===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/nd.c,v
retrieving revision 1.38
retrieving revision 1.41
diff -u -p -r1.38 -r1.41
--- OpenXM_contrib2/asir2018/engine/nd.c	2020/10/26 02:41:05	1.38
+++ OpenXM_contrib2/asir2018/engine/nd.c	2020/11/26 03:55:23	1.41
@@ -1,8 +1,8 @@
-/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.37 2020/10/06 06:31:19 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.40 2020/11/02 08:30:55 noro Exp $ */
 
 #include "nd.h"
 
-int Nnd_add,Nf4_red;
+int Nnd_add,Nf4_red,NcriB,NcriMF,Ncri2,Npairs;
 struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2;
 
 int diag_period = 6;
@@ -65,8 +65,9 @@ static int nd_module_rank,nd_poly_weight_len;
 static int *nd_poly_weight,*nd_module_weight;
 static NODE nd_tracelist;
 static NODE nd_alltracelist;
-static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf;
-static int nd_f4_td,nd_sba_f4step,nd_sba_pot,nd_sba_largelcm;
+static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf,nd_norb;
+static int nd_f4_td,nd_sba_f4step,nd_sba_pot,nd_sba_largelcm,nd_sba_dontsort,nd_sba_redundant_check;
+static int nd_top;
 static int *nd_gbblock;
 static NODE nd_nzlist,nd_check_splist;
 static int nd_splist;
@@ -115,6 +116,7 @@ NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,U
 NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col,
         NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred);
 int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat);
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig);
 NODE nd_f4_lf_trace_main(int m,int **indp);
 void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp);
 
@@ -1205,6 +1207,18 @@ INLINE int ndl_find_reducer(UINT *dg)
     return -1;
 }
 
+INLINE int ndl_find_reducer_nonsig(UINT *dg)
+{
+    RHist r;
+    int i;
+
+    for ( i = 0; i < nd_psn; i++ ) {
+      r = nd_psh[i];
+      if ( ndl_reducible(dg,DL(r)) ) return i;
+    }
+    return -1;
+}
+
 // ret=0,...,nd_psn-1 => reducer found
 // ret=nd_psn => reducer not found
 // ret=-1 => singular top reducible
@@ -2029,6 +2043,7 @@ void free_pbucket(PGeoBucket b) {
     GCFREE(b);
 }
 
+#if 0
 void add_pbucket_symbolic(PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -2046,7 +2061,32 @@ void add_pbucket_symbolic(PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket_symbolic(PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  if ( !d )
+    return;
+  m0 = g->m;
+  while ( 1 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_merge(g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
+#if 0
 void add_pbucket(int mod,PGeoBucket g,ND d)
 {
     int l,i,k,m;
@@ -2064,7 +2104,29 @@ void add_pbucket(int mod,PGeoBucket g,ND d)
     g->body[k] = d;
     g->m = MAX(g->m,k);
 }
+#else
+void add_pbucket(int mod,PGeoBucket g,ND d)
+{
+  int l,i,k,m,m0;
 
