version 1.71, 2005/10/12 14:43:36 |
version 1.87, 2005/10/31 10:03:48 |
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* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. |
* |
* |
* $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.70 2005/10/12 03:31:04 noro Exp $ |
* $OpenXM: OpenXM_contrib2/asir2000/builtin/strobj.c,v 1.86 2005/10/26 23:43:23 noro Exp $ |
*/ |
*/ |
#include "ca.h" |
#include "ca.h" |
#include "parse.h" |
#include "parse.h" |
Line 64 struct TeXSymbol { |
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Line 64 struct TeXSymbol { |
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}; |
}; |
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#define OPNAME(f) (((ARF)FA0(f))->name[0]) |
#define OPNAME(f) (((ARF)FA0(f))->name[0]) |
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#define IS_ZERO(f) (((f)->id==I_FORMULA) && FA0(f)==0 ) |
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#define IS_BINARYPWR(f) (((f)->id==I_BOP) &&(OPNAME(f)=='^')) |
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#define IS_NARYADD(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='+')) |
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#define IS_NARYMUL(f) (((f)->id==I_NARYOP) &&(OPNAME(f)=='*')) |
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extern char *parse_strp; |
extern char *parse_strp; |
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Line 83 void Pflatten_quote(); |
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Line 87 void Pflatten_quote(); |
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void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number(); |
void Pquote_is_integer(),Pquote_is_rational(),Pquote_is_number(); |
void Pquote_is_dependent(),Pquote_is_function(); |
void Pquote_is_dependent(),Pquote_is_function(); |
void Pquote_normalize(); |
void Pquote_normalize(); |
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void Pquote_normalize_comp(); |
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void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); |
void Pquote_to_funargs(),Pfunargs_to_quote(),Pget_function_name(); |
void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite(); |
void Pquote_unify(),Pget_quote_id(),Pquote_match_rewrite(); |
Line 121 struct ftab str_tab[] = { |
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Line 126 struct ftab str_tab[] = { |
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{"quote_is_function",Pquote_is_function,1}, |
{"quote_is_function",Pquote_is_function,1}, |
{"quote_is_dependent",Pquote_is_dependent,2}, |
{"quote_is_dependent",Pquote_is_dependent,2}, |
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{"quote_normalize",Pquote_normalize,1}, |
{"quote_normalize",Pquote_normalize,-2}, |
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{"quote_normalize_comp",Pquote_normalize_comp,2}, |
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{"quote_to_nary",Pquote_to_nary,1}, |
{"quote_to_nary",Pquote_to_nary,1}, |
{"quote_to_bin",Pquote_to_bin,2}, |
{"quote_to_bin",Pquote_to_bin,2}, |
Line 530 void Pwrite_to_tb(NODE arg,Q *rp) |
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Line 536 void Pwrite_to_tb(NODE arg,Q *rp) |
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} |
} |
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FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); |
FNODE partial_eval(FNODE), fnode_to_nary(FNODE), fnode_to_bin(FNODE,int); |
FNODE fnode_normalize(FNODE); |
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void Pquote_to_nary(NODE arg,QUOTE *rp) |
void Pquote_to_nary(NODE arg,QUOTE *rp) |
{ |
{ |
Line 660 void Pquote_match_rewrite(NODE arg,Obj *rp) |
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Line 665 void Pquote_match_rewrite(NODE arg,Obj *rp) |
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NEXTNODE(s0,s); |
NEXTNODE(s0,s); |
pair = BDY((LIST)BDY(t)); |
pair = BDY((LIST)BDY(t)); |
ind = (int)FA0((FNODE)BDY((QUOTE)BDY(pair))); |
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); |
BDY(s) = mknode(2,ind,value); |
} |
} |
if ( s0 ) NEXT(s) = 0; |
