=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/nd.c,v retrieving revision 1.112 retrieving revision 1.113 diff -u -p -r1.112 -r1.113 --- OpenXM_contrib2/asir2000/engine/nd.c 2004/10/06 11:58:52 1.112 +++ OpenXM_contrib2/asir2000/engine/nd.c 2004/10/06 12:09:19 1.113 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/nd.c,v 1.111 2004/09/21 07:19:01 noro Exp $ */ +/* $OpenXM$ */ #include "nd.h" @@ -916,7 +916,7 @@ ND nd_add(int mod,ND p1,ND p2) if ( !p1 ) return p2; else if ( !p2 ) return p1; else if ( mod == -1 ) return nd_add_sf(p1,p2); - else if ( !mod ) return nd_add_z(p1,p2); + else if ( !mod ) return nd_add_q(p1,p2); else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { @@ -961,16 +961,16 @@ ND nd_add(int mod,ND p1,ND p2) * done in a function. */ -int nm_destructive_add_z(NM *m1,NM *m2,NM *mr0,NM *mr) +int nm_destructive_add_q(NM *m1,NM *m2,NM *mr0,NM *mr) { NM s; - Z t; + Q t; int can; - t = addz(CZ(*m1),CZ(*m2)); + addq(CQ(*m1),CQ(*m2),&t); s = *m1; *m1 = NEXT(*m1); if ( t ) { - can = 1; NEXTNM2(*mr0,*mr,s); CZ(*mr) = (t); + can = 1; NEXTNM2(*mr0,*mr,s); CQ(*mr) = (t); } else { can = 2; FREENM(s); } @@ -978,12 +978,12 @@ int nm_destructive_add_z(NM *m1,NM *m2,NM *mr0,NM *mr) return can; } -ND nd_add_z(ND p1,ND p2) +ND nd_add_q(ND p1,ND p2) { int n,c,can; ND r; NM m1,m2,mr0,mr,s; - Z t; + Q t; if ( !p1 ) return p2; else if ( !p2 ) return p1; @@ -994,12 +994,12 @@ ND nd_add_z(ND p1,ND p2) switch ( c ) { case 0: #if defined(__x86_64__) - can += nm_destructive_add_z(&m1,&m2,&mr0,&mr); + can += nm_destructive_add_q(&m1,&m2,&mr0,&mr); #else - t = addz(CZ(m1),CZ(m2)); + addq(CQ(m1),CQ(m2),&t); s = m1; m1 = NEXT(m1); if ( t ) { - can++; NEXTNM2(mr0,mr,s); CZ(mr) = (t); + can++; NEXTNM2(mr0,mr,s); CQ(mr) = (t); } else { can += 2; FREENM(s); } @@ -1077,7 +1077,7 @@ ND nd_add_sf(ND p1,ND p2) } /* ret=1 : success, ret=0 : overflow */ -int nd_nf(int mod,ND g,NDV *ps,int full,Q *dn,ND *rp) +int nd_nf(int mod,ND g,NDV *ps,int full,NDC dn,ND *rp) { ND d; NM m,mrd,tail; @@ -1086,17 +1086,20 @@ int nd_nf(int mod,ND g,NDV *ps,int full,Q *dn,ND *rp) int c,c1,c2,dummy; RHist h; NDV p,red; - Z cg,cred,gcd; - Q tq,qq; + Q cg,cred,gcd,tq,qq; double hmag; - if ( dn && !mod ) - *dn = ONE; + if ( dn ) { + if ( mod ) + dn->m = 1; + else + dn->z = ONE; + } if ( !g ) { *rp = 0; return 1; } - if ( !mod ) hmag = ((double)z_mag(HCZ(g)))*nd_scale; + if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; sugar0 = sugar = SG(g); n = NV(g); @@ -1120,24 +1123,22 @@ int nd_nf(int mod,ND g,NDV *ps,int full,Q *dn,ND *rp) c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { - gcd = gcdz_cofactor(HCZ(g),HCZ(p),&cg,&cred); - CZ(mul) = chsgnz(cg); - nd_mul_c_z(d,cred); - nd_mul_c_z(g,cred); + igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred); + chsgnq(cg,&CQ(mul)); + nd_mul_c_q(d,cred); nd_mul_c_q(g,cred); if ( dn ) { - mulq(*dn,ztoq(cred),&tq); *dn = tq; + mulq(dn->z,cred,&tq); dn->z = tq; } } g = nd_add(mod,g,ndv_mul_nm(mod,mul,p)); - sugar = MAX(sugar,SG(p)+TD(DL(mul))); - if ( !mod && hmag && g && ((double)(z_mag(HCZ(g))) > hmag) ) { - tq = ztoq(HCZ(g)); + if ( !mod && hmag && g && ((double)(p_mag((P)HCQ(g))) > hmag) ) { + tq = HCQ(g); nd_removecont2(d,g); if ( dn ) { - divq(tq,ztoq(HCZ(g)),&qq); divq(*dn,qq,&tq); *dn = tq; + divq(tq,HCQ(g),&qq); divq(dn->z,qq,&tq); dn->z = tq; } - hmag = ((double)z_mag((P)HCZ(g)))*nd_scale; + hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; } } else if ( !full ) { *rp = g; @@ -1171,7 +1172,7 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp int sugar,psugar,n,h_reducible; PGeoBucket bucket; int c,c1,c2; - Z cg,cred,gcd,zzz; + Q cg,cred,gcd,zzz; RHist h; double hmag,gmag; int count = 0; @@ -1183,13 +1184,13 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp } sugar = SG(g); n = NV(g); - if ( !mod ) hmag = ((double)z_mag(HCZ(g)))*nd_scale; + if ( !mod ) hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; bucket = create_pbucket(); add_pbucket(mod,bucket,g); d = 0; mul = (NM)ALLOCA(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); while ( 1 ) { - hindex = mod?head_pbucket(mod,bucket):head_pbucket_z(bucket); + hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket); if ( hindex < 0 ) { if ( DP_Print > 3 ) printf("(%d %d)",count,hcount); if ( d ) SG(d) = sugar; @@ -1216,12 +1217,12 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { - gcd = gcdz_cofactor(HCZ(g),HCZ(p),&cg,&cred); - CZ(mul) = chsgnz(cg); - nd_mul_c_z(d,cred); - mulz_pbucket(bucket,cred); + igcd_cofactor(HCQ(g),HCQ(p),&gcd,&cg,&cred); + chsgnq(cg,&CQ(mul)); + nd_mul_c_q(d,cred); + mulq_pbucket(bucket,cred); g = bucket->body[hindex]; - gmag = (double)z_mag(HCZ(g)); + gmag = (double)p_mag((P)HCQ(g)); } red = ndv_mul_nm(mod,mul,p); bucket->body[hindex] = nd_remove_head(g); @@ -1237,7 +1238,7 @@ int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp return 1; } nd_removecont2(d,g); - hmag = ((double)z_mag(HCZ(g)))*nd_scale; + hmag = ((double)p_mag((P)HCQ(g)))*nd_scale; add_pbucket(mod,bucket,g); } } else if ( !full ) { @@ -1271,6 +1272,7 @@ int ndv_check_candidate(NODE input,int obpe,int oadv,E ND nf,d; NDV r; NODE t,s; + union oNDC dn; ndv_setup(0,0,cand); n = length(cand); @@ -1385,12 +1387,12 @@ void add_pbucket(int mod,PGeoBucket g,ND d) g->m = MAX(g->m,k); } -void mulz_pbucket(PGeoBucket g,Z c) +void mulq_pbucket(PGeoBucket g,Q c) { int k; for ( k = 0; k <= g->m; k++ ) - nd_mul_c_z(g->body[k],c); + nd_mul_c_q(g->body[k],c); } NM remove_head_pbucket_symbolic(PGeoBucket g) @@ -1471,10 +1473,10 @@ int head_pbucket(int mod,PGeoBucket g) } } -int head_pbucket_z(PGeoBucket g) +int head_pbucket_q(PGeoBucket g) { int j,i,c,k,nv; - Z sum,t; + Q sum,t; ND gi,gj; k = g->m; @@ -1485,25 +1487,26 @@ int head_pbucket_z(PGeoBucket g) if ( j < 0 ) { j = i; gj = g->body[j]; - sum = HCZ(gj); + sum = HCQ(gj); } else { nv = NV(gi); c = DL_COMPARE(HDL(gi),HDL(gj)); if ( c > 0 ) { - if ( sum ) HCZ(gj) = sum; + if ( sum ) HCQ(gj) = sum; else g->body[j] = nd_remove_head(gj); j = i; gj = g->body[j]; - sum = HCZ(gj); + sum = HCQ(gj); } else if ( c == 0 ) { - sum = addz(sum,HCZ(gi)); + addq(sum,HCQ(gi),&t); + sum = t; g->body[i] = nd_remove_head(gi); } } } if ( j < 0 ) return -1; else if ( sum ) { - HCZ(gj) = sum; + HCQ(gj) = sum; return j; } else g->body[j] = nd_remove_head(gj); @@ -1530,8 +1533,8 @@ void do_diagonalize(int sugar,int m) NODE r,g,t; ND h,nf,s,head; NDV nfv; - Z q,num,den; - Q dn; + Q q,num,den; + union oNDC dn; for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) { if ( nd_demand ) @@ -1542,10 +1545,12 @@ void do_diagonalize(int sugar,int m) s = nd_separate_head(s,&head); nd_nf(m,s,nd_ps,1,&dn,&nf); if ( !m ) { - HCZ(head) = mulz(HCZ(head),simpz((Z)NM(dn))); - if ( SGN(dn) < 0 ) HCZ(head) = chsgnz(HCZ(head)); - if ( DN(dn) ) - nd_mul_c_z(nf,simpz((Z)DN(dn))); + NTOQ(NM(dn.z),SGN(dn.z),num); + mulq(HCQ(head),num,&q); HCQ(head) = q; + if ( DN(dn.z) ) { + NTOQ(DN(dn.z),1,den); + nd_mul_c_q(nf,den); + } } nf = nd_add(m,head,nf); ndv_free(nfv); @@ -1571,6 +1576,8 @@ NODE nd_gb(int m,int ishomo,int checkonly) ND_pairs l; ND h,nf,s,head; NDV nfv; + Q q,num,den; + union oNDC dn; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { @@ -1631,7 +1638,8 @@ void do_diagonalize_trace(int sugar,int m) NODE r,g,t; ND h,nf,nfq,s,head; NDV nfv,nfqv; - Q dn; + Q q,den,num; + union oNDC dn; for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) { /* for nd_ps */ @@ -1651,10 +1659,12 @@ void do_diagonalize_trace(int sugar,int m) s = ndvtond(0,nfv); s = nd_separate_head(s,&head); nd_nf(0,s,nd_ps_trace,1,&dn,&nf); - HCZ(head) = mulz(HCZ(head),(Z)NM(dn)); - if ( SGN(dn) < 0 ) HCZ(head) = chsgnz(HCZ(head)); - if ( DN(dn) ) - nd_mul_c_z(nf,(Z)DN(dn)); + NTOQ(NM(dn.z),SGN(dn.z),num); + mulq(HCQ(head),num,&q); HCQ(head) = q; + if ( DN(dn.z) ) { + NTOQ(DN(dn.z),1,den); + nd_mul_c_q(nf,den); + } nf = nd_add(0,head,nf); ndv_free(nfv); nd_removecont(0,nf); @@ -1677,6 +1687,8 @@ NODE nd_gb_trace(int m,int ishomo) ND_pairs l; ND h,nf,nfq,s,head; NDV nfv,nfqv; + Q q,den,num; + union oNDC dn; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { @@ -1722,7 +1734,7 @@ again: } if ( nfq ) { /* m|HC(nfq) => failure */ - if ( !remzi(HCZ(nfq),m) ) return 0; + if ( !rem(NM(HCQ(nfq)),m) ) return 0; if ( DP_Print ) { printf("+"); fflush(stdout); } nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf); @@ -1762,8 +1774,9 @@ NODE ndv_reduceall(int m,NODE f) int i,n,stat; ND nf,g,head; NODE t,a0,a; - Q dn; + union oNDC dn; NDV *w; + Q q,num,den; n = length(f); #if 0 @@ -1783,10 +1796,12 @@ NODE ndv_reduceall(int m,NODE f) else { if ( DP_Print ) { printf("."); fflush(stdout); } if ( !m ) { - HCZ(head) = mulz(HCZ(head),simpz((Z)NM(dn))); - if ( SGN(dn) < 0 ) HCZ(head) = chsgnz(HCZ(head)); - if ( DN(dn) ) - nd_mul_c_z(nf,simpz((Z)DN(dn))); + NTOQ(NM(dn.z),SGN(dn.z),num); + mulq(HCQ(head),num,&q); HCQ(head) = q; + if ( DN(dn.z) ) { + NTOQ(DN(dn.z),1,den); + nd_mul_c_q(nf,den); + } } nf = nd_add(m,head,nf); ndv_free(nd_ps[i]); @@ -2417,7 +2432,7 @@ void nd_print(ND p) } } -void nd_print_z(ND p) +void nd_print_q(ND p) { NM m; @@ -2426,7 +2441,7 @@ void nd_print_z(ND p) else { for ( m = BDY(p); m; m = NEXT(m) ) { printf("+"); - printz(CZ(m)); + printexpr(CO,(Obj)CQ(m)); printf("*"); ndl_print(DL(m)); } @@ -2445,30 +2460,33 @@ void ndp_print(ND_pairs d) void nd_removecont(int mod,ND p) { int i,n; - Z *w; - Z dvr,t; + Q *w; + Q dvr,t; NM m; struct oVECT v; + N q,r; if ( mod == -1 ) nd_mul_c(mod,p,_invsf(HCM(p))); else if ( mod ) nd_mul_c(mod,p,invm(HCM(p),mod)); else { for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ ); - w = (Z *)ALLOCA(n*sizeof(Z)); + w = (Q *)ALLOCA(n*sizeof(Q)); v.len = n; v.body = (pointer *)w; - for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CZ(m); + for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CQ(m); removecont_array(w,n); - for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CZ(m) = w[i]; + for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CQ(m) = w[i]; } } void nd_removecont2(ND p1,ND p2) { int i,n1,n2,n; - Z *w; + Q *w; + Q dvr,t; NM m; struct oVECT v; + N q,r; if ( !p1 ) { nd_removecont(0,p2); return; @@ -2478,21 +2496,21 @@ void nd_removecont2(ND p1,ND p2) n1 = nd_length(p1); n2 = nd_length(p2); n = n1+n2; - w = (Z *)ALLOCA(n*sizeof(Z)); + w = (Q *)ALLOCA(n*sizeof(Q)); v.len = n; v.body = (pointer *)w; - for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) w[i] = CZ(m); - for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CZ(m); + for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) w[i] = CQ(m); + for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CQ(m); removecont_array(w,n); - for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) CZ(m) = w[i]; - for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CZ(m) = w[i]; + for ( m = BDY(p1), i = 0; i < n1; m = NEXT(m), i++ ) CQ(m) = w[i]; + for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CQ(m) = w[i]; } void ndv_removecont(int mod,NDV p) { int i,len; - Z *w; - Z dvr,t; + Q *w; + Q dvr,t; NMV m; if ( mod == -1 ) @@ -2501,10 +2519,13 @@ void ndv_removecont(int mod,NDV p) ndv_mul_c(mod,p,invm(HCM(p),mod)); else { len = p->len; - w = (Z *)ALLOCA(len*sizeof(Z)); - for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) w[i] = CZ(m); - removecont_array(w,len); - for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) CZ(m) = w[i]; + w = (Q *)ALLOCA(len*sizeof(Q)); + for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) w[i] = CQ(m); + sortbynm(w,len); + qltozl(w,len,&dvr); + for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) { + divq(CQ(m),dvr,&t); CQ(m) = t; + } } } @@ -2522,7 +2543,7 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos t = (NMV)ALLOCA(nmv_adv); for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) { ndl_homogenize(DL(m),DL(t),obpe,oepos,max); - CZ(mr) = CZ(m); + CQ(mr) = CQ(m); ndl_copy(DL(t),DL(mr)); } NV(p)++; @@ -2532,8 +2553,8 @@ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos void ndv_dehomogenize(NDV p,struct order_spec *ord) { int i,j,adj,len,newnvar,newwpd,newadv,newexporigin; - Z *w; - Z dvr,t; + Q *w; + Q dvr,t; NMV m,r; len = p->len; @@ -2545,7 +2566,7 @@ void ndv_dehomogenize(NDV p,struct order_spec *ord) if ( newwpd != nd_wpd ) { newadv = ROUND_FOR_ALIGN(sizeof(struct oNMV)+(newwpd-1)*sizeof(UINT)); for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NDV_NADV(r), i++ ) { - CZ(r) = CZ(m); + CQ(r) = CQ(m); for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j]; adj = nd_exporigin-newexporigin; for ( ; j < newwpd; j++ ) DL(r)[j] = DL(m)[j+adj]; @@ -2554,87 +2575,36 @@ void ndv_dehomogenize(NDV p,struct order_spec *ord) NV(p)--; } -int comp_z(Z *a,Z *b) +void removecont_array(Q *c,int n) { - return cmpz(*a,*b); -} - -Z zgcdv(VECT a) -{ - int i,j,n,nz; - Z g,gt,q,r; - Z *c; - - n = a->len; - c = (Z *)ALLOCA(n*sizeof(Z)); - for ( i = 0; i < n; i++ ) - c[i] = (Z)a->body[i]; - qsort(c,n,sizeof(Z),(int (*) (const void *,const void *))comp_z); - for ( ; n && ! *c; n--, c++ ); - - if ( !n ) - return 0; - else if ( n == 1 ) - return absz(c[0]); - - g = gcdz(c[0],c[1]); - for ( i = 2; i < n; i++ ) { - q = divz(c[i],g,&r); - gt = gcdz(g,r); - if ( !cmpz(g,gt) ) { - for ( j = i+1; j < n; j++ ) { - q = divz(c[j],g,&r); c[j] = r; - } - } else - g = gt; - } - return absz(g); -} - -Z zgcdv_estimate(VECT a) -{ - int n,i,m; - Z s,t,u,g; - Z *q; - - n = a->len; q = (Z *)a->body; - if ( n == 1 ) - return absz(q[0]); - - m = n/2; - for ( i = 0 , s = 0; i < m; i++ ) - s = sgnz(q[i])>=0 ? addz(s,q[i]) : subz(s,q[i]); - for ( t = 0; i < n; i++ ) - t = sgnz(q[i])>=0 ? addz(t,q[i]) : subz(t,q[i]); - g = gcdz(s,t); - return absz(g); -} - -void removecont_array(Z *c,int n) -{ struct oVECT v; - Z d0,d1,a,u,u1,gcd; + Q d0,d1,a,u,u1,gcd; int i,j; - Z q0,q1; - Z *q,*r; + N qn,rn,gn; + Q *q,*r; - q = (Z *)ALLOCA(n*sizeof(Z)); - r = (Z *)ALLOCA(n*sizeof(Z)); + q = (Q *)ALLOCA(n*sizeof(Q)); + r = (Q *)ALLOCA(n*sizeof(Q)); v.id = O_VECT; v.len = n; v.body = (pointer *)c; - d0 = zgcdv_estimate(&v); - /* c[i] = d0*q[i]+r[i] */ - for ( i = 0; i < n; i++ ) - q[i] = divz(c[i],d0,&r[i]); + igcdv_estimate(&v,&d0); + for ( i = 0; i < n; i++ ) { + divn(NM(c[i]),NM(d0),&qn,&rn); + NTOQ(qn,SGN(c[i])*SGN(d0),q[i]); + NTOQ(rn,SGN(c[i]),r[i]); + } for ( i = 0; i < n; i++ ) if ( r[i] ) break; if ( i < n ) { v.id = O_VECT; v.len = n; v.body = (pointer *)r; - /* d1 = GCD(r[0],...,r[n-1]) */ - d1 = zgcdv(&v); - /* q0 = d0/GCD(d0,d1) */ - gcd = gcdz_cofactor(d0,d1,&q0,&q1); + igcdv(&v,&d1); + gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd); + divsn(NM(d0),gn,&qn); NTOQ(qn,1,a); for ( i = 0; i < n; i++ ) { - /* q[i] = d0/gcd*q[i]+r[i]/gcd */ - q[i] = addz(mulz(q0,q[i]),divsz(r[i],gcd)); + mulq(a,q[i],&u); + if ( r[i] ) { + divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1); + addq(u,u1,&q[i]); + } else + q[i] = u; } } for ( i = 0; i < n; i++ ) c[i] = q[i]; @@ -2655,14 +2625,14 @@ void nd_mul_c(int mod,ND p,int mul) } } -void nd_mul_c_z(ND p,Z mul) +void nd_mul_c_q(ND p,Q mul) { NM m; - Z