=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/dist.c,v retrieving revision 1.2 retrieving revision 1.29 diff -u -p -r1.2 -r1.29 --- OpenXM_contrib2/asir2000/engine/dist.c 2000/04/05 08:32:17 1.2 +++ OpenXM_contrib2/asir2000/engine/dist.c 2004/03/05 02:26:52 1.29 @@ -1,9 +1,54 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/dist.c,v 1.1.1.1 1999/12/03 07:39:08 noro Exp $ */ +/* + * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED + * All rights reserved. + * + * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited, + * non-exclusive and royalty-free license to use, copy, modify and + * redistribute, solely for non-commercial and non-profit purposes, the + * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and + * conditions of this Agreement. For the avoidance of doubt, you acquire + * only a limited right to use the SOFTWARE hereunder, and FLL or any + * third party developer retains all rights, including but not limited to + * copyrights, in and to the SOFTWARE. + * + * (1) FLL does not grant you a license in any way for commercial + * purposes. You may use the SOFTWARE only for non-commercial and + * non-profit purposes only, such as academic, research and internal + * business use. + * (2) The SOFTWARE is protected by the Copyright Law of Japan and + * international copyright treaties. If you make copies of the SOFTWARE, + * with or without modification, as permitted hereunder, you shall affix + * to all such copies of the SOFTWARE the above copyright notice. + * (3) An explicit reference to this SOFTWARE and its copyright owner + * 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@sec.flab.fujitsu.co.jp of the detailed specification + * for such modification or the source code of the modified part of the + * SOFTWARE. + * + * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL + * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND + * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS + * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES' + * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY + * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY. + * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT, + * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY + * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL + * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES + * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES + * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY + * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF + * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART + * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY + * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, + * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. + * + * $OpenXM: OpenXM_contrib2/asir2000/engine/dist.c,v 1.28 2004/02/05 08:28:53 noro Exp $ +*/ #include "ca.h" -#define NV(p) ((p)->nv) -#define C(p) ((p)->c) - #define ORD_REVGRADLEX 0 #define ORD_GRADLEX 1 #define ORD_LEX 2 @@ -14,59 +59,70 @@ #define ORD_BGRADREV 7 #define ORD_BLEXREV 8 #define ORD_ELIM 9 +#define ORD_WEYL_ELIM 10 +#define ORD_HOMO_WW_DRL 11 +#define ORD_DRL_ZIGZAG 12 +#define ORD_HOMO_WW_DRL_ZIGZAG 13 +int cmpdl_drl_zigzag(), cmpdl_homo_ww_drl_zigzag(); + int (*cmpdl)()=cmpdl_revgradlex; int (*primitive_cmpdl[3])() = {cmpdl_revgradlex,cmpdl_gradlex,cmpdl_lex}; -void comm_muld(VL,DP,DP,DP *); -void weyl_muld(VL,DP,DP,DP *); -void weyl_muldm(VL,DP,MP,DP *); -void weyl_mulmm(VL,MP,MP,int,DP *); -void mkwc(int,int,Q *); - int do_weyl; int dp_nelim,dp_fcoeffs; -struct order_spec dp_current_spec; +struct order_spec *dp_current_spec; int *dp_dl_work; -int has_fcoef(DP); -int has_fcoef_p(P); +void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr); +void comm_quod(VL vl,DP p1,DP p2,DP *pr); +void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr); +void muldc_trunc(VL vl,DP p,P c,DL dl,DP *pr); -int has_fcoef(f) -DP f; +void order_init() { + struct order_spec *spec; + + create_order_spec(0,0,&spec); + initd(spec); +} + +int has_sfcoef(DP f) +{ MP t; if ( !f ) return 0; for ( t = BDY(f); t; t = NEXT(t) ) - if ( has_fcoef_p(t->c) ) + if ( has_sfcoef_p(t->c) ) break; return t ? 