if ( s0 ) NEXT(s) = 0; |
switch ( ac = argc(arg) ) { |
switch ( ac = argc(arg) ) { |
case 3: |
case 3: |
h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); |
h = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); |
*rp = eval(h); |
MKQUOTE(q,h); *rp = (Obj)q; |
break; |
break; |
case 4: |
case 4: |
c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); |
c = rewrite_fnode(BDY((QUOTE)ARG2(arg)),s0); |
if ( eval(c) ) { |
if ( eval(c) ) { |
h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0); |
h = rewrite_fnode(BDY((QUOTE)ARG3(arg)),s0); |
*rp = eval(h); |
MKQUOTE(q,h); *rp = (Obj)q; |
} else |
} else |
*rp = VOIDobj; |
*rp = VOIDobj; |
break; |
break; |
Line 1921 void Pfunargs_to_quote(NODE arg,QUOTE *rp) |
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Line 1926 void Pfunargs_to_quote(NODE arg,QUOTE *rp) |
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MKQUOTE(*rp,f); |
MKQUOTE(*rp,f); |
} |
} |
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FNODE fnode_apply(FNODE f,FNODE (*func)()); |
FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand); |
FNODE fnode_normalize(FNODE f); |
FNODE fnode_normalize(FNODE f,int expand); |
FNODE fnode_normalize_nary(FNODE f); |
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void Pquote_normalize(NODE arg,QUOTE *rp) |
void Pquote_normalize(NODE arg,QUOTE *rp) |
{ |
{ |
QUOTE q,r; |
QUOTE q,r; |
FNODE f; |
FNODE f; |
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int expand,ac; |
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ac = argc(arg); |
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if ( !ac ) error("quote_normalize : invalid argument"); |
q = (QUOTE)ARG0(arg); |
q = (QUOTE)ARG0(arg); |
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expand = ac==2 && ARG1(arg); |
if ( !q || OID(q) != O_QUOTE ) { |
if ( !q || OID(q) != O_QUOTE ) { |
*rp = q; |
*rp = q; |
return; |
return; |
} else { |
} else if ( q->normalized && (q->expanded || !expand) ) |
#if 0 |
*rp = q; |
f = flatten_fnode(BDY(q),"+"); |
else { |
f = flatten_fnode(f,"*"); |
f = fnode_normalize(BDY(q),expand); |
#endif |
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f = fnode_normalize(BDY(q)); |
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f = fnode_to_nary(f); |
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f = fnode_normalize_nary(f); |
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MKQUOTE(r,f); |
MKQUOTE(r,f); |
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r->normalized = 1; |
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if ( expand ) r->expanded = 1; |
*rp = r; |
*rp = r; |
} |
} |
} |
} |
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void Pquote_normalize_comp(NODE arg,Q *rp) |
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{ |
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QUOTE q1,q2; |
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FNODE f1,f2; |
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int r; |
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q1 = (QUOTE)ARG0(arg); f1 = (FNODE)BDY(q1); |
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q2 = (QUOTE)ARG1(arg); f2 = (FNODE)BDY(q2); |
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if ( !q1->normalized ) f1 = fnode_normalize(f1,0); |
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if ( !q2->normalized ) f2 = fnode_normalize(f2,0); |
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r = fnode_normalize_comp(f1,f2); |
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STOQ(r,*rp); |
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} |
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int fnode_is_number(FNODE f) |
int fnode_is_number(FNODE f) |
{ |
{ |
Obj obj; |
Obj obj; |
Line 2032 int fnode_is_integer(FNODE f) |
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Line 2052 int fnode_is_integer(FNODE f) |
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} |
} |
} |
} |
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int fnode_is_zero(FNODE f) |
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{ |
