=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/builtin/strobj.c,v retrieving revision 1.6 retrieving revision 1.94 diff -u -p -r1.6 -r1.94 --- OpenXM_contrib2/asir2000/builtin/strobj.c 2000/08/21 08:31:21 1.6 +++ OpenXM_contrib2/asir2000/builtin/strobj.c 2005/11/02 10:02:32 1.94 @@ -23,7 +23,7 @@ * shall be made on your publication or presentation in any form of the * results obtained by use of the SOFTWARE. * (4) In the event that you modify the SOFTWARE, you shall notify FLL by - * e-mail at risa-admin@flab.fujitsu.co.jp of the detailed specification + * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification * for such modification or the source code of the modified part of the * SOFTWARE. * @@ -45,24 +45,77 @@ * 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 1.5 2000/03/02 07:16:09 noro Exp $ + * $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.93 2005/11/02 09:39:10 noro Exp $ */ #include "ca.h" #include "parse.h" #include "ctype.h" -#if PARI +#if defined(PARI) #include "genpari.h" +# if !(PARI_VERSION_CODE > 131588) extern jmp_buf environnement; +# endif #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; +void Psprintf(); void Prtostr(), Pstrtov(), Peval_str(); void Pstrtoascii(), Pasciitostr(); void Pstr_len(), Pstr_chr(), Psub_str(); +void Pwrite_to_tb(); +void Ptb_to_string(); +void Pclear_tb(); +void Pstring_to_tb(); +void Pquotetotex_tb(); +void Pquotetotex(); +void Pquotetotex_env(); +void Pflatten_quote(); +void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number(); +void Pquote_is_dependent(),Pquote_is_function(); +void Pquote_normalize(); +void Pquote_normalize_comp(); +void Pquote_normalize_match(); + +void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); +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); +char *conv_rule(char *name); +char *conv_subs(char *name); +char *call_convfunc(char *name); +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_match(Obj f,Obj pat,NODE *rp); + struct ftab str_tab[] = { + {"sprintf",Psprintf,-99999999}, {"rtostr",Prtostr,1}, {"strtov",Pstrtov,1}, {"eval_str",Peval_str,1}, @@ -71,19 +124,923 @@ struct ftab str_tab[] = { {"str_len",Pstr_len,1}, {"str_chr",Pstr_chr,3}, {"sub_str",Psub_str,3}, + {"write_to_tb",Pwrite_to_tb,2}, + {"clear_tb",Pclear_tb,1}, + {"tb_to_string",Ptb_to_string,1}, + {"string_to_tb",Pstring_to_tb,1}, + {"get_quote_id",Pget_quote_id,1}, + + {"quote_is_number",Pquote_is_number,1}, + {"quote_is_rational",Pquote_is_rational,1}, + {"quote_is_integer",Pquote_is_integer,1}, + {"quote_is_function",Pquote_is_function,1}, + {"quote_is_dependent",Pquote_is_dependent,2}, + + {"quote_normalize",Pquote_normalize,-2}, + {"quote_normalize_comp",Pquote_normalize_comp,2}, + + {"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_match",Pquote_match,2}, + {"quote_normalize_match",Pquote_normalize_match,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}, }; +void write_tb(char *s,TB tb) +{ + if ( tb->next == tb->size ) { + tb->size *= 2; + tb->body = (char **)REALLOC(tb->body,tb->size*sizeof(char *)); + } + tb->body[tb->next] = s; + tb->next++; +} + +int register_symbol_table(Obj arg); +int register_conv_rule(Obj arg); +int register_conv_func(Obj arg); +int register_dp_vars(Obj arg); +int register_dp_vars_origin(Obj arg); +int register_dp_dvars_origin(Obj arg); +int register_dp_dvars_prefix(Obj arg); +int register_dp_vars_prefix(Obj arg); +int register_dp_vars_hweyl(Obj arg); +int register_show_lt(Obj arg); +char *objtostr(Obj obj); +static struct TeXSymbol *user_texsymbol; +static char **dp_vars; +static int dp_vars_len; +static char *dp_vars_prefix; +static char *dp_dvars_prefix; +static int dp_vars_origin; +static int dp_dvars_origin; +static int show_lt; +static FUNC convfunc; +static int is_lt; +static int conv_flag; +static int dp_vars_hweyl; + +#define CONV_TABLE (1U<<0) +#define CONV_SUBS (1U<<1) +#define CONV_DMODE (1U<<2) + +static struct { + char *name; + Obj value; + int (*reg)(); +} qtot_env[] = { + {"symbol_table",0,register_symbol_table}, + {"conv_rule",0,register_conv_rule}, + {"conv_func",0,register_conv_func}, + {"dp_vars",0,register_dp_vars}, + {"dp_vars_prefix",0,register_dp_vars_prefix}, + {"dp_dvars_prefix",0,register_dp_dvars_prefix}, + {"dp_vars_origin",0,register_dp_vars_origin}, + {"dp_dvars_origin",0,register_dp_dvars_origin}, + {"dp_vars_hweyl",0,register_dp_vars_hweyl}, + {"show_lt",0,register_show_lt}, + {0,0,0}, +}; + +#define PARTIAL "\\partial" + +char *conv_rule(char *name) +{ + char *body,*r; + int len; + + if ( convfunc ) + name = call_convfunc(name); + if ( conv_flag & CONV_TABLE ) { + r = symbol_name(name); + if ( r ) return r; + } + if ( (conv_flag & CONV_DMODE) && *name == 'd' ) { + body = conv_rule(name+1); + r = MALLOC_ATOMIC((strlen(PARTIAL)+strlen(body)+5)*sizeof(char)); + if ( !body || !(len=strlen(body)) ) + strcpy(r,PARTIAL); + else if ( len == 1 ) + sprintf(r,"%s_%s",PARTIAL,body); + else + sprintf(r,"%s_{%s}",PARTIAL,body); + return r; + } else + return conv_subs(name); +} + +int _is_delimiter(char c) +{ + if ( (c == ' ' || c == '_' || c == ',') ) return 1; + else return 0; +} + +int _is_alpha(char c) +{ + if ( isdigit(c) || c == '{' || _is_delimiter(c) ) return 0; + else return 1; +} + +char *conv_subs(char *name) +{ + int i,j,k,len,clen,slen,start,level; + char *buf,*head,*r,*h,*brace,*buf_conv; + char **subs; + + if ( !name || !(len=strlen(name)) ) return ""; + if ( !(conv_flag&CONV_SUBS) ) return name; + subs = (char **)ALLOCA(len*sizeof(char* )); + for ( i = 0, j = 0, start = i; ; j++ ) { + while ( (i < len) && _is_delimiter(name[i]) ) i++; + start = i; + if ( i == len ) break; + if ( name[i] == '{' ) { + for ( level = 1, i++; i < len && level; i++ ) { + if ( name[i] == '{' ) level++; + else if ( name[i] == '}' ) level--; + } + slen = i-start; + if ( slen >= 3 ) { + brace = (char *)ALLOCA((slen+1)*sizeof(char)); + strncpy(brace,name+start+1,slen-2); + brace[slen-2] = 0; + buf = conv_subs(brace); + subs[j] = (char *)ALLOCA((strlen(buf)+3)*sizeof(char)); + if ( strlen(buf) == 1 ) + strcpy(subs[j],buf); + else + sprintf(subs[j],"{%s}",buf); + } else + subs[j] = "{}"; + } else { + if ( isdigit(name[i]) ) + while ( i < len && isdigit(name[i]) ) i++; + else + while ( i < len && _is_alpha(name[i]) ) i++; + slen = i-start; + buf = (char *)ALLOCA((slen+1)*sizeof(char)); + strncpy(buf,name+start,slen); buf[slen] = 0; + buf_conv = symbol_name(buf); + subs[j] = buf_conv?buf_conv:buf; + } + } + for ( k = 0, clen = 0; k < j; k++ ) clen += strlen(subs[k]); + /* {subs(0)}_{{subs(1)},...,{subs(j-1)}} => {}:j+1 _:1 ,:j-2 */ + h = r = MALLOC_ATOMIC((clen+(j+1)*2+1+(j-2)+1)*sizeof(char)); + if ( j == 1 ) + sprintf(h,"{%s}",subs[0]); + else { + sprintf(h,"{%s}_{%s",subs[0],subs[1]); + h += strlen(h); + for ( k = 2; k < j; k++ ) { + sprintf(h,",%s",subs[k]); + h += strlen(h); + } + strcpy(h,"}"); + } + return r; +} + +char *call_convfunc(char *name) +{ + STRING str,r; + NODE arg; + + MKSTR(str,name); + arg = mknode(1,str); + r = (STRING)bevalf(convfunc,arg); + if ( !r || OID(r) != O_STR ) + error("call_convfunc : invalid result"); + return BDY(r); +} + +int register_symbol_table(Obj arg) +{ + NODE n,t; + Obj b; + STRING a0,a1; + struct TeXSymbol *uts; + int i,len; + + /* check */ + if ( !arg ) { + user_texsymbol = 0; + return 1; + } + if ( OID(arg) != O_LIST ) return 0; + + n = BDY((LIST)arg); + len = length(n); + uts = (struct TeXSymbol *)MALLOC((len+1)*sizeof(struct TeXSymbol)); + for ( i = 0; n; n = NEXT(n), i++ ) { + b = (Obj)BDY(n); + if ( !b || OID(b) != O_LIST ) return 0; + t = BDY((LIST)b); + if ( !t || !NEXT(t) ) return 0; + a0 = (STRING)BDY(t); + a1 = (STRING)BDY(NEXT(t)); + if ( !a0 ) return 0; + if ( OID(a0) == O_STR ) + uts[i].text = BDY(a0); + else if ( OID(a0) == O_P ) + uts[i].text = NAME(VR((P)a0)); + else + return 0; + if ( !a1 ) return 0; + if ( OID(a1) == O_STR ) + uts[i].symbol = BDY(a1); + else if ( OID(a1) == O_P ) + uts[i].symbol = NAME(VR((P)a1)); + else + return 0; + } + uts[i].text = 0; + uts[i].symbol = 0; + user_texsymbol = uts; + return 1; +} + +int register_dp_vars_origin(Obj arg) +{ + if ( INT(arg) ) { + dp_vars_origin = QTOS((Q)arg); + return 1; + } else return 0; +} + +int register_dp_dvars_origin(Obj arg) +{ + if ( INT(arg) ) { + dp_dvars_origin = QTOS((Q)arg); + return 1; + } else return 0; +} + +int register_dp_vars_hweyl(Obj arg) +{ + if ( INT(arg) ) { + dp_vars_hweyl = QTOS((Q)arg); + return 1; + } else return 0; +} + +int register_show_lt(Obj arg) +{ + if ( INT(arg) ) { + show_lt = QTOS((Q)arg); + return 1; + } else return 0; +} + +int register_conv_rule(Obj arg) +{ + if ( INT(arg) ) { + conv_flag = QTOS((Q)arg); + convfunc = 0; + return 1; + } else return 0; +} + +int register_conv_func(Obj arg) +{ + if ( !arg ) { + convfunc = 0; + return 1; + } else if ( OID(arg) == O_P && (int)(VR((P)arg))->attr == V_SR ) { + convfunc = (FUNC)(VR((P)arg)->priv); + /* f must be a function which takes single argument */ + return 1; + } else return 0; +} + +int register_dp_vars(Obj arg) +{ + int l,i; + char **r; + NODE n; + STRING a; + + if ( !arg ) { + dp_vars = 0; + dp_vars_len = 0; + return 1; + } else if ( OID(arg) != O_LIST ) + return 0; + else { + n = BDY((LIST)arg); + l = length(n); + r = (char **)MALLOC_ATOMIC(l*sizeof(char *)); + for ( i = 0; i < l; i++, n = NEXT(n) ) { + a = (STRING)BDY(n); + if ( !a ) return 0; + if ( OID(a) == O_STR ) + r[i] = BDY(a); + else if ( OID(a) == O_P ) + r[i] = NAME(VR((P)a)); + else + return 0; + } + dp_vars = r; + dp_vars_len = l; + return 1; + } +} + +int register_dp_vars_prefix(Obj arg) +{ + if ( !arg ) { + dp_vars_prefix = 0; + return 1; + } else if ( OID(arg) == O_STR ) { + dp_vars_prefix = BDY((STRING)arg); + return 1; + } else if ( OID(arg) == O_P ) { + dp_vars_prefix = NAME(VR((P)arg)); + return 1; + } else return 0; +} + +int register_dp_dvars_prefix(Obj arg) +{ + if ( !arg ) { + dp_dvars_prefix = 0; + return 1; + } else if ( OID(arg) == O_STR ) { + dp_dvars_prefix = BDY((STRING)arg); + return 1; + } else if ( OID(arg) == O_P ) { + dp_dvars_prefix = NAME(VR((P)arg)); + return 1; + } else return 0; +} + +void Pquotetotex_env(NODE arg,Obj *rp) +{ + int ac,i; + char *name; + NODE n,n0; + STRING s; + LIST l; + + ac = argc(arg); + if ( !ac ) { + n0 = 0; + for ( i = 0; qtot_env[i].name; i++ ) { + NEXTNODE(n0,n); MKSTR(s,qtot_env[i].name); BDY(n) = (pointer)s; + NEXTNODE(n0,n); BDY(n) = (Q)qtot_env[i].value; + } + NEXT(n) = 0; + MKLIST(l,n0); + *rp = (Obj)l; + } else if ( ac == 1 && !ARG0(arg) ) { + /* set to default */ + for ( i = 0; qtot_env[i].name; i++ ) { + (qtot_env[i].reg)(0); + qtot_env[i].value = 0; + } + *rp = 0; + } else if ( ac == 1 || ac == 2 ) { + asir_assert(ARG0(arg),O_STR,"quotetotex_env"); + name = BDY((STRING)ARG0(arg)); + for ( i = 0; qtot_env[i].name; i++ ) + if ( !strcmp(qtot_env[i].name,name) ) { + if ( ac == 2 ) { + if ( (qtot_env[i].reg)((Obj)ARG1(arg)) ) + qtot_env[i].value = (Obj)ARG1(arg); + else + error("quotetotex_env : invalid argument"); + } + *rp = qtot_env[i].value; + return; + } + *rp = 0; + } else + *rp = 0; +} + +void Pwrite_to_tb(NODE arg,Q *rp) +{ + int i; + Obj obj; + TB tb; + + asir_assert(ARG1(arg),O_TB,"write_to_tb"); + obj = ARG0(arg); + if ( !obj ) + write_tb("",ARG1(arg)); + else if ( OID(obj) == O_STR ) + write_tb(BDY((STRING)obj),ARG1(arg)); + else if ( OID(obj) == O_TB ) { + tb = (TB)obj; + for ( i = 0; i < tb->next; i++ ) + write_tb(tb->body[i],ARG1(arg)); + } + *rp = 0; +} + +FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); + +void Pquote_to_nary(NODE arg,QUOTE *rp) +{ + FNODE f; + + f = fnode_to_nary(BDY((QUOTE)ARG0(arg))); + MKQUOTE(*rp,f); +} + +void Pquote_to_bin(NODE arg,QUOTE *rp) +{ + FNODE f; + int direction; + + direction = QTOS((Q)ARG1(arg)); + f = fnode_to_bin(BDY((QUOTE)ARG0(arg)),direction); + + MKQUOTE(*rp,f); +} + +void Pquote_is_number(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"quote_is_number"); + ret = fnode_is_number(BDY(q)); + STOQ(ret,*rp); +} + +void Pquote_is_rational(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"quote_is_rational"); + ret = fnode_is_rational(BDY(q)); + STOQ(ret,*rp); +} + +void Pquote_is_integer(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"quote_is_integer"); + ret = fnode_is_integer(BDY(q)); + STOQ(ret,*rp); +} + +void Pquote_is_function(NODE arg,Q *rp) +{ + QUOTE q; + int ret; + + q = (QUOTE)ARG0(arg); + asir_assert(q,O_QUOTE,"quote_is_function"); + if ( q->id == I_FUNC || q->id == I_IFUNC ) + ret = 1; + else + ret = 0; + STOQ(ret,*rp); +} + +void Pquote_is_dependent(NODE arg,Q *rp) +{ + P x; + QUOTE q,v; + int ret; + V var; + + q = (QUOTE)ARG0(arg); + v = (QUOTE)ARG1(arg); + asir_assert(q,O_QUOTE,"quote_is_dependent"); + asir_assert(v,O_QUOTE,"quote_is_dependent"); + x = (P)eval(BDY(v)); + if ( !x || OID(x) != O_P ) + *rp = 0; + var = VR(x); + ret = fnode_is_dependent(BDY(q),var); + STOQ(ret,*rp); +} + + +void