===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v
retrieving revision 1.34
retrieving revision 1.50
diff -u -p -r1.34 -r1.50
--- OpenXM_contrib2/asir2000/engine/nd.c	2003/08/20 06:06:07	1.34
+++ OpenXM_contrib2/asir2000/engine/nd.c	2003/08/27 01:48:25	1.50
@@ -1,4 +1,4 @@
-/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.33 2003/08/19 05:29:11 noro Exp $ */
+/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.49 2003/08/26 01:54:18 noro Exp $ */
 
 #include "ca.h"
 #include "inline.h"
@@ -15,11 +15,14 @@
 
 #define REDTAB_LEN 32003
 
+/* GeoBucket for polynomial addition */
+
 typedef struct oPGeoBucket {
 	int m;
 	struct oND *body[32];
 } *PGeoBucket;
 
+/* distributed polynomial; linked list rep. */
 typedef struct oND {
 	struct oNM *body;
 	int nv;
@@ -27,6 +30,7 @@ typedef struct oND {
 	int sugar;
 } *ND;
 
+/* distributed polynomial; array rep. */
 typedef struct oNDV {
 	struct oNMV *body;
 	int nv;
@@ -34,6 +38,7 @@ typedef struct oNDV {
 	int sugar;
 } *NDV;
 
+/* monomial; linked list rep. */
 typedef struct oNM {
 	struct oNM *next;
 	union {
@@ -43,6 +48,7 @@ typedef struct oNM {
 	unsigned int dl[1];
 } *NM;
 
+/* monomial; array rep. */
 typedef struct oNMV {
 	union {
 		int m;
@@ -51,6 +57,7 @@ typedef struct oNMV {
 	unsigned int dl[1];
 } *NMV;
 
+/* history of reducer */
 typedef struct oRHist {
 	struct oRHist *next;
 	int index;
@@ -58,6 +65,7 @@ typedef struct oRHist {
 	unsigned int dl[1];
 } *RHist;
 
+/* S-pair list */
 typedef struct oND_pairs {
 	struct oND_pairs *next;
 	int i1,i2;
@@ -65,35 +73,56 @@ typedef struct oND_pairs {
 	unsigned int lcm[1];
 } *ND_pairs;
 
-int (*nd_compare_function)(unsigned int *a1,unsigned int *a2);
+/* index and shift count for each exponent */
+typedef struct oEPOS {
+	int i; /* index */
+	int s; /* shift */
+} *EPOS;
 
-double nd_scale=2;
+typedef struct oBlockMask {
+	int n;
+	struct order_pair *order_pair;
+	unsigned int **mask;
+} *BlockMask;
+
+typedef struct oBaseSet {
+	int len;
+	NDV *ps;
+	unsigned int **bound;
+} *BaseSet;
+
+int (*ndl_compare_function)(unsigned int *a1,unsigned int *a2);
+
+static double nd_scale=2;
 static unsigned int **nd_bound;
-int nd_nvar;
-int nd_isrlex;
-int nd_epw,nd_bpe,nd_wpd;
-unsigned int nd_mask[32];
-unsigned int nd_mask0,nd_mask1;
+static struct order_spec *nd_ord;
+static EPOS nd_epos;
+static BlockMask nd_blockmask;
+static int nd_nvar;
+static int nd_isrlex;
+static int nd_epw,nd_bpe,nd_wpd,nd_exporigin;
+static unsigned int nd_mask[32];
+static unsigned int nd_mask0,nd_mask1;
 
-NM _nm_free_list;
-ND _nd_free_list;
-ND_pairs _ndp_free_list;
+static NM _nm_free_list;
+static ND _nd_free_list;
+static ND_pairs _ndp_free_list;
 
 static NDV *nd_ps;
 static NDV *nd_psq;
-RHist *nd_psh;
-int nd_psn,nd_pslen;
+static RHist *nd_psh;
+static int nd_psn,nd_pslen;
 
-RHist *nd_red;
-int nd_red_len;
+static RHist *nd_red;
 
-int nd_found,nd_create,nd_notfirst;
-int nm_adv;
-int nmv_adv;
-int nd_dcomp;
+static int nd_found,nd_create,nd_notfirst;
+static int nm_adv;
+static int nmv_adv;
+static int nd_dcomp;
 
 extern int Top,Reverse,dp_nelim;
 
+/* fundamental macros */
 #define TD(d) (d[0])
 #define HDL(d) ((d)->body->dl)
 #define HTD(d) (TD(HDL(d)))
@@ -105,16 +134,27 @@ extern int Top,Reverse,dp_nelim;
 #define SG(a) ((a)->sugar)
 #define LEN(a) ((a)->len)
 #define LCM(a) ((a)->lcm)
+#define GET_EXP(d,a) (((d)[nd_epos[a].i]>>nd_epos[a].s)&nd_mask0)
+#define PUT_EXP(r,a,e) ((r)[nd_epos[a].i] |= ((e)<<nd_epos[a].s))
+#define XOR_EXP(r,a,e) ((r)[nd_epos[a].i] ^= ((e)<<nd_epos[a].s))
 
+/* macros for term comparison */
 #define TD_DL_COMPARE(d1,d2)\
-(TD(d1)>TD(d2)?1:(TD(d1)<TD(d2)?-1:ndl_lex_compare(d1+1,d2+1)))
-
+(TD(d1)>TD(d2)?1:(TD(d1)<TD(d2)?-1:ndl_lex_compare(d1,d2)))
+#if 0
 #define DL_COMPARE(d1,d2)\
-(nd_dcomp?TD_DL_COMPARE(d1,d2):(*nd_compare_function)(d1,d2))
+(nd_dcomp>0?TD_DL_COMPARE(d1,d2)\
+         :(nd_dcomp==0?ndl_lex_compare(d1,d2)\
+                     :(nd_blockmask?ndl_block_compare(d1,d2)\
+								   :(*ndl_compare_function)(d1,d2))))
+#else
+#define DL_COMPARE(d1,d2)\
+(nd_dcomp>0?TD_DL_COMPARE(d1,d2):(*ndl_compare_function)(d1,d2))
+#endif
 
-#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv))
+/* allocators */
 #define NEWRHist(r) \
-((r)=(RHist)MALLOC(sizeof(struct oRHist)+nd_wpd*sizeof(unsigned int)))
+((r)=(RHist)MALLOC(sizeof(struct oRHist)+(nd_wpd-1)*sizeof(unsigned int)))
 #define NEWND_pairs(m) \
 if(!_ndp_free_list)_NDP_alloc();\
 (m)=_ndp_free_list; _ndp_free_list = NEXT(_ndp_free_list)   
@@ -125,29 +165,37 @@ if(!_nm_free_list)_NM_alloc();\
 if(!_nd_free_list)_ND_alloc();\
 (d)=_nd_free_list; _nd_free_list = (ND)BDY(_nd_free_list);\
 NV(d)=(n); LEN(d)=(len); BDY(d)=(m)
+#define NEWNDV(d) ((d)=(NDV)MALLOC(sizeof(struct oNDV)))
+#define MKNDV(n,m,l,d) NEWNDV(d); NV(d)=(n); BDY(d)=(m); LEN(d) = l;
 
+/* allocate and link a new object */
 #define NEXTRHist(r,c) \
 if(!(r)){NEWRHist(r);(c)=(r);}else{NEWRHist(NEXT(c));(c)=NEXT(c);}
 #define NEXTNM(r,c) \
 if(!(r)){NEWNM(r);(c)=(r);}else{NEWNM(NEXT(c));(c)=NEXT(c);}
 #define NEXTNM2(r,c,s) \
 if(!(r)){(c)=(r)=(s);}else{NEXT(c)=(s);(c)=(s);}
+#define NEXTND_pairs(r,c) \
+if(!(r)){NEWND_pairs(r);(c)=(r);}else{NEWND_pairs(NEXT(c));(c)=NEXT(c);}
 
+/* deallocators */
 #define FREENM(m) NEXT(m)=_nm_free_list; _nm_free_list=(m)
 #define FREENDP(m) NEXT(m)=_ndp_free_list; _ndp_free_list=(m)
 #define FREEND(m) BDY(m)=(NM)_nd_free_list; _nd_free_list=(m)
 
-#define NEXTND_pairs(r,c) \
-if(!(r)){NEWND_pairs(r);(c)=(r);}else{NEWND_pairs(NEXT(c));(c)=NEXT(c);}
+/* macro for increasing pointer to NMV */
+#define NMV_ADV(m) (m = (NMV)(((char *)m)+nmv_adv))
 
-void nd_init_ord(struct order_spec *spec);
-int nd_check_candidate(NODE input,NODE cand);
+/* external functions */
+void GC_gcollect();
+NODE append_one(NODE,int);
+
+/* manipulation of coefficients */
 void nd_removecont(int mod,ND p);
 void nd_removecont2(ND p1,ND p2);
-void ndv_removecont(int mod,NDV p);
-void ndv_dehomogenize(NDV p);
-void ndv_mul_c_q(NDV p,Q mul);
-void nd_mul_c_q(ND p,Q mul);
+void removecont_array(Q *c,int n);
+
+/* GeoBucket functions */
 ND normalize_pbucket(int mod,PGeoBucket g);
 int head_pbucket(int mod,PGeoBucket g);
 int head_pbucket_q(PGeoBucket g);
@@ -155,78 +203,104 @@ void add_pbucket(int mod,PGeoBucket g,ND d);
 void free_pbucket(PGeoBucket b);
 void mulq_pbucket(PGeoBucket g,Q c);
 PGeoBucket create_pbucket();
-ND nd_remove_head(ND p);
 
