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Initial revision

/* $OpenXM: OpenXM_contrib2/asir2000/engine/H.c,v 1.1 1999/12/03 07:39:08 noro Exp $ */
#include "ca.h"
#include "inline.h"
#include "base.h"
#include <math.h>

void modfctrp(P,int,int,DCP *);
void gensqfrum(int,UM,struct oDUM *);
void srchum(int,UM,UM,UM);
UM *resberle(int,UM,UM *);
int substum(int,UM,int);
void ddd(int,UM,UM *);
void canzas(int,UM,int,UM *,UM *);
int divum(int,UM,UM,UM);
void randum(int,int,UM);
void pwrmodum(int,UM,int,UM,UM);
void spwrum(int,UM,UM *,UM,N,UM);
void spwrum0(int,UM,UM,N,UM);
void mulum(int,UM,UM,UM);
void mulsum(int,UM,int,UM);
void gcdum(int,UM,UM,UM);
void mult_mod_tab(UM,int,UM *,UM,int);
void make_qmat(UM,int,UM *,int ***);
void null_mod(int **,int,int,int *);
void null_to_sol(int **,int *,int,int,UM *);
void newddd(int,UM,UM *);
int irred_check(UM,int);
int berlekamp(UM,int,int,UM *,UM *);
int nfctr_mod(UM,int);
void minipoly_mod(int,UM,UM,UM);
int find_root(int,UM,int *);
void showum(UM);
void showumat(int **,int);
#if 1
#define Mulum mulum
#define Divum divum  
#define Mulsum mulsum
#define Gcdum gcdum  
#endif
    
#define FCTR 0
#define SQFR 1
#define DDD 2
#define NEWDDD 3
			
LUM LUMALLOC();

struct p_pair {
	UM p0;
	UM p1;
	struct p_pair *next;
};

void lnf_mod(int,int,UM,UM,struct p_pair *,UM,UM);

void berle(index,count,f,listp)
int index,count;
P f;
ML *listp;
{
	UM wf,wf1,wf2,wfs,gcd;
	ML flist;
	int fn,fn1,fm,m,n,fhd;
	register int i,j,inv,hd,*ptr,*ptr1;

	n = UDEG(f);
	wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
	wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
	for ( j = 0, fn = n + 1; (j < count) && (fn > 1); ) {
		m = sprime[index++];
		if ( !rem(NM((Q)UCOEF(f)),m) ) 
			continue;
		ptoum(m,f,wf); cpyum(wf,wf1); 
		diffum(m,wf1,wf2); gcdum(m,wf1,wf2,gcd);
		if ( DEG(gcd) > 0 ) 
			continue;
		hd = COEF(wf)[n]; inv = invm(hd,m);
		for ( i = n, ptr = COEF(wf); i >= 0; i-- ) 
			ptr[i] = ( ptr[i] * inv ) % m;
		fn1 = berlecnt(m,wf);
		if ( fn1 < fn ) {
			fn = fn1; fm = m; fhd = hd;
			for ( i = n, ptr = COEF(wf), ptr1 = COEF(wfs); i >= 0; i-- ) 
				ptr1[i] = ptr[i];
		}
		j++;
	}
	DEG(wfs) = n;
	*listp = flist = MLALLOC(fn); flist->n = fn; flist->mod = fm;
/*	berlemain(fm,wfs,(UM *)flist->c); */
	if ( fm == 2 )
		berlemain(fm,wfs,(UM *)flist->c);
	else
		newddd(fm,wfs,(UM *)flist->c);
	for ( i = DEG((UM)(flist->c[0])),
		ptr = COEF((UM)(flist->c[0])),
		hd = fhd, m = fm; i >= 0; i-- )
		ptr[i] = ( ptr[i] * hd ) % m;
}

int berlecnt(mod,f)
register int mod;
UM f;
{
	register int i,j,**c;
	int d,dr,n;
	UM w,q;
	int **almat();

	n = DEG(f); c = almat(n,n);
	w = W_UMALLOC(mod + n); q = W_UMALLOC(mod + n);
	for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) 
		c[d][i - 1] = 1;
	DEG(w) = d; COEF(w)[d] = 1;
	for ( j = d - 1; j >= 0; j-- )
		COEF(w)[j] = 0;
	for ( ; ( i < n ) && ( ( dr = divum(mod,w,f,q) ) != -1 ); i++ ) {
		for ( j = dr; j >= 0; j-- ) 
			COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
		for ( j = mod - 1; j >= 0; j-- ) 
			COEF(w)[j] = 0;
		DEG(w) = dr + mod;
	}
	for ( i = 1; i < n; i++ ) 
		c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
	return berlecntmain(mod,n,n-1,c);
}

/* XXX berlecntmain should not be used for large mod */

int berlecntmain(mod,n,m,c)
register int mod;
int n,m;
register int **c;
{
	register int *p1,*p2,i,j,k,l,a;
	int *tmp,inv;
	int cfs;

	for ( cfs = 1, j = k = 0; j < m; j++ ) {
		for ( i = k; ( n > i ) && ( c[i][j] == 0 ); i++ );
		if ( i == n ) {
			cfs++; continue;
		}
		if ( i != k ) {
			tmp = c[i]; c[i] = c[k]; c[k] = tmp;
		}
		p1 = c[k]; inv = invm((p1[j] + mod) % mod,mod);
		for ( l = j; l < m; l++ )
			p1[l] = ( p1[l] * inv ) % mod;
		for ( i = k + 1; i < n; c[i][j] = 0, i++ ) 
			if ( i != k && ( a = -c[i][j] ) ) 
				for ( l = j + 1, p2 = c[i]; l < m; l++ ) 
					p2[l] = (a*p1[l] + p2[l]) % mod;
		k++;
	}
	return ( cfs );
}

UM *berlemain(mod,f,fp)
register int mod;
UM f;
UM *fp;
{
	UM wg,ws,wf,f0,gcd,q;
	int n;
	register int i;

	n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
	if ( DEG(wg) <= 0 ) {
		f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
		return ( fp );
	}
	f0 = W_UMALLOC(n); cpyum(f,f0);
	ws = W_UMALLOC(n); wf = W_UMALLOC(n);
	q = W_UMALLOC(n); gcd = W_UMALLOC(n);
	for ( i = 0; i < mod; i++ ) {
		cpyum(f0,wf); cpyum(wg,ws);
		COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
		gcdum(mod,wf,ws,gcd);
		if ( DEG(gcd) > 0 ) {
			if ( DEG(gcd) < n ) {
				divum(mod,f0,gcd,q); f0 = q; fp = berlemain(mod,gcd,fp);
			}
			break;
		}
	}
	fp = berlemain(mod,f0,fp);
	return ( fp );
}

void hensel(index,count,f,listp)
int index,count;
P f;
ML *listp;
{
	register int i,j;
	int q,n,bound;
	int *p;
	int **pp;
	ML blist,clist,bqlist,cqlist,rlist;
	UM *b;
	LUM fl,tl;
	LUM *l;