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Q n; |
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n = eval(f); |
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if ( !n ) return 1; |
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else return 0; |
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} |
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int fnode_is_nonnegative_integer(FNODE f) |
int fnode_is_nonnegative_integer(FNODE f) |
{ |
{ |
Q n; |
Q n; |
Line 2100 int fnode_is_dependent(FNODE f,V v) |
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Line 2111 int fnode_is_dependent(FNODE f,V v) |
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} |
} |
} |
} |
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FNODE fnode_normalize(FNODE f) |
FNODE fnode_normalize_add(FNODE a1,FNODE a2,int expand); |
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FNODE fnode_normalize_mul(FNODE a1,FNODE a2,int expand); |
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FNODE fnode_normalize_pwr(FNODE a1,FNODE a2,int expand); |
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FNODE fnode_normalize_mul_coef(Num c,FNODE f,int expand); |
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FNODE fnode_expand_pwr(FNODE f,int n); |
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FNODE to_narymul(FNODE f); |
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FNODE to_naryadd(FNODE f); |
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FNODE fnode_node_to_naryadd(NODE n); |
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FNODE fnode_node_to_narymul(NODE n); |
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void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep); |
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void fnode_coef_body(FNODE f,Num *cp,FNODE *bp); |
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FNODE fnode_normalize(FNODE f,int expand) |
{ |
{ |
FNODE a2,mone; |
FNODE a1,a2,mone,r,b2; |
Q q; |
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NODE n; |
NODE n; |
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Q q; |
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STOQ(-1,q); |
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mone = mkfnode(1,I_FORMULA,q); |
switch ( f->id ) { |
switch ( f->id ) { |
case I_PAREN: |
case I_PAREN: |
return fnode_normalize(FA0(f)); |
return fnode_normalize(FA0(f),expand); |
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case I_MINUS: |
case I_MINUS: |
f = fnode_normalize(FA0(f)); |
return fnode_normalize_mul_coef((Num)q, |
return f->id==I_MINUS ? FA0(f) : mkfnode(1,I_MINUS,f); |
fnode_normalize(FA0(f),expand),expand); |
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case I_BOP: |
case I_BOP: |
/* arf fnode fnode */ |
/* arf fnode fnode */ |
f = fnode_apply(f,fnode_normalize); |
a1 = fnode_normalize(FA1(f),expand); |
switch ( ((ARF)FA0(f))->name[0] ) { |
a2 = fnode_normalize(FA2(f),expand); |
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switch ( OPNAME(f) ) { |
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case '+': |
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return fnode_normalize_add(a1,a2,expand); |
case '-': |
case '-': |
a2 = mkfnode(1,I_MINUS,FA2(f)); |
a2 = fnode_normalize_mul_coef((Num)q,a2,expand); |
return mkfnode(3,I_BOP,addfs,FA1(f),a2); |
return fnode_normalize_add(a1,a2,expand); |
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case '*': |
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return fnode_normalize_mul(a1,a2,expand); |
case '/': |
case '/': |
STOQ(-1,q); |
a2 = fnode_normalize_pwr(a2,mone,expand); |
mone = mkfnode(1,I_FORMULA,q); |
return fnode_normalize_mul(a1,a2,expand); |
a2 = mkfnode(3,I_BOP,pwrfs,FA2(f),mone); |
case '^': |
return mkfnode(3,I_BOP,mulfs,FA1(f),a2); |
return fnode_normalize_pwr(a1,a2,expand); |
default: |
default: |
return f; |
return mkfnode(3,I_BOP,FA0(f),a1,a2); |
} |
} |
break; |
break; |
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default: |
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return fnode_apply(f,fnode_normalize); |
