version 1.1, 2001/06/20 09:32:13 |
version 1.7, 2001/06/27 04:07:57 |
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/* $OpenXM$ */ |
/* $OpenXM: OpenXM_contrib2/asir2000/engine/Mgfs.c,v 1.6 2001/06/25 10:01:28 noro Exp $ */ |
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#include "ca.h" |
#include "ca.h" |
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extern int up_kara_mag, current_gfs_q1; |
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extern int *current_gfs_plus1; |
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void mulssfum(UM,int,UM); |
void mulssfum(UM,int,UM); |
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void kmulsfummain(UM,UM,UM); |
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inline int _ADDSF(a,b) |
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int a,b; |
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{ |
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if ( !a ) |
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return b; |
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else if ( !b ) |
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return a; |
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a = IFTOF(a); b = IFTOF(b); |
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if ( a > b ) { |
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/* tab[a]+tab[b] = tab[b](tab[a-b]+1) */ |
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a = current_gfs_plus1[a-b]; |
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if ( a < 0 ) |
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return 0; |
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else { |
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a += b; |
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if ( a >= current_gfs_q1 ) |
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a -= current_gfs_q1; |
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return FTOIF(a); |
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} |
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} else { |
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/* tab[a]+tab[b] = tab[a](tab[b-a]+1) */ |
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b = current_gfs_plus1[b-a]; |
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if ( b < 0 ) |
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return 0; |
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else { |
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b += a; |
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if ( b >= current_gfs_q1 ) |
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b -= current_gfs_q1; |
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return FTOIF(b); |
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} |
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} |
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} |
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inline int _MULSF(a,b) |
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int a,b; |
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{ |
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if ( !a || !b ) |
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return 0; |
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else { |
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a = IFTOF(a) + IFTOF(b); |
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if ( a >= current_gfs_q1 ) |
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a -= current_gfs_q1; |
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return FTOIF(a); |
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} |
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} |
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void addsfum(p1,p2,pr) |
void addsfum(p1,p2,pr) |
UM p1,p2,pr; |
UM p1,p2,pr; |
{ |
{ |
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c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); |
c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); |
} |
} |
for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) |
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++ ) |
for ( ; i <= dmax; i++ ) |
cr[i] = c1[i]; |
cr[i] = c1[i]; |
if ( dmax == dmin ) |
if ( dmax == dmin ) |
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for ( i = 0; i <= d2; i++, cr++ ) |
for ( i = 0; i <= d2; i++, cr++ ) |
if ( mul = *c2++ ) |
if ( mul = *c2++ ) |
for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ ) |
for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ ) |
*pcr = _addsf(_mulsf(*pc1,mul),*pcr); |
if ( *pc1 ) |
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*pcr = _ADDSF(_MULSF(*pc1,mul),*pcr); |
DEG(pr) = d1 + d2; |
DEG(pr) = d1 + d2; |
} |
} |
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for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i; |
for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i; |
i >= 0; i--, dp--, sp-- ) |
i >= 0; i--, dp--, sp-- ) |
*dp = _mulsf(*sp,n); |
*dp = _MULSF(*sp,n); |
} |
} |
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void kmulsfum(n1,n2,nr) |
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UM n1,n2,nr; |
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{ |
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UM n,t,s,m,carry; |
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int d,d1,d2,len,i,l; |
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unsigned int *r,*r0; |
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if ( !n1 || !n2 ) { |
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nr->d = -1; return; |
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} |
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d1 = DEG(n1)+1; d2 = DEG(n2)+1; |
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if ( (d1 < up_kara_mag) || (d2 < up_kara_mag) ) { |
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mulsfum(n1,n2,nr); return; |
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} |