1 : 0; } -int has_fcoef_p(f) -P f; +int has_sfcoef_p(P f) { DCP dc; if ( !f ) return 0; else if ( NUM(f) ) - return (NID((Num)f) == N_LM || NID((Num)f) == N_GF2N) ? 1 : 0; + return (NID((Num)f) == N_GFS) ? 1 : 0; else { for ( dc = DC(f); dc; dc = NEXT(dc) ) - if ( has_fcoef_p(COEF(dc)) ) + if ( has_sfcoef_p(COEF(dc)) ) return 1; return 0; } } -void initd(spec) -struct order_spec *spec; +void initd(struct order_spec *spec) { switch ( spec->id ) { + case 3: + cmpdl = cmpdl_composite; + dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int)); + break; case 2: cmpdl = cmpdl_matrix; dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int)); @@ -94,26 +150,32 @@ struct order_spec *spec; cmpdl = cmpdl_blexrev; break; case ORD_ELIM: cmpdl = cmpdl_elim; break; + case ORD_WEYL_ELIM: + cmpdl = cmpdl_weyl_elim; break; + case ORD_HOMO_WW_DRL: + cmpdl = cmpdl_homo_ww_drl; break; + case ORD_DRL_ZIGZAG: + cmpdl = cmpdl_drl_zigzag; break; + case ORD_HOMO_WW_DRL_ZIGZAG: + cmpdl = cmpdl_homo_ww_drl_zigzag; break; case ORD_LEX: default: cmpdl = cmpdl_lex; break; } break; } - dp_current_spec = *spec; + dp_current_spec = spec; } -void ptod(vl,dvl,p,pr) -VL vl,dvl; -P p; -DP *pr; +void ptod(VL vl,VL dvl,P p,DP *pr) { int isconst = 0; - int n,i; + int n,i,j,k; VL tvl; V v; DL d; MP m; DCP dc; + DCP *w; DP r,s,t,u; P x,c; @@ -128,15 +190,26 @@ DP *pr; for ( i = 0, tvl = dvl, v = VR(p); tvl && tvl->v != v; tvl = NEXT(tvl), i++ ); if ( !tvl ) { - for ( dc = DC(p), s = 0, MKV(v,x); dc; dc = NEXT(dc) ) { - ptod(vl,dvl,COEF(dc),&t); pwrp(vl,x,DEG(dc),&c); + for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ ); + w = (DCP *)ALLOCA(k*sizeof(DCP)); + for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ ) + w[j] = dc; + + for ( j = k-1, s = 0, MKV(v,x); j >= 0; j-- ) { + ptod(vl,dvl,COEF(w[j]),&t); pwrp(vl,x,DEG(w[j]),&c); muldc(vl,t,c,&r); addd(vl,r,s,&t); s = t; } *pr = s; } else { - for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) { - ptod(vl,dvl,COEF(dc),&t); - NEWDL(d,n); d->td = QTOS(DEG(dc)); d->d[i] = d->td; + for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ ); + w = (DCP *)ALLOCA(k*sizeof(DCP)); + for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ ) + w[j] = dc; + + for ( j = k-1, s = 0; j >= 0; j-- ) { + ptod(vl,dvl,COEF(w[j]),&t); + NEWDL(d,n); d->d[i] = QTOS(DEG(w[j])); + d->td = MUL_WEIGHT(d->d[i],i); NEWMP(m); m->dl = d; C(m) = (P)ONE; NEXT(m) = 0; MKDP(n,m,u); u->sugar = d->td; comm_muld(vl,t,u,&r); addd(vl,r,s,&t); s = t; } @@ -144,18 +217,18 @@ DP *pr; } } } - if ( !dp_fcoeffs && has_fcoef(*pr) ) - dp_fcoeffs = 1; +#if 0 + if ( !dp_fcoeffs && has_sfcoef(*pr) ) + dp_fcoeffs = N_GFS; +#endif } -void dtop(vl,dvl,p,pr) -VL vl,dvl; -DP p; -P *pr; +void dtop(VL vl,VL dvl,DP p,P *pr) { - int n,i; + int n,i,j,k; DL d; MP m; + MP *a; P r,s,t,u,w; Q q; VL tvl; @@ -163,7 +236,13 @@ P *pr; if ( !p ) *pr = 0; else { - for ( n = p->nv, m = BDY(p), s = 0; m; m = NEXT(m) ) { + for ( k = 0, m = BDY(p); m; m = NEXT(m), k++ ); + a = (MP *)ALLOCA(k*sizeof(MP)); + for ( j = 0, m = BDY(p); j < k; m = NEXT(m), j++ ) + a[j] = m; + + for ( n = p->nv, j = k-1, s = 0; j >= 0; j-- ) { + m = a[j]; t = C(m); if ( NUM(t) && NID((Num)t) == N_M ) { mptop(t,&u); t = u; @@ -179,9 +258,7 @@ P *pr; } } -void nodetod(node,dp) -NODE node; -DP *dp; +void nodetod(NODE node,DP *dp) { NODE t; int len,i,td; @@ -199,7 +276,7 @@ DP *dp; else if ( !NUM(e) || !RATN(e) || !INT(e) ) error("nodetod : invalid input"); else { - d->d[i] = QTOS((Q)e); td += d->d[i]; + d->d[i] = QTOS((Q)e); td += MUL_WEIGHT(d->d[i],i); } } d->td = td; @@ -207,8 +284,7 @@ DP *dp; MKDP(len,m,u); u->sugar = td; *dp = u; } -int sugard(m) -MP m; +int sugard(MP m) { int s; @@ -217,9 +293,7 @@ MP m; return s; } -void addd(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +void addd(VL vl,DP p1,DP p2,DP *pr) { int n; MP m1,m2,mr,mr0; @@ -268,12 +342,10 @@ DP p1,p2,*pr; /* for F4 symbolic reduction */ -void symb_addd(p1,p2,pr) -DP p1,p2,*pr; +void symb_addd(DP p1,DP p2,DP *pr) { int n; MP m1,m2,mr,mr0; - P t; if ( !p1 ) *pr = p2; @@ -315,10 +387,190 @@ DP p1,p2,*pr; } } -void subd(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +/* + * destructive merge of two list + * + * p1, p2 : list of DL + * return : a merged list + */ + +NODE symb_merge(NODE m1,NODE m2,int n) { + NODE top,prev,cur,m,t; + int c,i; + DL d1,d2; + + if ( !m1 ) + return m2; + else if ( !m2 ) + return m1; + else { + switch ( (*cmpdl)(n,(DL)BDY(m1),(DL)BDY(m2)) ) { + case 0: + top = m1; m = NEXT(m2); + break; + case 1: + top = m1; m = m2; + break; + case -1: + top = m2; m = m1; + break; + } + prev = top; cur = NEXT(top); + /* BDY(prev) > BDY(m) always holds */ + while ( cur && m ) { + d1 = (DL)BDY(cur); + d2 = (DL)BDY(m); +#if 1 + switch ( (*cmpdl)(n,(DL)BDY(cur),(DL)BDY(m)) ) { +#else + /* XXX only valid for DRL */ + if ( d1->td > d2->td ) + c = 1; + else if ( d1->td < d2->td ) + c = -1; + else { + for ( i = n-1; i >= 0 && d1->d[i] == d2->d[i]; i-- ); + if ( i < 0 ) + c = 0; + else if ( d1->d[i] < d2->d[i] ) + c = 1; + else + c = -1; + } + switch ( c ) { +#endif + case 0: + m = NEXT(m); + prev = cur; cur = NEXT(cur); + break; + case 1: + t = NEXT(cur); NEXT(cur) = m; m = t; + prev = cur; cur = NEXT(cur); + break; + case -1: + NEXT(prev) = m; m = cur; + prev = NEXT(prev); cur = NEXT(prev); + break; + } + } + if ( !cur ) + NEXT(prev) = m; + return top; + } +} + +void _adddl(int n,DL d1,DL d2,DL d3) +{ + int i; + + d3->td = d1->td+d2->td; + for ( i = 0; i < n; i++ ) + d3->d[i] = d1->d[i]+d2->d[i]; +} + +/* m1 <- m1 U dl*f, destructive */ + +NODE mul_dllist(DL dl,DP f); + +NODE symb_mul_merge(NODE m1,DL dl,DP f,int n) +{ + NODE top,prev,cur,n1; + DP g; + DL t,s; + MP m; + + if ( !m1 ) + return mul_dllist(dl,f); + else if ( !f ) + return m1; + else { + m = BDY(f); + NEWDL_NOINIT(t,n); + _adddl(n,m->dl,dl,t); + top = m1; prev = 0; cur = m1; + while ( m ) { + switch ( (*cmpdl)(n,(DL)BDY(cur),t) ) { + case 0: + prev = cur; cur = NEXT(cur); + if ( !cur ) { + MKDP(n,m,g); + NEXT(prev) = mul_dllist(dl,g); + return; + } + m = NEXT(m); + if ( m ) _adddl(n,m->dl,dl,t); + break; + case 1: + prev = cur; cur = NEXT(cur); + if ( !cur ) { + MKDP(n,m,g); + NEXT(prev) = mul_dllist(dl,g); + return; + } + break; + case -1: + NEWDL_NOINIT(s,n); + s->td = t->td; + bcopy(t->d,s->d,n*sizeof(int)); + NEWNODE(n1); + n1->body = (pointer)s; + NEXT(n1) = cur; + if ( !prev ) { + top = n1; cur = n1; + } else { + NEXT(prev) = n1; prev = n1; + } + m = NEXT(m); + if ( m ) _adddl(n,m->dl,dl,t); + break; + } + } + return top; + } +} + +DLBUCKET symb_merge_bucket(DLBUCKET m1,DLBUCKET m2,int n) +{ + DLBUCKET top,prev,cur,m,t; + + if ( !m1 ) + return m2; + else if ( !m2 ) + return m1; + else { + if ( m1->td == m2->td ) { + top = m1; + BDY(top) = symb_merge(BDY(top),BDY(m2),n); + m = NEXT(m2); + } else if ( m1->td > m2->td ) { + top = m1; m = m2; + } else { + top = m2; m = m1; + } + prev = top; cur = NEXT(top); + /* prev->td > m->td always holds */ + while ( cur && m ) { + if ( cur->td == m->td ) { + BDY(cur) = symb_merge(BDY(cur),BDY(m),n); + m = NEXT(m); + prev = cur; cur = NEXT(cur); + } else if ( cur->td > m->td ) { + t = NEXT(cur); NEXT(cur) = m; m = t; + prev = cur; cur = NEXT(cur); + } else { + NEXT(prev) = m; m = cur; + prev = NEXT(prev); cur = NEXT(prev); + } + } + if ( !cur ) + NEXT(prev) = m; + return top; + } +} + +void subd(VL vl,DP p1,DP p2,DP *pr) +{ DP t; if ( !p2 ) @@ -328,8 +580,7 @@ DP p1,p2,*pr; } } -void chsgnd(p,pr) -DP p,*pr; +void chsgnd(DP p,DP *pr) { MP