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} |
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} |
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FNODE fnode_simplify_add(FNODE f); |
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FNODE fnode_simplify_mul(FNODE f); |
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FNODE fnode_normalize_nary(FNODE f) |
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{ |
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NODE n; |
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switch ( f->id ) { |
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case I_PAREN: |
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return fnode_normalize_nary(FA0(f)); |
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case I_MINUS: |
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f = fnode_normalize_nary(FA0(f)); |
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return f->id==I_MINUS ? FA0(f) : mkfnode(1,I_MINUS,f); |
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case I_NARYOP: |
case I_NARYOP: |
f = fnode_apply(f,fnode_normalize_nary); |
switch ( OPNAME(f) ) { |
switch ( ((ARF)FA0(f))->name[0] ) { |
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/* XXX */ |
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case '+': |
case '+': |
return fnode_simplify_add(f); |
n = (NODE)FA1(f); |
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r = fnode_normalize(BDY(n),expand); n = NEXT(n); |
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for ( ; n; n = NEXT(n) ) { |
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a1 = fnode_normalize(BDY(n),expand); |
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r = fnode_normalize_add(r,a1,expand); |
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} |
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return r; |
case '*': |
case '*': |
return fnode_simplify_mul(f); |
n = (NODE)FA1(f); |
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r = fnode_normalize(BDY(n),expand); n = NEXT(n); |
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for ( ; n; n = NEXT(n) ) { |
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a1 = fnode_normalize(BDY(n),expand); |
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r = fnode_normalize_mul(r,a1,expand); |
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} |
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return r; |
default: |
default: |
return f; |
error("fnode_normallize : cannot happen"); |
} |
} |
break; |
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default: |
default: |
return fnode_apply(f,fnode_normalize_nary); |
return fnode_apply(f,fnode_normalize,expand); |
break; |
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} |
} |
} |
} |
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FNODE fnode_apply(FNODE f,FNODE (*func)()) |
FNODE fnode_apply(FNODE f,FNODE (*func)(),int expand) |
{ |
{ |
fid_spec_p spec; |
fid_spec_p spec; |
FNODE r; |
FNODE r; |
Line 2183 FNODE fnode_apply(FNODE f,FNODE (*func)()) |
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Line 2202 FNODE fnode_apply(FNODE f,FNODE (*func)()) |
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for ( i = 0; i < n; i++ ) { |
for ( i = 0; i < n; i++ ) { |
switch ( spec->type[i] ) { |
switch ( spec->type[i] ) { |
case A_fnode: |
case A_fnode: |
r->arg[i] = func(f->arg[i]); |
r->arg[i] = func(f->arg[i],expand); |
break; |
break; |
case A_node: |
case A_node: |
s = (NODE)f->arg[i]; |
s = (NODE)f->arg[i]; |
for ( t0 = 0; s; s = NEXT(s) ) { |
for ( t0 = 0; s; s = NEXT(s) ) { |
NEXTNODE(t0,t); |
NEXTNODE(t0,t); |
BDY(t) = (pointer)func((FNODE)BDY(s)); |
BDY(t) = (pointer)func((FNODE)BDY(s),expand); |
} |
} |
if ( t0 ) NEXT(t) = 0; |
if ( t0 ) NEXT(t) = 0; |
r->arg[i] = t0; |
r->arg[i] = t0; |
Line 2202 FNODE fnode_apply(FNODE f,FNODE (*func)()) |
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Line 2221 FNODE fnode_apply(FNODE f,FNODE (*func)()) |
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return r; |
return r; |
} |
} |
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NODE2 fnode_add_monomial(NODE2 s0,FNODE g); |