-void GC_gcollect();
-NODE append_one(NODE,int);
-NODE nd_reducebase(NODE x);
-
-void removecont_array(Q *c,int n);
-ND_pairs crit_B( ND_pairs d, int s );
-void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp);
-void nd_gr_trace(LIST f,LIST v,int m,int homo,struct order_spec *ord,LIST *rp);
-void nd_setup(int mod,NODE f);
-void nd_setup_trace(int mod,NODE f);
-int nd_newps(int mod,ND a);
-int nd_newps_trace(int mod,ND nf,ND nfq);
+/* manipulation of pairs and bases */
+int nd_newps(int mod,ND a,ND aq);
+ND_pairs nd_newpairs( NODE g, int t );
 ND_pairs nd_minp( ND_pairs d, ND_pairs *prest );
 NODE update_base(NODE nd,int ndp);
-static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest );
-int crit_2( int dp1, int dp2 );
-ND_pairs crit_F( ND_pairs d1 );
-ND_pairs crit_M( ND_pairs d1 );
-ND_pairs nd_newpairs( NODE g, int t );
 ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t);
+ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest );
+ND_pairs crit_B( ND_pairs d, int s );
+ND_pairs crit_M( ND_pairs d1 );
+ND_pairs crit_F( ND_pairs d1 );
+int crit_2( int dp1, int dp2 );
+
+/* top level functions */
+void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp);
+void nd_gr_trace(LIST f,LIST v,int m,int homo,struct order_spec *ord,LIST *rp);
 NODE nd_gb(int m,int checkonly);
 NODE nd_gb_trace(int m);
-void nd_free_private_storage();
-void _NM_alloc();
-void _ND_alloc();
-int ndl_td(unsigned int *d);
+
+/* ndl functions */
+int ndl_weight(unsigned int *d);
+int ndl_weight_mask(unsigned int *d,int i);
 void ndl_dehomogenize(unsigned int *p);
-ND nd_add(int mod,ND p1,ND p2);
-ND nd_add_q(ND p1,ND p2);
+void ndl_reconstruct(int obpe,EPOS oepos,unsigned int *d,unsigned int *r);
+INLINE int ndl_reducible(unsigned int *d1,unsigned int *d2);
+INLINE int ndl_lex_compare(unsigned int *d1,unsigned int *d2);
+INLINE int ndl_block_compare(unsigned int *d1,unsigned int *d2);
+INLINE int ndl_equal(unsigned int *d1,unsigned int *d2);
+INLINE void ndl_copy(unsigned int *d1,unsigned int *d2);
+INLINE void ndl_add(unsigned int *d1,unsigned int *d2,unsigned int *d);
+INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d);
+INLINE int ndl_hash_value(unsigned int *d);
+
+/* normal forms */
+INLINE int nd_find_reducer(ND g);
+INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len);
 int nd_sp(int mod,ND_pairs p,ND *nf);
-int nd_find_reducer(ND g);
-int nd_find_reducer_direct(ND g,NDV *ps,int len);
 int nd_nf(int mod,ND g,int full,ND *nf);
 int nd_nf_pbucket(int mod,ND g,int full,ND *nf);
-int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp);
-int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp);
-ND nd_reduce(ND p1,ND p2);
-ND nd_reduce_special(ND p1,ND p2);
+int nd_nf_direct(int mod,ND g,BaseSet base,int full,ND *rp);
+
+/* finalizers */
+NODE nd_reducebase(NODE x);
 NODE nd_reduceall(int m,NODE f);
 int nd_gbcheck(int m,NODE f);
 int nd_membercheck(int m,NODE f);
+
+/* allocators */
+void nd_free_private_storage();
+void _NM_alloc();
+void _ND_alloc();
 void nd_free(ND p);
-void ndv_free(NDV p);
+void nd_free_redlist();
+
+/* printing */
 void ndl_print(unsigned int *dl);
 void nd_print(ND p);
 void nd_print_q(ND p);
-void ndv_print(NDV p);
-void ndv_print_q(NDV p);
 void ndp_print(ND_pairs d);
-int nd_length(ND p);
-void nd_mul_c(int mod,ND p,int mul);
-void nd_free_redlist();
-void nd_append_red(unsigned int *d,int i);
-unsigned int *nd_compute_bound(ND p);
-unsigned int *dp_compute_bound(DP p);
+
+
+/* setup, reconstruct */
+void nd_init_ord(struct order_spec *spec);
 ND_pairs nd_reconstruct(int mod,int trace,ND_pairs ndp);
 void nd_reconstruct_direct(int mod,NDV *ps,int len);
+void nd_setup(int mod,int trace,NODE f);
 void nd_setup_parameters();
-void nd_realloc(ND p,int obpe);
+BlockMask nd_create_blockmask(struct order_spec *ord);
+int nd_get_exporigin(struct order_spec *ord);
+
+/* ND functions */
+int nd_check_candidate(NODE input,NODE cand);
+void nd_mul_c(int mod,ND p,int mul);
+void nd_mul_c_q(ND p,Q mul);
+ND nd_remove_head(ND p);
+int nd_length(ND p);
+void nd_append_red(unsigned int *d,int i);
+unsigned int *ndv_compute_bound(NDV p);
+unsigned int *dp_compute_bound(DP p);
 ND nd_copy(ND p);
-void ndl_dup(int obpe,unsigned int *d,unsigned int *r);
+ND nd_add(int mod,ND p1,ND p2);
+ND nd_add_q(ND p1,ND p2);
+INLINE int nd_length(ND p);
 
-#define NMV_ADV(m) (m = (NMV)(((char *)m)+nmv_adv))
-#define NEWNDV(d) ((d)=(NDV)MALLOC(sizeof(struct oNDV)))
-#define MKNDV(n,m,l,d) NEWNDV(d); NV(d)=(n); BDY(d)=(m); LEN(d) = l;
+/* NDV functions */
 void ndv_mul_c(int mod,NDV p,int mul);
+void ndv_mul_c_q(NDV p,Q mul);
+void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos);
+ND ndv_mul_nm(int mod,NDV p,NM m0);
+void ndv_dehomogenize(NDV p,struct order_spec *spec);
+void ndv_removecont(int mod,NDV p);
+void ndv_print(NDV p);
+void ndv_print_q(NDV p);
+void ndv_free(NDV p);
+
+/* converters */
 NDV ndtondv(int mod,ND p);
 ND ndvtond(int mod,NDV p);
-ND ndv_mul_nm(int mod,NDV p,NM m0);
-void ndv_realloc(NDV p,int obpe,int oadv);
 NDV dptondv(int,DP);
 DP ndvtodp(int,NDV);
 ND dptond(int,DP);
@@ -247,7 +321,7 @@ void _NM_alloc()
 	int i;
 
 	for ( i = 0; i < 1024; i++ ) {
-		p = (NM)GC_malloc(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int));
+		p = (NM)GC_malloc(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
 		p->next = _nm_free_list; _nm_free_list = p;
 	}
 }
@@ -270,7 +344,7 @@ void _NDP_alloc()
 
 	for ( i = 0; i < 1024; i++ ) {
 		p = (ND_pairs)GC_malloc(sizeof(struct oND_pairs)
-			+nd_wpd*sizeof(unsigned int));
+			+(nd_wpd-1)*sizeof(unsigned int));
 		p->next = _ndp_free_list; _ndp_free_list = p;
 	}
 }
@@ -288,7 +362,7 @@ INLINE int nd_length(ND p)
 	}
 }
 
-int ndl_reducible(unsigned int *d1,unsigned int *d2)
+INLINE int ndl_reducible(unsigned int *d1,unsigned int *d2)
 {
 	unsigned int u1,u2;
 	int i,j;
@@ -296,7 +370,7 @@ int ndl_reducible(unsigned int *d1,unsigned int *d2)
 	if ( TD(d1) < TD(d2) ) return 0;
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				if ( (u1&0xf0000000) < (u2&0xf0000000) ) return 0;
 				if ( (u1&0xf000000) < (u2&0xf000000) ) return 0;
@@ -310,7 +384,7 @@ int ndl_reducible(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 6:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				if ( (u1&0x3f000000) < (u2&0x3f000000) ) return 0;
 				if ( (u1&0xfc0000) < (u2&0xfc0000) ) return 0;
@@ -321,7 +395,7 @@ int ndl_reducible(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 8:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				if ( (u1&0xff000000) < (u2&0xff000000) ) return 0;
 				if ( (u1&0xff0000) < (u2&0xff0000) ) return 0;
@@ -331,7 +405,7 @@ int ndl_reducible(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 16:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				if ( (u1&0xffff0000) < (u2&0xffff0000) ) return 0;
 				if ( (u1&0xffff) < (u2&0xffff) ) return 0;
@@ -339,12 +413,12 @@ int ndl_reducible(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 32:
-			for ( i = 1; i <= nd_wpd; i++ )
+			for ( i = nd_exporigin; i < nd_wpd; i++ )
 				if ( d1[i] < d2[i] ) return 0;
 			return 1;
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				for ( j = 0; j < nd_epw; j++ )
 					if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0;
@@ -359,35 +433,44 @@ void ndl_dehomogenize(unsigned int *d)
 	unsigned int h;
 	int i,bits;
 