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if ( d1 < d2 ) { |
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n = n1; n1 = n2; n2 = n; |
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d = d1; d1 = d2; d2 = d; |
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} |
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if ( d2 > (d1+1)/2 ) { |
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kmulsfummain(n1,n2,nr); return; |
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} |
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d = (d1/d2)+((d1%d2)!=0); |
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len = (d+1)*d2; |
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r0 = (unsigned int *)ALLOCA(len*sizeof(int)); |
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bzero((char *)r0,len*sizeof(int)); |
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m = W_UMALLOC(d2+1); |
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carry = W_UMALLOC(d2+1); |
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t = W_UMALLOC(d1+d2+1); |
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s = W_UMALLOC(d1+d2+1); |
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for ( DEG(carry) = -1, i = 0, r = r0; i < d; i++, r += d2 ) { |
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extractum(n1,i*d2,d2,m); |
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if ( m ) { |
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kmulsfum(m,n2,t); |
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addsfum(t,carry,s); |
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c_copyum(s,d2,r); |
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extractum(s,d2,d2,carry); |
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} else { |
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c_copyum(carry,d2,r); |
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carry = 0; |
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} |
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} |
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c_copyum(carry,d2,r); |
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for ( l = len - 1; !r0[l]; l-- ); |
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l++; |
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DEG(nr) = l-1; |
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bcopy((char *)r0,(char *)COEF(nr),l*sizeof(int)); |
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} |
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void kmulsfummain(n1,n2,nr) |
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UM n1,n2,nr; |
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{ |
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int d1,d2,h,len; |
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UM n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2; |
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d1 = DEG(n1)+1; d2 = DEG(n2)+1; h = (d1+1)/2; |
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n1lo = W_UMALLOC(d1+1); n1hi = W_UMALLOC(d1+1); |
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n2lo = W_UMALLOC(d2+1); n2hi = W_UMALLOC(d2+1); |
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lo = W_UMALLOC(d1+d2+1); hi = W_UMALLOC(d1+d2+1); |
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mid1 = W_UMALLOC(d1+d2+1); mid2 = W_UMALLOC(d1+d2+1); |
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mid = W_UMALLOC(d1+d2+1); |
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s1 = W_UMALLOC(d1+d2+1); s2 = W_UMALLOC(d1+d2+1); |
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extractum(n1,0,h,n1lo); extractum(n1,h,d1-h,n1hi); |
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extractum(n2,0,h,n2lo); extractum(n2,h,d2-h,n2hi); |
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kmulsfum(n1hi,n2hi,hi); kmulsfum(n1lo,n2lo,lo); |
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len = DEG(hi)+1+2*h; t1 = W_UMALLOC(len-1); DEG(t1) = len-1; |
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bzero((char *)COEF(t1),len*sizeof(int)); |
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if ( lo ) |
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bcopy((char *)COEF(lo),(char *)COEF(t1),(DEG(lo)+1)*sizeof(int)); |
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if ( hi ) |
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bcopy((char *)COEF(hi),(char *)(COEF(t1)+2*h),(DEG(hi)+1)*sizeof(int)); |
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addsfum(hi,lo,mid1); |
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subsfum(n1hi,n1lo,s1); subsfum(n2lo,n2hi,s2); |
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kmulsfum(s1,s2,mid2); addsfum(mid1,mid2,mid); |
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if ( mid ) { |
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len = DEG(mid)+1+h; t2 = W_UMALLOC(len-1); DEG(t2) = len-1; |
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bzero((char *)COEF(t2),len*sizeof(int)); |
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bcopy((char *)COEF(mid),(char *)(COEF(t2)+h),(DEG(mid)+1)*sizeof(int)); |
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addsfum(t1,t2,nr); |
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} else |
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copyum(t1,nr); |
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} |
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int divsfum(p1,p2,pq) |
int divsfum(p1,p2,pq) |
UM p1,p2,pq; |
UM p1,p2,pq; |
{ |
{ |
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if ( ( hd = c2[d2] ) != _onesf() ) { |
if ( ( hd = c2[d2] ) != _onesf() ) { |
inv = _invsf(hd); |
inv = _invsf(hd); |
for ( pc1 = c2 + d2; pc1 >= c2; pc1-- ) |
for ( pc1 = c2 + d2; pc1 >= c2; pc1-- ) |
*pc1 = _mulsf(*pc1,inv); |
*pc1 = _MULSF(*pc1,inv); |
} else |
} else |
inv = _onesf(); |
inv = _onesf(); |
for ( i = dd, ct = c1+d1; i >= 0; i-- ) |
for ( i = dd, ct = c1+d1; i >= 0; i-- ) |
