=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v retrieving revision 1.16 retrieving revision 1.58 diff -u -p -r1.16 -r1.58 --- OpenXM_contrib2/asir2000/engine/nd.c 2003/07/31 02:56:13 1.16 +++ OpenXM_contrib2/asir2000/engine/nd.c 2003/09/05 07:00:37 1.58 @@ -1,10 +1,8 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.15 2003/07/31 01:02:39 noro Exp $ */ +/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.57 2003/09/05 05:02:53 noro Exp $ */ #include "ca.h" #include "inline.h" -#define USE_NDV 1 - #if defined(__GNUC__) #define INLINE inline #elif defined(VISUAL) @@ -13,188 +11,306 @@ #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; + 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; +/* index and shift count for each exponent */ +typedef struct oEPOS { + int i; /* index */ + int s; /* shift */ +} *EPOS; + +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_mod,nd_nvar; -int is_rlex; -int nd_epw,nd_bpe,nd_wpd; -unsigned int nd_mask[32]; -unsigned int nd_mask0,nd_mask1; -NM _nm_free_list; -ND _nd_free_list; -ND_pairs _ndp_free_list; -RHist *nd_red; -int nd_red_len; +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; -extern int Top,Reverse; -int nd_psn,nd_pslen; -int nd_found,nd_create,nd_notfirst; -int *nd_psl; -RHist *nd_psh; -int nm_adv; -#define NM_ADV(m) (m = (NM)(((char *)m)+nm_adv)) +static NM _nm_free_list; +static ND _nd_free_list; +static ND_pairs _ndp_free_list; -void GC_gcollect(); -NODE append_one(NODE,int); +static NDV *nd_ps; +static NDV *nd_ps_trace; +static RHist *nd_psh; +static int nd_psn,nd_pslen; -#define HTD(d) ((d)->body->td) +static RHist *nd_red; + +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,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))) #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 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)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 + +/* 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)) +#define NMV_PREV(m) (m = (NMV)(((char *)m)-nmv_adv)) -void nd_removecont(ND p); -void ndv_removecont(NDV p); -void ndv_mul_c_q(NDV p,Q mul); -void nd_mul_c_q(ND p,Q mul); +/* external functions */ +void GC_gcollect(); +NODE append_one(NODE,int); -ND_pairs crit_B( ND_pairs d, int s ); -void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp); -NODE nd_setup(int mod,NODE f); -int nd_newps(int mod,ND a); +/* manipulation of coefficients */ +void nd_removecont(int mod,ND p); +void nd_removecont2(ND p1,ND p2); +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); +void free_pbucket(PGeoBucket b); +void mulq_pbucket(PGeoBucket g,Q c); +PGeoBucket create_pbucket(); + +/* 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); -NODE nd_gb(int m,NODE f); +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); + +/* 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); +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(); -int ndl_td(unsigned int *d); -ND nd_add(ND p1,ND p2); -ND nd_mul_nm(ND p,NM m0); -ND nd_mul_ind_nm(int index,NM m0); -ND nd_mul_term(ND p,int td,unsigned int *d); -int nd_sp(int mod,ND_pairs p,ND *nf); -int nd_find_reducer(ND g); -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); void nd_free(ND 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_monic(ND p); -void nd_mul_c(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); -ND_pairs nd_reconstruct(ND_pairs); -void nd_setup_parameters(); -void nd_realloc(ND p,int obpe); -ND nd_copy(ND p); -void ndl_dup(int obpe,unsigned int *d,unsigned int *r); -#if USE_NDV -static NDV *nd_ps; -#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; +/* 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(); +BlockMask nd_create_blockmask(struct order_spec *ord); +EPOS nd_create_epos(struct order_spec *ord); +int nd_get_exporigin(struct order_spec *ord); -int nmv_adv; -int nmv_len; -NDV ndv_red; +/* 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); +ND nd_add(int mod,ND p1,ND p2); +ND nd_add_q(ND p1,ND p2); +INLINE int nd_length(ND p); -void ndv_mul_c(NDV p,int mul); -ND ndv_add(ND p1,NDV p2); -ND ndv_add_q(ND p1,NDV p2); +/* 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); -void ndv_mul_nm(int mod,NDV pv,NM m,NDV r); -ND ndv_mul_nm_create(int mod,NDV p,NM m0); -void ndv_realloc(NDV p,int obpe,int oadv); +ND ndvtond(int mod,NDV p); NDV dptondv(int,DP); DP ndvtodp(int,NDV); -#else -static ND *nd_ps; -ND dptond(DP); -DP ndtodp(ND); -#endif +ND dptond(int,DP); +DP ndtodp(int,ND); void nd_free_private_storage() { @@ -239,7 +355,7 @@ void _NDP_alloc() } } -INLINE nd_length(ND p) +INLINE int nd_length(ND p) { NM m; int i; @@ -257,9 +373,10 @@ 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; @@ -273,7 +390,7 @@ 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; @@ -284,7 +401,7 @@ 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; @@ -294,7 +411,7 @@ 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; @@ -302,12 +419,12 @@ 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; @@ -316,14 +433,50 @@ INLINE int ndl_reducible(unsigned int *d1,unsigned int } } +void ndl_dehomogenize(unsigned int *d) +{ + unsigned int mask; + unsigned int h; + int i,bits; + + 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 { + h = GET_EXP(d,nd_nvar-1); + XOR_EXP(d,nd_nvar-1,h); + TD(d) -= h; + } + } +} + void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned int *d) { unsigned int t1,t2,u,u1,u2; - int i,j; + int i,j,l; switch ( nd_bpe ) { case 4: - for ( i = 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; @@ -337,7 +490,7 @@ 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; @@ -348,7 +501,7 @@ 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; @@ -358,7 +511,7 @@ 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; @@ -366,13 +519,13 @@ 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; @@ -381,14 +534,30 @@ void ndl_lcm(unsigned int *d1,unsigned *d2,unsigned in } break; } + 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 = 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); @@ -396,24 +565,87 @@ int ndl_td(unsigned int *d) return t; } -INLINE int