+  m0 = g->m;
+  while ( d != 0 ) {
+    l = LEN(d);
+    for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+    /* 2^(k-1) < l <= 2^k (=m) */
+    if ( g->body[k] == 0 ) {
+      g->body[k] = d;
+      m0 = MAX(k,m0);
+      break;
+    } else { 
+      d = nd_add(mod,g->body[k],d);
+      g->body[k] = 0; 
+    }
+  }
+  g->m = m0;
+}
+#endif
+
 void mulq_pbucket(PGeoBucket g,Z c)
 {
     int k;
@@ -2388,6 +2450,7 @@ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,i
   Z q;
   union oNDC dn,hc;
   int diag_count = 0;
+  int Nnfnz = 0,Nnfz = 0;
   P cont;
   LIST list;
 struct oEGT eg1,eg2,eg_update;
@@ -2424,16 +2487,17 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!Top,&nf)
-      :nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf)
+      :nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( nf ) {
+      Nnfnz++;
       if ( checkonly || gensyz ) return 0;
       if ( nd_newelim ) {
         if ( nd_module ) {
@@ -2472,23 +2536,28 @@ get_eg(&eg1);
 get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2);
       g = update_base(g,nh);
       FREENDP(l);
-   } else {
-     if ( nd_gentrace && gensyz ) {
-       nd_tracelist = reverse_node(nd_tracelist); 
-       MKLIST(list,nd_tracelist);
-       STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
-       MKNODE(t,list,nd_alltracelist); 
-       nd_alltracelist = t; nd_tracelist = 0;
-     }
-     if ( DP_Print ) { printf("."); fflush(stdout); }
-       FREENDP(l);
-     }
+    } else {
+      Nnfz++;
+      if ( nd_gentrace && gensyz ) {
+        nd_tracelist = reverse_node(nd_tracelist); 
+        MKLIST(list,nd_tracelist);
+        STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t);
+        MKNODE(t,list,nd_alltracelist); 
+        nd_alltracelist = t; nd_tracelist = 0;
+      }
+      if ( DP_Print ) { printf("."); fflush(stdout); }
+        FREENDP(l);
+    }
   }
   conv_ilist(nd_demand,0,g,indp);
-  if ( !checkonly && DP_Print ) { printf("nd_gb done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); }
- 
-  if ( DP_Print )
-    print_eg("update",&eg_update);
+  if ( !checkonly && DP_Print ) { 
+    printf("\nnd_gb done. Nnd_add=%d,Npairs=%d, Nnfnz=%d,Nnfz=%d,",Nnd_add,Npairs,Nnfnz,Nnfz);
+    printf("Nremoved=%d\n",NcriB+NcriMF+Ncri2);
+    fflush(asir_out);
+  }
+  if ( DP_Print ) {
+    print_eg("update",&eg_update); fprintf(asir_out,"\n");
+  }
   return g;
 }
 
@@ -2595,6 +2664,60 @@ int small_lcm(ND_pairs l)
 #endif
 }
 
+ND_pairs find_smallest_lcm(ND_pairs l)
+{
+  SIG sig;
+  int i,minindex;
+  NODE t;
+  ND_pairs r;
+  struct oSIG sig1;
+  static DL mul,quo,minlm;
+  static int nvar;
+
+  if ( nvar < nd_nvar ) {
+    nvar = nd_nvar; 
+    NEWDL(quo,nvar); NEWDL(mul,nvar);
+    NEWDL(minlm,nvar);
+  }
+  sig = l->sig;
+  // find mg s.t. m*s(g)=sig and m*lm(g) is minimal
+  _ndltodl(l->lcm,minlm); minindex = -1;
+  for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) {
+    i = (long)BDY(t);
+    if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) {
+      _ndltodl(DL(nd_psh[i]),mul);
+      _addtodl(nd_nvar,quo,mul);
+      if ( (*cmpdl)(nd_nvar,minlm,mul) > 0 ) {
+        minindex = i;
+        _copydl(nd_nvar,mul,minlm);
+      }
+    }
+  }
+  // l->lcm is minimal; return l itself
+  if ( minindex < 0 ) return l;
+  for ( i = 0; i < nd_psn; i++ ) {
+    if ( i == minindex ) continue;
+    _ndltodl(DL(nd_psh[i]),mul);
+    if ( _dl_redble_ext(mul,minlm,quo,nd_nvar) ) {
+      _addtodl(nd_nvar,nd_ps[i]->sig->dl,quo);
+      sig1.pos = nd_ps[i]->sig->pos;
+      sig1.dl = quo;
+      if ( comp_sig(sig,&sig1) > 0 ) {
+//        printf("X");
+        NEWND_pairs(r);
+        r->sig = sig;
+        r->i1 = minindex;
+        r->i2 = i;
+        dltondl(nd_nvar,minlm,r->lcm);
+        r->next = 0;
+        return r;
+      }
+    }
+  }
+  // there is no suitable spair 
+  return 0;
+}
+
 ND_pairs remove_large_lcm(ND_pairs d)
 {
   struct oND_pairs root;
@@ -2603,10 +2726,17 @@ ND_pairs remove_large_lcm(ND_pairs d)
   root.next = d;
   prev = &root; p = d;
   while ( p ) {
+#if 0
     if ( small_lcm(p) ) {
       // remove p
       prev->next = p->next;
     } else
+#else
+    if ( find_smallest_lcm(p) == 0 ) {
+      // remove p
+      prev->next = p->next;
+    } else
+#endif
       prev = p;
     p = p->next;
   }
@@ -2619,10 +2749,10 @@ NODE conv_ilist_s(int demand,int trace,int **indp);
 
