=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v retrieving revision 1.74 retrieving revision 1.104 diff -u -p -r1.74 -r1.104 --- OpenXM_contrib2/asir2000/builtin/strobj.c 2005/10/14 07:49:21 1.74 +++ OpenXM_contrib2/asir2000/builtin/strobj.c 2005/11/30 05:08:00 1.104 @@ -45,7 +45,7 @@ * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. * - * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.73 2005/10/14 07:39:38 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.103 2005/11/30 04:51:46 noro Exp $ */ #include "ca.h" #include "parse.h" @@ -58,12 +58,24 @@ extern jmp_buf environnement; #endif #include +#if defined(__GNUC__) +#define INLINE inline +#elif defined(VISUAL) +#define INLINE __inline +#else +#define INLINE +#endif + struct TeXSymbol { char *text; char *symbol; }; #define OPNAME(f) (((ARF)FA0(f))->name[0]) +#define IS_ZERO(f) (((f)->id==I_FORMULA) && FA0(f)==0 ) +#define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^')) +#define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+')) +#define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*')) extern char *parse_strp; @@ -83,10 +95,21 @@ void Pflatten_quote(); void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number(); void Pquote_is_dependent(),Pquote_is_function(); void Pquote_normalize(); +void Pnquote_comp(); +void Pnquote_match(); +void Pquote_to_nbp(); +void Pshuffle_mul(), Pharmonic_mul(); +void Pnbp_hm(), Pnbp_ht(), Pnbp_hc(), Pnbp_rest(); +void Pnbm_deg(); +void Pnbm_hp_rest(); +void Pnbm_hxky(), Pnbm_xky_rest(); +void Pnbm_hv(), Pnbm_rest(); + void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); -void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite(); +void Pquote_match(),Pget_quote_id(),Pquote_match_rewrite(); void Pquote_to_nary(),Pquote_to_bin(); +void fnode_do_assign(NODE arg); void do_assign(NODE arg); void fnodetotex_tb(FNODE f,TB tb); char *symbol_name(char *name); @@ -97,7 +120,7 @@ void tb_to_string(TB tb,STRING *rp); void fnodenodetotex_tb(NODE n,TB tb); void fargstotex_tb(char *opname,FNODE f,TB tb); int top_is_minus(FNODE f); -int quote_unify(Obj f,Obj pat,NODE *rp); +int quote_match(Obj f,Obj pat,NODE *rp); struct ftab str_tab[] = { {"sprintf",Psprintf,-99999999}, @@ -121,17 +144,35 @@ struct ftab str_tab[] = { {"quote_is_function",Pquote_is_function,1}, {"quote_is_dependent",Pquote_is_dependent,2}, - {"quote_normalize",Pquote_normalize,1}, + {"quote_normalize",Pquote_normalize,-2}, + {"quote_match",Pquote_match,2}, + {"quote_match_rewrite",Pquote_match_rewrite,-4}, + {"nquote_comp",Pnquote_comp,2}, + {"nquote_match",Pnquote_match,-3}, + {"quote_to_nbp",Pquote_to_nbp,1}, + {"shuffle_mul",Pshuffle_mul,2}, + {"harmonic_mul",Pharmonic_mul,2}, + + {"nbp_hm", Pnbp_hm,1}, + {"nbp_ht", Pnbp_ht,1}, + {"nbp_hc", Pnbp_hc,1}, + {"nbp_rest", Pnbp_rest,1}, + {"nbm_deg", Pnbm_deg,1}, + {"nbm_hxky", Pnbm_hxky,1}, + {"nbm_xky_rest", Pnbm_xky_rest,1}, + {"nbm_hp_rest", Pnbm_hp_rest,1}, + {"nbm_hv", Pnbm_hv,1}, + {"nbm_rest", Pnbm_rest,1}, + {"quote_to_nary",Pquote_to_nary,1}, {"quote_to_bin",Pquote_to_bin,2}, + {"quotetotex_tb",Pquotetotex_tb,2}, {"quotetotex",Pquotetotex,1}, {"quotetotex_env",Pquotetotex_env,-99999999}, {"flatten_quote",Pflatten_quote,-2}, {"quote_to_funargs",Pquote_to_funargs,1}, - {"quote_unify",Pquote_unify,2}, - {"quote_match_rewrite",Pquote_match_rewrite,-4}, {"funargs_to_quote",Pfunargs_to_quote,1}, {"get_function_name",Pget_function_name,1}, {0,0,0}, @@ -530,7 +571,6 @@ void Pwrite_to_tb(NODE arg,Q *rp) } FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); -FNODE fnode_normalize(FNODE); void Pquote_to_nary(NODE arg,QUOTE *rp) { @@ -618,7 +658,7 @@ void Pquote_is_dependent(NODE arg,Q *rp) } -void Pquote_unify(NODE arg,Q *rp) +void Pquote_match(NODE arg,Q *rp) { FNODE f,g; Obj obj; @@ -629,10 +669,10 @@ void Pquote_unify(NODE arg,Q *rp) #if 0 g = partial_eval(BDY(((QUOTE)ARG0(arg)))); MKQUOTE(q,g); - ret = quote_unify((Obj)q,(Obj)ARG1(arg),&r); + ret = quote_match((Obj)q,(Obj)ARG1(arg),&r); #else obj = (Obj)ARG0(arg); - ret = quote_unify(obj,(Obj)ARG1(arg),&r); + ret = quote_match(obj,(Obj)ARG1(arg),&r); #endif if ( ret ) { do_assign(r); @@ -641,6 +681,26 @@ void Pquote_unify(NODE arg,Q *rp) *rp = 0; } +void Pnquote_match(NODE arg,Q *rp) +{ + QUOTE fq,pq; + FNODE f,p; + int ret; + Q mode; + NODE r; + + mode = argc(arg)==3 ? (Q)ARG2(arg) : 0; + fq = (QUOTE)ARG0(arg); Pquote_normalize(mknode(2,fq,mode),&fq); f = (FNODE)BDY(fq); + pq = (QUOTE)ARG1(arg); Pquote_normalize(mknode(2,pq,mode),&pq); p = (FNODE)BDY(pq); + ret = nfnode_match(f,p,&r); + if ( ret ) { + fnode_do_assign(r); + *rp = ONE; + } else + *rp = 0; +} + + FNODE rewrite_fnode(FNODE,NODE); extern Obj VOIDobj; @@ -654,26 +714,26 @@ void Pquote_match_rewrite(NODE arg,Obj *rp) int ret,ind,ac; obj = (Obj)ARG0(arg); - ret = quote_unify(obj,(Obj)ARG1(arg),&r); + ret = quote_match(obj,(Obj)ARG1(arg),&r); if ( ret ) { for ( t = r, s0 = 0; t; t = NEXT(t) ) { NEXTNODE(s0,s); pair = BDY((LIST)BDY(t)); ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); - value = mkfnode(1,I_FORMULA,BDY(NEXT(pair))); + value = BDY((QUOTE)(BDY(NEXT(pair)))); BDY(s) = mknode(2,ind,value); } if ( s0 ) NEXT(s) = 0; switch ( ac = argc(arg) ) { case 3: h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); - *rp = eval(h); + MKQUOTE(q,h); *rp = (Obj)q; break; case 4: c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); if ( eval(c) ) { h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0); - *rp = eval(h); + MKQUOTE(q,h); *rp = (Obj)q; } else *rp = VOIDobj; break; @@ -699,6 +759,30 @@ void do_assign(NODE arg) } } +/* [[index,fnode],...] */ + +void fnode_do_assign(NODE arg) +{ + NODE t,pair; + int pv; + FNODE f; + QUOTE value; + QUOTEARG qa; + + for ( t = arg; t; t = NEXT(t) ) { + pair = (NODE)BDY(t); + pv = (int)BDY(pair); + f = (FNODE)(BDY(NEXT(pair))); + if ( f->id == I_FUNC_HEAD ) { + /* XXX : I_FUNC_HEAD is a dummy id to pass FUNC */ + MKQUOTEARG(qa,A_func,FA0(f)); + value = (QUOTE)qa; + } else + MKQUOTE(value,f); + ASSPV(pv,value); + } +} + /* /* consistency check and merge */ @@ -734,14 +818,14 @@ int merge_matching_node(NODE n,NODE a,NODE *rp) return 1; } -int quote_unify_node(NODE f,NODE pat,NODE *rp) { +int quote_match_node(NODE f,NODE pat,NODE *rp) { NODE r,a,tf,tp,r1; int ret; if ( length(f) != length(pat) ) return 0; r = 0; for ( tf = f, tp = pat; tf; tf = NEXT(tf), tp = NEXT(tp) ) { - ret = quote_unify((Obj)BDY(tf),(Obj)BDY(tp),&a); + ret = quote_match((Obj)BDY(tf),(Obj)BDY(tp),&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -753,7 +837,7 @@ int quote_unify_node(NODE f,NODE pat,NODE *rp) { /* f = [a,b,c,...] pat = [X,Y,...] rpat matches the rest of f */ -int quote_unify_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { +int quote_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { QUOTE q; Q id; FNODE fn; @@ -765,7 +849,7 @@ int quote_unify_cons(NODE f,NODE pat,Obj rpat,NODE *rp if ( length(f) < length(pat) ) return 0; r = 0; for ( tf = f, tp = pat; tp; tf = NEXT(tf), tp = NEXT(tp) ) { - ret = quote_unify((Obj)BDY(tf),(Obj)BDY(tp),&a); + ret = quote_match((Obj)BDY(tf),(Obj)BDY(tp),&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -777,7 +861,7 @@ int quote_unify_cons(NODE f,NODE pat,Obj rpat,NODE *rp MKLIST(alist,a); arg = mknode(1,alist); Pfunargs_to_quote(arg,&q); - ret = quote_unify((Obj)q,rpat,&a); + ret = quote_match((Obj)q,rpat,&a); if ( !ret ) return 0; ret = merge_matching_node(r,a,&r1); if ( !ret ) return 0; @@ -796,7 +880,7 @@ void get_quote_id_arg(QUOTE f,int *id,NODE *r) /* *rp : [[quote(A),quote(1)],...] */ -int quote_unify(Obj f, Obj pat, NODE *rp) +int quote_match(Obj f, Obj pat, NODE *rp) { NODE tf,tp,head,body; NODE parg,farg,r; @@ -815,7 +899,7 @@ int quote_unify(Obj f, Obj pat, NODE *rp) return 0; else if ( OID(pat) == O_LIST ) { if ( OID(f) == O_LIST ) - return quote_unify_node(BDY((LIST)f),BDY((LIST)pat),rp); + return quote_match_node(BDY((LIST)f),BDY((LIST)pat),rp); else return 0; } else if ( OID(pat) == O_QUOTE ) { @@ -842,10 +926,10 @@ int quote_unify(Obj f, Obj pat, NODE *rp) tp = BDY((LIST)BDY(parg)); if ( pid == I_LIST ) - return quote_unify_node(tf,tp,rp); + return quote_match_node(tf,tp,rp); else { rpat = (Obj)BDY(NEXT(parg)); - return quote_unify_cons(tf,tp,rpat,rp); + return quote_match_cons(tf,tp,rpat,rp); } case I_PVAR: @@ -861,7 +945,7 @@ int quote_unify(Obj f, Obj pat, NODE *rp) if ( id == I_FUNC ) { r = mknode(2,BDY(parg),BDY(farg)); MKLIST(l,r); head = mknode(1,l); - ret = quote_unify(BDY(NEXT(farg)), + ret = quote_match(BDY(NEXT(farg)), BDY(NEXT(parg)),&body); if ( !ret ) return 0; else return merge_matching_node(head,body,rp); @@ -889,7 +973,7 @@ int quote_unify(Obj f, Obj pat, NODE *rp) get_quote_id_arg((QUOTE)pat,&pid,&parg); get_quote_id_arg((QUOTE)f,&id,&farg); if ( compqa(CO,BDY(farg),BDY(parg)) ) return 0; - return quote_unify_node(NEXT(farg),NEXT(parg),rp); + return quote_match_node(NEXT(farg),NEXT(parg),rp); default: if ( OID(f) != O_QUOTE ) return 0; @@ -897,7 +981,7 @@ int quote_unify(Obj f, Obj pat, NODE *rp) if ( id != pid ) return 0; get_quote_id_arg((QUOTE)pat,&pid,&parg); get_quote_id_arg((QUOTE)f,&id,&farg); - return quote_unify_node(farg,parg,rp); + return quote_match_node(farg,parg,rp); } } } @@ -1263,14 +1347,14 @@ FNODE strip_paren(FNODE); void fnodetotex_tb(FNODE f,TB tb) { - NODE n,t,t0; + NODE n,t,t0,args; char vname[BUFSIZ],prefix[BUFSIZ]; char *opname,*vname_conv,*prefix_conv; Obj obj; int i,len,allzero,elen,elen2,si; C cplx; char *r; - FNODE fi,f2; + FNODE fi,f2,f1; write_tb(" ",tb); if ( !f ) { @@ -1351,6 +1435,46 @@ void fnodetotex_tb(FNODE f,TB tb) break; } break; + case I_NARYOP: + args = (NODE)FA1(f); + write_tb("(",tb); + switch ( OPNAME(f) ) { + case '+': + fnodetotex_tb((FNODE)BDY(args),tb); + for ( args = NEXT(args); args; args = NEXT(args) ) { + write_tb("+",tb); + fnodetotex_tb((FNODE)BDY(args),tb); + } + break; + case '*': + f1 = (FNODE)BDY(args); + if ( f1->id == I_FORMULA && MUNIQ(FA0(f1)) ) + write_tb("-",tb); + else + fnodetotex_tb(f1,tb); + write_tb(" ",tb); + for ( args = NEXT(args); args; args = NEXT(args) ) { + /* XXX special care for DP */ + f2 = (FNODE)BDY(args); + if ( f2->id == I_EV ) { + n = (NODE)FA0(f2); + for ( i = 0; n; n = NEXT(n), i++ ) { + fi = (FNODE)BDY(n); + if ( fi->id != I_FORMULA || FA0(fi) ) + break; + } + if ( n ) + fnodetotex_tb(f2,tb); + } else + fnodetotex_tb(f2,tb); + } + break; + default: + error("invalid nary op"); + break; + } + write_tb(")",tb); + break; case I_COP: switch( (cid)FA0(f) ) { @@ -1743,6 +1867,9 @@ int top_is_minus(FNODE f) return opname[0]=='-'; } } + case I_NARYOP: + return top_is_minus((FNODE)BDY((NODE)FA1(f))); + default: return 0; } @@ -1921,27 +2048,276 @@ void Pfunargs_to_quote(NODE arg,QUOTE *rp) MKQUOTE(*rp,f); } -FNODE fnode_apply(FNODE f,FNODE (*func)()); -FNODE fnode_normalize(FNODE f); +FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand); +FNODE fnode_normalize(FNODE f,int expand); void Pquote_normalize(NODE arg,QUOTE *rp) { QUOTE q,r; FNODE f; + int expand,ac; + ac = argc(arg); + if ( !ac ) error("quote_normalize : invalid argument"); q = (QUOTE)ARG0(arg); - if ( !q || OID(q) != O_QUOTE ) { + if ( ac == 2 ) + expand = QTOS((Q)ARG1(arg)); + if ( !q || OID(q) != O_QUOTE ) *rp = q; - return; - } else { - f = fnode_normalize(BDY(q)); + else { + f = fnode_normalize(BDY(q),expand); MKQUOTE(r,f); *rp = r; } } -int fnode_is_number(FNODE f) +NBP fnode_to_nbp(FNODE f); + +void Pquote_to_nbp(NODE arg,NBP *rp) { + QUOTE q; + FNODE f; + + q = (QUOTE)ARG0(arg); f = (FNODE)BDY(q); + f = fnode_normalize(f,0); + *rp = fnode_to_nbp(f); +} + +void Pshuffle_mul(NODE arg,NBP *rp) +{ + NBP p1,p2; + + p1 = (NBP)ARG0(arg); + p2 = (NBP)ARG1(arg); + shuffle_mulnbp(CO,p1,p2,rp); +} + +void Pharmonic_mul(NODE arg,NBP *rp) +{ + NBP p1,p2; + + p1 = (NBP)ARG0(arg); + p2 = (NBP)ARG1(arg); + harmonic_mulnbp(CO,p1,p2,rp); +} + +void Pnbp_hm(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + MKNODE(n,m,0); + MKNBP(*rp,n); + } +} + +void Pnbp_ht(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + NBM m,m1; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + NEWNBM(m1); + m1->d = m->d; m1->c = ONE; m1->b = m->b; + MKNODE(n,m1,0); + MKNBP(*rp,n); + } +} + +void Pnbp_hc(NODE arg, Q *rp) +{ + NBP p; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + m = (NBM)BDY(BDY(p)); + *rp = m->c; + } +} + +void Pnbp_rest(NODE arg, NBP *rp) +{ + NBP p; + NODE n; + + p = (NBP)ARG0(arg); + if ( !p ) *rp = 0; + else { + n = BDY(p); + if ( !NEXT(n) ) *rp = 0; + else + MKNBP(*rp,NEXT(n)); + } +} + +void Pnbm_deg(NODE arg, Q *rp) +{ + NBP p; + NBM m; + + p = (NBP)ARG0(arg); + if ( !p ) + STOQ(-1,*rp); + else { + m = (NBM)BDY(BDY(p)); + STOQ(m->d,*rp); + } +} + +void Pnbm_hp_rest(NODE arg, LIST *rp) +{ + NBP p,h,r; + NBM m,m1; + NODE n; + int *b,*b1; + int d,d1,v,i,j,k; + + p = (NBP)ARG0(arg); + if ( !p ) + MKLIST(*rp,0); + else { + m = (NBM)BDY(BDY(p)); + b = m->b; d = m->d; + if ( !d ) + MKLIST(*rp,0); + else { + v = NBM_GET(b,0); + for ( i = 1; i < d; i++ ) + if ( NBM_GET(b,i) != v ) break; + NEWNBM(m1); NEWNBMBDY(m1,i); + b1 = m1->b; m1->d = i; m1->c = ONE; + if ( v ) for ( j = 0; j < i; j++ ) NBM_SET(b1,j); + else for ( j = 0; j < i; j++ ) NBM_CLR(b1,j); + MKNODE(n,m1,0); MKNBP(h,n); + + d1 = d-i; + NEWNBM(m1); NEWNBMBDY(m1,d1); + b1 = m1->b; m1->d = d1; m1->c = ONE; + for ( j = 0, k = i; j < d1; j++, k++ ) + if ( NBM_GET(b,k) ) NBM_SET(b1,j); + else NBM_CLR(b1,j); + MKNODE(n,m1,0); MKNBP(r,n); + n = mknode(2,h,r); + MKLIST(*rp,n); + } + } +} + +void Pnbm_hxky(NODE arg, LIST *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_xky_nbm((NBM)BDY(BDY(p)),0,rp,0); +} + +void Pnbm_xky_rest(NODE arg,NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_xky_nbm((NBM)BDY(BDY(p)),0,0,rp); +} + +void Pnbm_hv(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_nbm((NBM)BDY(BDY(p)),0,rp,0); +} + +void Pnbm_rest(NODE arg, NBP *rp) +{ + NBP p; + + p = (NBP)ARG0(arg); + if ( !p ) + *rp = 0; + else + separate_nbm((NBM)BDY(BDY(p)),0,0,rp); +} + +NBP fnode_to_nbp(FNODE f) +{ + Q r; + int n,i; + NBM m; + V v; + NBP u,u1,u2; + NODE t,b; + + if ( f->id == I_FORMULA ) { + r = eval(f); + NEWNBM(m); + if ( OID(r) == O_N ) { + m->d = 0; m->c = (Q)r; m->b = 0; + } else { + v = VR((P)r); + m->d = 1; m->c = ONE; NEWNBMBDY(m,1); + if ( !strcmp(NAME(v),"x") ) NBM_SET(m->b,0); + else NBM_CLR(m->b,0); + } + MKNODE(b,m,0); MKNBP(u,b); + return u; + } else if ( IS_NARYADD(f) ) { + t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); + for ( t = NEXT(t); t; t = NEXT(t) ) { + u1 = fnode_to_nbp((FNODE)BDY(t)); + addnbp(CO,u,u1,&u2); u = u2; + } + return u; + } else if ( IS_NARYMUL(f) ) { + t = (NODE)FA1(f); u = fnode_to_nbp((FNODE)BDY(t)); + for ( t = NEXT(t); t; t = NEXT(t) ) { + u1 = fnode_to_nbp((FNODE)BDY(t)); + mulnbp(CO,u,u1,&u2); u = u2; + } + return u; + } else if ( IS_BINARYPWR(f) ) { + u = fnode_to_nbp((FNODE)FA1(f)); + r = eval((FNODE)FA2(f)); + pwrnbp(CO,u,r,&u1); + return u1; + } +} + +void Pnquote_comp(NODE arg,Q *rp) +{ + QUOTE q1,q2; + FNODE f1,f2; + int r; + + q1 = (QUOTE)ARG0(arg); f1 = (FNODE)BDY(q1); + q2 = (QUOTE)ARG1(arg); f2 = (FNODE)BDY(q2); + f1 = fnode_normalize(f1,0); + f2 = fnode_normalize(f2,0); + r = nfnode_comp(f1,f2); + STOQ(r,*rp); +} + +INLINE int fnode_is_number(FNODE f) +{ Obj obj; switch ( f->id ) { @@ -2025,15 +2401,6 @@ int fnode_is_integer(FNODE f) } } -int fnode_is_zero(FNODE f) -{ - Q n; - - n = eval(f); - if ( !n ) return 1; - else return 0; -} - int fnode_is_nonnegative_integer(FNODE f) { Q n; @@ -2093,51 +2460,63 @@ int fnode_is_dependent(FNODE f,V v) } } -FNODE fnode_normalize_add(FNODE a1,FNODE a2); -FNODE fnode_normalize_mul(FNODE a1,FNODE a2); -FNODE fnode_normalize_pwr(FNODE a1,FNODE a2); +FNODE nfnode_add(FNODE a1,FNODE a2,int expand); +FNODE nfnode_mul(FNODE a1,FNODE a2,int expand); +FNODE nfnode_pwr(FNODE a1,FNODE a2,int expand); +FNODE nfnode_mul_coef(Num c,FNODE f,int expand); +FNODE fnode_expand_pwr(FNODE f,int n,int expand); FNODE to_narymul(FNODE f); FNODE to_naryadd(FNODE f); -FNODE fnode_normalize_mul_coef(Num c,FNODE f); +FNODE fnode_node_to_naryadd(NODE n); +FNODE fnode_node_to_narymul(NODE n); void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); void fnode_coef_body(FNODE f,Num *cp,FNODE *bp); -FNODE fnode_normalize(FNODE f) +FNODE fnode_normalize(FNODE f,int expand) { FNODE a1,a2,mone,r,b2; NODE n; - Num invc2,c2; Q q; + if ( f->normalized && (f->expanded == expand) ) return f; STOQ(-1,q); mone = mkfnode(1,I_FORMULA,q); switch ( f->id ) { case I_PAREN: - return fnode_normalize(FA0(f)); + r = fnode_normalize(FA0(f),expand); + break; case I_MINUS: - return fnode_normalize_mul_coef((Num)q,fnode_normalize(FA0(f))); + r = nfnode_mul_coef((Num)q, + fnode_normalize(FA0(f),expand),expand); + break; case I_BOP: /* arf fnode fnode */ - a1 = fnode_normalize(FA1(f)); - a2 = fnode_normalize(FA2(f)); + a1 = fnode_normalize(FA1(f),expand); + a2 = fnode_normalize(FA2(f),expand); switch ( OPNAME(f) ) { case '+': - return fnode_normalize_add(a1,a2); + r = nfnode_add(a1,a2,expand); + break; case '-': - a2 = fnode_normalize_mul_coef((Num)q,a2); - return fnode_normalize_add(a1,a2); + a2 = nfnode_mul_coef((Num)q,a2,expand); + r = nfnode_add(a1,a2,expand); + break; case '*': - return fnode_normalize_mul(a1,a2); + r = nfnode_mul(a1,a2,expand); + break; case '/': - a2 = fnode_normalize_pwr(a2,mone); - return fnode_normalize_mul(a1,a2); + a2 = nfnode_pwr(a2,mone,expand); + r = nfnode_mul(a1,a2,expand); + break; case '^': - return fnode_normalize_pwr(a1,a2); + r = nfnode_pwr(a1,a2,expand); + break; default: - return mkfnode(3,I_BOP,FA0(f),a1,a2); + r = mkfnode(3,I_BOP,FA0(f),a1,a2); + break; } break; @@ -2145,30 +2524,34 @@ FNODE fnode_normalize(FNODE f) switch ( OPNAME(f) ) { case '+': n = (NODE)FA1(f); - r = fnode_normalize(BDY(n)); n = NEXT(n); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); for ( ; n; n = NEXT(n) ) { - a1 = fnode_normalize(BDY(n)); - r = fnode_normalize_add(r,a1); + a1 = fnode_normalize(BDY(n),expand); + r = nfnode_add(r,a1,expand); } - return r; + break; case '*': n = (NODE)FA1(f); - r = fnode_normalize(BDY(n)); n = NEXT(n); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); for ( ; n; n = NEXT(n) ) { - a1 = fnode_normalize(BDY(n)); - r = fnode_normalize_mul(r,a1); + a1 = fnode_normalize(BDY(n),expand); + r = nfnode_mul(r,a1,expand); } - return r; + break; default: error("fnode_normallize : cannot happen"); } + break; default: - return fnode_apply(f,fnode_normalize); + return fnode_apply(f,fnode_normalize,expand); } + r->normalized = 1; + r->expanded = expand; + return r; } -FNODE fnode_apply(FNODE f,FNODE (*func)()) +FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand) { fid_spec_p spec; FNODE r; @@ -2181,13 +2564,13 @@ FNODE fnode_apply(FNODE f,FNODE (*func)()) for ( i = 0; i < n; i++ ) { switch ( spec->type[i] ) { case A_fnode: - r->arg[i] = func(f->arg[i]); + r->arg[i] = func(f->arg[i],expand); break; case A_node: s = (NODE)f->arg[i]; for ( t0 = 0; s; s = NEXT(s) ) { NEXTNODE(t0,t); - BDY(t) = (pointer)func((FNODE)BDY(s)); + BDY(t) = (pointer)func((FNODE)BDY(s),expand); } if ( t0 ) NEXT(t) = 0; r->arg[i] = t0; @@ -2200,33 +2583,28 @@ FNODE fnode_apply(FNODE f,FNODE (*func)()) return r; } -FNODE fnode_normalize_add(FNODE f1,FNODE f2) +FNODE nfnode_add(FNODE f1,FNODE f2,int expand) { NODE n1,n2,r0,r; FNODE b1,b2; int s; Num c1,c2,c; - if ( fnode_is_zero(f1) ) return f2; - else if ( fnode_is_zero(f2) ) return f1; - if ( f1->id != I_NARYOP || OPNAME(f1) != '+' ) f1 = to_naryadd(f1); - if ( f2->id != I_NARYOP || OPNAME(f2) != '+' ) f2 = to_naryadd(f2); - n1 = (NODE)FA1(f1); - n2 = (NODE)FA1(f2); + if ( IS_ZERO(f1) ) return f2; + else if ( IS_ZERO(f2) ) return f1; + f1 = to_naryadd(f1); f2 = to_naryadd(f2); + n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); r0 = 0; while ( n1 && n2 ) { - fnode_coef_body(BDY(n1),&c1,&b1); - fnode_coef_body(BDY(n2),&c2,&b2); - s = compfnode(b1,b2); - if ( s > 0 ) { + fnode_coef_body(BDY(n1),&c1,&b1); fnode_coef_body(BDY(n2),&c2,&b2); + if ( (s = nfnode_comp(b1,b2)) > 0 ) { NEXTNODE(r0,r); BDY(r) = BDY(n1); n1 = NEXT(n1); } else if ( s < 0 ) { NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2); } else { addnum(0,c1,c2,&c); if ( c ) { - NEXTNODE(r0,r); - BDY(r) = UNIQ(c) ? b1 : fnode_normalize_mul_coef(c,b1); + NEXTNODE(r0,r); BDY(r) = nfnode_mul_coef(c,b1,expand); } n1 = NEXT(n1); n2 = NEXT(n2); } @@ -2240,128 +2618,179 @@ FNODE fnode_normalize_add(FNODE f1,FNODE f2) else if ( r0 ) NEXT(r) = 0; - if ( !r0 ) - return mkfnode(1,I_FORMULA,0); - else if ( !NEXT(r0) ) - return