Return to gmpq.c CVS log

Up to [local] / OpenXM_contrib2 / asir2000 / engine

Improved nd_f4_red_mod64().

#include "ca.h"
#include "gmp.h"
#include "base.h"
#include "inline.h"

mpz_t ONEMPZ;
GZ ONEGZ;
int lf_lazy;
GZ current_mod_lf;
int current_mod_lf_size;

void isqrtgz(GZ a,GZ *r);
void bshiftgz(GZ a,int n,GZ *r);

void *gc_realloc(void *p,size_t osize,size_t nsize)
{
	return (void *)Risa_GC_realloc(p,nsize);	
}

void gc_free(void *p,size_t size)
{
	Risa_GC_free(p);
}

void init_gmpq()
{
	mp_set_memory_functions(Risa_GC_malloc,gc_realloc,gc_free);

	mpz_init(ONEMPZ); mpz_set_ui(ONEMPZ,1); MPZTOGZ(ONEMPZ,ONEGZ);
}

GZ utogz(unsigned int u)
{
	mpz_t z;
	GZ r;

	if ( !u ) return 0;
	mpz_init(z); mpz_set_ui(z,u); MPZTOGZ(z,r); return r;
}

GZ stogz(int s)
{
	mpz_t z;
	GZ r;

	if ( !s ) return 0;
	mpz_init(z); mpz_set_si(z,s); MPZTOGZ(z,r); return r;
}

GQ mpqtogzq(mpq_t a)
{
	GZ z;
	GQ q;

	if ( INTMPQ(a) ) {
		MPZTOGZ(mpq_numref(a),z); return (GQ)z;
	} else {
		MPQTOGQ(a,q); return q;
	}
}

GZ ztogz(Q a)
{
	mpz_t z;
	mpq_t b;
	N nm;
	GZ s;

	if ( !a ) return 0;
	nm = NM(a);
	mpz_init(z);
	mpz_import(z,PL(nm),-1,sizeof(BD(nm)[0]),0,0,BD(nm));
	if ( SGN(a)<0 ) mpz_neg(z,z);
	MPZTOGZ(z,s);
	return s;
}

Q gztoz(GZ a)
{
	N nm;
	Q q;
	int sgn;
	size_t len;

	if ( !a ) return 0;
	len = WORDSIZE_IN_N(BDY((GZ)a)); nm = NALLOC(len);
	mpz_export(BD(nm),&len,-1,sizeof(int),0,0,BDY((GZ)a));
	PL(nm) = len;
	sgn = mpz_sgn(BDY((GZ)a)); NTOQ(nm,sgn,q);
	return q;
}

void dupgz(GZ a,GZ *b)
{
  mpz_t t;

  if ( !a ) *b = a;
  else {
    mpz_init(t); mpz_set(t,BDY(a)); MPZTOGZ(t,*b);
  }
}

int n_bits_gz(GZ a)
{
	return a ? mpz_sizeinbase(BDY(a),2) : 0;
}

GQ qtogq(Q a)
{
	mpz_t z;
	mpq_t b;
	N nm,dn;
	GZ s;
	GQ r;

	if ( !a ) return 0;
	if ( INT(a) ) {
		nm = NM(a);
		mpz_init(z);
		mpz_import(z,PL(nm),-1,sizeof(BD(nm)[0]),0,0,BD(nm));
		if ( SGN(a)<0 ) mpz_neg(z,z);
		MPZTOGZ(z,s);
		return (GQ)s;
	} else {
		nm = NM(a); dn = DN(a);
		mpq_init(b);
		mpz_import(mpq_numref(b),PL(nm),-1,sizeof(BD(nm)[0]),0,0,BD(nm));
		mpz_import(mpq_denref(b),PL(dn),-1,sizeof(BD(dn)[0]),0,0,BD(dn));
		if ( SGN(a)<0 ) mpq_neg(b,b);
		MPQTOGQ(b,r);
		return r;
	}
}

Q gqtoq(GQ a)
{
	N nm,dn;
	Q q;
	int sgn;
	size_t len;

	if ( !a ) return 0;
	if ( NID(a) == N_GZ ) {
		len = WORDSIZE_IN_N(BDY((GZ)a)); nm = NALLOC(len);
		mpz_export(BD(nm),&len,-1,sizeof(int),0,0,BDY((GZ)a));
		PL(nm) = len;
		sgn = mpz_sgn(BDY((GZ)a)); NTOQ(nm,sgn,q);
	} else {
		len = WORDSIZE_IN_N(mpq_numref(BDY(a))); nm = NALLOC(len);
		mpz_export(BD(nm),&len,-1,sizeof(int),0,0,mpq_numref(BDY(a)));
		PL(nm) = len;
		len = WORDSIZE_IN_N(mpq_denref(BDY(a))); dn = NALLOC(len);
		mpz_export(BD(dn),&len,-1,sizeof(int),0,0,mpq_denref(BDY(a)));
		PL(dn) = len;
		sgn = mpz_sgn(mpq_numref(BDY(a))); NDTOQ(nm,dn,sgn,q);
	}
	return q;
}