m,mr,mr0; @@ -345,9 +596,7 @@ DP p,*pr; } } -void muld(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +void muld(VL vl,DP p1,DP p2,DP *pr) { if ( ! do_weyl ) comm_muld(vl,p1,p2,pr); @@ -355,12 +604,13 @@ DP p1,p2,*pr; weyl_muld(vl,p1,p2,pr); } -void comm_muld(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +void comm_muld(VL vl,DP p1,DP p2,DP *pr) { MP m; DP s,t,u; + int i,l,l1; + static MP *w; + static int wlen; if ( !p1 || !p2 ) *pr = 0; @@ -369,19 +619,108 @@ DP p1,p2,*pr; else if ( OID(p2) <= O_P ) muldc(vl,p1,(P)p2,pr); else { - for ( m = BDY(p2), s = 0; m; m = NEXT(m) ) { - muldm(vl,p1,m,&t); addd(vl,s,t,&u); s = u; + for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ ); + for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ ); + if ( l1 < l ) { + t = p1; p1 = p2; p2 = t; + l = l1; } + if ( l > wlen ) { + if ( w ) GC_free(w); + w = (MP *)MALLOC(l*sizeof(MP)); + wlen = l; + } + for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ ) + w[i] = m; + for ( s = 0, i = l-1; i >= 0; i-- ) { + muldm(vl,p1,w[i],&t); addd(vl,s,t,&u); s = u; + } + bzero(w,l*sizeof(MP)); *pr = s; } } -void muldm(vl,p,m0,pr) -VL vl; -DP p; -MP m0; -DP *pr; +/* discard terms which is not a multiple of dl */ + +void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr) { + MP m; + DP s,t,u; + int i,l,l1; + static MP *w; + static int wlen; + + if ( !p1 || !p2 ) + *pr = 0; + else if ( OID(p1) <= O_P ) + muldc_trunc(vl,p2,(P)p1,dl,pr); + else if ( OID(p2) <= O_P ) + muldc_trunc(vl,p1,(P)p2,dl,pr); + else { + for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ ); + for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ ); + if ( l1 < l ) { + t = p1; p1 = p2; p2 = t; + l = l1; + } + if ( l > wlen ) { + if ( w ) GC_free(w); + w = (MP *)MALLOC(l*sizeof(MP)); + wlen = l; + } + for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ ) + w[i] = m; + for ( s = 0, i = l-1; i >= 0; i-- ) { + muldm_trunc(vl,p1,w[i],dl,&t); addd(vl,s,t,&u); s = u; + } + bzero(w,l*sizeof(MP)); + *pr = s; + } +} + +void comm_quod(VL vl,DP p1,DP p2,DP *pr) +{ + MP m,m0; + DP s,t; + int i,n,sugar; + DL d1,d2,d; + Q a,b; + + if ( !p2 ) + error("comm_quod : invalid input"); + if ( !p1 ) + *pr = 0; + else { + n = NV(p1); + d2 = BDY(p2)->dl; + m0 = 0; + sugar = p1->sugar; + while ( p1 ) { + d1 = BDY(p1)->dl; + NEWDL(d,n); + d->td = d1->td - d2->td; + for ( i = 0; i < n; i++ ) + d->d[i] = d1->d[i]-d2->d[i]; + NEXTMP(m0,m); + m->dl = d; + divq((Q)BDY(p1)->c,(Q)BDY(p2)->c,&a); chsgnq(a,&b); + C(m) = (P)b; + muldm_trunc(vl,p2,m,d2,&t); + addd(vl,p1,t,&s); p1 = s; + C(m) = (P)a; + } + if ( m0 ) { + NEXT(m) = 0; MKDP(n,m0,*pr); + } else + *pr = 0; + /* XXX */ + if ( *pr ) + (*pr)->sugar = sugar - d2->td; + } +} + +void muldm(VL vl,DP p,MP m0,DP *pr) +{ MP m,mr,mr0; P c; DL d; @@ -405,12 +744,50 @@ DP *pr; } } -void weyl_muld(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr) { + MP m,mr,mr0; + P c; + DL d,tdl; + int n,i; + + if ( !p ) + *pr = 0; + else { + n = NV(p); + NEWDL(tdl,n); + for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl; + m; m = NEXT(m) ) { + _adddl(n,m->dl,d,tdl); + for ( i = 0; i < n; i++ ) + if ( tdl->d[i] < dl->d[i] ) + break; + if ( i < n ) + continue; + NEXTMP(mr0,mr); + mr->dl = tdl; + NEWDL(tdl,n); + if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) ) + mulq((Q)C(m),(Q)c,(Q *)&C(mr)); + else + mulp(vl,C(m),c,&C(mr)); + } + if ( mr0 ) { + NEXT(mr) = 0; MKDP(NV(p),mr0,*pr); + } else + *pr = 0; + if ( *pr ) + (*pr)->sugar = p->sugar + m0->dl->td; + } +} + +void weyl_muld(VL vl,DP p1,DP p2,DP *pr) +{ MP m; DP s,t,u; + int i,l; + static MP *w; + static int wlen; if ( !p1 || !p2 ) *pr = 0; @@ -419,90 +796,207 @@ DP p1,p2,*pr; else if ( OID(p2) <= O_P ) muldc(vl,p1,(P)p2,pr); else { - for ( m = BDY(p2), s = 0; m; m = NEXT(m) ) { - weyl_muldm(vl,p1,m,&t); addd(vl,s,t,&u); s = u; + for ( m = BDY(p1), l = 0; m; m = NEXT(m), l++ ); + if ( l > wlen ) { + if ( w ) GC_free(w); + w = (MP *)MALLOC(l*sizeof(MP)); + wlen = l; } + for ( m = BDY(p1), i = 0; i < l; m = NEXT(m), i++ ) + w[i] = m; + for ( s = 0, i = l-1; i >= 0; i-- ) { + weyl_muldm(vl,w[i],p2,&t); addd(vl,s,t,&u); s = u; + } + bzero(w,l*sizeof(MP)); *pr = s; } } -void weyl_muldm(vl,p,m0,pr) -VL vl; -DP p; -MP m0; -DP *pr; +/* monomial * polynomial */ + +void weyl_muldm(VL vl,MP m0,DP p,DP *pr) { DP r,t,t1; MP m; - int n; + DL d0; + int n,n2,l,i,j,tlen; + static MP *w,*psum; + static struct cdl *tab; + static int wlen; + static int rtlen; if ( !p ) *pr = 0; else { - for ( r = 0, m = BDY(p), n = NV(p); m; m = NEXT(m) ) { - weyl_mulmm(vl,m,m0,n,&t); - addd(vl,r,t,&t1); r = t1; + for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ ); + if ( l > wlen ) { + if ( w ) GC_free(w); + w = (MP *)MALLOC(l*sizeof(MP)); + wlen = l; } + for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ ) + w[i] = m; + + n = NV(p); n2 = n>>1; + d0 = m0->dl; + for ( i = 0, tlen = 1; i < n2; i++ ) + tlen *= d0->d[n2+i]+1; + if ( tlen > rtlen ) { + if ( tab ) GC_free(tab); + if ( psum ) GC_free(psum); + rtlen = tlen; + tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl)); + psum = (MP *)MALLOC(rtlen*sizeof(MP)); + } + bzero(psum,tlen*sizeof(MP)); + for ( i = l-1; i >= 0; i-- ) { + bzero(tab,tlen*sizeof(struct cdl)); + weyl_mulmm(vl,m0,w[i],n,tab,tlen); + for ( j = 0; j < tlen; j++ ) { + if ( tab[j].c ) { + NEWMP(m); m->dl = tab[j].d; C(m) = tab[j].c; NEXT(m) = psum[j]; + psum[j] = m; + } + } + } + for ( j = tlen-1, r = 0; j >= 0; j-- ) + if ( psum[j] ) { + MKDP(n,psum[j],t); addd(vl,r,t,&t1); r = t1; + } if ( r ) r->sugar = p->sugar + m0->dl->td; *pr = r; } } -/* m0 = x0^d0*x1^d1*... * dx0^d(n/2)*dx1^d(n/2+1)*... */ +/* m0 = x0^d0*x1^d1*... * dx0^e0*dx1^e1*... */ +/* rtab : array of length (e0+1)*(e1+1)*... */ -void weyl_mulmm(vl,m0,m1,n,pr) -VL vl; -MP m0,m1; -int n; -DP *pr; +void weyl_mulmm(VL vl,MP m0,MP m1,int n,struct cdl *rtab,int rtablen) { - MP m,mr,mr0; - DP r,t,t1; - P c,c0,c1,cc; - DL d,d0,d1; - int i,j,a,b,k,l,n2,s,min; - Q *tab; + P c,c0,c1; + DL d,d0,d1,dt; + int i,j,a,b,k,l,n2,s,min,curlen; + struct cdl *p; + static Q *ctab; + static struct cdl *tab; + static int tablen; + static struct cdl *tmptab; + static int tmptablen; - if ( !m0 || !m1 ) - *pr = 0; - else { - c0 = C(m0); c1 = C(m1); - mulp(vl,c0,c1,&c); - d0 = m0->dl; d1 = m1->dl; - n2 = n>>1; - for ( i = 0, r = (DP)ONE; i < n2; i++ ) { - a = d0->d[i]; b = d1->d[n2+i]; - k = d0->d[n2+i]; l = d1->d[i]; - /* compute xi^a*(Di^k*xi^l)*Di^b */ - min = MIN(k,l); - tab = (Q *)ALLOCA((min+1)*sizeof(Q)); - mkwc(k,l,tab); - for ( mr0 = 0, s = 0, j = 0; j <= min; j++ ) { - NEXTMP(mr0,mr); + + if ( !m0 || !m1 ) { + rtab[0].c = 0; + rtab[0].d = 0; + return; + } + c0 = C(m0); c1 = C(m1); + mulp(vl,c0,c1,&c); + d0 = m0->dl; d1 = m1->dl; + n2 = n>>1; + curlen = 1; + NEWDL(d,n); + if ( n & 1 ) + /* offset of h-degree */ + d->td = d->d[n-1] = d0->d[n-1]+d1->d[n-1]; + else + d->td = 0; + rtab[0].c = c; + rtab[0].d = d; + + if ( rtablen > tmptablen ) { + if ( tmptab ) GC_free(tmptab); + tmptab = (struct cdl *)MALLOC(rtablen*sizeof(struct cdl)); + tmptablen = rtablen; + } + for ( i = 0; i < n2; i++ ) { + a = d0->d[i]; b = d1->d[n2+i]; + k = d0->d[n2+i]; l = d1->d[i]; + + /* degree of xi^a*(Di^k*xi^l)*Di^b */ + a += l; + b += k; + s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i); + + if ( !k || !l ) { + for ( j = 0, p = rtab; j < curlen; j++, p++ ) { + if ( p->c ) { + dt = p->d; + dt->d[i] = a; + dt->d[n2+i] = b; + dt->td += s; + } + } + curlen *= k+1; + continue; + } + if ( k+1 > tablen ) { + if ( tab ) GC_free(tab); + if ( ctab ) GC_free(ctab); + tablen = k+1; + tab = (struct cdl *)MALLOC(tablen*sizeof(struct cdl)); + ctab = (Q *)MALLOC(tablen*sizeof(Q)); + } + /* compute xi^a*(Di^k*xi^l)*Di^b */ + min = MIN(k,l); + mkwc(k,l,ctab); + bzero(tab,(k+1)*sizeof(struct