BDY(r0); - else - return mkfnode(2,I_NARYOP,addfs,r0); + return fnode_node_to_naryadd(r0); } -FNODE fnode_normalize_mul(FNODE f1,FNODE f2) +FNODE fnode_node_to_naryadd(NODE n) { + if ( !n ) return mkfnode(1,I_FORMULA,0); + else if ( !NEXT(n) ) return BDY(n); + else return mkfnode(2,I_NARYOP,addfs,n); +} + +FNODE fnode_node_to_narymul(NODE n) +{ + if ( !n ) return mkfnode(1,I_FORMULA,ONE); + else if ( !NEXT(n) ) return BDY(n); + else return mkfnode(2,I_NARYOP,mulfs,n); +} + +FNODE nfnode_mul(FNODE f1,FNODE f2,int expand) +{ NODE n1,n2,r0,r,r1; - FNODE b1,b2,e1,e2,cc; + FNODE b1,b2,e1,e2,cc,t,t1; FNODE *m; int s; Num c1,c2,c,e; - int l1,l2,l,i,j; + int l1,l,i,j; - if ( fnode_is_zero(f1) || fnode_is_zero(f2) ) return 0; + if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); + else if ( fnode_is_number(f1) ) + return nfnode_mul_coef((Num)eval(f1),f2,expand); + else if ( fnode_is_number(f2) ) + return nfnode_mul_coef((Num)eval(f2),f1,expand); - if ( f1->id != I_NARYOP || OPNAME(f1) != '*' ) f1 = to_narymul(f1); - if ( f2->id != I_NARYOP || OPNAME(f2) != '*' ) f2 = to_narymul(f2); - n1 = (NODE)FA1(f1); - n2 = (NODE)FA1(f2); - if ( fnode_is_number(BDY(n1)) ) - if ( fnode_is_number(BDY(n2)) ) { - mulnum(0,eval(BDY(n1)),eval(BDY(n2)),&c); - n1 = NEXT(n1); n2 = NEXT(n2); - } else { - c = eval(BDY(n1)); n1 = NEXT(n1); + if ( expand && IS_NARYADD(f1) ) { + t = mkfnode(1,I_FORMULA,0); + for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) { + t1 = nfnode_mul(BDY(n1),f2,expand); + t = nfnode_add(t,t1,expand); } - else if ( fnode_is_number(BDY(n2)) ) { - c = eval(BDY(n2)); n2 = NEXT(n2); - } else - c = (Num)ONE; + return t; + } + if ( expand && IS_NARYADD(f2) ) { + t = mkfnode(1,I_FORMULA,0); + for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) { + t1 = nfnode_mul(f1,BDY(n2),expand); + t = nfnode_add(t,t1,expand); + } + return t; + } + + fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); + mulnum(0,c1,c2,&c); if ( !c ) return mkfnode(1,I_FORMULA,0); - l1 = length(n1); - l2 = length(n2); - l = l1+l2; + + n1 = (NODE)FA1(to_narymul(b1)); n2 = (NODE)FA1(to_narymul(b2)); + l1 = length(n1); l = l1+length(n2); m = (FNODE *)ALLOCA(l*sizeof(FNODE)); for ( r = n1, i = 0; i < l1; r = NEXT(r), i++ ) m[i] = BDY(r); for ( r = n2; r; r = NEXT(r) ) { - if ( i == 0 ) + if ( i == 0 || (expand == 2) ) m[i++] = BDY(r); else { - fnode_base_exp(m[i-1],&b1,&e1); - fnode_base_exp(BDY(r),&b2,&e2); - if ( compfnode(b1,b2) ) { - for ( j = i-1; j >= 0; j-- ) { - MKNODE(r1,m[j],r); r = r1; - } - cc = mkfnode(1,I_FORMULA,c); - MKNODE(r1,cc,r); r = r1; - return mkfnode(2,I_NARYOP,mulfs,r); - } else { - addnum(0,eval(e1),eval(e2),&e); - if ( !e ) i--; - else if ( UNIQ(e) ) - m[i-1] = b1; - else - m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e)); - } + fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); + if ( compfnode(b1,b2) ) break; + addnum(0,eval(e1),eval(e2),&e); + if ( !e ) i--; + else if ( UNIQ(e) ) + m[i-1] = b1; + else + m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e)); } } - if ( !i ) return mkfnode(1,I_FORMULA,c); - else { - r = 0; - for ( j = i-1; j >= 0; j-- ) { - MKNODE(r1,m[j],r); r = r1; - } - cc = mkfnode(1,I_FORMULA,c); - MKNODE(r1,cc,r); - r = r1; - return mkfnode(2,I_NARYOP,mulfs,r); + for ( j = i-1; j >= 0; j-- ) { + MKNODE(r1,m[j],r); r = r1; } + if ( !UNIQ(c) ) { + cc = mkfnode(1,I_FORMULA,c); MKNODE(r1,cc,r); r = r1; + } + return fnode_node_to_narymul(r); } -FNODE fnode_normalize_pwr(FNODE f1,FNODE f2) +FNODE nfnode_pwr(FNODE f1,FNODE f2,int expand) { - FNODE b,b1,e1,e,cc,r; - Num c,c1; - NODE arg,n; + FNODE b,b1,e1,e,cc,r,mf2,mone,inv; + Num c,c1,nf2; + int ee; + NODE arg,n,t0,t1; + Q q; - if ( fnode_is_zero(f2) ) return mkfnode(1,I_FORMULA,ONE); - else if ( fnode_is_zero(f1) ) return mkfnode(1,I_FORMULA,0); - else if ( fnode_is_one(f2) ) return f1; - else if ( fnode_is_number(f1) ) + if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); + else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0); + else if ( fnode_is_number(f1) ) { if ( fnode_is_integer(f2) ) { - pwrnum(0,(Num)eval(f1),(Num)eval(f2),&c); - return mkfnode(1,I_FORMULA,c); + if ( fnode_is_one(f2) ) return f1; + else { + pwrnum(0,(Num)eval(f1),(Num)eval(f2),&c); + return mkfnode(1,I_FORMULA,c); + } } else return mkfnode(3,I_BOP,pwrfs,f1,f2); - else if ( f1->id == I_BOP && OPNAME(f1) == '^' ) { + } else if ( IS_BINARYPWR(f1) ) { b1 = FA1(f1); e1 = FA2(f1); - e = fnode_normalize_mul(e1,f2); + e = nfnode_mul(e1,f2,expand); if ( fnode_is_one(e) ) return b1; else return mkfnode(3,I_BOP,FA0(f1),b1,e); - } else if ( f1->id == I_NARYOP && OPNAME(f1) == '*' ) { + } else if ( expand && IS_NARYMUL(f1) && fnode_is_number(f2) + && fnode_is_integer(f2) ) { fnode_coef_body(f1,&c1,&b1); - if ( fnode_is_integer(f2) ) { - pwrnum(0,(Num)c1,(Num)eval(f2),&c); - cc = mkfnode(1,I_FORMULA,c); - b = fnode_normalize_pwr(b1,f2); - if ( fnode_is_one(cc) ) - return b; - else { - NEWFNODE(r,2); - r->id = I_NARYOP; FA0(r) = mulfs; FA1(r) = mknode(2,cc,b); - return r; + nf2 = (Num)eval(f2); + pwrnum(0,(Num)c1,nf2,&c); + ee = QTOS((Q)nf2); + cc = mkfnode(1,I_FORMULA,c); + if ( fnode_is_nonnegative_integer(f2) ) + b = fnode_expand_pwr(b1,ee,expand); + else { + STOQ(-1,q); + mone = mkfnode(1,I_FORMULA,q); + b1 = to_narymul(b1); + for ( t0 = 0, n = (NODE)FA1(b1); n; n = NEXT(n) ) { + inv = mkfnode(3,I_BOP,pwrfs,BDY(n),mone); + MKNODE(t1,inv,t0); t0 = t1; } - } else - return mkfnode(3,I_BOP,pwrfs,f1,f2); + b1 = fnode_node_to_narymul(t0); + b = fnode_expand_pwr(b1,-ee,expand); + } + if ( fnode_is_one(cc) ) + return b; + else + return fnode_node_to_narymul(mknode(2,cc,b)); + } else if ( expand && fnode_is_integer(f2) + && fnode_is_nonnegative_integer(f2) ) { + q = (Q)eval(f2); + if ( PL(NM(q)) > 1 ) error("nfnode_pwr : exponent too large"); + return fnode_expand_pwr(f1,QTOS(q),expand); } else return mkfnode(3,I_BOP,pwrfs,f1,f2); } +FNODE fnode_expand_pwr(FNODE f,int n,int expand) +{ + int n1,i; + FNODE f1,f2,fn; + Q q; + + if ( !n ) return mkfnode(1,I_FORMULA,ONE); + else if ( IS_ZERO(f) ) return mkfnode(1,I_FORMULA,0); + else if ( n == 1 ) return f; + else { + switch ( expand ) { + case 1: + n1 = n/2; + f1 = fnode_expand_pwr(f,n1,expand); + f2 = nfnode_mul(f1,f1,expand); + if ( n%2 ) f2 = nfnode_mul(f2,f,1); + return f2; + case 2: + for ( i = 1, f1 = f; i < n; i++ ) + f1 = nfnode_mul(f1,f,expand); + return f1; + case 0: default: + STOQ(n,q); + fn = mkfnode(1,I_FORMULA,q); + return mkfnode(3,I_BOP,pwrfs,f,fn); + } + } +} + /* f = b^e */ void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep) { - if ( f->id == I_BOP && OPNAME(f) == '^' ) { + if ( IS_BINARYPWR(f) ) { *bp = FA1(f); *ep = FA2(f); } else { *bp = f; *ep = mkfnode(1,I_FORMULA,ONE); @@ -2373,11 +2802,10 @@ FNODE to_naryadd(FNODE f) FNODE r; NODE n; - NEWFNODE(r,2); - r->id = I_NARYOP; - FA0(r) = addfs; - MKNODE(n,f,0); - FA1(r) = n; + if ( IS_NARYADD(f) ) return f; + + NEWFNODE(r,2); r->id = I_NARYOP; + FA0(r) = addfs; MKNODE(n,f,0); FA1(r) = n; return r; } @@ -2386,80 +2814,552 @@ FNODE to_narymul(FNODE f) FNODE r; NODE n; - NEWFNODE(r,2); - r->id = I_NARYOP; - FA0(r) = mulfs; - MKNODE(n,f,0); - FA1(r) = n; + if ( IS_NARYMUL(f) ) return f; + + NEWFNODE(r,2); r->id = I_NARYOP; + FA0(r) = mulfs; MKNODE(n,f,0); FA1(r) = n; return r; } -FNODE fnode_normalize_mul_coef(Num c,FNODE f) +FNODE nfnode_mul_coef(Num c,FNODE f,int expand) { - FNODE cc; + FNODE b1,cc; Num c1,c2; - NODE n,r0,r; + NODE n,r,r0; if ( !c ) return mkfnode(I_FORMULA,0); - else if ( UNIQ(c) ) - return f; - else if ( fnode_is_number(f) ) { - mulnum(0,c,eval(f),&c1); return mkfnode(1,I_FORMULA,c1); - } else if ( f->id == I_NARYOP && OPNAME(f) == '*' ) { - cc = (FNODE)BDY((NODE)FA1(f)); - if ( fnode_is_number(cc) ) { - mulnum(0,c,eval(cc),&c2); - if ( UNIQ(c2) ) - n = NEXT((NODE)FA1(f)); - else { - cc = mkfnode(1,I_FORMULA,c2); - MKNODE(n,cc,NEXT((NODE)FA1(f))); - } - } else { - cc = mkfnode(1,I_FORMULA,c); - MKNODE(n,cc,(NODE)FA1(f)); + else { + fnode_coef_body(f,&c1,&b1); + mulnum(0,c,c1,&c2); + if ( UNIQ(c2) ) return b1; + else { + cc = mkfnode(1,I_FORMULA,c2); + if ( fnode_is_number(b1) ) { + if ( !fnode_is_one(b1) ) + error("nfnode_mul_coef : cannot happen"); + else + return cc; + } else if ( IS_NARYMUL(b1) ) { + MKNODE(n,cc,FA1(b1)); + return fnode_node_to_narymul(n); + } else if ( expand && IS_NARYADD(b1) ) { + for ( r0 = 0, n = (NODE)FA1(b1); n; n = NEXT(n) ) { + NEXTNODE(r0,r); + BDY(r) = nfnode_mul_coef(c2,BDY(n),expand); + } + if ( r0 ) NEXT(r) = 0; + return fnode_node_to_naryadd(r0); + } else + return fnode_node_to_narymul(mknode(2,cc,b1)); } - if ( NEXT(n) ) - return mkfnode(2,I_NARYOP,FA0(f),n); - else - return (FNODE)BDY(n); - } else if ( f->id == I_NARYOP && OPNAME(f) == '+' ) { - for ( r0 = 0, n = (NODE)FA1(f); n; n = NEXT(n) ) { - NEXTNODE(r0,r); - BDY(r) = fnode_normalize_mul_coef(c,BDY(n)); - } - if ( r0 ) NEXT(r) = 0; - return mkfnode(2,I_NARYOP,FA0(f),r0); - } else { - cc = mkfnode(1,I_FORMULA,c); - n = mknode(2,cc,f); - return mkfnode(2,I_NARYOP,mulfs,n); } } void fnode_coef_body(FNODE f,Num *cp,FNODE *bp) { FNODE c; - NODE n; if ( fnode_is_number(f) ) { *cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE); - } else if ( f->id == I_NARYOP && OPNAME(f) == '*' ) { - c = (FNODE)BDY((NODE)FA1(f)); + } else if ( IS_NARYMUL(f) ) { + c=(FNODE)BDY((NODE)FA1(f)); if ( fnode_is_number(c) ) { *cp = eval(c); - n = NEXT((NODE)FA1(f)); - if ( !n ) - *bp = mkfnode(1,I_FORMULA,ONE); - else if ( !NEXT(n) ) - *bp = BDY(n); - else - *bp = mkfnode(2,I_NARYOP,FA0(f),n); + *bp = fnode_node_to_narymul(NEXT((NODE)FA1(f))); } else { *cp = (Num)ONE; *bp = f; } } else { *cp = (Num)ONE; *bp = f; + } +} + +int nfnode_comp_pwr(FNODE f1,FNODE f2); + +int nfnode_comp(FNODE f1,FNODE f2) +{ + NODE n1,n2; + int r,i1,i2,ret; + char *nm1,*nm2; + FNODE b1,b2,e1,e2,g,a1,a2,fn1,fn2; + Num ee,ee1,c1,c2; + + if ( IS_NARYADD(f1) || IS_NARYADD(f2) ) { + f1 = to_naryadd(f1); f2 = to_naryadd(f2); + n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); + while ( n1 && n2 ) + if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; + else { + n1 = NEXT(n1); n2 = NEXT(n2); + } + return n1?1:(n2?