-	if ( nd_isrlex ) {
-		if ( nd_bpe == 32 ) {
-			h = d[1];
-			for ( i = 2; i <= nd_wpd; i++ )
-				d[i-1] = d[i];
-			d[i-1] = 0;
-			TD(d) -= h;
+	if ( nd_blockmask ) {
+		h = GET_EXP(d,nd_nvar-1);
+		XOR_EXP(d,nd_nvar-1,h);
+		TD(d) -= h;
+		d[nd_exporigin-1] -= h;
+	} else {
+		if ( nd_isrlex ) {
+			if ( nd_bpe == 32 ) {
+				h = d[nd_exporigin];
+				for ( i = nd_exporigin+1; i < nd_wpd; i++ )
+					d[i-1] = d[i];
+				d[i-1] = 0;
+				TD(d) -= h;
+			} else {
+				bits = nd_epw*nd_bpe;
+				mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1);
+				h = (d[nd_exporigin]>>((nd_epw-1)*nd_bpe))&nd_mask0;
+				for ( i = nd_exporigin; i < nd_wpd; i++ )
+					d[i] = ((d[i]<<nd_bpe)&mask)
+						|(i+1<nd_wpd?((d[i+1]>>((nd_epw-1)*nd_bpe))&nd_mask0):0);
+				TD(d) -= h;
+			}
 		} else {
-			bits = nd_epw*nd_bpe;
-			mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1);
-			h = (d[1]>>((nd_epw-1)*nd_bpe))&nd_mask0;
-			for ( i = 1; i <= nd_wpd; i++ )
-				d[i] = ((d[i]<<nd_bpe)&mask)
-					|(i+1<nd_wpd?((d[i+1]>>((nd_epw-1)*nd_bpe))&nd_mask0):0);
+			h = GET_EXP(d,nd_nvar-1);
+			XOR_EXP(d,nd_nvar-1,h);
 			TD(d) -= h;
 		}
-	} else 
-		TD(d) -= ((d[(nd_nvar-1)/nd_epw+1]>>
-			((nd_epw-((nd_nvar-1)%nd_epw)-1)*nd_bpe))&((1<<nd_bpe)-1));
+	}
 }
 
 void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned int *d)
 {
 	unsigned int t1,t2,u,u1,u2;
-	int i,j;
+	int i,j,l;
 
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = (u1&0xf0000000); t2 = (u2&0xf0000000); u = t1>t2?t1:t2;
 				t1 = (u1&0xf000000); t2 = (u2&0xf000000); u |= t1>t2?t1:t2;
@@ -401,7 +484,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 6:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = (u1&0x3f000000); t2 = (u2&0x3f000000); u = t1>t2?t1:t2;
 				t1 = (u1&0xfc0000); t2 = (u2&0xfc0000); u |= t1>t2?t1:t2;
@@ -412,7 +495,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 8:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = (u1&0xff000000); t2 = (u2&0xff000000); u = t1>t2?t1:t2;
 				t1 = (u1&0xff0000); t2 = (u2&0xff0000); u |= t1>t2?t1:t2;
@@ -422,7 +505,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 16:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = (u1&0xffff0000); t2 = (u2&0xffff0000); u = t1>t2?t1:t2;
 				t1 = (u1&0xffff); t2 = (u2&0xffff); u |= t1>t2?t1:t2;
@@ -430,13 +513,13 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 32:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i]; 
 				d[i] = u1>u2?u1:u2;
 			}
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i]; 
 				for ( j = 0, u = 0; j < nd_epw; j++ ) {
 					t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2;
@@ -445,15 +528,20 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 	}
-	TD(d) = ndl_td(d);
+	TD(d) = ndl_weight(d);
+	if ( nd_blockmask ) {
+		l = nd_blockmask->n;
+		for ( j = 0; j < l; j++ )
+			d[j+1] = ndl_weight_mask(d,j);
+	}
 }
 
-int ndl_td(unsigned int *d)
+int ndl_weight(unsigned int *d)
 {
 	unsigned int t,u;
 	int i,j;
 
-	for ( t = 0, i = 1; i <= nd_wpd; i++ ) {
+	for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) {
 		u = d[i];
 		for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
 			t += (u&nd_mask0); 
@@ -461,11 +549,28 @@ int ndl_td(unsigned int *d)
 	return t;
 }
 
-INLINE int ndl_lex_compare(unsigned int *d1,unsigned int *d2)
+int ndl_weight_mask(unsigned int *d,int index)
 {
+	unsigned int t,u;
+	unsigned int *mask;
+	int i,j;
+
+	mask = nd_blockmask->mask[index];
+	for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) {
+		u = d[i]&mask[i];
+		for ( j = 0; j < nd_epw; j++, u>>=nd_bpe )
+			t += (u&nd_mask0); 
+	}
+	return t;
+}
+
+int ndl_lex_compare(unsigned int *d1,unsigned int *d2)
+{
 	int i;
 
-	for ( i = 0; i < nd_wpd; i++, d1++, d2++ )
+	d1 += nd_exporigin;
+	d2 += nd_exporigin;
+	for ( i = nd_exporigin; i < nd_wpd; i++, d1++, d2++ )
 		if ( *d1 > *d2 )
 			return nd_isrlex ? -1 : 1;
 		else if ( *d1 < *d2 )
@@ -473,12 +578,39 @@ INLINE int ndl_lex_compare(unsigned int *d1,unsigned i
 	return 0;
 }
 
+int ndl_block_compare(unsigned int *d1,unsigned int *d2)
+{
+	int i,l,j,ord_o,ord_l;
+	struct order_pair *op;
+	unsigned int t1,t2,m;
+	unsigned int *mask;
+
+	l = nd_blockmask->n;
+	op = nd_blockmask->order_pair; 
+	for ( j = 0; j < l; j++ ) {
+		mask = nd_blockmask->mask[j];
+		ord_o = op[j].order;
+		if ( ord_o < 2 )
+			if ( (t1=d1[j+1]) > (t2=d2[j+1]) ) return 1;
+			else if ( t1 < t2 ) return -1;
+		for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+			m = mask[i];
+			t1 = d1[i]&m;
+			t2 = d2[i]&m;
+			if ( t1 > t2 )
+				return !ord_o ? -1 : 1;
+			else if ( t1 < t2 )
+				return !ord_o ? 1 : -1;
+		}
+	}
+	return 0;
+}
+
 INLINE int ndl_equal(unsigned int *d1,unsigned int *d2)
 {
 	int i;
 
-	if ( *d1++ != *d2++ ) return 0;
-	for ( i = 1; i <= nd_wpd; i++ )
+	for ( i = 0; i < nd_wpd; i++ )
 		if ( *d1++ != *d2++ )
 			return 0;
 	return 1;
@@ -489,49 +621,51 @@ INLINE void ndl_copy(unsigned int *d1,unsigned int *d2
 	int i;
 
 	switch ( nd_wpd ) {
-		case 1:
+		case 2:
 			TD(d2) = TD(d1);
 			d2[1] = d1[1];
 			break;
-		case 2:
+		case 3:
 			TD(d2) = TD(d1);
 			d2[1] = d1[1];
 			d2[2] = d1[2];
 			break;
 		default:
-			for ( i = 0; i <= nd_wpd; i++ )
+			for ( i = 0; i < nd_wpd; i++ )
 				d2[i] = d1[i];
 			break;
 	}
 }
 
-/* XXX : TD is not added */
-
 INLINE void ndl_add(unsigned int *d1,unsigned int *d2,unsigned int *d)
 {
 	int i;
 
+#if 1
 	switch ( nd_wpd ) {
-		case 1:
+		case 2:
+			TD(d) = TD(d1)+TD(d2);
 			d[1] = d1[1]+d2[1];
 			break;
-		case 2:
+		case 3:
+			TD(d) = TD(d1)+TD(d2);
 			d[1] = d1[1]+d2[1];
 			d[2] = d1[2]+d2[2];
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ )
-				d[i] = d1[i]+d2[i];
+			for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i];
 			break;
 	}
+#else
+	for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i];
+#endif
 }
 
 INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d)
 {
 	int i;
 
-	for ( i = 0; i <= nd_wpd; i++ )
-		d[i] = d1[i]-d2[i];
+	for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]-d2[i];
 }
 
 int ndl_disjoint(unsigned int *d1,unsigned int *d2)
@@ -541,7 +675,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = u1&0xf0000000; t2 = u2&0xf0000000; if ( t1&&t2 ) return 0;
 				t1 = u1&0xf000000; t2 = u2&0xf000000; if ( t1&&t2 ) return 0;
@@ -555,7 +689,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 6:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = u1&0x3f000000; t2 = u2&0x3f000000; if ( t1&&t2 ) return 0;
 				t1 = u1&0xfc0000; t2 = u2&0xfc0000; if ( t1&&t2 ) return 0;
@@ -566,7 +700,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 8:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = u1&0xff000000; t2 = u2&0xff000000; if ( t1&&t2 ) return 0;
 				t1 = u1&0xff0000; t2 = u2&0xff0000; if ( t1&&t2 ) return 0;
@@ -576,7 +710,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 16:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				t1 = u1&0xffff0000; t2 = u2&0xffff0000; if ( t1&&t2 ) return 0;
 				t1 = u1&0xffff; t2 = u2&0xffff; if ( t1&&t2 ) return 0;
@@ -584,12 +718,12 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 32:
-			for ( i = 1; i <= nd_wpd; i++ )
+			for ( i = nd_exporigin; i < nd_wpd; i++ )
 				if ( d1[i] && d2[i] ) return 0;
 			return 1;
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				for ( j = 0; j < nd_epw; j++ ) {
 					if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0;
@@ -611,7 +745,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 	ind = 0;
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u2 = d2[i];
 				if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1;
 				if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1;
@@ -625,7 +759,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 6:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u2 = d2[i];
 				if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1;
 				if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1;
@@ -636,7 +770,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 8:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u2 = d2[i];
 				if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1;
 				if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1;
@@ -646,7 +780,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 16:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u2 = d2[i];
 				if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1;
 				if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1;
@@ -654,12 +788,12 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 32:
-			for ( i = 1; i <= nd_wpd; i++ )
+			for ( i = nd_exporigin; i < nd_wpd; i++ )
 				if ( d1[i]+d2[i]<d1[i] ) return 1;
 			return 0;
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ ) {
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
 				u2 = d2[i];
 				k = (nd_epw-1)*nd_bpe;
 				for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
@@ -672,65 +806,65 @@ int ndl_check_bound2(int index,unsigned int *d2)
 
 int ndl_check_bound2_direct(unsigned int *d1,unsigned int *d2)
 {
-	unsigned int u1,u2;
-	int i,j,k;
+	unsigned int u2;
+	int i,j,ind,k;
 
