===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v
retrieving revision 1.27
retrieving revision 1.41
diff -u -p -r1.27 -r1.41
--- OpenXM_contrib2/asir2000/engine/nd.c	2003/08/10 01:31:24	1.27
+++ 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 1.26 2003/08/07 09:47:08 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"
@@ -11,64 +11,76 @@
 #define INLINE
 #endif
 
+#define USE_GEOBUCKET 1
+
 #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;
+	int len;
 	int sugar;
 } *ND;
 
+/* distributed polynomial; array rep. */
 typedef struct oNDV {
 	struct oNMV *body;
 	int nv;
-	int sugar;
 	int len;
+	int sugar;
 } *NDV;
 
+/* monomial; linked list rep. */
 typedef struct oNM {
 	struct oNM *next;
 	union {
 		int m;
 		Q z;
 	} c;
-	int td;
 	unsigned int dl[1];
 } *NM;
 
+/* monomial; array rep. */
 typedef struct oNMV {
 	union {
 		int m;
 		Q z;
 	} c;
-	int td;
 	unsigned int dl[1];
 } *NMV;
 
+/* history of reducer */
 typedef struct oRHist {
 	struct oRHist *next;
 	int index;
-	int td,sugar;
+	int sugar;
 	unsigned int dl[1];
 } *RHist;
 
+/* S-pair list */
 typedef struct oND_pairs {
 	struct oND_pairs *next;
 	int i1,i2;
-	int td,sugar;
+	int sugar;
 	unsigned int lcm[1];
 } *ND_pairs;
 
+int (*nd_compare_function)(unsigned int *a1,unsigned int *a2);
+
 double nd_scale=2;
 static unsigned int **nd_bound;
+struct order_spec *nd_ord;
 int nd_nvar;
-int is_rlex;
-int nd_epw,nd_bpe,nd_wpd;
+int nd_isrlex;
+int nd_epw,nd_bpe,nd_wpd,nd_exporigin;
 unsigned int nd_mask[32];
 unsigned int nd_mask0,nd_mask1;
 
@@ -78,135 +90,186 @@ ND_pairs _ndp_free_list;
 
 static NDV *nd_ps;
 static NDV *nd_psq;
-int *nd_psl;
 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;
 int nmv_adv;
+int nd_dcomp;
 
-extern int Top,Reverse;
+extern int Top,Reverse,dp_nelim;
 
-#define HTD(d) ((d)->body->td)
+/* fundamental macros */
+#define TD(d) (d[0])
 #define HDL(d) ((d)->body->dl)
+#define HTD(d) (TD(HDL(d)))
 #define HCM(d) ((d)->body->c.m)
 #define HCQ(d) ((d)->body->c.z)
 #define CM(a) ((a)->c.m)
 #define CQ(a) ((a)->c.z)
 #define DL(a) ((a)->dl)
-#define TD(a) ((a)->td)
 #define SG(a) ((a)->sugar)
 #define LEN(a) ((a)->len)
+#define LCM(a) ((a)->lcm)
 
-#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv))
+/* macros for term comparison */
+#define TD_DL_COMPARE(d1,d2)\
+(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))
+
+/* allocators */
 #define NEWRHist(r) \
 ((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)   
-#define NEWNM(m) if(!_nm_free_list)_NM_alloc(); (m)=_nm_free_list; _nm_free_list = NEXT(_nm_free_list)   
-#define MKND(n,m,d) if(!_nd_free_list)_ND_alloc(); (d)=_nd_free_list; _nd_free_list = (ND)BDY(_nd_free_list); (d)->nv=(n); BDY(d)=(m)
+#define NEWND_pairs(m) \
+if(!_ndp_free_list)_NDP_alloc();\
+(m)=_ndp_free_list; _ndp_free_list = NEXT(_ndp_free_list)   
+#define NEWNM(m)\
+if(!_nm_free_list)_NM_alloc();\
+(m)=_nm_free_list; _nm_free_list = NEXT(_nm_free_list)   
+#define MKND(n,m,len,d)\
+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))
 
-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);
-void add_pbucket(int mod,PGeoBucket g,ND d,int l);
+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);
-int ndl_dehomogenize(unsigned int *p);
-ND nd_add(int mod,ND p1,ND p2);
-ND nd_add_q(ND p1,ND p2);
-ND nd_mul_nm(int mod,ND p,NM m0);
-ND nd_mul_ind_nm(int mod,int index,NM m0);
+
+/* ndl functions */
+int ndl_weight(unsigned int *d);
+void ndl_dehomogenize(unsigned int *p);
+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);
 int nd_nf(int mod,ND g,int full,ND *nf);
-ND nd_reduce(ND p1,ND p2);
-ND nd_reduce_special(ND p1,ND p2);
+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);
+
+/* 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);
-void nd_mul_c(int mod,ND p,int mul);
-void nd_free_redlist();
-void nd_append_red(unsigned int *d,int td,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);
+
+/* 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 *nd_compute_bound(ND 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);
+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);
@@ -255,7 +318,7 @@ void _NDP_alloc()
 	}
 }
 
-INLINE nd_length(ND p)
+INLINE int nd_length(ND p)
 {
 	NM m;
 	int i;
@@ -273,9 +336,10 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 	unsigned int u1,u2;
 	int i,j;
 
+	if ( TD(d1) < TD(d2) ) return 0;
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 0; 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;
@@ -289,7 +353,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 			return 1;
 			break;
 		case 6:
-			for ( i = 0; 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;
@@ -300,7 +364,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 			return 1;
 			break;
 		case 8:
-			for ( i = 0; 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;
@@ -310,7 +374,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 			return 1;
 			break;
 		case 16:
-			for ( i = 0; 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;
@@ -318,12 +382,12 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 			return 1;
 			break;
 		case 32:
-			for ( i = 0; 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 = 0; 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;
@@ -332,33 +396,31 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int
 	}
 }
 
-/* returns the exponent of homo variable */
-
-int ndl_dehomogenize(unsigned int *d)
+void ndl_dehomogenize(unsigned int *d)
 {
 	unsigned int mask;
 	unsigned int h;
-	int i;
+	int i,bits;
 
-	if ( is_rlex ) {
+	if ( nd_isrlex ) {
 		if ( nd_bpe == 32 ) {
-			h = d[0];
-			for ( i = 1; 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;
-			return h;
+			TD(d) -= h;
 		} else {
-			mask = (1<<(nd_epw*nd_bpe))-1;
-			h = (d[0]>>((nd_epw-1)*nd_bpe))&nd_mask0;
-			for ( i = 0; i < nd_wpd; i++ )
+			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);
-			return h;
+			TD(d) -= h;
 		}
-	} else {
-		/* do nothing */
-		return d[nd_wpd-1];
-	}
+	} else 
+		TD(d) -= ((d[(nd_nvar-1)/nd_epw+nd_exporigin]>>
+			((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)
@@ -368,7 +430,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 0; 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;
@@ -382,7 +444,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 6:
-			for ( i = 0; 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;
@@ -393,7 +455,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 8:
-			for ( i = 0; 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;
@@ -403,7 +465,7 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 16:
-			for ( i = 0; 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;
@@ -411,13 +473,13 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 		case 32:
-			for ( i = 0; 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 = 0; 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;
@@ -426,14 +488,15 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in
 			}
 			break;
 	}
+	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 = 0; 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); 
@@ -441,15 +504,17 @@ int ndl_td(unsigned int *d)
 	return t;
 }
 
-INLINE int ndl_compare(unsigned int *d1,unsigned int *d2)
+INLINE 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 is_rlex ? -1 : 1;
+			return nd_isrlex ? -1 : 1;
 		else if ( *d1 < *d2 )
-			return is_rlex ? 1 : -1;
+			return nd_isrlex ? 1 : -1;
 	return 0;
 }
 