if ( tmp = *ct-- ) { |
if ( tmp = *ct-- ) { |
tmp = _chsgnsf(tmp); |
tmp = _chsgnsf(tmp); |
for ( j = d2-1, pct = ct, pc1 = c2+j; j >= 0; j--, pct--, pc1-- ) |
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() ) { |
if ( inv != _onesf() ) { |
for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ ) |
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++ ) |
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 ( 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-- ) |
for ( DEG(pq) = j = dd, pc1 = c1+d1, pct = COEF(pq)+j; j >= 0; j-- ) |
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for ( i = DEG(f), dp = COEF(fd)+i-1, sp = COEF(f)+i; |
for ( i = DEG(f), dp = COEF(fd)+i-1, sp = COEF(f)+i; |
i >= 1; i--, dp--, sp-- ) { |
i >= 1; i--, dp--, sp-- ) { |
*dp = _mulsf(*sp,_itosf(i)); |
*dp = _MULSF(*sp,_itosf(i)); |
} |
} |
degum(fd,DEG(f) - 1); |
degum(fd,DEG(f) - 1); |
} |
} |
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i = DEG(f); sp = COEF(f)+i; |
i = DEG(f); sp = COEF(f)+i; |
inv = _invsf(*sp); |
inv = _invsf(*sp); |
for ( ; i >= 0; i--, sp-- ) |
for ( ; i >= 0; i--, sp-- ) |
*sp = _mulsf(*sp,inv); |
*sp = _MULSF(*sp,inv); |
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} |
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void addsfarray(int,int *,int *); |
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void mulsfarray_trunc(int,int *,int *,int *); |
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void mulsflum(n,f1,f2,fr) |
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int n; |
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LUM f1,f2,fr; |
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{ |
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int max; |
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int i,j,**p1,**p2,*px; |
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int *w,*w1,*w2; |
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p1 = (int **)COEF(f1); p2 = (int **)COEF(f2); |
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w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2)); |
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for ( i = DEG(f1); i >= 0; i-- ) { |
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for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
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w1[i] = ( j == -1 ? 0 : 1 ); |
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} |
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for ( i = DEG(f2); i >= 0; i-- ) { |
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for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); |
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w2[i] = ( j == -1 ? 0 : 1 ); |
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} |
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for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) { |
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for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- ) |
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px[i] = 0; |
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for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ ) |
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if ( w1[i] != 0 && w2[j - i] != 0 ) { |
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mulsfarray_trunc(n,p1[i],p2[j - i],w); addsfarray(n,w,px); |
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} |
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} |
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} |
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/* f1 = f1->c[0]+f1->c[1]*y+..., f2 = f2->c[0]+f2->c[1]*y+... mod y^n */ |
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void mulsfbm(bound,f1,f2,fr) |
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int bound; |
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BM f1,f2,fr; |
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{ |
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UM mul,t,s; |
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int i,j,h,d1,d2; |
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if ( DEG(f1) < bound || DEG(f2) < bound ) |
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error("mulsfbm : invalid input"); |
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d1 = degsfbm(bound,f1); |
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d2 = degsfbm(bound,f2); |
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t = W_UMALLOC(d1+d2); |
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s = W_UMALLOC(d1+d2); |
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for ( i = 0; i < bound; i++ ) { |
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mul = COEF(f2)[i]; |
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if ( DEG(mul) >= 0 ) |
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for ( j = 0; i+j < bound; j++ ) { |
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if ( COEF(f1)[j] ) { |
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kmulsfum(COEF(f1)[j],mul,t); |
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addsfum(t,COEF(fr)[i+j],s); |
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cpyum(s,COEF(fr)[i+j]); |
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} |
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} |
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} |
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DEG(fr) = bound; |
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} |
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int degsfbm(bound,f) |
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int bound; |
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BM f; |
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{ |
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int d,i; |
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d = DEG(COEF(f)[0]); |
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for ( i = 1; i < bound; i++ ) |