 NODE nd_sba_buch(int m,int ishomo,int **indp)
 {
-  int i,j,nh,sugar,stat;
+  int i,j,nh,sugar,stat,pos;
   NODE r,t,g;
   ND_pairs d;
-  ND_pairs l;
+  ND_pairs l,l1;
   ND h,nf,s,head,nf1;
   NDV nfv;
   Z q;
@@ -2631,26 +2761,29 @@ NODE nd_sba_buch(int m,int ishomo,int **indp)
   LIST list;
   SIG sig;
   NODE *syzlist;
-  int Nredundant;
+  int Nnominimal,Nredundant;
   DL lcm,quo,mul;
   struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero;
+  int Nnfs=0,Nnfz=0,Nnfnz=0;
 
 init_eg(&eg_remove);
   syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE));
   Nsyz = 0;
   Nnd_add = 0;
+  Nnominimal = 0;
   Nredundant = 0;
   d = 0;
-  for ( i = 0; i < nd_psn; i++ ) {
-    d = update_pairs_s(d,i,syzlist);
-  }
   for ( i = 0; i < nd_psn; i++ )
     for ( j = i+1; j < nd_psn; j++ ) {
       NEWSIG(sig); sig->pos = j;
       _copydl(nd_nvar,nd_sba_hm[i],sig->dl);
       syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig);
     }
+  for ( i = 0; i < nd_psn; i++ ) {
+    d = update_pairs_s(d,i,syzlist);
+  }
   sugar = 0;
+  pos = 0;
   NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar);
 init_eg(&eg_create);
 init_eg(&eg_merge);
@@ -2667,9 +2800,10 @@ again:
        if ( !(len%100) ) fprintf(asir_out,"(%d)",len);
       }
     l = d; d = d->next;
+#if 0
     if ( small_lcm(l) ) {
       if ( DP_Print ) fprintf(asir_out,"M");
-      Nredundant++;
+      Nnominimal++;
       continue;
     }
     if ( SG(l) != sugar ) {
@@ -2677,7 +2811,33 @@ again:
       if ( DP_Print ) fprintf(asir_out,"%d",sugar);
     }
     sig = l->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
     stat = nd_sp(m,0,l,&h);
+#else
+    l1 = find_smallest_lcm(l);
+    if ( l1 == 0 ) {
+      if ( DP_Print ) fprintf(asir_out,"M");
+      Nnominimal++;
+      continue;
+    }
+    if ( SG(l1) != sugar ) {
+      sugar = SG(l1);
+      if ( DP_Print ) fprintf(asir_out,"%d",sugar);
+    }
+    sig = l1->sig;
+    if ( DP_Print && nd_sba_pot ) {
+      if ( sig->pos != pos ) {
+        fprintf(asir_out,"[%d]",sig->pos);
+        pos = sig->pos;
+      }
+    }
+    stat = nd_sp(m,0,l1,&h);
+#endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
@@ -2685,9 +2845,9 @@ again:
     }
 get_eg(&eg1);
 #if USE_GEOBUCKET
-    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+    stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
 get_eg(&eg2); 
     if ( !stat ) {
@@ -2695,10 +2855,22 @@ get_eg(&eg2); 
       d = nd_reconstruct(0,d);
       goto again;
     } else if ( stat == -1 ) {
+      Nnfs++;
       if ( DP_Print ) { printf("S"); fflush(stdout); }
       FREENDP(l);
     } else if ( nf ) {
-      if ( DP_Print ) { printf("+"); fflush(stdout); }
+      Nnfnz++;
+      if ( DP_Print ) { 
+        if ( nd_sba_redundant_check ) {
+          if ( ndl_find_reducer_nonsig(HDL(nf)) >= 0 ) {
+            Nredundant++;
+            printf("R"); 
+          } else 
+            printf("+"); 
+        } else
+          printf("+"); 
+        fflush(stdout); 
+      }
       add_eg(&eg_nf,&eg1,&eg2);
       hc = HCU(nf);
       nd_removecont(m,nf);
@@ -2709,6 +2881,7 @@ get_eg(&eg2); 
       nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh);
       FREENDP(l);
    } else {
+      Nnfz++;
       add_eg(&eg_nfzero,&eg1,&eg2);
      // syzygy
 get_eg(&eg1);
@@ -2721,8 +2894,12 @@ get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2);
  }
  g = conv_ilist_s(nd_demand,0,indp);
  if ( DP_Print ) { 
-   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nsamesig,Nredundant);
+   printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nnominimal=%d\n",Nnd_add,Nsyz,Nsamesig,Nnominimal);
+   printf("Nnfnz=%d,Nnfz=%d,Nnfsingular=%d\n",Nnfnz,Nnfz,Nnfs);
    fflush(stdout); 
+   if ( nd_sba_redundant_check )
+   printf("Nredundant=%d\n",Nredundant);
+   fflush(stdout); 
    print_eg("create",&eg_create);
    print_eg("merge",&eg_merge);
    print_eg("remove",&eg_remove);
@@ -2760,7 +2937,7 @@ again:
       d = nd_reconstruct(0,d);
       goto again;
     }
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
     if ( !stat ) {
       NEXT(l) = d; d = l;
       d = nd_reconstruct(0,d);
@@ -2935,9 +3112,9 @@ again:
       goto again;
     }
 #if USE_GEOBUCKET
-    stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf);
+    stat = nd_nf_pbucket(m,h,nd_ps,!nd_top&&!Top,&nf);
 #else
-    stat = nd_nf(m,0,h,nd_ps,!Top,&nf);
+    stat = nd_nf(m,0,h,nd_ps,!nd_top&&!Top,&nf);
 #endif
     if ( !stat ) {
       NEXT(l) = d; d = l;
@@ -2950,7 +3127,7 @@ again:
       } else
         nfq = 0;
       if ( !nfq ) {
-        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,&nfq) ) {
+        if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!nd_top&&!Top,&nfq) ) {
           NEXT(l) = d; d = l;
           d = nd_reconstruct(1,d);
           goto again;
@@ -3016,7 +3193,7 @@ again:
     }
   }
   conv_ilist(nd_demand,1,g,indp);
-  if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); }
+  if ( DP_Print ) { printf("\nnd_gb_trace done.\n"); fflush(stdout); }
   return g;
 }
 
