=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v retrieving revision 1.38 retrieving revision 1.59 diff -u -p -r1.38 -r1.59 --- OpenXM_contrib2/asir2000/engine/nd.c 2003/08/20 08:56:29 1.38 +++ OpenXM_contrib2/asir2000/engine/nd.c 2003/09/05 13:20:14 1.59 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.37 2003/08/20 08:38:20 noro Exp $ */ +/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.58 2003/09/05 07:00:37 noro Exp $ */ #include "ca.h" #include "inline.h" @@ -15,11 +15,14 @@ #define REDTAB_LEN 32003 +/* GeoBucket for polynomial addition */ + typedef struct oPGeoBucket { int m; struct oND *body[32]; } *PGeoBucket; +/* distributed polynomial; linked list rep. */ typedef struct oND { struct oNM *body; int nv; @@ -27,6 +30,7 @@ typedef struct oND { int sugar; } *ND; +/* distributed polynomial; array rep. */ typedef struct oNDV { struct oNMV *body; int nv; @@ -34,6 +38,7 @@ typedef struct oNDV { int sugar; } *NDV; +/* monomial; linked list rep. */ typedef struct oNM { struct oNM *next; union { @@ -43,6 +48,7 @@ typedef struct oNM { unsigned int dl[1]; } *NM; +/* monomial; array rep. */ typedef struct oNMV { union { int m; @@ -51,6 +57,7 @@ typedef struct oNMV { unsigned int dl[1]; } *NMV; +/* history of reducer */ typedef struct oRHist { struct oRHist *next; int index; @@ -58,6 +65,7 @@ typedef struct oRHist { unsigned int dl[1]; } *RHist; +/* S-pair list */ typedef struct oND_pairs { struct oND_pairs *next; int i1,i2; @@ -65,35 +73,57 @@ typedef struct oND_pairs { unsigned int lcm[1]; } *ND_pairs; -int (*nd_compare_function)(unsigned int *a1,unsigned int *a2); +/* index and shift count for each exponent */ +typedef struct oEPOS { + int i; /* index */ + int s; /* shift */ +} *EPOS; -double nd_scale=2; +typedef struct oBlockMask { + int n; + struct order_pair *order_pair; + unsigned int **mask; +} *BlockMask; + +typedef struct oBaseSet { + int len; + NDV *ps; + unsigned int **bound; +} *BaseSet; + +int (*ndl_compare_function)(unsigned int *a1,unsigned int *a2); + +static double nd_scale=2; static unsigned int **nd_bound; -int nd_nvar; -int nd_isrlex; -int nd_epw,nd_bpe,nd_wpd; -unsigned int nd_mask[32]; -unsigned int nd_mask0,nd_mask1; +static struct order_spec *nd_ord; +static EPOS nd_epos; +static BlockMask nd_blockmask; +static int nd_nvar; +static int nd_isrlex; +static int nd_epw,nd_bpe,nd_wpd,nd_exporigin; +static unsigned int nd_mask[32]; +static unsigned int nd_mask0,nd_mask1; -NM _nm_free_list; -ND _nd_free_list; -ND_pairs _ndp_free_list; +static NM _nm_free_list; +static ND _nd_free_list; +static ND_pairs _ndp_free_list; static NDV *nd_ps; -static NDV *nd_psq; -RHist *nd_psh; -int nd_psn,nd_pslen; +static NDV *nd_ps_trace; +static RHist *nd_psh; +static int nd_psn,nd_pslen; -RHist *nd_red; -int nd_red_len; +static RHist *nd_red; -int nd_found,nd_create,nd_notfirst; -int nm_adv; -int nmv_adv; -int nd_dcomp; +static int nd_found,nd_create,nd_notfirst; +static int nm_adv; +static int nmv_adv; +static int nd_dcomp; -extern int Top,Reverse,dp_nelim; +extern int Top,Reverse,dp_nelim,do_weyl; +extern int *current_weyl_weight_vector; +/* fundamental macros */ #define TD(d) (d[0]) #define HDL(d) ((d)->body->dl) #define HTD(d) (TD(HDL(d))) @@ -105,16 +135,27 @@ extern int Top,Reverse,dp_nelim; #define SG(a) ((a)->sugar) #define LEN(a) ((a)->len) #define LCM(a) ((a)->lcm) +#define GET_EXP(d,a) (((d)[nd_epos[a].i]>>nd_epos[a].s)&nd_mask0) +#define PUT_EXP(r,a,e) ((r)[nd_epos[a].i] |= ((e)<TD(d2)?1:(TD(d1)TD(d2)?1:(TD(d1)0?TD_DL_COMPARE(d1,d2)\ + :(nd_dcomp==0?ndl_lex_compare(d1,d2)\ + :(nd_blockmask?ndl_block_compare(d1,d2)\ + :(*ndl_compare_function)(d1,d2)))) +#else +#define DL_COMPARE(d1,d2)\ +(nd_dcomp>0?TD_DL_COMPARE(d1,d2):(*ndl_compare_function)(d1,d2)) +#endif -#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv)) +/* allocators */ #define NEWRHist(r) \ -((r)=(RHist)MALLOC(sizeof(struct oRHist)+nd_wpd*sizeof(unsigned int))) +((r)=(RHist)MALLOC(sizeof(struct oRHist)+(nd_wpd-1)*sizeof(unsigned int))) #define NEWND_pairs(m) \ if(!_ndp_free_list)_NDP_alloc();\ (m)=_ndp_free_list; _ndp_free_list = NEXT(_ndp_free_list) @@ -125,29 +166,38 @@ 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)) +#define NMV_PREV(m) (m = (NMV)(((char *)m)-nmv_adv)) -void nd_init_ord(struct order_spec *spec); -int nd_check_candidate(NODE input,NODE cand); +/* external functions */ +void GC_gcollect(); +NODE append_one(NODE,int); + +/* manipulation of coefficients */ void nd_removecont(int mod,ND p); void nd_removecont2(ND p1,ND p2); -void ndv_removecont(int mod,NDV p); -void ndv_dehomogenize(NDV p); -void ndv_mul_c_q(NDV p,Q mul); -void nd_mul_c_q(ND p,Q mul); +void removecont_array(Q *c,int n); + +/* GeoBucket functions */ ND normalize_pbucket(int mod,PGeoBucket g); int head_pbucket(int mod,PGeoBucket g); int head_pbucket_q(PGeoBucket g); @@ -155,78 +205,108 @@ 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 trace,int homo,struct order_spec *ord,LIST *rp); NODE nd_gb(int m,int checkonly); NODE nd_gb_trace(int m); -void nd_free_private_storage(); -void _NM_alloc(); -void _ND_alloc(); -int ndl_td(unsigned int *d); + +/* ndl functions */ +int ndl_weight(unsigned int *d); +int ndl_weight_mask(unsigned int *d,int i); +void ndl_set_blockweight(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); -int nd_sp(int mod,ND_pairs p,ND *nf); -int nd_find_reducer(ND g); -int nd_find_reducer_direct(ND g,NDV *ps,int len); -int nd_nf(int mod,ND g,int full,ND *nf); -int nd_nf_pbucket(int mod,ND g,int full,ND *nf); -int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp); -int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp); -ND nd_reduce(ND p1,ND p2); -ND nd_reduce_special(ND p1,ND p2); +void ndl_reconstruct(int obpe,EPOS oepos,unsigned int *d,unsigned int *r); +INLINE int ndl_reducible(unsigned int *d1,unsigned int *d2); +INLINE int ndl_lex_compare(unsigned int *d1,unsigned int *d2); +INLINE int ndl_block_compare(unsigned int *d1,unsigned int *d2); +INLINE int ndl_equal(unsigned int *d1,unsigned int *d2); +INLINE void ndl_copy(unsigned int *d1,unsigned int *d2); +INLINE void ndl_add(unsigned int *d1,unsigned int *d2,unsigned int *d); +INLINE void ndl_addto(unsigned int *d1,unsigned int *d2); +INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d); +INLINE int ndl_hash_value(unsigned int *d); + +/* normal forms */ +INLINE int nd_find_reducer(ND g); +INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len); +int nd_sp(int