FNODE fnode_normalize_add(FNODE f1,FNODE f2,int expand) |
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{ |
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NODE n1,n2,r0,r; |
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FNODE b1,b2; |
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int s; |
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Num c1,c2,c; |
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FNODE fnode_simplify_add(FNODE f) |
if ( IS_ZERO(f1) ) return f2; |
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else if ( IS_ZERO(f2) ) return f1; |
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f1 = to_naryadd(f1); f2 = to_naryadd(f2); |
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n1 = (NODE)FA1(f1); n2 = (NODE)FA1(f2); |
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r0 = 0; |
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while ( n1 && n2 ) { |
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fnode_coef_body(BDY(n1),&c1,&b1); fnode_coef_body(BDY(n2),&c2,&b2); |
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if ( (s = fnode_normalize_comp(b1,b2)) > 0 ) { |
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NEXTNODE(r0,r); BDY(r) = BDY(n1); n1 = NEXT(n1); |
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} else if ( s < 0 ) { |
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NEXTNODE(r0,r); BDY(r) = BDY(n2); n2 = NEXT(n2); |
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} else { |
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addnum(0,c1,c2,&c); |
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if ( c ) { |
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NEXTNODE(r0,r); BDY(r) = fnode_normalize_mul_coef(c,b1,expand); |
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} |
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n1 = NEXT(n1); n2 = NEXT(n2); |
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} |
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} |
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if ( n1 ) |
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if ( r0 ) NEXT(r) = n1; |
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else r0 = n1; |
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else if ( n2 ) |
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if ( r0 ) NEXT(r) = n2; |
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else r0 = n2; |
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else if ( r0 ) |
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NEXT(r) = 0; |
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return fnode_node_to_naryadd(r0); |
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} |
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FNODE fnode_node_to_naryadd(NODE n) |
{ |
{ |
NODE n; |
if ( !n ) return mkfnode(1,I_FORMULA,0); |
NODE r0,r,t,u; |
else if ( !NEXT(n) ) return BDY(n); |
NODE2 s,s0; |
else return mkfnode(2,I_NARYOP,addfs,n); |
FNODE g,m; |
} |
QUOTE q; |
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n = (NODE)FA1(f); |
FNODE fnode_node_to_narymul(NODE n) |
s0 = 0; |
{ |
for ( t = n; t; t = NEXT(t) ) { |
if ( !n ) return mkfnode(1,I_FORMULA,ONE); |
g = (FNODE)BDY(t); |
else if ( !NEXT(n) ) return BDY(n); |
s0 = fnode_add_monomial(s0,g); |
else return mkfnode(2,I_NARYOP,mulfs,n); |
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} |
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FNODE fnode_normalize_mul(FNODE f1,FNODE f2,int expand) |
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{ |
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NODE n1,n2,r0,r,r1; |
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FNODE b1,b2,e1,e2,cc,t,t1; |
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FNODE *m; |
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int s; |
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Num c1,c2,c,e; |
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int l1,l,i,j; |
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if ( IS_ZERO(f1) || IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,0); |