@@ -3104,9 +3281,17 @@ NODE ndv_reduceall(int m,NODE f)
   return a0;
 }
 
+int ndplength(ND_pairs d)
+{
+  int i;
+  for ( i = 0; d; i++ ) d = NEXT(d);
+  return i;
+}
+
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t, int gensyz)
 {
   ND_pairs d1,nd,cur,head,prev,remove;
+  int len0;
 
   if ( !g ) return d;
   /* for testing */
@@ -3123,8 +3308,10 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
   }
   d = crit_B(d,t);
   d1 = nd_newpairs(g,t);
+  len0 = ndplength(d1); 
   d1 = crit_M(d1);
   d1 = crit_F(d1);
+  NcriMF += len0-ndplength(d1); 
   if ( gensyz || do_weyl )
     head = d1;
   else {
@@ -3134,7 +3321,7 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
         remove = cur;
         if ( !prev ) head = cur = NEXT(cur);
         else cur = NEXT(prev) = NEXT(cur);
-        FREENDP(remove);
+        FREENDP(remove); Ncri2++;
       } else {
         prev = cur; cur = NEXT(cur);
       }
@@ -3189,7 +3376,7 @@ ND_pairs nd_newpairs( NODE g, int t )
       if ( nd_gbblock[i] >= 0 )
         continue;
     }
-    NEXTND_pairs(r0,r);
+    NEXTND_pairs(r0,r); Npairs++;
     r->i1 = (long)BDY(h);
     r->i2 = t;
     ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
@@ -3461,7 +3648,7 @@ ND_pairs crit_B( ND_pairs d, int s )
           } else {
             cur = NEXT(prev) = NEXT(cur);
           }
-          FREENDP(remove);
+          FREENDP(remove); NcriB++;
         } else {
           prev = cur; cur = NEXT(cur);
         }
@@ -4041,6 +4228,7 @@ void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int 
     int obpe,oadv,ompos,cbpe;
     VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     if ( !m && Demand ) nd_demand = 1;
     else nd_demand = 0;
@@ -4320,7 +4508,7 @@ void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int
         ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos);
   }
 