mod,int trace,ND_pairs p,ND *nf); +int nd_nf(int mod,ND g,NDV *ps,int full,ND *nf); +int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *nf); +int nd_nf_direct(int mod,ND g,BaseSet base,int full,ND *rp); + +/* finalizers */ +NODE nd_reducebase(NODE x); NODE nd_reduceall(int m,NODE f); int nd_gbcheck(int m,NODE f); int nd_membercheck(int m,NODE f); + +/* allocators */ +void nd_free_private_storage(); +void _NM_alloc(); +void _ND_alloc(); void nd_free(ND p); -void ndv_free(NDV p); +void nd_free_redlist(); + +/* printing */ void ndl_print(unsigned int *dl); void nd_print(ND p); void nd_print_q(ND p); -void ndv_print(NDV p); -void ndv_print_q(NDV p); void ndp_print(ND_pairs d); -int nd_length(ND p); -void nd_mul_c(int mod,ND p,int mul); -void nd_free_redlist(); -void nd_append_red(unsigned int *d,int i); -unsigned int *nd_compute_bound(ND p); -unsigned int *dp_compute_bound(DP p); + + +/* setup, reconstruct */ +void nd_init_ord(struct order_spec *spec); ND_pairs nd_reconstruct(int mod,int trace,ND_pairs ndp); void nd_reconstruct_direct(int mod,NDV *ps,int len); +void nd_setup(int mod,int trace,NODE f); void nd_setup_parameters(); -void nd_realloc(ND p,int obpe); +BlockMask nd_create_blockmask(struct order_spec *ord); +EPOS nd_create_epos(struct order_spec *ord); +int nd_get_exporigin(struct order_spec *ord); + +/* ND functions */ +int nd_check_candidate(NODE input,NODE cand); +void nd_mul_c(int mod,ND p,int mul); +void nd_mul_c_q(ND p,Q mul); +ND nd_remove_head(ND p); +int nd_length(ND p); +void nd_append_red(unsigned int *d,int i); +unsigned int *ndv_compute_bound(NDV p); 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 */ +ND weyl_ndv_mul_nm(int mod,NM m0,NDV p); +void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *tab,int tlen); void ndv_mul_c(int mod,NDV p,int mul); +void ndv_mul_c_q(NDV p,Q mul); +void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos); +ND ndv_mul_nm(int mod,NM m0,NDV p); +void ndv_dehomogenize(NDV p,struct order_spec *spec); +void ndv_removecont(int mod,NDV p); +void ndv_print(NDV p); +void ndv_print_q(NDV p); +void ndv_free(NDV p); + +/* converters */ NDV ndtondv(int mod,ND p); ND ndvtond(int mod,NDV p); -ND ndv_mul_nm(int mod,NDV p,NM m0); -void ndv_realloc(NDV p,int obpe,int oadv); NDV dptondv(int,DP); DP ndvtodp(int,NDV); ND dptond(int,DP); @@ -247,7 +327,7 @@ 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 +350,7 @@ 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; } } @@ -296,7 +376,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int 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 +390,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int 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 +401,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int 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 +411,7 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int 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 +419,12 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int return 1; break; case 32: - for ( i = 1; i <= nd_wpd; i++ ) + for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d1[i] < d2[i] ) return 0; return 1; break; default: - for ( i = 1; i <= nd_wpd; i++ ) { + for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0; j < nd_epw; j++ ) if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0; @@ -359,35 +439,44 @@ void ndl_dehomogenize(unsigned int *d) unsigned int h; int i,bits; - if ( nd_isrlex ) { - if ( nd_bpe == 32 ) { - h = d[1]; - for ( i = 2; i <= nd_wpd; i++ ) - d[i-1] = d[i]; - d[i-1] = 0; - TD(d) -= h; + if ( nd_blockmask ) { + h = GET_EXP(d,nd_nvar-1); + XOR_EXP(d,nd_nvar-1,h); + TD(d) -= h; + d[nd_exporigin-1] -= h; + } else { + if ( nd_isrlex ) { + if ( nd_bpe == 32 ) { + h = d[nd_exporigin]; + for ( i = nd_exporigin+1; i < nd_wpd; i++ ) + d[i-1] = d[i]; + d[i-1] = 0; + TD(d) -= h; + } else { + bits = nd_epw*nd_bpe; + mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1); + h = (d[nd_exporigin]>>((nd_epw-1)*nd_bpe))&nd_mask0; + for ( i = nd_exporigin; i < nd_wpd; i++ ) + d[i] = ((d[i]<>((nd_epw-1)*nd_bpe))&nd_mask0):0); + TD(d) -= h; + } } else { - bits = nd_epw*nd_bpe; - mask = bits==32?0xffffffff:((1<<(nd_epw*nd_bpe))-1); - h = (d[1]>>((nd_epw-1)*nd_bpe))&nd_mask0; - for ( i = 1; i <= nd_wpd; i++ ) - d[i] = ((d[i]<>((nd_epw-1)*nd_bpe))&nd_mask0):0); + h = GET_EXP(d,nd_nvar-1); + XOR_EXP(d,nd_nvar-1,h); TD(d) -= h; } - } else - TD(d) -= ((d[(nd_nvar-1)/nd_epw+1]>> - ((nd_epw-((nd_nvar-1)%nd_epw)-1)*nd_bpe))&((1<t2?t1:t2; t1 = (u1&0xf000000); t2 = (u2&0xf000000); u |= t1>t2?t1:t2; @@ -401,7 +490,7 @@ 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 +501,7 @@ 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 +511,7 @@ 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 +519,13 @@ 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 +534,30 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in } break; } - TD(d) = ndl_td(d); + TD(d) = ndl_weight(d); + if ( nd_blockmask ) { + l = nd_blockmask->n; + for ( j = 0; j < l; j++ ) + d[j+1] = ndl_weight_mask(d,j); + } } -int ndl_td(unsigned int *d) +void ndl_set_blockweight(unsigned int *d) { + int l,j; + + if ( nd_blockmask ) { + l = nd_blockmask->n; + for ( j = 0; j < l; j++ ) + d[j+1] = ndl_weight_mask(d,j); + } +} + +int ndl_weight(unsigned int *d) { unsigned int t,u; int i,j; - for ( t = 0, i = 1; i <= nd_wpd; i++ ) { + for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) { u = d[i]; for ( j = 0; j < nd_epw; j++, u>>=nd_bpe ) t += (u&nd_mask0); @@ -461,11 +565,28 @@ int ndl_td(unsigned int *d) return t; } -INLINE int ndl_lex_compare(unsigned int *d1,unsigned int *d2) +int ndl_weight_mask(unsigned int *d,int index) { + unsigned int t,u; + unsigned int *mask; + int i,j; + + mask = nd_blockmask->mask[index]; + for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) { + u = d[i]&mask[i]; + for ( j = 0; j < nd_epw; j++, u>>=nd_bpe ) + t += (u&nd_mask0); + } + return t; +} + +int ndl_lex_compare(unsigned int *d1,unsigned int *d2) +{ int i; - for ( i = 0; i < nd_wpd; i++, d1++, d2++ ) + d1 += nd_exporigin; + d2 += nd_exporigin; + for ( i = nd_exporigin; i < nd_wpd; i++, d1++, d2++ ) if ( *d1 > *d2 ) return nd_isrlex ? -1 : 1; else if ( *d1 < *d2 ) @@ -473,12 +594,57 @@ INLINE int ndl_lex_compare(unsigned int *d1,unsigned i return 0; } +int ndl_block_compare(unsigned int *d1,unsigned int *d2) +{ + int i,l,j,ord_o,ord_l; + struct order_pair *op; + unsigned int t1,t2,m; + unsigned int *mask; + + l = nd_blockmask->n; + op = nd_blockmask->order_pair; + for ( j = 0; j < l; j++ ) { + mask = nd_blockmask->mask[j]; + ord_o = op[j].order; + if ( ord_o < 2 ) + if ( (t1=d1[j+1]) > (t2=d2[j+1]) ) return 1; + else if ( t1 < t2 ) return -1; + for ( i = nd_exporigin; i < nd_wpd; i++ ) { + m = mask[i]; + t1 = d1[i]&m; + t2 = d2[i]&m; + if ( t1 > t2 ) + return !ord_o ? -1 : 1; + else if ( t1 < t2 ) + return !ord_o ? 