@@ -458,7 +523,7 @@ INLINE int ndl_equal(unsigned int *d1,unsigned int *d2
 	int i;
 
 	for ( i = 0; i < nd_wpd; i++ )
-		if ( d1[i] != d2[i] )
+		if ( *d1++ != *d2++ )
 			return 0;
 	return 1;
 }
@@ -468,13 +533,15 @@ INLINE void ndl_copy(unsigned int *d1,unsigned int *d2
 	int i;
 
 	switch ( nd_wpd ) {
-		case 1:
-			d2[0] = d1[0];
-			break;
 		case 2:
-			d2[0] = d1[0];
+			TD(d2) = TD(d1);
 			d2[1] = d1[1];
 			break;
+		case 3:
+			TD(d2) = TD(d1);
+			d2[1] = d1[1];
+			d2[2] = d1[2];
+			break;
 		default:
 			for ( i = 0; i < nd_wpd; i++ )
 				d2[i] = d1[i];
@@ -487,13 +554,15 @@ INLINE void ndl_add(unsigned int *d1,unsigned int *d2,
 	int i;
 
 	switch ( nd_wpd ) {
-		case 1:
-			d[0] = d1[0]+d2[0];
-			break;
 		case 2:
-			d[0] = d1[0]+d2[0];
+			TD(d) = TD(d1)+TD(d2);
 			d[1] = d1[1]+d2[1];
 			break;
+		case 3:
+			TD(d) = TD(d1)+TD(d2);
+			d[1] = d1[1]+d2[1];
+			d[2] = d1[2]+d2[2];
+			break;
 		default:
 			for ( i = 0; i < nd_wpd; i++ )
 				d[i] = d1[i]+d2[i];
@@ -501,29 +570,10 @@ INLINE void ndl_add(unsigned int *d1,unsigned int *d2,
 	}
 }
 
-INLINE void ndl_add2(unsigned int *d1,unsigned int *d2)
+INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d)
 {
 	int i;
 
-	switch ( nd_wpd ) {
-		case 1:
-			d2[0] += d1[0];
-			break;
-		case 2:
-			d2[0] += d1[0];
-			d2[1] += d1[1];
-			break;
-		default:
-			for ( i = 0; i < nd_wpd; i++ )
-				d2[i] += d1[i];
-			break;
-	}
-}
-
-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];
 }
@@ -535,7 +585,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 0; 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;
@@ -549,7 +599,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 6:
-			for ( i = 0; 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;
@@ -560,7 +610,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 8:
-			for ( i = 0; 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;
@@ -570,7 +620,7 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 16:
-			for ( i = 0; 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;
@@ -578,12 +628,12 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2)
 			return 1;
 			break;
 		case 32:
-			for ( i = 0; 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 = 0; 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;
@@ -605,7 +655,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 	ind = 0;
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 0; 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;
@@ -619,7 +669,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 6:
-			for ( i = 0; 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;
@@ -630,7 +680,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 8:
-			for ( i = 0; 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;
@@ -640,7 +690,7 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 16:
-			for ( i = 0; 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;
@@ -648,12 +698,12 @@ int ndl_check_bound2(int index,unsigned int *d2)
 			return 0;
 			break;
 		case 32:
-			for ( i = 0; 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 = 0; 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 )
@@ -671,7 +721,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 
 	switch ( nd_bpe ) {
 		case 4:
-			for ( i = 0; 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;
@@ -685,7 +735,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			break;
 		case 6:
-			for ( i = 0; 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;
@@ -696,7 +746,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			break;
 		case 8:
-			for ( i = 0; 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;
@@ -706,7 +756,7 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			break;
 		case 16:
-			for ( i = 0; 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;
@@ -714,12 +764,12 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 			return 0;
 			break;
 		case 32:
-			for ( i = 0; 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 = 0; 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 )
@@ -731,12 +781,12 @@ int ndl_check_bound2_direct(unsigned int *d1,unsigned 
 	}
 }
 
-INLINE int ndl_hash_value(int td,unsigned int *d)
+INLINE int ndl_hash_value(unsigned int *d)
 {
 	int i;
 	int r;
 
-	r = td;
+	r = 0;
 	for ( i = 0; i < nd_wpd; i++ )	
 		r = ((r<<16)+d[i])%REDTAB_LEN;
 	return r;
@@ -745,32 +795,35 @@ INLINE int ndl_hash_value(int td,unsigned int *d)
 INLINE int nd_find_reducer(ND g)
 {
 	RHist r;
+	unsigned int *dg;
 	int d,k,i;
 
-	d = ndl_hash_value(HTD(g),HDL(g));
+	dg = HDL(g);
+#if 1
+	d = ndl_hash_value(HDL(g));
 	for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) {
-		if ( HTD(g) == TD(r) && ndl_equal(HDL(g),DL(r)) ) {
+		if ( ndl_equal(dg,DL(r)) ) {
 			if ( k > 0 ) nd_notfirst++;
 			nd_found++;
 			return r->index;
 		}
 	}
-
+#endif
 	if ( Reverse )
 		for ( i = nd_psn-1; i >= 0; i-- ) {
 			r = nd_psh[i];
-			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
+			if ( ndl_reducible(dg,DL(r)) ) {
 				nd_create++;
-				nd_append_red(HDL(g),HTD(g),i);
+				nd_append_red(dg,i);
 				return i;
 			}
 		}
 	else
 		for ( i = 0; i < nd_psn; i++ ) {
 			r = nd_psh[i];
-			if ( HTD(g) >= TD(r) && ndl_reducible(HDL(g),DL(r)) ) {
+			if ( ndl_reducible(dg,DL(r)) ) {
 				nd_create++;
-				nd_append_red(HDL(g),HTD(g),i);
+				nd_append_red(dg,i);
 				return i;
 			}
 		}
@@ -779,22 +832,23 @@ INLINE int nd_find_reducer(ND g)
 
 INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len)
 {
-	int i;
 	NDV r;
+	RHist s;
+	int d,k,i;
 
 	if ( Reverse )
 		for ( i = len-1; i >= 0; i-- ) {
 			r = ps[i];
-			if ( HTD(g) >= HTD(r) && ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),HTD(g),i);
+			if ( ndl_reducible(HDL(g),HDL(r)) ) {
+				nd_append_red(HDL(g),i);
 				return i;
 			}
 		}
 	else
 		for ( i = 0; i < len; i++ ) {
 			r = ps[i];
-			if ( HTD(g) >= HTD(r) && ndl_reducible(HDL(g),HDL(r)) ) {
-				nd_append_red(HDL(g),HTD(g),i);
+			if ( ndl_reducible(HDL(g),HDL(r)) ) {
+				nd_append_red(HDL(g),i);
 				return i;
 			}
 		}
@@ -804,34 +858,26 @@ INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len
 ND nd_add(int mod,ND p1,ND p2)
 {
 	int n,c;
-	int t;
+	int t,can,td1,td2;
 	ND r;
 	NM m1,m2,mr0,mr,s;
 
-	if ( !p1 )
-		return p2;
-	else if ( !p2 )
-		return p1;
-	else if ( !mod )
-		return nd_add_q(p1,p2);
+	if ( !p1 ) return p2;
+	else if ( !p2 ) return p1;
+	else if ( !mod ) return nd_add_q(p1,p2);
 	else {
+		can = 0;
 		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
-			if ( TD(m1) > TD(m2) )
-				c = 1;
-			else if ( TD(m1) < TD(m2) )
-				c = -1;
-			else
-				c = ndl_compare(DL(m1),DL(m2));
+			c = DL_COMPARE(DL(m1),DL(m2));
 			switch ( c ) {
 				case 0:
 					t = ((CM(m1))+(CM(m2))) - mod;
-					if ( t < 0 )
-						t += mod;
+					if ( t < 0 ) t += mod;
 					s = m1; m1 = NEXT(m1);
 					if ( t ) {
-						NEXTNM2(mr0,mr,s); CM(mr) = (t);
+						can++; NEXTNM2(mr0,mr,s); CM(mr) = (t);
 					} else {
-						FREENM(s);
+						can += 2; FREENM(s);
 					}
 					s = m2; m2 = NEXT(m2); FREENM(s);
 					break;
@@ -844,20 +890,15 @@ ND nd_add(int mod,ND p1,ND p2)
 			}
 		}
 		if ( !mr0 )
-			if ( m1 )
-				mr0 = m1;
-			else if ( m2 )
-				mr0 = m2;
-			else
-				return 0;
-		else if ( m1 )
-			NEXT(mr) = m1;
-		else if ( m2 )
-			NEXT(mr) = m2;
-		else
-			NEXT(mr) = 0;
+			if ( m1 ) mr0 = m1;
+			else if ( m2 ) mr0 = m2;
+			else return 0;
+		else if ( m1 ) NEXT(mr) = m1;
+		else if ( m2 ) NEXT(mr) = m2;
+		else NEXT(mr) = 0;
 		BDY(p1) = mr0;
 		SG(p1) = MAX(SG(p1),SG(p2));
+		LEN(p1) = LEN(p1)+LEN(p2)-can;
 		FREEND(p2);
 		return p1;
 	}
@@ -865,31 +906,25 @@ ND nd_add(int mod,ND p1,ND p2)
 