-  ndv_setup(m,0,fd0,0,0,1);
+  ndv_setup(m,0,fd0,nd_sba_dontsort,0,1);
   x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm);
   if ( !x ) {
     *rp = 0; return;
@@ -4608,6 +4796,7 @@ void nd_gr_trace(LIST f,LIST v,int trace,int homo,int 
     Z jq,bpe;
     VECT hvect;
 
+    NcriB = NcriMF = Ncri2 = 0;
     nd_module = 0;
     nd_lf = 0;
     parse_nd_option(current_option);
@@ -6727,6 +6916,7 @@ NODE ndv_reducebase(NODE x,int *perm)
     NDVI w;
     NODE t,t0;
 
+    if ( nd_norb ) return x;
     len = length(x);
     w = (NDVI)MALLOC(len*sizeof(struct oNDVI));
     for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) {
@@ -7402,7 +7592,7 @@ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndA
 }
 #endif
 
-int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred)
+int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig)
 {
     int i,j,k,len,pos,prev;
     UINT c,c1,c2,c3,up,lo,dmy;
@@ -7419,7 +7609,7 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
     for ( i = 0; i < nred; i++ ) {
         ivect = imat[i];
         k = ivect->head; svect[k] %= m;
-        if ( (c = svect[k]) != 0 ) {
+        if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) {
             maxrs = MAX(maxrs,rp0[i]->sugar);
             c = m-c; redv = nd_ps[rp0[i]->index];
             len = LEN(redv); mr = BDY(redv);
@@ -7429,12 +7619,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     ivc = ivect->index.c;
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivc[j]; c1 = CM(mr); prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 2:
@@ -7442,12 +7632,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivs[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
                 case 4:
@@ -7455,12 +7645,12 @@ int ndv_reduce_vect(int m,UINT *svect,int col,IndArray
                     for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) {
                         pos = prev+ivi[j]; c1 = CM(mr);
                         prev = pos;
-            if ( c1 ) {
-              c2 = svect[pos];
+                        if ( c1 ) {
+                          c2 = svect[pos];
                           DMA(c1,c,c2,up,lo);
                           if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3;
                           } else svect[pos] = lo;
-            }
+                        }
                     }
                     break;
             }
@@ -7728,6 +7918,29 @@ NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhea
     }
 }
 
+NDV vect_to_ndv_s(UINT *vect,int col,UINT *s0vect)
+{
+    int j,k,len;
+    UINT *p;
+    UINT c;
+    NDV r;
+    NMV mr0,mr;
+
+    for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++;
+    if ( !len ) return 0;
+    else {
+        mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len);
+        mr = mr0; 
+        p = s0vect;
+        for ( j = k = 0; j < col; j++, p += nd_wpd )
+          if ( (c = vect[k++]) != 0 ) {
+            ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr);
+          }
+        MKNDV(nd_nvar,mr0,len,r);
+        return r;
+    }
+}
+
 NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect)
 {
     int j,k,len;
@@ -8038,6 +8251,7 @@ NODE nd_f4(int m,int checkonly,int **indp)
     fprintf(asir_out,"number of red=%d,",Nf4_red);
     fprintf(asir_out,"symb=%.3fsec,conv=%.3fsec,elim1=%.3fsec,elim2=%.3fsec\n",
       f4_symb.exectime,f4_conv.exectime,f4_elim1.exectime,f4_elim2.exectime);
+    fprintf(asir_out,"number of removed pairs=%d\n,",NcriB+NcriMF+Ncri2);
   }
   conv_ilist(nd_demand,0,g,indp);
     return g;
@@ -8399,7 +8613,7 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
         if ( m == -1 ) 
             maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred);
         else
-            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred);
+            maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,0);
         for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
         if ( i < col ) {
             spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT));
@@ -8455,7 +8669,84 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s
     return r0;
 }
 
+NODE nd_f4_red_main_s(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
+        NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,NODE *syzlistp)
+{
+    int spcol,sprow,a;
+    int i,j,k,l,rank;
+    NODE r0,r;
+    ND_pairs sp;
+    ND spol;
+    UINT **spmat;
+    UINT *svect,*cvect;
+    UINT *v;
+    int *colstat;
+    struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2;
+    int maxrs;
+    int *spsugar;
+    ND_pairs *spactive;
+    SIG *spsig;
 