+	ind = 0;
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 1; i <= nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>28)&0xf)+((u2>>28)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>24)&0xf)+((u2>>24)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>20)&0xf)+((u2>>20)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>16)&0xf)+((u2>>16)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>12)&0xf)+((u2>>12)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>8)&0xf)+((u2>>8)&0xf) >= 0x10 ) return 1;
-				if ( ((u1>>4)&0xf)+((u2>>4)&0xf) >= 0x10 ) return 1;
-				if ( (u1&0xf)+(u2&0xf) >= 0x10 ) return 1;
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+				u2 = d2[i];
+				if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>20)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>16)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>12)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>8)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+((u2>>4)&0xf) >= 0x10 ) return 1;
+				if ( d1[ind++]+(u2&0xf) >= 0x10 ) return 1;
 			}
 			return 0;
 			break;
 		case 6:
-			for ( i = 1; i <= nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>24)&0x3f)+((u2>>24)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>18)&0x3f)+((u2>>18)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>12)&0x3f)+((u2>>12)&0x3f) >= 0x40 ) return 1;
-				if ( ((u1>>6)&0x3f)+((u2>>6)&0x3f) >= 0x40 ) return 1;
-				if ( (u1&0x3f)+(u2&0x3f) >= 0x40 ) return 1;
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+				u2 = d2[i];
+				if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1;
+				if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1;
+				if ( d1[ind++]+((u2>>12)&0x3f) >= 0x40 ) return 1;
+				if ( d1[ind++]+((u2>>6)&0x3f) >= 0x40 ) return 1;
+				if ( d1[ind++]+(u2&0x3f) >= 0x40 ) return 1;
 			}
 			return 0;
 			break;
 		case 8:
-			for ( i = 1; i <= nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-				if ( ((u1>>24)&0xff)+((u2>>24)&0xff) >= 0x100 ) return 1;
-				if ( ((u1>>16)&0xff)+((u2>>16)&0xff) >= 0x100 ) return 1;
-				if ( ((u1>>8)&0xff)+((u2>>8)&0xff) >= 0x100 ) return 1;
-				if ( (u1&0xff)+(u2&0xff) >= 0x100 ) return 1;
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+				u2 = d2[i];
+				if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1;
+				if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1;
+				if ( d1[ind++]+((u2>>8)&0xff) >= 0x100 ) return 1;
+				if ( d1[ind++]+(u2&0xff) >= 0x100 ) return 1;
 			}
 			return 0;
 			break;
 		case 16:
-			for ( i = 1; i <= nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
-					if ( ((u1>>16)&0xffff)+((u2>>16)&0xffff) > 0x10000 ) return 1;
-					if ( (u2&0xffff)+(u2&0xffff) > 0x10000 ) return 1;
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+				u2 = d2[i];
+				if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1;
+				if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1;
 			}
 			return 0;
 			break;
 		case 32:
-			for ( i = 1; i <= nd_wpd; i++ )
+			for ( i = nd_exporigin; i < nd_wpd; i++ )
 				if ( d1[i]+d2[i]<d1[i] ) return 1;
 			return 0;
 			break;
 		default:
-			for ( i = 1; i <= nd_wpd; i++ ) {
-				u1 = d1[i]; u2 = d2[i];
+			for ( i = nd_exporigin; i < nd_wpd; i++ ) {
+				u2 = d2[i];
 				k = (nd_epw-1)*nd_bpe;
 				for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
-					if ( ((u1>>k)&nd_mask0)+((u2>>k)&nd_mask0) > nd_mask0 )
-						return 1;
+					if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1;
 			}
 			return 0;
 			break;
@@ -743,7 +877,7 @@ INLINE int ndl_hash_value(unsigned int *d)
 	int r;
 
 	r = 0;
-	for ( i = 0; i <= nd_wpd; i++ )	
+	for ( i = 0; i < nd_wpd; i++ )	
 		r = ((r<<16)+d[i])%REDTAB_LEN;
 	return r;
 }
@@ -755,6 +889,7 @@ INLINE int nd_find_reducer(ND g)
 	int d,k,i;
 
 	dg = HDL(g);
+#if 1
 	d = ndl_hash_value(HDL(g));
 	for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
 		if ( ndl_equal(dg,DL(r)) ) {
@@ -763,6 +898,7 @@ INLINE int nd_find_reducer(ND g)
 			return r->index;
 		}
 	}
+#endif
 	if ( Reverse )
 		for ( i = nd_psn-1; i >= 0; i-- ) {
 			r = nd_psh[i];
@@ -793,18 +929,14 @@ INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len
 	if ( Reverse )
 		for ( i = len-1; i >= 0; i-- ) {
 			r = ps[i];
-			if ( ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),i);
+			if ( ndl_reducible(HDL(g),HDL(r)) )
 				return i;
-			}
 		}
 	else
 		for ( i = 0; i < len; i++ ) {
 			r = ps[i];
-			if ( ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),i);
+			if ( ndl_reducible(HDL(g),HDL(r)) )
 				return i;
-			}
 		}
 	return -1;
 }
@@ -926,7 +1058,7 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 
 	sugar0 = sugar = SG(g);
 	n = NV(g);
-	mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int));
+	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
 	for ( d = 0; g; ) {
 		index = nd_find_reducer(g);
 		if ( index >= 0 ) {
@@ -998,7 +1130,7 @@ int nd_nf_pbucket(int mod,ND g,int full,ND *rp)
 	bucket = create_pbucket();
 	add_pbucket(mod,bucket,g);
 	d = 0;
-	mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int));
+	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
 	while ( 1 ) {
 		hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
 		if ( hindex < 0 ) {
@@ -1070,13 +1202,15 @@ int nd_nf_pbucket(int mod,ND g,int full,ND *rp)
 	}
 }
 
-int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp)
+int nd_nf_direct(int mod,ND g,BaseSet base,int full,ND *rp)
 {
 	ND d;
 	NM m,mrd,tail;
 	NM mul;
-	int n,sugar,psugar,sugar0,stat,index;
+	NDV *ps;
+	int n,sugar,psugar,sugar0,stat,index,len;
 	int c,c1,c2;
+	unsigned int **bound;
 	RHist h;
 	NDV p,red;
 	Q cg,cred,gcd;
@@ -1094,15 +1228,18 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 	hmag = 0;
 #endif
 
+	ps = base->ps;
+	bound = base->bound;
+	len = base->len;
 	sugar0 = sugar = SG(g);
 	n = NV(g);
-	mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int));
+	mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int));
 	for ( d = 0; g; ) {
 		index = nd_find_reducer_direct(g,ps,len);
 		if ( index >= 0 ) {
 			p = ps[index];
 			ndl_sub(HDL(g),HDL(p),DL(mul));
-			if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) {
+			if ( ndl_check_bound2_direct(bound[index],DL(mul)) ) {
 				nd_free(g); nd_free(d);
 				return 0;
 			}
@@ -1142,124 +1279,36 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 	return 1;
 }
 
-int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp)
-{
-	int hindex,index;
-	NDV p;
-	ND u,d,red;
-	NODE l;
-	NM mul,m,mrd,tail;
-	int sugar,psugar,n,h_reducible;
-	PGeoBucket bucket;
-	int c,c1,c2;
-	Q cg,cred,gcd,zzz;
-	RHist h;
-	double hmag,gmag;
-
-	if ( !g ) {
-		*rp = 0;
-		return 1;
-	}
-	sugar = SG(g);
-	n = NV(g);
-#if 0
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-#else
-	/* XXX */
-	hmag = 0;
-#endif
-	bucket = create_pbucket();
-	add_pbucket(mod,bucket,g);
-	d = 0;
-	mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int));
-	while ( 1 ) {
-		hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket);
-		if ( hindex < 0 ) {
-			if ( d )
-				SG(d) = sugar;
-			*rp = d;
-			return 1;
-		}
-		g = bucket->body[hindex];
-		index = nd_find_reducer_direct(g,ps,len);
-		if ( index >= 0 ) {
-			p = ps[index];
-			ndl_sub(HDL(g),HDL(p),DL(mul));
-			if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) {
-				nd_free(d);
-				free_pbucket(bucket);
-				*rp = 0;
-				return 0;
-			}
- 			if ( mod ) {
-				c1 = invm(HCM(p),mod); c2 = mod-HCM(g);
-				DMAR(c1,c2,0,mod,c); CM(mul) = c;
-			} else {
-				igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred);
-				chsgnq(cg,&CQ(mul));
-				nd_mul_c_q(d,cred);
-				mulq_pbucket(bucket,cred);
-				g = bucket->body[hindex];
-				gmag = (double)p_mag((P)HCQ(g));
-			}
-			red = ndv_mul_nm(mod,p,mul);
-			bucket->body[hindex] = nd_remove_head(g);
-			red = nd_remove_head(red);
-			add_pbucket(mod,bucket,red);
-			sugar = MAX(sugar,SG(p)+TD(DL(mul)));
-			if ( !mod && hmag && (gmag > hmag) ) {
-				g = normalize_pbucket(mod,bucket);
-				if ( !g ) {
-					if ( d ) SG(d) = sugar;
-					*rp = d;
-					return 1;
-				}
-				nd_removecont2(d,g);
-				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
-				add_pbucket(mod,bucket,g);
-			}
-		} else if ( !full ) {
-			g = normalize_pbucket(mod,bucket);
-			if ( g ) SG(g) = sugar;
-			*rp = g;
-			return 1;
-		} else {
-			m = BDY(g); 
-			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
-			} else {
-				FREEND(g); g = 0;
-			}
-			bucket->body[hindex] = g;
-			NEXT(m) = 0;
-			if ( d ) {
-				NEXT(tail)=m; tail=m; LEN(d)++;
-			} else {
-				MKND(n,m,1,d); tail = BDY(d);
-			}
-		}
-	}
-}
-
 /* input : list of DP, cand : list of DP */
 
 int nd_check_candidate(NODE input,NODE cand)
 {
 	int n,i,stat;
 	ND nf,d;
-	NODE t;
+	NODE t,s;
 