-1:0); + } + if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { + fnode_coef_body(f1,&c1,&b1); + fnode_coef_body(f2,&c2,&b2); + if ( !compfnode(b1,b2) ) return compnum(0,c1,c2); + b1 = to_narymul(b1); b2 = to_narymul(b2); + n1 = (NODE)FA1(b1); n2 = (NODE)FA1(b2); + while ( 1 ) { + while ( n1 && n2 && !compfnode(BDY(n1),BDY(n2)) ) { + n1 = NEXT(n1); n2 = NEXT(n2); + } + if ( !n1 || !n2 ) { + return n1?1:(n2?-1:0); + } + fnode_base_exp(BDY(n1),&b1,&e1); + fnode_base_exp(BDY(n2),&b2,&e2); + + if ( r = nfnode_comp(b1,b2) ) { + if ( r > 0 ) + return nfnode_comp(e1,mkfnode(1,I_FORMULA,0)); + else if ( r < 0 ) + return nfnode_comp(mkfnode(1,I_FORMULA,0),e2); + } else { + n1 = NEXT(n1); n2 = NEXT(n2); + if ( fnode_is_number(e1) && fnode_is_number(e2) ) { + /* f1 = t b^e1 ... , f2 = t b^e2 ... */ + subnum(0,eval(e1),eval(e2),&ee); + r = compnum(0,ee,0); + if ( r > 0 ) { + g = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,ee)); + MKNODE(n1,g,n1); + } else if ( r < 0 ) { + chsgnnum(ee,&ee1); + g = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,ee1)); + MKNODE(n2,g,n2); + } + } else { + r = nfnode_comp(e1,e2); + if ( r > 0 ) return 1; + else if ( r < 0 ) return -1; + } + } + } + } + if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) + return nfnode_comp_pwr(f1,f2); + + /* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, I_IFUNC or I_PVAR */ + /* I_IFUNC > I_PVAR > I_FUNC > I_FORMULA */ + switch ( f1->id ) { + case I_FORMULA: + switch ( f2->id ) { + case I_FORMULA: + return arf_comp(CO,FA0(f1),FA0(f2)); + case I_FUNC: case I_IFUNC: case I_PVAR: + return -1; + default: + error("nfnode_comp : undefined"); + } + break; + case I_FUNC: + switch ( f2->id ) { + case I_FORMULA: + return 1; + case I_PVAR: case I_IFUNC: + return -1; + case I_FUNC: + nm1 = ((FUNC)FA0(f1))->name; nm2 = ((FUNC)FA0(f2))->name; + r = strcmp(nm1,nm2); + if ( r > 0 ) return 1; + else if ( r < 0 ) return -1; + else { + /* compare args */ + n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); + while ( n1 && n2 ) + if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; + else { + n1 = NEXT(n1); n2 = NEXT(n2); + } + return n1?1:(n2?-1:0); + } + break; + default: + error("nfnode_comp : undefined"); + } + case I_PVAR: + switch ( f2->id ) { + case I_FORMULA: case I_FUNC: + return 1; + case I_IFUNC: + return -1; + case I_PVAR: + i1 = (int)FA0(f1); i2 = (int)FA0(f2); + if ( i1 > i2 ) return 1; + else if ( i1 < i2 ) return -1; + else return 0; + default: + error("nfnode_comp : undefined"); + } + break; + case I_IFUNC: + switch ( f2->id ) { + case I_FORMULA: case I_FUNC: case I_PVAR: + return 1; + case I_IFUNC: + i1 = (int)FA0((FNODE)FA0(f1)); + i2 = (int)FA0((FNODE)FA0(f2)); + if ( i1 > i2 ) return 1; + else if ( i1 < i2 ) return -1; + else { + /* compare args */ + n1 = FA0((FNODE)FA1(f1)); n2 = FA0((FNODE)FA1(f2)); + while ( n1 && n2 ) + if ( r = nfnode_comp(BDY(n1),BDY(n2)) ) return r; + else { + n1 = NEXT(n1); n2 = NEXT(n2); + } + return n1?1:(n2?-1:0); + } + break; + + default: + error("nfnode_comp : undefined"); + } + break; + default: + error("nfnode_comp : undefined"); + } +} + +int nfnode_comp_pwr(FNODE f1,FNODE f2) +{ + FNODE b1,b2,e1,e2; + int r; + + fnode_base_exp(f1,&b1,&e1); + fnode_base_exp(f2,&b2,&e2); + if ( r = nfnode_comp(b1,b2) ) { + if ( r > 0 ) + return nfnode_comp(e1,mkfnode(1,I_FORMULA,0)); + else if ( r < 0 ) + return nfnode_comp(mkfnode(1,I_FORMULA,0),e2); + } else return nfnode_comp(e1,e2); +} + +NODE append_node(NODE a1,NODE a2) +{ + NODE t,t0; + + if ( !a1 ) + return a2; + else { + for ( t0 = 0; a1; a1 = NEXT(a1) ) { + NEXTNODE(t0,t); BDY(t) = BDY(a1); + } + NEXT(t) = a2; + return t0; + } +} + +int nfnode_match(FNODE f,FNODE pat,NODE *rp) +{ + NODE m,m1,m2,base,exp,fa,pa,n; + LIST l; + QUOTE qp,qf; + FNODE fbase,fexp,a,fh; + FUNC ff,pf; + int r; + + if ( !pat ) + if ( !f ) { + *rp = 0; + return 1; + } else + return 0; + else if ( !f ) + return 0; + switch ( pat->id ) { + case I_PVAR: + /* [[pat,f]] */ + *rp = mknode(1,mknode(2,(int)FA0(pat),f)); + return 1; + + case I_FORMULA: + if ( f->id == I_FORMULA && !arf_comp(CO,(Obj)FA0(f),(Obj)FA0(pat)) ) { + *rp = 0; return 1; + } else + return 0; + + case I_BOP: + /* OPNAME should be "^" */ + if ( !IS_BINARYPWR(pat) ) + error("nfnode_match : invalid BOP"); + if ( IS_BINARYPWR(f) ) { + fbase = FA1(f); fexp = FA2(f); + } else { + fbase = f; fexp = mkfnode(1,I_FORMULA,ONE); + } + if ( !nfnode_match(fbase,FA1(pat),&base) ) return 0; + a = rewrite_fnode(FA2(pat),base); + if ( !nfnode_match(fexp,a,&exp) ) return 0; + else { + *rp = append_node(base,exp); + return 1; + } + break; + + case I_FUNC: case I_IFUNC: + if ( f->id != I_FUNC ) return 0; + ff = (FUNC)FA0(f); + if ( pat->id == I_FUNC ) { + pf = (FUNC)FA0(pat); + if ( strcmp(ff->fullname,pf->fullname) ) return 0; + m = 0; + } else { + /* XXX : I_FUNC_HEAD is a dummy id to pass FUNC */ + fh = mkfnode(1,I_FUNC_HEAD,FA0(f)); + m = mknode(1,mknode(2,FA0((FNODE)FA0(pat)),fh),0); + } + /* FA1(f) and FA1(pat) are I_LIST */ + fa = (NODE)FA0((FNODE)FA1(f)); + pa = (NODE)FA0((FNODE)FA1(pat)); + while ( fa && pa ) { + a = rewrite_fnode(BDY(pa),m); + if ( !nfnode_match(BDY(fa),a,&m1) ) return 0; + m = append_node(m1,m); + fa = NEXT(fa); pa = NEXT(pa); + } + if ( fa || pa ) return 