+    get_eg(&eg0);
+    /* elimination (1st step) */
+    spmat = (UINT **)MALLOC(nsp*sizeof(UINT *));
+    spsugar = (int *)MALLOC(nsp*sizeof(int));
+    spsig = (SIG *)MALLOC(nsp*sizeof(SIG));
+    for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) {
+        nd_sp(m,0,sp,&spol);
+        if ( !spol ) {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+          continue;
+        }
+        svect = (UINT *)MALLOC(col*sizeof(UINT));
+        nd_to_vect(m,s0vect,col,spol,svect);
+        maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred,spol->sig);
+        for ( i = 0; i < col; i++ ) if ( svect[i] ) break;
+        if ( i < col ) {
+            spmat[sprow] = svect;
+            spsugar[sprow] = MAX(maxrs,SG(spol));
+            spsig[sprow] = sp->sig;
+            sprow++;
+        } else {
+          syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig);
+        }
+        nd_free(spol);
+    }
+    get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); add_eg(&f4_elim1,&eg0,&eg1);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime);
+        fflush(asir_out);
+    }
+    /* free index arrays */
+    for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c);
+
+    /* elimination (2nd step) */
+    colstat = (int *)MALLOC(col*sizeof(int));
+    rank = nd_gauss_elim_mod_s(spmat,spsugar,0,sprow,col,m,colstat,spsig);
+    r0 = 0;
+    for ( i = 0; i < sprow; i++ ) {
+        if ( spsugar[i] >= 0 ) {
+          NEXTNODE(r0,r);
+          BDY(r) = vect_to_ndv_s(spmat[i],col,s0vect);
+          SG((NDV)BDY(r)) = spsugar[i];
+          ((NDV)BDY(r))->sig = spsig[i];
+        } else
+          syzlistp[spsig[i]->pos] = insert_sig(syzlistp[spsig[i]->pos],spsig[i]);
+        GCFREE(spmat[i]);
+    }
+    if ( r0 ) NEXT(r) = 0;
+    get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2);
+    init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2);
+    if ( DP_Print ) {
+        fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime);
+        fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ",
+            nsp,nred,sprow,col,rank);
+        fprintf(asir_out,"%.3fsec,",eg_f4.exectime);
+    }
+    return r0;
+}
+
+
 /* for small finite fields */
 
 NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col,
@@ -8867,7 +9158,57 @@ int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs 
     return rank;
 }
 
+int nd_gauss_elim_mod_s(UINT **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
+{
+  int i,j,k,l,rank,s,imin;
+  UINT inv;
+  UINT a;
+  UINT *t,*pivot,*pk;
+  UINT *ck;
+  UINT *ct;
+  ND_pairs pair;
+  SIG sg;
+  int *used;
 
+  used = (int *)MALLOC(row*sizeof(int));
+  for ( j = 0; j < col; j++ ) {
+    for ( i = 0; i < row; i++ )
+      a = mat[i][j] %= md;
+    for ( i = 0; i < row; i++ )
+      if ( !used[i] && mat[i][j] ) break;
+    if ( i == row ) {
+      colstat[j] = 0;
+      continue;
+    } else {
+      colstat[j] = 1;
+      used[i] = 1;
+    }
+    /* column j is normalized */
+    s = sugar[i];
+    inv = invm(mat[i][j],md);
+    /* normalize pivot row */
+    for ( k = j, pk = mat[i]+j; k < col; k++, pk++, ck++ ) {
+      DMAR(*pk,inv,0,md,*pk);
+    }
+    for ( k = i+1; k < row; k++ ) {
+      if ( (a = mat[k][j]) != 0 ) {
+        sugar[k] = MAX(sugar[k],s);
+        red_by_vect(md,mat[k]+j,mat[i]+j,(int)(md-a),col-j);
+        Nf4_red++;
+      }
+    }
+  }
+  rank = 0;
+  for ( i = 0; i < row; i++ ) {
+    for ( j = 0; j < col; j++ )
+      if ( mat[i][j] ) break;
+    if ( j == col ) sugar[i] = -1;
+    else rank++;
+  }
+  return rank;
+}
+
+
 int nd_gauss_elim_sf(UINT **mat0,int *sugar,int row,int col,int md,int *colstat)
 {
     int i,j,k,l,inv,a,rank,s;
@@ -9569,11 +9910,13 @@ void parse_nd_option(NODE opt)
   char *key;
   Obj value;
 