-	nd_setup(0,cand);
+#if 0
+	for ( t = 0; cand; cand = NEXT(cand) ) {
+		MKNODE(s,BDY(cand),t); t = s;
+	}
+	cand = t;
+#endif
+
+	nd_setup(0,0,cand);
 	n = length(cand);
 
 	/* membercheck : list is a subset of Id(cand) ? */
 	for ( t = input; t; t = NEXT(t) ) {
+again:
 		d = dptond(0,(DP)BDY(t));
-		stat = nd_nf_direct(0,d,nd_psq,n,0,&nf);
-		if ( !stat ) nd_reconstruct_direct(0,nd_psq,n);
-		else if ( nf ) return 0;
+		stat = nd_nf(0,d,0,&nf);
+		if ( !stat ) {
+			nd_reconstruct(0,0,0);
+			goto again;
+		} else if ( nf ) return 0;
+		printf("."); fflush(stdout);
 	}
+	printf("\n");
 	/* gbcheck : cand is a GB of Id(cand) ? */
 	if ( !nd_gb(0,1) ) return 0;
 	/* XXX */
@@ -1451,7 +1500,11 @@ again:
 			d = nd_reconstruct(m,0,d);
 			goto again;
 		}
+#if USE_GEOBUCKET
 		stat = m?nd_nf_pbucket(m,h,!Top,&nf):nd_nf(m,h,!Top,&nf);
+#else
+		stat = nd_nf(m,h,!Top,&nf);
+#endif
 		if ( !stat ) {
 			NEXT(l) = d; d = l;
 			d = nd_reconstruct(m,0,d);
@@ -1459,7 +1512,7 @@ again:
 		} else if ( nf ) {
 			if ( checkonly ) return 0;
 			printf("+"); fflush(stdout);
-			nh = nd_newps(m,nf);
+			nh = m?nd_newps(m,nf,0):nd_newps(m,0,nf);
 			d = update_pairs(d,g,nh);
 			g = update_base(g,nh);
 			FREENDP(l);
@@ -1502,7 +1555,11 @@ again:
 			d = nd_reconstruct(m,1,d);
 			goto again;
 		}
+#if USE_GEOBUCKET
 		stat = nd_nf_pbucket(m,h,!Top,&nf);
+#else
+		stat = nd_nf(m,h,!Top,&nf);
+#endif
 		if ( !stat ) {
 			NEXT(l) = d; d = l;
 			d = nd_reconstruct(m,1,d);
@@ -1513,9 +1570,9 @@ again:
 			nd_nf(0,h,!Top,&nfq);
 			if ( nfq ) {
 				printf("+"); fflush(stdout);
-				nh = nd_newps_trace(m,nf,nfq);
+				nh = nd_newps(m,nf,nfq);
 				/* failure; m|HC(nfq) */
-				if ( nf < 0 ) return 0;
+				if ( nh < 0 ) return 0;
 				d = update_pairs(d,g,nh);
 				g = update_base(g,nh);
 			} else {
@@ -1547,33 +1604,51 @@ NODE nd_reduceall(int m,NODE f)
 	NDV *w,*ps;
 	ND nf,g;
 	NODE t,a0,a;
+	struct oBaseSet base;
+	unsigned int **bound;
 
 	for ( n = 0, t = f; t; t = NEXT(t), n++ );
 	ps = (NDV *)ALLOCA(n*sizeof(NDV));
-	for ( i = 0, t = f; i < n; i++, t = NEXT(t) )
+	bound = (unsigned int **)ALLOCA(n*sizeof(unsigned int *));
+	for ( i = 0, t = f; i < n; i++, t = NEXT(t) ) {
 		ps[i] = (NDV)BDY(t);
+		bound[i] = ndv_compute_bound(ps[i]);
+	}
 	qsort(ps,n,sizeof(NDV),(int (*)(const void *,const void *))ndv_compare);
-	w = (NDV *)ALLOCA((n-1)*sizeof(NDV));
-	for ( i = 0; i < n; i++ ) {
-		for ( j = 0; j < i; j++ ) w[j] = (NDV)ps[j];
-		for ( j = i+1; j < n; j++ ) w[j-1] = ps[j];
+	base.ps = (NDV *)ALLOCA((n-1)*sizeof(NDV));
+	base.bound = (unsigned int **)ALLOCA((n-1)*sizeof(unsigned int *));
+	base.len = n-1;
+	i = 0;
+	while ( i < n ) {
+		for ( j = 0; j < i; j++ ) {
+			base.ps[j] = ps[j]; base.bound[j] = bound[j];
+		}
+		for ( j = i+1; j < n; j++ ) {
+			base.ps[j-1] = ps[j]; base.bound[j-1] = bound[j];
+		}
 		g = ndvtond(m,ps[i]);
-		stat = nd_nf_direct(m,g,w,n-1,1,&nf);
+		stat = nd_nf_direct(m,g,&base,1,&nf);
 		if ( !stat )
 			nd_reconstruct_direct(m,ps,n);
 		else if ( !nf ) {
 			printf("."); fflush(stdout);
 			ndv_free(ps[i]);
-			for ( j = i+1; j < n; j++ ) ps[j-1] = ps[j];
+			for ( j = i+1; j < n; j++ ) {
+				ps[j-1] = ps[j]; bound[j-1] = bound[j];
+			}
 			n--;
+			base.len = n-1;
 		} else {
 			printf("."); fflush(stdout);
 			ndv_free(ps[i]);
 			nd_removecont(m,nf);
 			ps[i] = ndtondv(m,nf);
+			bound[i] = ndv_compute_bound(ps[i]);
 			nd_free(nf);
+			i++;
 		}
 	}
+	printf("\n");
 	for ( a0 = 0, i = 0; i < n; i++ ) {
 		NEXTNODE(a0,a);
 		BDY(a) = (pointer)ps[i];
@@ -1643,7 +1718,7 @@ ND_pairs crit_B( ND_pairs d, int s )
 	t = DL(nd_psh[s]);
 	prev = 0;
 	head = cur = d;
-	lcm = (unsigned int *)ALLOCA((nd_wpd+1)*sizeof(unsigned int));
+	lcm = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
 	while ( cur ) {
 		tl = cur->lcm;
 		if ( ndl_reducible(tl,t)
@@ -1751,7 +1826,7 @@ int crit_2( int dp1, int dp2 )
 	return ndl_disjoint(DL(nd_psh[dp1]),DL(nd_psh[dp2]));
 }
 
-static ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest )
+ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest )
 {
 	ND_pairs w,p,r,s;
 	unsigned int *d;
@@ -1763,11 +1838,9 @@ static ND_pairs equivalent_pairs( ND_pairs d1, ND_pair
 	for ( r = 0; s; s = p ) {
 		p = NEXT(s);
 		if ( ndl_equal(d,LCM(s)) ) {
-			NEXT(s) = w;
-			w = s;
+			NEXT(s) = w; w = s;
 		} else {
-			NEXT(s) = r;
-			r = s;
+			NEXT(s) = r; r = s;
 		}
 	}
 	*prest = r;
@@ -1809,9 +1882,7 @@ ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 	for ( ml = 0, l = m; p; p = NEXT(l = p) )
 		if ( (SG(p) < s) 
 			|| ((SG(p) == s) && (DL_COMPARE(LCM(p),LCM(m)) < 0)) ) {
-			ml = l;
-			m = p;
-			s = SG(m);
+			ml = l; m = p; s = SG(m);
 		}
 	if ( !ml ) *prest = NEXT(m);
 	else {
@@ -1822,7 +1893,7 @@ ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 	return m;
 }
 