 ND nd_add_q(ND p1,ND p2)
 {
-	int n,c;
+	int n,c,can;
 	ND r;
 	NM m1,m2,mr0,mr,s;
 	Q t;
 
-	if ( !p1 )
-		return p2;
-	else if ( !p2 )
-		return p1;
+	if ( !p1 ) return p2;
+	else if ( !p2 ) return p1;
 	else {
+		can = 0;
 		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
-			if ( TD(m1) > TD(m2) )
-				c = 1;
-			else if ( TD(m1) < TD(m2) )
-				c = -1;
-			else
-				c = ndl_compare(DL(m1),DL(m2));
+			c = DL_COMPARE(DL(m1),DL(m2));
 			switch ( c ) {
 				case 0:
 					addq(CQ(m1),CQ(m2),&t);
 					s = m1; m1 = NEXT(m1);
 					if ( t ) {
-						NEXTNM2(mr0,mr,s); CQ(mr) = (t);
+						can++; NEXTNM2(mr0,mr,s); CQ(mr) = (t);
 					} else {
-						FREENM(s);
+						can += 2; FREENM(s);
 					}
 					s = m2; m2 = NEXT(m2); FREENM(s);
 					break;
@@ -902,26 +937,20 @@ ND nd_add_q(ND p1,ND p2)
 			}
 		}
 		if ( !mr0 )
-			if ( m1 )
-				mr0 = m1;
-			else if ( m2 )
-				mr0 = m2;
-			else
-				return 0;
-		else if ( m1 )
-			NEXT(mr) = m1;
-		else if ( m2 )
-			NEXT(mr) = m2;
-		else
-			NEXT(mr) = 0;
+			if ( m1 ) mr0 = m1;
+			else if ( m2 ) mr0 = m2;
+			else return 0;
+		else if ( m1 ) NEXT(mr) = m1;
+		else if ( m2 ) NEXT(mr) = m2;
+		else NEXT(mr) = 0;
 		BDY(p1) = mr0;
 		SG(p1) = MAX(SG(p1),SG(p2));
+		LEN(p1) = LEN(p1)+LEN(p2)-can;
 		FREEND(p2);
 		return p1;
 	}
 }
 
-#if 1
 /* ret=1 : success, ret=0 : overflow */
 int nd_nf(int mod,ND g,int full,ND *rp)
 {
@@ -929,7 +958,7 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 	NM m,mrd,tail;
 	NM mul;
 	int n,sugar,psugar,sugar0,stat,index;
-	int c,c1,c2;
+	int c,c1,c2,dummy;
 	RHist h;
 	NDV p,red;
 	Q cg,cred,gcd;
@@ -939,8 +968,7 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 		*rp = 0;
 		return 1;
 	}
-	if ( !mod )
-		hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
+	if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
 
 	sugar0 = sugar = SG(g);
 	n = NV(g);
@@ -950,12 +978,6 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 		if ( index >= 0 ) {
 			h = nd_psh[index];
 			ndl_sub(HDL(g),DL(h),DL(mul));
-			TD(mul) = HTD(g)-TD(h);
-#if 0
-			if ( d && (SG(p)+TD(mul)) > sugar ) {
-				goto afo;				
-			}
-#endif
 			if ( ndl_check_bound2(index,DL(mul)) ) {
 				nd_free(g); nd_free(d);
 				return 0;
@@ -971,7 +993,7 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 				nd_mul_c_q(d,cred); nd_mul_c_q(g,cred);
 			}
 			g = nd_add(mod,g,ndv_mul_nm(mod,p,mul));
-			sugar = MAX(sugar,SG(p)+TD(mul));
+			sugar = MAX(sugar,SG(p)+TD(DL(mul)));
 			if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) {
 				nd_removecont2(d,g);
 				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
@@ -980,40 +1002,37 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 			*rp = g;
 			return 1;
 		} else {
-afo:
 			m = BDY(g); 
 			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
+				BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
 			} else {
 				FREEND(g); g = 0;
 			}
 			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
+				NEXT(tail)=m; tail=m; LEN(d)++;
 			} else {
-				MKND(n,m,d);
-				tail = BDY(d);
+				MKND(n,m,1,d); tail = BDY(d);
 			}
 		}
 	}
-	if ( d )
-		SG(d) = sugar;
+	if ( d ) SG(d) = sugar;
 	*rp = d;
 	return 1;
 }
-#else
-int nd_nf(int mod,ND g,int full,ND *rp)
+
+int nd_nf_pbucket(int mod,ND g,int full,ND *rp)
 {
 	int hindex,index;
 	NDV p;
 	ND u,d,red;
 	NODE l;
-	NM mul,m,mrd;
+	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;
@@ -1021,15 +1040,15 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 	}
 	sugar = SG(g);
 	n = NV(g);
+	if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
 	bucket = create_pbucket();
-	add_pbucket(mod,bucket,g,nd_length(g));
+	add_pbucket(mod,bucket,g);
 	d = 0;
 	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 ) {
-			if ( d )
-				SG(d) = sugar;
+			if ( d ) SG(d) = sugar;
 			*rp = d;
 			return 1;
 		}
@@ -1038,7 +1057,6 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 		if ( index >= 0 ) {
 			h = nd_psh[index];
 			ndl_sub(HDL(g),DL(h),DL(mul));
-			TD(mul) = HTD(g)-TD(h);
 			if ( ndl_check_bound2(index,DL(mul)) ) {
 				nd_free(d);
 				free_pbucket(bucket);
@@ -1056,64 +1074,48 @@ int nd_nf(int mod,ND g,int full,ND *rp)
 				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,LEN(p)-1);
-			sugar = MAX(sugar,SG(p)+TD(mul));
+			add_pbucket(mod,bucket,red);
+			psugar = SG(p)+TD(DL(mul));
+			sugar = MAX(sugar,psugar);
+			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;
+			if ( g ) SG(g) = sugar;
 			*rp = g;
 			return 1;
 		} else {
 			m = BDY(g); 
 			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
+				BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
 			} else {
 				FREEND(g); g = 0;
 			}
 			bucket->body[hindex] = g;
 			NEXT(m) = 0;
 			if ( d ) {
-				for ( mrd = BDY(d); NEXT(mrd); mrd = NEXT(mrd) );
-				NEXT(mrd) = m;
+				NEXT(tail)=m; tail=m; LEN(d)++;
 			} else {
-				MKND(n,m,d);
+				MKND(n,m,1,d); tail = BDY(d);
 			}
 		}
 	}
 }
-#endif
 