Pquote_match(NODE arg,Q *rp) +{ + FNODE f,g; + Obj obj; + QUOTE q; + NODE r; + int ret; + +#if 0 + g = partial_eval(BDY(((QUOTE)ARG0(arg)))); + MKQUOTE(q,g); + ret = quote_match((Obj)q,(Obj)ARG1(arg),&r); +#else + obj = (Obj)ARG0(arg); + ret = quote_match(obj,(Obj)ARG1(arg),&r); +#endif + if ( ret ) { + do_assign(r); + *rp = ONE; + } else + *rp = 0; +} + +void Pquote_normalize_match(NODE arg,Q *rp) +{ + QUOTE fq,pq; + FNODE f,p; + int ret; + NODE r; + + fq = (QUOTE)ARG0(arg); Pquote_normalize(mknode(2,fq,0),&fq); f = (FNODE)BDY(fq); + pq = (QUOTE)ARG1(arg); Pquote_normalize(mknode(2,pq,0),&pq); p = (FNODE)BDY(pq); + ret = fnode_normalize_match(f,p,&r); + if ( ret ) { + fnode_do_assign(r); + *rp = ONE; + } else + *rp = 0; +} + +FNODE rewrite_fnode(FNODE,NODE); + +extern Obj VOIDobj; + +void Pquote_match_rewrite(NODE arg,Obj *rp) +{ + FNODE f,g,h,c,value; + Obj obj; + QUOTE q; + NODE r,t,s,s0,pair; + int ret,ind,ac; + + obj = (Obj)ARG0(arg); + 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 = 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); + 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); + MKQUOTE(q,h); *rp = (Obj)q; + } else + *rp = VOIDobj; + break; + default: + error("quote_match_rewrite : invalid argument"); + } + } else + *rp = VOIDobj; +} + +void do_assign(NODE arg) +{ + NODE t,pair; + int pv; + + QUOTE value; + + for ( t = arg; t; t = NEXT(t) ) { + pair = BDY((LIST)BDY(t)); + pv = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); + value = (QUOTE)(BDY(NEXT(pair))); + ASSPV(pv,value); + } +} + +/* [[index,fnode],...] */ + +void fnode_do_assign(NODE arg) +{ + NODE t,pair; + int pv; + FNODE f; + QUOTE value; + + for ( t = arg; t; t = NEXT(t) ) { + pair = (NODE)BDY(t); + pv = (int)BDY(pair); + f = (FNODE)(BDY(NEXT(pair))); + MKQUOTE(value,f); + ASSPV(pv,value); + } +} + +/* +/* consistency check and merge + */ + +int merge_matching_node(NODE n,NODE a,NODE *rp) +{ + NODE ta,ba,tn,bn; + QUOTE pa,va,pn,vn; + + if ( !n ) { + *rp = a; + return 1; + } + for ( ta = a; ta; ta = NEXT(ta) ) { + ba = BDY((LIST)BDY(ta)); + if ( !ba ) continue; + pa = (QUOTE)BDY(ba); va = (QUOTE)BDY(NEXT(ba)); + for ( tn = n; tn; tn = NEXT(tn) ) { + bn = BDY((LIST)BDY(tn)); + if ( !bn ) continue; + pn = (QUOTE)BDY(bn); vn = (QUOTE)BDY(NEXT(bn)); + if ( !compquote(CO,pa,pn) ) { + if ( !compquote(CO,va,vn) ) break; + else return 0; + } + } + if ( !tn ) { + MKNODE(tn,(pointer)BDY(ta),n); + n = tn; + } + } + *rp = n; + return 1; +} + +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_match((Obj)BDY(tf),(Obj)BDY(tp),&a); + if ( !ret ) return 0; + ret = merge_matching_node(r,a,&r1); + if ( !ret ) return 0; + else r = r1; + } + *rp = r; + return 1; +} + +/* f = [a,b,c,...] pat = [X,Y,...] rpat matches the rest of f */ + +int quote_match_cons(NODE f,NODE pat,Obj rpat,NODE *rp) { + QUOTE q; + Q id; + FNODE fn; + NODE r,a,tf,tp,r1,arg; + int ret; + LIST list,alist; + + /* matching of the head part */ + if ( length(f) < length(pat) ) return 0; + r = 0; + for ( tf = f, tp = pat; tp; tf = NEXT(tf), tp = NEXT(tp) ) { + 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; + else r = r1; + } + /* matching of the rest */ + MKLIST(list,tf); + STOQ(I_LIST,id); a = mknode(2,id,list); + MKLIST(alist,a); + arg = mknode(1,alist); + Pfunargs_to_quote(arg,&q); + ret = quote_match((Obj)q,rpat,&a); + if ( !ret ) return 0; + ret = merge_matching_node(r,a,&r1); + if ( !ret ) return 0; + *rp = r1; + return 1; +} + +void get_quote_id_arg(QUOTE f,int *id,NODE *r) +{ + LIST fa; + NODE arg,fab; + + arg = mknode(1,f); Pquote_to_funargs(arg,&fa); fab = BDY((LIST)fa); + *id = QTOS((Q)BDY(fab)); *r = NEXT(fab); +} + +/* *rp : [[quote(A),quote(1)],...] */ + +int quote_match(Obj f, Obj pat, NODE *rp) +{ + NODE tf,tp,head,body; + NODE parg,farg,r; + Obj rpat; + LIST fa,l; + int pid,id; + FUNC ff,pf; + int ret; + QUOTE q; + FNODE g; + + if ( !f ) + if ( !pat ) { + *rp = 0; return 1; + } else + return 0; + else if ( OID(pat) == O_LIST ) { + if ( OID(f) == O_LIST ) + return quote_match_node(BDY((LIST)f),BDY((LIST)pat),rp); + else + return 0; + } else if ( OID(pat) == O_QUOTE ) { + pid = ((FNODE)BDY((QUOTE)pat))->id; + switch ( pid ) { + case I_FORMULA: + if ( compquote(CO,f,pat) ) + return 0; + else { + *rp = 0; return 1; + } + break; + + case I_LIST: case I_CONS: + get_quote_id_arg((QUOTE)pat,&pid,&parg); + if ( OID(f) == O_LIST ) + tf = BDY((LIST)f); + else if ( OID(f) == O_QUOTE + && ((FNODE)BDY((QUOTE)f))->id == pid ) { + get_quote_id_arg((QUOTE)f,&id,&farg); + tf = BDY((LIST)BDY(farg)); + } else + return 0; + + tp = BDY((LIST)BDY(parg)); + if ( pid == I_LIST ) + return quote_match_node(tf,tp,rp); + else { + rpat = (Obj)BDY(NEXT(parg)); + return quote_match_cons(tf,tp,rpat,rp); + } + + case I_PVAR: + /* [[pat,f]] */ + r = mknode(2,pat,f); MKLIST(l,r); + *rp = mknode(1,l); + return 1; + + case I_IFUNC: + /* F(X,Y,...) = ... */ + get_quote_id_arg((QUOTE)f,&id,&farg); + get_quote_id_arg((QUOTE)pat,&pid,&parg); + if ( id == I_FUNC ) { + r = mknode(2,BDY(parg),BDY(farg)); MKLIST(l,r); + head = mknode(1,l); + ret = quote_match(BDY(NEXT(farg)), + BDY(NEXT(parg)),&body); + if ( !ret ) return 0; + else return merge_matching_node(head,body,rp); + } else + return 0; + + case I_NARYOP: case I_BOP: case I_FUNC: + /* X+Y = ... */ + /* f(...) = ... */ + if ( OID(f) != O_QUOTE ) return 0; + id = ((FNODE)BDY((QUOTE)f))->id; + if ( pid == I_FUNC ) + ; + else { + /* XXX converting to I_BOP */ + if ( pid == I_NARYOP ) { + g = fnode_to_bin(BDY((QUOTE)pat),1); + MKQUOTE(q,g); pat = (Obj)q; + } + if ( id == I_NARYOP ) { + g = fnode_to_bin(BDY((QUOTE)f),1); + MKQUOTE(q,g); f = (Obj)q; + } + } + 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_match_node(NEXT(farg),NEXT(parg),rp); + + default: + if ( OID(f) != O_QUOTE ) return 0; + id = ((FNODE)BDY((QUOTE)f))->id; + if ( id != pid ) return 0; + get_quote_id_arg((QUOTE)pat,&pid,&parg); + get_quote_id_arg((QUOTE)f,&id,&farg); + return quote_match_node(farg,parg,rp); + } + } +} + +void Pquotetotex(NODE arg,STRING *rp) +{ + TB tb; + + NEWTB(tb); + /* XXX for DP */ + is_lt = 1; + fnodetotex_tb(BDY((QUOTE)ARG0(arg)),tb); + tb_to_string(tb,rp); +} + +void Pquotetotex_tb(NODE arg,Q *rp) +{ + int i; + TB tb; + + asir_assert(ARG1(arg),O_TB,"quotetotex_tb"); + /* XXX for DP */ + is_lt = 1; + fnodetotex_tb(BDY((QUOTE)ARG0(arg)),ARG1(arg)); + *rp = 0; +} + +void Pstring_to_tb(NODE arg,TB *rp) +{ + TB