-int nd_newps(int mod,ND a)
+int nd_newps(int mod,ND a,ND aq)
 {
 	int len;
 	RHist r;
@@ -1836,95 +1907,31 @@ int nd_newps(int mod,ND a)
 		nd_bound = (unsigned int **)
 			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
 	}
-	nd_removecont(mod,a);
-	nd_bound[nd_psn] = nd_compute_bound(a);
-	NEWRHist(r); SG(r) = SG(a); ndl_copy(HDL(a),DL(r)); 
-	nd_psh[nd_psn] = r;
-	b = ndtondv(mod,a);
-	len = LEN(b);
-	if ( mod )
-		nd_ps[nd_psn] = b;
-	else
-		nd_psq[nd_psn] = b;
-	nd_free(a);
-	return nd_psn++;
-}
-
-int nd_newps_trace(int mod,ND nf,ND nfq)
-{
-	int len;
-	RHist r;
-	NDV b;
-
-	if ( nd_psn == nd_pslen ) {
-		nd_pslen *= 2;
-		nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV));
-		nd_psq = (NDV *)REALLOC((char *)nd_psq,nd_pslen*sizeof(NDV));
-		nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist));
-		nd_bound = (unsigned int **)
-			REALLOC((char *)nd_bound,nd_pslen*sizeof(unsigned int *));
+	if ( a && aq ) {
+		/* trace lifting */
+		if ( !rem(NM(HCQ(aq)),mod) )
+			return -1;
 	}
-	if ( !rem(NM(HCQ(nfq)),mod) ) return -1;
-	nd_removecont(mod,nf);
-	nd_ps[nd_psn] = ndtondv(mod,nf);
-
-	nd_removecont(0,nfq);
-	nd_psq[nd_psn] = ndtondv(0,nfq);
-
-	nd_bound[nd_psn] = nd_compute_bound(nfq);
-	NEWRHist(r); SG(r) = SG(nf); ndl_copy(HDL(nf),DL(r)); 
-	nd_psh[nd_psn] = r;
-	nd_free(nf); nd_free(nfq);
-	return nd_psn++;
-}
-
-void nd_setup(int mod,NODE f)
-{
-	int i,j,td,len,max;
-	NODE s,s0,f0;
-	unsigned int *d;
-	RHist r;
-	NDV a;
-
-	nd_found = 0; nd_notfirst = 0; nd_create = 0;
-
-	nd_psn = length(f); nd_pslen = 2*nd_psn;
-	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
-	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
-	nd_bound = (unsigned int **)MALLOC(nd_pslen*sizeof(unsigned int *));
-	for ( max = 0, i = 0, s = f; i < nd_psn; i++, s = NEXT(s) ) {
-		nd_bound[i] = d = dp_compute_bound((DP)BDY(s));
-		for ( j = 0; j < nd_nvar; j++ )
-			max = MAX(d[j],max);
+	NEWRHist(r); nd_psh[nd_psn] = r;
+	if ( aq ) {
+		nd_removecont(0,aq);
+		nd_psq[nd_psn] = ndtondv(0,aq);
+		nd_bound[nd_psn] = ndv_compute_bound(nd_psq[nd_psn]);
+		SG(r) = SG(aq); ndl_copy(HDL(aq),DL(r));
 	}
-	if ( !nd_red )
-		nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist));
-	bzero(nd_red,REDTAB_LEN*sizeof(RHist));
-
-	if ( max < 2 ) nd_bpe = 2;
-	else if ( max < 4 ) nd_bpe = 4;
-	else if ( max < 64 ) nd_bpe = 6;
-	else if ( max < 256 ) nd_bpe = 8;
-	else if ( max < 65536 ) nd_bpe = 16;
-	else nd_bpe = 32;
-
-	nd_setup_parameters();
-	nd_free_private_storage();
-	len = 0;
-	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
-		NEWRHist(r);
-		a = dptondv(mod,(DP)BDY(f));
-		ndv_removecont(mod,a);
-		len = MAX(len,LEN(a));
-		SG(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-		if ( mod ) nd_ps[i] = a;
-		else nd_psq[i] = a;
-		nd_psh[i] = r;
+	if ( a ) {
+		nd_removecont(mod,a);
+		nd_ps[nd_psn] = ndtondv(mod,a);
+		if ( !aq ) {
+			nd_bound[nd_psn] = ndv_compute_bound(nd_ps[nd_psn]);
+			SG(r) = SG(a); ndl_copy(HDL(a),DL(r));
+		}
 	}
+	nd_free(a); nd_free(aq);
+	return nd_psn++;
 }
 
-void nd_setup_trace(int mod,NODE f)
+void nd_setup(int mod,int trace,NODE f)
 {
 	int i,j,td,len,max;
 	NODE s,s0,f0;
@@ -1957,13 +1964,19 @@ void nd_setup_trace(int mod,NODE f)
 
 	nd_setup_parameters();
 	nd_free_private_storage();
-	len = 0;
 	for ( i = 0; i < nd_psn; i++, f = NEXT(f) ) {
-		a = dptondv(mod,(DP)BDY(f)); ndv_removecont(mod,a); nd_ps[i] = a;
-		a = dptondv(0,(DP)BDY(f)); ndv_removecont(0,a); nd_psq[i] = a;
 		NEWRHist(r);
-		len = MAX(len,LEN(a));
+		a = dptondv(mod,(DP)BDY(f)); ndv_removecont(mod,a);
 		SG(r) = HTD(a); ndl_copy(HDL(a),DL(r));
+
+		if ( trace ) {
+			nd_ps[i] = a;
+			a = dptondv(0,(DP)BDY(f)); ndv_removecont(0,a);
+			nd_psq[i] = a;
+		} else {
+			if ( mod ) nd_ps[i] = a;
+			else nd_psq[i] = a;
+		}
 		nd_psh[i] = r;
 	}
 }
@@ -1985,10 +1998,11 @@ void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,
 		NEXTNODE(fd0,fd); BDY(fd) = (pointer)b;
 	}
 	if ( fd0 ) NEXT(fd) = 0;
-	nd_setup(m,fd0);
+	nd_setup(m,0,fd0);
 	x = nd_gb(m,0);
 	fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n",
 		nd_found,nd_notfirst,nd_create);
+	x = nd_reducebase(x);
 	x = nd_reduceall(m,x);
 	for ( r0 = 0, t = x; t; t = NEXT(t) ) {
 		NEXTNODE(r0,r); 
@@ -2041,18 +2055,19 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o
 		nd_init_ord(ord);
 	}
 	do {
-		nd_setup_trace(m,fd0);
+		nd_setup(m,1,fd0);
 		cand = nd_gb_trace(m);
 		if ( !cand ) continue;
 		if ( homo ) {
 			/* dehomogenization */
 			for ( t = cand; t; t = NEXT(t) )
-				ndv_dehomogenize((NDV)BDY(t));
+				ndv_dehomogenize((NDV)BDY(t),ord);
 			nd_nvar--;
-			nd_setup_parameters();
 			initd(ord);
-			cand = nd_reducebase(cand);
+			nd_init_ord(ord);
+			nd_setup_parameters();
 		}
+		cand = nd_reducebase(cand);
 		fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n",
 			nd_found,nd_notfirst,nd_create);
 		cand = nd_reduceall(0,cand);
@@ -2075,36 +2090,69 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o
 void dltondl(int n,DL dl,unsigned int *r)
 {
 	unsigned int *d;
-	int i;
+	int i,j,l,s,ord_l,ord_o;
+	struct order_pair *op;
 
 	d = dl->d;
-	bzero(r,(nd_wpd+1)*sizeof(unsigned int));
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			r[(n-1-i)/nd_epw+1] |= (d[i]<<((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe));
-	else
-		for ( i = 0; i < n; i++ )
-			r[i/nd_epw+1] |= d[i]<<((nd_epw-(i%nd_epw)-1)*nd_bpe);
-	TD(r) = ndl_td(r);
+	for ( i = 0; i < nd_wpd; i++ ) r[i] = 0;
+	if ( nd_blockmask ) {
+		l = nd_blockmask->n;
+		op = nd_blockmask->order_pair;
+		for ( j = 0, s = 0; j < l; j++ ) {
+			ord_o = op[j].order;
+			ord_l = op[j].length;
+			if ( !ord_o )
+				for ( i = 0; i < ord_l; i++ )
+					PUT_EXP(r,s+ord_l-i-1,d[s+i]);
+			else
+				for ( i = 0; i < ord_l; i++ )
+					PUT_EXP(r,s+i,d[s+i]);
+			s += ord_l;
+		}
+		TD(r) = ndl_weight(r);
+		for ( j = 0; j < l; j++ )
+			r[j+1] = ndl_weight_mask(r,j);
+	} else {
+		if ( nd_isrlex )
+			for ( i = 0; i < n; i++ ) PUT_EXP(r,n-1-i,d[i]);
+		else
+			for ( i = 0; i < n; i++ ) PUT_EXP(r,i,d[i]);
+		TD(r) = ndl_weight(r);
+	}
 }
 
 DL ndltodl(int n,unsigned int *ndl)
 {
 	DL dl;
 	int *d;
-	int i;
+	int i,j,l,s,ord_l,ord_o;
+	struct order_pair *op;
 
 	NEWDL(dl,n);
 	dl->td = TD(ndl);
 	d = dl->d;
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			d[i] = (ndl[(n-1-i)/nd_epw+1]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe))
-				&((1<<nd_bpe)-1);
-	else
-		for ( i = 0; i < n; i++ )
-			d[i] = (ndl[i/nd_epw+1]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
-				&((1<<nd_bpe)-1);
+	if ( nd_blockmask ) {
+		l = nd_blockmask->n;
+		op = nd_blockmask->order_pair;
+		for ( j = 0, s = 0; j < l; j++ ) {
+			ord_o = op[j].order;
+			ord_l = op[j].length;
+			if ( !ord_o )
+				for ( i = 0; i < ord_l; i++ )
+					d[s+i] = GET_EXP(ndl,s+ord_l-i-1);
+			else
+				for ( i = 0; i < ord_l; i++ )
+					d[s+i] = GET_EXP(ndl,s+i);
+			s += ord_l;
+		}
+	} else {
+		if ( nd_isrlex )
+			for ( i = 0; i < n; i++ )
+				d[i] = GET_EXP(ndl,n-1-i);
+		else
+			for ( i = 0; i < n; i++ )
+				d[i] = GET_EXP(ndl,i);
+	}
 	return dl;
 }
 
@@ -2157,20 +2205,30 @@ DP ndtodp(int mod,ND p)
 void ndl_print(unsigned int *dl)
 {
 	int n;
-	int i;
+	int i,j,l,ord_o,ord_l,s,s0;
+	struct order_pair *op;
 
 	n = nd_nvar;
 	printf("<<");
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ )
-			printf(i==n-1?"%d":"%d,",
-				(dl[(n-1-i)/nd_epw+1]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe))
-					&((1<<nd_bpe)-1));
-	else
-		for ( i = 0; i < n; i++ )
-			printf(i==n-1?"%d":"%d,",
-				(dl[i/nd_epw+1]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
-					&((1<<nd_bpe)-1));
+	if ( nd_blockmask ) {
+		l = nd_blockmask->n;
+		op = nd_blockmask->order_pair;
+		for ( j = 0, s = s0 = 0; j < l; j++ ) {
+			ord_o = op[j].order;
+			ord_l = op[j].length;
+			if ( !ord_o )
+				for ( i = 0, s0 += ord_l; i < ord_l; i++, s++ )
+					printf(s==n-1?"%d":"%d,",GET_EXP(dl,s0-i-1));
+			else
+				for ( i = 0; i < ord_l; i++, s++ )
+					printf(s==n-1?"%d":"%d,",GET_EXP(dl,s));
+		}
+	} else {
+		if ( nd_isrlex )
+			for ( i = 0; i < n; i++ ) printf(i==n-1?"%d":"%d,",GET_EXP(dl,n-1-i));
+		else
+			for ( i = 0; i < n; i++ ) printf(i==n-1?"%d":"%d,",GET_EXP(dl,i));
+	}
 	printf(">>");
 }
 
