=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/Mgfs.c,v retrieving revision 1.19 retrieving revision 1.20 diff -u -p -r1.19 -r1.20 --- OpenXM_contrib2/asir2000/engine/Mgfs.c 2015/08/14 13:51:54 1.19 +++ OpenXM_contrib2/asir2000/engine/Mgfs.c 2018/03/29 01:32:51 1.20 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM_contrib2/asir2000/engine/Mgfs.c,v 1.18 2015/08/06 10:01:52 fujimoto Exp $ */ +/* $OpenXM: OpenXM_contrib2/asir2000/engine/Mgfs.c,v 1.19 2015/08/14 13:51:54 fujimoto Exp $ */ #include "ca.h" #include "inline.h" @@ -17,347 +17,347 @@ extern int *current_gfs_plus1; INLINE int _ADDSF(int a,int b) { - if ( !a ) - return b; - else if ( !b ) - return a; + if ( !a ) + return b; + else if ( !b ) + return a; - a = IFTOF(a); b = IFTOF(b); + 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 ( !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); - } - } + 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; + 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); - } + 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 ) { - cpyum(p2,pr); - return; - } - if ( DEG(p2) == -1 ) { - cpyum(p1,pr); - return; - } - if ( DEG(p1) >= DEG(p2) ) { - c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); - } else { - 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]); - for ( ; i <= dmax; i++ ) - cr[i] = c1[i]; - if ( dmax == dmin ) - degum(pr,dmax); - else - DEG(pr) = dmax; + int *c1,*c2,*cr,i,dmax,dmin; + + if ( DEG(p1) == -1 ) { + cpyum(p2,pr); + return; + } + if ( DEG(p2) == -1 ) { + cpyum(p1,pr); + return; + } + if ( DEG(p1) >= DEG(p2) ) { + c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); + } else { + 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]); + for ( ; i <= dmax; i++ ) + cr[i] = c1[i]; + if ( dmax == dmin ) + degum(pr,dmax); + else + DEG(pr) = dmax; } void subsfum(UM p1,UM p2,UM pr) { - int *c1,*c2,*cr,i; - int dmax,dmin; + int *c1,*c2,*cr,i; + int dmax,dmin; - if ( DEG(p1) == -1 ) { - for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); - i >= 0; i-- ) - cr[i] = _chsgnsf(c2[i]); - return; - } - if ( DEG(p2) == -1 ) { - cpyum(p1,pr); - return; - } - c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); - if ( DEG(p1) >= DEG(p2) ) { - dmax = DEG(p1); dmin = DEG(p2); - for ( i = 0; i <= dmin; i++ ) - cr[i] = _subsf(c1[i],c2[i]); - for ( ; i <= dmax; i++ ) - cr[i] = c1[i]; - } else { - dmax = DEG(p2); dmin = DEG(p1); - for ( i = 0; i <= dmin; i++ ) - cr[i] = _subsf(c1[i],c2[i]); - for ( ; i <= dmax; i++ ) - cr[i] = _chsgnsf(c2[i]); - } - if ( dmax == dmin ) - degum(pr,dmax); - else - DEG(pr) = dmax; + if ( DEG(p1) == -1 ) { + for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); + i >= 0; i-- ) + cr[i] = _chsgnsf(c2[i]); + return; + } + if ( DEG(p2) == -1 ) { + cpyum(p1,pr); + return; + } + c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); + if ( DEG(p1) >= DEG(p2) ) { + dmax = DEG(p1); dmin = DEG(p2); + for ( i = 0; i <= dmin; i++ ) + cr[i] = _subsf(c1[i],c2[i]); + for ( ; i <= dmax; i++ ) + cr[i] = c1[i]; + } else { + dmax = DEG(p2); dmin = DEG(p1); + for ( i = 0; i <= dmin; i++ ) + cr[i] = _subsf(c1[i],c2[i]); + for ( ; i <= dmax; i++ ) + cr[i] = _chsgnsf(c2[i]); + } + if ( dmax == dmin ) + degum(pr,dmax); + else + DEG(pr) = dmax; } - + void gcdsfum(UM p1,UM p2,UM pr) { - int inv; - UM t1,t2,q,tum; - int drem; + int inv; + UM t1,t2,q,tum; + int drem; - if ( DEG(p1) < 0 ) - cpyum(p2,pr); - else if ( DEG(p2) < 0 ) - cpyum(p1,pr); - else { - if ( DEG(p1) >= DEG(p2) ) { - t1 = p1; t2 = p2; - } else { - t1 = p2; t2 = p1; - } - q = W_UMALLOC(DEG(t1)); - while ( ( drem = divsfum(t1,t2,q) ) >= 0 ) { - tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; - } - inv = _invsf(COEF(t2)[DEG(t2)]); - mulssfum(t2,inv,pr); - } + if ( DEG(p1) < 0 ) + cpyum(p2,pr); + else if ( DEG(p2) < 0 ) + cpyum(p1,pr); + else { + if ( DEG(p1) >= DEG(p2) ) { + t1 = p1; t2 = p2; + } else { + t1 = p2; t2 = p1; + } + q = W_UMALLOC(DEG(t1)); + while ( ( drem = divsfum(t1,t2,q) ) >= 0 ) { + tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; + } + inv = _invsf(COEF(t2)[DEG(t2)]); + mulssfum(t2,inv,pr); + } } void mulsfum(UM p1,UM p2,UM pr) { - int *pc1,*pcr; - int *c1,*c2,*cr; - int mul; - int i,j,d1,d2; + int *pc1,*pcr; + int *c1,*c2,*cr; + int mul; + int i,j,d1,d2; - if ( ( (d1 = DEG(p1)) < 0) || ( (d2 = DEG(p2)) < 0 ) ) { - DEG(pr) = -1; - return; - } - c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); - bzero((char *)cr,(int)((d1+d2+1)*sizeof(int))); - for ( i = 0; i <= d2; i++, cr++ ) - if ( mul = *c2++ ) - for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ ) - if ( *pc1 ) - *pcr = _ADDSF(_MULSF(*pc1,mul),*pcr); - DEG(pr) = d1 + d2; + if ( ( (d1 = DEG(p1)) < 0) || ( (d2 = DEG(p2)) < 0 ) ) { + DEG(pr) = -1; + return; + } + c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); + bzero((char *)cr,(int)((d1+d2+1)*sizeof(int))); + for ( i = 0; i <= d2; i++, cr++ ) + if ( mul = *c2++ ) + for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ ) + if ( *pc1 ) + *pcr = _ADDSF(_MULSF(*pc1,mul),*pcr); + DEG(pr) = d1 + d2; } void mulssfum(UM p,int n,UM pr) { - int *sp,*dp; - int i; + 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); + for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i; + i >= 0; i--, dp--, sp-- ) + *dp = _MULSF(*sp,n); } - + 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; + 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(d1+d2+1); - carry = W_UMALLOC(d1+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)); + 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(d1+d2+1); + carry = W_UMALLOC(d1+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,d; - UM n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2; + int d1,d2,h,len,d; + 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; - d = d1+d2+1; - n1lo = W_UMALLOC(d); n1hi = W_UMALLOC(d); - n2lo = W_UMALLOC(d); n2hi = W_UMALLOC(d); - lo = W_UMALLOC(d); hi = W_UMALLOC(d); - mid1 = W_UMALLOC(d); mid2 = W_UMALLOC(d); - mid = W_UMALLOC(d); - s1 = W_UMALLOC(d); s2 = W_UMALLOC(d); - 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)); + d1 = DEG(n1)+1; d2 = DEG(n2)+1; h = (d1+1)/2; + d = d1+d2+1; + n1lo = W_UMALLOC(d); n1hi = W_UMALLOC(d); + n2lo = W_UMALLOC(d); n2hi = W_UMALLOC(d); + lo = W_UMALLOC(d); hi = W_UMALLOC(d); + mid1 = W_UMALLOC(d); mid2 = W_UMALLOC(d); + mid = W_UMALLOC(d); + s1 = W_UMALLOC(d); s2 = W_UMALLOC(d); + 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); + 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; - int i,j, d1,d2,dd; + int *pc1,*pct; + int *c1,*c2,*ct; + int inv,hd,tmp; + int i,j, d1,d2,dd; - if ( (d1 = DEG(p1)) < (d2 = DEG(p2)) ) { - DEG(pq) = -1; - return d1; - } - c1 = COEF(p1); c2 = COEF(p2); dd = d1-d2; - if ( ( hd = c2[d2] ) != _onesf() ) { - inv = _invsf(hd); - for ( pc1 = c2 + d2; pc1 >= c2; pc1-- ) - *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); - } - if ( inv != _onesf() ) { - for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ ) - *pc1 = _MULSF(*pc1,inv); - for ( pc1 = c2, pct = c2+d2; pc1 <= pct; pc1++ ) - *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-- ) - *pct-- = *pc1--; - return i; + if ( (d1 = DEG(p1)) < (d2 = DEG(p2)) ) { + DEG(pq) = -1; + return d1; + } + c1 = COEF(p1); c2 = COEF(p2); dd = d1-d2; + if ( ( hd = c2[d2] ) != _onesf() ) { + inv = _invsf(hd); + for ( pc1 = c2 + d2; pc1 >= c2; pc1-- ) + *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); + } + if ( inv != _onesf() ) { + for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ ) + *pc1 = _MULSF(*pc1,inv); + for ( pc1 = c2, pct = c2+d2; pc1 <= pct; pc1++ ) + *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-- ) + *pct-- = *pc1--; + return i; } void diffsfum(UM f,UM