tb; + + asir_assert(ARG0(arg),O_STR,"string_to_tb"); + NEWTB(tb); + tb->body[0] = BDY((STRING)ARG0(arg)); + tb->next++; + *rp = tb; +} + +void Ptb_to_string(NODE arg,STRING *rp) +{ + TB tb; + + asir_assert(ARG0(arg),O_TB,"tb_to_string"); + tb = (TB)ARG0(arg); + tb_to_string(tb,rp); +} + +void tb_to_string(TB tb,STRING *rp) +{ + int j,len; + char *all,*p,*q; + + for ( j = 0, len = 0; j < tb->next; j++ ) + len += strlen(tb->body[j]); + all = (char *)MALLOC_ATOMIC((len+1)*sizeof(char)); + for ( j = 0, p = all; j < tb->next; j++ ) + for ( q = tb->body[j]; *q; *p++ = *q++ ); + *p = 0; + MKSTR(*rp,all); +} + +void Pclear_tb(NODE arg,Q *rp) +{ + TB tb; + int j; + + asir_assert(ARG0(arg),O_TB,"clear_tb"); + tb = (TB)ARG0(arg); + for ( j = 0; j < tb->next; j++ ) + tb->body[j] = 0; + tb->next = 0; + *rp = 0; +} + void Pstr_len(arg,rp) NODE arg; Q *rp; { - STRING str; - int r; + Obj obj; + TB tb; + int r,i; - str = (STRING)ARG0(arg); - asir_assert(str,O_STR,"str_chr"); - r = strlen(BDY(str)); + obj = (Obj)ARG0(arg); + if ( !obj || (OID(obj) != O_STR && OID(obj) != O_TB) ) + error("str_len : invalid argument"); + if ( OID(obj) == O_STR) + r = strlen(BDY((STRING)obj)); + else if ( OID(obj) == O_TB ) { + tb = (TB)obj; + for ( r = i = 0; i < tb->next; i++ ) + r += strlen(tb->body[i]); + } STOQ(r,*rp); } @@ -105,7 +1062,7 @@ Q *rp; p = BDY(str); spos = QTOS(start); chr = BDY(terminator)[0]; - if ( spos > strlen(p) ) + if ( spos > (int)strlen(p) ) r = -1; else { ind = strchr(p+spos,chr); @@ -203,15 +1160,19 @@ Obj *rp; { FNODE fnode; char *cmd; -#if PARI +#if defined(PARI) + void recover(int); + recover(0); +# if !(PARI_VERSION_CODE > 131588) if ( setjmp(environnement) ) { avma = top; recover(1); resetenv(""); } +# endif #endif cmd = BDY((STRING)ARG0(arg)); - exprparse(0,cmd,&fnode); + exprparse_create_var(0,cmd,&fnode); *rp = eval(fnode); } @@ -223,7 +1184,7 @@ STRING *rp; int len; len = estimate_length(CO,ARG0(arg)); - b = (char *)MALLOC(len+1); + b = (char *)MALLOC_ATOMIC(len+1); soutput_init(b); sprintexpr(CO,ARG0(arg)); MKSTR(*rp,b); @@ -233,7 +1194,7 @@ void Pstrtov(arg,rp) NODE arg; P *rp; { - char *p,*t; + char *p; p = BDY((STRING)ARG0(arg)); #if 0 @@ -249,4 +1210,1788 @@ P *rp; #else makevar(p,rp); #endif +} + +static struct TeXSymbol texsymbol[] = { + {"sin","\\sin"}, + {"cos","\\cos"}, + {"tan","\\tan"}, + {"sinh","\\sinh"}, + {"cosh","\\cosh"}, + {"tanh","\\tanh"}, + {"exp","\\exp"}, + {"log","\\log"}, + +/* Greek Letters (lower case) */ + {"alpha","\\alpha"}, + {"beta","\\beta"}, + {"gamma","\\gamma"}, + {"delta","\\delta"}, + {"epsilon","\\epsilon"}, + {"varepsilon","\\varepsilon"}, + {"zeta","\\zeta"}, + {"eta","\\eta"}, + {"theta","\\theta"}, + {"vartheta","\\vartheta"}, + {"iota","\\iota"}, + {"kappa","\\kappa"}, + {"lambda","\\lambda"}, + {"mu","\\mu"}, + {"nu","\\nu"}, + {"xi","\\xi"}, + {"pi","\\pi"}, + {"varpi","\\varpi"}, + {"rho","\\rho"}, + {"sigma","\\sigma"}, + {"varsigma","\\varsigma"}, + {"tau","\\tau"}, + {"upsilon","\\upsilon"}, + {"phi","\\phi"}, + {"varphi","\\varphi"}, + {"chi","\\chi"}, + {"omega","\\omega"}, + +/* Greek Letters, (upper case) */ + {"ggamma","\\Gamma"}, + {"ddelta","\\Delta"}, + {"ttheta","\\Theta"}, + {"llambda","\\Lambda"}, + {"xxi","\\Xi"}, + {"ppi","\\Pi"}, + {"ssigma","\\Sigma"}, + {"uupsilon","\\Upsilon"}, + {"pphi","\\Phi"}, + {"ppsi","\\Psi"}, + {"oomega","\\Omega"}, + + /* Our own mathematical functions */ + {"algebra_tensor","\\otimes"}, + {"base_where","{\\rm \\ where \\ }"}, + /* Mathematical constants */ + {"c_pi","\\pi"}, + {"c_i","\\sqrt{-1}"}, + + /* Temporary */ + {0,0} +}; + +char *symbol_name(char *name) +{ + int i; + + if ( !name || strlen(name) == 0 ) + return ""; + if ( !(conv_flag & CONV_TABLE) ) + return name; + + if ( user_texsymbol ) + for ( i = 0; user_texsymbol[i].text; i++ ) + if ( !strcmp(user_texsymbol[i].text,name) ) + return user_texsymbol[i].symbol; + for ( i = 0; texsymbol[i].text; i++ ) + if ( !strcmp(texsymbol[i].text,name) ) + return texsymbol[i].symbol; + return 0; +} + +void Pget_function_name(NODE arg,STRING *rp) +{ + QUOTEARG qa; + ARF f; + char *opname; + + qa = (QUOTEARG)BDY(arg); + if ( !qa || OID(qa) != O_QUOTEARG || qa->type != A_arf ) + *rp = 0; + else { + f = (ARF)BDY(qa); + opname = f->name; + MKSTR(*rp,opname); + } +} + +FNODE strip_paren(FNODE); + +void fnodetotex_tb(FNODE f,TB tb) +{ + 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,f1; + + write_tb(" ",tb); + if ( !f ) { + write_tb("0",tb); + return; + } + switch ( f->id ) { + /* unary operators */ + case I_NOT: + write_tb("\\neg (",tb); + fnodetotex_tb((FNODE)FA0(f),tb); + write_tb(")",tb); + break; + case I_PAREN: + write_tb("(",tb); + fnodetotex_tb((FNODE)FA0(f),tb); + write_tb(")",tb); + break; + case I_MINUS: + write_tb("-",tb); + fnodetotex_tb((FNODE)FA0(f),tb); + break; + + /* binary operators */ + /* arg list */ + /* I_AND, I_OR => FA0(f), FA1(f) */ + /* otherwise => FA1(f), FA2(f) */ + case I_BOP: + opname = ((ARF)FA0(f))->name; + switch ( opname[0] ) { + case '+': + fnodetotex_tb((FNODE)FA1(f),tb); + if ( !top_is_minus((FNODE)FA2(f)) ) write_tb(opname,tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case '-': + if ( FA1(f) ) fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(opname,tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case '*': + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" ",tb); + /* XXX special care for DP */ + f2 = (FNODE)FA2(f); + 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((FNODE)FA2(f),tb); + } else + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case '/': + write_tb("\\frac{",tb); + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb("} {",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + write_tb("}",tb); + break; + case '^': + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb("^{",tb); + fnodetotex_tb(strip_paren((FNODE)FA2(f)),tb); + write_tb("} ",tb); + break; + case '%': + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" {\\rm mod}\\, ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + default: + error("invalid binary operator"); + 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) ) { + case C_EQ: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" = ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case C_NE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\neq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case C_GT: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" > ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case C_LT: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" < ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case C_GE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\geq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case C_LE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\leq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + } + break; + + case I_LOP: + switch( (lid)FA0(f) ) { + case L_EQ: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" = ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_NE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\neq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_GT: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" > ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_LT: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" < ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_GE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\geq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_LE: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" \\leq ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_AND: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" {\\rm \\ and\\ } ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_OR: + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(" {\\rm \\ or\\ } ",tb); + fnodetotex_tb((FNODE)FA2(f),tb); + break; + case L_NOT: + /* XXX : L_NOT is a unary operator */ + write_tb("\\neg (",tb); + fnodetotex_tb((FNODE)FA1(f),tb); + write_tb(")",tb); + return; + } + break; + + case I_AND: + fnodetotex_tb((FNODE)FA0(f),tb); + write_tb(" {\\rm \\ and\\ } ",tb); + fnodetotex_tb((FNODE)FA1(f),tb); + break; + + case I_OR: + fnodetotex_tb((FNODE)FA0(f),tb); + write_tb(" {\\rm \\ or\\ } ",tb); + fnodetotex_tb((FNODE)FA1(f),tb); + break; + + /* ternary operators */ + case I_CE: + error("fnodetotex_tb : not implemented yet"); + break; + + /* lists */ + case I_LIST: + write_tb(" [ ",tb); + n = (NODE)FA0(f); + fnodenodetotex_tb(n,tb); + write_tb("]",tb); + break; + + /* function */ + case I_FUNC: + if ( !strcmp(((FUNC)FA0(f))->name,"@pi") ) + write_tb("\\pi",tb); + else if ( !strcmp(((FUNC)FA0(f))->name,"@e") ) + write_tb("e",tb); + else { + opname = conv_rule(((FUNC)FA0(f))->name); + write_tb(opname,tb); + write_tb("(",tb); + fargstotex_tb(opname,FA1(f),tb); + write_tb(")",tb); + } + break; + + /* XXX */ + case I_CAR: + opname = conv_rule("car"); + write_tb(opname,tb); + write_tb("(",tb); + fargstotex_tb(opname,FA0(f),tb); + write_tb(")",tb); + break; + + case I_CDR: + opname = conv_rule("cdr"); + write_tb(opname,tb); + write_tb("(",tb); + fargstotex_tb(opname,FA0(f),tb); + write_tb(")",tb); + break; + + /* exponent vector */ + case I_EV: + n = (NODE)FA0(f); + if ( dp_vars_hweyl ) { + elen = length(n); + elen2 = elen>>1; + elen = elen2<<1; + } + allzero = 1; + if ( show_lt && is_lt ) + write_tb("\\underline{",tb); + for ( t0 = 0, i = 0; n; n = NEXT(n), i++ ) { + fi = (FNODE)BDY(n); + if ( fi->id == I_FORMULA && !FA0(fi) ) continue; + allzero = 0; + if ( dp_vars && i < dp_vars_len ) { + strcpy(vname,dp_vars[i]); + vname_conv = conv_rule(vname); + } else { + if ( dp_vars_hweyl ) { + if ( i < elen2 ) { + strcpy(prefix,dp_vars_prefix?dp_vars_prefix:"x"); + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_vars_origin; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } else if ( i < elen ) { + strcpy(prefix, + dp_dvars_prefix?dp_dvars_prefix:"\\partial"); + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_dvars_origin-elen2; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } else { + strcpy(prefix,"h"); + vname_conv = conv_rule(prefix); + } + } else { + strcpy(prefix,dp_vars_prefix?dp_vars_prefix:"x"); + prefix_conv = conv_rule(prefix); + vname_conv = (char *)ALLOCA(strlen(prefix_conv)+50); + si = i+dp_vars_origin; + sprintf(vname_conv,(si>=0&&si<10)?"%s_%d":"%s_{%d}", + prefix_conv,si); + } + } + if ( fi->id == I_FORMULA && UNIQ(FA0(fi)) ) { + len = strlen(vname_conv); + opname = MALLOC_ATOMIC(len+2); + sprintf(opname,"%s ",vname_conv); + write_tb(opname,tb); + } else { + len = strlen(vname_conv); + /* 2: ^{ */ + opname = MALLOC_ATOMIC(len+1+2); + sprintf(opname,"%s^{",vname_conv); + write_tb(opname,tb); + fnodetotex_tb((FNODE)BDY(n),tb); + write_tb("} ",tb); + } + } + /* XXX */ + if ( allzero ) + write_tb(" 1 ",tb); + if ( show_lt && is_lt ) { + write_tb("}",tb); + is_lt = 0; + } + break; + + /* string */ + case I_STR: + write_tb((char *)FA0(f),tb); + break; + + /* internal object */ + case I_FORMULA: + obj = (Obj)FA0(f); + if ( !obj ) + write_tb("0",tb); + else if ( OID(obj) == O_N && NID(obj) == N_C ) { + cplx = (C)obj; + write_tb("(",tb); + if ( cplx->r ) { + r = objtostr((Obj)cplx->r); write_tb(r,tb); + } + if ( cplx->i ) { + if ( cplx->r && compnum(0,cplx->i,0) > 0 ) { + write_tb("+",tb); + if ( !UNIQ(cplx->i) ) { + r = objtostr((Obj)cplx->i); write_tb(r,tb); + } + } else if ( MUNIQ(cplx->i) ) + write_tb("-",tb); + else if ( !UNIQ(cplx->i) ) { + r = objtostr((Obj)cplx->i); write_tb(r,tb); + } + write_tb("\\sqrt{-1}",tb); + } + write_tb(")",tb); + } else if ( OID(obj) == O_P ) + write_tb(conv_rule(VR((P)obj)->name),tb); + else + write_tb(objtostr(obj),tb); + break; + + /* program variable */ + case I_PVAR: + if ( FA1(f) ) + error("fnodetotex_tb : not implemented yet"); + GETPVNAME(FA0(f),opname); + write_tb(opname,tb); + break; + + default: + error("fnodetotex_tb : not implemented yet"); + } +} + +char *objtostr(Obj obj) +{ + int len; + char *r; + + len = estimate_length(CO,obj); + r = (char *)MALLOC_ATOMIC(len+1); + soutput_init(r); + sprintexpr(CO,obj); + return r; +} + +void Psprintf(NODE arg,STRING *rp) +{ + STRING string; + char *s,*t,*r; + int argc,n,len; + NODE node; + + string = (STRING)ARG0(arg); + asir_assert(string,O_STR,"sprintf"); + s = BDY(string); + for(n = 0, t = s; *t; t++) { + if (*t=='%' && *(t+1)=='a') { + n++; + } + } + for(node = NEXT(arg), argc = 0, len = strlen(s); node; node = NEXT(node), argc++) { + len += estimate_length(CO,BDY(node)); + } + if (argc < n) { + error("sprintf: invalid argument"); + } + r = (char *)MALLOC_ATOMIC(len); + for(node = NEXT(arg), t = r; *s; s++) { + if (*s=='%' && *(s+1)=='a') { + strcpy(t,objtostr(BDY(node))); + node = NEXT(node); + t = strchr(t,0); + s++; + }else { + *t++ = *s; + } + } + *t = 0; + MKSTR(*rp,r); +} + +void fnodenodetotex_tb(NODE n,TB tb) +{ + for ( ; n; n = NEXT(n) ) { + is_lt = 1; + fnodetotex_tb((FNODE)BDY(n),tb); + if ( NEXT(n) ) write_tb(", ",tb); + } +} + +void fargstotex_tb(char *name,FNODE f,TB tb) +{ + NODE n; + + if ( !strcmp(name,"matrix") ) { + error("fargstotex_tb : not implemented yet"); + } else if ( !strcmp(name,"vector") ) { + error("fargstotex_tb : not implemented yet"); + } else { + if ( f->id == I_LIST ) { + n = (NODE)FA0(f); + fnodenodetotex_tb(n,tb); + } else + fnodetotex_tb(f,tb); + } +} + +int top_is_minus(FNODE f) +{ + char *opname; + int len; + Obj obj; + + if ( !f ) + return 0; + switch ( f->id ) { + case I_MINUS: + return 1; + case I_BOP: + opname = ((ARF)FA0(f))->name; + switch ( opname[0] ) { + case '+': case '*': case '/': case '^': case '%': + return top_is_minus((FNODE)FA1(f)); + case '-': + if ( FA1(f) ) + return top_is_minus((FNODE)FA1(f)); + else + return 1; + default: + return 0; + } + break; + case I_COP: + return top_is_minus((FNODE)FA1(f)); + case I_LOP: + if ( (lid)FA0(f) == L_NOT ) return 0; + else return top_is_minus((FNODE)FA1(f)); + case I_AND: case I_OR: + return top_is_minus((FNODE)FA0(f)); + case I_FORMULA: + obj = (Obj)FA0(f); + if ( !obj ) + return 0; + else { + switch ( OID(obj) ) { + case O_N: + return mmono((P)obj); + case O_P: + /* must be a variable */ + opname = conv_rule(VR((P)obj)->name); + return opname[0]=='-'; + default: + /* ??? */ + len = estimate_length(CO,obj); + opname = (char *)MALLOC_ATOMIC(len+1); + soutput_init(opname); + sprintexpr(CO,obj); + return opname[0]=='-'; + } + } + case I_NARYOP: + return top_is_minus((FNODE)BDY((NODE)FA1(f))); + + default: + return 0; + } +} + +FNODE flatten_fnode(FNODE,char *); + +void Pflatten_quote(NODE arg,Obj *rp) +{ + FNODE f; + QUOTE q; + + if ( !ARG0(arg) || OID((Obj)ARG0(arg)) != O_QUOTE ) + *rp = (Obj)ARG0(arg); + else if ( argc(arg) == 1 ) { + f = flatten_fnode(BDY((QUOTE)ARG0(arg)),"+"); + f = flatten_fnode(f,"*"); + MKQUOTE(q,f); + *rp = (Obj)q; + } else { + f = flatten_fnode(BDY((QUOTE)ARG0(arg)),BDY((STRING)ARG1(arg))); + MKQUOTE(q,f); + *rp = (Obj)q; + } +} + +void Pget_quote_id(NODE arg,Q *rp) +{ + FNODE f; + QUOTE q; + + q = (QUOTE)ARG0(arg); + if ( !q || OID(q) != O_QUOTE ) + error("get_quote_id : invalid argument"); + f = BDY(q); + STOQ((int)f->id,*rp); +} + +void Pquote_to_funargs(NODE arg,LIST *rp) +{ + fid_spec_p spec; + QUOTE q; + QUOTEARG qa; + FNODE f; + STRING s; + QUOTE r; + int i; + Q id,a; + LIST l; + NODE t0,t,w,u,u0; + + q = (QUOTE)ARG0(arg); + if ( !q || OID(q) != O_QUOTE ) + error("quote_to_funargs : invalid argument"); + f = BDY(q); + if ( !f ) { + MKLIST(*rp,0); + return; + } + get_fid_spec(f->id,&spec); + if ( !spec ) + error("quote_to_funargs : not supported yet"); + t0 = 0; + STOQ((int)f->id,id); + NEXTNODE(t0,t); + BDY(t) = (pointer)id; + for ( i = 0; spec->type[i] != A_end; i++ ) { + NEXTNODE(t0,t); + switch ( spec->type[i] ) { + case A_fnode: + MKQUOTE(r,(FNODE)f->arg[i]); + BDY(t) = (pointer)r; + break; + case A_int: + STOQ((int)f->arg[i],a); + BDY(t) = (pointer)a; + break; + case A_str: + MKSTR(s,(char *)f->arg[i]); + BDY(t) = (pointer)s; + break; + case A_internal: + BDY(t) = (pointer)f->arg[i]; + break; + case A_node: + w = (NODE)f->arg[i]; + for ( u0 = 0; w; w = NEXT(w) ){ + NEXTNODE(u0,u); + MKQUOTE(r,(FNODE)BDY(w)); + BDY(u) = (pointer)r; + } + if ( u0 ) NEXT(u) = 0; + MKLIST(l,u0); + BDY(t) = (pointer)l; + break; + default: + MKQUOTEARG(qa,spec->type[i],f->arg[i]); + BDY(t) = (pointer)qa; + break; + } + } + if ( t0 ) NEXT(t) = 0; + MKLIST(*rp,t0); +} + +void Pfunargs_to_quote(NODE arg,QUOTE *rp) +{ + fid_spec_p spec; + QUOTE q; + QUOTEARG qa; + FNODE f; + STRING s; + QUOTE r,b; + int i; + LIST l; + fid id; + Obj a; + NODE t0,t,u0,u,w; + + l = (LIST)ARG0(arg); + if ( !l || OID(l) != O_LIST || !(t=BDY(l)) ) + error("funargs_to_quote : invalid argument"); + t = BDY(l); + id = (fid)QTOS((Q)BDY(t)); t = NEXT(t); + get_fid_spec(id,&spec); + if ( !spec ) + error("funargs_to_quote : not supported yet"); + for ( i = 0; spec->type[i] != A_end; i++ ); + NEWFNODE(f,i); + f->id = id; + for ( i = 0; spec->type[i] != A_end; i++, t = NEXT(t) ) { + if ( !t ) + error("funargs_to_quote : argument mismatch"); + a = (Obj)BDY(t); + switch ( spec->type[i] ) { + case A_fnode: + if ( !a || OID(a) != O_QUOTE ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = BDY((QUOTE)a); + break; + case A_int: + if ( !INT(a) ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = (pointer)QTOS((Q)a); + break; + case A_str: + if ( !a || OID(a) != O_STR ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = (pointer)BDY((STRING)a); + break; + case A_internal: + f->arg[i] = (pointer)a; + break; + case A_node: + if ( !a || OID(a) != O_LIST ) + error("funargs_to_quote : invalid argument"); + u0 = 0; + for ( w = BDY((LIST)a); w; w = NEXT(w) ) { + NEXTNODE(u0,u); + b = (QUOTE)BDY(w); + if ( !b || OID(b) != O_QUOTE ) + error("funargs_to_quote : invalid argument"); + BDY(u) = BDY(b); + } + if ( u0 ) NEXT(u) = 0; + f->arg[i] = (pointer)u0; + break; + default: + if ( !a || OID(a) != O_QUOTEARG || + ((QUOTEARG)a)->type != spec->type[i] ) + error("funargs_to_quote : invalid argument"); + f->arg[i] = BDY((QUOTEARG)a); + break; + } + } + MKQUOTE(*rp,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); + expand = ac==2 && ARG1(arg); + if ( !q || OID(q) != O_QUOTE ) { + *rp = q; + return; + } else if ( q->normalized && (q->expanded || !expand) ) + *rp = q; + else { + f = fnode_normalize(BDY(q),expand); + MKQUOTE(r,f); + r->normalized = 1; + if ( expand ) r->expanded = 1; + *rp = r; + } +} + +void Pquote_normalize_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); + if ( !q1->normalized ) f1 = fnode_normalize(f1,0); + if ( !q2->normalized ) f2 = fnode_normalize(f2,0); + r = fnode_normalize_comp(f1,f2); + STOQ(r,*rp); +} + +INLINE int fnode_is_number(FNODE f) +{ + Obj obj; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_number(FA0(f)); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_number(BDY((QUOTE)obj)); + else if ( NUM(obj) ) return 1; + else return 0; + + case I_BOP: + return fnode_is_number(FA1(f)) && fnode_is_number(FA2(f)); + + default: + return 0; + } +} + +int fnode_is_rational(FNODE f) +{ + Obj obj; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_number(FA0(f)); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_rational(BDY((QUOTE)obj)); + else if ( NUM(obj) && RATN(obj) ) return 1; + else return 0; + + case I_BOP: + if ( !strcmp(((ARF)FA0(f))->name,"^") ) + return fnode_is_rational(FA1(f)) && fnode_is_integer(FA2(f)); + else + return fnode_is_rational(FA1(f)) && fnode_is_rational(FA2(f)); + + default: + return 0; + } +} + +int fnode_is_integer(FNODE f) +{ + Obj obj; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_integer(FA0(f)); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 1; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_integer(BDY((QUOTE)obj)); + else if ( INT(obj)) return 1; + else return 0; + + case I_BOP: + switch ( ((ARF)FA0(f))->name[0] ) { + case '^': + return fnode_is_integer(FA1(f)) + && fnode_is_nonnegative_integer(FA2(f)); + case '/': + return fnode_is_integer(FA1(f)) && + ( fnode_is_one(FA2(f)) || fnode_is_minusone(FA2(f)) ); + default: + return fnode_is_integer(FA1(f)) && fnode_is_integer(FA2(f)); + } + break; + + default: + return 0; + } +} + +int fnode_is_nonnegative_integer(FNODE f) +{ + Q n; + + n = eval(f); + if ( !n || (INT(n) && SGN(n) > 0) ) return 1; + else return 0; +} + +int fnode_is_one(FNODE f) +{ + Q n; + + n = eval(f); + if ( UNIQ(n) ) return 1; + else return 0; +} + +int fnode_is_minusone(FNODE f) +{ + Q n; + + n = eval(f); + if ( MUNIQ(n) ) return 1; + else return 0; +} + +int fnode_is_dependent(FNODE f,V v) +{ + Obj obj; + FNODE arg; + NODE t; + + switch ( f->id ) { + case I_MINUS: case I_PAREN: + return fnode_is_dependent(FA0(f),v); + + case I_FORMULA: + obj = FA0(f); + if ( !obj ) return 0; + else if ( OID(obj) == O_QUOTE ) + return fnode_is_dependent(BDY((QUOTE)obj),v); + else if ( obj_is_dependent(obj,v) ) return 1; + else return 0; + + case I_BOP: + return fnode_is_dependent(FA1(f),v) || fnode_is_dependent(FA2(f),v); + + case I_FUNC: + arg = (FNODE)FA1(f); + for ( t = FA0(arg); t; t = NEXT(t) ) + if ( fnode_is_dependent(BDY(t),v) ) return 1; + return 0; + + default: + return 0; + } +} + +FNODE fnode_normalize_add(FNODE a1,FNODE a2,int expand); +FNODE fnode_normalize_mul(FNODE a1,FNODE a2,int expand); +FNODE fnode_normalize_pwr(FNODE a1,FNODE a2,int expand); +FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand); +FNODE fnode_expand_pwr(FNODE f,int n); +FNODE to_narymul(FNODE f); +FNODE to_naryadd(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,int expand) +{ + FNODE a1,a2,mone,r,b2; + NODE n; + 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: + r = fnode_normalize(FA0(f),expand); + break; + + case I_MINUS: + r = fnode_normalize_mul_coef((Num)q, + fnode_normalize(FA0(f),expand),expand); + break; + + case I_BOP: + /* arf fnode fnode */ + a1 = fnode_normalize(FA1(f),expand); + a2 = fnode_normalize(FA2(f),expand); + switch ( OPNAME(f) ) { + case '+': + r = fnode_normalize_add(a1,a2,expand); + break; + case '-': + a2 = fnode_normalize_mul_coef((Num)q,a2,expand); + r = fnode_normalize_add(a1,a2,expand); + break; + case '*': + r = fnode_normalize_mul(a1,a2,expand); + break; + case '/': + a2 = fnode_normalize_pwr(a2,mone,expand); + r = fnode_normalize_mul(a1,a2,expand); + break; + case '^': + r = fnode_normalize_pwr(a1,a2,expand); + break; + default: + r = mkfnode(3,I_BOP,FA0(f),a1,a2); + break; + } + break; + + case I_NARYOP: + switch ( OPNAME(f) ) { + case '+': + n = (NODE)FA1(f); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); + for ( ; n; n = NEXT(n) ) { + a1 = fnode_normalize(BDY(n),expand); + r = fnode_normalize_add(r,a1,expand); + } + break; + case '*': + n = (NODE)FA1(f); + r = fnode_normalize(BDY(n),expand); n = NEXT(n); + for ( ; n; n = NEXT(n) ) { + a1 = fnode_normalize(BDY(n),expand); + r = fnode_normalize_mul(r,a1,expand); + } + break; + default: + error("fnode_normallize : cannot happen"); + } + break; + + default: + return fnode_apply(f,fnode_normalize,expand); + } + r->normalized = 1; + r->expanded = expand; + return r; +} + +FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand) +{ + fid_spec_p spec; + FNODE r; + int i,n; + NODE t,t0,s; + + get_fid_spec(f->id,&spec); + for ( n = 0; spec->type[n] != A_end; n++ ); + NEWFNODE(r,n); r->id = f->id; + for ( i = 0; i < n; i++ ) { + switch ( spec->type[i] ) { + case A_fnode: + 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),expand); + } + if ( t0 ) NEXT(t) = 0; + r->arg[i] = t0; + break; + default: + r->arg[i] = f->arg[i]; + break; + } + } + return r; +} + +FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand) +{ + NODE n1,n2,r0,r; + FNODE b1,b2; + int s; + Num c1,c2,c; + + 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); + if ( (s = fnode_normalize_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) = fnode_normalize_mul_coef(c,b1,expand); + } + n1 = NEXT(n1); n2 = NEXT(n2); + } + } + if ( n1 ) + if ( r0 ) NEXT(r) = n1; + else r0 = n1; + else if ( n2 ) + if ( r0 ) NEXT(r) = n2; + else r0 = n2; + else if ( r0 ) + NEXT(r) = 0; + + return fnode_node_to_naryadd(r0); +} + +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 fnode_normalize_mul(FNODE f1,FNODE f2,int expand) +{ + NODE n1,n2,r0,r,r1; + FNODE b1,b2,e1,e2,cc,t,t1; + FNODE *m; + int s; + Num c1,c2,c,e; + int l1,l,i,j; + + if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); + else if ( fnode_is_number(f1) ) + return fnode_normalize_mul_coef((Num)eval(f1),f2,expand); + else if ( fnode_is_number(f2) ) + return fnode_normalize_mul_coef((Num)eval(f2),f1,expand); + + if ( expand && IS_NARYADD(f1) ) { + t = mkfnode(1,I_FORMULA,0); + for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) { + t1 = fnode_normalize_mul(BDY(n1),f2,expand); + t = fnode_normalize_add(t,t1,expand); + } + return t; + } + if ( expand && IS_NARYADD(f2) ) { + t = mkfnode(1,I_FORMULA,0); + for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) { + t1 = fnode_normalize_mul(f1,BDY(n2),expand); + t = fnode_normalize_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); + + + 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 ) + m[i++] = BDY(r); + else { + 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)); + } + } + 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,int expand) +{ + FNODE b,b1,e1,e,cc,r,mf2,mone,inv; + Num c,c1,nf2; + int ee; + NODE arg,n,t0,t1; + Q q; + + 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) ) { + 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 ( IS_BINARYPWR(f1) ) { + b1 = FA1(f1); e1 = FA2(f1); + e = fnode_normalize_mul(e1,f2,expand); + if ( fnode_is_one(e) ) + return b1; + else + return mkfnode(3,I_BOP,FA0(f1),b1,e); + } else if ( expand && IS_NARYMUL(f1) && fnode_is_number(f2) + && fnode_is_integer(f2) ) { + fnode_coef_body(f1,&c1,&b1); + 