cdl)); + if ( n & 1 ) + for ( j = 0; j <= min; j++ ) { NEWDL(d,n); - d->d[i] = l-j+a; d->d[n2+i] = k-j+b; - d->td = d->d[i]+d->d[n2+i]; /* XXX */ - s = MAX(s,d->td); /* XXX */ - mr->c = (P)tab[j]; - mr->dl = d; + d->d[i] = a-j; d->d[n2+i] = b-j; + d->td = s; + d->d[n-1] = s-(MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i)); + tab[j].d = d; + tab[j].c = (P)ctab[j]; } - if ( mr0 ) - NEXT(mr) = 0; - MKDP(n,mr0,t); - if ( t ) - t->sugar = s; - comm_muld(vl,r,t,&t1); r = t1; + else + for ( j = 0; j <= min; j++ ) { + NEWDL(d,n); + d->d[i] = a-j; d->d[n2+i] = b-j; + d->td = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); /* XXX */ + tab[j].d = d; + tab[j].c = (P)ctab[j]; + } + bzero(ctab,(min+1)*sizeof(Q)); + comm_muld_tab(vl,n,rtab,curlen,tab,k+1,tmptab); + curlen *= k+1; + bcopy(tmptab,rtab,curlen*sizeof(struct cdl)); + } +} + +/* direct product of two cdl tables + rt[] = [ + t[0]*t1[0],...,t[n-1]*t1[0], + t[0]*t1[1],...,t[n-1]*t1[1], + ... + t[0]*t1[n1-1],...,t[n-1]*t1[n1-1] + ] +*/ + +void comm_muld_tab(VL vl,int nv,struct cdl *t,int n,struct cdl *t1,int n1,struct cdl *rt) +{ + int i,j; + struct cdl *p; + P c; + DL d; + + bzero(rt,n*n1*sizeof(struct cdl)); + for ( j = 0, p = rt; j < n1; j++ ) { + c = t1[j].c; + d = t1[j].d; + if ( !c ) + break; + for ( i = 0; i < n; i++, p++ ) { + if ( t[i].c ) { + mulp(vl,t[i].c,c,&p->c); + adddl(nv,t[i].d,d,&p->d); + } } - muldc(vl,r,c,pr); } } -void muldc(vl,p,c,pr) -VL vl; -DP p; -P c; -DP *pr; +void muldc(VL vl,DP p,P c,DP *pr) { MP m,mr,mr0; @@ -527,14 +1021,39 @@ DP *pr; } } -void divsdc(vl,p,c,pr) -VL vl; -DP p; -P c; -DP *pr; +void muldc_trunc(VL vl,DP p,P c,DL dl,DP *pr) { MP m,mr,mr0; + DL mdl; + int i,n; + if ( !p || !c ) { + *pr = 0; return; + } + n = NV(p); + for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) { + mdl = m->dl; + for ( i = 0; i < n; i++ ) + if ( mdl->d[i] < dl->d[i] ) + break; + if ( i < n ) + break; + NEXTMP(mr0,mr); + if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) ) + mulq((Q)C(m),(Q)c,(Q *)&C(mr)); + else + mulp(vl,C(m),c,&C(mr)); + mr->dl = m->dl; + } + NEXT(mr) = 0; MKDP(NV(p),mr0,*pr); + if ( *pr ) + (*pr)->sugar = p->sugar; +} + +void divsdc(VL vl,DP p,P c,DP *pr) +{ + MP m,mr,mr0; + if ( !c ) error("disvsdc : division by 0"); else if ( !p ) @@ -549,10 +1068,7 @@ DP *pr; } } -void adddl(n,d1,d2,dr) -int n; -DL d1,d2; -DL *dr; +void adddl(int n,DL d1,DL d2,DL *dr) { DL dt; int i; @@ -569,10 +1085,19 @@ DL *dr; } } -int compd(vl,p1,p2) -VL vl; -DP p1,p2; +/* d1 += d2 */ + +void adddl_destructive(int n,DL d1,DL d2) { + int i; + + d1->td += d2->td; + for ( i = 0; i < n; i++ ) + d1->d[i] += d2->d[i]; +} + +int compd(VL vl,DP p1,DP p2) +{ int n,t; MP m1,m2; @@ -595,9 +1120,7 @@ DP p1,p2; } } -int cmpdl_lex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_lex(int n,DL d1,DL d2) { int i; @@ -605,9 +1128,7 @@ DL d1,d2; return i == n ? 0 : (d1->d[i] > d2->d[i] ? 1 : -1); } -int cmpdl_revlex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_revlex(int n,DL d1,DL d2) { int i; @@ -615,9 +1136,7 @@ DL d1,d2; return i < 0 ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1); } -int cmpdl_gradlex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_gradlex(int n,DL d1,DL d2) { if ( d1->td > d2->td ) return 1; @@ -627,21 +1146,83 @@ DL d1,d2; return cmpdl_lex(n,d1,d2); } -int cmpdl_revgradlex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_revgradlex(int n,DL d1,DL d2) { + register int i,c; + register int *p1,*p2; + if ( d1->td > d2->td ) return 1; else if ( d1->td < d2->td ) return -1; - else - return cmpdl_revlex(n,d1,d2); + else { + i = n-1; + p1 = d1->d+n-1; + p2 = d2->d+n-1; + while ( i >= 7 ) { + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + i -= 8; + } + switch ( i ) { + case 6: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 5: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 4: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 