@@ -2283,25 +2341,27 @@ void ndv_removecont(int mod,NDV p)
 	}
 }
 
-void ndv_dehomogenize(NDV p)
+void ndv_dehomogenize(NDV p,struct order_spec *ord)
 {
-	int i,len,newnvar,newwpd,newadv;
+	int i,j,adj,len,newnvar,newwpd,newadv,newexporigin;
 	Q *w;
 	Q dvr,t;
 	NMV m,r;
-	unsigned int *d;
 #define NEWADV(m) (m = (NMV)(((char *)m)+newadv))
 
 	len = p->len;
 	newnvar = nd_nvar-1;
-	newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0);
+	newexporigin = nd_get_exporigin(ord);
+	newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0)+newexporigin;
 	for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
 		ndl_dehomogenize(DL(m));
 	if ( newwpd != nd_wpd ) {
-		d = (unsigned int *)ALLOCA((newwpd+1)*sizeof(unsigned int));
-		newadv = sizeof(struct oNMV)+newwpd*sizeof(unsigned int);
+		newadv = sizeof(struct oNMV)+(newwpd-1)*sizeof(unsigned int);
 		for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NEWADV(r), i++ ) {
-			CQ(r) = CQ(m); ndl_copy(DL(m),d); ndl_copy(d,DL(r));
+			CQ(r) = CQ(m);
+			for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j];
+			adj = nd_exporigin-newexporigin;
+			for ( ; j < newwpd; j++ ) DL(r)[j] = DL(m)[j+adj];
 		}
 	}
 	NV(p)--;
@@ -2409,7 +2469,8 @@ unsigned int *dp_compute_bound(DP p)
 	d1 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
 	d2 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int));
 	m = BDY(p);
-	bcopy(DL(m)->d,d1,nd_nvar*sizeof(unsigned int));
+	d = DL(m)->d;
+	for ( i = 0; i < nd_nvar; i++ ) d1[i] = d[i];
 	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
 		d = DL(m)->d;
 		for ( i = 0; i < nd_nvar; i++ )
@@ -2418,39 +2479,61 @@ unsigned int *dp_compute_bound(DP p)
 	}
 	l = (nd_nvar+31);
 	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
-	bzero(t,l*sizeof(unsigned int));
-	bcopy(d1,t,nd_nvar*sizeof(unsigned int));
+	for ( i = 0; i < nd_nvar; i++ ) t[i] = d1[i];
+	for ( ; i < l; i++ ) t[i] = 0;
 	return t;
 }
 
-unsigned int *nd_compute_bound(ND p)
+unsigned int *ndv_compute_bound(NDV p)
 {
 	unsigned int *d1,*d2,*t;
-	int i,l;
-	NM m;
+	int i,l,len;
+	NMV m;
 
 	if ( !p )
 		return 0;
 	d1 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
 	d2 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int));
-	bcopy(HDL(p),d1,nd_wpd*sizeof(unsigned int));
-	for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) {
+	len = LEN(p);
+	m = BDY(p); ndl_copy(DL(m),d1); NMV_ADV(m);
+	for ( i = 1; i < len; i++, NMV_ADV(m) ) {
 		ndl_lcm(DL(m),d1,d2);
 		t = d1; d1 = d2; d2 = t;
 	}
 	l = nd_nvar+31;
 	t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int));
-	bzero(t,l*sizeof(unsigned int));
-	for ( i = 0; i < nd_nvar; i++ )
-		t[i] = (d1[i/nd_epw+1]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))&nd_mask0;
+	for ( i = 0; i < nd_nvar; i++ ) t[i] = GET_EXP(d1,i);
+	for ( ; i < l; i++ ) t[i] = 0;
 	return t;
 }
 
+int nd_get_exporigin(struct order_spec *ord)
+{
+	switch ( nd_ord->id ) {
+		case 0:
+			return 1;
+		case 1:
+			/* block order */
+			/* d[0]:weight d[1]:w0,...,d[nd_exporigin-1]:w(n-1) */
+			return ord->ord.block.length+1;
+		case 2:
+			error("nd_setup_parameters : matrix order is not supported yet.");
+	}
+}
+
 void nd_setup_parameters() {
-	int i;
+	int i,n,elen;
 
 	nd_epw = (sizeof(unsigned int)*8)/nd_bpe;
-	nd_wpd = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0);
+	elen = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0);
+
+	nd_exporigin = nd_get_exporigin(nd_ord);
+	nd_wpd = nd_exporigin+elen;
+	nd_epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS));
+	for ( i = 0; i < nd_nvar; i++ ) {
+		nd_epos[i].i = nd_exporigin + i/nd_epw;
+		nd_epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe;
+	}
 	if ( nd_bpe < 32 ) {
 		nd_mask0 = (1<<nd_bpe)-1;
 	} else {
@@ -2462,22 +2545,24 @@ void nd_setup_parameters() {
 		nd_mask[nd_epw-i-1] = (nd_mask0<<(i*nd_bpe));
 		nd_mask1 |= (1<<(nd_bpe-1))<<(i*nd_bpe);
 	}
-	nm_adv = sizeof(struct oNM)+nd_wpd*sizeof(unsigned int);
-	nmv_adv = sizeof(struct oNMV)+nd_wpd*sizeof(unsigned int);
+	nm_adv = sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int);
+	nmv_adv = sizeof(struct oNMV)+(nd_wpd-1)*sizeof(unsigned int);
+	nd_blockmask = nd_create_blockmask(nd_ord);
 }
 
-/* mod < 0 => realloc nd_ps and pd_psq */
-
 ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
 {
-	int i,obpe,oadv;
+	int i,obpe,oadv,h;
 	NM prev_nm_free_list;
 	RHist mr0,mr;
 	RHist r;
+	RHist *old_red;
 	ND_pairs s0,s,t,prev_ndp_free_list;
+	EPOS oepos;
 
 	obpe = nd_bpe;
 	oadv = nmv_adv;
+	oepos = nd_epos;
 	if ( obpe < 4 ) nd_bpe = 4;
 	else if ( obpe < 6 ) nd_bpe = 6;
 	else if ( obpe < 8 ) nd_bpe = 8;
@@ -2491,30 +2576,38 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
 	_nm_free_list = 0;
 	_ndp_free_list = 0;
 	if ( mod != 0 )
-		for ( i = nd_psn-1; i >= 0; i-- ) ndv_realloc(nd_ps[i],obpe,oadv);
+		for ( i = nd_psn-1; i >= 0; i-- ) ndv_realloc(nd_ps[i],obpe,oadv,oepos);
 	if ( !mod || trace )
-		for ( i = nd_psn-1; i >= 0; i-- ) ndv_realloc(nd_psq[i],obpe,oadv);
+		for ( i = nd_psn-1; i >= 0; i-- ) ndv_realloc(nd_psq[i],obpe,oadv,oepos);
 	s0 = 0;
 	for ( t = d; t; t = NEXT(t) ) {
 		NEXTND_pairs(s0,s);
 		s->i1 = t->i1;
 		s->i2 = t->i2;
 		SG(s) = SG(t);
-		ndl_dup(obpe,LCM(t),LCM(s));
+		ndl_reconstruct(obpe,oepos,LCM(t),LCM(s));
 	}
+	
+	old_red = (RHist *)ALLOCA(REDTAB_LEN*sizeof(RHist));
 	for ( i = 0; i < REDTAB_LEN; i++ ) {
-		for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) {
-			NEXTRHist(mr0,mr);
+		old_red[i] = nd_red[i];
+		nd_red[i] = 0;
+	}
+	for ( i = 0; i < REDTAB_LEN; i++ )
+		for ( r = old_red[i]; r; r = NEXT(r) ) {
+			NEWRHist(mr);
 			mr->index = r->index;
 			SG(mr) = SG(r);
-			ndl_dup(obpe,DL(r),DL(mr));
+			ndl_reconstruct(obpe,oepos,DL(r),DL(mr));
+			h = ndl_hash_value(DL(mr));
+			NEXT(mr) = nd_red[h];
+			nd_red[h] = mr;
 		}
-		if ( mr0 ) NEXT(mr) = 0;
-		nd_red[i] = mr0;
-	}
+	for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0;
+	old_red = 0;
 	for ( i = 0; i < nd_psn; i++ ) {
 		NEWRHist(r); SG(r) = SG(nd_psh[i]);
-		ndl_dup(obpe,DL(nd_psh[i]),DL(r));
+		ndl_reconstruct(obpe,oepos,DL(nd_psh[i]),DL(r));
 		nd_psh[i] = r;
 	}
 	if ( s0 ) NEXT(s) = 0;
@@ -2526,14 +2619,18 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
 
 void nd_reconstruct_direct(int mod,NDV *ps,int len)
 {
-	int i,obpe,oadv;
+	int i,obpe,oadv,h;
+	unsigned int **bound;
 	NM prev_nm_free_list;
 	RHist mr0,mr;
 	RHist r;
+	RHist *old_red;
 	ND_pairs s0,s,t,prev_ndp_free_list;
+	EPOS oepos;
 
 	obpe = nd_bpe;
 	oadv = nmv_adv;
+	oepos = nd_epos;
 	if ( obpe < 4 ) nd_bpe = 4;
 	else if ( obpe < 6 ) nd_bpe = 6;
 	else if ( obpe < 8 ) nd_bpe = 8;
@@ -2545,73 +2642,67 @@ void nd_reconstruct_direct(int mod,NDV *ps,int len)
 	prev_nm_free_list = _nm_free_list;
 	prev_ndp_free_list = _ndp_free_list;
 	_nm_free_list = 0; _ndp_free_list = 0;
-	if ( mod != 0 )
-		for ( i = len-1; i >= 0; i-- ) ndv_realloc(ps[i],obpe,oadv);
-	for ( i = 0; i < REDTAB_LEN; i++ ) {
-		for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) {
-			NEXTRHist(mr0,mr);
-			mr->index = r->index;
-			SG(mr) = SG(r);
-			ndl_dup(obpe,DL(r),DL(mr));
-		}
-		if ( mr0 ) NEXT(mr) = 0;
-		nd_red[i] = mr0;
-	}
+	for ( i = len-1; i >= 0; i-- ) ndv_realloc(ps[i],obpe,oadv,oepos);
 	prev_nm_free_list = 0;
 	prev_ndp_free_list = 0;
 	GC_gcollect();
 }
 