-/* 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;
-
-	nd_setup(0,cand);
-
-	/* membercheck : list is a subset of Id(cand) ? */
-	for ( t = input; t; t = NEXT(t) ) {
-		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;
-	}
-	/* gbcheck : cand is a GB of Id(cand) ? */
-	if ( !nd_gb(0,1) )
-		return 0;
-	/* XXX */
-	return 1;
-}
-
 int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp)
 {
 	ND d;
@@ -1146,7 +1148,6 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 		if ( index >= 0 ) {
 			p = ps[index];
 			ndl_sub(HDL(g),HDL(p),DL(mul));
-			TD(mul) = HTD(g)-HTD(p);
 			if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) {
 				nd_free(g); nd_free(d);
 				return 0;
@@ -1160,7 +1161,7 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 				nd_mul_c_q(d,cred); nd_mul_c_q(g,cred);
 			}
 			g = nd_add(mod,g,ndv_mul_nm(mod,p,mul));
-			sugar = MAX(sugar,SG(p)+TD(mul));
+			sugar = MAX(sugar,SG(p)+TD(DL(mul)));
 			if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) {
 				nd_removecont2(d,g);
 				hmag = ((double)p_mag((P)HCQ(g)))*nd_scale;
@@ -1171,35 +1172,156 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full
 		} else {
 			m = BDY(g); 
 			if ( NEXT(m) ) {
-				BDY(g) = NEXT(m); NEXT(m) = 0;
+				BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--;
 			} else {
 				FREEND(g); g = 0;
 			}
 			if ( d ) {
-				NEXT(tail)=m;
-				tail=m;
+				NEXT(tail)=m; tail=m; LEN(d)++;
 			} else {
-				MKND(n,m,d);
-				tail = BDY(d);
+				MKND(n,m,1,d); tail = BDY(d);
 			}
 		}
 	}
-	if ( d )
-		SG(d) = sugar;
+	if ( d ) SG(d) = sugar;
 	*rp = d;
 	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-1)*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;
+
+	nd_setup(0,0,cand);
+	n = length(cand);
+
+	/* membercheck : list is a subset of Id(cand) ? */
+	for ( t = input; t; t = NEXT(t) ) {
+		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;
+	}
+	/* gbcheck : cand is a GB of Id(cand) ? */
+	if ( !nd_gb(0,1) ) return 0;
+	/* XXX */
+	return 1;
+}
+
 ND nd_remove_head(ND p)
 {
 	NM m;
 
 	m = BDY(p);
 	if ( !NEXT(m) ) {
-		FREEND(p);
-		p = 0;
-	} else
-		BDY(p) = NEXT(m);
+		FREEND(p); p = 0;
+	} else {
+		BDY(p) = NEXT(m); LEN(p)--;
+	}
 	FREENM(m);
 	return p;
 }
@@ -1224,14 +1346,17 @@ void free_pbucket(PGeoBucket b) {
 	GC_free(b);
 }
 
-void add_pbucket(int mod,PGeoBucket g,ND d,int l)
+void add_pbucket(int mod,PGeoBucket g,ND d)
 {
-	int k,m;
+	int l,i,k,m;
 
-	for ( k = 0, m = 1; l > m; k++, m <<= 2 );
-	/* 4^(k-1) < l <= 4^k */
+	if ( !d )
+		return;
+	l = LEN(d);
+	for ( k = 0, m = 1; l > m; k++, m <<= 1 );
+	/* 2^(k-1) < l <= 2^k (=m) */
 	d = nd_add(mod,g->body[k],d);
-	for ( ; d && nd_length(d) > 1<<(2*k); k++ ) {
+	for ( ; d && LEN(d) > m; k++, m <<= 1 ) {
 		g->body[k] = 0;
 		d = nd_add(mod,g->body[k+1],d);
 	}
@@ -1247,7 +1372,6 @@ void mulq_pbucket(PGeoBucket g,Q c)
 		nd_mul_c_q(g->body[k],c);
 }
 
-/* XXX not completed */
 int head_pbucket(int mod,PGeoBucket g)
 {
 	int j,i,c,k,nv,sum;
@@ -1266,33 +1390,22 @@ int head_pbucket(int mod,PGeoBucket g)
 				dj = HDL(gj);
 				sum = HCM(gj);
 			} else {
-				di = HDL(gi);
-				nv = NV(gi);
-				if ( HTD(gi) > HTD(gj) )
-					c = 1;
-				else if ( HTD(gi) < HTD(gj) )
-					c = -1;
-				else
-					c = ndl_compare(di,dj);
+				c = DL_COMPARE(HDL(gi),dj);
 				if ( c > 0 ) {
-					if ( sum )
-						HCM(gj) = sum;
-					else
-						g->body[j] = nd_remove_head(gj);
+					if ( sum ) HCM(gj) = sum;
+					else g->body[j] = nd_remove_head(gj);
 					j = i;
 					gj = g->body[j];
 					dj = HDL(gj);
 					sum = HCM(gj);
 				} else if ( c == 0 ) {
 					sum = sum+HCM(gi)-mod;
-					if ( sum < 0 )
-						sum += mod;
+					if ( sum < 0 ) sum += mod;
 					g->body[i] = nd_remove_head(gi);
 				}
 			}
 		}
-		if ( j < 0 )
-			return -1;
+		if ( j < 0 ) return -1;
 		else if ( sum ) {
 			HCM(gj) = sum;
 			return j;
@@ -1305,37 +1418,25 @@ int head_pbucket_q(PGeoBucket g)
 {
 	int j,i,c,k,nv;
 	Q sum,t;
-	unsigned int *di,*dj;
 	ND gi,gj;
 
 	k = g->m;
 	while ( 1 ) {
 		j = -1;
 		for ( i = 0; i <= k; i++ ) {
-			if ( !(gi = g->body[i]) )
-				continue;
+			if ( !(gi = g->body[i]) ) continue;
 			if ( j < 0 ) {
 				j = i;
 				gj = g->body[j];
-				dj = HDL(gj);
 				sum = HCQ(gj);
 			} else {
-				di = HDL(gi);
 				nv = NV(gi);
-				if ( HTD(gi) > HTD(gj) )
-					c = 1;
-				else if ( HTD(gi) < HTD(gj) )
-					c = -1;
-				else
-					c = ndl_compare(di,dj);
+				c = DL_COMPARE(HDL(gi),HDL(gj));
 				if ( c > 0 ) {
-					if ( sum )
-						HCQ(gj) = sum;
-					else
-						g->body[j] = nd_remove_head(gj);
+					if ( sum ) HCQ(gj) = sum;
+					else g->body[j] = nd_remove_head(gj);
 					j = i;
 					gj = g->body[j];
-					dj = HDL(gj);
 					sum = HCQ(gj);
 				} else if ( c == 0 ) {
 					addq(sum,HCQ(gi),&t);
@@ -1344,8 +1445,7 @@ int head_pbucket_q(PGeoBucket g)
 				}
 			}
 		}
-		if ( j < 0 )
-			return -1;
+		if ( j < 0 ) return -1;
 		else if ( sum ) {
 			HCQ(gj) = sum;
 			return j;
@@ -1360,8 +1460,11 @@ ND normalize_pbucket(int mod,PGeoBucket g)
 	ND r,t;
 
 	r = 0;
-	for ( i = 0; i <= g->m; i++ )
+	for ( i = 0; i <= g->m; i++ ) {
 		r = nd_add(mod,r,g->body[i]);
+		g->body[i] = 0;
+	}
+	g->m = -1;
 	return r;
 }
 
@@ -1394,7 +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);
@@ -1402,7 +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);
@@ -1412,11 +1519,9 @@ again:
 		}
 	}
 	if ( m )
-		for ( t = g; t; t = NEXT(t) )
-			BDY(t) = (pointer)nd_ps[(int)BDY(t)];
+		for ( t = g; t; t = NEXT(t) ) BDY(t) = (pointer)nd_ps[(int)BDY(t)];
 	else
-		for ( t = g; t; t = NEXT(t) )
-			BDY(t) = (pointer)nd_psq[(int)BDY(t)];
+		for ( t = g; t; t = NEXT(t) ) BDY(t) = (pointer)nd_psq[(int)BDY(t)];
 	return g;
 }
 
@@ -1447,7 +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);
@@ -1458,9 +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 {
@@ -1478,17 +1587,12 @@ again:
 
 int ndv_compare(NDV *p1,NDV *p2)
 {
-	int td1,td2;
-
-	td1 = HTD(*p1); td2 = HTD(*p2);
-	if ( td1 > td2 ) return 1;
-	else if ( td1 < td2 ) return -1;
-	else return ndl_compare(HDL(*p1),HDL(*p2));
+	return DL_COMPARE(HDL(*p1),HDL(*p2));
 }
 
 int ndv_compare_rev(NDV *p1,NDV *p2)
 {
-	return -ndv_compare(p1,p2);
+	return -DL_COMPARE(HDL(*p1),HDL(*p2));
 }
 