3: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 2: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 1: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + case 0: + c = (*p1--) - (*p2--); if ( c ) goto LAST; + return 0; + default: + return 0; + } +LAST: + if ( c > 0 ) return -1; + else return 1; + } } -int cmpdl_blex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_blex(int n,DL d1,DL d2) { int c; @@ -653,9 +1234,7 @@ DL d1,d2; } } -int cmpdl_bgradlex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_bgradlex(int n,DL d1,DL d2) { int e1,e2,c; @@ -673,9 +1252,7 @@ DL d1,d2; } } -int cmpdl_brevgradlex(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_brevgradlex(int n,DL d1,DL d2) { int e1,e2,c; @@ -693,9 +1270,7 @@ DL d1,d2; } } -int cmpdl_brevrev(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_brevrev(int n,DL d1,DL d2) { int e1,e2,f1,f2,c,i; @@ -722,9 +1297,7 @@ DL d1,d2; } } -int cmpdl_bgradrev(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_bgradrev(int n,DL d1,DL d2) { int e1,e2,f1,f2,c,i; @@ -751,9 +1324,7 @@ DL d1,d2; } } -int cmpdl_blexrev(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_blexrev(int n,DL d1,DL d2) { int e1,e2,f1,f2,c,i; @@ -774,9 +1345,7 @@ DL d1,d2; } } -int cmpdl_elim(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_elim(int n,DL d1,DL d2) { int e1,e2,i; @@ -791,24 +1360,136 @@ DL d1,d2; return cmpdl_revgradlex(n,d1,d2); } -int cmpdl_order_pair(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_weyl_elim(int n,DL d1,DL d2) { + int e1,e2,i; + + for ( i = 1, e1 = 0, e2 = 0; i <= dp_nelim; i++ ) { + e1 += d1->d[n-i]; e2 += d2->d[n-i]; + } + if ( e1 > e2 ) + return 1; + else if ( e1 < e2 ) + return -1; + else if ( d1->td > d2->td ) + return 1; + else if ( d1->td < d2->td ) + return -1; + else return -cmpdl_revlex(n,d1,d2); +} + +/* + a special ordering + 1. total order + 2. (-w,w) for the first 2*m variables + 3. DRL for the first 2*m variables +*/ + +extern int *current_weyl_weight_vector; + +int cmpdl_homo_ww_drl(int n,DL d1,DL d2) +{ + int e1,e2,m,i; + int *p1,*p2; + + if ( d1->td > d2->td ) + return 1; + else if ( d1->td < d2->td ) + return -1; + + m = n>>1; + for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) { + e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]); + e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]); + } + if ( e1 > e2 ) + return 1; + else if ( e1 < e2 ) + return -1; + + e1 = d1->td - d1->d[n-1]; + e2 = d2->td - d2->d[n-1]; + if ( e1 > e2 ) + return 1; + else if ( e1 < e2 ) + return -1; + + for ( i= n - 1, p1 = d1->d+n-1, p2 = d2->d+n-1; + i >= 0 && *p1 == *p2; i--, p1--, p2-- ); + return i < 0 ? 0 : (*p1 < *p2 ? 1 : -1); +} + +int cmpdl_drl_zigzag(int n,DL d1,DL d2) +{ + int i,t,m; + int *p1,*p2; + + if ( d1->td > d2->td ) + return 1; + else if ( d1->td < d2->td ) + return -1; + else { + m = n>>1; + for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) { + if ( t = p1[m+i] - p2[m+i] ) return t > 0 ? -1 : 1; + if ( t = p1[i] - p2[i] ) return t > 0 ? -1 : 1; + } + return 0; + } +} + +int cmpdl_homo_ww_drl_zigzag(int n,DL d1,DL d2) +{ + int e1,e2,m,i,t; + int *p1,*p2; + + if ( d1->td > d2->td ) + return 1; + else if ( d1->td < d2->td ) + return -1; + + m = n>>1; + for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) { + e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]); + e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]); + } + if ( e1 > e2 ) + return 1; + else if ( e1 < e2 ) + return -1; + + e1 = d1->td - d1->d[n-1]; + e2 = d2->td - d2->d[n-1]; + if ( e1 > e2 ) + return 1; + else if ( e1 < e2 ) + return -1; + + for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) { + if ( t = p1[m+i] - p2[m+i] ) return t > 0 ? -1 : 1; + if ( t = p1[i] - p2[i] ) return t > 0 ? -1 : 1; + } + return 0; +} + +int cmpdl_order_pair(int n,DL d1,DL d2) +{ int e1,e2,i,j,l; int *t1,*t2; - int len; + int