ndl_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 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; } +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; for ( i = 0; i < nd_wpd; i++ ) - if ( d1[i] != d2[i] ) + if ( *d1++ != *d2++ ) return 0; return 1; } @@ -423,13 +655,15 @@ 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]; @@ -441,46 +675,56 @@ INLINE void ndl_add(unsigned int *d1,unsigned int *d2, { int i; +#if 1 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]; + for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; break; } +#else + for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; +#endif } -INLINE void ndl_add2(unsigned int *d1,unsigned int *d2) +/* d1 += d2 */ +INLINE void ndl_addto(unsigned int *d1,unsigned int *d2) { int i; +#if 1 switch ( nd_wpd ) { - case 1: - d2[0] += d1[0]; - break; case 2: - d2[0] += d1[0]; - d2[1] += d1[1]; + 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++ ) - d2[i] += d1[i]; + 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 } -void ndl_sub(unsigned int *d1,unsigned int *d2,unsigned int *d) +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) @@ -490,7 +734,7 @@ 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; @@ -504,7 +748,7 @@ 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; @@ -515,7 +759,7 @@ 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; @@ -525,7 +769,7 @@ 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; @@ -533,12 +777,12 @@ 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; @@ -550,216 +794,84 @@ int ndl_disjoint(unsigned int *d1,unsigned int *d2) } } -ND nd_reduce(ND p1,ND p2) +int ndl_check_bound2(int index,unsigned int *d2) { - int c,c1,c2,t,td,td2,mul; - NM m2,prev,head,cur,new; - unsigned int *d; + unsigned int u2; + unsigned int *d1; + int i,j,ind,k; - if ( !p1 ) - return 0; - else { - c2 = invm(HCM(p2),nd_mod); - c1 = nd_mod-HCM(p1); - DMAR(c1,c2,0,nd_mod,mul); - td = HTD(p1)-HTD(p2); - d = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int)); - ndl_sub(HDL(p1),HDL(p2),d); - prev = 0; head = cur = BDY(p1); - NEWNM(new); - for ( m2 = BDY(p2); m2; ) { - td2 = TD(new) = TD(m2)+td; - ndl_add(DL(m2),d,DL(new)); - if ( !cur ) { - c1 = CM(m2); - DMAR(c1,mul,0,nd_mod,c2); - CM(new) = c2; - if ( !prev ) { - prev = new; - NEXT(prev) = 0; - head = prev; - } else { - NEXT(prev) = new; - NEXT(new) = 0; - prev = new; - } - m2 = NEXT(m2); - NEWNM(new); - continue; + d1 = nd_bound[index]; + ind = 0; + switch ( nd_bpe ) { + case 4: + 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; } - if ( TD(cur) > td2 ) - c = 1; - else if ( TD(cur) < td2 ) - c = -1; - else - c = ndl_compare(DL(cur),DL(new)); - switch ( c ) { - case 0: - c2 = CM(m2); - c1 = CM(cur); - DMAR(c2,mul,c1,nd_mod,t); - if ( t ) - CM(cur) = t; - else if ( !prev ) { - head = NEXT(cur); - FREENM(cur); - cur = head; - } else { - NEXT(prev) = NEXT(cur); - FREENM(cur); - cur = NEXT(prev); - } - m2 = NEXT(m2); - break; - case 1: - prev = cur; - cur = NEXT(cur); - break; - case -1: - if ( !prev ) { - /* cur = head */ - prev = new; - c2 = CM(m2); - DMAR(c2,mul,0,nd_mod,c1); - CM(prev) = c1; - NEXT(prev) = head; - head = prev; - } else { - c2 = CM(m2); - DMAR(c2,mul,0,nd_mod,c1); - CM(new) = c1; - NEXT(prev) = new; - NEXT(new) = cur; - prev = new; - } - NEWNM(new); - m2 = NEXT(m2); - break; + return 0; + break; + case 6: + 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; } - } - FREENM(new); - if ( head ) { - BDY(p1) = head; - SG(p1) = MAX(SG(p1),SG(p2)+td); - return p1; - } else { - FREEND(p1); return 0; - } - - } -} - -/* HDL(p1) = HDL(p2) */ - -ND nd_reduce_special(ND p1,ND p2) -{ - int c,c1,c2,t,td,td2,mul; - NM m2,prev,head,cur,new; - - if ( !p1 ) - return 0; - else { - c2 = invm(HCM(p2),nd_mod); - c1 = nd_mod-HCM(p1); - DMAR(c1,c2,0,nd_mod,mul); - prev = 0; head = cur = BDY(p1); - NEWNM(new); - for ( m2 = BDY(p2); m2; ) { - td2 = TD(new) = TD(m2); - if ( !cur ) { - c1 = CM(m2); - DMAR(c1,mul,0,nd_mod,c2); - CM(new) = c2; - bcopy(DL(m2),DL(new),nd_wpd*sizeof(unsigned int)); - if ( !prev ) { - prev = new; - NEXT(prev) = 0; - head = prev; - } else { - NEXT(prev) = new; - NEXT(new) = 0; - prev = new; - } - m2 = NEXT(m2); - NEWNM(new); - continue; + break; + case 8: + 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; } - if ( TD(cur) > td2 ) - c = 1; - else if ( TD(cur) < td2 ) - c = -1; - else - c = ndl_compare(DL(cur),DL(m2)); - switch ( c ) { - case 0: - c2 = CM(m2); - c1 = CM(cur); - DMAR(c2,mul,c1,nd_mod,t); - if ( t ) - CM(cur) = t; - else if ( !prev ) { - head = NEXT(cur); - FREENM(cur); - cur = head; - } else { - NEXT(prev) = NEXT(cur); - FREENM(cur); - cur = NEXT(prev); - } - m2 = NEXT(m2); - break; - case 1: - prev = cur; - cur = NEXT(cur); - break; - case -1: - bcopy(DL(m2),DL(new),nd_wpd*sizeof(unsigned int)); - if ( !prev ) { - /* cur = head */ - prev = new; - c2 = CM(m2); - DMAR(c2,mul,0,nd_mod,c1); - CM(prev) = c1; - NEXT(prev) = head; - head = prev; - } else { - c2 = CM(m2); - DMAR(c2,mul,0,nd_mod,c1); - CM(new) = c1; - NEXT(prev) = new; - NEXT(new) = cur; - prev = new; - } - NEWNM(new); - m2 = NEXT(m2); - break; + return 0; + break; + case 16: + 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; } - } - FREENM(new); - if ( head ) { - BDY(p1) = head; - SG(p1)= MAX(SG(p1),SG(p2)+td); - return p1; - } else { - FREEND(p1); return 0; - } - + break; + case 32: + for ( i = nd_exporigin; i < nd_wpd; i++ ) + if ( d1[i]+d2[i]>k)&nd_mask0) > nd_mask0 ) return 1; + } + return 0; + break; } } -int ndl_check_bound2(int index,unsigned int *d2) +int ndl_check_bound2_direct(unsigned int *d1,unsigned int *d2) { unsigned int u2; - unsigned int *d1; int i,j,ind,k; - d1 = nd_bound[index]; 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; @@ -773,7 +885,7 @@ 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; @@ -784,7 +896,7 @@ 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; @@ -794,7 +906,7 @@ 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; @@ -802,12 +914,12 @@ 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] 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; } } return -1; } -ND nd_add(ND