 NODE nd_reduceall(int m,NODE f)
@@ -1505,10 +1609,8 @@ NODE nd_reduceall(int m,NODE f)
 	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];
+		for ( j = 0; j < i; j++ ) w[j] = (NDV)ps[j];
+		for ( j = i+1; j < n; j++ ) w[j-1] = ps[j];
 		g = ndvtond(m,ps[i]);
 		stat = nd_nf_direct(m,g,w,n-1,1,&nf);
 		if ( !stat )
@@ -1516,8 +1618,7 @@ NODE nd_reduceall(int m,NODE f)
 		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];
 			n--;
 		} else {
 			printf("."); fflush(stdout);
@@ -1548,23 +1649,18 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */
 	while ( cur ) {
 		if ( crit_2( cur->i1,cur->i2 ) ) {
 			remove = cur;
-			if ( !prev ) {
-				head = cur = NEXT(cur);
-			} else {
-				cur = NEXT(prev) = NEXT(cur);
-			}
+			if ( !prev ) head = cur = NEXT(cur);
+			else cur = NEXT(prev) = NEXT(cur);
 			FREENDP(remove);
 		} else {
-			prev = cur;
-			cur = NEXT(cur);
+			prev = cur; cur = NEXT(cur);
 		}
 	}
 	if ( !d )
 		return head;
 	else {
 		nd = d;
-		while ( NEXT(nd) )
-			nd = NEXT(nd);
+		while ( NEXT(nd) ) nd = NEXT(nd);
 		NEXT(nd) = head;
 		return d;
 	}
@@ -1574,20 +1670,18 @@ ND_pairs nd_newpairs( NODE g, int t )
 {
 	NODE h;
 	unsigned int *dl;
-	int td,ts,s;
+	int ts,s;
 	ND_pairs r,r0;
 
 	dl = DL(nd_psh[t]);
-	td = TD(nd_psh[t]);
-	ts = SG(nd_psh[t]) - td;
+	ts = SG(nd_psh[t]) - TD(dl);
 	for ( r0 = 0, h = g; h; h = NEXT(h) ) {
 		NEXTND_pairs(r0,r);
 		r->i1 = (int)BDY(h);
 		r->i2 = t;
 		ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm);
-		TD(r) = ndl_td(r->lcm);
-		s = SG(nd_psh[r->i1])-TD(nd_psh[r->i1]);
-		SG(r) = MAX(s,ts) + TD(r);
+		s = SG(nd_psh[r->i1])-TD(DL(nd_psh[r->i1]));
+		SG(r) = MAX(s,ts) + TD(LCM(r));
 	}
 	NEXT(r) = 0;
 	return r0;
@@ -1617,39 +1711,34 @@ ND_pairs crit_B( ND_pairs d, int s )
 			}
 			FREENDP(remove);
 		} else {
-			prev = cur;
-			cur = NEXT(cur);
+			prev = cur; cur = NEXT(cur);
 		}
 	}
 	return head;
 }
 
+/* XXX : check is necessary */
+
 ND_pairs crit_M( ND_pairs d1 )
 {
 	ND_pairs e,d2,d3,dd,p;
 	unsigned int *id,*jd;
-	int itd,jtd;
 
 	for ( dd = 0, e = d1; e; e = d3 ) {
 		if ( !(d2 = NEXT(e)) ) {
 			NEXT(e) = dd;
 			return e;
 		}
-		id = e->lcm;
-		itd = TD(e);
+		id = LCM(e);
 		for ( d3 = 0; d2; d2 = p ) {
-			p = NEXT(d2),
-			jd = d2->lcm;
-			jtd = TD(d2);
-			if ( jtd == itd  )
-				if ( id == jd );
-				else if ( ndl_reducible(jd,id) ) continue;
-				else if ( ndl_reducible(id,jd) ) goto delit;
-				else ;
-			else if ( jtd > itd )
+			p = NEXT(d2);
+			jd = LCM(d2);
+			if ( ndl_equal(jd,id) )
+				;
+			else if ( TD(jd) > TD(id) )
 				if ( ndl_reducible(jd,id) ) continue;
 				else ;
-			else if ( ndl_reducible(id,jd ) ) goto delit;
+			else if ( ndl_reducible(id,jd) ) goto delit;
 			NEXT(d2) = d3;
 			d3 = d2;
 		}
@@ -1716,25 +1805,21 @@ 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;
-	int td;
 
 	w = d1;
-	d = w->lcm;
-	td = TD(w);
+	d = LCM(w);
 	s = NEXT(w);
 	NEXT(w) = 0;
 	for ( r = 0; s; s = p ) {
 		p = NEXT(s);
-		if ( td == TD(s) && ndl_equal(d,s->lcm) ) {
-			NEXT(s) = w;
-			w = s;
+		if ( ndl_equal(d,LCM(s)) ) {
+			NEXT(s) = w; w = s;
 		} else {
-			NEXT(s) = r;
-			r = s;
+			NEXT(s) = r; r = s;
 		}
 	}
 	*prest = r;
@@ -1745,14 +1830,11 @@ NODE update_base(NODE nd,int ndp)
 {
 	unsigned int *dl, *dln;
 	NODE last, p, head;
-	int td,tdn;
 
 	dl = DL(nd_psh[ndp]);
-	td = TD(nd_psh[ndp]);
 	for ( head = last = 0, p = nd; p; ) {
 		dln = DL(nd_psh[(int)BDY(p)]);
-		tdn = TD(nd_psh[(int)BDY(p)]);
-		if ( tdn >= td && ndl_reducible( dln, dl ) ) {
+		if ( ndl_reducible( dln, dl ) ) {
 			p = NEXT(p);
 			if ( last ) NEXT(last) = p;
 		} else {
@@ -1768,45 +1850,19 @@ ND_pairs nd_minp( ND_pairs d, ND_pairs *prest )
 {
 	ND_pairs m,ml,p,l;
 	unsigned int *lcm;
-	int s,td,len,tlen,c;
+	int s,td,len,tlen,c,c1;
 
 	if ( !(p = NEXT(m = d)) ) {
 		*prest = p;
 		NEXT(m) = 0;
 		return m;
 	}
-	lcm = m->lcm;
 	s = SG(m);
-	td = TD(m);
-	len = nd_psl[m->i1]+nd_psl[m->i2];
-	for ( ml = 0, l = m; p; p = NEXT(l = p) ) {
-		if (SG(p) < s)
-			goto find;
-		else if ( SG(p) == s ) {
-			if ( TD(p) < td )
-				goto find;
-			else if ( TD(p) == td ) {
-				c = ndl_compare(p->lcm,lcm);
-				if ( c < 0 )
-					goto find;
-#if 0
-				else if ( c == 0 ) {
-					tlen = nd_psl[p->i1]+nd_psl[p->i2];
-					if ( tlen < len )
-						goto find;
-				}
-#endif
-			}
+	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);
 		}
-		continue;
-find:
-		ml = l;
-		m = p;
-		lcm = m->lcm;
-		s = SG(m);
-		td = TD(m);
-		len = tlen;
-	}
 	if ( !ml ) *prest = NEXT(m);
 	else {
 		NEXT(ml) = NEXT(m);
@@ -1816,7 +1872,7 @@ find:
 	return m;
 }
 
-int nd_newps(int mod,ND a)
+int nd_newps(int mod,ND a,ND aq)
 {
 	int len;
 	RHist r;
@@ -1824,62 +1880,36 @@ int nd_newps(int mod,ND a)
 
 	if ( nd_psn == nd_pslen ) {
 		nd_pslen *= 2;
-		nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
 		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 *));
 	}
-	nd_removecont(mod,a);
-	nd_bound[nd_psn] = nd_compute_bound(a);
-	NEWRHist(r); SG(r) = SG(a); TD(r) = HTD(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_psl[nd_psn] = len;
-	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_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int));
-		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); TD(r) = HTD(nf); ndl_copy(HDL(nf),DL(r)); 
-	nd_psh[nd_psn] = r;
-
-	len = LEN(nd_psq[nd_psn]);
-	nd_psl[nd_psn] = len;
-
-	nd_free(nf); nd_free(nfq);
+	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 ( 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(int mod,NODE f)
+void nd_setup(int mod,int trace,NODE f)
 {
 	int i,j,td,len,max;
 	NODE s,s0,f0;
@@ -1890,7 +1920,6 @@ void nd_setup(int mod,NODE f)
 	nd_found = 0; nd_notfirst = 0; nd_create = 0;
 
 	nd_psn = length(f); nd_pslen = 2*nd_psn;
-	nd_psl = (int *)MALLOC(nd_pslen*sizeof(int));
 	nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
 	nd_psq = (NDV *)MALLOC(nd_pslen*sizeof(NDV));
 	nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist));
@@ -1904,87 +1933,32 @@ void nd_setup(int mod,NODE f)
 		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;
+	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); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-		if ( mod )
+		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;
-		else
+			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;
 	}
 }
 
