=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Mgfs.c,v retrieving revision 1.1 retrieving revision 1.14 diff -u -p -r1.1 -r1.14 --- OpenXM_contrib2/asir2000/engine/Mgfs.c 2001/06/20 09:32:13 1.1 +++ OpenXM_contrib2/asir2000/engine/Mgfs.c 2002/09/27 08:40:49 1.14 @@ -1,12 +1,84 @@ -/* $OpenXM$ */ +/* $OpenXM: OpenXM_contrib2/asir2000/engine/Mgfs.c,v 1.13 2002/09/27 04:24:04 noro Exp $ */ #include "ca.h" +#include "inline.h" -void mulssfum(UM,int,UM); +extern int up_kara_mag, current_gfs_q1; +extern int *current_gfs_plus1; -void addsfum(p1,p2,pr) -UM p1,p2,pr; +#if defined(__GNUC__) +#define INLINE inline +#elif defined(VISUAL) +#define INLINE __inline +#else +#define INLINE +#endif + +INLINE int _ADDSF(int a,int b) { + if ( !a ) + return b; + else if ( !b ) + return a; + + a = IFTOF(a); b = IFTOF(b); + + if ( !current_gfs_ntoi ) { + a = a+b-current_gfs_q; + if ( a == 0 ) + return 0; + else { + if ( a < 0 ) + a += current_gfs_q; + return FTOIF(a); + } + } + + if ( a > b ) { + /* tab[a]+tab[b] = tab[b](tab[a-b]+1) */ + a = current_gfs_plus1[a-b]; + if ( a < 0 ) + return 0; + else { + a += b; + if ( a >= current_gfs_q1 ) + a -= current_gfs_q1; + return FTOIF(a); + } + } else { + /* tab[a]+tab[b] = tab[a](tab[b-a]+1) */ + b = current_gfs_plus1[b-a]; + if ( b < 0 ) + return 0; + else { + b += a; + if ( b >= current_gfs_q1 ) + b -= current_gfs_q1; + return FTOIF(b); + } + } +} + +INLINE int _MULSF(int a,int b) +{ + int c; + + if ( !a || !b ) + return 0; + else if ( !current_gfs_ntoi ) { + a = IFTOF(a); b = IFTOF(b); + DMAR(a,b,0,current_gfs_q,c); + return FTOIF(c); + } else { + a = IFTOF(a) + IFTOF(b); + if ( a >= current_gfs_q1 ) + a -= current_gfs_q1; + return FTOIF(a); + } +} + +void addsfum(UM p1,UM p2,UM pr) +{ int *c1,*c2,*cr,i,dmax,dmin; if ( DEG(p1) == -1 ) { @@ -23,7 +95,7 @@ UM p1,p2,pr; c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); } for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) - cr[i] = _addsf(c1[i],c2[i]); + cr[i] = _ADDSF(c1[i],c2[i]); for ( ; i <= dmax; i++ ) cr[i] = c1[i]; if ( dmax == dmin ) @@ -32,8 +104,7 @@ UM p1,p2,pr; DEG(pr) = dmax; } -void subsfum(p1,p2,pr) -UM p1,p2,pr; +void subsfum(UM p1,UM p2,UM pr) { int *c1,*c2,*cr,i; int dmax,dmin; @@ -68,8 +139,7 @@ UM p1,p2,pr; DEG(pr) = dmax; } -void gcdsfum(p1,p2,pr) -UM p1,p2,pr; +void gcdsfum(UM p1,UM p2,UM pr) { int inv; UM t1,t2,q,tum; @@ -93,8 +163,8 @@ UM p1,p2,pr; mulssfum(t2,inv,pr); } } -void mulsfum(p1,p2,pr) -UM p1,p2,pr; + +void mulsfum(UM p1,UM p2,UM pr) { int *pc1,*pcr; int *c1,*c2,*cr; @@ -110,25 +180,104 @@ UM p1,p2,pr; for ( i = 0; i <= d2; i++, cr++ ) if ( mul = *c2++ ) for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ ) - *pcr = _addsf(_mulsf(*pc1,mul),*pcr); + if ( *pc1 ) + *pcr = _ADDSF(_MULSF(*pc1,mul),*pcr); DEG(pr) = d1 + d2; } -void mulssfum(p,n,pr) -int n; -UM p,pr; +void mulssfum(UM p,int n,UM pr) { int *sp,*dp; int i; for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i; i >= 0; i--, dp--, sp-- ) - *dp = _mulsf(*sp,n); + *dp = _MULSF(*sp,n); } -int divsfum(p1,p2,pq) -UM p1,p2,pq; +void kmulsfum(UM n1,UM n2,UM nr) { + UM n,t,s,m,carry; + int d,d1,d2,len,i,l; + unsigned int *r,*r0; + + if ( !n1 || !n2 ) { + nr->d = -1; return; + } + d1 = DEG(n1)+1; d2 = DEG(n2)+1; + if ( (d1 < up_kara_mag) || (d2 < up_kara_mag) ) { + mulsfum(n1,n2,nr); return; + } + if ( d1 < d2 ) { + n = n1; n1 = n2; n2 = n; + d = d1; d1 = d2; d2 = d; + } + if ( d2 > (d1+1)/2 ) { + kmulsfummain(n1,n2,nr); return; + } + d = (d1/d2)+((d1%d2)!=0); + len = (d+1)*d2; + r0 = (unsigned int *)ALLOCA(len*sizeof(int)); + bzero((char *)r0,len*sizeof(int)); + m = W_UMALLOC(d2+1); + carry = W_UMALLOC(d2+1); + t = W_UMALLOC(d1+d2+1); + s = W_UMALLOC(d1+d2+1); + for ( DEG(carry) = -1, i = 0, r = r0; i < d; i++, r += d2 ) { + extractum(n1,i*d2,d2,m); + if ( m ) { + kmulsfum(m,n2,t); + addsfum(t,carry,s); + c_copyum(s,d2,r); + extractum(s,d2,d2,carry); + } else { + c_copyum(carry,d2,r); + carry = 0; + } + } + c_copyum(carry,d2,r); + for ( l = len - 1; !r0[l]; l-- ); + l++; + DEG(nr) = l-1; + bcopy((char *)r0,(char *)COEF(nr),l*sizeof(int)); +} + +void kmulsfummain(UM n1,UM n2,UM nr) +{ + int d1,d2,h,len; + UM n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2; + + d1 = DEG(n1)+1; d2 = DEG(n2)+1; h = (d1+1)/2; + n1lo = W_UMALLOC(d1+1); n1hi = W_UMALLOC(d1+1); + n2lo = W_UMALLOC(d2+1); n2hi = W_UMALLOC(d2+1); + lo = W_UMALLOC(d1+d2+1); hi = W_UMALLOC(d1+d2+1); + mid1 = W_UMALLOC(d1+d2+1); mid2 = W_UMALLOC(d1+d2+1); + mid = W_UMALLOC(d1+d2+1); + s1 = W_UMALLOC(d1+d2+1); s2 = W_UMALLOC(d1+d2+1); + extractum(n1,0,h,n1lo); extractum(n1,h,d1-h,n1hi); + extractum(n2,0,h,n2lo); extractum(n2,h,d2-h,n2hi); + kmulsfum(n1hi,n2hi,hi); kmulsfum(n1lo,n2lo,lo); + len = DEG(hi)+1+2*h; t1 = W_UMALLOC(len-1); DEG(t1) = len-1; + bzero((char *)COEF(t1),len*sizeof(int)); + if ( lo ) + bcopy((char *)COEF(lo),(char *)COEF(t1),(DEG(lo)+1)*sizeof(int)); + if ( hi ) + bcopy((char *)COEF(hi),(char *)(COEF(t1)+2*h),(DEG(hi)+1)*sizeof(int)); + + addsfum(hi,lo,mid1); + subsfum(n1hi,n1lo,s1); subsfum(n2lo,n2hi,s2); + kmulsfum(s1,s2,mid2); addsfum(mid1,mid2,mid); + if ( mid ) { + len = DEG(mid)+1+h; t2 = W_UMALLOC(len-1); DEG(t2) = len-1; + bzero((char *)COEF(t2),len*sizeof(int)); + bcopy((char *)COEF(mid),(char *)(COEF(t2)+h),(DEG(mid)+1)*sizeof(int)); + addsfum(t1,t2,nr); + } else + copyum(t1,nr); +} + +int divsfum(UM p1,UM p2,UM pq) +{ int *pc1,*pct; int *c1,*c2,*ct; int inv,hd,tmp; @@ -142,20 +291,20 @@ UM p1,p2,pq; if ( ( hd = c2[d2] ) != _onesf() ) { inv = _invsf(hd); for ( pc1 = c2 + d2; pc1 >= c2; pc1-- ) - *pc1 = _mulsf(*pc1,inv); + *pc1 = _MULSF(*pc1,inv); } else inv = _onesf(); for ( i = dd, ct = c1+d1; i >= 0; i-- ) if ( tmp = *ct-- ) { tmp = _chsgnsf(tmp); for ( j = d2-1, pct = ct, pc1 = c2+j; j >= 0; j--, pct--, pc1-- ) - *pct = _addsf(_mulsf(*pc1,tmp),*pct); + *pct = _ADDSF(_MULSF(*pc1,tmp),*pct); } if ( inv != _onesf() ) { for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ ) - *pc1 = _mulsf(*pc1,inv); + *pc1 = _MULSF(*pc1,inv); for ( pc1 = c2, pct = c2+d2; pc1 <= pct; pc1++ ) - *pc1 = _mulsf(*pc1,hd); + *pc1 = _MULSF(*pc1,hd); } for ( i = d2-1, pc1 = c1+i; i >= 0 && !(*pc1); pc1--, i-- ); for ( DEG(pq) = j = dd, pc1 = c1+d1, pct = COEF(pq)+j; j >= 0; j-- ) @@ -163,21 +312,19 @@ UM p1,p2,pq; return i; } -void diffsfum(f,fd) -UM f,fd; +void diffsfum(UM f,UM fd) { int *dp,*sp; int i; for ( i = DEG(f), dp = COEF(fd)+i-1, sp = COEF(f)+i; i >= 1; i--, dp--, sp-- ) { - *dp = _mulsf(*sp,_itosf(i)); + *dp = _MULSF(*sp,_itosf(i)); } degum(fd,DEG(f) - 1); } -void monicsfum(f) -UM f; +void monicsfum(UM f) { int *sp; int i,inv; @@ -185,5 +332,445 @@ UM f; i = DEG(f); sp = COEF(f)+i; inv = _invsf(*sp); for ( ; i >= 0; i--, sp-- ) - *sp = _mulsf(*sp,inv); + *sp = _MULSF(*sp,inv); +} + +int compsfum(UM a,UM b) +{ + int i,da,db; + + if ( !a ) + return !b?0:1; + else if ( !b ) + return 1; + else if ( (da = DEG(a)) > (db = DEG(b)) ) + return 1; + else if ( da < db ) + return -1; + else { + for ( i = da; i >= 0 && COEF(a)[i] == COEF(b)[i]; i-- ); + if ( i < 0 ) + return 0; + else if ( (unsigned int)COEF(a)[i] > (unsigned int)COEF(b)[i] ) + return 1; + else + return -1; + } +} + +void addsfarray(int,int *,int *); +void mulsfarray_trunc(int,int *,int *,int *); + +/* f1 = f1->c[0]+f1->c[1]*y+..., f2 = f2->c[0]+f2->c[1]*y+... mod y^n */ + +void mulsfbm(BM f1,BM f2,BM fr) +{ + UM mul,t,s; + int i,j,d1,d2,dy; + + dy = MIN(DEG(f1),DEG(f2)); + + d1 = degbm(f1); + d2 = degbm(f2); + t = W_UMALLOC(d1+d2); + s = W_UMALLOC(d1+d2); + + for ( i = 