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else if ( fnode_is_number(f1) ) |
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return fnode_normalize_mul_coef((Num)eval(f1),f2,expand); |
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else if ( fnode_is_number(f2) ) |
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return fnode_normalize_mul_coef((Num)eval(f2),f1,expand); |
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if ( expand && IS_NARYADD(f1) ) { |
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t = mkfnode(1,I_FORMULA,0); |
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for ( n1 = (NODE)FA1(f1); n1; n1 = NEXT(n1) ) { |
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t1 = fnode_normalize_mul(BDY(n1),f2,expand); |
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t = fnode_normalize_add(t,t1,expand); |
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} |
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return t; |
} |
} |
if ( !s0 ) |
if ( expand && IS_NARYADD(f2) ) { |
return mkfnode(1,I_FORMULA,0); |
t = mkfnode(1,I_FORMULA,0); |
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for ( n2 = (NODE)FA1(f2); n2; n2 = NEXT(n2) ) { |
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t1 = fnode_normalize_mul(f1,BDY(n2),expand); |
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t = fnode_normalize_add(t,t1,expand); |
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} |
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return t; |
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} |
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fnode_coef_body(f1,&c1,&b1); fnode_coef_body(f2,&c2,&b2); |
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mulnum(0,c1,c2,&c); |
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if ( !c ) return mkfnode(1,I_FORMULA,0); |
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n1 = (NODE)FA1(to_narymul(b1)); n2 = (NODE)FA1(to_narymul(b2)); |
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l1 = length(n1); l = l1+length(n2); |
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m = (FNODE *)ALLOCA(l*sizeof(FNODE)); |
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for ( r = n1, i = 0; i < l1; r = NEXT(r), i++ ) m[i] = BDY(r); |
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for ( r = n2; r; r = NEXT(r) ) { |
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if ( i == 0 ) |
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m[i++] = BDY(r); |
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else { |
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fnode_base_exp(m[i-1],&b1,&e1); fnode_base_exp(BDY(r),&b2,&e2); |
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if ( compfnode(b1,b2) ) break; |
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addnum(0,eval(e1),eval(e2),&e); |
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if ( !e ) i--; |
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else if ( UNIQ(e) ) |
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m[i-1] = b1; |
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else |
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m[i-1] = mkfnode(3,I_BOP,pwrfs,b1,mkfnode(1,I_FORMULA,e)); |
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} |
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} |
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for ( j = i-1; j >= 0; j-- ) { |
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MKNODE(r1,m[j],r); r = r1; |
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} |
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if ( !UNIQ(c) ) { |
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cc = mkfnode(1,I_FORMULA,c); MKNODE(r1,cc,r); r = r1; |
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} |
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return fnode_node_to_narymul(r); |
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} |
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FNODE fnode_normalize_pwr(FNODE f1,FNODE f2,int expand) |