-void nd_setup_trace(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_psl = (int *)MALLOC(nd_pslen*sizeof(int));
-	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);
-	}
-	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) ) {
-		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));
-		SG(r) = HTD(a); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r));
-		nd_psh[i] = r;
-	}
-}
-
 void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp)
 {
 	struct order_spec ord1;
@@ -1994,25 +1968,15 @@ void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,
 
 	get_vars((Obj)f,&fv); pltovl(v,&vv);
 	nd_nvar = length(vv);
-	if ( ord->id )
-		error("nd_gr : unsupported order");
-	switch ( ord->ord.simple ) {
-		case 0:
-			is_rlex = 1;
-			break;
-		case 1:
-			is_rlex = 0;
-			break;
-		default:
-			error("nd_gr : unsupported order");
-	}
+	nd_init_ord(ord);
+	/* XXX for DP */
 	initd(ord);
 	for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
 		ptod(CO,vv,(P)BDY(t),&b);
 		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);
@@ -2041,16 +2005,9 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o
 
 	get_vars((Obj)f,&fv); pltovl(v,&vv);
 	nd_nvar = length(vv);
-	if ( ord->id )
-		error("nd_gr : unsupported order");
 	initd(ord);
 	if ( homo ) {
 		homogenize_order(ord,nd_nvar,&ord1);
-		switch ( ord1.ord.simple ) {
-			case 0: is_rlex = 1; break;
-			case 1: is_rlex = 0; break;
-			default: error("nd_gr : unsupported order");
-		}
 		for ( fd0 = 0, in0 = 0, t = BDY(f); t; t = NEXT(t) ) {
 			ptod(CO,vv,(P)BDY(t),&c);
 			if ( c ) {
@@ -2060,14 +2017,10 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o
 		}
 		if ( fd0 ) NEXT(fd) = 0;
 		if ( in0 ) NEXT(in) = 0;
+		nd_init_ord(&ord1);
 		initd(&ord1);
 		nd_nvar++;
 	} else {
-		switch ( ord->ord.simple ) {
-			case 0: is_rlex = 1; break;
-			case 1: is_rlex = 0; break;
-			default: error("nd_gr : unsupported order");
-		}
 		for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) {
 			ptod(CO,vv,(P)BDY(t),&c);
 			if ( c ) {
@@ -2076,9 +2029,10 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o
 		}
 		if ( fd0 ) NEXT(fd) = 0;
 		in0 = fd0;
+		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 ) {
@@ -2115,31 +2069,32 @@ void dltondl(int n,DL dl,unsigned int *r)
 	int i;
 
 	d = dl->d;
-	bzero(r,nd_wpd*sizeof(unsigned int));
-	if ( is_rlex )
+	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] |= (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] |= d[i]<<((nd_epw-(i%nd_epw)-1)*nd_bpe);
+			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,int td,unsigned int *ndl)
+DL ndltodl(int n,unsigned int *ndl)
 {
 	DL dl;
 	int *d;
 	int i;
 
 	NEWDL(dl,n);
-	TD(dl) = td;
+	dl->td = TD(ndl);
 	d = dl->d;
-	if ( is_rlex )
+	if ( nd_isrlex )
 		for ( i = 0; i < n; i++ )
-			d[i] = (ndl[(n-1-i)/nd_epw]>>((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]>>((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;
 }
@@ -2149,24 +2104,20 @@ ND dptond(int mod,DP p)
 	ND d;
 	NM m0,m;
 	MP t;
-	int n;
+	int n,l;
 
 	if ( !p )
 		return 0;
 	n = NV(p);
 	m0 = 0;
-	for ( t = BDY(p); t; t = NEXT(t) ) {
+	for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ ) {
 		NEXTNM(m0,m);
-		if ( mod )
-			CM(m) = ITOS(C(t));
-		else
-			CQ(m) = (Q)C(t);
-		TD(m) = TD(DL(t));
+		if ( mod ) CM(m) = ITOS(C(t));
+		else CQ(m) = (Q)C(t);
 		dltondl(n,DL(t),DL(m));
 	}
 	NEXT(m) = 0;
-	MKND(n,m0,d);
-	NV(d) = n;
+	MKND(n,m0,l,d);
 	SG(d) = SG(p);
 	return d;
 }
@@ -2184,11 +2135,9 @@ DP ndtodp(int mod,ND p)
 	m0 = 0;
 	for ( t = BDY(p); t; t = NEXT(t) ) {
 		NEXTMP(m0,m);
-		if ( mod )
-			C(m) = STOI(CM(t));
-		else
-			C(m) = (P)CQ(t);
-		DL(m) = ndltodl(n,TD(t),DL(t));
+		if ( mod ) C(m) = STOI(CM(t));
+		else C(m) = (P)CQ(t);
+		DL(m) = ndltodl(n,DL(t));
 	}
 	NEXT(m) = 0;
 	MKDP(n,m0,d);
@@ -2203,15 +2152,15 @@ void ndl_print(unsigned int *dl)
 
 	n = nd_nvar;
 	printf("<<");
-	if ( is_rlex )
+	if ( nd_isrlex )
 		for ( i = 0; i < n; i++ )
 			printf(i==n-1?"%d":"%d,",
-				(dl[(n-1-i)/nd_epw]>>((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]>>((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(">>");
 }
@@ -2252,9 +2201,7 @@ void ndp_print(ND_pairs d)
 {
 	ND_pairs t;
 
-	for ( t = d; t; t = NEXT(t) ) {
-		printf("%d,%d ",t->i1,t->i2);
-	}
+	for ( t = d; t; t = NEXT(t) ) printf("%d,%d ",t->i1,t->i2);
 	printf("\n");
 }
 
@@ -2267,15 +2214,13 @@ void nd_removecont(int mod,ND p)
 	struct oVECT v;
 	N q,r;
 
-	if ( mod )
-		nd_mul_c(mod,p,invm(HCM(p),mod));
+	if ( mod ) nd_mul_c(mod,p,invm(HCM(p),mod));
 	else {
 		for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
 		w = (Q *)ALLOCA(n*sizeof(Q));
 		v.len = n;
 		v.body = (pointer *)w;
-		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ )
-			w[i] = CQ(m);
+		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
 		removecont_array(w,n);
 		for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
 	}
@@ -2301,10 +2246,8 @@ void nd_removecont2(ND p1,ND p2)
 	w = (Q *)ALLOCA(n*sizeof(Q));
 	v.len = n;
 	v.body = (pointer *)w;
-	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ )
-		w[i] = CQ(m);
-	for ( m = BDY(p2); i < n; m = NEXT(m), i++ )
-		w[i] = CQ(m);
+	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) w[i] = CQ(m);
+	for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CQ(m);
 	removecont_array(w,n);
 	for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) CQ(m) = w[i];	
 	for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i];	
@@ -2322,8 +2265,7 @@ void ndv_removecont(int mod,NDV p)
 	else {
 		len = p->len;
 		w = (Q *)ALLOCA(len*sizeof(Q));
-		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ )
-			w[i] = CQ(m);
+		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) w[i] = CQ(m);
 		sortbynm(w,len);
 		qltozl(w,len,&dvr);
 		for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) {
@@ -2343,14 +2285,14 @@ 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++ )
-		TD(m) -= ndl_dehomogenize(DL(m));
+		ndl_dehomogenize(DL(m));
 	if ( newwpd != nd_wpd ) {
 		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); TD(r) = TD(m); ndl_copy(DL(m),d); ndl_copy(d,DL(r));
+			CQ(r) = CQ(m); ndl_copy(DL(m),d); ndl_copy(d,DL(r));
 		}
 	}
 	NV(p)--;
@@ -2373,9 +2315,7 @@ void removecont_array(Q *c,int n)
 		NTOQ(qn,SGN(c[i])*SGN(d0),q[i]);
 		NTOQ(rn,SGN(c[i]),r[i]);
 	}
-	for ( i = 0; i < n; i++ )
-		if ( r[i] )
-			break;
+	for ( i = 0; i < n; i++ ) if ( r[i] ) break;
 	if ( i < n ) {
 		v.id = O_VECT; v.len = n; v.body = (pointer *)r;
 		igcdv(&v,&d1);
@@ -2390,8 +2330,7 @@ void removecont_array(Q *c,int n)
 				q[i] = u;
 		}
 	}
-	for ( i = 0; i < n; i++ )
-		c[i] = q[i];
+	for ( i = 0; i < n; i++ ) c[i] = q[i];
 }
 