	if ( UDEG(f) == 1 ) {
		*listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
		return;
	}
	berle(index,count,f,&blist);
	if ( blist->n == 1 ) {
		*listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
		return;
	}
	gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
	n = bqlist->n; q = bqlist->mod;
	bqlist->bound = cqlist->bound = bound = mignotte(q,f);
	if ( bound == 1 ) {
		*listp = rlist = MLALLOC(n); 
		rlist->n = n; rlist->mod = q; rlist->bound = bound;
		for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
			tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
			for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
					pp[j][0] = p[j];
		}
	} else {
		W_LUMALLOC((int)UDEG(f),bound,fl);
		ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
	}
}

void hsq(index,count,f,nindex,dcp)
int index,count,*nindex;
P f;
DCP *dcp;
{
	register int i,j,k;
	register int **pp,**fpp;
	register int *px,*py;
	int **wpp;
	int n,dr,tmp,m,b,e,np,dt;
	LUM fpa,wb0,wb1,lcpa,tpa,tlum;
	struct oDUM *dct;
	UM wt,wq0,wq,wr,wm,wm0,wa,ws,wb;
	LUM *llist,*ll;
	UM *dlist,*l,*c;
	ML list,fp,cfp;
	DCP dc;

	sqfrum(index,count,f,nindex,&dct,&fp);
	np = fp->n; m = fp->mod;
	if ( ( np == 1 ) && ( dct[0].n == 1 ) ) {
		NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; *dcp = dc;
		return;
	}
	for ( i = 0, dt = 0; i < np; i++ ) 
		dt = MAX(DEG(dct[i].f),dt);
	b = mig(m,dt,f); fp->bound = b;	
	if ( np == 1 ) {
		nthrootchk(f,dct,fp,dcp);
		return;
	}
	list = W_MLALLOC(np); list->n = np; list->mod = m; list->bound = 1;
	for ( i = 0, ll = (LUM *)list->c; i < np; i++ ) {
		W_LUMALLOC(DEG(dct[i].f),b,ll[i]);
		for ( j = 0, px = COEF(dct[i].f), pp = COEF(ll[i]);
			j <= DEG(ll[i]); j++ )
				pp[j][0] = px[j];
	}
	dtestsql(f,list,dct,&dc);
	if ( dc ) {
		*dcp = dc;
		return;
	}
	n = UDEG(f);
	W_LUMALLOC(n,b,fpa); W_LUMALLOC(0,b,lcpa);
	W_LUMALLOC(n,b,wb0); W_LUMALLOC(n,b,wb1);
	W_LUMALLOC(n,b,tpa);
	wt = W_UMALLOC(n); ws = W_UMALLOC(n);
	wr = W_UMALLOC(n);
	wq = W_UMALLOC(2*n); wq0 = W_UMALLOC(n); 
	wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
	wa = W_UMALLOC(2*n); 
	ptolum(m,b,f,fpa); DEG(lcpa) = 0;
	for ( i = 0, pp = COEF(lcpa), fpp = COEF(fpa); i < b; i++ ) 
		pp[0][i] = fpp[n][i];
	gcdgen(f,fp,&cfp);
	llist = (LUM *) ALLOCA(np*sizeof(LUM));
	dlist = (UM *) ALLOCA(np*sizeof(UM));
	l = (UM *)fp->c; c = (UM *)cfp->c;
	for ( i = 0; i < np; i++ ) {
		W_LUMALLOC(DEG(l[i]),b,llist[i]);
		for ( j = DEG(l[i]), pp = COEF(llist[i]), px = COEF(l[i]); j >= 0; j-- ) 
			pp[j][0] = px[j];
		if ( ( e = dct[i].n ) != 1 ) {
			wb = dct[i].f; 
			dlist[i] = W_UMALLOC(DEG(wb)*e); cpyum(l[i],dlist[i]);
			divum(m,dlist[i],wb,wq); DEG(dlist[i])= DEG(wq);
			for ( k = 0; k <= DEG(wq); k++ ) 
				COEF(dlist[i])[k] = dmb(m,COEF(wq)[k],e,&tmp);
		}
	}
	for ( i = 1; i < b; i++ ) {
		mullum(m,i+1,lcpa,llist[0],wb0);
		for ( j = 1; j < np; j++ ) {
			mullum(m,i+1,llist[j],wb0,wb1);
			tlum = wb0; wb0 = wb1; wb1 = tlum;
		} 
		for ( j = n, px = COEF(wt), pp = COEF(fpa), wpp = COEF(wb0);
			j >= 0; j-- ) 
			px[j] = ( pp[j][i] - wpp[j][i] + m ) % m;
		degum(wt,n);
		for ( j = n, px = COEF(wq0); j >= 0; j-- )
			px[j] = 0;
		for ( j = 1; j < np; j++ ) {
			mulum(m,wt,c[j],wm); dr = divum(m,wm,l[j],wq);
			for ( k = DEG(wq), px = COEF(wq0), py = COEF(wq); k >= 0; k-- ) 
				px[k] = ( px[k] + py[k] ) % m;
			for ( k = dr, pp = COEF(llist[j]), px = COEF(wm); k >= 0; k-- ) 
				pp[k][i] = px[k];
		}
		degum(wq0,n); mulum(m,wq0,l[0],wm);
		mulum(m,wt,c[0],wm0); addum(m,wm,wm0,wa);
		for ( j = DEG(wa), pp = COEF(llist[0]), px = COEF(wa); j >= 0; j-- ) 
			pp[j][i] = px[j];
		for ( j = n, px = COEF(wq0); j >= 0; j-- ) 
			px[j] = 0;
		for ( j = 0; j < np; j++ ) 
			if ( dct[j].n == 1 ) 
				for ( k = 0,
					pp = COEF(llist[j]),
					wpp = COEF(((LUM *)list->c)[j]); 
					k <= DEG(llist[j]); k++ )
					wpp[k][i] = pp[k][i];
			else {
				pwrlum(m,i+1,((LUM *)list->c)[j],dct[j].n,tpa);
				for ( k = 0,
					pp = COEF(llist[j]),
					wpp = COEF(tpa); 
					k <= DEG(l[j]); k++ )
					COEF(wt)[k] = (pp[k][i]-wpp[k][i]+m)%m;
				degum(wt,DEG(l[j])); dr = divum(m,wt,dlist[j],ws);
				if ( dr >= 0 ) {
					*dcp = 0;
					return;
				} else
					for ( k = 0,
						pp = COEF(((LUM *)list->c)[j]); 
						k <= DEG(ws); k++ )
						pp[k][i] = COEF(ws)[k];
			}
		list->bound = i+1; dtestsql(f,list,dct,&dc);
		if ( dc ) {
			*dcp = dc;
			return;
		} 
	}
	*dcp = 0;
}

void gcdgen(f,blist,clistp)
P f;
ML blist,*clistp;
{
	register int i;
	int n,d,mod,np;
	UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
	UM *in,*out;
	ML clist;

	n = UDEG(f); mod = blist->mod; np = blist->n;
	d = 2*n;
	q = W_UMALLOC(d); wf = W_UMALLOC(d);
	wm = W_UMALLOC(d); wx = W_UMALLOC(d);
	wy = W_UMALLOC(d); wu = W_UMALLOC(d);
	wv = W_UMALLOC(d); wg = W_UMALLOC(d);
	wa = W_UMALLOC(d); wb = W_UMALLOC(d);
	ptoum(mod,f,wf); DEG(wg) = 0; COEF(wg)[0] = 1;
	*clistp = clist = MLALLOC(np); clist->mod = mod; clist->n = np;
	for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
		divum(mod,wf,in[i],q); tum = wf; wf = q; q = tum;
		cpyum(wf,wx); cpyum(in[i],wy);
		eucum(mod,wx,wy,wa,wb); mulum(mod,wa,wg,wm);
		DEG(wm) = divum(mod,wm,in[i],q); out[i] = UMALLOC(DEG(wm));
		cpyum(wm,out[i]); mulum(mod,q,wf,wu);
		mulum(mod,wg,wb,wv); addum(mod,wu,wv,wg);
	}
}