1 : -1; + } + } + return 0; +} + +/* TDH -> WW -> TD-> RL */ + +int ndl_ww_lex_compare(unsigned int *d1,unsigned int *d2) +{ + int i,m,e1,e2; + + if ( TD(d1) > TD(d2) ) return 1; + else if ( TD(d1) < TD(d2) ) return -1; + m = nd_nvar>>1; + for ( i = 0, e1 = e2 = 0; i < m; i++ ) { + e1 += current_weyl_weight_vector[i]*(GET_EXP(d1,m+i)-GET_EXP(d1,i)); + e2 += current_weyl_weight_vector[i]*(GET_EXP(d2,m+i)-GET_EXP(d2,i)); + } + if ( e1 > e2 ) return 1; + else if ( e1 < e2 ) return -1; + return ndl_lex_compare(d1,d2); +} + 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; @@ -489,17 +655,17 @@ 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; } @@ -509,28 +675,56 @@ INLINE void ndl_add(unsigned int *d1,unsigned int *d2, { int i; - TD(d) = TD(d1)+TD(d2); +#if 1 switch ( nd_wpd ) { - case 1: + case 2: + TD(d) = TD(d1)+TD(d2); d[1] = d1[1]+d2[1]; break; - case 2: + case 3: + TD(d) = TD(d1)+TD(d2); d[1] = d1[1]+d2[1]; d[2] = d1[2]+d2[2]; break; default: - for ( i = 1; i <= nd_wpd; i++ ) - d[i] = d1[i]+d2[i]; + for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; break; } +#else + for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; +#endif } +/* d1 += d2 */ +INLINE void ndl_addto(unsigned int *d1,unsigned int *d2) +{ + int i; + +#if 1 + switch ( nd_wpd ) { + case 2: + TD(d1) += TD(d2); + d1[1] += d2[1]; + break; + case 3: + TD(d1) += TD(d2); + d1[1] += d2[1]; + d1[2] += d2[2]; + break; + default: + for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i]; + break; + } +#else + for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i]; +#endif +} + INLINE void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d) { int i; - for ( i = 0; i <= nd_wpd; i++ ) - d[i] = d1[i]-d2[i]; + for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]-d2[i]; } int ndl_disjoint(unsigned int *d1,unsigned int *d2) @@ -540,7 +734,7 @@ 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; @@ -554,7 +748,7 @@ 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; @@ -565,7 +759,7 @@ 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; @@ -575,7 +769,7 @@ 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; @@ -583,12 +777,12 @@ 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; @@ -610,7 +804,7 @@ 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; @@ -624,7 +818,7 @@ 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; @@ -635,7 +829,7 @@ 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; @@ -645,7 +839,7 @@ 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; @@ -653,12 +847,12 @@ 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]>28)&0xf)+((u2>>28)&0xf) >= 0x10 ) return 1; - if ( ((u1>>24)&0xf)+((u2>>24)&0xf) >= 0x10 ) return 1; - if ( ((u1>>20)&0xf)+((u2>>20)&0xf) >= 0x10 ) return 1; - if ( ((u1>>16)&0xf)+((u2>>16)&0xf) >= 0x10 ) return 1; - if ( ((u1>>12)&0xf)+((u2>>12)&0xf) >= 0x10 ) return 1; - if ( ((u1>>8)&0xf)+((u2>>8)&0xf) >= 0x10 ) return 1; - if ( ((u1>>4)&0xf)+((u2>>4)&0xf) >= 0x10 ) return 1; - if ( (u1&0xf)+(u2&0xf) >= 0x10 ) return 1; + for ( i = nd_exporigin; i < nd_wpd; i++ ) { + u2 = d2[i]; + if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>20)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>16)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>12)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>8)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+((u2>>4)&0xf) >= 0x10 ) return 1; + if ( d1[ind++]+(u2&0xf) >= 0x10 ) return 1; } return 0; break; case 6: - for ( i = 1; i <= nd_wpd; i++ ) { - u1 = d1[i]; u2 = d2[i]; - if ( ((u1>>24)&0x3f)+((u2>>24)&0x3f) >= 0x40 ) return 1; - if ( ((u1>>18)&0x3f)+((u2>>18)&0x3f) >= 0x40 ) return 1; - if ( ((u1>>12)&0x3f)+((u2>>12)&0x3f) >= 0x40 ) return 1; - if ( ((u1>>6)&0x3f)+((u2>>6)&0x3f) >= 0x40 ) return 1; - if ( (u1&0x3f)+(u2&0x3f) >= 0x40 ) return 1; + for ( i = nd_exporigin; i < nd_wpd; i++ ) { + u2 = d2[i]; + if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1; + if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1; + if ( d1[ind++]+((u2>>12)&0x3f) >= 0x40 ) return 1; + if ( d1[ind++]+((u2>>6)&0x3f) >= 0x40 ) return 1; + if ( d1[ind++]+(u2&0x3f) >= 0x40 ) return 1; } return 0; break; case 8: - for ( i = 1; i <= nd_wpd; i++ ) { - u1 = d1[i]; u2 = d2[i]; - if ( ((u1>>24)&0xff)+((u2>>24)&0xff) >= 0x100 ) return 1; - if ( ((u1>>16)&0xff)+((u2>>16)&0xff) >= 0x100 ) return 1; - if ( ((u1>>8)&0xff)+((u2>>8)&0xff) >= 0x100 ) return 1; - if ( (u1&0xff)+(u2&0xff) >= 0x100 ) return 1; + for ( i = nd_exporigin; i < nd_wpd; i++ ) { + u2 = d2[i]; + if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1; + if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1; + if ( d1[ind++]+((u2>>8)&0xff) >= 0x100 ) return 1; + if ( d1[ind++]+(u2&0xff) >= 0x100 ) return 1; } return 0; break; case 16: - for ( i = 1; i <= nd_wpd; i++ ) { - u1 = d1[i]; u2 = d2[i]; - if ( ((u1>>16)&0xffff)+((u2>>16)&0xffff) > 0x10000 ) return 1; - if ( (u2&0xffff)+(u2&0xffff) > 0x10000 ) return 1; + for ( i = nd_exporigin; i < nd_wpd; i++ ) { + u2 = d2[i]; + if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1; + if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1; } return 0; break; case 32: - for ( i = 1; i <= nd_wpd; i++ ) + for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d1[i]+d2[i]>k)&nd_mask0)+((u2>>k)&nd_mask0) > nd_mask0 ) - return 1; + if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1; } return 0; break; @@ -742,7 +936,7 @@ 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; } @@ -754,6 +948,7 @@ 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)) ) { @@ -762,6 +957,7 @@ 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]; @@ -792,18 +988,14 @@ INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len if ( Reverse ) for ( i = len-1; i >= 0; i-- ) { r = ps[i]; - if ( ndl_reducible(HDL(g),HDL(r)) ) { - nd_append_red(HDL(g),i); + if ( ndl_reducible(HDL(g),HDL(r)) ) return i; - } } else for ( i = 0; i < len; i++ ) { r = ps[i]; - if ( ndl_reducible(HDL(g),HDL(r)) ) { - nd_append_red(HDL(g),i); + if ( ndl_reducible(HDL(g),HDL(r)) ) return i; - } } return -1; } @@ -905,7 +1097,7 @@ ND nd_add_q(ND p1,ND p2) } /* ret=1 : success, ret=0 : overflow */ -int nd_nf(int mod,ND g,int full,ND *rp) +int nd_nf(int mod,ND g,NDV *ps,int full,ND *rp) { ND d; NM m,mrd,tail; @@ -925,7 +1117,7 @@ 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 ) { @@ -935,17 +1127,16 @@ int nd_nf(int mod,ND g,int full,ND *rp) nd_free(g); nd_free(d); return 0; } + p = ps[index]; if ( mod ) { - p = nd_ps[index]; c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { - p = nd_psq[index]; igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred); chsgnq(cg,&CQ(mul)); nd_mul_c_q(d,cred); nd_mul_c_q(g,cred); } - g = nd_add(mod,g,ndv_mul_nm(mod,p,mul)); + g = nd_add(mod,g,ndv_mul_nm(mod,mul,p)); sugar = MAX(sugar,SG(p)+TD(DL(mul))); if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) { nd_removecont2(d,g); @@ -973,7 +1164,7 @@ int nd_nf(int mod,ND g,int full,ND *rp) return 1; } -int nd_nf_pbucket(int mod,ND g,int full,ND *rp) +int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp) { int hindex,index; NDV p; @@ -997,7 +1188,7 @@ 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 ) { @@ -1016,12 +1207,11 @@ int nd_nf_pbucket(int mod,ND g,int full,ND *rp) *rp = 0; return 0; } + p = ps[index]; if ( mod ) { - p = nd_ps[index]; c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { - p = nd_psq[index]; igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred); chsgnq(cg,&CQ(mul)); nd_mul_c_q(d,cred); @@ -1029,7 +1219,7 @@ int nd_nf_pbucket(int mod,ND g,int full,ND *rp) g = bucket->body[hindex]; gmag = (double)p_mag((P)HCQ(g)); } - red = ndv_mul_nm(mod,p,mul); + red = ndv_mul_nm(mod,mul,p); bucket->body[hindex] = nd_remove_head(g); red = nd_remove_head(red); add_pbucket(mod,bucket,red); @@ -1069,13 +1259,15 @@ int nd_nf_pbucket(int mod,ND g,int full,ND *rp) } } -int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full,ND *rp) +int nd_nf_direct(int mod,ND g,BaseSet base,int full,ND *rp) { ND d; NM m,mrd,tail; NM mul; - int n,sugar,psugar,sugar0,stat,index; + NDV *ps; + int n,sugar,psugar,sugar0,stat,index,len; int c,c1,c2; + unsigned int **bound; RHist h; NDV p,red; Q cg,cred,gcd; @@ -1093,15 +1285,18 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full hmag = 0; #endif + ps = base->ps; + bound = base->bound; + len = base->len; sugar0 = sugar = SG(g); n = NV(g); - mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int)); + mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int)); for ( d = 0; g; ) { index = nd_find_reducer_direct(g,ps,len); if ( index >= 0 ) { p = ps[index]; ndl_sub(HDL(g),HDL(p),DL(mul)); - if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) { + if ( ndl_check_bound2_direct(bound[index],DL(mul)) ) { nd_free(g); nd_free(d); return 0; } @@ -1113,7 +1308,7 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full chsgnq(cg,&CQ(mul)); nd_mul_c_q(d,cred); nd_mul_c_q(g,cred); } - g = nd_add(mod,g,ndv_mul_nm(mod,p,mul)); + g = nd_add(mod,g,ndv_mul_nm(mod,mul,p)); sugar = MAX(sugar,SG(p)+TD(DL(mul))); if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) { nd_removecont2(d,g); @@ -1141,124 +1336,36 @@ int nd_nf_direct(int mod,ND g,NDV *ps,int len,int full return 1; } -int nd_nf_direct_pbucket(int mod,ND g,NDV *ps,int len,int full,ND *rp) -{ - int hindex,index; - NDV p; - ND u,d,red; - NODE l; - NM mul,m,mrd,tail; - int sugar,psugar,n,h_reducible; - PGeoBucket bucket; - int c,c1,c2; - Q cg,cred,gcd,zzz; - RHist h; - double hmag,gmag; - - if ( !g ) { - *rp = 0; - return 1; - } - sugar = SG(g); - n = NV(g); -#if 0 - if ( !mod ) - hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; -#else - /* XXX */ - hmag = 0; -#endif - bucket = create_pbucket(); - add_pbucket(mod,bucket,g); - d = 0; - mul = (NM)ALLOCA(sizeof(struct oNM)+nd_wpd*sizeof(unsigned int)); - while ( 1 ) { - hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket); - if ( hindex < 0 ) { - if ( d ) - SG(d) = sugar; - *rp = d; - return 1; - } - g = bucket->body[hindex]; - index = nd_find_reducer_direct(g,ps,len); - if ( index >= 0 ) { - p = ps[index]; - ndl_sub(HDL(g),HDL(p),DL(mul)); - if ( ndl_check_bound2_direct(HDL(p),DL(mul)) ) { - nd_free(d); - free_pbucket(bucket); - *rp = 0; - return 0; - } - if ( mod ) { - c1 = invm(HCM(p),mod); c2 = mod-HCM(g); - DMAR(c1,c2,0,mod,c); CM(mul) = c; - } else { - igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred); - chsgnq(cg,&CQ(mul)); - nd_mul_c_q(d,cred); - mulq_pbucket(bucket,cred); - g = bucket->body[hindex]; - gmag = (double)p_mag((P)HCQ(g)); - } - red = ndv_mul_nm(mod,p,mul); - bucket->body[hindex] = nd_remove_head(g); - red = nd_remove_head(red); - add_pbucket(mod,bucket,red); - sugar = MAX(sugar,SG(p)+TD(DL(mul))); - if ( !mod && hmag && (gmag > hmag) ) { - g = normalize_pbucket(mod,bucket); - if ( !g ) { - if ( d ) SG(d) = sugar; - *rp = d; - return 1; - } - nd_removecont2(d,g); - hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; - add_pbucket(mod,bucket,g); - } - } else if ( !full ) { - g = normalize_pbucket(mod,bucket); - if ( g ) SG(g) = sugar; - *rp = g; - return 1; - } else { - m = BDY(g); - if ( NEXT(m) ) { - BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--; - } else { - FREEND(g); g = 0; - } - bucket->body[hindex] = g; - NEXT(m) = 0; - if ( d ) { - NEXT(tail)=m; tail=m; LEN(d)++; - } else { - MKND(n,m,1,d); tail = BDY(d); - } - } - } -} - /* input : list of DP, cand : list of DP */ int nd_check_candidate(NODE input,NODE cand) { int n,i,stat; ND nf,d; - NODE t; + NODE t,s; - nd_setup(0,cand); +#if 0 + for ( t = 0; cand; cand = NEXT(cand) ) { + MKNODE(s,BDY(cand),t); t = s; + } + cand = t; +#endif + + nd_setup(0,0,cand); n = length(cand); /* membercheck : list is a subset of Id(cand) ? */ for ( t = input; t; t = NEXT(t) ) { +again: d = dptond(0,(DP)BDY(t)); - stat = nd_nf_direct(0,d,nd_psq,n,0,&nf); - if ( !stat ) nd_reconstruct_direct(0,nd_psq,n); - else if ( nf ) return 0; + stat = nd_nf(0,d,nd_ps,0,&nf); + if ( !stat ) { + nd_reconstruct(0,0,0); + goto again; + } else if ( nf ) return 0; + printf("."); fflush(stdout); } + printf("\n"); /* gbcheck : cand is a GB of Id(cand) ? */ if ( !nd_gb(0,1) ) return 0; /* XXX */ @@ -1444,13 +1551,17 @@ again: sugar = SG(l); fprintf(asir_out,"%d",sugar); } - stat = nd_sp(m,l,&h); + stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(m,0,d); goto again; } - stat = m?nd_nf_pbucket(m,h,!Top,&nf):nd_nf(m,h,!Top,&nf); +#if