P ptogp(P a)
{
	DCP dc,dcr,dcr0;
	P b;

	if ( !a ) return 0;
	if ( NUM(a) ) return (P)qtogq((Q)a);
	for ( dc = DC(a), dcr0 = 0; dc; dc = NEXT(dc) ) {
		NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = (P)ptogp(COEF(dc));
	}
	NEXT(dcr) = 0; MKP(VR(a),dcr0,b);
	return b;
}

P gptop(P a)
{
	DCP dc,dcr,dcr0;
	P b;

	if ( !a ) return 0;
	if ( NUM(a) ) b = (P)gqtoq((GQ)a); 
	else {
		for ( dc = DC(a), dcr0 = 0; dc; dc = NEXT(dc) ) {
			NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); 
			COEF(dcr) = (P)gptop(COEF(dc));
		}
		NEXT(dcr) = 0; MKP(VR(a),dcr0,b);
	}
	return b;
}

void addgz(GZ n1,GZ n2,GZ *nr)
{
	mpz_t t;
	int s1,s2;

	if ( !n1 ) *nr = n2;
	else if ( !n2 ) *nr = n1;
	else {
		mpz_init(t); mpz_add(t,BDY(n1),BDY(n2)); MPZTOGZ(t,*nr);
	}
}

void subgz(GZ n1,GZ n2,GZ *nr)
{
	mpz_t t;

	if ( !n1 ) 
		if ( !n2 ) 
			*nr = 0;
		else {
			t[0] = BDY(n2)[0]; mpz_neg(t,t); MPZTOGZ(t,*nr);
		}
	else if ( !n2 ) 
		*nr = n1;
	else if ( n1 == n2 ) 
		*nr = 0;
	else {
		mpz_init(t); mpz_sub(t,BDY(n1),BDY(n2)); MPZTOGZ(t,*nr);
	}
}

void mulgz(GZ n1,GZ n2,GZ *nr)
{
	mpz_t t;

	if ( !n1 || !n2 ) *nr = 0;
#if 1
	else if ( UNIGZ(n1) ) *nr = n2;
	else if ( UNIGZ(n2) ) *nr = n1;
	else if ( MUNIGZ(n1) ) chsgngz(n2,nr);
	else if ( MUNIGZ(n2) ) chsgngz(n1,nr);
#endif
	else {
		mpz_init(t); mpz_mul(t,BDY(n1),BDY(n2)); MPZTOGZ(t,*nr);
	}
}

/* nr += n1*n2 */

void muladdtogz(GZ n1,GZ n2,GZ *nr)
{
    GZ t;

	if ( n1 && n2 ) {
        if ( !(*nr) ) {
          NEWGZ(t); mpz_init(BDY(t)); *nr = t;
        }
        mpz_addmul(BDY(*nr),BDY(n1),BDY(n2));
    }
}

void mul1gz(GZ n1,int n2,GZ *nr)
{
	mpz_t t;

	if ( !n1 || !n2 ) *nr = 0;
	else {
		mpz_init(t); mpz_mul_ui(t,BDY(n1),(long)n2); MPZTOGZ(t,*nr);
	}
}

void divgz(GZ n1,GZ n2,GZ *nq)
{
	mpz_t t;
	mpq_t a, b, q;

	if ( !n2 ) {
		error("division by 0");
		*nq = 0;
	} else if ( !n1 ) 
		*nq = 0;
	else if ( n1 == n2 ) {
		mpz_init(t); mpz_set_ui(t,1); MPZTOGZ(t,*nq);
	} else {
		MPZTOMPQ(BDY(n1),a); MPZTOMPQ(BDY(n2),b);
		mpq_init(q); mpq_div(q,a,b); *nq = (GZ)mpqtogzq(q);
	}
}

void remgz(GZ n1,GZ n2,GZ *nr)
{
	mpz_t r;

	if ( !n2 ) {
		error("division by 0");
		*nr = 0;
	} else if ( !n1 || n1 == n2 )
		*nr = 0;
	else {
		mpz_init(r);
		mpz_mod(r,BDY(n1),BDY(n2));
		if ( !mpz_sgn(r) ) *nr = 0;
		else MPZTOGZ(r,*nr);
	}
}

