back(t.rdim[i]);
              new_reduction.push_back(re[i]);
            }
            re[i] = c;
          }
          //cout << "  sub-";
          sub->insert(trtab[tnum], re);
        }
        //cout << "  new_reduction = '" << new_reduction << "'\n";
        sub->prepare();
        /*cout << "  " << new_reduction.size() << " == " << int(sub->trres.ndim()) << "?\n";
          assert(new_reduction.size() == sub->trres.ndim());*/
        trtab[bv.first_true()] = tref_or_reduction(sub, new_reduction); 
        trtab[bv.first_true()].rdim = new_rdim;
        std::vector<tref_or_reduction> trtab2; trtab2.reserve(trtab.size() - bv.card() + 1);
        for (size_type i=0; i < trtab.size(); ++i)
          if (!bv.is_in(i) || i == bv.first_true())
            trtab2.push_back(trtab[i]);
        trtab.swap(trtab2);
        //cout << "make_sub_reductions[" << iter << "] : still " << trtab.size() << " tensors\n";
        /*for (size_type i=0; i < trtab.size(); ++i)
          cout << "    dim = " << trtab[i].tr().ndim() << " : '" << trtab[i].ridx << "'\n";
        */
        ++iter;
      } else {
        //cout << "Ok, no more reductions (bv.card() == " << bv.card() << ")\n\n";
        break;
      }
    } while (1);
  }
 
  void tensor_reduction::prepare(const tensor_ref* tr_out) {
    pre_prepare();
    make_sub_reductions();
 
    /* create the output tensor */
    if (tr_out == NULL) {
      trres = tensor_ref(reduced_range);
      out_data.resize(trres.card());
      pout_data = &out_data[0];
      trres.set_base(pout_data);
    } else {
      GMM_ASSERT3(tr_out->ndim() == reduced_range.size(), "");
      for (dim_type i=0; i < tr_out->ndim(); ++i)
        GMM_ASSERT3(tr_out->dim(i) == reduced_range[i], "");
      trres = *tr_out;
    }
 
    /* prepare the mapping from each dimension of each tensor to the global range 
       (the first dimensions are reserved for non-reduced dimensions, i.e. those
       of 'reduced_range'
    */
    tensor_ranges global_range; /* global range across all tensors of the 
                                   reduction */
    std::string   global_chars; /* name of indexes (or ' ') for each dimension
                                   of global_range */
    global_range.reserve(16); 
    global_range.assign(reduced_range.begin(), reduced_range.end());
    global_chars.insert(size_type(0), reduced_range.size(), ' ');    
    for (trtab_iterator it = trtab.begin(); it != trtab.end(); ++it) {
      assert(it->rdim.size() == it->tr().ndim());
      it->gdim = it->rdim;
      for (dim_type i=0; i < it->ridx.size(); ++i) {
        if (it->rdim[i] == dim_type(-1)) {
          assert(it->ridx[i] != ' '); 
          std::string::size_type p = global_chars.find(it->ridx[i]);
          if (p == std::string::npos) {
            global_chars.push_back(it->ridx[i]);
            global_range.push_back(it->tr().dim(i));
            it->gdim[i] = dim_type(global_range.size() - 1);
          } else {
            GMM_ASSERT1(it->tr().dim(i) == global_range[p],
                        "inconsistent dimensions for reduction index " 
                        << it->ridx[i] << "(" << int(it->tr().dim(i)) 
                        << " != " << int(global_range[p]) << ")");
            it->gdim[i] = dim_type(p);
          }
        }
      }
      //cout << " rdim = " << it->rdim << ", gdim = " << it->gdim << "\n";
    }
    //cout << "global_range = " << global_range << ", global_chars = '" << global_chars << "'\n";
    
    std::vector<dim_type> reorder(global_chars.size(), dim_type(-1));
    /* increase the dimension of the tensor holding the result */
    for (dim_type i=0; i < reduced_range.size(); ++i) reorder[i] = i;
    //cout << "reorder = '" << reorder << "'\n";
    trres.permute(reorder);
    std::vector<tensor_ref> tt; tt.reserve(trtab.size()+1);
    tt.push_back(trres);
 
    /* permute all tensors (and increase their number of dimensions) */
    for (trtab_iterator it = trtab.begin(); it != trtab.end(); ++it) {
      std::fill(reorder.begin(), reorder.end(), dim_type(-1));
      for (dim_type i=0; i < it->gdim.size(); ++i) {
        reorder[it->gdim[i]] = i;
      }
      //cout << "reorder = '" << reorder << "'\n";
      it->tr().permute(reorder);
      tt.push_back(it->tr());
      //cout << "MTI[" << it-trtab.begin() << "/" << trtab.size() << "] : " << (tensor_shape&)it->tr();
    }
    