/*
	henprep(f,&blist,&clist,&bqlist,&cqlist);
 */

void henprep(f,blist,clist,bqlistp,cqlistp)
P f;
ML blist,clist,*bqlistp,*cqlistp;
{
	register int i,j,k,*px,*py,*pz;
	int n,pmax,dr,tmp,p,p1,mod,np,b,q;
	UM w,wm,wn,wa,wt,wq,wf,quot,tum,*in,*inc,*out,*outc;
	ML bqlist,cqlist;

	n = UDEG(f); p = mod = blist->mod; np = blist->n;
/*	for ( b = 1, q = mod; q <= (unsigned int)(LBASE / (L)mod); q *= mod, b++ ); */
	for ( b = 1, q = mod; q <= ((1<<27) / mod); q *= mod, b++ ); 
	w = W_UMALLOC(n); ptoum(q,f,w);
	wm = W_UMALLOC(2*n); wn = W_UMALLOC(2*n);
	wa = W_UMALLOC(2*n); wt = W_UMALLOC(2*n);
	wq = W_UMALLOC(2*n); wf = W_UMALLOC(2*n);
	quot = W_UMALLOC(2*n);
	*bqlistp = bqlist = MLALLOC(np); *cqlistp = cqlist = MLALLOC(np);
	for ( i = 0; i < n+2; i++ )
		COEF(wq)[i] = 0;
	for ( i = 0,
		  in = (UM *)blist->c, inc = (UM *)clist->c,
		  out = (UM *)bqlist->c, outc = (UM *)cqlist->c;
		  i < np; i++ ) {
		out[i] = C_UMALLOC(n+1); cpyum(in[i],out[i]);
		outc[i] = C_UMALLOC(n+1); cpyum(inc[i],outc[i]);
	}
	for ( pmax = 1, i = b; i > 0; i-- ) 
		pmax *= mod;
	for ( i = 1; i < b; i++, p = p1 ) {
		cpyum(out[0],wm);
		for ( j = 1; j < np; j++ ) {
			mulum(pmax,wm,out[j],wn);
			tum = wm; wm = wn; wn = tum;
		}
		for ( j = n, px = COEF(w), py = COEF(wm), pz = COEF(wt); j >= 0; j-- ) {
			tmp = ( ( px[j] - py[j] ) / p ) % mod;
			pz[j] = ( tmp >= 0? tmp : tmp + mod );
		}
		degum(wt,n);
		for ( j = 1; j < np; j++ ) {
			mulum(mod,wt,inc[j],wm); dr = divum(mod,wm,in[j],quot);
			for ( k = DEG(quot); k >= 0; k-- ) 
				COEF(wq)[k] = ( COEF(wq)[k] + COEF(quot)[k] ) % mod;
			for ( k = dr, px = COEF(out[j]), py = COEF(wm); k >= 0; k-- ) 
				px[k] += p * py[k];
		}
		degum(wq,n); mulum(mod,wq,in[0],wm); 
		mulum(mod,wt,inc[0],wn); addum(mod,wm,wn,wa);
		for ( j = DEG(wa), px = COEF(out[0]), py = COEF(wa); j >= 0; j-- ) 
			px[j] += p * py[j];
		for ( j = n, px = COEF(wq); j >= 0; j-- ) 
			px[j] = 0;
		p1 = p * mod;
		for ( j = n, px = COEF(wt); j >= 1; j-- ) 
			px[j] = 0;
		px[0] = 1;
		for ( j = 0; j < np; j++ ) {
			cpyum(w,wf);
			for ( k = DEG(wf), px = COEF(wf); k >= 0; k-- )
				px[k] %= p1;
			divum(p1,wf,out[j],quot); mulum(p1,outc[j],quot,wm);
			for ( k = DEG(wm), px = COEF(wt), py = COEF(wm); k >= 0; k-- ) 
				px[k] = ( px[k] - py[k] ) % p1;
		}
		degum(wt,n);
		for ( j = DEG(wt), px = COEF(wt); j >= 0; j-- ) 
			px[j] = ((tmp=(px[j]/p)%mod)>= 0?tmp:tmp + mod);
		for ( j = 0; j < np; j++ ) {
			mulum(mod,wt,outc[j],wm); dr = divum(mod,wm,in[j],quot);
			for ( k = dr, px = COEF(outc[j]), py = COEF(wm); k >= 0; k-- ) 
				px[k] += p * py[k];
			degum(outc[j],MAX(DEG(outc[j]),dr));
		}
	}
	bqlist->n = cqlist->n = np;
	bqlist->mod = cqlist->mod = q;
}

/*
	henmain(fl,bqlist,cqlist,listp)
*/

void henmain(f,bqlist,cqlist,listp)
LUM f;
ML bqlist,cqlist,*listp;
{
	register int i,j,k;
	int *px,*py;
	int **pp,**pp1;
	int n,np,mod,bound,dr,tmp;
	UM wt,wq0,wq,wr,wm,wm0,wa,q;
	LUM wb0,wb1,tlum;
	UM *b,*c;
	LUM *l;
	ML list;

	n = DEG(f); np = bqlist->n; mod = bqlist->mod; bound = bqlist->bound;
	*listp = list = MLALLOC(n);
	list->n = np; list->mod = mod; list->bound = bound;
	W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
	wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
	wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
	wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
	b = (UM *)bqlist->c; c = (UM *)cqlist->c; l = (LUM *)list->c; 
	for ( i = 0; i < np; i++ ) {
		l[i] = LUMALLOC(DEG(b[i]),bound);
		for ( j = DEG(b[i]), pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- ) 
			pp[j][0] = px[j];
	}
	for ( i = 1; i < bound; i++ ) {
		mullum(mod,i+1,l[0],l[1],wb0);
		for ( j = 2; j < np; j++ ) {
			mullum(mod,i+1,l[j],wb0,wb1);
			tlum = wb0; wb0 = wb1; wb1 = tlum;
		}
		for ( j = n, px = COEF(wt); j >= 0; j-- )
			px[j] = 0;
		for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- ) {
			tmp = ( pp[j][i] - pp1[j][i] ) % mod;
			COEF(wt)[j] = ( tmp < 0 ? tmp + mod : tmp );
		}
		degum(wt,n);
		for ( j = n, px = COEF(wq0); j >= 0; j-- )
			px[j] = 0;
		for ( j = 1; j < np; j++ ) {
			mulum(mod,wt,c[j],wm); dr = divum(mod,wm,b[j],q);
			for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- ) 
				px[k] = ( px[k] + py[k] ) % mod;
			for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- ) 
				pp[k][i] = px[k];
		}
		degum(wq0,n); mulum(mod,wq0,b[0],wm);
		mulum(mod,wt,c[0],wm0); addum(mod,wm,wm0,wa);
		for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- ) 
			pp[j][i] = px[j];
		for ( j = n, px = COEF(wq0); j >= 0; j-- ) 
			px[j] = 0;
	}
}