 void nd_mul_c(int mod,ND p,int mul)
@@ -2399,8 +2338,7 @@ void nd_mul_c(int mod,ND p,int mul)
 	NM m;
 	int c,c1;
 
-	if ( !p )
-		return;
+	if ( !p ) return;
 	for ( m = BDY(p); m; m = NEXT(m) ) {
 		c1 = CM(m);
 		DMAR(c1,mul,0,mod,c);
@@ -2413,8 +2351,7 @@ void nd_mul_c_q(ND p,Q mul)
 	NM m;
 	Q c;
 
-	if ( !p )
-		return;
+	if ( !p ) return;
 	for ( m = BDY(p); m; m = NEXT(m) ) {
 		mulq(CQ(m),mul,&c); CQ(m) = c;
 	}
@@ -2424,8 +2361,7 @@ void nd_free(ND p)
 {
 	NM t,s;
 
-	if ( !p )
-		return;
+	if ( !p ) return;
 	t = BDY(p);
 	while ( t ) {
 		s = NEXT(t);
@@ -2440,15 +2376,14 @@ void ndv_free(NDV p)
 	GC_free(BDY(p));
 }
 
-void nd_append_red(unsigned int *d,int td,int i)
+void nd_append_red(unsigned int *d,int i)
 {
 	RHist m,m0;
 	int h;
 
 	NEWRHist(m);
-	h = ndl_hash_value(td,d);
+	h = ndl_hash_value(d);
 	m->index = i;
-	TD(m) = td;
 	ndl_copy(d,DL(m));
 	NEXT(m) = nd_red[h];
 	nd_red[h] = m;
@@ -2465,7 +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++ )
@@ -2474,8 +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;
 }
 
@@ -2489,16 +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]>>((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;
 }
 
@@ -2507,6 +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 {
@@ -2522,30 +2472,23 @@ void nd_setup_parameters() {
 	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;
 	oadv = nmv_adv;
-	if ( obpe < 4 )
-		nd_bpe = 4;
-	else if ( obpe < 6 )
-		nd_bpe = 6;
-	else if ( obpe < 8 )
-		nd_bpe = 8;
-	else if ( obpe < 16 )
-		nd_bpe = 16;
-	else if ( obpe < 32 )
-		nd_bpe = 32;
-	else
-		error("nd_reconstruct : exponent too large");
+	if ( obpe < 4 ) nd_bpe = 4;
+	else if ( obpe < 6 ) nd_bpe = 6;
+	else if ( obpe < 8 ) nd_bpe = 8;
+	else if ( obpe < 16 ) nd_bpe = 16;
+	else if ( obpe < 32 ) nd_bpe = 32;
+	else error("nd_reconstruct : exponent too large");
 
 	nd_setup_parameters();
 	prev_nm_free_list = _nm_free_list;
@@ -2553,34 +2496,38 @@ 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);
 	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);
 	s0 = 0;
 	for ( t = d; t; t = NEXT(t) ) {
 		NEXTND_pairs(s0,s);
 		s->i1 = t->i1;
 		s->i2 = t->i2;
-		TD(s) = TD(t);
 		SG(s) = SG(t);
-		ndl_dup(obpe,t->lcm,s->lcm);
+		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);
-			TD(mr) = TD(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]);
-		TD(r) = TD(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;
@@ -2592,41 +2539,50 @@ 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;
 	oadv = nmv_adv;
-	if ( obpe < 4 )
-		nd_bpe = 4;
-	else if ( obpe < 6 )
-		nd_bpe = 6;
-	else if ( obpe < 8 )
-		nd_bpe = 8;
-	else if ( obpe < 16 )
-		nd_bpe = 16;
-	else if ( obpe < 32 )
-		nd_bpe = 32;
-	else
-		error("nd_reconstruct_direct : exponent too large");
+	if ( obpe < 4 ) nd_bpe = 4;
+	else if ( obpe < 6 ) nd_bpe = 6;
+	else if ( obpe < 8 ) nd_bpe = 8;
+	else if ( obpe < 16 ) nd_bpe = 16;
+	else if ( obpe < 32 ) nd_bpe = 32;
+	else error("nd_reconstruct_direct : exponent too large");
 
 	nd_setup_parameters();
 	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);
+	_nm_free_list = 0; _ndp_free_list = 0;
+	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++ ) {
+		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_reconstruct(obpe,DL(r),DL(mr));
+			h = ndl_hash_value(DL(mr));
+			NEXT(mr) = nd_red[h];
+			nd_red[h] = mr;
+		}
+	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;
 
@@ -2634,19 +2590,19 @@ void ndl_dup(int obpe,unsigned int *d,unsigned int *r)
 	oepw = (sizeof(unsigned int)*8)/obpe;
 	cepw = nd_epw;
 	cbpe = nd_bpe;
-	for ( i = 0; i < nd_wpd; i++ )
-		r[i] = 0;
-	if ( is_rlex )
+	TD(r) = TD(d);
+	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]>>((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] |= (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]>>((oepw-(i%oepw)-1)*obpe))
+			ei = (d[i/oepw+nd_exporigin]>>((oepw-(i%oepw)-1)*obpe))
 				&((1<<obpe)-1);
-			r[i/cepw] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
+			r[i/cepw+nd_exporigin] |= (ei<<((cepw-(i%cepw)-1)*cbpe));
 		}
 }
 
@@ -2659,8 +2615,7 @@ void nd_realloc(ND p,int obpe)
 		for ( mr0 = 0; m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
 			CM(mr) = CM(m);
-			TD(mr) = TD(m);
-			ndl_dup(obpe,DL(m),DL(mr));
+			ndl_reconstruct(obpe,DL(m),DL(mr));
 		}
 		NEXT(mr) = 0; 
 		BDY(p) = mr0;
@@ -2670,21 +2625,19 @@ 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-1)*sizeof(unsigned int);
 		for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
 			NEXTNM(mr0,mr);
 			CM(mr) = CM(m);
-			TD(mr) = TD(m);
 			ndl_copy(DL(m),DL(mr));
 		}
 		NEXT(mr) = 0; 
-		MKND(NV(p),mr0,r);
+		MKND(NV(p),mr0,LEN(p),r);
 		SG(r) = SG(p);
 		return r;
 	}
@@ -2703,19 +2656,15 @@ int nd_sp(int mod,ND_pairs p,ND *rp)
 	} else {
 		p1 = nd_psq[p->i1]; p2 = nd_psq[p->i2];
 	}
-	lcm = p->lcm;
-	td = TD(p);
+	lcm = LCM(p);
 	NEWNM(m);
 	CQ(m) = HCQ(p2);
-	TD(m) = td-HTD(p1); ndl_sub(lcm,HDL(p1),DL(m));
-	if ( ndl_check_bound2(p->i1,DL(m)) )
-		return 0;
+	ndl_sub(lcm,HDL(p1),DL(m));
+	if ( ndl_check_bound2(p->i1,DL(m)) ) return 0;
 	t1 = ndv_mul_nm(mod,p1,m);
-	if ( mod )
-		CM(m) = mod-HCM(p1); 
-	else
-		chsgnq(HCQ(p1),&CQ(m));
-	TD(m) = td-HTD(p2); ndl_sub(lcm,HDL(p2),DL(m));
+	if ( mod ) CM(m) = mod-HCM(p1); 
+	else chsgnq(HCQ(p1),&CQ(m));
+	ndl_sub(lcm,HDL(p2),DL(m));
 	if ( ndl_check_bound2(p->i2,DL(m)) ) {
 		nd_free(t1);
 		return 0;
@@ -2731,13 +2680,10 @@ void ndv_mul_c(int mod,NDV p,int mul)
 	NMV m;
 	int c,c1,len,i;
 