    /* now, the iterator can be built */
    mti.init(tt,false);
  }
  
  static void do_reduction1(bgeot::multi_tensor_iterator &mti) {
    do {
      scalar_type s1 = 0;
      do { 
        s1 += mti.p(1); 
      } while (mti.bnext(1));
      mti.p(0) += s1;
    } while (mti.bnext(0));
  }
 
  static bool do_reduction2v(bgeot::multi_tensor_iterator &mti) {
    BLAS_INT n = mti.vectorized_size();
    const std::vector<stride_type> &s = mti.vectorized_strides();
    if (n && s[0] && s[1] && s[2] == 0) {
      BLAS_INT incx = s[1], incy = s[0];
      /*mti.print();
        scalar_type *b[3]; 
        for (int i=0; i < 3; ++i)       b[i] = &mti.p(i);*/
      do {
        /*cout << "vectorized_ reduction2a : n=" << n << ", s = " << s << " mti.p=" << &mti.p(0)-b[0] << "," 
          << &mti.p(1)-b[1] << "," << &mti.p(2)-b[2] << "\n";*/
        gmm::daxpy_(&n, &mti.p(2), &mti.p(1), &incx, &mti.p(0), &incy);
      } while (mti.vnext());
      return true;
    } else return false;
  }
  static void do_reduction2a(bgeot::multi_tensor_iterator &mti) {
    if (!do_reduction2v(mti)) {
      do {
        mti.p(0) += mti.p(1)*mti.p(2);
      } while (mti.bnext(0));
    }
  }
 
  static void do_reduction2b(bgeot::multi_tensor_iterator &mti) {
    do {
      scalar_type s1 = 0;
      do { 
        scalar_type s2 = 0;
        do {
          s2 += mti.p(2);
        } while (mti.bnext(2));
        s1 += mti.p(1)*s2; 
      } while (mti.bnext(1));
      mti.p(0) += s1;
    } while (mti.bnext(0));    
  }
 
  static bool do_reduction3v(bgeot::multi_tensor_iterator &mti) {
    BLAS_INT n = mti.vectorized_size();
    const std::vector<stride_type> &s = mti.vectorized_strides();
    if (n && s[0] && s[1] && s[2] == 0 && s[3] == 0) {
      BLAS_INT incx = s[1], incy = s[0];
      do {
        double v = mti.p(2)*mti.p(3);
        gmm::daxpy_(&n, &v, &mti.p(1), &incx, &mti.p(0), &incy);
      } while (mti.vnext());
      return true;
    } else return false;
  }
 
  static void do_reduction3a(bgeot::multi_tensor_iterator &mti) {
    if (!do_reduction3v(mti)) {
      do {
        mti.p(0) += mti.p(1)*mti.p(2)*mti.p(3);
      } while (mti.bnext(0));
    }
  }
 
  static void do_reduction3b(bgeot::multi_tensor_iterator &mti) {
    do {
      scalar_type s1 = 0;
      do { 
        scalar_type s2 = 0;
        do {
          scalar_type s3 = 0;
          do { 
            s3 += mti.p(3);
          } while (mti.bnext(3));
          s2 += mti.p(2)*s3;
        } while (mti.bnext(2));
        s1 += mti.p(1)*s2; 
      } while (mti.bnext(1));
      mti.p(0) += s1;
    } while (mti.bnext(0));     
  }
 
  void tensor_reduction::do_reduction() {
    /* on s'assure que le tenseur destination a bien ete remis a zero
       avant le calcul (c'est obligatoire malheureusement, consequence
       de l'utilisation de masque qui ne s'arretent pas forcement sur les 
       'frontieres' entre les differents tenseurs reduits) */
    //std::fill(out_data.begin(), out_data.end(), 0.);
    if (out_data.size()) memset(&out_data[0], 0, out_data.size()*sizeof(out_data[0]));
    for (unsigned i=0; i < trtab.size(); ++i) {
      if (trtab[i].is_reduction()) { 
        trtab[i].reduction->do_reduction(); 
        trtab[i].reduction->result(trtab[i].tr());
        //cout << "resultat intermediaire: " << trtab[i].tr() << endl;
      }
    }
    mti.rewind();
    dim_type N = dim_type(trtab.size());
    if (N == 1) {
      do_reduction1(mti);
    } else if (N == 2) {
      if (!mti.bnext_useful(2) && !mti.bnext_useful(1)) {
        do_reduction2a(mti);
      } else {
        do_reduction2b(mti);
      }
    } else if (N == 3) {
      if (!mti.bnext_useful(1) && (!mti.bnext_useful(2)) && !mti.bnext_useful(3)) {
        do_reduction3a(mti);
      } else {
        do_reduction3b(mti);
      }
    } else if (N == 4) {
      do {
        scalar_type s1 = 0;
        do { 
          scalar_type s2 = 0;
          do {
            scalar_type s3 = 0;
            do { 
              scalar_type s4 = 0;
              do {
                s4 += mti.p(4);
              } while (mti.bnext(4));
              s3 += mti.p(3)*s4;
            } while (mti.bnext(3));
            s2 += mti.p(2)*s3;
          } while (mti.bnext(2));
          s1 += mti.p(1)*s2; 
        } while (mti.bnext(1));
        mti.p(0) += s1;
      } while (mti.bnext(0));   
    } else {
      GMM_ASSERT1(false, "unhandled reduction case ! (N=" << int(N) << ")");
    }
  }
 