static double M;
static int E;

int mignotte(q,f)
int q;
P f;
{
	int p;
	unsigned int *b;
	N c;
	DCP dc;

	for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
		c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
		sqad(b[p-1],(p-1)*BSH);
	}
	if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
	c = NM((Q)COEF(DC(f))); p = PL(c); M *= ((double)BD(c)[p-1]+1.0); E += (p-1) * BSH;
	return (int)ceil( (0.31*(E+UDEG(f)+1)+log10((double)M)) / log10((double)q) );
}

int mig(q,d,f)
int q,d;
P f;
{
	int p;
	unsigned int *b;
	N c;
	DCP dc;

	for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
		c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
		sqad(b[p-1],(p-1)*BSH);
	}
	if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
	c = NM((Q)COEF(DC(f))); p = PL(c);
	M *= (BD(c)[p-1]+1); E += (p-1) * BSH;
	return (int)ceil( (0.31*(E+d+1)+log10((double)M)) / log10((double)q) );
}

void sqad(man,exp)
unsigned int man;
int exp;
{
	int e,sqe;
	unsigned int t;
	double man1,d,sqm;
	int diff;

	if ( man == BMASK ) {
		e = BSH; man1 = 1.0;
	} else {
		man += 1;
		for ( e = 0, t = man; t; e++, t >>= 1 );	
		e--; d = (double)(1<<e);
		man1 = ((double)man)/d;
	}
	exp += e; sqm = man1 * man1; sqe = 2 * exp;
	if ( sqm >= 2.0 ) {
		sqm /= 2.0; sqe++;
	}
	diff = E - sqe;
	if ( diff > 18 ) 
		return;
	if ( diff < -18 ) {
		M = sqm; E = sqe;
		return;
	}
	if ( diff >= 0 )
		M += (sqm / (double)(1<<diff));
	else {
		M = ( ( M / (double)(1<<-diff)) + sqm ); E = sqe;
	}
	if ( M >= 2.0 ) {
		M /= 2.0; E++;
	}
}

void ptolum(q,bound,f,fl)
int q,bound;
P f;
LUM fl;
{
	DCP dc;
	int i,j;
	int **pp;
	int d,br,s;
	unsigned int r;
	int *c;
	unsigned int *m,*w;

	for ( dc = DC(f), pp = COEF(fl); dc; dc = NEXT(dc) ) {
		d = PL(NM((Q)COEF(dc))); m = BD(NM((Q)COEF(dc)));
		c = pp[QTOS(DEG(dc))]; w = (unsigned int *)W_ALLOC(d);
		for ( i = 0; i < d; i++ )
			w[i] = m[i];
		for ( i = 0; d >= 1; ) {
			for ( j = d - 1, r = 0; j >= 0; j-- ) {
				DSAB(q,r,w[j],w[j],r)
			}
			c[i++] = (int)r;
			if ( !w[d-1] ) 
				d--;
		}
		if ( SGN((Q)COEF(dc)) < 0 ) 
			for (i = 0, br = 0; i < bound; i++ ) 
				if ( ( s = -(c[i] + br) ) < 0 ) {
					c[i] = s + q; br = 1;
				} else {
					c[i] = 0; br = 0;
				}
	}
}

void modfctrp(p,mod,flag,dcp)
P p;
int mod,flag;
DCP *dcp;
{
	int cm,n,i,j,k;
	DCP dc,dc0;
	P zp;
	Q c,q;
	UM mp;
	UM *tl;
	struct oDUM *udc,*udc1;

	if ( !p ) {
		*dcp = 0; return;
	}
	ptozp(p,1,&c,&zp); 
	if ( DN(c) || !(cm = rem(NM(c),mod)) ) {
		*dcp = 0; return;
	}
	mp = W_UMALLOC(UDEG(p));
	ptoum(mod,zp,mp);
	if ( (n = DEG(mp)) < 0 ) {
		*dcp = 0; return;
	} else if ( n == 0 ) {
		cm = dmar(cm,COEF(mp)[0],0,mod); STOQ(cm,q); 
		NEWDC(dc); COEF(dc) = (P)q; DEG(dc) = ONE; 
		NEXT(dc) = 0; *dcp = dc;
		return;
	}
	if ( COEF(mp)[n] != 1 ) {
		cm = dmar(cm,COEF(mp)[n],0,mod);
		i = invm(COEF(mp)[n],mod);
		for ( j = 0; j <= n; j++ )
			COEF(mp)[j] = dmar(COEF(mp)[j],i,0,mod);
	}
	W_CALLOC(n+1,struct oDUM,udc);
	gensqfrum(mod,mp,udc);
	switch ( flag ) {
		case FCTR:
			tl = (UM *)ALLOCA((n+1)*sizeof(UM));
			W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
			for ( i = 0,j = 0; udc[i].f; i++ )
				if ( DEG(udc[i].f) == 1 ) {
					udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
				} else {
					bzero((char *)tl,(n+1)*sizeof(UM));
					berlemain(mod,udc[i].f,tl);
					for ( k = 0; tl[k]; k++, j++ ) {
						udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
					}
				}
			udc = udc1; break;
		case SQFR:
			break;
		case DDD:
			tl = (UM *)ALLOCA((n+1)*sizeof(UM));
			W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
			for ( i = 0,j = 0; udc[i].f; i++ )
				if ( DEG(udc[i].f) == 1 ) {
					udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
				} else {
					bzero((char *)tl,(n+1)*sizeof(UM));
					ddd(mod,udc[i].f,tl);
					for ( k = 0; tl[k]; k++, j++ ) {
						udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
					}
				}
			udc = udc1; break;
		case NEWDDD:
			tl = (UM *)ALLOCA((n+1)*sizeof(UM));
			W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
			for ( i = 0,j = 0; udc[i].f; i++ )
				if ( DEG(udc[i].f) == 1 ) {
					udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
				} else {
					bzero((char *)tl,(n+1)*sizeof(UM));
					if ( mod == 2 )
						berlemain(mod,udc[i].f,tl);
					else
						newddd(mod,udc[i].f,tl);
					for ( k = 0; tl[k]; k++, j++ ) {
						udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
					}
				}
			udc = udc1; break;
	}
	NEWDC(dc0); STOQ(cm,q); COEF(dc0) = (P)q; DEG(dc0) = ONE; dc = dc0;
	for ( n = 0; udc[n].f; n++ ) {
		NEWDC(NEXT(dc)); dc = NEXT(dc);
		STOQ(udc[n].n,DEG(dc)); umtop(VR(p),udc[n].f,&COEF(dc));
	}
	NEXT(dc) = 0; *dcp = dc0;
}