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{ |
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FNODE b,b1,e1,e,cc,r; |
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Num c,c1; |
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NODE arg,n; |
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Q q; |
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if ( IS_ZERO(f2) ) return mkfnode(1,I_FORMULA,ONE); |
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else if ( IS_ZERO(f1) ) return mkfnode(1,I_FORMULA,0); |
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else if ( fnode_is_one(f2) ) return f1; |
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else if ( fnode_is_number(f1) ) |
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if ( fnode_is_integer(f2) ) { |
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pwrnum(0,(Num)eval(f1),(Num)eval(f2),&c); |
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return mkfnode(1,I_FORMULA,c); |
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} else |
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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 ( IS_NARYMUL(f1) && fnode_is_integer(f2) ) { |
|
fnode_coef_body(f1,&c1,&b1); |
|
pwrnum(0,(Num)c1,(Num)eval(f2),&c); |
|
cc = mkfnode(1,I_FORMULA,c); |
|
b = fnode_normalize_pwr(b1,f2,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("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 { |
else { |
for ( s = s0, r0 = 0; s; s = NEXT(s) ) { |
n1 = n/2; |
NEXTNODE(r0,r); |
f1 = fnode_expand_pwr(f,n1); |
if ( UNIQ(s->body1) ) |
f2 = fnode_normalize_mul(f1,f1,1); |
BDY(r) = s->body2; |
if ( n%2 ) f2 = fnode_normalize_mul(f2,f,1); |
else if ( MUNIQ(s->body1) ) |
return f2; |
BDY(r) = mkfnode(1,I_MINUS,s->body2); |
} |
else { |
} |
objtoquote(s->body1,&q); |
|
m = (FNODE)s->body2; |
/* f = b^e */ |
if ( m->id == I_NARYOP && OPNAME(m) == '*' ) { |
void fnode_base_exp(FNODE f,FNODE *bp,FNODE *ep) |
MKNODE(u,BDY(q),FA1(m)); FA1(m) = u; |
{ |
BDY(r) = m; |
if ( IS_BINARYPWR(f) ) { |
} else { |
*bp = FA1(f); *ep = FA2(f); |
u = mknode(2,BDY(q),m); |
} else { |
BDY(r) = mkfnode(2,I_NARYOP,mulfs,u); |
*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)); |
} |
} |
if ( r0 ) NEXT(r) = 0; |
|
if ( length(r0) == 1 ) |
|
return (FNODE)BDY(r0); |
|
else |
|
return mkfnode(2,I_NARYOP,FA0(f),r0); |
|
} |
} |
} |
} |
|
|
NODE2 fnode_add_monomial(NODE2 r,FNODE g) |
void fnode_coef_body(FNODE f,Num *cp,FNODE *bp) |
{ |
{ |
Num c,c1; |
FNODE c; |
FNODE b; |
|
NODE arg; |
|
NODE2 prev,cur,t; |
|
int a; |
|
|
|
if ( fnode_is_number(g) ) { |
if ( fnode_is_number(f) ) { |
c = (Num)eval(g); |
*cp = eval(f); *bp = mkfnode(1,I_FORMULA,ONE); |
b = mkfnode(1,I_FORMULA,ONE); |
} else if ( IS_NARYMUL(f) ) { |
} else if ( g->id == I_NARYOP && OPNAME(g) == '*' ) { |
c=(FNODE)BDY((NODE)FA1(f)); |
arg = (NODE)FA1(g); |
if ( fnode_is_number(c) ) { |
if ( fnode_is_number(BDY(arg)) ) { |
*cp = eval(c); |
c = (Num)eval(BDY(arg)); |
*bp = fnode_node_to_narymul(NEXT((NODE)FA1(f))); |
if ( length(arg) > 2 ) |
|
b = mkfnode(2,I_NARYOP,FA0(g),NEXT(arg)); |
|
else |
|
b = BDY(NEXT(arg)); |
|
} else { |
} else { |
c = (Num)ONE; |
*cp = (Num)ONE; *bp = f; |
b = g; |
|
} |
} |
} else { |
} else { |
c = (Num)ONE; |
*cp = (Num)ONE; *bp = f; |
b = g; |
|
} |
} |
|
} |
|
|
for ( prev = 0, cur = r; cur; prev = cur, cur = NEXT(cur) ) { |
int fnode_normalize_comp_pwr(FNODE f1,FNODE f2); |
a = compfnode(b,cur->body2); |
|
if ( a > 0 ) { |
int fnode_normalize_comp(FNODE f1,FNODE f2) |
MKNODE2(t,c,b,cur); |
{ |
if ( !prev ) |
NODE n1,n2; |
return t; |
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 { |
else { |
NEXT(prev) = t; return r; |
n1 = NEXT(n1); n2 = NEXT(n2); |
} |
} |
} else if ( a == 0 ) { |
return n1?1:(n2?-1:0); |
addnum(0,cur->body1,c,&c1); |
} |
if ( !c1 ) { |
if ( IS_NARYMUL(f1) || IS_NARYMUL(f2) ) { |
if ( !prev ) |
fnode_coef_body(f1,&c1,&b1); |
return NEXT(cur); |
fnode_coef_body(f2,&c2,&b2); |
else { |
if ( !compfnode(b1,b2) ) return compnum(0,c1,c2); |
NEXT(prev) = NEXT(cur); return r; |
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 { |
} else { |
cur->body1 = c1; return r; |