-	if ( !p )
-		return;
+	if ( !p ) return;
 	len = LEN(p);
 	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
-		c1 = CM(m);
-		DMAR(c1,mul,0,mod,c);
-		CM(m) = c;
+		c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c;
 	}
 }
 
@@ -2747,8 +2693,7 @@ void ndv_mul_c_q(NDV p,Q mul)
 	Q c;
 	int len,i;
 
-	if ( !p )
-		return;
+	if ( !p ) return;
 	len = LEN(p);
 	for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
 		mulq(CQ(m),mul,&c); CQ(m) = c;
@@ -2764,13 +2709,13 @@ ND ndv_mul_nm(int mod,NDV p,NM m0)
 	Q q;
 	ND r;
 
-	if ( !p )
-		return 0;
+	if ( !p ) return 0;
 	else {
 		n = NV(p); m = BDY(p);
-		d = DL(m0); td = TD(m0); 
+		d = DL(m0);
 		len = LEN(p);
 		mr0 = 0;
+		td = TD(d);
 		if ( mod ) {
 			c = CM(m0);
 			for ( i = 0; i < len; i++, NMV_ADV(m) ) {
@@ -2778,7 +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(mr) = TD(m)+td;
 				ndl_add(DL(m),d,DL(mr));
 			}
 		} else {
@@ -2786,13 +2730,12 @@ 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(mr) = TD(m)+td;
 				ndl_add(DL(m),d,DL(mr));
 			}
 		}
 		NEXT(mr) = 0; 
-		MKND(NV(p),mr0,r);
-		SG(r) = SG(p) + td;
+		MKND(NV(p),mr0,len,r);
+		SG(r) = SG(p) + TD(d);
 		return r;
 	}
 }
@@ -2807,20 +2750,15 @@ void ndv_realloc(NDV p,int obpe,int oadv)
 
 	if ( p ) {
 		m = BDY(p); len = LEN(p);
-		if ( nmv_adv > oadv )
-			mr0 = (NMV)REALLOC(BDY(p),len*nmv_adv);
-		else
-			mr0 = BDY(p);
+		mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p);
 		m = (NMV)((char *)mr0+(len-1)*oadv);
 		mr = (NMV)((char *)mr0+(len-1)*nmv_adv);
 		t = (NMV)ALLOCA(nmv_adv);
 		for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) {
 			CQ(t) = CQ(m);
-			TD(t) = TD(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);
-			TD(mr) = TD(t);
 			ndl_copy(DL(t),DL(mr));
 		}
 		BDY(p) = mr0;
@@ -2834,15 +2772,10 @@ NDV ndtondv(int mod,ND p)
 	NM t;
 	int i,len;
 
-	if ( !p )
-		return 0;
-	len = nd_length(p);	
-	if ( mod )
-		m0 = m = (NMV)MALLOC_ATOMIC(len*nmv_adv);
-	else
-		m0 = m = (NMV)MALLOC(len*nmv_adv);
+	if ( !p ) return 0;
+	len = LEN(p);
+	m0 = m = (NMV)(mod?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv));
 	for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) {
-		TD(m) = TD(t);
 		ndl_copy(DL(t),DL(m));
 		CQ(m) = CQ(t);
 	}
@@ -2858,18 +2791,16 @@ ND ndvtond(int mod,NDV p)
 	NMV t;
 	int i,len;
 
-	if ( !p )
-		return 0;
+	if ( !p ) return 0;
 	m0 = 0;
 	len = p->len;
 	for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) {
 		NEXTNM(m0,m);
-		TD(m) = TD(t);
 		ndl_copy(DL(t),DL(m));
 		CQ(m) = CQ(t);
 	}
 	NEXT(m) = 0;
-	MKND(NV(p),m0,d);
+	MKND(NV(p),m0,len,d);
 	SG(d) = SG(p);
 	return d;
 }
@@ -2882,8 +2813,7 @@ NDV dptondv(int mod,DP p)
 	DP q;
 	int l,i,n;
 
-	if ( !p )
-		return 0;
+	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;
@@ -2892,11 +2822,8 @@ NDV dptondv(int mod,DP p)
 		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) ) {
-		if ( mod )
-			CM(m) = ITOS(C(t));
-		else
-			CQ(m) = (Q)C(t);
-		TD(m) = TD(DL(t));
+		if ( mod ) CM(m) = ITOS(C(t));
+		else CQ(m) = (Q)C(t);
 		dltondl(n,DL(t),DL(m));
 	}
 	MKNDV(n,m0,l,d);
@@ -2911,18 +2838,15 @@ DP ndvtodp(int mod,NDV p)
 	NMV t;
 	int len,i,n;
 
-	if ( !p )
-		return 0;
+	if ( !p ) return 0;
 	m0 = 0;
 	len = LEN(p);
 	n = NV(p);
 	for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) {
 		NEXTMP(m0,m);
-		if ( mod ) 
-			C(m) = STOI(CM(t));
-		else
-			C(m) = (P)CQ(t);
-		DL(m) = ndltodl(n,TD(t),DL(t));
+		if ( mod ) C(m) = STOI(CM(t));
+		else C(m) = (P)CQ(t);
+		DL(m) = ndltodl(n,DL(t));
 	}
 	NEXT(m) = 0;
 	MKDP(NV(p),m0,d);
@@ -2935,8 +2859,7 @@ void ndv_print(NDV p)
 	NMV m;
 	int i,len;
     
-	if ( !p )
-		printf("0\n");
+	if ( !p ) printf("0\n");
 	else {
 		len = LEN(p);
 		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
@@ -2952,8 +2875,7 @@ void ndv_print_q(NDV p)
 	NMV m;
 	int i,len;
     
-	if ( !p )
-		printf("0\n");
+	if ( !p ) printf("0\n");
 	else {
 		len = LEN(p);
 		for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) {
@@ -2966,18 +2888,6 @@ void ndv_print_q(NDV p)
 	}
 }
 
-int nd_equal(ND a,ND b)
-{
-	NM ma,mb;
-
-	if ( (!a && b)||(a&& !b)||(NV(a) != NV(b))||(SG(a) != SG(b)) ) return 0;
-	for ( ma = BDY(a), mb = BDY(b); ma && mb; ma = NEXT(ma), mb = NEXT(mb) ) {
-		if ( (TD(ma) != TD(mb)) || !ndl_equal(DL(ma),DL(mb)) ) return 0;
-	}
-	if ( !ma && !mb ) return 1;
-	else return 0;
-}
-
 NODE nd_reducebase(NODE x)
 {
 	int len,i,j;
@@ -3000,3 +2910,29 @@ NODE nd_reducebase(NODE x)
 	NEXT(t) = 0; x = t0;
 	return x;
 }
+
+void nd_init_ord(struct order_spec *ord)
+{
+	if ( ord->id )
+		error("nd_gr : unsupported order");
+	nd_dcomp = 0;
+	switch ( ord->ord.simple ) {
+		case 0:
+			nd_dcomp = 1;
+			nd_isrlex = 1;
+			break;
+		case 1:
+			nd_dcomp = 1;
+			nd_isrlex = 0;
+			break;
+		case 9:
+			/* td1->td->rlex */
+			nd_dcomp = -dp_nelim;
+			nd_isrlex = 1;
+			break;
+		default:
+			error("nd_gr : unsupported order");
+	}
+	nd_ord = ord;
+}
+