len,head; struct order_pair *pair; - len = dp_current_spec.ord.block.length; - pair = dp_current_spec.ord.block.order_pair; + len = dp_current_spec->ord.block.length; + pair = dp_current_spec->ord.block.order_pair; + head = 0; for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) { l = pair[i].length; switch ( pair[i].order ) { case 0: for ( j = 0, e1 = e2 = 0; j < l; j++ ) { - e1 += t1[j]; e2 += t2[j]; + e1 += MUL_WEIGHT(t1[j],head+j); + e2 += MUL_WEIGHT(t2[j],head+j); } if ( e1 > e2 ) return 1; @@ -822,7 +1503,8 @@ DL d1,d2; break; case 1: for ( j = 0, e1 = e2 = 0; j < l; j++ ) { - e1 += t1[j]; e2 += t2[j]; + e1 += MUL_WEIGHT(t1[j],head+j); + e2 += MUL_WEIGHT(t2[j],head+j); } if ( e1 > e2 ) return 1; @@ -842,23 +1524,90 @@ DL d1,d2; default: error("cmpdl_order_pair : invalid order"); break; } - t1 += l; t2 += l; + t1 += l; t2 += l; head += l; } return 0; } -int cmpdl_matrix(n,d1,d2) -int n; -DL d1,d2; +int cmpdl_composite(int nv,DL d1,DL d2) { + int n,i,j,k,start,s,len; + int *dw; + struct sparse_weight *sw; + struct weight_or_block *worb; + int *w,*t1,*t2; + + n = dp_current_spec->ord.composite.length; + worb = dp_current_spec->ord.composite.w_or_b; + w = dp_dl_work; + for ( i = 0, t1 = d1->d, t2 = d2->d; i < nv; i++ ) + w[i] = t1[i]-t2[i]; + for ( i = 0; i < n; i++, worb++ ) { + len = worb->length; + switch ( worb->type ) { + case IS_DENSE_WEIGHT: + dw = worb->body.dense_weight; + for ( j = 0, s = 0; j < len; j++ ) + s += dw[j]*w[j]; + if ( s > 0 ) return 1; + else if ( s < 0 ) return -1; + break; + case IS_SPARSE_WEIGHT: + sw = worb->body.sparse_weight; + for ( j = 0, s = 0; j < len; j++ ) + s += sw[j].value*w[sw[j].pos]; + if ( s > 0 ) return 1; + else if ( s < 0 ) return -1; + break; + case IS_BLOCK: + start = worb->body.block.start; + switch ( worb->body.block.order ) { + case 0: + for ( j = 0, k = start, s = 0; j < len; j++, k++ ) { + s += MUL_WEIGHT(w[k],k); + } + if ( s > 0 ) return 1; + else if ( s < 0 ) return -1; + else { + for ( j = k-1; j >= start && w[j] == 0; j-- ); + if ( j >= start ) + return w[j] < 0 ? 1 : -1; + } + break; + case 1: + for ( j = 0, k = start, s = 0; j < len; j++, k++ ) { + s += MUL_WEIGHT(w[k],k); + } + if ( s > 0 ) return 1; + else if ( s < 0 ) return -1; + else { + for ( j = 0, k = start; j < len && w[j] == 0; j++, k++ ); + if ( j < len ) + return w[j] > 0 ? 1 : -1; + } + break; + case 2: + for ( j = 0, k = start; j < len && w[j] == 0; j++, k++ ); + if ( j < len ) + return w[j] > 0 ? 1 : -1; + break; + } + break; + } + } + return 0; +} + +int cmpdl_matrix(int n,DL d1,DL d2) +{ int *v,*w,*t1,*t2; int s,i,j,len; int **matrix; for ( i = 0, t1 = d1->d, t2 = d2->d, w = dp_dl_work; i < n; i++ ) w[i] = t1[i]-t2[i]; - len = dp_current_spec.ord.matrix.row; - matrix = dp_current_spec.ord.matrix.matrix; + len = dp_current_spec->ord.matrix.row; + matrix = dp_current_spec->ord.matrix.matrix; for ( j = 0; j < len; j++ ) { v = matrix[j]; for ( i = 0, s = 0; i < n; i++ ) @@ -869,4 +1618,57 @@ DL d1,d2; return -1; } return 0; +} + +GeoBucket create_bucket() +{ + GeoBucket g; + + g = CALLOC(1,sizeof(struct oGeoBucket)); + g->m = 32; + return g; +} + +void add_bucket(GeoBucket g,NODE d,int nv) +{ + int l,k,m; + + l = length(d); + for ( k = 0, m = 1; l > m; k++, m <<= 1 ); + /* 2^(k-1) < l <= 2^k */ + d = symb_merge(g->body[k],d,nv); + for ( ; length(d) > (1<<(k)); k++ ) { + g->body[k] = 0; + d = symb_merge(g->body[k+1],d,nv); + } + g->body[k] = d; + g->m = MAX(g->m,k); +} + +DL remove_head_bucket(GeoBucket g,int nv) +{ + int j,i,c,m; + DL d; + + j = -1; + m = g->m; + for ( i = 0; i <= m; i++ ) { + if ( !g->body[i] ) + continue; + if ( j < 0 ) j = i; + else { + c = (*cmpdl)(nv,g->body[i]->body,g->body[j]->body); + if ( c > 0 ) + j = i; + else if ( c == 0 ) + g->body[i] = NEXT(g->body[i]); + } + } + if ( j < 0 ) + return 0; + else { + d = g->body[j]->body; + g->body[j] = NEXT(g->body[j]); + return d; + } }