===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v
retrieving revision 1.34
retrieving revision 1.41
diff -u -p -r1.34 -r1.41
--- OpenXM_contrib2/asir2000/engine/nd.c	2003/08/20 06:06:07	1.34
+++ OpenXM_contrib2/asir2000/engine/nd.c	2003/08/21 07:39:25	1.41
@@ -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 1.40 2003/08/21 04:44:36 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;
@@ -69,9 +77,10 @@ int (*nd_compare_function)(unsigned int *a1,unsigned i
 
 double nd_scale=2;
 static unsigned int **nd_bound;
+struct order_spec *nd_ord;
 int nd_nvar;
 int nd_isrlex;
-int nd_epw,nd_bpe,nd_wpd;
+int nd_epw,nd_bpe,nd_wpd,nd_exporigin;
 unsigned int nd_mask[32];
 unsigned int nd_mask0,nd_mask1;
 
@@ -85,7 +94,6 @@ RHist *nd_psh;
 int nd_psn,nd_pslen;
 
 RHist *nd_red;
-int nd_red_len;
 
 int nd_found,nd_create,nd_notfirst;
 int nm_adv;
@@ -94,6 +102,7 @@ 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)))
@@ -106,15 +115,15 @@ extern int Top,Reverse,dp_nelim;
 #define LEN(a) ((a)->len)
 #define LCM(a) ((a)->lcm)
 
+/* 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)))
 #define DL_COMPARE(d1,d2)\
 (nd_dcomp?TD_DL_COMPARE(d1,d2):(*nd_compare_function)(d1,d2))
 
-#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 +134,37 @@ 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);
@@ -155,37 +172,40 @@ 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);
 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,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_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);
+INLINE int nd_find_reducer(ND g);
+INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len);
+
+/* normal forms */
 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);
@@ -193,40 +213,63 @@ 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);
+
+/* 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_realloc(ND p,int obpe);
+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);
+
+
+/* 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();
+
+/* ND functions */
+int nd_check_candidate(NODE input,NODE cand);
 void nd_mul_c(int mod,ND p,int mul);
-void nd_free_redlist();
+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 *nd_compute_bound(ND p);
 unsigned int *dp_compute_bound(DP p);
-ND_pairs nd_reconstruct(int mod,int trace,ND_pairs ndp);
-void nd_reconstruct_direct(int mod,NDV *ps,int len);
-void nd_setup_parameters();
-void nd_realloc(ND p,int obpe);
 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);
+ND ndv_mul_nm(int mod,NDV p,NM m0);
+void ndv_dehomogenize(NDV p);
+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 +290,7 @@ 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 +313,7 @@ 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 +331,7 @@ 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 +339,7 @@ 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 +353,7 @@ 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 +364,7 @@ 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 +374,7 @@ 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 +382,12 @@ 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;
@@ -361,22 +404,22 @@ void ndl_dehomogenize(unsigned int *d)
 
 	if ( nd_isrlex ) {
 		if ( nd_bpe == 32 ) {
-			h = d[1];
-			for ( i = 2; i <= nd_wpd; i++ )
+			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[1]>>((nd_epw-1)*nd_bpe))&nd_mask0;
-			for ( i = 1; i <= nd_wpd; i++ )
+			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 
-		TD(d) -= ((d[(nd_nvar-1)/nd_epw+1]>>
+		TD(d) -= ((d[(nd_nvar-1)/nd_epw+nd_exporigin]>>
 			((nd_epw-((nd_nvar-1)%nd_epw)-1)*nd_bpe))&((1<<nd_bpe)-1));
 }
 
@@ -387,7 +430,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 
 	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 +444,7 @@ 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 +455,7 @@ 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 +465,7 @@ 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 +473,13 @@ 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 +488,15 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 	}
-	TD(d) = ndl_td(d);
+	TD(d) = ndl_weight(d);
 }
 
-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); 
@@ -465,7 +508,9 @@ INLINE int ndl_lex_compare(unsigned int *d1,unsigned i
 {
 	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 )
@@ -477,8 +522,7 @@ 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;
@@ -489,38 +533,38 @@ 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;
 
 	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++ )
+			for ( i = 0; i < nd_wpd; i++ )
 				d[i] = d1[i]+d2[i];
 			break;
 	}
@@ -530,7 +574,7 @@ INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,
 {
 	int i;
 
-	for ( i = 0; i <= nd_wpd; i++ )
+	for ( i = 0; i < nd_wpd; i++ )
 		d[i] = d1[i]-d2[i];
 }
 