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); + 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; + } + b1 = fnode_node_to_narymul(t0); + b = fnode_expand_pwr(b1,-ee); + } + 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("fnode_normalize_pwr : exponent too large"); + return fnode_expand_pwr(f1,QTOS(q)); + } else + return mkfnode(3,I_BOP,pwrfs,f1,f2); +} + +FNODE fnode_expand_pwr(FNODE f,int n) +{ + int n1; + FNODE f1,f2; + + 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 { + n1 = n/2; + f1 = fnode_expand_pwr(f,n1); + f2 = fnode_normalize_mul(f1,f1,1); + if ( n%2 ) f2 = fnode_normalize_mul(f2,f,1); + return f2; + } +} + +/* f = b^e */ +void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep) +{ + if ( IS_BINARYPWR(f) ) { + *bp = FA1(f); *ep = FA2(f); + } else { + *bp = f; *ep = mkfnode(1,I_FORMULA,ONE); + } +} + +FNODE to_naryadd(FNODE f) +{ + FNODE r; + NODE 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; +} + +FNODE to_narymul(FNODE f) +{ + FNODE r; + NODE 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,int expand) +{ + FNODE b1,cc; + Num c1,c2; + NODE n,r,r0; + + if ( !c ) + return mkfnode(I_FORMULA,0); + 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("fnode_normalize_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) = fnode_normalize_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)); + } + } +} + +void fnode_coef_body(FNODE f,Num *cp,FNODE *bp) +{ + FNODE c; + + if ( fnode_is_number(f) ) { + *cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE); + } else if ( IS_NARYMUL(f) ) { + c=(FNODE)BDY((NODE)FA1(f)); + if ( fnode_is_number(c) ) { + *cp = eval(c); + *bp = fnode_node_to_narymul(NEXT((NODE)FA1(f))); + } else { + *cp = (Num)ONE; *bp = f; + } + } else { + *cp = (Num)ONE; *bp = f; + } +} + +int fnode_normalize_comp_pwr(FNODE f1,FNODE f2); + +int fnode_normalize_comp(FNODE f1,FNODE f2) +{ + NODE n1,n2; + int r,i1,i2; + char *nm1,*nm2; + FNODE b1,b2,e1,e2,g; + 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 = fnode_normalize_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 = fnode_normalize_comp(b1,b2) ) { + if ( r > 0 ) + return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0)); + else if ( r < 0 ) + return fnode_normalize_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 = fnode_normalize_comp(e1,e2); + if ( r > 0 ) return 1; + else if ( r < 0 ) return -1; + } + } + } + } + if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) + return fnode_normalize_comp_pwr(f1,f2); + + /* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, or I_PVAR */ + 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_PVAR: + return -1; + default: + error("fnode_normalize_comp : undefined"); + } + break; + case I_FUNC: + switch ( f2->id ) { + case I_FORMULA: + 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 = fnode_normalize_comp(BDY(n1),BDY(n2)) ) return r; + else { + n1 = NEXT(n1); n2 = NEXT(n2); + } + return n1?1:(n2?-1:0); + } + break; + case I_PVAR: + return -1; + default: + error("fnode_normalize_comp : undefined"); + } + case I_PVAR: + switch ( f2->id ) { + case I_FORMULA: case I_FUNC: + 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("fnode_normalize_comp : undefined"); + } + break; + default: + error("fnode_normalize_comp : undefined"); + } +} + +int fnode_normalize_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 = fnode_normalize_comp(b1,b2) ) { + if ( r > 0 ) + return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0)); + else if ( r < 0 ) + return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2); + } else return fnode_normalize_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 fnode_normalize_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; + FUNC ff,pf; + int r; + + switch ( pat->id ) { + case I_PVAR: + /* [[pat,f]] */ + *rp = mknode(1,mknode(2,(int)FA0(pat),f),0); + 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("fnode_normalize_match : invalid BOP"); + if ( IS_BINARYPWR(f) ) { + fbase = FA1(f); fexp = FA2(f); + } else { + fbase = f; fexp = mkfnode(1,I_FORMULA,ONE); + } + if ( !fnode_normalize_match(fbase,FA1(pat),&base) ) return 0; + a = rewrite_fnode(FA2(pat),base); + if ( !fnode_normalize_match(fexp,a,&exp) ) return 0; + else { + *rp = append_node(base,exp); + return 1; + } + break; + + case I_FUNC: + if ( f->id != I_FUNC ) return 0; + ff = (FUNC)FA0(f); pf = (FUNC)FA0(pat); + if ( strcmp(ff->fullname,pf->fullname) ) return 0; + /* FA1(f) and FA1(pat) are I_LIST */ + fa = (NODE)FA0((FNODE)FA1(f)); + pa = (NODE)FA0((FNODE)FA1(pat)); + m = 0; + while ( fa && pa ) { + a = rewrite_fnode(BDY(pa),m); + if ( !fnode_normalize_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 fnode_normalize_match_naryadd(f,pat,rp); + else if ( IS_NARYMUL(pat) ) + return fnode_normalize_match_narymul(f,pat,rp); + else + error("fnode_normalize_match : invalid NARYOP"); + break; + + default: + error("fnode_normalize_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 mkfnode(1,I_FORMULA,ONE); + 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 mkfnode(1,I_FORMULA,ONE); + else { + for ( k = 0, t = a; k <= i; k++, t = NEXT(t) ); + return fnode_node_to_narymul(t); + } +} + +int fnode_normalize_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 fnode_normalize_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) ) { + fnode_normalize_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); + fnode_normalize_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 ( fnode_normalize_match(BDY(s),pivot,&m) ) { + fr = fnode_removeith_naryadd(f,fi); + prr = rewrite_fnode(pr,m); + if ( fnode_normalize_match(fr,prr,&m1) ) { + *rp = append_node(m,m1); + return 1; + } + } + } + return 0; + } + } +} + +int fnode_normalize_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 fnode_normalize_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 ( !fnode_normalize_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 ( !fnode_normalize_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 ( fnode_normalize_match(BDY(s),pivot,&m) ) { + fleft = fnode_left_narymul(f,fi); + pleft1 = rewrite_fnode(pleft,m); + if ( fnode_normalize_match(fleft,pleft1,&m1) ) { + m = append_node(m1,m); + fright = fnode_right_narymul(f,fi); + pright1 = rewrite_fnode(pright,m); + if ( fnode_normalize_match(fright,pright1,&m1) ) { + *rp = append_node(m1,m); + return 1; + } + } + } + } + return 0; + } + } }