p1,ND p2) +INLINE int nd_find_reducer_direct(ND g,NDV *ps,int len) { + NDV r; + RHist s; + int d,k,i; + + if ( Reverse ) + for ( i = len-1; i >= 0; i-- ) { + r = ps[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)) ) + return i; + } + return -1; +} + +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 ) + 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; ) { + c = DL_COMPARE(DL(m1),DL(m2)); + switch ( c ) { + case 0: + t = ((CM(m1))+(CM(m2))) - mod; + if ( t < 0 ) t += mod; + s = m1; m1 = NEXT(m1); + if ( t ) { + can++; NEXTNM2(mr0,mr,s); CM(mr) = (t); + } else { + can += 2; FREENM(s); + } + s = m2; m2 = NEXT(m2); FREENM(s); + break; + case 1: + s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); + break; + case -1: + s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); + break; + } + } + 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; + BDY(p1) = mr0; + SG(p1) = MAX(SG(p1),SG(p2)); + LEN(p1) = LEN(p1)+LEN(p2)-can; + FREEND(p2); return p1; + } +} + +ND nd_add_q(ND p1,ND p2) +{ + int n,c,can; + ND r; + NM m1,m2,mr0,mr,s; + Q t; + + 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: - t = ((CM(m1))+(CM(m2))) - nd_mod; - if ( t < 0 ) - t += nd_mod; + addq(CQ(m1),CQ(m2),&t); s = m1; m1 = NEXT(m1); if ( t ) { - NEXTNM2(mr0,mr,s); CM(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; @@ -905,122 +1082,306 @@ ND nd_add(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) +int nd_nf(int mod,ND g,NDV *ps,int full,ND *rp) { ND d; NM m,mrd,tail; NM mul; int n,sugar,psugar,sugar0,stat,index; - int c,c1,c2; -#if USE_NDV + int c,c1,c2,dummy; + RHist h; NDV p,red; -#else - ND p,red; -#endif Q cg,cred,gcd; + double hmag; if ( !g ) { *rp = 0; return 1; } + if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; + sugar0 = sugar = SG(g); n = NV(g); mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(unsigned int)); for ( d = 0; g; ) { index = nd_find_reducer(g); if ( index >= 0 ) { - p = nd_ps[index]; - ndl_sub(HDL(g),HDL(p),DL(mul)); - TD(mul) = HTD(g)-HTD(p); -#if 0 - if ( d && (SG(p)+TD(mul)) > sugar ) { - goto afo; - } -#endif + h = nd_psh[index]; + ndl_sub(HDL(g),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) { nd_free(g); nd_free(d); return 0; } -#if USE_NDV + p = ps[index]; if ( mod ) { - c1 = invm(HCM(p),nd_mod); c2 = nd_mod-HCM(g); - DMAR(c1,c2,0,nd_mod,c); CM(mul) = c; - ndv_mul_nm(mod,nd_ps[index],mul,ndv_red); - g = ndv_add(g,ndv_red); + c1 = invm(HCM(p),mod); c2 = mod-HCM(g); + DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { - igcd_cofactor(HCQ(g),HCQ(nd_ps[index]),&gcd,&cg,&cred); + 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,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); + hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; + } + } else if ( !full ) { + *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; + } + if ( d ) { + NEXT(tail)=m; tail=m; LEN(d)++; + } else { + MKND(n,m,1,d); tail = BDY(d); + } + } + } + if ( d ) SG(d) = sugar; + *rp = d; + return 1; +} + +int nd_nf_pbucket(int mod,ND g,NDV *ps,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 ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; + 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(g); + if ( index >= 0 ) { + h = nd_psh[index]; + ndl_sub(HDL(g),DL(h),DL(mul)); + if ( ndl_check_bound2(index,DL(mul)) ) { + nd_free(d); + free_pbucket(bucket); + *rp = 0; + return 0; + } + p = ps[index]; + 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); - nd_mul_c_q(g,cred); - ndv_mul_nm(mod,nd_ps[index],mul,ndv_red); - g = ndv_add_q(g,ndv_red); + mulq_pbucket(bucket,cred); + g = bucket->body[hindex]; + gmag = (double)p_mag((P)HCQ(g)); } - sugar = MAX(sugar,SG(ndv_red)); + red = ndv_mul_nm(mod,mul,p); + bucket->body[hindex] = nd_remove_head(g); + red = nd_remove_head(red); + 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; + *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); + } + } + } +} + +int nd_nf_direct(int mod,ND g,BaseSet base,int full,ND *rp) +{ + ND d; + NM m,mrd,tail; + NM mul; + 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; + double hmag; + + if ( !g ) { + *rp = 0; + return 1; + } +#if 0 + if ( !mod ) + hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; #else - c1 = invm(HCM(p),nd_mod); c2 = nd_mod-HCM(g); - DMAR(c1,c2,0,nd_mod,c); CM(mul) = c; - red = nd_mul_ind_nm(index,mul); - g = nd_add(g,red); - sugar = MAX(sugar,SG(red)); + /* XXX */ + 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-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(bound[index],DL(mul)) ) { + nd_free(g); nd_free(d); + 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); nd_mul_c_q(g,cred); + } + 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); + hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; + } } else if ( !full ) { *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 +/* 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,s; + +#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(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 */ + 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; } @@ -1034,24 +1395,45 @@ PGeoBucket create_pbucket() return g; } -void add_pbucket(PGeoBucket g,ND d) +void free_pbucket(PGeoBucket b) { + int i; + + for ( i = 0; i <= b->m; i++ ) + if ( b->body[i] ) { + nd_free(b->body[i]); + b->body[i] = 0; + } + GC_free(b); +} + +void add_pbucket(int mod,PGeoBucket g,ND d) { - int l,k,m; + int l,i,k,m; - l = nd_length(d); - for ( k = 0, m = 1; l > m; k++, m <<= 2 ); - /* 4^(k-1) < l <= 4^k */ - d = nd_add(g->body[k],d); - for ( ; d && nd_length(d) > 1<<(2*k); 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 && LEN(d) > m; k++, m <<= 1 ) { g->body[k] = 0; - d = nd_add(g->body[k+1],d); + d = nd_add(mod,g->body[k+1],d); } g->body[k] = d; g->m = MAX(g->m,k); } -int head_pbucket(PGeoBucket g) +void mulq_pbucket(PGeoBucket g,Q c) { + int k; + + for ( k = 0; k <= g->m; k++ ) + nd_mul_c_q(g->body[k],c); +} + +int head_pbucket(int mod,PGeoBucket g) +{ int j,i,c,k,nv,sum; unsigned int *di,*dj; ND gi,gj; @@ -1068,33 +1450,22 @@ int head_pbucket(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)-nd_mod; - if ( sum < 0 ) - sum += nd_mod; + sum = sum+HCM(gi)-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; @@ -1103,85 +1474,126 @@ int head_pbucket(PGeoBucket g) } } -ND normalize_pbucket(PGeoBucket g) +int head_pbucket_q(PGeoBucket g) { + int j,i,c,k,nv; + Q sum,t; + ND gi,gj; + + k = g->m; + while ( 1 ) { + j = -1; + for ( i = 0; i <= k; i++ ) { + if ( !