@@ -541,7 +585,7 @@ 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 +599,7 @@ 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 +610,7 @@ 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 +620,7 @@ 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 +628,12 @@ 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 +655,7 @@ 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 +669,7 @@ 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 +680,7 @@ 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 +690,7 @@ 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 +698,12 @@ 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 )
@@ -677,7 +721,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 
 	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>>28)&0xf)+((u2>>28)&0xf) >= 0x10 ) return 1;
 				if ( ((u1>>24)&0xf)+((u2>>24)&0xf) >= 0x10 ) return 1;
@@ -691,7 +735,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			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>>24)&0x3f)+((u2>>24)&0x3f) >= 0x40 ) return 1;
 				if ( ((u1>>18)&0x3f)+((u2>>18)&0x3f) >= 0x40 ) return 1;
@@ -702,7 +746,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			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>>24)&0xff)+((u2>>24)&0xff) >= 0x100 ) return 1;
 				if ( ((u1>>16)&0xff)+((u2>>16)&0xff) >= 0x100 ) return 1;
@@ -712,7 +756,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			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>>16)&0xffff)+((u2>>16)&0xffff) > 0x10000 ) return 1;
 					if ( (u2&0xffff)+(u2&0xffff) > 0x10000 ) return 1;
@@ -720,12 +764,12 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			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++ ) {
 				u1 = d1[i]; u2 = d2[i];
 				k = (nd_epw-1)*nd_bpe;
 				for ( j = 0; j < nd_epw; j++, k -= nd_bpe )
@@ -743,7 +787,7 @@ 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 +799,7 @@ 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 +808,7 @@ 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];
@@ -926,7 +972,7 @@ 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 +1044,7 @@ 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 ) {
@@ -1096,7 +1142,7 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 
 	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 ) {
@@ -1172,7 +1218,7 @@ int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,
 	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 ) {
@@ -1250,7 +1296,7 @@ int nd_check_candidate(NODE input,NODE cand)
 	ND nf,d;
 	NODE t;
 
-	nd_setup(0,cand);
+	nd_setup(0,0,cand);
 	n = length(cand);
 
 	/* membercheck : list is a subset of Id(cand) ? */
@@ -1451,7 +1497,11 @@ 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 +1509,7 @@ 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 +1552,11 @@ 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 +1567,9 @@ 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 {
@@ -1643,7 +1697,7 @@ 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 +1805,7 @@ 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 +1817,9 @@ 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 +1861,7 @@ 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 +1872,7 @@ 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 +1886,30 @@ 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] = nd_compute_bound(aq);
+		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] = nd_compute_bound(a);
+			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 +1942,19 @@ 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;
 	}
 }
@@ -1985,7 +1976,7 @@ 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);
@@ -2041,7 +2032,7 @@ 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 ) {
@@ -2078,14 +2069,14 @@ void dltondl(int n,DL dl,unsigned int *r)
 	int i;
 
 	d = dl->d;
-	bzero(r,(nd_wpd+1)*sizeof(unsigned int));
+	for ( i = 0; i < nd_wpd; i++ ) r[i] = 0;
 	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));
+			r[(n-1-i)/nd_epw+nd_exporigin] |= (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);
+			r[i/nd_epw+nd_exporigin] |= d[i]<<((nd_epw-(i%nd_epw)-1)*nd_bpe);
+	TD(r) = ndl_weight(r);
 }
 
 DL ndltodl(int n,unsigned int *ndl)
@@ -2099,11 +2090,11 @@ DL ndltodl(int n,unsigned int *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))
+			d[i] = (ndl[(n-1-i)/nd_epw+nd_exporigin]>>((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))
+			d[i] = (ndl[i/nd_epw+nd_exporigin]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
 				&((1<<nd_bpe)-1);
 	return dl;
 }
@@ -2164,12 +2155,12 @@ void ndl_print(unsigned int *dl)
 	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))
+				(dl[(n-1-i)/nd_epw+nd_exporigin]>>((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))
+				(dl[i/nd_epw+nd_exporigin]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))
 					&((1<<nd_bpe)-1));
 	printf(">>");
 }
@@ -2294,12 +2285,12 @@ void ndv_dehomogenize(NDV p)
 
 	len = p->len;
 	newnvar = nd_nvar-1;
-	newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0);
+	newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0)+nd_exporigin;
 	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);
+		d = (unsigned int *)ALLOCA(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));
 		}
@@ -2409,7 +2400,8 @@ 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++ )
@@ -2418,8 +2410,8 @@ 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;
 }
 