void gensqfrum(mod,p,dc)
int mod;
UM p;
struct oDUM *dc;
{
	int n,i,j,d;
	UM t,s,g,f,f1,b;

	if ( (n = DEG(p)) == 1 ) {
		dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
		return;
	}
	t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
	f = W_UMALLOC(n); f1 = W_UMALLOC(n); b = W_UMALLOC(n);
	diffum(mod,p,t); cpyum(p,s); Gcdum(mod,t,s,g); 
	if ( !DEG(g) ) {
		dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
		return;
	}
	cpyum(p,b); cpyum(p,t); Divum(mod,t,g,f);
	for ( i = 0, d = 0; DEG(f); i++ ) {
		while ( 1 ) {
			cpyum(b,t);
			if ( Divum(mod,t,f,s) >= 0 )
				break;
			else {
				cpyum(s,b); d++;
			}
		}
		cpyum(b,t); cpyum(f,s); Gcdum(mod,t,s,f1);
		Divum(mod,f,f1,s); cpyum(f1,f);
		dc[i].f = UMALLOC(DEG(s)); cpyum(s,dc[i].f); dc[i].n = d;
	}
	if ( DEG(b) > 0 ) {
		d = 1;
		while ( 1 ) {
			cpyum(b,t);
			for ( j = DEG(t); j >= 0; j-- )
				if ( COEF(t)[j] && (j % mod) )
					break;
			if ( j >= 0 )
				break;
			else {
				DEG(s) = DEG(t)/mod;
				for ( j = 0; j <= DEG(t); j++ )
					COEF(s)[j] = COEF(t)[j*mod];	
				cpyum(s,b); d *= mod;
			}
		}
		gensqfrum(mod,b,dc+i);
		for ( j = i; dc[j].f; j++ )
			dc[j].n *= d;
	}
}

#if 0
void srchum(mod,p1,p2,gr)
int mod;
UM p1,p2,gr;
{
	UM m,m1,m2,q,r,t,g1,g2;
	int lc,d,d1,d2,i,j,k,l,l1,l2,l3,tmp,adj;
	V v;

	d = MAX(DEG(p1),DEG(p2));
	g1 = W_UMALLOC(d); g2 = W_UMALLOC(d);
	bzero((char *)g1,(d+2)*sizeof(int)); bzero((char *)g2,(d+2)*sizeof(int));
	if ( d == DEG(p1) ) {
		cpyum(p1,g1); cpyum(p2,g2);
	} else {
		cpyum(p1,g2); cpyum(p2,g1);
	}
	if ( ( d1 = DEG(g1) ) > ( d2 = DEG(g2) ) ) {
		j = d1 - 1; adj = 1;
	} else 
		j = d2;
	lc = 1;
	r = W_UMALLOC(d1+d2); q = W_UMALLOC(d1+d2); 
	m1 = W_UMALLOC(d1+d2); t = W_UMALLOC(d1+d2);
	bzero((char *)r,(d1+d2+2)*sizeof(int)); bzero((char *)q,(d1+d2+2)*sizeof(int)); 
	bzero((char *)m1,(d1+d2+2)*sizeof(int)); bzero((char *)t,(d1+d2+2)*sizeof(int)); 
	m = W_UMALLOC(0); bzero((char *)m,2*sizeof(int));
	adj = pwrm(mod,COEF(g2)[DEG(g2)],DEG(g1));
	DEG(m) = 0; COEF(m)[0] = invm(COEF(g2)[DEG(g2)],mod);
	Mulum(mod,g2,m,r); cpyum(r,g2);
	while ( 1 ) {
		if ( ( k = DEG(g2) ) < 0 ) {
			DEG(gr) = -1;
			return;
		}
		if ( k == j ) {
			if ( k == 0 ) {
				DEG(m) = 0; COEF(m)[0] = adj;
				Mulum(mod,g2,m,gr);
				return;
			} else {
				DEG(m) = 0; 
				COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
				Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,t);
				DEG(m) = 0; COEF(m)[0] = dmb(mod,lc,lc,&tmp);
				Divum(mod,r,m,q); cpyum(g2,g1); cpyum(q,g2);
				lc = COEF(g1)[DEG(g1)]; j = k - 1;
			}
		} else {
			d = j - k;
			DEG(m) = 0; COEF(m)[0] = pwrm(mod,COEF(g2)[DEG(g2)],d);
			Mulum(mod,g2,m,m1); l = pwrm(mod,lc,d);
			DEG(m) = 0; COEF(m)[0] = l; Divum(mod,m1,m,t);
			if ( k == 0 ) {
				DEG(m) = 0; COEF(m)[0] = adj;
				Mulum(mod,t,m,gr);
				return;
			} else {
				DEG(m) = 0; 
				COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
				Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,q);
				l1 = dmb(mod,lc,lc,&tmp); l2 = dmb(mod,l,l1,&tmp);
				DEG(m) = 0; COEF(m)[0] = l2;
				Divum(mod,r,m,q); cpyum(t,g1); cpyum(q,g2);
				if ( d % 2 ) 
					for ( i = DEG(g2); i >= 0; i-- ) 
						COEF(g2)[i] = ( mod - COEF(g2)[i] ) % mod;
				lc = COEF(g1)[DEG(g1)]; j = k - 1;
			}
		}
	}
}

UM *resberle(mod,f,fp)
register int mod;
UM f;
UM *fp;
{
	UM w,wg,ws,wf,f0,gcd,q,res;
	int n;
	register int i;

	n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
	if ( DEG(wg) <= 0 ) {
		f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
		return ( fp );
	}
	f0 = W_UMALLOC(n); cpyum(f,f0);
	ws = W_UMALLOC(n); wf = W_UMALLOC(n);
	q = W_UMALLOC(n); gcd = W_UMALLOC(n);
	res = W_UMALLOC(2*n);
	srchum(mod,f,wg,res);
	for ( i = 0; i < mod; i++ ) {
		if ( substum(mod,res,i)	)
			continue;
		cpyum(f0,wf); cpyum(wg,ws);
		COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
		Gcdum(mod,wf,ws,gcd);
		if ( DEG(gcd) > 0 ) {
			if ( DEG(gcd) < n ) {
				Divum(mod,f0,gcd,q); f0 = q; fp = resberle(mod,gcd,fp);
			}
			break;
		}
	}
	fp = resberle(mod,f0,fp);
	return ( fp );
}

int substum(mod,p,a)
int mod;
UM p;
int a;
{
	int i,j,s;
	int *c;

	if ( DEG(p) < 0 )
		return 0;
	if ( DEG(p) == 0 )
		return COEF(p)[0];
	for ( i = DEG(p), c = COEF(p), s = c[i]; i >= 0; ) {
		for ( j = i--; (i>=0) && !c[i]; i-- );
		if ( i >= 0 )
			s = (s*pwrm(mod,a,j-i)%mod+c[i])%mod;
		else
			s = s*pwrm(mod,a,j)%mod;
	}
	return s;
}
#endif