void divqrgz(GZ n1,GZ n2,GZ *nq,GZ *nr)
{
	mpz_t t, a, b, q, r;

	if ( !n2 ) {
		error("division by 0");
		*nq = 0; *nr = 0;
	} else if ( !n1 ) {
		*nq = 0; *nr = 0;
	} else if ( n1 == n2 ) {
		mpz_init(t); mpz_set_ui(t,1); MPZTOGZ(t,*nq); *nr = 0;
	} else {
		mpz_init(q); mpz_init(r);
		mpz_fdiv_qr(q,r,BDY(n1),BDY(n2));
		if ( !mpz_sgn(q) ) *nq = 0;
		else MPZTOGZ(q,*nq);
		if ( !mpz_sgn(r) ) *nr = 0;
		else MPZTOGZ(r,*nr);
	}
}

void divsgz(GZ n1,GZ n2,GZ *nq)
{
	mpz_t t;
	mpq_t a, b, q;

	if ( !n2 ) {
		error("division by 0");
		*nq = 0;
	} else if ( !n1 ) 
		*nq = 0;
	else if ( n1 == n2 ) {
		mpz_init(t); mpz_set_ui(t,1); MPZTOGZ(t,*nq);
	} else {
		mpz_init(t); mpz_divexact(t,BDY(n1),BDY(n2)); MPZTOGZ(t,*nq);
	}
}

void chsgngz(GZ n,GZ *nr)
{
	mpz_t t;

	if ( !n )
		*nr = 0;
	else {
		t[0] = BDY(n)[0]; mpz_neg(t,t); MPZTOGZ(t,*nr);
	}
}

void pwrgz(GZ n1,Q n,GZ *nr)
{
	mpq_t t,q;
	mpz_t z;
	GQ p,r;

	if ( !n || UNIGZ(n1) ) *nr = ONEGZ;
	else if ( !n1 ) *nr = 0;
	else if ( !INT(n) ) {
		error("can't calculate fractional power."); *nr = 0;
	} else if ( MUNIGZ(n1) ) *nr = BD(NM(n))[0]%2 ? n1 : ONEGZ;
	else if ( PL(NM(n)) > 1 ) {
		error("exponent too big."); *nr = 0;
	} else if ( NID(n1)==N_GZ && SGN(n)>0 ) {
		mpz_init(z); mpz_pow_ui(z,BDY(n1),QTOS(n)); MPZTOGZ(z,*nr);
	} else {
		MPZTOMPQ(BDY(n1),q); MPQTOGQ(q,r);
		pwrgq(r,n,&p); *nr = (GZ)p;
	}
}

int cmpgz(GZ q1,GZ q2)
{
	int sgn;

	if ( !q1 ) 
		if ( !q2 ) 
			return 0;
		else
			return -mpz_sgn(BDY(q2));
	else if ( !q2 ) 
		return mpz_sgn(BDY(q1));
	else if ( (sgn = mpz_sgn(BDY(q1))) != mpz_sgn(BDY(q2)) ) 
			return sgn;
	else {
		sgn = mpz_cmp(BDY(q1),BDY(q2));
		if ( sgn > 0 ) return 1;
		else if ( sgn < 0 ) return -1;
		else return 0;
	}
}

void gcdgz(GZ n1,GZ n2,GZ *nq)
{
	mpz_t t;

	if ( !n1 ) *nq = n2;
	else if ( !n2 ) *nq = n1;
	else {
		mpz_init(t); mpz_gcd(t,BDY(n1),BDY(n2));
		MPZTOGZ(t,*nq);
	}
}

void invgz(GZ n1,GZ *nq)
{
	mpz_t t;

	mpz_init(t); mpz_invert(t,BDY(n1),BDY(current_mod_lf));
	MPZTOGZ(t,*nq);
}

void lcmgz(GZ n1,GZ n2,GZ *nq)
{
	GZ g,t;

	if ( !n1 || !n2 ) *nq = 0;
	else {
		gcdgz(n1,n2,&g); divsgz(n1,g,&t);
		mulgz(n2,t,nq);
	}
}

void gcdvgz(VECT v,GZ *q)
{
	int n,i;
	GZ *b;
	GZ g,g1;

	n = v->len;
	b = (GZ *)v->body;
	g = b[0];
	for ( i = 1; i < n; i++ ) {
		gcdgz(g,b[i],&g1); g = g1;
	}
	*q = g;
}

void gcdvgz_estimate(VECT v,GZ *q)
{
	int n,m,i;
	GZ s,t,u;
	GZ *b;