0; i <= dy; i++ ) { + mul = COEF(f2)[i]; + if ( DEG(mul) >= 0 ) + for ( j = 0; i+j <= dy; j++ ) { + if ( COEF(f1)[j] ) { + kmulsfum(COEF(f1)[j],mul,t); + addsfum(t,COEF(fr)[i+j],s); + cpyum(s,COEF(fr)[i+j]); + } + } + } + DEG(fr) = dy; +} + +int degbm(BM f) +{ + int d,i,dy; + + dy = DEG(f); + d = DEG(COEF(f)[0]); + for ( i = 1; i <= dy; i++ ) + d = MAX(DEG(COEF(f)[i]),d); + return d; +} + +/* g += f */ + +void addtosfbm(BM f,BM g) +{ + int i,d1,d2,dy; + UM t; + + dy = DEG(g); + if ( DEG(f) > dy ) + error("addtosfbm : invalid input"); + dy = MIN(DEG(f),dy); + d1 = degbm(f); + d2 = degbm(g); + t = W_UMALLOC(MAX(d1,d2)); + for ( i = 0; i <= dy; i++ ) { + addsfum(COEF(f)[i],COEF(g)[i],t); + cpyum(t,COEF(g)[i]); + } +} + +void eucsfum(UM f1,UM f2,UM a,UM b) +{ + UM g1,g2,a1,a2,a3,wm,q,tum; + int d,dr; + + /* XXX */ + d = DEG(f1) + DEG(f2) + 10; + g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); + a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); + q = W_UMALLOC(d); + DEG(a1) = 0; COEF(a1)[0] = _onesf(); DEG(a2) = -1; + cpyum(f1,g1); cpyum(f2,g2); + while ( 1 ) { + dr = divsfum(g1,g2,q); tum = g1; g1 = g2; g2 = tum; + if ( ( DEG(g2) = dr ) == -1 ) + break; + mulsfum(a2,q,wm); subsfum(a1,wm,a3); dr = divsfum(a3,f2,q); + tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; + } + if ( COEF(g1)[0] != _onesf() ) + mulssfum(a2,_invsf(COEF(g1)[0]),a); + else + cpyum(a2,a); + mulsfum(a,f1,wm); + if ( DEG(wm) >= 0 ) + COEF(wm)[0] = _subsf(COEF(wm)[0],_onesf()); + else { + DEG(wm) = 0; COEF(wm)[0] = _chsgnsf(_onesf()); + } + divsfum(wm,f2,q); mulssfum(q,_chsgnsf(_onesf()),b); +} + +void shiftsfum(UM,int,UM); + +void shiftsflum(int n,LUM f,int ev) +{ + int d,i,j; + UM w,w1; + int *coef; + int **c; + + d = f->d; + c = f->c; + w = W_UMALLOC(n); + w1 = W_UMALLOC(n); + for ( i = 0; i <= d; i++ ) { + coef = c[i]; + for ( j = n-1; j >= 0 && coef[j] == 0; j-- ); + if ( j <= 0 ) + continue; + DEG(w) = j; bcopy(coef,COEF(w),(j+1)*sizeof(int)); + shiftsfum(w,ev,w1); + bcopy(COEF(w1),coef,(j+1)*sizeof(int)); + } +} + +/* f(x) -> g(x) = f(x+a) */ + +void shiftsfum(UM f,int a,UM g) +{ + int n,i; + UM pwr,xa,w,t; + int *c; + + n = DEG(f); + if ( n <= 0 ) + cpyum(f,g); + else { + c = COEF(f); + + /* g = 0 */ + DEG(g) = -1; + + /* pwr = 1 */ + pwr = W_UMALLOC(n); DEG(pwr) = 0; COEF(pwr)[0] = _onesf(); + + /* xa = x+a */ + xa = W_UMALLOC(n); DEG(xa) = 1; + COEF(xa)[0] = a; COEF(xa)[1] = _onesf(); + + w = W_UMALLOC(n); + t = W_UMALLOC(n); + + /* g += pwr*c[0] */ + for ( i = 0; i <= n; i++ ) { + mulssfum(pwr,c[i],w); addsfum(g,w,t); cpyum(t,g); + if ( i < n ) { + mulsfum(pwr,xa,t); cpyum(t,pwr); + } + } + } +} + +/* f(y) -> f(y+a) */ + +void shiftsfbm(BM f,int a) +{ + int i,j,d,dy; + UM pwr,ya,w,t,s; + UM *c; + + dy = DEG(f); + c = COEF(f); + d = degbm(f); + + w = W_UMALLOC(d); + t = W_UMALLOC(d); + s = W_UMALLOC(dy); + + /* pwr = 1 */ + pwr = W_UMALLOC(dy); DEG(pwr) = 0; COEF(pwr)[0] = _onesf(); + + /* ya = y+a */ + ya = W_UMALLOC(1); DEG(ya) = 1; + COEF(ya)[0] = a; COEF(ya)[1] = _onesf(); + + for ( i = 0; i <= dy; i++ ) { + /* c[i] does not change */ + for ( j = 0; j < i; j++ ) { + mulssfum(c[i],COEF(pwr)[j],w); + addsfum(w,c[j],t); cpyum(t,c[j]); + } + if ( i < dy ) { + mulsfum(pwr,ya,s); cpyum(s,pwr); + } + } +} + +void clearbm(int n,BM f) +{ + int i,dy; + UM *c; + + dy = DEG(f); + for ( c = COEF(f), i = 0; i <= dy; i++ ) + clearum(c[i],n); +} + +static void create_bmono(P c,V x,int i,V y,int j,P *mono); + +struct lb { + int pos,len; + int *r; + int *hist; +}; + +static NODE insert_lb(NODE g,struct lb *a) +{ + NODE prev,cur,n; + + prev = 0; cur = g; + while ( cur ) { + if ( a->pos < ((struct lb *)BDY(cur))->pos ) { + MKNODE(n,a,cur); + if ( !prev ) + return n; + else { + NEXT(prev) = n; + return g; + } + } else { + prev = cur; + cur = NEXT(cur); + } + } + MKNODE(n,a,0); + NEXT(prev) = n; + return g; +} + +static void lnf(int *r,int *h,int n,int len,NODE g) +{ + struct lb *t; + int pos,i,j,len1,c; + int *r1,*h1; + + for ( ; g; g = NEXT(g) ) { + t = (struct lb *)BDY(g); + pos = t->pos; + if ( c = r[pos] ) { + c = _chsgnsf(c); + r1 = t->r; + h1 = t->hist; + len1 = t->len; + for ( i = pos; i < n; i++ ) + if ( r1[i] ) + r[i] = _ADDSF(r[i],_MULSF(r1[i],c)); + for ( i = 0; i < len1; i++ ) + if ( h1[i] ) + h[i] = _ADDSF(h[i],_MULSF(h1[i],c)); + } + } + for ( i = 0; i < n && !r[i]; i++ ); + if ( i < n ) { + c = _invsf(r[i]); + for ( j = i; j < n; j++ ) + if ( r[j] ) + r[j] = _MULSF(r[j],c); + for ( j = 0; j < len; j++ ) + if ( h[j] ) + h[j] = _MULSF(h[j],c); + } +} + +void sfmintdeg(VL vl,P fx,int dy,int c,P *fr) +{ + V x,y; + int dx,dxdy,i,j,k,l,d,len,len0,u,dyk; + UP *rx; + DCP dc; + P t,f,mono,f1; + UP ut,h; + int ***nf; + int *r,*hist,*prev,*r1; + struct lb *lb; + GFS s; + NODE g; + + x = vl->v; + y = NEXT(vl)->v; + dx = getdeg(x,fx); + dxdy = dx*dy; + /* rx = -(fx-x^dx) */ + rx = (UP *)CALLOC(dx,sizeof(UP)); + for ( dc = DC(fx); dc; dc = NEXT(dc)) { + chsgnp(COEF(dc),&t); + ptoup(t,&ut); + rx[QTOS(DEG(dc))] = ut; + } + /* nf[d] = normal form table