  void tensor_reduction::clear() {
    trtab.clear(); 
    trres.clear(); 
    reduced_range.resize(0);
    reduction_chars.clear();
 
    out_data.resize(0);
    pout_data = 0; trtab.reserve(10);
    mti.clear();
  }
 
 
  void tensor_mask::print(std::ostream &o) const {
    index_type c=card(true);
    check_assertions();
    o << "   mask : card=" << c << "(card_=" << card_ << ", uptodate=" << card_uptodate << "), indexes=";
    for (dim_type i=0; i < idxs.size(); ++i) 
      o << (i==0?"":", ") << int(idxs[i]) << ":" << int(r[i]);
    o << "   ";
    if (c == size()) o << " FULL" << endl;
    else {
      o << "m={";
      if (idxs.size() == 1) {
        for (index_type i=0; i < m.size(); ++i) o << (m[i] ? 1 : 0);
      } else {
        for (tensor_ranges_loop l(r); !l.finished(); l.next()) {
          if (l.cnt[0] == 0 && l.cnt[1] == 0 && r.size()>2) {
            o << "\n   -> (:,:";
            for (dim_type i=2; i < r.size(); ++i) o << "," << l.cnt[i]; 
            o << ")={";
          }
          o << (m[lpos(l.cnt)] ? 1 : 0);
          if (l.cnt[0] == r[0]-1) {
            if (l.cnt[1] != r[1]-1) o << ","; 
            else if (idxs.size() > 2) o << "}";
          }
        }
      }
      o << "}" << endl;
    }
  }
 
 
 
  void tensor_shape::print(std::ostream& o) const {
    o << "  tensor_shape: n=" << idx2mask.size() << ", idx2mask=";
    for (dim_type i=0; i < idx2mask.size(); ++i) {
      if (i) o << ",";
      if (idx2mask[i].is_valid()) {
        o << "r" << dim(i) << ":m" << int(idx2mask[i].mask_num) << "/" << int(idx2mask[i].mask_dim);
      } else o << " (na) ";
    }
    o << endl;
    //      o << "     masks[1.."<< masks_.size() << "]={" << endl;
    for (dim_type i=0; i < masks_.size(); ++i) o << masks_[i];
    o << "  ^-- end tensor_shape" << endl;
  }
 
  void tensor_ref::print(std::ostream& o) const {
    o << "tensor_ref, n=" << int(ndim()) << ", card=" << card(true) << ", base=" << base() << endl;
    for (dim_type i=0; i < strides().size(); ++i) {
      o << " * strides["<<i<<"]={";
      for (size_type j=0; j < strides()[i].size(); ++j) o << (j>0?",":"") << strides()[i][j];
      o << "}" << endl;
    }
    multi_tensor_iterator mti(*this, true);
    do {
      for (dim_type i = 0; i < mti.ndim(); ++i) {
        o << (i==0?"(":",");
        if (index_is_valid(i))
          o << mti.index(i);
        else o << "*";
      }
      o << ")";
      if (base()) {
        o << " = " << mti.p(0) << "\t@base+" << &mti.p(0) - base();
      } else o << "\t@" << size_t(&mti.p(0))/sizeof(scalar_type);
      o << endl;
    } while (mti.qnext1());
 
    o << "^---- end tensor_ref" << endl;
  }
 
  std::ostream& operator<<(std::ostream& o, const tensor_mask& m) { 
    m.print(o); return o; 
  }
  std::ostream& operator<<(std::ostream& o, const tensor_shape& ts) { 
    ts.print(o); return o; 
  }
  std::ostream& operator<<(std::ostream& o, const tensor_ref& tr) {
    tr.print(o); return o;
  }
  void print_tm(const tensor_mask& tm) { tm.print_(); }
  void print_ts(const tensor_shape& ts) { ts.print_(); }
  void print_tr(const tensor_ref& tr) { tr.print_(); }
}