fd) { - int *dp,*sp; - int i; + 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%current_gfs_p)); - } - degum(fd,DEG(f) - 1); + for ( i = DEG(f), dp = COEF(fd)+i-1, sp = COEF(f)+i; + i >= 1; i--, dp--, sp-- ) { + *dp = _MULSF(*sp,_itosf(i%current_gfs_p)); + } + degum(fd,DEG(f) - 1); } void monicsfum(UM f) { - int *sp; - int i,inv; + int *sp; + int i,inv; - i = DEG(f); sp = COEF(f)+i; - inv = _invsf(*sp); - for ( ; i >= 0; i--, sp-- ) - *sp = _MULSF(*sp,inv); + i = DEG(f); sp = COEF(f)+i; + inv = _invsf(*sp); + for ( ; i >= 0; i--, sp-- ) + *sp = _MULSF(*sp,inv); } int compsfum(UM a,UM b) { - int i,da,db; + 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; - } + 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 *); @@ -367,412 +367,412 @@ void mulsfarray_trunc(int,int *,int *,int *); void mulsfbm(BM f1,BM f2,BM fr) { - UM mul,t,s; - int i,j,d1,d2,dy; + UM mul,t,s; + int i,j,d1,d2,dy; - dy = MIN(DEG(f1),DEG(f2)); + dy = MIN(DEG(f1),DEG(f2)); - d1 = degbm(f1); - d2 = degbm(f2); - t = W_UMALLOC(d1+d2); - s = W_UMALLOC(d1+d2); + 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; + 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; + 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; + 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; + 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]); - } + 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; + 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); + /* 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; + 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)); - } + 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; + int n,i; + UM pwr,xa,w,t; + int *c; - n = DEG(f); - if ( n <= 0 ) - cpyum(f,g); - else { - c = COEF(f); + n = DEG(f); + if ( n <= 0 ) + cpyum(f,g); + else { + c = COEF(f); - /* g = 0 */ - DEG(g) = -1; + /* g = 0 */ + DEG(g) = -1; - /* pwr = 1 */ - pwr = W_UMALLOC(n); DEG(pwr) = 0; COEF(pwr)[0] = _onesf(); + /* 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(); + /* 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); + 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); - } - } - } + /* 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; + int i,j,d,dy; + UM pwr,ya,w,t,s; + UM *c; - dy = DEG(f); - c = COEF(f); - d = degbm(f); + dy = DEG(f); + c = COEF(f); + d = degbm(f); - w = W_UMALLOC(d); - t = W_UMALLOC(d); - s = W_UMALLOC(dy); + 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(); + /* 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(); + /* 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); - } - } + 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; + int i,dy; + UM *c; - dy = DEG(f); - for ( c = COEF(f), i = 0; i <= dy; i++ ) - clearum(c[i],n); + 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; + int pos,len; + int *r; + int *hist; }; static NODE insert_lb(NODE g,struct lb *a) { - NODE prev,cur,n; + 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; + 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; + 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); - } + 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; + 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 *)); + 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; + /* 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(); + 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; + 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); + /* 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; + 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)); + 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; + /* 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); - } - } - } + 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; + 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; + 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; }