USE_GEOBUCKET + stat = m?nd_nf_pbucket(m,h,nd_ps,!Top,&nf):nd_nf(m,h,nd_ps,!Top,&nf); +#else + stat = nd_nf(m,h,nd_ps,!Top,&nf); +#endif if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(m,0,d); @@ -1458,7 +1569,7 @@ again: } else if ( nf ) { if ( checkonly ) return 0; printf("+"); fflush(stdout); - nh = nd_newps(m,nf); + nh = nd_newps(m,nf,0); d = update_pairs(d,g,nh); g = update_base(g,nh); FREENDP(l); @@ -1467,10 +1578,7 @@ again: FREENDP(l); } } - if ( m ) - 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_ps[(int)BDY(t)]; return g; } @@ -1495,24 +1603,28 @@ again: sugar = SG(l); fprintf(asir_out,"%d",sugar); } - stat = nd_sp(m,l,&h); + stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(m,1,d); goto again; } - stat = nd_nf_pbucket(m,h,!Top,&nf); +#if USE_GEOBUCKET + stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf); +#else + stat = nd_nf(m,h,nd_ps,!Top,&nf); +#endif if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(m,1,d); goto again; } else if ( nf ) { /* overflow does not occur */ - nd_sp(0,l,&h); - nd_nf(0,h,!Top,&nfq); + nd_sp(0,1,l,&h); + nd_nf(0,h,nd_ps_trace,!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 ( nh < 0 ) return 0; d = update_pairs(d,g,nh); @@ -1526,7 +1638,7 @@ again: FREENDP(l); } for ( t = g; t; t = NEXT(t) ) - BDY(t) = (pointer)nd_psq[(int)BDY(t)]; + BDY(t) = (pointer)nd_ps_trace[(int)BDY(t)]; return g; } @@ -1546,33 +1658,49 @@ NODE nd_reduceall(int m,NODE f) NDV *w,*ps; ND nf,g; NODE t,a0,a; + struct oBaseSet base; + unsigned int **bound; for ( n = 0, t = f; t; t = NEXT(t), n++ ); ps = (NDV *)ALLOCA(n*sizeof(NDV)); - for ( i = 0, t = f; i < n; i++, t = NEXT(t) ) - ps[i] = (NDV)BDY(t); + bound = (unsigned int **)ALLOCA(n*sizeof(unsigned int *)); + for ( i = 0, t = f; i < n; i++, t = NEXT(t) ) ps[i] = (NDV)BDY(t); 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 ( i = 0; i < n; i++ ) bound[i] = ndv_compute_bound(ps[i]); + base.ps = (NDV *)ALLOCA((n-1)*sizeof(NDV)); + base.bound = (unsigned int **)ALLOCA((n-1)*sizeof(unsigned int *)); + base.len = n-1; + i = 0; + while ( i < n ) { + for ( j = 0; j < i; j++ ) { + base.ps[j] = ps[j]; base.bound[j] = bound[j]; + } + for ( j = i+1; j < n; j++ ) { + base.ps[j-1] = ps[j]; base.bound[j-1] = bound[j]; + } g = ndvtond(m,ps[i]); - stat = nd_nf_direct(m,g,w,n-1,1,&nf); + stat = nd_nf_direct(m,g,&base,1,&nf); if ( !stat ) nd_reconstruct_direct(m,ps,n); else if ( !nf ) { printf("."); fflush(stdout); ndv_free(ps[i]); - for ( j = i+1; j < n; j++ ) ps[j-1] = ps[j]; + for ( j = i+1; j < n; j++ ) { + ps[j-1] = ps[j]; bound[j-1] = bound[j]; + } n--; + base.len = n-1; } else { printf("."); fflush(stdout); ndv_free(ps[i]); nd_removecont(m,nf); ps[i] = ndtondv(m,nf); + bound[i] = ndv_compute_bound(ps[i]); nd_free(nf); + i++; } } + printf("\n"); for ( a0 = 0, i = 0; i < n; i++ ) { NEXTNODE(a0,a); BDY(a) = (pointer)ps[i]; @@ -1590,15 +1718,19 @@ ND_pairs update_pairs( ND_pairs d, NODE /* of index */ d1 = nd_newpairs(g,t); d1 = crit_M(d1); d1 = crit_F(d1); - prev = 0; cur = head = d1; - while ( cur ) { - if ( crit_2( cur->i1,cur->i2 ) ) { - remove = cur; - if ( !prev ) head = cur = NEXT(cur); - else cur = NEXT(prev) = NEXT(cur); - FREENDP(remove); - } else { - prev = cur; cur = NEXT(cur); + if ( do_weyl ) + head = d1; + else { + prev = 0; cur = head = d1; + while ( cur ) { + if ( crit_2( cur->i1,cur->i2 ) ) { + remove = cur; + if ( !prev ) head = cur = NEXT(cur); + else cur = NEXT(prev) = NEXT(cur); + FREENDP(remove); + } else { + prev = cur; cur = NEXT(cur); + } } } if ( !d ) @@ -1642,7 +1774,7 @@ 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) @@ -1662,8 +1794,6 @@ ND_pairs crit_B( ND_pairs d, int s ) return head; } -/* XXX : check is necessary */ - ND_pairs crit_M( ND_pairs d1 ) { ND_pairs e,d2,d3,dd,p; @@ -1750,7 +1880,7 @@ 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; @@ -1762,11 +1892,9 @@ 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; @@ -1808,9 +1936,7 @@ 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 { @@ -1821,132 +1947,67 @@ 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; 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 ( aq ) { + /* trace lifting */ + if ( !rem(NM(HCQ(aq)),mod) ) + return -1; } - 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_ps_trace = (NDV *)REALLOC((char *)nd_ps_trace,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 ( !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); + NEWRHist(r); nd_psh[nd_psn] = r; + nd_removecont(mod,a); nd_ps[nd_psn] = ndtondv(mod,a); + if ( aq ) { + nd_removecont(0,aq); nd_ps_trace[nd_psn] = ndtondv(0,aq); + nd_bound[nd_psn] = ndv_compute_bound(nd_ps_trace[nd_psn]); + SG(r) = SG(aq); ndl_copy(HDL(aq),DL(r)); + nd_free(a); nd_free(aq); + } else { + nd_bound[nd_psn] = ndv_compute_bound(nd_ps[nd_psn]); + SG(r) = SG(a); ndl_copy(HDL(a),DL(r)); + nd_free(a); + } 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; unsigned int *d; RHist r; NDV a; + MP t; 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_ps_trace = (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) ) { - 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; - } -} - -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_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)); + for ( max = 0, s = f; s; s = NEXT(s) ) + for ( t = BDY((DP)BDY(s)); t; t = NEXT(t) ) { + d = t->dl->d; + for ( j = 0; j < nd_nvar; j++ ) max = MAX(d[j],max); + } + if ( max < 2 ) nd_bpe = 2; else if ( max < 4 ) nd_bpe = 4; else if ( max < 64 ) nd_bpe = 6; @@ -1956,13 +2017,16 @@ 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)); + nd_ps[i] = a; + if ( trace ) { + a = dptondv(0,(DP)BDY(f)); ndv_removecont(0,a); + nd_ps_trace[i] = a; + } + nd_bound[i] = ndv_compute_bound(a); nd_psh[i] = r; } } @@ -1984,10 +2048,11 @@ void nd_gr(LIST f,LIST v,int m,struct order_spec *ord, NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; } if ( fd0 ) NEXT(fd) = 0; - nd_setup(m,fd0); + nd_setup(m,0,fd0); x = nd_gb(m,0); fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n", nd_found,nd_notfirst,nd_create); + x = nd_reducebase(x); x = nd_reduceall(m,x); for ( r0 = 0, t = x; t; t = NEXT(t) ) { NEXTNODE(r0,r); @@ -2003,16 +2068,27 @@ void nd_gr(LIST f,LIST v,int m,struct order_spec *ord, MKLIST(*rp,r0); } -void nd_gr_trace(LIST f,LIST v,int m,int homo,struct order_spec *ord,LIST *rp) +void nd_gr_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp) { struct order_spec ord1; VL fv,vv,vc; NODE