-  nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0;
+  nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_norb = 0; nd_gbblock = 0;
   nd_newelim = 0; nd_intersect = 0; nd_nzlist = 0;
   nd_splist = 0; nd_check_splist = 0;
   nd_sugarweight = 0; nd_f4red =0; nd_rank0 = 0;
   nd_f4_td = 0; nd_sba_f4step = 2; nd_sba_pot = 0; nd_sba_largelcm = 0;
+  nd_sba_dontsort = 0; nd_top = 0; nd_sba_redundant_check = 0;
+
   for ( t = opt; t; t = NEXT(t) ) {
     p = BDY((LIST)BDY(t));
     key = BDY((STRING)BDY(p));
@@ -9584,6 +9927,8 @@ void parse_nd_option(NODE opt)
       nd_gensyz = value?1:0;
     else if ( !strcmp(key,"nora") )
       nd_nora = value?1:0;
+    else if ( !strcmp(key,"norb") )
+      nd_norb = value?1:0;
     else if ( !strcmp(key,"gbblock") ) {
       if ( value && OID(value) == O_LIST ) {
         u = BDY((LIST)value);
@@ -9632,6 +9977,12 @@ void parse_nd_option(NODE opt)
       nd_sba_pot = value?1:0;
     } else if ( !strcmp(key,"sba_largelcm") ) {
       nd_sba_largelcm = value?1:0;
+    } else if ( !strcmp(key,"sba_dontsort") ) {
+      nd_sba_dontsort = value?1:0;
+    } else if ( !strcmp(key,"sba_redundant_check") ) {
+      nd_sba_redundant_check = value?1:0;
+    } else if ( !strcmp(key,"top") ) {
+      nd_top = value?1:0;
     }
   }
 }
@@ -10598,7 +10949,6 @@ int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_
   GCFREE(cmat);
   return rank;
 }
-#endif
 
 int nd_gauss_elim_mod64_s(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig)
 {
@@ -10740,6 +11090,7 @@ NODE nd_f4_red_mod64_main_s(int m,ND_pairs sp0,int nsp
     }
     return r0;
 }
+#endif
 
 NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,NODE *syzlistp)
 {
@@ -10778,7 +11129,11 @@ NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0
     fflush(asir_out);
   }
   if ( m > 0 )
+#if SIZEOF_LONG==8
     r0 = nd_f4_red_mod64_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#else
+    r0 = nd_f4_red_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp);
+#endif
   else
 //    r0 = nd_f4_red_q_main_s(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred);
     error("nd_f4_red_q_main_s : not implemented yet");
@@ -10888,7 +11243,7 @@ NODE nd_sba_f4(int m,int **indp)
   int i,nh,stat,index,f4red,f4step;
   int col,rank,len,k,j,a,sugar,nbase,psugar,ms;
   NODE r,g,rp0,nflist;
-  ND_pairs d,l,t;
+  ND_pairs d,l,t,l1;
   ND h,nf;
   NDV nfv;
   union oNDC hc;
@@ -10916,12 +11271,22 @@ NODE nd_sba_f4(int m,int **indp)
     if ( ms == psugar && f4step >= nd_sba_f4step ) {
 again:
       l = d; d = d->next;
+#if 0
       if ( small_lcm(l) ) {
         if ( DP_Print ) fprintf(asir_out,"M");
         continue;
       }
       sig = l->sig;
       stat = nd_sp(m,0,l,&h);
+#else
+      l1 = find_smallest_lcm(l);
+      if ( l1 == 0 ) {
+        if ( DP_Print ) fprintf(asir_out,"M");
+        continue;
+      }
+      sig = l1->sig;
+      stat = nd_sp(m,0,l1,&h);
+#endif
       if ( !stat ) {
         NEXT(l) = d; d = l;
         d = nd_reconstruct(0,d);
@@ -10929,9 +11294,9 @@ again:
       }
   get_eg(&eg1);
   #if USE_GEOBUCKET
-      stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+      stat = m?nd_nf_pbucket_s(m,h,nd_ps,!nd_top&&!Top,&nf):nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
   #else
-      stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf);
+      stat = nd_nf_s(m,0,h,nd_ps,!nd_top&&!Top,&nf);
   #endif
   get_eg(&eg2); 
       if ( !stat ) {