-void ndl_dup(int obpe,unsigned int *d,unsigned int *r)
+void ndl_reconstruct(int obpe,EPOS oepos,unsigned int *d,unsigned int *r)
 {
-	int n,i,ei,oepw,cepw,cbpe;
+	int n,i,ei,oepw,omask0,j,s,ord_l,ord_o,l;
+	struct order_pair *op;
+#define GET_EXP_OLD(d,a) (((d)[oepos[a].i]>>oepos[a].s)&omask0)
+#define PUT_EXP_OLD(r,a,e) ((r)[oepos[a].i] |= ((e)<<oepos[a].s))
 
 	n = nd_nvar;
 	oepw = (sizeof(unsigned int)*8)/obpe;
-	cepw = nd_epw;
-	cbpe = nd_bpe;
+	omask0 = (1<<obpe)-1;
 	TD(r) = TD(d);
-	for ( i = 1; i <= nd_wpd; i++ ) r[i] = 0;
-	if ( nd_isrlex )
-		for ( i = 0; i < n; i++ ) {
-			ei = (d[(n-1-i)/oepw+1]>>((oepw-((n-1-i)%oepw)-1)*obpe))
-				&((1<<obpe)-1);
-			r[(n-1-i)/cepw+1] |= (ei<<((cepw-((n-1-i)%cepw)-1)*cbpe));
+	for ( i = nd_exporigin; i < nd_wpd; i++ ) r[i] = 0;
+	if ( nd_blockmask ) {
+		l = nd_blockmask->n;
+		op = nd_blockmask->order_pair;
+		for ( i = 1; i < nd_exporigin; i++ )
+			r[i] = d[i];
+		for ( j = 0, s = 0; j < l; j++ ) {
+			ord_o = op[j].order;
+			ord_l = op[j].length;
+			if ( !ord_o )
+				for ( i = 0; i < ord_l; i++ ) {
+					ei =  GET_EXP_OLD(d,s+ord_l-i-1);
+					PUT_EXP(r,s+ord_l-i-1,ei);
+				}
+			else
+				for ( i = 0; i < ord_l; i++ ) {
+					ei =  GET_EXP_OLD(d,s+i);
+					PUT_EXP(r,s+i,ei);
+				}
+			s += ord_l;
 		}
-	else
-		for ( i = 0; i < n; i++ ) {
-			ei = (d[i/oepw+1]>>((oepw-(i%oepw)-1)*obpe))
-				&((1<<obpe)-1);
-			r[i/cepw+1] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
-		}
-}
-
-void nd_realloc(ND p,int obpe)
-{
-	NM m,mr,mr0;
-
-	if ( p ) {
-		m = BDY(p);
-		for ( mr0 = 0; m; m = NEXT(m) ) {
-			NEXTNM(mr0,mr);
-			CM(mr) = CM(m);
-			ndl_dup(obpe,DL(m),DL(mr));
-		}
-		NEXT(mr) = 0; 
-		BDY(p) = mr0;
+	} else {
+		if ( nd_isrlex )
+			for ( i = 0; i < n; i++ ) {
+				ei = GET_EXP_OLD(d,n-1-i);
+				PUT_EXP(r,n-1-i,ei);
+			}
+		else
+			for ( i = 0; i < n; i++ ) {
+				ei = GET_EXP_OLD(d,i);
+				PUT_EXP(r,i,ei);
+			}
 	}
 }
 
 ND nd_copy(ND p)
 {
 	NM m,mr,mr0;
-	int c,n,s;
+	int c,n;
 	ND r;
 
 	if ( !p )
 		return 0;
 	else {
-		s = sizeof(struct oNM)+nd_wpd*sizeof(unsigned int);
 		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
 			CM(mr) = CM(m);
@@ -2704,7 +2795,6 @@ ND ndv_mul_nm(int mod,NDV p,NM m0)
 				c1 = CM(m);
 				DMAR(c1,c,0,mod,c2);
 				CM(mr) = c2;
-				TD(DL(mr)) = TD(DL(m))+td;
 				ndl_add(DL(m),d,DL(mr));
 			}
 		} else {
@@ -2712,7 +2802,6 @@ ND ndv_mul_nm(int mod,NDV p,NM m0)
 			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
 				NEXTNM(mr0,mr);
 				mulq(CQ(m),q,&CQ(mr));
-				TD(DL(mr)) = TD(DL(m))+td;
 				ndl_add(DL(m),d,DL(mr));
 			}
 		}
@@ -2723,7 +2812,7 @@ ND ndv_mul_nm(int mod,NDV p,NM m0)
 	}
 }
 
-void ndv_realloc(NDV p,int obpe,int oadv)
+void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos)
 {
 	NMV m,mr,mr0,t;
 	int len,i,k;
@@ -2740,7 +2829,7 @@ void ndv_realloc(NDV p,int obpe,int oadv)
 		for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
 			CQ(t) = CQ(m);
 			for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0;
-			ndl_dup(obpe,DL(m),DL(t));
+			ndl_reconstruct(obpe,oepos,DL(m),DL(t));
 			CQ(mr) = CQ(t);
 			ndl_copy(DL(t),DL(mr));
 		}
@@ -2796,15 +2885,17 @@ NDV dptondv(int mod,DP p)
 	DP q;
 	int l,i,n;
 
-	if ( !p ) return 0;
-	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ );
 	if ( mod ) {
 		_dp_mod(p,mod,0,&q); p = q;
+	}
+	if ( !p ) return 0;
+	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ );
+	if ( mod )
 		m0 = m = (NMV)MALLOC_ATOMIC(l*nmv_adv);
-	} else
+	else
 		m0 = m = (NMV)MALLOC(l*nmv_adv);
 	n = NV(p);
-	for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) {
+	for ( t = BDY(p); t; t = NEXT(t), NMV_ADV(m) ) {
 		if ( mod ) CM(m) = ITOS(C(t));
 		else CQ(m) = (Q)C(t);
 		dltondl(n,DL(t),DL(m));
@@ -2894,27 +2985,62 @@ NODE nd_reducebase(NODE x)
 	return x;
 }
 
+/* XXX incomplete */
+
 void nd_init_ord(struct order_spec *ord)
 {
-	if ( ord->id )
-		error("nd_gr : unsupported order");
-	nd_dcomp = 0;
-	switch ( ord->ord.simple ) {
+	switch ( ord->id ) {
 		case 0:
-			nd_dcomp = 1;
-			nd_isrlex = 1;
+			switch ( ord->ord.simple ) {
+				case 0:
+					nd_dcomp = 1;
+					nd_isrlex = 1;
+					break;
+				case 1:
+					nd_dcomp = 1;
+					nd_isrlex = 0;
+					break;
+				case 2:
+					nd_dcomp = 0;
+					nd_isrlex = 0;
+					ndl_compare_function = ndl_lex_compare;
+					break;
+				default:
+					error("nd_gr : unsupported order");
+			}
 			break;
 		case 1:
-			nd_dcomp = 1;
+			/* XXX */
+			nd_dcomp = -1;
 			nd_isrlex = 0;
+			ndl_compare_function = ndl_block_compare;
 			break;
-		case 9:
-			/* td1->td->rlex */
-			nd_dcomp = -dp_nelim;
-			nd_isrlex = 1;
+		case 2:
+			error("nd_init_ord : matrix order is not supported yet.");
 			break;
-		default:
-			error("nd_gr : unsupported order");
 	}
+	nd_ord = ord;
 }
 
+BlockMask nd_create_blockmask(struct order_spec *ord)
+{
+	int n,i,j,s,l;
+	unsigned int *t;
+	BlockMask bm;
+
+	if ( !ord->id )
+		return 0;
+	n = ord->ord.block.length;
+	bm = (BlockMask)MALLOC(sizeof(struct oBlockMask));
+	bm->n = n;
+	bm->order_pair = ord->ord.block.order_pair;
+	bm->mask = (unsigned int **)MALLOC(n*sizeof(unsigned int *));
+	for ( i = 0, s = 0; i < n; i++ ) {
+		bm->mask[i] = t
+			= (unsigned int *)MALLOC_ATOMIC(nd_wpd*sizeof(unsigned int));
+		for ( j = 0; j < nd_wpd; j++ ) t[j] = 0;
+		l = bm->order_pair[i].length;
+		for ( j = 0; j < l; j++, s++ ) PUT_EXP(t,s,nd_mask0);		
+	}
+	return bm;
+}