0; + else { + *rp = m; + return 1; + } + + case I_NARYOP: + if ( IS_NARYADD(pat) ) + return nfnode_match_naryadd(f,pat,rp); + else if ( IS_NARYMUL(pat) ) + return nfnode_match_narymul(f,pat,rp); + else + error("nfnode_match : invalid NARYOP"); + break; + + default: + error("nfnode_match : invalid pattern"); + } +} + +/* remove i-th element */ + +FNODE fnode_removeith_naryadd(FNODE p,int i) +{ + int k,l; + NODE t,r0,r,a; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_removeith_naryadd: invalid index"); + else if ( i == 0 ) + return fnode_node_to_naryadd(NEXT(a)); + else { + for ( r0 = 0, k = 0, t = a; k < i; k++, t = NEXT(t) ) { + NEXTNODE(r0,r); + BDY(r) = BDY(t); + } + NEXT(r) = NEXT(t); + return fnode_node_to_naryadd(r0); + } + +} + +/* a0,...,a(i-1) */ +FNODE fnode_left_narymul(FNODE p,int i) +{ + int k,l; + NODE t,r0,r,a; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_left_narymul : invalid index"); + if ( i == 0 ) return 0; + else if ( i == 1 ) return (FNODE)BDY(a); + else { + for ( r0 = 0, k = 0, t = a; k < i; k++, t = NEXT(t) ) { + NEXTNODE(r0,r); + BDY(r) = BDY(t); + } + NEXT(r) = 0; + return fnode_node_to_narymul(r0); + } +} + +/* a(i+1),...,a(l-1) */ +FNODE fnode_right_narymul(FNODE p,int i) +{ + NODE a,t; + int l,k; + + a = (NODE)FA1(p); + l = length(a); + if ( i < 0 || i >= l ) error("fnode_right_narymul : invalid index"); + if ( i == l-1 ) return 0; + else { + for ( k = 0, t = a; k <= i; k++, t = NEXT(t) ); + return fnode_node_to_narymul(t); + } +} + +int nfnode_match_naryadd(FNODE f,FNODE p,NODE *rp) +{ + int fl,pl,fi,pi; + NODE fa,pa,t,s,m,m1; + FNODE fr,pr,prr,pivot; + + f = to_naryadd(f); + fa = (NODE)FA1(f); fl = length(fa); + pa = (NODE)FA1(p); pl = length(pa); + if ( fl < pl ) return 0; + else if ( pl == 1 ) { + if ( fl == 1 ) + return nfnode_match(BDY(fa),BDY(pa),rp); + else + return 0; + } else { + for ( t = pa, pi = 0; t; t = NEXT(t), pi++ ) + if ( ((FNODE)BDY(t))->id != I_PVAR ) break; + if ( !t ) { + /* all are I_PVAR */ + m = 0; + for ( t = pa, s = fa; NEXT(t); t = NEXT(t), s = NEXT(s) ) { + nfnode_match(BDY(s),BDY(t),&m1); + m = append_node(m1,m); + } + if ( !NEXT(s) ) + fr = (FNODE)BDY(s); + else + fr = mkfnode(2,I_NARYOP,FA0(f),s); + nfnode_match(fr,BDY(t),&m1); + *rp = append_node(m1,m); + return 1; + } else { + pivot = (FNODE)BDY(t); + pr = fnode_removeith_naryadd(p,pi); + for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { + if ( nfnode_match(BDY(s),pivot,&m) ) { + fr = fnode_removeith_naryadd(f,fi); + prr = rewrite_fnode(pr,m); + if ( nfnode_match(fr,prr,&m1) ) { + *rp = append_node(m,m1); + return 1; + } + } + } + return 0; + } + } +} + +int nfnode_match_narymul(FNODE f,FNODE p,NODE *rp) +{ + int fl,pl,fi,pi; + NODE fa,pa,t,s,m,m1; + FNODE fr,pr,pleft,pleft1,pright,pright1,fleft,fright,pivot; + + f = to_narymul(f); + fa = (NODE)FA1(f); fl = length(fa); + pa = (NODE)FA1(p); pl = length(pa); + if ( fl < pl ) return 0; + else if ( pl == 1 ) { + if ( fl == 1 ) + return nfnode_match(BDY(fa),BDY(pa),rp); + else + return 0; + } else { + for ( t = pa, pi = 0; t; t = NEXT(t), pi++ ) + if ( ((FNODE)BDY(t))->id != I_PVAR ) break; + if ( !t ) { + /* all are I_PVAR */ + m = 0; + for ( t = pa, s = fa; NEXT(t); t = NEXT(t), s = NEXT(s) ) { + pr = rewrite_fnode(BDY(t),m); + if ( !nfnode_match(BDY(s),pr,&m1) ) return 0; + m = append_node(m1,m); + } + if ( !NEXT(s) ) + fr = (FNODE)BDY(s); + else + fr = mkfnode(2,I_NARYOP,FA0(f),s); + pr = rewrite_fnode(BDY(t),m); + if ( !nfnode_match(fr,pr,&m1) ) return 0; + *rp = append_node(m1,m); + return 1; + } else { + pivot = (FNODE)BDY(t); + pleft = fnode_left_narymul(p,pi); + pright = fnode_right_narymul(p,pi); + /* XXX : incomplete */ + for ( s = fa, fi = 0; s; s = NEXT(s), fi++ ) { + if ( fi < pi ) continue; + if ( nfnode_match(BDY(s),pivot,&m) ) { + fleft = fnode_left_narymul(f,fi); + pleft1 = rewrite_fnode(pleft,m); + if ( nfnode_match(fleft,pleft1,&m1) ) { + m = append_node(m1,m); + fright = fnode_right_narymul(f,fi); + pright1 = rewrite_fnode(pright,m); + if ( nfnode_match(fright,pright1,&m1) ) { + *rp = append_node(m1,m); + return 1; + } + } + } + } + return 0; + } + } +} + +NODE nfnode_pvars(FNODE pat,NODE found) +{ + int ind; + NODE prev,t; + int *pair; + + switch ( pat->id ) { + case I_PVAR: + ind = (int)FA0(pat); + for ( prev = 0, t = found; t; prev = t, t = NEXT(t) ) { + pair = (int *)BDY(t); + if ( pair[0] == ind ) { + pair[1]++; + return found; + } + } + pair = (int *)MALLOC_ATOMIC(sizeof(int)*2); + pair[0] = ind; pair[1] = 1; + if ( !prev ) + MKNODE(found,pair,0); + else + MKNODE(NEXT(prev),pair,0); + return found; + + case I_FORMULA: + return found; + + case I_BOP: + /* OPNAME should be "^" */ + if ( !IS_BINARYPWR(pat) ) + error("nfnode_pvar : invalid BOP"); + found = nfnode_pvars(FA1(pat),found); + found = nfnode_pvars(FA2(pat),found); + return found; + + case I_FUNC: + t = (NODE)FA0((FNODE)FA1(pat)); + for ( ; t; t = NEXT(t) ) + found = nfnode_pvars(BDY(t),found); + return found; + + case I_NARYOP: + t = (NODE)FA1(pat); + for ( ; t; t = NEXT(t) ) + found = nfnode_pvars(BDY(t),found); + return found; + + default: + error("nfnode_match : invalid pattern"); } }