@@ -2433,16 +2425,17 @@ unsigned int *nd_compute_bound(ND 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));
+	ndl_copy(HDL(p),d1);
 	for ( m = NEXT(BDY(p)); m; m = NEXT(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 < l; i++ ) t[i] = 0;
 	for ( i = 0; i < nd_nvar; i++ )
-		t[i] = (d1[i/nd_epw+1]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))&nd_mask0;
+		t[i] = (d1[i/nd_epw+nd_exporigin]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))&nd_mask0;
+	for ( ; i < l; i++ ) t[i] = 0;
 	return t;
 }
 
@@ -2451,6 +2444,19 @@ void nd_setup_parameters() {
 
 	nd_epw = (sizeof(unsigned int)*8)/nd_bpe;
 	nd_wpd = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0);
+	switch ( nd_ord->id ) {
+		case 0:
+			nd_exporigin = 1;
+			break;
+		case 1:
+			/* block order */
+			nd_exporigin = nd_ord->ord.block.length;
+			break;
+		case 2:
+			error("nd_setup_parameters : matrix order is not supported yet.");
+			break;
+	}
+	nd_wpd += nd_exporigin;
 	if ( nd_bpe < 32 ) {
 		nd_mask0 = (1<<nd_bpe)-1;
 	} else {
@@ -2462,18 +2468,17 @@ 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);
 }
 
-/* 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;
 
 	obpe = nd_bpe;
@@ -2500,21 +2505,29 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d)
 		s->i1 = t->i1;
 		s->i2 = t->i2;
 		SG(s) = SG(t);
-		ndl_dup(obpe,LCM(t),LCM(s));
+		ndl_reconstruct(obpe,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,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,DL(nd_psh[i]),DL(r));
 		nd_psh[i] = r;
 	}
 	if ( s0 ) NEXT(s) = 0;
@@ -2526,10 +2539,11 @@ 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;
 	NM prev_nm_free_list;
 	RHist mr0,mr;
 	RHist r;
+	RHist *old_red;
 	ND_pairs s0,s,t,prev_ndp_free_list;
 
 	obpe = nd_bpe;
@@ -2545,24 +2559,30 @@ 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 = len-1; i >= 0; i-- ) ndv_realloc(ps[i],obpe,oadv);
+	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,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;
 	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,unsigned int *d,unsigned int *r)
 {
 	int n,i,ei,oepw,cepw,cbpe;
 
@@ -2571,18 +2591,18 @@ void ndl_dup(int obpe,unsigned int *d,unsigned int *r)
 	cepw = nd_epw;
 	cbpe = nd_bpe;
 	TD(r) = TD(d);
-	for ( i = 1; i <= nd_wpd; i++ ) r[i] = 0;
+	for ( i = nd_exporigin; 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))
+			ei = (d[(n-1-i)/oepw+nd_exporigin]>>((oepw-((n-1-i)%oepw)-1)*obpe))
 				&((1<<obpe)-1);
-			r[(n-1-i)/cepw+1] |= (ei<<((cepw-((n-1-i)%cepw)-1)*cbpe));
+			r[(n-1-i)/cepw+nd_exporigin] |= (ei<<((cepw-((n-1-i)%cepw)-1)*cbpe));
 		}
 	else
 		for ( i = 0; i < n; i++ ) {
-			ei = (d[i/oepw+1]>>((oepw-(i%oepw)-1)*obpe))
+			ei = (d[i/oepw+nd_exporigin]>>((oepw-(i%oepw)-1)*obpe))
 				&((1<<obpe)-1);
-			r[i/cepw+1] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
+			r[i/cepw+nd_exporigin] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
 		}
 }
 
@@ -2595,7 +2615,7 @@ void nd_realloc(ND p,int obpe)
 		for ( mr0 = 0; m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
 			CM(mr) = CM(m);
-			ndl_dup(obpe,DL(m),DL(mr));
+			ndl_reconstruct(obpe,DL(m),DL(mr));
 		}
 		NEXT(mr) = 0; 
 		BDY(p) = mr0;
@@ -2605,13 +2625,12 @@ void nd_realloc(ND p,int obpe)
 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 +2723,6 @@ 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 +2730,6 @@ 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));
 			}
 		}
@@ -2740,7 +2757,7 @@ 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,DL(m),DL(t));
 			CQ(mr) = CQ(t);
 			ndl_copy(DL(t),DL(mr));
 		}
@@ -2916,5 +2933,6 @@ void nd_init_ord(struct order_spec *ord)
 		default:
 			error("nd_gr : unsupported order");
 	}
+	nd_ord = ord;
 }