void ddd(mod,f,r)
int mod;
UM f,*r;
{
	register int i,j;
	int d,n;
	UM q,s,t,u,v,w,g,x,m;
	UM *base;

	n = DEG(f);
	if ( n == 1 ) {
		r[0] = UMALLOC(1); cpyum(f,r[0]); r[1] = 0; return;
	}
	base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
	w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
	base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
	t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
	pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
	for ( i = 2; i < n; i++ ) {
		mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
		base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
	}
	v = W_UMALLOC(n); cpyum(f,v);
	DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
	x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
	t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
	for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
		for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
			if ( COEF(w)[i] ) {
				Mulsum(mod,base[i],COEF(w)[i],s); 
				addum(mod,s,t,u); cpyum(u,t);
			}
		cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
		if ( DEG(g) >= 1 ) {
			canzas(mod,g,d,base,r+j); j += DEG(g)/d;
			Divum(mod,v,g,q); cpyum(q,v);
			DEG(w) = Divum(mod,w,v,q);
			for ( i = 0; i < DEG(v); i++ )
				DEG(base[i]) = Divum(mod,base[i],v,q);
		}
	}
	if ( DEG(v) ) {
		r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
	}
	r[j] = 0;
}

#if 0
void canzas(mod,f,d,base,r)
int mod;
UM f,*base,*r;
{
	UM t,s,u,w,g,o,q;
	N n1,n2,n3,n4,n5;
	UM *b;
	int n,m,i;

	if ( DEG(f) == d ) {
		r[0] = UMALLOC(d); cpyum(f,r[0]);
		return;
	} else {
		n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
		for ( i = 0, m = 0; i < n; i++ )
			m = MAX(m,DEG(base[i]));
		q = W_UMALLOC(m);
		for ( i = 0; i < n; i++ ) {
			b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
			DEG(b[i]) = Divum(mod,b[i],f,q);
		}
		t = W_UMALLOC(2*d);
		s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f)); 
		w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
		o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
		STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
		STON(2,n4); divsn(n3,n4,&n5);
		while ( 1 ) {
			randum(mod,2*d,t); spwrum(mod,f,b,t,n5,s);
			subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
			if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
				canzas(mod,g,d,b,r); 
				cpyum(f,w); Divum(mod,w,g,s);
				canzas(mod,s,d,b,r+DEG(g)/d); 
				return;
			}
		}
	}
}
#else
void canzas(mod,f,d,base,r)
int mod;
UM f,*base,*r;
{
	UM t,s,u,w,g,o,q;
	N n1,n2,n3,n4,n5;
	UM *b;
	int n,m,i;

	if ( DEG(f) == d ) {
		r[0] = UMALLOC(d); cpyum(f,r[0]);
		return;
	} else {
		n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
		for ( i = 0, m = 0; i < n; i++ )
			m = MAX(m,DEG(base[i]));
		q = W_UMALLOC(m);
		for ( i = 0; i < n; i++ ) {
			b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
			DEG(b[i]) = Divum(mod,b[i],f,q);
		}
		t = W_UMALLOC(2*d);
		s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f)); 
		w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
		o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
		STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
		STON(2,n4); divsn(n3,n4,&n5);
		while ( 1 ) {
			randum(mod,2*d,t); spwrum0(mod,f,t,n5,s);
			subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
			if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
				canzas(mod,g,d,b,r); 
				cpyum(f,w); Divum(mod,w,g,s);
				canzas(mod,s,d,b,r+DEG(g)/d); 
				return;
			}
		}
	}
}
#endif

void randum(mod,d,p)
int mod,d;
UM p;
{
	unsigned int n;
	int i;

	n = ((unsigned int)random()) % d; DEG(p) = n; COEF(p)[n] = 1;
	for ( i = 0; i < (int)n; i++ )
		COEF(p)[i] = ((unsigned int)random()) % mod;
}

void pwrmodum(mod,p,e,f,pr)
int mod,e;
UM p,f,pr;
{
	UM wt,ws,q;

	if ( e == 0 ) {
		DEG(pr) = 0; COEF(pr)[0] = 1;
	} else if ( DEG(p) < 0 ) 
		DEG(pr) = -1;
	else if ( e == 1 ) {
		q = W_UMALLOC(DEG(p)); cpyum(p,pr);
		DEG(pr) = divum(mod,pr,f,q);
	} else if ( DEG(p) == 0 ) {
		DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
	} else {
		wt = W_UMALLOC(2*DEG(f)); ws = W_UMALLOC(2*DEG(f));
		q = W_UMALLOC(2*DEG(f));
		pwrmodum(mod,p,e/2,f,wt);
		if ( !(e%2) )  {
			mulum(mod,wt,wt,pr); DEG(pr) = divum(mod,pr,f,q);
		} else {
			mulum(mod,wt,wt,ws); DEG(ws) = divum(mod,ws,f,q);
			mulum(mod,ws,p,pr); DEG(pr) = divum(mod,pr,f,q);
		}
	}
}

void spwrum(mod,m,base,f,e,r)
int mod;
UM f,m,r;
UM *base;
N e;
{
	int a,n,i;
	N e1,an;
	UM t,s,u,q,r1,r2;

	if ( !e ) {
		DEG(r) = 0; COEF(r)[0] = 1;
	} else if ( UNIN(e) )
		cpyum(f,r);
	else if ( (PL(e) == 1) && (BD(e)[0] < (unsigned int)mod) )
		spwrum0(mod,m,f,e,r);
	else {
		a = divin(e,mod,&e1); STON(a,an);
		n = DEG(m); t = W_UMALLOC(n); s = W_UMALLOC(n); 
		u = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
		for ( DEG(t) = -1, i = 0; i <= DEG(f); i++ )
			if ( COEF(f)[i] ) {
				Mulsum(mod,base[i],COEF(f)[i],s); 
				addum(mod,s,t,u); cpyum(u,t);
			}
		r1 = W_UMALLOC(n); spwrum0(mod,m,f,an,r1);
		r2 = W_UMALLOC(n); spwrum(mod,m,base,t,e1,r2);
		Mulum(mod,r1,r2,u); DEG(u) = Divum(mod,u,m,q);
		cpyum(u,r);
	}
}

void spwrum0(mod,m,f,e,r)
int mod;
UM f,m,r;
N e;
{
	UM t,s,q;
	N e1;
	int a;

	if ( !e ) {
		DEG(r) = 0; COEF(r)[0] = 1;
	} else if ( UNIN(e) )
		cpyum(f,r);
	else {
		a = divin(e,2,&e1);
		t = W_UMALLOC(2*DEG(m)); spwrum0(mod,m,f,e1,t);
		s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
		Mulum(mod,t,t,s); DEG(s) = Divum(mod,s,m,q);
		if ( a ) {
			Mulum(mod,s,f,t); DEG(t) = Divum(mod,t,m,q); cpyum(t,r);
        } else
			cpyum(s,r);
	}
}