fd,fd0,in0,in,r,r0,t,s,cand; + int m,nocheck,nvar,mindex; DP a,b,c,h; P p; get_vars((Obj)f,&fv); pltovl(v,&vv); - nd_nvar = length(vv); + nvar = length(vv); + nocheck = 0; + mindex = 0; + + /* setup modulus */ + if ( trace < 0 ) { + trace = -trace; + nocheck = 1; + } + m = trace > 1 ? trace : get_lprime(mindex); + initd(ord); if ( homo ) { homogenize_order(ord,nd_nvar,&ord1); @@ -2025,9 +2101,6 @@ 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 { for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { ptod(CO,vv,(P)BDY(t),&c); @@ -2037,21 +2110,37 @@ 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); + while ( 1 ) { + if ( homo ) { + nd_init_ord(&ord1); + initd(&ord1); + nd_nvar = nvar+1; + } else { + nd_init_ord(ord); + nd_nvar = nvar; + } + nd_setup(m,1,fd0); cand = nd_gb_trace(m); - if ( !cand ) continue; + if ( !cand ) { + /* failure */ + if ( trace > 1 ) { + *rp = 0; return; + } else + m = get_lprime(++mindex); + continue; + } + if ( homo ) { /* dehomogenization */ for ( t = cand; t; t = NEXT(t) ) - ndv_dehomogenize((NDV)BDY(t)); - nd_nvar--; - nd_setup_parameters(); + ndv_dehomogenize((NDV)BDY(t),ord); + nd_nvar = nvar; initd(ord); - cand = nd_reducebase(cand); + nd_init_ord(ord); + nd_setup_parameters(); } + cand = nd_reducebase(cand); fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n", nd_found,nd_notfirst,nd_create); cand = nd_reduceall(0,cand); @@ -2062,7 +2151,16 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o } if ( r0 ) NEXT(r) = 0; cand = r0; - } while ( !nd_check_candidate(in0,cand) ); + if ( nocheck || nd_check_candidate(in0,cand) ) + /* success */ + break; + else if ( trace > 1 ) { + /* failure */ + *rp = 0; return; + } else + /* try the next modulus */ + m = get_lprime(++mindex); + } /* dp->p */ for ( r = cand; r; r = NEXT(r) ) { dtop(CO,vv,BDY(r),&p); @@ -2074,36 +2172,47 @@ void nd_gr_trace(LIST f,LIST v,int m,int homo,struct o void dltondl(int n,DL dl,unsigned int *r) { unsigned int *d; - int i; + int i,j,l,s,ord_l; + struct order_pair *op; d = dl->d; - 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)); - else - for ( i = 0; i < n; i++ ) - r[i/nd_epw+1] |= d[i]<<((nd_epw-(i%nd_epw)-1)*nd_bpe); - TD(r) = ndl_td(r); + for ( i = 0; i < nd_wpd; i++ ) r[i] = 0; + if ( nd_blockmask ) { + l = nd_blockmask->n; + op = nd_blockmask->order_pair; + for ( j = 0, s = 0; j < l; j++ ) { + ord_l = op[j].length; + for ( i = 0; i < ord_l; i++, s++ ) PUT_EXP(r,s,d[s]); + } + TD(r) = ndl_weight(r); + for ( j = 0; j < l; j++ ) + r[j+1] = ndl_weight_mask(r,j); + } else { + for ( i = 0; i < n; i++ ) PUT_EXP(r,i,d[i]); + TD(r) = ndl_weight(r); + } } DL ndltodl(int n,unsigned int *ndl) { DL dl; int *d; - int i; + int i,j,l,s,ord_l; + struct order_pair *op; NEWDL(dl,n); dl->td = TD(ndl); d = dl->d; - if ( nd_isrlex ) - for ( i = 0; i < n; i++ ) - d[i] = (ndl[(n-1-i)/nd_epw+1]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe)) - &((1<>((nd_epw-(i%nd_epw)-1)*nd_bpe)) - &((1<n; + op = nd_blockmask->order_pair; + for ( j = 0, s = 0; j < l; j++ ) { + ord_l = op[j].length; + for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s); + } + } else { + for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i); + } return dl; } @@ -2156,20 +2265,22 @@ DP ndtodp(int mod,ND p) void ndl_print(unsigned int *dl) { int n; - int i; + int i,j,l,ord_l,s,s0; + struct order_pair *op; n = nd_nvar; printf("<<"); - if ( nd_isrlex ) - for ( i = 0; i < n; i++ ) - printf(i==n-1?"%d":"%d,", - (dl[(n-1-i)/nd_epw+1]>>((nd_epw-((n-1-i)%nd_epw)-1)*nd_bpe)) - &((1<>((nd_epw-(i%nd_epw)-1)*nd_bpe)) - &((1<n; + op = nd_blockmask->order_pair; + for ( j = 0, s = s0 = 0; j < l; j++ ) { + ord_l = op[j].length; + for ( i = 0; i < ord_l; i++, s++ ) + printf(s==n-1?"%d":"%d,",GET_EXP(dl,s)); + } + } else { + for ( i = 0; i < n; i++ ) printf(i==n-1?"%d":"%d,",GET_EXP(dl,i)); + } printf(">>"); } @@ -2282,25 +2393,27 @@ void ndv_removecont(int mod,NDV p) } } -void ndv_dehomogenize(NDV p) +void ndv_dehomogenize(NDV p,struct order_spec *ord) { - int i,len,newnvar,newwpd,newadv; + int i,j,adj,len,newnvar,newwpd,newadv,newexporigin; Q *w; Q dvr,t; NMV m,r; - unsigned int *d; #define NEWADV(m) (m = (NMV)(((char *)m)+newadv)) len = p->len; newnvar = nd_nvar-1; - newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0); + newexporigin = nd_get_exporigin(ord); + newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0)+newexporigin; for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) ndl_dehomogenize(DL(m)); if ( newwpd != nd_wpd ) { - d = (unsigned int *)ALLOCA((newwpd+1)*sizeof(unsigned int)); - newadv = sizeof(struct oNMV)+newwpd*sizeof(unsigned int); + newadv = sizeof(struct oNMV)+(newwpd-1)*sizeof(unsigned int); for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NEWADV(r), i++ ) { - CQ(r) = CQ(m); ndl_copy(DL(m),d); ndl_copy(d,DL(r)); + CQ(r) = CQ(m); + for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j]; + adj = nd_exporigin-newexporigin; + for ( ; j < newwpd; j++ ) DL(r)[j] = DL(m)[j+adj]; } } NV(p)--; @@ -2397,61 +2510,59 @@ void nd_append_red(unsigned int *d,int i) nd_red[h] = m; } -unsigned int *dp_compute_bound(DP p) +unsigned int *ndv_compute_bound(NDV p) { - unsigned int *d,*d1,*d2,*t; - MP m; - int i,l; - - if ( !p ) - return 0; - d1 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int)); - d2 = (unsigned int *)ALLOCA(nd_nvar*sizeof(unsigned int)); - m = BDY(p); - 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++ ) - d2[i] = d[i] > d1[i] ? d[i] : d1[i]; - t = d1; d1 = d2; d2 = t; - } - l = (nd_nvar+31); - t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int)); - for ( i = 0; i < nd_nvar; i++ ) t[i] = d1[i]; - for ( ; i < l; i++ ) t[i] = 0; - return t; -} - -unsigned int *nd_compute_bound(ND p) -{ unsigned int *d1,*d2,*t; - int i,l; - NM m; + unsigned int u; + int i,j,k,l,len,ind; + NMV m; if ( !p ) return 0; d1 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int)); d2 = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int)); - ndl_copy(HDL(p),d1); - for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) { + len = LEN(p); + m = BDY(p); ndl_copy(DL(m),d1); NMV_ADV(m); + for ( i = 1; i < len; i++, NMV_ADV(m) ) { ndl_lcm(DL(m),d1,d2); t = d1; d1 = d2; d2 = t; } l = nd_nvar+31; t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int)); - 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; - for ( ; i < l; i++ ) t[i] = 0; + for ( i = nd_exporigin, ind = 0; i < nd_wpd; i++ ) { + u = d1[i]; + k = (nd_epw-1)*nd_bpe; + for ( j = 0; j < nd_epw; j++, k -= nd_bpe, ind++ ) + t[ind] = (u>>k)&nd_mask0; + } + for ( ; ind < l; ind++ ) t[ind] = 0; return t; } +int nd_get_exporigin(struct order_spec *ord) +{ + switch ( ord->id ) { + case 0: + return 1; + case 1: + /* block order */ + /* d[0]:weight d[1]:w0,...,d[nd_exporigin-1]:w(n-1) */ + return ord->ord.block.length+1; + case 2: + error("nd_get_exporigin : matrix order is not supported yet."); + } +} + void nd_setup_parameters() { - int i; + int i,j,n,elen,ord_o,ord_l,l,s; + struct order_pair *op; nd_epw = (sizeof(unsigned int)*8)/nd_bpe; - nd_wpd = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0); + elen = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0); + + nd_exporigin = nd_get_exporigin(nd_ord); + nd_wpd = nd_exporigin+elen; + if ( nd_bpe < 32 ) { nd_mask0 = (1< realloc nd_ps and pd_psq */ - ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d) { int i,obpe,oadv,h; @@ -2477,9 +2588,11 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d) RHist r; RHist *old_red; ND_pairs s0,s,t,prev_ndp_free_list; + EPOS oepos; obpe = nd_bpe; oadv = nmv_adv; + oepos = nd_epos; if ( obpe < 4 ) nd_bpe = 4; else if ( obpe < 6 ) nd_bpe = 6; else if ( obpe < 8 ) nd_bpe = 8; @@ -2492,17 +2605,17 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d) prev_ndp_free_list = _ndp_free_list; _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); - 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_ps[i],obpe,oadv,oepos); + if ( trace ) + for ( i = nd_psn-1; i >= 0; i-- ) + ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos); s0 = 0; for ( t = d; t; t = NEXT(t) ) { NEXTND_pairs(s0,s); s->i1 = t->i1; s->i2 = t->i2; SG(s) = SG(t); - ndl_dup(obpe,LCM(t),LCM(s)); + ndl_reconstruct(obpe,oepos,LCM(t),LCM(s)); } old_red = (RHist *)ALLOCA(REDTAB_LEN*sizeof(RHist)); @@ -2515,7 +2628,7 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d) NEWRHist(mr); mr->index = r->index; SG(mr) = SG(r); - ndl_dup(obpe,DL(r),DL(mr)); + ndl_reconstruct(obpe,oepos,DL(r),DL(mr)); h = ndl_hash_value(DL(mr)); NEXT(mr) = nd_red[h]; nd_red[h] = mr; @@ -2524,7 +2637,7 @@ ND_pairs nd_reconstruct(int mod,int trace,ND_pairs d) old_red = 0; for ( i = 0; i < nd_psn; i++ ) { NEWRHist(r); SG(r) = SG(nd_psh[i]); - ndl_dup(obpe,DL(nd_psh[i]),DL(r)); + ndl_reconstruct(obpe,oepos,DL(nd_psh[i]),DL(r)); nd_psh[i] = r; } if ( s0 ) NEXT(s) = 0; @@ -2537,14 +2650,17 @@ 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,h; + unsigned int **bound; NM prev_nm_free_list; RHist mr0,mr; RHist r; RHist *old_red; ND_pairs s0,s,t,prev_ndp_free_list; + EPOS oepos; obpe = nd_bpe; oadv = nmv_adv; + oepos = nd_epos; if ( obpe < 4 ) nd_bpe = 4; else if ( obpe < 6 ) nd_bpe = 6; else if ( obpe < 8 ) nd_bpe = 8; @@ -2556,80 +2672,53 @@ 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); - 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_dup(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; + for ( i = len-1; i >= 0; i-- ) ndv_realloc(ps[i],obpe,oadv,oepos); prev_nm_free_list = 0; prev_ndp_free_list = 0; GC_gcollect(); } -void ndl_dup(int obpe,unsigned int *d,unsigned int *r) +void ndl_reconstruct(int obpe,EPOS oepos,unsigned int *d,unsigned int *r) { - int n,i,ei,oepw,cepw,cbpe; + int n,i,ei,oepw,omask0,j,s,ord_l,l; + struct order_pair *op; +#define GET_EXP_OLD(d,a) (((d)[oepos[a].i]>>oepos[a].s)&omask0) +#define PUT_EXP_OLD(r,a,e) ((r)[oepos[a].i] |= ((e)<>((oepw-((n-1-i)%oepw)-1)*obpe)) - &((1<n; + op = nd_blockmask->order_pair; + for ( i = 1; i < nd_exporigin; i++ ) + r[i] = d[i]; + for ( j = 0, s = 0; j < l; j++ ) { + ord_l = op[j].length; + for ( i = 0; i < ord_l; i++, s++ ) { + ei = GET_EXP_OLD(d,s); + PUT_EXP(r,s,ei); + } } - else + } else { for ( i = 0; i < n; i++ ) { - ei = (d[i/oepw+1]>>((oepw-(i%oepw)-1)*obpe)) - &((1<i1]; p2 = nd_ps[p->i2]; + if ( trace ) { + p1 = nd_ps_trace[p->i1]; p2 = nd_ps_trace[p->i2]; } else { - p1 = nd_psq[p->i1]; p2 = nd_psq[p->i2]; + p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2]; } lcm = LCM(p); NEWNM(m); CQ(m) = HCQ(p2); 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 ( ndl_check_bound2(p->i1,DL(m)) ) + return 0; + t1 = ndv_mul_nm(mod,m,p1); if ( mod ) CM(m) = mod-HCM(p1); else chsgnq(HCQ(p1),&CQ(m)); ndl_sub(lcm,HDL(p2),DL(m)); @@ -2668,7 +2758,7 @@ int nd_sp(int mod,ND_pairs p,ND *rp) nd_free(t1); return 0; } - t2 = ndv_mul_nm(mod,p2,m); + t2 = ndv_mul_nm(mod,m,p2); *rp = nd_add(mod,t1,t2); FREENM(m); return 1; @@ -2699,8 +2789,142 @@ void ndv_mul_c_q(NDV p,Q mul) } } -ND ndv_mul_nm(int mod,NDV p,NM m0) +ND weyl_ndv_mul_nm(int mod,NM m0,NDV p) { + int n2,i,j,l,n,tlen; + unsigned int *d0; + NM *tab,*psum; + ND s,r; + NM t; + NMV m1; + + if ( !p ) return 0; + n = NV(p); n2 = n>>1; + d0 = DL(m0); + l = LEN(p); + for ( i = 0, tlen = 1; i < n2; i++ ) tlen *= (GET_EXP(d0,n2+i)+1); + tab = (NM *)ALLOCA(tlen*sizeof(NM)); + psum = (NM *)ALLOCA(tlen*sizeof(NM)); + for ( i = 0; i < tlen; i++ ) psum[i] = 0; + m1 = (NMV)(((char *)BDY(p))+nmv_adv*(l-1)); + for ( i = l-1; i >= 0; i--, NMV_PREV(m1) ) { + /* m0(NM) * m1(NMV) => tab(NM) */ + weyl_mul_nm_nmv(n,mod,m0,m1,tab,tlen); + for ( j = 0; j < tlen; j++ ) { + if ( tab[j] ) { + NEXT(tab[j]) = psum[j]; psum[j] = tab[j]; + } + } + } + for ( i = tlen-1, r = 0; i >= 0; i-- ) + if ( psum[i] ) { + for ( j = 0, t = psum[i]; t; t = NEXT(t), j++ ); + MKND(n,psum[i],j,s); + r = nd_add(mod,r,s); + } + if ( r ) SG(r) = SG(p)+TD(d0); + return r; +} + +/* product of monomials */ +/* XXX block order is not handled correctly */ + +void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *tab,int tlen) { + int i,n2,j,s,curlen,homo,h,a,b,k,l,u,min; + unsigned int *d0,*d1,*d,*dt,*ctab; + Q *ctab_q; + Q q,q1; + unsigned int c0,c1,c; + NM *p; + NM m,t; + + for ( i = 0; i < tlen; i++ ) tab[i] = 0; + if ( !m0 || !m1 ) return; + d0 = DL(m0); d1 = DL(m1); n2 = n>>1; + NEWNM(m); d = DL(m); + if ( mod ) { + c0 = CM(m0); c1 = CM(m1); DMAR(c0,c1,0,mod,c); CM(m) = c; + } else + mulq(CQ(m0),CQ(m1),&CQ(m)); + for ( i = 0; i < nd_wpd; i++ ) d[i] = 0; + homo = n&1 ? 