(gi = g->body[i]) ) continue; + if ( j < 0 ) { + j = i; + gj = g->body[j]; + sum = HCQ(gj); + } else { + nv = NV(gi); + c = DL_COMPARE(HDL(gi),HDL(gj)); + if ( c > 0 ) { + if ( sum ) HCQ(gj) = sum; + else g->body[j] = nd_remove_head(gj); + j = i; + gj = g->body[j]; + sum = HCQ(gj); + } else if ( c == 0 ) { + addq(sum,HCQ(gi),&t); + sum = t; + g->body[i] = nd_remove_head(gi); + } + } + } + if ( j < 0 ) return -1; + else if ( sum ) { + HCQ(gj) = sum; + return j; + } else + g->body[j] = nd_remove_head(gj); + } +} + +ND normalize_pbucket(int mod,PGeoBucket g) +{ int i; ND r,t; r = 0; - for ( i = 0; i <= g->m; i++ ) - r = nd_add(r,g->body[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; } -ND nd_nf(ND g,int full) +/* return value = 0 => input is not a GB */ + +NODE nd_gb(int m,int checkonly) { - ND u,p,d,red; - NODE l; - NM m,mrd; - int sugar,psugar,n,h_reducible,h; - PGeoBucket bucket; + int i,nh,sugar,stat; + NODE r,g,t; + ND_pairs d; + ND_pairs l; + ND h,nf; - if ( !g ) { - return 0; + g = 0; d = 0; + for ( i = 0; i < nd_psn; i++ ) { + d = update_pairs(d,g,i); + g = update_base(g,i); } - sugar = SG(g); - n = NV(g); - bucket = create_pbucket(); - add_pbucket(bucket,g); - d = 0; - while ( 1 ) { - h = head_pbucket(bucket); - if ( h < 0 ) { - if ( d ) - SG(d) = sugar; - return d; + sugar = 0; + while ( d ) { +again: + l = nd_minp(d,&d); + if ( SG(l) != sugar ) { + sugar = SG(l); + fprintf(asir_out,"%d",sugar); } - g = bucket->body[h]; - red = nd_find_reducer(g); - if ( red ) { - bucket->body[h] = nd_remove_head(g); - red = nd_remove_head(red); - add_pbucket(bucket,red); - sugar = MAX(sugar,SG(red)); - } else if ( !full ) { - g = normalize_pbucket(bucket); - if ( g ) - SG(g) = sugar; - return g; + stat = nd_sp(m,0,l,&h); + if ( !stat ) { + NEXT(l) = d; d = l; + d = nd_reconstruct(m,0,d); + goto again; + } +#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); + goto again; + } else if ( nf ) { + if ( checkonly ) return 0; + printf("+"); fflush(stdout); + nh = nd_newps(m,nf,0); + d = update_pairs(d,g,nh); + g = update_base(g,nh); + FREENDP(l); } else { - m = BDY(g); - if ( NEXT(m) ) { - BDY(g) = NEXT(m); NEXT(m) = 0; - } else { - FREEND(g); g = 0; - } - bucket->body[h] = g; - NEXT(m) = 0; - if ( d ) { - for ( mrd = BDY(d); NEXT(mrd); mrd = NEXT(mrd) ); - NEXT(mrd) = m; - } else { - MKND(n,m,d); - } + printf("."); fflush(stdout); + FREENDP(l); } } + for ( t = g; t; t = NEXT(t) ) BDY(t) = (pointer)nd_ps[(int)BDY(t)]; + return g; } -#endif -NODE nd_gb(int m,NODE f) +NODE nd_gb_trace(int m) { int i,nh,sugar,stat; - NODE r,g,gall; + NODE r,g,t; ND_pairs d; ND_pairs l; - ND h,nf; + ND h,nf,nfq; - for ( gall = g = 0, d = 0, r = f; r; r = NEXT(r) ) { - i = (int)BDY(r); + g = 0; d = 0; + for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i); g = update_base(g,i); - gall = append_one(gall,i); } sugar = 0; while ( d ) { @@ -1191,32 +1603,112 @@ 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(d); + d = nd_reconstruct(m,1,d); goto again; } - stat = nd_nf(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(d); + d = nd_reconstruct(m,1,d); goto again; } else if ( nf ) { - printf("+"); fflush(stdout); - nh = nd_newps(m,nf); - d = update_pairs(d,g,nh); - g = update_base(g,nh); - gall = append_one(gall,nh); - FREENDP(l); + /* overflow does not occur */ + nd_sp(0,1,l,&h); + nd_nf(0,h,nd_ps_trace,!Top,&nfq); + if ( nfq ) { + printf("+"); fflush(stdout); + nh = nd_newps(m,nf,nfq); + /* failure; m|HC(nfq) */ + if ( nh < 0 ) return 0; + d = update_pairs(d,g,nh); + g = update_base(g,nh); + } else { + printf("*"); fflush(stdout); + } } else { printf("."); fflush(stdout); - FREENDP(l); } + FREENDP(l); } + for ( t = g; t; t = NEXT(t) ) + BDY(t) = (pointer)nd_ps_trace[(int)BDY(t)]; return g; } +int ndv_compare(NDV *p1,NDV *p2) +{ + return DL_COMPARE(HDL(*p1),HDL(*p2)); +} + +int ndv_compare_rev(NDV *p1,NDV *p2) +{ + return -DL_COMPARE(HDL(*p1),HDL(*p2)); +} + +NODE nd_reduceall(int m,NODE f) +{ + int i,j,n,stat; + 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)); + 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); + 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,&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]; 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]; + } + NEXT(a) = 0; + return a0; +} + ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t) { ND_pairs d1,nd,cur,head,prev,remove; @@ -1226,27 +1718,26 @@ 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); + 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 { - cur = NEXT(prev) = NEXT(cur); + prev = cur; cur = NEXT(cur); } - FREENDP(remove); - } else { - 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; } @@ -1256,20 +1747,18 @@ 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 = HDL(nd_ps[t]); - td = HTD(nd_ps[t]); - ts = SG(nd_ps[t]) - td; + dl = DL(nd_psh[t]); + 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(HDL(nd_ps[r->i1]),dl,r->lcm); - TD(r) = ndl_td(r->lcm); - s = SG(nd_ps[r->i1])-HTD(nd_ps[r->i1]); - SG(r) = MAX(s,ts) + TD(r); + ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm); + 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; @@ -1282,15 +1771,15 @@ ND_pairs crit_B( ND_pairs d, int s ) int td,tdl; if ( !d ) return 0; - t = HDL(nd_ps[s]); + t = DL(nd_psh[s]); prev = 0; head = cur = d; lcm = (unsigned int *)ALLOCA(nd_wpd*sizeof(unsigned int)); while ( cur ) { tl = cur->lcm; if ( ndl_reducible(tl,t) - && (ndl_lcm(HDL(nd_ps[cur->i1]),t,lcm),!ndl_equal(lcm,tl)) - && (ndl_lcm(HDL(nd_ps[cur->i2]),t,lcm),!ndl_equal(lcm,tl)) ) { + && (ndl_lcm(DL(nd_psh[cur->i1]),t,lcm),!ndl_equal(lcm,tl)) + && (ndl_lcm(DL(nd_psh[cur->i2]),t,lcm),!ndl_equal(lcm,tl)) ) { remove = cur; if ( !prev ) { head = cur = NEXT(cur); @@ -1299,8 +1788,7 @@ ND_pairs crit_B( ND_pairs d, int s ) } FREENDP(remove); } else { - prev = cur; - cur = NEXT(cur); + prev = cur; cur = NEXT(cur); } } return head; @@ -1310,28 +1798,22 @@ 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; } @@ -1395,28 +1877,24 @@ ND_pairs crit_F( ND_pairs d1 ) int crit_2( int dp1, int dp2 ) { - return ndl_disjoint(HDL(nd_ps[dp1]),HDL(nd_ps[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; @@ -1427,14 +1905,11 @@ NODE update_base(NODE nd,int ndp) { unsigned int *dl, *dln; NODE last, p, head; - int td,tdn; - dl = HDL(nd_ps[ndp]); - td = HTD(nd_ps[ndp]); + dl = DL(nd_psh[ndp]); for ( head = last = 0, p = nd; p; ) { - dln = HDL(nd_ps[(int)BDY(p)]); - tdn = HTD(nd_ps[(int)BDY(p)]); - if ( tdn >= td && ndl_reducible( dln, dl ) ) { + dln = DL(nd_psh[(int)BDY(p)]); + if ( ndl_reducible( dln, dl ) ) { p = NEXT(p); if ( last ) NEXT(last) = p; } else { @@ -1450,45 +1925,19 @@ 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); @@ -1498,116 +1947,88 @@ find: 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 ( aq ) { + /* trace lifting */ + if ( !rem(NM(HCQ(aq)),mod) ) + return -1; + } if ( nd_psn == nd_pslen ) { nd_pslen *= 2; - nd_psl = (int *)REALLOC((char *)nd_psl,nd_pslen*sizeof(int)); -#if USE_NDV nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV)); -#else - nd_ps = (ND *)REALLOC((char *)nd_ps,nd_pslen*sizeof(ND)); -#endif + 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 ( mod ) - nd_monic(a); - else - nd_removecont(a); - nd_bound[nd_psn] = nd_compute_bound(a); - NEWRHist(r); TD(r) = HTD(a); ndl_copy(HDL(a),DL(r)); nd_psh[nd_psn] = r; -#if USE_NDV - nd_ps[nd_psn]= ndtondv(mod,a); - nd_free(a); - nd_psl[nd_psn] = len = LEN(nd_ps[nd_psn]); - if ( len > nmv_len ) { - nmv_len = 2*len; - BDY(ndv_red) = (NMV)REALLOC(BDY(ndv_red),nmv_len*nmv_adv); + 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); } -#else - nd_ps[nd_psn] = a; - nd_psl[nd_psn] = nd_length(a); -#endif return nd_psn++; } -NODE 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_psl = (int *)MALLOC(nd_pslen*sizeof(int)); -#if USE_NDV nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV)); -#else - nd_ps = (ND *)MALLOC(nd_pslen*sizeof(ND)); -#endif + 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; + 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; + 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) ) { -#if USE_NDV - nd_ps[i] = dptondv(mod,(DP)BDY(f)); - if ( mod ) - ndv_mul_c(nd_ps[i],invm(HCM(nd_ps[i]),nd_mod)); - else - ndv_removecont(nd_ps[i]); - len = MAX(len,LEN(nd_ps[i])); -#else - nd_ps[i] = dptond((DP)BDY(f)); - nd_mul_c(nd_ps[i],1); - nd_psl[i] = nd_length(nd_ps[i]); -#endif - NEWRHist(r); TD(r) = HTD(nd_ps[i]); ndl_copy(HDL(nd_ps[i]),DL(r)); + NEWRHist(r); + 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; } -#if USE_NDV - nmv_len = 16*len; - NEWNDV(ndv_red); - if ( mod ) - BDY(ndv_red) = (NMV)MALLOC_ATOMIC(nmv_len*nmv_adv); - else - BDY(ndv_red) = (NMV)MALLOC(nmv_len*nmv_adv); -#endif - for ( s0 = 0, i = 0; i < nd_psn; i++ ) { - NEXTNODE(s0,s); BDY(s) = (pointer)i; - } - if ( s0 ) NEXT(s) = 0; - return s0; } void nd_gr(LIST f,LIST v,int m,struct order_spec *ord,LIST *rp) @@ -1619,114 +2040,206 @@ 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); - nd_mod = m; for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { ptod(CO,vv,(P)BDY(t),&b); - if ( m ) - _dp_mod(b,m,0,&c); - else - c = b; - if ( c ) { - NEXTNODE(fd0,fd); BDY(fd) = (pointer)c; - } + NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; } if ( fd0 ) NEXT(fd) = 0; - s = nd_setup(m,fd0); - x = nd_gb(m,s); -#if 0 - x = nd_reduceall(x,m); -#endif - for ( r0 = 0; x; x = NEXT(x) ) { + 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); -#if USE_NDV - a = ndvtodp(m,nd_ps[(int)BDY(x)]); -#else - a = ndtodp(m,nd_ps[(int)BDY(x)]); -#endif - if ( m ) + if ( m ) { + a = ndvtodp(m,BDY(t)); _dtop_mod(CO,vv,a,(P *)&BDY(r)); - else + } else { + a = ndvtodp(m,BDY(t)); dtop(CO,vv,a,(P *)&BDY(r)); + } } if ( r0 ) NEXT(r) = 0; MKLIST(*rp,r0); - fprintf(asir_out,"found=%d,notfirst=%d,create=%d\n", - nd_found,nd_notfirst,nd_create); } +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); + 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); + for ( fd0 = 0, in0 = 0, t = BDY(f); t; t = NEXT(t) ) { + ptod(CO,vv,(P)BDY(t),&c); + if ( c ) { + dp_homo(c,&h); NEXTNODE(fd0,fd); BDY(fd) = (pointer)h; + NEXTNODE(in0,in); BDY(in) = (pointer)c; + } + } + if ( fd0 ) NEXT(fd) = 0; + if ( in0 ) NEXT(in) = 0; + } else { + for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { + ptod(CO,vv,(P)BDY(t),&c); + if ( c ) { + NEXTNODE(fd0,fd); BDY(fd) = (pointer)c; + } + } + if ( fd0 ) NEXT(fd) = 0; + in0 = 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 ) { + /* 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),ord); + nd_nvar = nvar; + initd(ord); + 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); + initd(ord); + for ( r0 = 0; cand; cand = NEXT(cand) ) { + NEXTNODE(r0,r); + BDY(r) = (pointer)ndvtodp(0,(NDV)BDY(cand)); + } + if ( r0 ) NEXT(r) = 0; + cand = r0; + 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); + BDY(r) = (pointer)p; + } + MKLIST(*rp,cand); +} + 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; - bzero(r,nd_wpd*sizeof(unsigned int)); - if ( is_rlex ) - for ( i = 0; i < n; i++ ) - r[(n-1-i)/nd_epw] |= (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); + 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,int td,unsigned int *ndl) +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); - TD(dl) = td; + dl->td = TD(ndl); d = dl->d; - if ( is_rlex ) - for ( i = 0; i < n; i++ ) - d[i] = (ndl[(n-1-i)/nd_epw]>>((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; } -ND dptond(DP p) +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); - CM(m) = ITOS(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; } -DP ndtodp(ND p) +DP ndtodp(int mod,ND p) { DP d; MP m0,m; @@ -1739,8 +2252,9 @@ DP ndtodp(ND p) m0 = 0; for ( t = BDY(p); t; t = NEXT(t) ) { NEXTMP(m0,m); - C(m) = STOI(CM(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); @@ -1751,20 +2265,22 @@ DP ndtodp(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 ( is_rlex ) - 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)) - &((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(">>"); } @@ -1804,66 +2320,149 @@ 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"); } -void nd_removecont(ND p) +void nd_removecont(int mod,ND p) { int i,n; Q *w; Q dvr,t; NM m; + struct oVECT v; + N q,r; - for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ ); - w = (Q *)ALLOCA(n*sizeof(Q)); - for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) - w[i] = CQ(m); - sortbynm(w,n); - qltozl(w,n,&dvr); - for ( m = BDY(p); m; m = NEXT(m) ) { - divq(CQ(m),dvr,&t); CQ(m) = t; + 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); + removecont_array(w,n); + for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i]; } } -void ndv_removecont(NDV p) +void nd_removecont2(ND p1,ND p2) { + int i,n1,n2,n; + Q *w; + Q dvr,t; + NM m; + struct oVECT v; + N q,r; + + if ( !p1 ) { + nd_removecont(0,p2); return; + } else if ( !p2 ) { + nd_removecont(0,p1); return; + } + n1 = nd_length(p1); + n2 = nd_length(p2); + n = n1+n2; + 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); + 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]; +} + +void ndv_removecont(int mod,NDV p) +{ int i,len; Q *w; Q dvr,t; NMV m; + if ( mod ) + ndv_mul_c(mod,p,invm(HCM(p),mod)); + 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); + sortbynm(w,len); + qltozl(w,len,&dvr); + for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) { + divq(CQ(m),dvr,&t); CQ(m) = t; + } + } +} + +void ndv_dehomogenize(NDV p,struct order_spec *ord) +{ + int i,j,adj,len,newnvar,newwpd,newadv,newexporigin; + Q *w; + Q dvr,t; + NMV m,r; +#define NEWADV(m) (m = (NMV)(((char *)m)+newadv)) + len = p->len; - w = (Q *)ALLOCA(len*sizeof(Q)); + newnvar = nd_nvar-1; + 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++ ) - w[i] = CQ(m); - sortbynm(w,len); - qltozl(w,len,&dvr); - for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) { - divq(CQ(m),dvr,&t); CQ(m) = t; + ndl_dehomogenize(DL(m)); + if ( newwpd != nd_wpd ) { + 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); + 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)--; } -void nd_monic(ND p) +void removecont_array(Q *c,int n) { - if ( !p ) - return; - else - nd_mul_c(p,invm(HCM(p),nd_mod)); + struct oVECT v; + Q d0,d1,a,u,u1,gcd; + int i; + N qn,rn,gn; + Q *q,*r; + + q = (Q *)ALLOCA(n*sizeof(Q)); + r = (Q *)ALLOCA(n*sizeof(Q)); + v.id = O_VECT; v.len = n; v.body = (pointer *)c; + igcdv_estimate(&v,&d0); + for ( i = 0; i < n; i++ ) { + divn(NM(c[i]),NM(d0),&qn,&rn); + 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; + if ( i < n ) { + v.id = O_VECT; v.len = n; v.body = (pointer *)r; + igcdv(&v,&d1); + gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd); + divsn(NM(d0),gn,&qn); NTOQ(qn,1,a); + for ( i = 0; i < n; i++ ) { + mulq(a,q[i],&u); + if ( r[i] ) { + divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1); + addq(u,u1,&q[i]); + } else + q[i] = u; + } + } + for ( i = 0; i < n; i++ ) c[i] = q[i]; } -void nd_mul_c(ND p,int mul) +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,nd_mod,c); + DMAR(c1,mul,0,mod,c); CM(m) = c; } } @@ -1873,8 +2472,7 @@ 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; } @@ -1884,8 +2482,7 @@ void nd_free(ND p) { NM t,s; - if ( !p ) - return; + if ( !p ) return; t = BDY(p); while ( t ) { s = NEXT(t); @@ -1895,73 +2492,77 @@ void nd_free(ND p) FREEND(p); } -void nd_append_red(unsigned int *d,int td,int i) +void ndv_free(NDV p) { + GC_free(BDY(p)); +} + +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; } -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); - bcopy(DL(m)->d,d1,nd_nvar*sizeof(unsigned int)); - 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)); - bzero(t,l*sizeof(unsigned int)); - bcopy(d1,t,nd_nvar*sizeof(unsigned int)); - 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)); - bcopy(HDL(p),d1,nd_wpd*sizeof(unsigned int)); - for ( m = NEXT(BDY(p)); m; m = NEXT(m) ) { + len = LEN(p); + m = BDY(p); ndl_copy(DL(m),d1); NMV_ADV(m); + for ( i = 1; i < len; i++, NMV_ADV(m) ) { ndl_lcm(DL(m),d1,d2); t = d1; d1 = d2; d2 = t; } l = nd_nvar+31; t = (unsigned int *)MALLOC_ATOMIC(l*sizeof(unsigned int)); - bzero(t,l*sizeof(unsigned int)); - for ( i = 0; i < nd_nvar; i++ ) - t[i] = (d1[i/nd_epw]>>((nd_epw-(i%nd_epw)-1)*nd_bpe))&nd_mask0; + 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<= 0; i-- ) { -#if USE_NDV - ndv_realloc(nd_ps[i],obpe,oadv); -#else - nd_realloc(nd_ps[i],obpe); -#endif - } + 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; - TD(s) = TD(t); SG(s) = SG(t); - ndl_dup(obpe,t->lcm,s->lcm); + ndl_reconstruct(obpe,oepos,LCM(t),LCM(s)); } + + old_red = (RHist *)ALLOCA(REDTAB_LEN*sizeof(RHist)); for ( i = 0; i < REDTAB_LEN; i++ ) { - for ( mr0 = 0, r = nd_red[i]; r; r = NEXT(r) ) { - NEXTRHist(mr0,mr); + old_red[i] = nd_red[i]; + nd_red[i] = 0; + } + for ( i = 0; i < REDTAB_LEN; i++ ) + for ( r = old_red[i]; r; r = NEXT(r) ) { + NEWRHist(mr); mr->index = r->index; - TD(mr) = TD(r); - ndl_dup(obpe,DL(r),DL(mr)); + SG(mr) = SG(r); + ndl_reconstruct(obpe,oepos,DL(r),DL(mr)); + h = ndl_hash_value(DL(mr)); + NEXT(mr) = nd_red[h]; + nd_red[h] = mr; } - if ( mr0 ) NEXT(mr) = 0; - nd_red[i] = mr0; - } + for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0; + old_red = 0; for ( i = 0; i < nd_psn; i++ ) { - NEWRHist(r); TD(r) = TD(nd_psh[i]); ndl_dup(obpe,DL(nd_psh[i]),DL(r)); + NEWRHist(r); SG(r) = SG(nd_psh[i]); + ndl_reconstruct(obpe,oepos,DL(nd_psh[i]),DL(r)); nd_psh[i] = r; } if ( s0 ) NEXT(s) = 0; prev_nm_free_list = 0; prev_ndp_free_list = 0; -#if USE_NDV - BDY(ndv_red) = (NMV)REALLOC(BDY(ndv_red),nmv_len*nmv_adv); -#endif GC_gcollect(); return s0; } -void ndl_dup(int obpe,unsigned int *d,unsigned int *r) +void nd_reconstruct_direct(int mod,NDV *ps,int len) { - int n,i,ei,oepw,cepw,cbpe; + 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; - n = nd_nvar; - 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 ) - for ( i = 0; i < n; i++ ) { - ei = (d[(n-1-i)/oepw]>>((oepw-((n-1-i)%oepw)-1)*obpe)) - &((1<>((oepw-(i%oepw)-1)*obpe)) - &((1<= 0; i-- ) ndv_realloc(ps[i],obpe,oadv,oepos); + prev_nm_free_list = 0; + prev_ndp_free_list = 0; + GC_gcollect(); } -void nd_realloc(ND p,int obpe) +void ndl_reconstruct(int obpe,EPOS oepos,unsigned int *d,unsigned int *r) { - NM m,mr,mr0; + 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)<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); + } } - NEXT(mr) = 0; - BDY(p) = mr0; + } else { + for ( i = 0; i < n; i++ ) { + ei = GET_EXP_OLD(d,i); + PUT_EXP(r,i,ei); + } } } ND nd_copy(ND p) { NM m,mr,mr0; - int c,n,s; + int c,n; ND r; if ( !p ) return 0; else { - s = sizeof(struct oNM)+(nd_wpd-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; } } -#if USE_NDV -int nd_sp(int mod,ND_pairs p,ND *rp) +int nd_sp(int mod,int trace,ND_pairs p,ND *rp) { NM m; NDV p1,p2; @@ -2122,47 +2739,40 @@ int nd_sp(int mod,ND_pairs p,ND *rp) unsigned int *lcm; int td; - p1 = nd_ps[p->i1]; - p2 = nd_ps[p->i2]; - lcm = p->lcm; - td = TD(p); + if ( trace ) { + p1 = nd_ps_trace[p->i1]; p2 = nd_ps_trace[p->i2]; + } else { + p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2]; + } + lcm = LCM(p); NEWNM(m); - if ( mod ) CM(m) = HCM(p2); - else CQ(m) = HCQ(p2); - TD(m) = td-HTD(p1); ndl_sub(lcm,HDL(p1),DL(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_create(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)); + 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)); if ( ndl_check_bound2(p->i2,DL(m)) ) { nd_free(t1); return 0; } - ndv_mul_nm(mod,p2,m,ndv_red); + t2 = ndv_mul_nm(mod,m,p2); + *rp = nd_add(mod,t1,t2); FREENM(m); - if ( mod ) - *rp = ndv_add(t1,ndv_red); - else - *rp = ndv_add_q(t1,ndv_red); return 1; } -void ndv_mul_c(NDV p,int mul) +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,nd_mod,c); - CM(m) = c; + c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c; } } @@ -2172,48 +2782,148 @@ 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; } } -void ndv_mul_nm(int mod,NDV p,NM m0,NDV r) +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) { - NMV m,mr,mr0; - unsigned int *d,*dt,*dm; - int c,n,td,i,c1,c2,len; - Q q; + 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; - if ( !p ) - /* XXX */ - LEN(r) = 0; - else { - n = NV(p); m = BDY(p); len = LEN(p); - d = DL(m0); td = TD(m0); - mr = BDY(r); + 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 ) { - c = CM(m0); - for ( ; len > 0; len--, NMV_ADV(m), NMV_ADV(mr) ) { - c1 = CM(m); DMAR(c1,c,0,nd_mod,c2); CM(mr) = c2; - TD(mr) = TD(m)+td; ndl_add(DL(m),d,DL(mr)); - } + ctab = (unsigned int *)ALLOCA((min+1)*sizeof(unsigned int)); + mkwcm(k,l,mod,ctab); } else { - q = CQ(m0); - for ( ; len > 0; len--, NMV_ADV(m), NMV_ADV(mr) ) { - mulq(CQ(m),q,&CQ(mr)); - TD(mr) = TD(m)+td; ndl_add(DL(m),d,DL(mr)); + 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; + } + } } } - NV(r) = NV(p); - LEN(r) = LEN(p); - SG(r) = SG(p) + td; + curlen *= k+1; } + FREENM(m); } -ND ndv_mul_nm_create(int mod,NDV p,NM m0) +ND ndv_mul_nm(int mod,NM m0,NDV p) { NM mr,mr0; NMV m; @@ -2222,21 +2932,22 @@ ND ndv_mul_nm_create(int mod,NDV p,NM m0) Q q; ND r; - if ( !p ) - return 0; + 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); 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) ) { NEXTNM(mr0,mr); c1 = CM(m); - DMAR(c1,c,0,nd_mod,c2); + DMAR(c1,c,0,mod,c2); CM(mr) = c2; - TD(mr) = TD(m)+td; ndl_add(DL(m),d,DL(mr)); } } else { @@ -2244,191 +2955,34 @@ ND ndv_mul_nm_create(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; } } -ND ndv_add(ND p1,NDV p2) +void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos) { - register NM prev,cur,new; - int c,c1,c2,t,td,td2,mul,len,i; - NM head; - unsigned int *d; - NMV m2; - Q q; - - if ( !p1 ) - return 0; - else { - prev = 0; head = cur = BDY(p1); - NEWNM(new); len = LEN(p2); - for ( m2 = BDY(p2), i = 0; cur && i < len; ) { - td2 = TD(new) = TD(m2); - if ( TD(cur) > td2 ) { - prev = cur; cur = NEXT(cur); - continue; - } else if ( TD(cur) < td2 ) c = -1; - else if ( nd_wpd == 1 ) { - if ( DL(cur)[0] > DL(m2)[0] ) c = is_rlex ? -1 : 1; - else if ( DL(cur)[0] < DL(m2)[0] ) c = is_rlex ? 1 : -1; - else c = 0; - } - else c = ndl_compare(DL(cur),DL(m2)); - switch ( c ) { - case 0: - t = CM(m2)+CM(cur)-nd_mod; - if ( t < 0 ) t += nd_mod; - if ( t ) CM(cur) = t; - else if ( !prev ) { - head = NEXT(cur); FREENM(cur); cur = head; - } else { - NEXT(prev) = NEXT(cur); FREENM(cur); cur = NEXT(prev); - } - NMV_ADV(m2); i++; - break; - case 1: - prev = cur; cur = NEXT(cur); - break; - case -1: - ndl_copy(DL(m2),DL(new)); - CQ(new) = CQ(m2); - if ( !prev ) { - /* cur = head */ - prev = new; NEXT(prev) = head; head = prev; - } else { - NEXT(prev) = new; NEXT(new) = cur; prev = new; - } - NEWNM(new); NMV_ADV(m2); i++; - break; - } - } - for ( ; i < len; i++, NMV_ADV(m2) ) { - td2 = TD(new) = TD(m2); CQ(new) = CQ(m2); ndl_copy(DL(m2),DL(new)); - if ( !prev ) { - prev = new; NEXT(prev) = 0; head = prev; - } else { - NEXT(prev) = new; NEXT(new) = 0; prev = new; - } - NEWNM(new); - } - FREENM(new); - if ( head ) { - BDY(p1) = head; SG(p1) = MAX(SG(p1),SG(p2)); - return p1; - } else { - FREEND(p1); - return 0; - } - - } -} - -ND ndv_add_q(ND p1,NDV p2) -{ - register NM prev,cur,new; - int c,c1,c2,t,td,td2,mul,len,i; - NM head; - unsigned int *d; - NMV m2; - Q q; - - if ( !p1 ) - return 0; - else { - prev = 0; head = cur = BDY(p1); - NEWNM(new); len = LEN(p2); - for ( m2 = BDY(p2), i = 0; cur && i < len; ) { - td2 = TD(new) = TD(m2); - if ( TD(cur) > td2 ) { - prev = cur; cur = NEXT(cur); - continue; - } else if ( TD(cur) < td2 ) c = -1; - else if ( nd_wpd == 1 ) { - if ( DL(cur)[0] > DL(m2)[0] ) c = is_rlex ? -1 : 1; - else if ( DL(cur)[0] < DL(m2)[0] ) c = is_rlex ? 