#if 0
void Mulum(mod,p1,p2,pr)
register int mod;
UM p1,p2,pr;
{
	register int *pc1,*pcr;
	register int mul,i,j,d1,d2;
	int *c1,*c2,*cr;

	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,(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++ )
				*pcr = (*pc1 * mul + *pcr) % mod;
	DEG(pr) = d1 + d2;
}

void Mulsum(mod,p,n,pr)
register int mod,n;
UM p,pr;
{
	register int *sp,*dp;
	register int i;

	for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i; 
		  i >= 0; i--, dp--, sp-- )
		*dp = (*sp * n) % mod;
}
	
int Divum(mod,p1,p2,pq)
register int mod;
UM p1,p2,pq;
{
	register int *pc1,*pct;
	register int tmp,i,j,inv;
	int *c1,*c2,*ct;
	int d1,d2,dd,hd;

	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] ) != 1 ) {
		inv = invm(hd,mod);
		for ( pc1 = c2 + d2; pc1 >= c2; pc1-- )
			*pc1 = (*pc1 * inv) % mod;
	} else 
		inv = 1;
	for ( i = dd, ct = c1+d1; i >= 0; i-- ) 
		if ( tmp = *ct-- ) {
			tmp = mod - tmp;
			for ( j = d2-1, pct = ct, pc1 = c2+j; j >= 0; j--, pct--, pc1-- )
				*pct = (*pc1 * tmp + *pct) % mod;
		}
	if ( inv != 1 ) {
		for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ )
			*pc1 = (*pc1 * inv) % mod;
		for ( pc1 = c2, pct = c2+d2, inv = hd; pc1 <= pct; pc1++ )
			*pc1 = (*pc1 * inv) % mod;
	}
	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 Gcdum(mod,p1,p2,pr)
register int mod;
UM p1,p2,pr;
{
	register int *sp,*dp;
	register int i,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 = Divum(mod,t1,t2,q) ) >= 0 ) {
			tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
		}
		inv = invm(COEF(t2)[DEG(t2)],mod);
		Mulsum(mod,t2,inv,pr);
	}
}
#endif

void mult_mod_tab(p,mod,tab,r,d)
UM p,r;
UM *tab;
int mod,d;
{
	UM w,w1,c;
	int n,i;
	int *pc;

	w = W_UMALLOC(d); w1 = W_UMALLOC(d);
	c = W_UMALLOC(1); DEG(c) = 0;
	n = DEG(p); DEG(r) = -1;
	for ( i = 0, pc = COEF(p); i <= n; i++ )
		if ( pc[i] ) {
			COEF(c)[0] = pc[i];
			mulum(mod,tab[i],c,w);
			addum(mod,r,w,w1);
			cpyum(w1,r);
		}
}

void make_qmat(p,mod,tab,mp)
UM p;
int mod;
UM *tab;
int ***mp;
{
	int n,i,j;
	int *c;
	UM q,r;
	int **mat;

	n = DEG(p);
	*mp = mat = almat(n,n);
	for ( j = 0; j < n; j++ ) {
		r = W_UMALLOC(DEG(tab[j])); q = W_UMALLOC(DEG(tab[j]));	
		cpyum(tab[j],r); DEG(r) = divum(mod,r,p,q);
		for ( i = 0, c = COEF(r); i <= DEG(r); i++ )
			mat[i][j] = c[i];
	}
	for ( i = 0; i < n; i++ )
		mat[i][i] = (mat[i][i]+mod-1) % mod;
}

void null_mod(mat,mod,n,ind)
int **mat;
int *ind;
int mod,n;
{
	int i,j,l,s,h,inv;
	int *t,*u;

	bzero((char *)ind,n*sizeof(int));
	ind[0] = 0;
	for ( i = j = 0; j < n; i++, j++ ) {
		for ( ; j < n; j++ ) {
			for ( l = i; l < n; l++ )
				if ( mat[l][j] )
					break;
			if ( l < n ) {
				t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
			} else
				ind[j] = 1;
		}
		if ( j == n )
			break;
		inv = invm(mat[i][j],mod);
		for ( s = j, t = mat[i]; s < n; s++ )
			t[s] =  dmar(t[s],inv,0,mod);
		for ( l = 0; l < n; l++ ) {
			if ( l == i )
				continue;
			for ( s = j, u = mat[l], h = (mod-u[j])%mod; s < n; s++ )
				u[s] = dmar(h,t[s],u[s],mod);
		}
	}
}

void null_to_sol(mat,ind,mod,n,r)
int **mat;
int *ind;
int mod,n;
UM *r;
{
	int i,j,k,l;
	int *c;
	UM w;

	for ( i = 0, l = 0; i < n; i++ ) {
		if ( !ind[i] )
			continue;
		w = UMALLOC(n);
		for ( j = k = 0, c = COEF(w); j < n; j++ )
			if ( ind[j] )
				c[j] = 0;
			else
				c[j] = mat[k++][i];
		c[i] = mod-1;
		for ( j = n; j >= 0; j-- )
			if ( c[j] )
				break;
		DEG(w) = j;
		r[l++] = w;
	}
}
/*
make_qmat(p,mod,tab,mp)
null_mod(mat,mod,n,ind)
null_to_sol(mat,ind,mod,n,r)
*/

void newddd(mod,f,r)
int mod;
UM f,*r;
{
	register int i,j;
	int d,n;
	UM q,s,t,u,v,w,g,x,m;
	UM *base;

	n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
	w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
	base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
	t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
	pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
	for ( i = 2; i < n; i++ ) {
/*		fprintf(stderr,"i=%d\n",i); */
		mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
		base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
	}
	v = W_UMALLOC(n); cpyum(f,v);
	DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
	x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
	t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
	for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
/*		fprintf(stderr,"d=%d\n",d); */
		for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
			if ( COEF(w)[i] ) {
				Mulsum(mod,base[i],COEF(w)[i],s); 
				addum(mod,s,t,u); cpyum(u,t);
			}
		cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
		if ( DEG(g) >= 1 ) {
			berlekamp(g,mod,d,base,r+j); j += DEG(g)/d;
			Divum(mod,v,g,q); cpyum(q,v);
			DEG(w) = Divum(mod,w,v,q);
			for ( i = 0; i < DEG(v); i++ )
				DEG(base[i]) = Divum(mod,base[i],v,q);
		}
	}
	if ( DEG(v) ) {
		r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
	}
	r[j] = 0;
}

int nfctr_mod(f,mod)
int mod;
UM f;
{
	register int i,j;
	int d,n;
	UM q,s,t,u,v,w,g,x,m;
	UM *base;

	n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
	w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
	base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
	t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
	pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
	for ( i = 2; i < n; i++ ) {
/*		fprintf(stderr,"i=%d\n",i); */
		mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
		base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
	}
	v = W_UMALLOC(n); cpyum(f,v);
	DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
	x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
	t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
	for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
/*		fprintf(stderr,"d=%d\n",d); */
		for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
			if ( COEF(w)[i] ) {
				Mulsum(mod,base[i],COEF(w)[i],s); 
				addum(mod,s,t,u); cpyum(u,t);
			}
		cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
		if ( DEG(g) >= 1 ) {
			j += DEG(g)/d;
			Divum(mod,v,g,q); cpyum(q,v);
			DEG(w) = Divum(mod,w,v,q);
			for ( i = 0; i < DEG(v); i++ )
				DEG(base[i]) = Divum(mod,base[i],v,q);
		}
	}
	if ( DEG(v) ) j++;
	return j;
}