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; |
|
} |
} |
} |
} |
} |
} |
} |
MKNODE2(t,c,b,0); |
if ( IS_BINARYPWR(f1) || IS_BINARYPWR(f2) ) |
if ( !r ) |
return fnode_normalize_comp_pwr(f1,f2); |
return t; |
|
else { |
/* now, IDs of f1 and f2 must be I_FORMULA, I_FUNC, or I_PVAR */ |
NEXT(prev) = t; return r; |
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"); |
} |
} |
} |
} |
|
|
FNODE fnode_simplify_mul(FNODE f) |
int fnode_normalize_comp_pwr(FNODE f1,FNODE f2) |
{ |
{ |
int l,i,j; |
FNODE b1,b2,e1,e2; |
FNODE *b; |
int r; |
Obj *e; |
|
NODE n,t,r,r1; |
|
FNODE g,base; |
|
QUOTE q; |
|
Obj exp,exp1; |
|
Num c,c1; |
|
|
|
n = (NODE)FA1(f); |
fnode_base_exp(f1,&b1,&e1); |
for ( l = 0, t = n; t; t = NEXT(t), l++ ); |
fnode_base_exp(f2,&b2,&e2); |
b = (FNODE *)MALLOC(l*sizeof(FNODE)); |
if ( r = fnode_normalize_comp(b1,b2) ) { |
e = (Obj *)MALLOC(l*sizeof(Obj)); |
if ( r > 0 ) |
c = (Num)ONE; |
return fnode_normalize_comp(e1,mkfnode(1,I_FORMULA,0)); |
for ( i = 0, t = n; t; t = NEXT(t) ) { |
else if ( r < 0 ) |
g = (FNODE)BDY(t); |
return fnode_normalize_comp(mkfnode(1,I_FORMULA,0),e2); |
if ( fnode_is_number(g) ) { |
} else return fnode_normalize_comp(e1,e2); |
if ( fnode_is_zero(g) ) |
} |
return mkfnode(1,I_FORMULA,0); |
|
else { |
int fnode_normalize_unify(FNODE f,FNODE pat,NODE *rp) |
mulnum(0,c,(Num)eval(g),&c1); c = c1; |
{ |
} |
NODE m,m1,m2,base,exp,fa,pa,n; |
} else { |
LIST l; |
if ( g->id == I_MINUS ) { |
QUOTE qp,qf; |
chsgnnum(c,&c1); c = c1; |
FNODE fbase,fexp; |
g = FA0(g); |
FUNC ff,pf; |
} |
int r; |
if ( g->id == I_BOP && ((ARF)FA0(g))->name[0] == '^' ) { |
|
base = FA1(g); |
switch ( pat->id ) { |
exp = (Obj)eval(FA2(g)); |
case I_PVAR: |
|
/* [[pat,f]] */ |
|
MKQUOTE(qf,f); |
|
MKQUOTE(qp,pat); |
|
n = mknode(2,qp,qf); MKLIST(l,n); |
|
*rp = mknode(1,l); |
|
return 1; |
|
|
|
case I_FORMULA: |
|
if ( !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_unify : invalid BOP"); |
|
if ( IS_BINARYPWR(f) ) { |
|
fbase = FA1(f); fexp = FA2(f); |
} else { |
} else { |
base = g; exp = (Obj)ONE; |
fbase = f; fexp = mkfnode(1,I_FORMULA,ONE); |
} |
} |
if ( i > 0 && !compfnode(b[i-1],base) ) { |
r = fnode_normalize_unify(fbase,FA1(pat),&base); |
arf_add(CO,e[i-1],exp,&exp1); |
if ( !r ) return 0; |
if ( !exp1 ) |
r = fnode_normalize_unify(fexp,FA2(pat),&exp); |
i--; |
if ( !r ) return 0; |
else |
else return merge_matching_node(base,exp,rp); |
e[i-1] = exp1; |
break; |
} else { |
|
b[i] = base; |
case I_FUNC: |
e[i] = exp; |
if ( f->id != I_FUNC ) return 0; |
i++; |
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 ) { |
|
r = fnode_normalize_unify(BDY(fa),BDY(pa),&m1); |
|
if ( !r ) return 0; |
|
r = merge_matching_node(m,m1,&m2); |
|
if ( !r ) return 0; |
|
else m = m2; |
} |
} |
} |
if ( fa || pa ) return 0; |
} |
|
if ( !i ) { |
|
/* coeff only */ |
|
g = mkfnode(1,I_FORMULA,c); |
|
return g; |
|
} else { |
|
r = 0; |
|
for ( j = i-1; j >= 0; j-- ) { |
|
if ( UNIQ(e[j]) ) |
|
g = b[j]; |
|
else { |
else { |
objtoquote(e[j],&q); |
*rp = m; |
g = mkfnode(3,I_BOP,pwrfs,b[j],BDY(q)); |
return 1; |
} |
} |
MKNODE(r1,g,r); r = r1; |
|
} |
case I_NARYOP: |
g = mkfnode(1,I_FORMULA,c); |
if ( IS_NARYADD(pat) ) |
MKNODE(r1,g,r); r = r1; |
return fnode_normalize_unify_naryadd(f,pat,rp); |
return mkfnode(2,I_NARYOP,FA0(f),r); |
else if ( IS_NARYMUL(pat) ) |
|
return fnode_normalize_unify_narymul(f,pat,rp); |
|
else |
|
error("fnode_normalize_unify : invalid NARYOP"); |
|
break; |
|
|
|
default: |
|
error("fnode_normalize_unify : invalid pattern"); |
} |
} |
} |
} |
|
|
|
int fnode_normalize_unify_naryadd(FNODE f,FNODE pat,NODE *rp){} |
|
|
|
int fnode_normalize_unify_narymul(FNODE f,FNODE pat,NODE *rp){} |
|
|
|
/* |
|
int fnode_normalize_unify_naryadd(FNODE f,FNODE pat,NODE *rp) |
|
{ |
|
int lf,lp; |
|
|
|
f = to_naryadd(f); |
|
lf = length((NODE)FA1(f)); |
|
lp = length((NODE)FA1(pat)); |
|
if ( lf < lp ) return 0; |
|
else if ( lp == 1 ) { |
|
if ( lf == 1 ) |
|
return fnode_normalize_unify( |
|
BDY((NODE)FA1(f)),BDY((NODE)FA1(pat)),rp); |
|
else |
|
return 0; |
|
} else { |
|
sel = (int *)ALLOCA(lf); |
|
} |
|
} |
|
*/ |
|
|