1 : -1; - else c = 0; - } - else c = ndl_compare(DL(cur),DL(m2)); - switch ( c ) { - case 0: - addq(CQ(cur),CQ(m2),&q); - if ( q ) - CQ(cur) = q; - else if ( !prev ) { - head = NEXT(cur); FREENM(cur); cur = head; - } else { - NEXT(prev) = NEXT(cur); FREENM(cur); cur = NEXT(prev); - } - NMV_ADV(m2); i++; - break; - case 1: - prev = cur; cur = NEXT(cur); - break; - case -1: - ndl_copy(DL(m2),DL(new)); - CQ(new) = CQ(m2); - if ( !prev ) { - /* cur = head */ - prev = new; NEXT(prev) = head; head = prev; - } else { - NEXT(prev) = new; NEXT(new) = cur; prev = new; - } - NEWNM(new); NMV_ADV(m2); i++; - break; - } - } - for ( ; i < len; i++, NMV_ADV(m2) ) { - td2 = TD(new) = TD(m2); CQ(new) = CQ(m2); ndl_copy(DL(m2),DL(new)); - if ( !prev ) { - prev = new; NEXT(prev) = 0; head = prev; - } else { - NEXT(prev) = new; NEXT(new) = 0; prev = new; - } - NEWNM(new); - } - FREENM(new); - if ( head ) { - BDY(p1) = head; SG(p1) = MAX(SG(p1),SG(p2)); - return p1; - } else { - FREEND(p1); - return 0; - } - - } -} - -void ndv_realloc(NDV p,int obpe,int oadv) -{ 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); - 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,oepos,DL(m),DL(t)); CQ(mr) = CQ(t); - TD(mr) = TD(t); ndl_copy(DL(t),DL(mr)); } BDY(p) = mr0; @@ -2442,15 +2996,10 @@ 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); } @@ -2459,33 +3008,49 @@ NDV ndtondv(int mod,ND p) return d; } +ND ndvtond(int mod,NDV p) +{ + ND d; + NM m,m0; + NMV t; + int i,len; + + if ( !p ) return 0; + m0 = 0; + len = p->len; + for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) { + NEXTNM(m0,m); + ndl_copy(DL(t),DL(m)); + CQ(m) = CQ(t); + } + NEXT(m) = 0; + MKND(NV(p),m0,len,d); + SG(d) = SG(p); + return d; +} + NDV dptondv(int mod,DP p) { NDV d; NMV m0,m; MP t; + DP q; int l,i,n; - if ( !p ) - return 0; + 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 m0 = m = (NMV)MALLOC(l*nmv_adv); n = NV(p); - if ( mod ) { - for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) { - CM(m) = ITOS(C(t)); - TD(m) = TD(DL(t)); - dltondl(n,DL(t),DL(m)); - } - } else { - for ( t = BDY(p), i = 0; i < l; i++, t = NEXT(t), NMV_ADV(m) ) { - CQ(m) = (Q)C(t); - TD(m) = TD(DL(t)); - dltondl(n,DL(t),DL(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)); } MKNDV(n,m0,l,d); SG(d) = SG(p); @@ -2499,23 +3064,15 @@ 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); - if ( mod ) { - for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { - NEXTMP(m0,m); - C(m) = STOI(CM(t)); - DL(m) = ndltodl(n,TD(t),DL(t)); - } - } else { - for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { - NEXTMP(m0,m); - C(m) = (P)CQ(t); - DL(m) = ndltodl(n,TD(t),DL(t)); - } + 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,DL(t)); } NEXT(m) = 0; MKDP(NV(p),m0,d); @@ -2528,8 +3085,7 @@ 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) ) { @@ -2545,8 +3101,7 @@ 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) ) { @@ -2558,118 +3113,139 @@ void ndv_print_q(NDV p) printf("\n"); } } -#else -int nd_sp(ND_pairs p,ND *rp) + +NODE nd_reducebase(NODE x) { - NM m; - ND p1,p2; - ND t1,t2; - unsigned int *lcm; - int td; + int len,i,j; + NDV *w; + NODE t,t0; - p1 = nd_ps[p->i1]; - p2 = nd_ps[p->i2]; - lcm = p->lcm; - td = TD(p); - NEWNM(m); - CM(m) = HCM(p2); TD(m) = td-HTD(p1); ndl_sub(lcm,HDL(p1),DL(m)); - if ( ndl_check_bound2(p->i1,DL(m)) ) - return 0; - t1 = nd_mul_ind_nm(p->i1,m); - CM(m) = nd_mod-HCM(p1); TD(m) = td-HTD(p2); ndl_sub(lcm,HDL(p2),DL(m)); - if ( ndl_check_bound2(p->i2,DL(m)) ) { - nd_free(t1); - return 0; + len = length(x); + w = (NDV *)ALLOCA(len*sizeof(NDV)); + for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) w[i] = BDY(t); + for ( i = 0; i < len; i++ ) { + for ( j = 0; j < i; j++ ) { + if ( w[i] && w[j] ) + if ( ndl_reducible(HDL(w[i]),HDL(w[j])) ) w[i] = 0; + else if ( ndl_reducible(HDL(w[j]),HDL(w[i])) ) w[j] = 0; + } } - t2 = nd_mul_ind_nm(p->i2,m); - FREENM(m); - *rp = nd_add(t1,t2); - return 1; + for ( i = len-1, t0 = 0; i >= 0; i-- ) { + if ( w[i] ) { NEXTNODE(t0,t); BDY(t) = (pointer)w[i]; } + } + NEXT(t) = 0; x = t0; + return x; } -ND nd_mul_nm(ND p,NM m0) +/* XXX incomplete */ + +void nd_init_ord(struct order_spec *ord) { - NM m,mr,mr0; - unsigned int *d,*dt,*dm; - int c,n,td,i,c1,c2; - int *pt,*p1,*p2; - ND r; + switch ( ord->id ) { + case 0: + 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: + /* XXX */ + nd_dcomp = -1; + nd_isrlex = 0; + ndl_compare_function = ndl_block_compare; + break; + case 2: + error("nd_init_ord : matrix order is not supported yet."); + break; + } + nd_ord = ord; +} - if ( !p ) +BlockMask nd_create_blockmask(struct order_spec *ord) +{ + int n,i,j,s,l; + unsigned int *t; + BlockMask bm; + + if ( !ord->id ) return 0; - else { - n = NV(p); m = BDY(p); - d = DL(m0); td = TD(m0); c = CM(m0); - mr0 = 0; - for ( ; m; m = NEXT(m) ) { - NEXTNM(mr0,mr); - c1 = CM(m); - DMAR(c1,c,0,nd_mod,c2); - CM(mr) = c2; - 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; - return r; + 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; } -ND nd_mul_ind_nm(int index,NM m0) +EPOS nd_create_epos(struct order_spec *ord) { - register int c1,c2,c; - register NM m,new,prev; - NM mr0; - unsigned int *d; - int n,td,i,len,d0,d1; - ND p,r; + int i,j,l,s,ord_l,ord_o; + EPOS epos; + struct order_pair *op; - p = nd_ps[index]; - len = nd_psl[index]; - n = NV(p); m = BDY(p); - d = DL(m0); td = TD(m0); c = CM(m0); - - NEWNM(mr0); - c1 = CM(m); DMAR(c1,c,0,nd_mod,c2); CM(mr0) = c2; - TD(mr0) = TD(m)+td; ndl_add(DL(m),d,DL(mr0)); - prev = mr0; m = NEXT(m); - len--; - - switch ( nd_wpd ) { - case 1: - d0 = d[0]; - while ( len-- ) { - c1 = CM(m); DMAR(c1,c,0,nd_mod,c2); - NEWNM(new); CM(new) = c2; - TD(new) = TD(m)+td; DL(new)[0] = DL(m)[0]+d0; - m = NEXT(m); NEXT(prev) = new; prev = new; + 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 2: - d0 = d[0]; d1 = d[1]; - while ( len-- ) { - c1 = CM(m); DMAR(c1,c,0,nd_mod,c2); - NEWNM(new); CM(new) = c2; - TD(new) = TD(m)+td; - DL(new)[0] = DL(m)[0]+d0; - DL(new)[1] = DL(m)[1]+d1; - m = NEXT(m); NEXT(prev) = new; prev = new; + 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; - default: - while ( len-- ) { - c1 = CM(m); DMAR(c1,c,0,nd_mod,c2); - NEWNM(new); CM(new) = c2; - TD(new) = TD(m)+td; ndl_add(DL(m),d,DL(new)); - m = NEXT(m); NEXT(prev) = new; prev = new; - } - break; + case 2: + error("nd_create_epos : matrix order is not supported yet."); } - - NEXT(prev) = 0; - MKND(NV(p),mr0,r); - SG(r) = SG(p) + td; - return r; + return epos; } -#endif