int irred_check(f,mod)
UM f;
int mod;
{
	register int i,j;
	int d,n;
	UM q,s,t,u,v,w,g,x,m,f1,b;
	UM *base;

	if ( (n = DEG(f)) == 1 )
		return 1;
	t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
	f1 = W_UMALLOC(n); b = W_UMALLOC(n);
	diffum(mod,f,t); cpyum(f,s); Gcdum(mod,t,s,g); 
	if ( DEG(g) )
		return 0;

	base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
	w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
	base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
	t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
	pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
	for ( i = 2; i < n; i++ ) {
/*		fprintf(stderr,"i=%d\n",i); */
		mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
		base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
	}
	v = W_UMALLOC(n); cpyum(f,v);
	DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
	x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
	t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
	for ( j = 0, d = 1; 2*d <= n; d++ ) {
/*		fprintf(stderr,"d=%d\n",d); */
		for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
			if ( COEF(w)[i] ) {
				Mulsum(mod,base[i],COEF(w)[i],s); 
				addum(mod,s,t,u); cpyum(u,t);
			}
		cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
		if ( DEG(g) >= 1 )
			return 0;
	}
	return 1;
}

int berlekamp(p,mod,df,tab,r)
UM p;
int mod,df;
UM *tab,*r;
{
	int n,i,j,k,nf,d,nr;
	int **mat;
	int *ind;
	UM mp,w,q,gcd,w1,w2;
	UM *u;
	int *root;

	n = DEG(p);
	ind = ALLOCA(n*sizeof(int));
	make_qmat(p,mod,tab,&mat);
	null_mod(mat,mod,n,ind);
	for ( i = 0, d = 0; i < n; i++ )
		if ( ind[i] )
			d++;
	if ( d == 1 ) {
		r[0] = UMALLOC(n); cpyum(p,r[0]); return 1;
	}
	u = ALLOCA(d*sizeof(UM *));
	r[0] = UMALLOC(n); cpyum(p,r[0]);
	null_to_sol(mat,ind,mod,n,u);
	root = ALLOCA(d*sizeof(int));
	w = W_UMALLOC(n); mp = W_UMALLOC(d);
	w1 = W_UMALLOC(n); w2 = W_UMALLOC(n);
	for ( i = 1, nf = 1; i < d; i++ ) {
		minipoly_mod(mod,u[i],p,mp);
		nr = find_root(mod,mp,root);
		for ( j = 0; j < nf; j++ ) {
			if ( DEG(r[j]) == df )
				continue;
			for ( k = 0; k < nr; k++ ) {
				cpyum(u[i],w1); cpyum(r[j],w2);
				COEF(w1)[0] = (mod-root[k]) % mod;
				gcdum(mod,w1,w2,w);
				if ( DEG(w) > 0 && DEG(w) < DEG(r[j]) ) {
					gcd = UMALLOC(DEG(w));
					q = UMALLOC(DEG(r[j])-DEG(w));
					cpyum(w,gcd); divum(mod,r[j],w,q);
					r[j] = q; r[nf++] = gcd;
				}
				if ( nf == d )
					return d;
			}
		}
	}
}

void minipoly_mod(mod,f,p,mp)
int mod;
UM f,p,mp;
{
	struct p_pair *list,*l,*l1,*lprev;	
	int n,d;
	UM u,p0,p1,np0,np1,q,w;

	list = (struct p_pair *)MALLOC(sizeof(struct p_pair));
	list->p0 = u = W_UMALLOC(0); DEG(u) = 0; COEF(u)[0] = 1;
	list->p1 = W_UMALLOC(0); cpyum(list->p0,list->p1);
	list->next = 0;
	n = DEG(p); w = UMALLOC(2*n);
	p0 = UMALLOC(2*n); cpyum(list->p0,p0);
	p1 = UMALLOC(2*n); cpyum(list->p1,p1);
	q = W_UMALLOC(2*n);
	while ( 1 ) {
		COEF(p0)[DEG(p0)] = 0; DEG(p0)++; COEF(p0)[DEG(p0)] = 1;
		mulum(mod,f,p1,w); DEG(w) = divum(mod,w,p,q); cpyum(w,p1);
		np0 = UMALLOC(n); np1 = UMALLOC(n);
		lnf_mod(mod,n,p0,p1,list,np0,np1);
		if ( DEG(np1) < 0 ) {
			cpyum(np0,mp); return;
		} else {
			l1 = (struct p_pair *)MALLOC(sizeof(struct p_pair));
			l1->p0 = np0; l1->p1 = np1;
			for ( l = list, lprev = 0, d = DEG(np1);
				l && (DEG(l->p1) > d); lprev = l, l = l->next );
			if ( lprev ) {
				lprev->next = l1; l1->next = l;
			} else {
				l1->next = list; list = l1;
			}
		}
	}
}

void lnf_mod(mod,n,p0,p1,list,np0,np1)
int mod,n;
UM p0,p1;
struct p_pair *list;
UM np0,np1;
{
	int inv,h,d1;
	UM t0,t1,s0,s1;
	struct p_pair *l;

	cpyum(p0,np0); cpyum(p1,np1);
	t0 = W_UMALLOC(n); t1 = W_UMALLOC(n);
	s0 = W_UMALLOC(n); s1 = W_UMALLOC(n);
	for ( l = list; l; l = l->next ) {
		d1 = DEG(np1);
		if ( d1 == DEG(l->p1) ) {
			inv = invm((mod-COEF(l->p1)[d1])%mod,mod);
			h = dmar(COEF(np1)[d1],inv,0,mod);
			mulsum(mod,l->p0,h,t0); addum(mod,np0,t0,s0); cpyum(s0,np0);
			mulsum(mod,l->p1,h,t1); addum(mod,np1,t1,s1); cpyum(s1,np1);
		}
	}
}

int find_root(mod,p,root)
int mod;
UM p;
int *root;
{
	UM *r;
	int i,j;

	r = ALLOCA((DEG(p)+1)*sizeof(UM));
	ddd(mod,p,r);
	for ( i = 0, j = 0; r[i]; i++ )
		if ( DEG(r[i]) == 1 )
			root[j++] = (mod - COEF(r[i])[0]) % mod;
	return j;
}

void showum(p)
UM p;
{
	int i;
	int *c;

	for ( i = DEG(p), c = COEF(p); i >= 0; i-- )
		if ( c[i] )
			printf("+%dx^%d",c[i],i);
	printf("\n");
}

void showumat(mat,n)
int **mat;
int n;
{
	int i,j;

	for ( i = 0; i < n; i++ ) {
		for ( j = 0; j < n; j++ )
			printf("%d ",mat[i][j]);
		printf("\n");
	}
}