c; + Q c; - if ( !p || uniz(mul) ) return; + if ( !p ) return; for ( m = BDY(p); m; m = NEXT(m) ) { - CZ(m) = mulz(CZ(m),mul); + mulq(CQ(m),mul,&c); CQ(m) = c; } } @@ -2969,14 +2939,14 @@ int nd_sp(int mod,int trace,ND_pairs p,ND *rp) } lcm = LCM(p); NEWNM(m); - CZ(m) = HCZ(p2); + CQ(m) = HCQ(p2); ndl_sub(lcm,HDL(p1),DL(m)); if ( ndl_check_bound2(p->i1,DL(m)) ) return 0; t1 = ndv_mul_nm(mod,m,p1); if ( mod == -1 ) CM(m) = _chsgnsf(HCM(p1)); else if ( mod ) CM(m) = mod-HCM(p1); - else CZ(m) = chsgnz(HCZ(p1)); + else chsgnq(HCQ(p1),&CQ(m)); ndl_sub(lcm,HDL(p2),DL(m)); if ( ndl_check_bound2(p->i2,DL(m)) ) { nd_free(t1); @@ -3004,16 +2974,16 @@ void ndv_mul_c(int mod,NDV p,int mul) } } -void ndv_mul_c_z(NDV p,Z mul) +void ndv_mul_c_q(NDV p,Q mul) { NMV m; - Z c; + Q c; int len,i; if ( !p ) return; len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { - CZ(m) = mulz(CZ(m),mul); + mulq(CQ(m),mul,&c); CQ(m) = c; } } @@ -3060,8 +3030,8 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta { int i,n2,j,s,curlen,homo,h,a,b,k,l,u,min; UINT *d0,*d1,*d,*dt,*ctab; - Z *ctab_z; - Z q,q1; + Q *ctab_q; + Q q,q1; UINT c0,c1,c; NM *p; NM m,t; @@ -3073,7 +3043,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta if ( mod ) { c0 = CM(m0); c1 = CM(m1); DMAR(c0,c1,0,mod,c); CM(m) = c; } else - CZ(m) = mulz(CZ(m0),CZ(m1)); + mulq(CQ(m0),CQ(m1),&CQ(m)); for ( i = 0; i < nd_wpd; i++ ) d[i] = 0; homo = n&1 ? 1 : 0; if ( homo ) { @@ -3106,8 +3076,8 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta ctab = (UINT *)ALLOCA((min+1)*sizeof(UINT)); mkwcm(k,l,mod,ctab); } else { - ctab_z = (Z *)ALLOCA((min+1)*sizeof(Z)); - mkwcz(k,l,ctab_z); + ctab_q = (Q *)ALLOCA((min+1)*sizeof(Q)); + mkwc(k,l,ctab_q); } for ( j = min; j >= 0; j-- ) { for ( u = 0; u < nd_wpd; u++ ) d[u] = 0; @@ -3119,7 +3089,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta } else TD(d) = h; if ( nd_blockmask ) ndl_weight_mask(d); if ( mod ) c = ctab[j]; - else q = ctab_z[j]; + else q = ctab_q[j]; p = tab+curlen*j; if ( j == 0 ) { for ( u = 0; u < curlen; u++, p++ ) { @@ -3128,7 +3098,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta if ( mod ) { c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(tab[u]) = c1; } else { - CZ(tab[u]) = mulz(CZ(tab[u]),q); + mulq(CQ(tab[u]),q,&q1); CQ(tab[u]) = q1; } } } @@ -3140,7 +3110,7 @@ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *ta if ( mod ) { c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(t) = c1; } else - CZ(t) = mulz(CZ(tab[u]),q); + mulq(CQ(tab[u]),q,&CQ(t)); *p = t; } } @@ -3157,6 +3127,7 @@ ND ndv_mul_nm_symbolic(NM m0,NDV p) NMV m; UINT *d,*dt,*dm; int c,n,td,i,c1,c2,len; + Q q; ND r; if ( !p ) return 0; @@ -3185,7 +3156,7 @@ ND ndv_mul_nm(int mod,NM m0,NDV p) NMV m; UINT *d,*dt,*dm; int c,n,td,i,c1,c2,len; - Z q; + Q q; ND r; if ( !p ) return 0; @@ -3217,10 +3188,10 @@ ND ndv_mul_nm(int mod,NM m0,NDV p) ndl_add(DL(m),d,DL(mr)); } } else { - q = CZ(m0); + q = CQ(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); - CZ(mr) = mulz(CZ(m),q); + mulq(CQ(m),q,&CQ(mr)); ndl_add(DL(m),d,DL(mr)); } } @@ -3235,6 +3206,7 @@ ND nd_quo(int mod,PGeoBucket bucket,NDV d) { NM mq0,mq; NMV tm; + Q q; int i,nv,sg,c,c1,c2,hindex; ND p,t,r; N tnm; @@ -3245,7 +3217,7 @@ ND nd_quo(int mod,PGeoBucket bucket,NDV d) mq0 = 0; tm = (NMV)ALLOCA(nmv_adv); while ( 1 ) { - hindex = mod?head_pbucket(mod,bucket):head_pbucket_z(bucket); + hindex = mod?head_pbucket(mod,bucket):head_pbucket_q(bucket); if ( hindex < 0 ) break; p = bucket->body[hindex]; NEXTNM(mq0,mq); @@ -3256,8 +3228,9 @@ ND nd_quo(int mod,PGeoBucket bucket,NDV d) DMAR(c1,c2,0,mod,c); CM(mq) = c; CM(tm) = mod-c; } else { - CZ(mq) = divsz(HCZ(p),HCZ(d)); - CZ(tm) = chsgnz(CZ(mq)); + divsn(NM(HCQ(p)),NM(HCQ(d)),&tnm); + NTOQ(tnm,SGN(HCQ(p))*SGN(HCQ(d)),CQ(mq)); + chsgnq(CQ(mq),&CQ(tm)); } t = ndv_mul_nmv_trunc(mod,tm,d,HDL(d)); bucket->body[hindex] = nd_remove_head(p); @@ -3289,10 +3262,10 @@ void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos) mr = (NMV)((char *)mr0+(len-1)*nmv_adv); t = (NMV)ALLOCA(nmv_adv); for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) { - CZ(t) = CZ(m); + CQ(t) = CQ(m); for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0; ndl_reconstruct(DL(m),DL(t),obpe,oepos); - CZ(mr) = CZ(t); + CQ(mr) = CQ(t); ndl_copy(DL(t),DL(mr)); } BDY(p) = mr0; @@ -3310,7 +3283,7 @@ NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos for ( i = 0; i < len; i++, NMV_OADV(m), NMV_ADV(mr) ) { ndl_zero(DL(mr)); ndl_reconstruct(DL(m),DL(mr),obpe,oepos); - CZ(mr) = CZ(m); + CQ(mr) = CQ(m); } MKNDV(NV(p),mr0,len,r); SG(r) = SG(p); @@ -3330,7 +3303,7 @@ NDV ndv_dup(int mod,NDV p) m0 = m = (NMV)(mod?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv)); for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) { ndl_copy(DL(t),DL(m)); - CZ(m) = CZ(t); + CQ(m) = CQ(t); } MKNDV(NV(p),m0,len,d); SG(d) = SG(p); @@ -3346,7 +3319,7 @@ ND nd_dup(ND p) for ( m0 = 0, t = BDY(p); t; t = NEXT(t) ) { NEXTNM(m0,m); ndl_copy(DL(t),DL(m)); - CZ(m) = CZ(t); + CQ(m) = CQ(t); } if ( m0 ) NEXT(m) = 0; MKND(NV(p),m0,LEN(p),d); @@ -3377,8 +3350,10 @@ void ndv_mod(int mod,NDV p) } else for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { - r = remzi(CZ(t),mod); + r = rem(NM(CQ(t)),mod); if ( r ) { + if ( SGN(CQ(t)) < 0 ) + r = mod-r; CM(d) = r; ndl_copy(DL(t),DL(d)); NMV_ADV(d); @@ -3414,7 +3389,7 @@ ND ptond(VL vl,VL dvl,P p) else if ( NUM(p) ) { NEWNM(m); ndl_zero(DL(m)); - CZ(m) = qtoz((Q)p); + CQ(m) = (Q)p; NEXT(m) = 0; MKND(nd_nvar,m,1,r); SG(r) = 0; @@ -3472,7 +3447,7 @@ P ndvtop(int mod,VL vl,VL dvl,NDV p) } else if ( mod ) { STOQ(CM(m),q); c = (P)q; } else - c = (P)ztoq(CZ(m)); + c = CP(m); d = DL(m); for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) { MKV(tvl->v,r); e = GET_EXP(d,i); STOQ(e,q); @@ -3502,7 +3477,7 @@ NDV ndtondv(int mod,ND p) #endif for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) { ndl_copy(DL(t),DL(m)); - CZ(m) = CZ(t); + CQ(m) = CQ(t); } MKNDV(NV(p),m0,len,d); SG(d) = SG(p); @@ -3522,7 +3497,7 @@ ND ndvtond(int mod,NDV p) for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) { NEXTNM(m0,m); ndl_copy(DL(t),DL(m)); - CZ(m) = CZ(t); + CQ(m) = CQ(t); } NEXT(m) = 0; MKND(NV(p),m0,len,d); @@ -3547,7 +3522,7 @@ void ndv_print(NDV p) } } -void ndv_print_z(NDV p) +void ndv_print_q(NDV p) { NMV m; int i,len; @@ -3557,7 +3532,7 @@ void ndv_print_z(NDV p) len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { printf("+"); - printz(CZ(m)); + printexpr(CO,(Obj)CQ(m)); printf("*"); ndl_print(DL(m)); } @@ -3732,6 +3707,7 @@ void nd_nf_p(P f,LIST g,LIST v,int m,struct order_spec NDV ndv; VL vv,tv; int stat,nvar,max,e; + union oNDC dn; pltovl(v,&vv); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); @@ -3793,7 +3769,7 @@ int nd_to_vect(int mod,UINT *s0,int n,ND d,UINT *r) return i; } -int nd_to_vect_z(UINT *s0,int n,ND d,Z *r) +int nd_to_vect_q(UINT *s0,int n,ND d,Q *r) { NM m; UINT *t,*s; @@ -3803,7 +3779,7 @@ int nd_to_vect_z(UINT *s0,int n,ND d,Z *r) for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) { t = DL(m); for ( ; !ndl_equal(t,s); s += nd_wpd, i++ ); - r[i] = CZ(m); + r[i] = CQ(m); } for ( i = 0; !r[i]; i++ ); return i; @@ -3858,10 +3834,10 @@ IndArray nm_ind_pair_to_vect_compress(int mod,UINT *s0 } -int ndv_reduce_vect_z(Z *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred) +int ndv_reduce_vect_q(Q *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev; - Z cs,mcs,c1,c2,cr,gcd,t; + Q cs,mcs,c1,c2,cr,gcd,t; IndArray ivect; unsigned char *ivc; unsigned short *ivs; @@ -3879,32 +3855,34 @@ int ndv_reduce_vect_z(Z *svect,int col,IndArray *imat, maxrs = MAX(maxrs,rp0[i]->sugar); redv = nd_ps[rp0[i]->index]; len = LEN(redv); mr = BDY(redv); - gcd = gcdz_cofactor(svect[k],CZ(mr),&cs,&cr); - mcs = chsgnz(cs); - if ( !uniz(cr) ) - for ( j = 0; j < col; j++ ) - svect[j] = mulz(svect[j],cr); + igcd_cofactor(svect[k],CQ(mr),&gcd,&cs,&cr); + chsgnq(cs,&mcs); + if ( !UNIQ(cr) ) { + for ( j = 0; j < col; j++ ) { + mulq(svect[j],cr,&c1); svect[j] = c1; + } + } svect[k] = 0; prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; prev = pos; - svect[pos] = addz(svect[pos],mulz(CZ(mr),mcs)); + mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t; } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; prev = pos; - svect[pos] = addz(svect[pos],mulz(CZ(mr),mcs)); + mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t; } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; prev = pos; - svect[pos] = addz(svect[pos],mulz(CZ(mr),mcs)); + mulq(CQ(mr),mcs,&c2); addq(svect[pos],c2,&t); svect[pos] = t; } break; } @@ -4052,11 +4030,11 @@ NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhea } } -NDV vect_to_ndv_z(Z *vect,int spcol,int col,int *rhead,UINT *s0vect) +NDV vect_to_ndv_q(Q *vect,int spcol,int col,int *rhead,UINT *s0vect) { int j,k,len; UINT *p; - Z c; + Q c; NDV r; NMV mr0,mr; @@ -4072,7 +4050,9 @@ NDV vect_to_ndv_z(Z *vect,int spcol,int col,int *rhead for ( j = k = 0; j < col; j++, p += nd_wpd ) if ( !rhead[j] ) { if ( c = vect[k++] ) { - ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr); + if ( DN(c) ) + error("afo"); + ndl_copy(p,DL(mr)); CQ(mr) = c; NMV_ADV(mr); } } MKNDV(nd_nvar,mr0,len,r); @@ -4236,7 +4216,7 @@ NODE nd_f4_red(int m,ND_pairs sp0,UINT *s0vect,int col if ( m ) r0 = nd_f4_red_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred); else - r0 = nd_f4_red_z_main(sp0,nsp,s0vect,col,rvect,rhead,imat,nred); + r0 = nd_f4_red_q_main(sp0,nsp,s0vect,col,rvect,rhead,imat,nred); return r0; } @@ -4313,7 +4293,7 @@ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s return r0; } -NODE nd_f4_red_z_main(ND_pairs sp0,int nsp,UINT *s0vect,int col, +NODE nd_f4_red_q_main(ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred) { int spcol,sprow,a; @@ -4321,8 +4301,8 @@ NODE nd_f4_red_z_main(ND_pairs sp0,int nsp,UINT *s0vec NODE r0,r; ND_pairs sp; ND spol; - Z **spmat; - Z *svect,*v; + Q **spmat; + Q *svect,*v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; @@ -4331,17 +4311,17 @@ NODE nd_f4_red_z_main(ND_pairs sp0,int nsp,UINT *s0vec spcol = col-nred; get_eg(&eg0); /* elimination (1st step) */ - spmat = (Z **)ALLOCA(nsp*sizeof(Z *)); - svect = (Z *)ALLOCA(col*sizeof(Z)); - spsugar = (int *)ALLOCA(nsp*sizeof(Z)); + spmat = (Q **)ALLOCA(nsp*sizeof(Q *)); + svect = (Q *)ALLOCA(col*sizeof(Q)); + spsugar = (int *)ALLOCA(nsp*sizeof(Q)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(0,0,sp,&spol); if ( !spol ) continue; - nd_to_vect_z(s0vect,col,spol,svect); - maxrs = ndv_reduce_vect_z(svect,col,imat,rvect,nred); + nd_to_vect_q(s0vect,col,spol,svect); + maxrs = ndv_reduce_vect_q(svect,col,imat,rvect,nred); for ( i = 0; i < col; i++ ) if ( svect[i] ) break; if ( i < col ) { - spmat[sprow] = v = (Z *)MALLOC(spcol*sizeof(Z)); + spmat[sprow] = v = (Q *)MALLOC(spcol*sizeof(Q)); for ( j = k = 0; j < col; j++ ) if ( !rhead[j] ) v[k++] = svect[j]; spsugar[sprow] = MAX(maxrs,SG(spol)); @@ -4359,11 +4339,11 @@ NODE nd_f4_red_z_main(ND_pairs sp0,int nsp,UINT *s0vec /* elimination (2nd step) */ colstat = (int *)ALLOCA(spcol*sizeof(int)); - rank = nd_gauss_elim_z(spmat,spsugar,sprow,spcol,colstat); + rank = nd_gauss_elim_q(spmat,spsugar,sprow,spcol,colstat); r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = - (pointer)vect_to_ndv_z(spmat[i],spcol,col,rhead,s0vect); + (pointer)vect_to_ndv_q(spmat[i],spcol,col,rhead,s0vect); SG((NDV)BDY(r)) = spsugar[i]; /* GC_free(spmat[i]); */ } @@ -4637,15 +4617,11 @@ void nd_exec_f4_red_dist() fflush(nd_write); } -/* XXX */ -int generic_gauss_elim_z(MAT m,MAT *nm,Z *dn,int **ri,int **ci) -{} - -int nd_gauss_elim_z(Z **mat0,int *sugar,int row,int col,int *colstat) +int nd_gauss_elim_q(Q **mat0,int *sugar,int row,int col,int *colstat) { int mod,i,j,t,c,rank,rank0,inv; int *ci,*ri; - Z dn; + Q dn; MAT m,nm; int **wmat; @@ -4655,15 +4631,17 @@ int nd_gauss_elim_z(Z **mat0,int *sugar,int row,int co for ( i = 0; i < row; i++ ) { wmat[i] = (int *)ALLOCA(col*sizeof(int)); for ( j = 0; j < col; j++ ) { - if ( mat0[i][j] ) - wmat[i][j] = remzi(mat0[i][j],mod); - else + if ( mat0[i][j] ) { + t = rem(NM(mat0[i][j]),mod); + if ( SGN(mat0[i][j]) < 0 ) t = mod-t; + wmat[i][j] = t; + } else wmat[i][j] = 0; } } rank0 = nd_gauss_elim_mod(wmat,sugar,row,col,mod,colstat); NEWMAT(m); m->row = row; m->col = col; m->body = (pointer **)mat0; - rank = generic_gauss_elim_z(m,&nm,&dn,&ri,&ci); + rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci); if ( rank != rank0 ) error("afo"); for ( i = 0; i < row; i++ ) @@ -4671,16 +4649,18 @@ int nd_gauss_elim_z(Z **mat0,int *sugar,int row,int co mat0[i][j] = 0; c = col-rank; for ( i = 0; i < rank; i++ ) { - mat0[i][ri[i]] = dn; + mat0[i][ri[i]] = dn; for ( j = 0; j < c; j++ ) - mat0[i][ci[j]] = (Z)BDY(nm)[i][j]; + mat0[i][ci[j]] = (Q)BDY(nm)[i][j]; } - inv = invm(remzi(dn,mod),mod); + inv = invm(rem(NM(dn),mod),mod); + if ( SGN(dn) < 0 ) inv = mod-inv; for ( i = 0; i < row; i++ ) for ( j = 0; j < col; j++ ) { - if ( mat0[i][j] ) - t = remzi(mat0[i][j],mod); - else + if ( mat0[i][j] ) { + t = rem(NM(mat0[i][j]),mod); + if ( SGN(mat0[i][j]) < 0 ) t = mod-t; + } else t = 0; c = dmar(t,inv,0,mod); if ( wmat[i][j] != c ) @@ -4844,7 +4824,7 @@ void ndv_save(NDV p,int index) write_int(s,&len); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { - saveobj(s,(Obj)ztoq(CZ(m))); + saveobj(s,(Obj)CQ(m)); dl = DL(m); td = TD(dl); write_int(s,&td); @@ -4880,7 +4860,7 @@ NDV ndv_load(int index) m0 = m = MALLOC(len*nmv_adv); for ( i = 0; i < len; i++, NMV_ADV(m) ) { - loadobj(s,&obj); CZ(m) = qtoz((Q)obj); + loadobj(s,&obj); CQ(m) = (Q)obj; dl = DL(m); ndl_zero(dl); read_int(s,&td); TD(dl) = td; @@ -4901,7 +4881,7 @@ void nd_det(int mod,MAT f,P *rp) VL fv,tv; int n,i,j,max,e,nvar,sgn,k0,l0,len0,len,k,l,a; pointer **m; - Z mone; + Q mone; NDV **dm; NDV *t,*mi,*mj; NDV d,s,mij,mjj; @@ -4934,7 +4914,7 @@ void nd_det(int mod,MAT f,P *rp) } d = ptondv(CO,fv,(P)ONE); if ( mod ) ndv_mod(mod,d); - mone = chsgnz(qtoz(ONE)); + chsgnq(ONE,&mone); for ( j = 0, sgn = 1; j < n; j++ ) { if ( DP_Print ) fprintf(stderr,"j=%d\n",j); for ( i = j; i < n && !dm[i][j]; i++ ); @@ -4964,7 +4944,7 @@ void nd_det(int mod,MAT f,P *rp) if ( mod ) ndv_mul_c(mod,mij,mod-1); else - ndv_mul_c_z(mij,mone); + ndv_mul_c_q(mij,mone); for ( k = j+1; k < n; k++ ) { if ( DP_Print ) fprintf(stderr,"k=%d ",k); bucket = create_pbucket(); @@ -4993,7 +4973,7 @@ void nd_det(int mod,MAT f,P *rp) if ( mod ) ndv_mul_c(mod,d,mod-1); else - ndv_mul_c_z(d,mone); + ndv_mul_c_q(d,mone); *rp = ndvtop(mod,CO,fv,d); } @@ -5004,7 +4984,7 @@ ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d) NMV m; UINT *d0,*dt,*dm; int c,n,td,i,c1,c2,len; - Z q; + Q q; ND r; if ( !p ) return 0; @@ -5025,12 +5005,12 @@ ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d) } } } else { - q = CZ(m0); + q = CQ(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { ndl_add(DL(m),d0,DL(tnm)); if ( ndl_reducible(DL(tnm),d) ) { NEXTNM(mr0,mr); - CZ(mr) = mulz(CZ(m),q); + mulq(CQ(m),q,&CQ(mr)); ndl_copy(DL(tnm),DL(mr)); } }