of monomials with total degree d */ + nf = (int ***)CALLOC(dx+dy+1,sizeof(int **)); /* xxx */ + nf[0] = (int **)CALLOC(1,sizeof(int *)); + + /* nf[0][0] = 1 */ + r = (int *)CALLOC(dxdy,sizeof(int)); + r[0] = _onesf(); + nf[0][0] = r; + + hist = (int *)CALLOC(1,sizeof(int)); + hist[0] = _onesf(); + + lb = (struct lb *)CALLOC(1,sizeof(struct lb)); + lb->pos = 0; + lb->r = r; + lb->hist = hist; + lb->len = 1; + + /* g : table of normal form as linear form */ + MKNODE(g,lb,0); + + len = 1; + h = UPALLOC(dy); + for ( d = 1; ; d++ ) { + if ( d > c ){ + return; + } + nf[d] = (int **)CALLOC(d+1,sizeof(int *)); + len0 = len; + len += d+1; + + for ( i = d; i >= 0; i-- ) { + /* nf(x^(d-i)*y^i) = nf(y*nf(x^(d-i)*y^(i-1))) */ + /* nf(x^d) = nf(nf(x^(d-1))*x) */ + r = (int *)CALLOC(dxdy,sizeof(int)); + if ( i == 0 ) { + prev = nf[d-1][0]; + bcopy(prev,r+dy,(dxdy-dy)*sizeof(int)); + + /* create the head coeff */ + for ( l = 0, k = dxdy-dy; l < dy; l++, k++ ) { + iftogfs(prev[k],&s); + COEF(h)[l] = (Num)s; + } + for ( l = dy-1; l >= 0 && !COEF(h)[l]; l--); + DEG(h) = l; + + for ( k = 0, dyk = 0; k < dx; k++, dyk += dy ) { + tmulup(rx[k],h,dy,&ut); + if ( ut ) + for ( l = 0; l < dy; l++ ) { + s = (GFS)COEF(ut)[l]; + if ( s ) { + u = CONT(s); + r[dyk+l] = _ADDSF(r[dyk+l],FTOIF(u)); + } + } + } + } else { + prev = nf[d-1][i-1]; + for ( k = 0, dyk = 0; k < dx; k++, dyk += dy ) { + for ( l = 1; l < dy; l++ ) + r[dyk+l] = prev[dyk+l-1]; + } + } + nf[d][i] = r; + hist = (int *)CALLOC(len,sizeof(int)); + hist[len0+i] = _onesf(); + r1 = (int *)CALLOC(dxdy,sizeof(int)); + bcopy(r,r1,dxdy*sizeof(int)); + lnf(r1,hist,dxdy,len,g); + for ( k = 0; k < dxdy && !r1[k]; k++ ); + if ( k == dxdy ) { + f = 0; + for ( k = j = 0; k <= d; k++ ) + for ( i = 0; i <= k; i++, j++ ) + if ( hist[j] ) { + iftogfs(hist[j],&s); + /* mono = s*x^(k-i)*y^i */ + create_bmono((P)s,x,k-i,y,i,&mono); + addp(vl,f,mono,&f1); + f = f1; + } + *fr = f; + return; + } else { + lb = (struct lb *)CALLOC(1,sizeof(struct lb)); + lb->pos = k; + lb->r = r1; + lb->hist = hist; + lb->len = len; + g = insert_lb(g,lb); + } + } + } +} + +static void create_bmono(P c,V x,int i,V y,int j,P *mono) +{ + P t,s; + + if ( !i ) + if ( !j ) + t = c; + else { + /* c*y^j */ + MKV(y,t); + COEF(DC(t)) = c; + STOQ(j,DEG(DC(t))); + } + else if ( !j ) { + /* c*x^i */ + MKV(x,t); + COEF(DC(t)) = c; + STOQ(i,DEG(DC(t))); + } else { + MKV(y,s); + COEF(DC(s)) = c; + STOQ(j,DEG(DC(s))); + MKV(x,t); + COEF(DC(t)) = s; + STOQ(i,DEG(DC(t))); + } + *mono = t; }