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d = MAX(DEG(COEF(f)[i]),d); |
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return d; |
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} |
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/* g += f */ |
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void addtosfbm(bound,f,g) |
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int bound; |
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BM f,g; |
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{ |
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int i,d1,d2; |
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UM t; |
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d1 = degsfbm(bound,f); |
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d2 = degsfbm(bound,g); |
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t = W_UMALLOC(MAX(d1,d2)); |
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for ( i = 0; i < bound; i++ ) { |
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addsfum(COEF(f)[i],COEF(g)[i],t); |
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cpyum(t,COEF(g)[i]); |
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} |
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} |
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void addsfarray(n,a1,a2) |
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int n; |
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int *a1,*a2; |
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{ |
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int i; |
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for ( i = 0; i < n; i++, a1++, a2++ ) |
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if ( *a1 ) |
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*a2 = _ADDSF(*a1,*a2); |
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} |
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void mulsfarray_trunc(n,a1,a2,r) |
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int n; |
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int *a1,*a2,*r; |
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{ |
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int mul,i,j; |
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int *c1,*c2,*cr; |
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int *pc1,*pc2,*pcr; |
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bzero(r,n*sizeof(int)); |
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c1 = a1; c2 = a2; cr = r; |
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for ( i = 0; i < n; i++, cr++ ) { |
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if ( mul = *c2++ ) |
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for ( j = 0, pc1 = c1, pcr = cr; j+i < n; j++, pc1++, pcr++ ) |
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if ( *pc1 ) |
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*pcr = _ADDSF(_MULSF(*pc1,mul),*pcr); |
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} |
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} |
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void eucsfum(f1,f2,a,b) |
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UM f1,f2,a,b; |
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{ |
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UM g1,g2,a1,a2,a3,wm,q,tum; |
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int d,dr; |
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/* XXX */ |
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d = DEG(f1) + DEG(f2) + 10; |
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g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); |
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a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); |
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q = W_UMALLOC(d); |
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DEG(a1) = 0; COEF(a1)[0] = _onesf(); DEG(a2) = -1; |
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cpyum(f1,g1); cpyum(f2,g2); |
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while ( 1 ) { |
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dr = divsfum(g1,g2,q); tum = g1; g1 = g2; g2 = tum; |
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if ( ( DEG(g2) = dr ) == -1 ) |
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break; |
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mulsfum(a2,q,wm); subsfum(a1,wm,a3); dr = divsfum(a3,f2,q); |
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tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; |
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} |
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if ( COEF(g1)[0] != _onesf() ) |
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mulssfum(a2,_invsf(COEF(g1)[0]),a); |
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else |
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cpyum(a2,a); |
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mulsfum(a,f1,wm); |
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if ( DEG(wm) >= 0 ) |
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COEF(wm)[0] = _subsf(COEF(wm)[0],_onesf()); |
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else { |
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DEG(wm) = 0; COEF(wm)[0] = _chsgnsf(_onesf()); |
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} |
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divsfum(wm,f2,q); mulssfum(q,_chsgnsf(_onesf()),b); |
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} |
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void shiftsfum(UM,int,UM); |
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void shiftsflum(n,f,ev) |
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int n; |
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LUM f; |
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int ev; |