1 : 0; + if ( homo ) { + /* offset of h-degree */ + h = GET_EXP(d0,n-1)+GET_EXP(d1,n-1); + PUT_EXP(DL(m),n-1,h); + TD(DL(m)) = h; + if ( nd_blockmask ) ndl_set_blockweight(DL(m)); + } + tab[0] = m; + NEWNM(m); d = DL(m); + for ( i = 0, curlen = 1; i < n2; i++ ) { + a = GET_EXP(d0,i); b = GET_EXP(d1,n2+i); + k = GET_EXP(d0,n2+i); l = GET_EXP(d1,i); + /* xi^a*(Di^k*xi^l)*Di^b */ + a += l; b += k; + s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i); + if ( !k || !l ) { + for ( j = 0; j < curlen; j++ ) + if ( t = tab[j] ) { + dt = DL(t); + PUT_EXP(dt,i,a); PUT_EXP(dt,n2+i,b); TD(dt) += s; + if ( nd_blockmask ) ndl_set_blockweight(dt); + } + curlen *= k+1; + continue; + } + min = MIN(k,l); + if ( mod ) { + ctab = (unsigned int *)ALLOCA((min+1)*sizeof(unsigned int)); + mkwcm(k,l,mod,ctab); + } else { + ctab_q = (Q *)ALLOCA((min+1)*sizeof(Q)); + mkwc(k,l,ctab_q); + } + for ( j = min; j >= 0; j-- ) { + for ( u = 0; u < nd_wpd; u++ ) d[u] = 0; + PUT_EXP(d,i,a-j); PUT_EXP(d,n2+i,b-j); + h = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); + if ( homo ) { + TD(d) = s; + PUT_EXP(d,n-1,s-h); + } else TD(d) = h; + if ( nd_blockmask ) ndl_set_blockweight(d); + if ( mod ) c = ctab[j]; + else q = ctab_q[j]; + p = tab+curlen*j; + if ( j == 0 ) { + for ( u = 0; u < curlen; u++, p++ ) { + if ( tab[u] ) { + ndl_addto(DL(tab[u]),d); + if ( mod ) { + c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(tab[u]) = c1; + } else { + mulq(CQ(tab[u]),q,&q1); CQ(tab[u]) = q1; + } + } + } + } else { + for ( u = 0; u < curlen; u++, p++ ) { + if ( tab[u] ) { + NEWNM(t); + ndl_add(DL(tab[u]),d,DL(t)); + if ( mod ) { + c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(t) = c1; + } else + mulq(CQ(tab[u]),q,&CQ(t)); + *p = t; + } + } + } + } + curlen *= k+1; + } + FREENM(m); +} + +ND ndv_mul_nm(int mod,NM m0,NDV p) +{ NM mr,mr0; NMV m; unsigned int *d,*dt,*dm; @@ -2709,6 +2933,8 @@ ND ndv_mul_nm(int mod,NDV p,NM m0) ND r; if ( !p ) return 0; + else if ( do_weyl ) + return weyl_ndv_mul_nm(mod,m0,p); else { n = NV(p); m = BDY(p); d = DL(m0); @@ -2739,13 +2965,12 @@ ND ndv_mul_nm(int mod,NDV p,NM m0) } } -void ndv_realloc(NDV p,int obpe,int oadv) +void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos) { NMV m,mr,mr0,t; int len,i,k; #define NMV_OPREV(m) (m = (NMV)(((char *)m)-oadv)) -#define NMV_PREV(m) (m = (NMV)(((char *)m)-nmv_adv)) if ( p ) { m = BDY(p); len = LEN(p); @@ -2756,7 +2981,7 @@ void ndv_realloc(NDV p,int obpe,int oadv) for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) { CQ(t) = CQ(m); for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0; - ndl_dup(obpe,DL(m),DL(t)); + ndl_reconstruct(obpe,oepos,DL(m),DL(t)); CQ(mr) = CQ(t); ndl_copy(DL(t),DL(mr)); } @@ -2812,15 +3037,17 @@ NDV dptondv(int mod,DP p) DP q; int l,i,n; - if ( !p ) return 0; - for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ ); if ( mod ) { _dp_mod(p,mod,0,&q); p = q; + } + if ( !p ) return 0; + for ( t = BDY(p), l = 0; t; t = NEXT(t), l++ ); + if ( mod ) m0 = m = (NMV)MALLOC_ATOMIC(l*nmv_adv); - } else + else m0 = m = (NMV)MALLOC(l*nmv_adv); n = NV(p); - for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) { + for ( t = BDY(p); t; t = NEXT(t), NMV_ADV(m) ) { if ( mod ) CM(m) = ITOS(C(t)); else CQ(m) = (Q)C(t); dltondl(n,DL(t),DL(m)); @@ -2910,27 +3137,153 @@ NODE nd_reducebase(NODE x) return x; } +/* XXX incomplete */ + void nd_init_ord(struct order_spec *ord) { - if ( ord->id ) - error("nd_gr : unsupported order"); - nd_dcomp = 0; - switch ( ord->ord.simple ) { + switch ( ord->id ) { case 0: - nd_dcomp = 1; - nd_isrlex = 1; + switch ( ord->ord.simple ) { + case 0: + nd_dcomp = 1; + nd_isrlex = 1; + break; + case 1: + nd_dcomp = 1; + nd_isrlex = 0; + break; + case 2: + nd_dcomp = 0; + nd_isrlex = 0; + ndl_compare_function = ndl_lex_compare; + break; + case 11: + /* XXX */ + nd_dcomp = 0; + nd_isrlex = 1; + ndl_compare_function = ndl_ww_lex_compare; + break; + default: + error("nd_gr : unsupported order"); + } break; case 1: - nd_dcomp = 1; + /* XXX */ + nd_dcomp = -1; nd_isrlex = 0; + ndl_compare_function = ndl_block_compare; break; - case 9: - /* td1->td->rlex */ - nd_dcomp = -dp_nelim; - nd_isrlex = 1; + case 2: + error("nd_init_ord : matrix order is not supported yet."); break; - default: - error("nd_gr : unsupported order"); } + nd_ord = ord; +} + +BlockMask nd_create_blockmask(struct order_spec *ord) +{ + int n,i,j,s,l; + unsigned int *t; + BlockMask bm; + + if ( !ord->id ) + return 0; + n = ord->ord.block.length; + bm = (BlockMask)MALLOC(sizeof(struct oBlockMask)); + bm->n = n; + bm->order_pair = ord->ord.block.order_pair; + bm->mask = (unsigned int **)MALLOC(n*sizeof(unsigned int *)); + for ( i = 0, s = 0; i < n; i++ ) { + bm->mask[i] = t + = (unsigned int *)MALLOC_ATOMIC(nd_wpd*sizeof(unsigned int)); + for ( j = 0; j < nd_wpd; j++ ) t[j] = 0; + l = bm->order_pair[i].length; + for ( j = 0; j < l; j++, s++ ) PUT_EXP(t,s,nd_mask0); + } + return bm; +} + +EPOS nd_create_epos(struct order_spec *ord) +{ + int i,j,l,s,ord_l,ord_o; + EPOS epos; + struct order_pair *op; + + epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS)); + switch ( ord->id ) { + case 0: + if ( nd_isrlex ) { + for ( i = 0; i < nd_nvar; i++ ) { + epos[i].i = nd_exporigin + (nd_nvar-1-i)/nd_epw; + epos[i].s = (nd_epw-((nd_nvar-1-i)%nd_epw)-1)*nd_bpe; + } + } else { + for ( i = 0; i < nd_nvar; i++ ) { + epos[i].i = nd_exporigin + i/nd_epw; + epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe; + } + } + break; + case 1: + /* block order */ + l = ord->ord.block.length; + op = ord->ord.block.order_pair; + for ( j = 0, s = 0; j < l; j++ ) { + ord_o = op[j].order; + ord_l = op[j].length; + if ( !ord_o ) + for ( i = 0; i < ord_l; i++ ) { + epos[s+i].i = nd_exporigin + (s+ord_l-i-1)/nd_epw; + epos[s+i].s = (nd_epw-((s+ord_l-i-1)%nd_epw)-1)*nd_bpe; + } + else + for ( i = 0; i < ord_l; i++ ) { + epos[s+i].i = nd_exporigin + (s+i)/nd_epw; + epos[s+i].s = (nd_epw-((s+i)%nd_epw)-1)*nd_bpe; + } + s += ord_l; + } + break; + case 2: + error("nd_create_epos : matrix order is not supported yet."); + } + return epos; +} + +/* external interface */ + +void nd_nf_p(P f,LIST g,LIST v,int m,struct order_spec *ord,P *rp) +{ + NODE t; + ND nd,nf; + VL vv; + DP d,r,dm; + int stat; + + pltovl(v,&vv); + nd_nvar = length(vv); + nd_init_ord(ord); + initd(ord); + for ( t = BDY(g); NEXT(t); t = NEXT(t) ) { + ptod(CO,vv,(P)BDY(t),&d); BDY(t) = (pointer)d; + } + ptod(CO,vv,(P)BDY(t),&d); BDY(t) = (pointer)d; + NEWNODE(NEXT(t)); ptod(CO,vv,f,&d); BDY(NEXT(t)) = d; NEXT(NEXT(t)) = 0; + nd_setup(m,0,BDY(g)); + nd_psn--; + nd_scale=2; + while ( 1 ) { + nd = (pointer)ndvtond(m,nd_ps[nd_psn]); + stat = nd_nf(m,nd,nd_ps,1,&nf); + if ( !stat ) { + nd_psn++; + nd_reconstruct(m,0,0); + nd_psn--; + } else + break; + } + r = (DP)ndtodp(m,nf); + if ( m ) _dtop_mod(CO,vv,r,rp); + else dtop(CO,vv,r,rp); }