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{ |
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int d,i,j; |
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UM w,w1; |
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int *coef; |
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int **c; |
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d = f->d; |
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c = f->c; |
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w = W_UMALLOC(n); |
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w1 = W_UMALLOC(n); |
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for ( i = 0; i <= d; i++ ) { |
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coef = c[i]; |
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for ( j = n-1; j >= 0 && coef[j] == 0; j-- ); |
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if ( j <= 0 ) |
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continue; |
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DEG(w) = j; bcopy(coef,COEF(w),(j+1)*sizeof(int)); |
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shiftsfum(w,ev,w1); |
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bcopy(COEF(w1),coef,(j+1)*sizeof(int)); |
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} |
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} |
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/* f(x) -> g(x) = f(x+a) */ |
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void shiftsfum(f,a,g) |
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UM f; |
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int a; |
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UM g; |
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{ |
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int n,i; |
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UM pwr,xa,w,t; |
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int *c; |
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n = DEG(f); |
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if ( n <= 0 ) |
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cpyum(f,g); |
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else { |
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c = COEF(f); |
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/* g = 0 */ |
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DEG(g) = -1; |
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/* pwr = 1 */ |
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pwr = W_UMALLOC(n); DEG(pwr) = 0; COEF(pwr)[0] = _onesf(); |
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/* xa = x+a */ |
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xa = W_UMALLOC(n); DEG(xa) = 1; |
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COEF(xa)[0] = a; COEF(xa)[1] = _onesf(); |
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w = W_UMALLOC(n); |
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t = W_UMALLOC(n); |
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/* g += pwr*c[0] */ |
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for ( i = 0; i <= n; i++ ) { |
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mulssfum(pwr,c[i],w); addsfum(g,w,t); cpyum(t,g); |
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if ( i < n ) { |
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mulsfum(pwr,xa,t); cpyum(t,pwr); |
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} |
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} |
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} |
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} |
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/* f(y) -> f(y+a) */ |
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void shiftsfbm(bound,f,a) |
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int bound; |
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BM f; |
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int a; |
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{ |
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int i,j,d; |
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UM pwr,ya,w,t,s; |
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UM *c; |
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if ( bound <= 0 ) |
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return; |
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else { |
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c = COEF(f); |
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d = DEG(c[0]); |
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for ( i = 1; i < bound; i++ ) |
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d = MAX(DEG(c[i]),d); |
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w = W_UMALLOC(d); |
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t = W_UMALLOC(d); |
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s = W_UMALLOC(bound); |
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/* pwr = 1 */ |
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pwr = W_UMALLOC(bound); 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 < bound; 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 < bound-1 ) { |
|
mulsfum(pwr,ya,s); cpyum(s,pwr); |
|
} |
|
} |
|
} |
|
} |
|
|
|
/* clear the body of f */ |
|
|
|
void clearsflum(bound,n,f) |
|
int bound,n; |
|
LUM f; |
|
{ |
|
int **c; |
|
int i; |
|
|
|
DEG(f) = 0; |
|
for ( c = COEF(f), i = 0; i <= n; i++ ) |
|
bzero(c[i],(bound+1)*sizeof(int)); |
|
} |
|
|
|
void clearsfbm(bound,n,f) |
|
int bound,n; |
|
BM f; |
|
{ |
|
int i; |
|
UM *c; |
|
|
|
DEG(f) = bound; |
|
for ( c = COEF(f), i = 0; i < bound; i++ ) |
|
clearum(c[i],n); |
|
} |
|
|
|
/* f += g */ |
|
|
|
void addtosflum(bound,g,f) |
|
int bound; |
|
LUM g,f; |
|
{ |
|
int dg,i,j; |
|
int **cg,**cf; |
|
|
|
dg = DEG(g); |
|
cg = COEF(g); |
|
cf = COEF(f); |
|
for ( i = 0; i <= dg; i++ ) |
|
for ( j = 0; j <= bound; j++ ) |
|
cf[i][j] = _ADDSF(cf[i][j],cg[i][j]); |
} |
} |