	n = v->len;
	b = (GZ *)v->body;
	if ( n == 1 ) {
		if ( mpz_sgn(BDY(b[0]))<0 ) chsgngz(b[0],q);
		else *q = b[0];
	}
	m = n/2;
	for ( i = 0, s = 0; i < m; i++ ) {
		if ( b[i] && mpz_sgn(BDY(b[i]))<0 ) subgz(s,b[i],&u);
		else addgz(s,b[i],&u);
		s = u;
	}
	for ( i = 0, t = 0; i < n; i++ ) {
		if ( b[i] && mpz_sgn(BDY(b[i]))<0 ) subgz(t,b[i],&u);
		else addgz(t,b[i],&u);
		t = u;
	}
	gcdgz(s,t,q);
}

void addgq(GQ n1,GQ n2,GQ *nr)
{
	mpq_t q1,q2,t;

	if ( !n1 ) *nr = n2;
	else if ( !n2 ) *nr = n1;
	else {
		if ( NID(n1) == N_GZ ) MPZTOMPQ(BDY((GZ)n1),q1);
		else q1[0] = BDY(n1)[0];
		if ( NID(n2) == N_GZ ) MPZTOMPQ(BDY((GZ)n2),q2);
		else q2[0] = BDY(n2)[0];
		mpq_init(t); mpq_add(t,q1,q2); *nr = mpqtogzq(t);
	}
}

void subgq(GQ n1,GQ n2,GQ *nr)
{
	mpq_t q1,q2,t;

	if ( !n1 ) 
		if ( !n2 ) *nr = 0;
		else {
			if ( NID(n1) == N_GZ ) chsgngz((GZ)n1,(GZ *)nr);
			else {
				mpq_init(t); mpq_neg(t,BDY(n2)); MPQTOGQ(t,*nr);
			}
		}
	else if ( !n2 ) *nr = n1;
	else if ( n1 == n2 ) *nr = 0;
	else {
		if ( NID(n1) == N_GZ ) MPZTOMPQ(BDY((GZ)n1),q1);
		else q1[0] = BDY(n1)[0];
		if ( NID(n2) == N_GZ ) MPZTOMPQ(BDY((GZ)n2),q2);
		else q2[0] = BDY(n2)[0];
		mpq_init(t); mpq_sub(t,q1,q2); *nr = mpqtogzq(t);
	}
}

void mulgq(GQ n1,GQ n2,GQ *nr)
{
	mpq_t t,q1,q2;

	if ( !n1 || !n2 ) *nr = 0;
	else {
		if ( NID(n1) == N_GZ ) MPZTOMPQ(BDY((GZ)n1),q1);
		else q1[0] = BDY(n1)[0];
		if ( NID(n2) == N_GZ ) MPZTOMPQ(BDY((GZ)n2),q2);
		else q2[0] = BDY(n2)[0];
		mpq_init(t); mpq_mul(t,q1,q2); *nr = mpqtogzq(t);
	}
}

void divgq(GQ n1,GQ n2,GQ *nq)
{
	mpq_t t,q1,q2;

	if ( !n2 ) {
		error("division by 0");
		*nq = 0;
		return;
	} else if ( !n1 ) *nq = 0;
	else if ( n1 == n2 ) *nq = (GQ)ONEGZ;
	else {
		if ( NID(n1) == N_GZ ) MPZTOMPQ(BDY((GZ)n1),q1);
		else q1[0] = BDY(n1)[0];
		if ( NID(n2) == N_GZ ) MPZTOMPQ(BDY((GZ)n2),q2);
		else q2[0] = BDY(n2)[0];
		mpq_init(t); mpq_div(t,q1,q2); *nq = mpqtogzq(t);
	}
}

void chsgngq(GQ n,GQ *nr)
{
	mpq_t t;

	if ( !n ) *nr = 0;
	else if ( NID(n) == N_GZ ) chsgngz((GZ)n,(GZ *)nr);
	else {
		mpq_init(t); mpq_neg(t,BDY(n)); MPQTOGQ(t,*nr);
	}
}

void pwrgq(GQ n1,Q n,GQ *nr)
{
	int e;
	mpz_t nm,dn;
	mpq_t t;

	if ( !n || UNIGZ((GZ)n1) || UNIGQ(n1) ) *nr = (GQ)ONEGZ;
	else if ( !n1 ) *nr = 0;
	else if ( !INT(n) ) {
		error("can't calculate fractional power."); *nr = 0;
	} else if ( PL(NM(n)) > 1 ) {
		error("exponent too big."); *nr = 0;
	} else {
		e = QTOS(n);
		if ( e < 0 ) {
			e = -e;
			if ( NID(n1)==N_GZ ) {
				nm[0] = ONEMPZ[0];
				dn[0] = BDY((GZ)n1)[0];
			} else {
				nm[0] = mpq_denref(BDY(n1))[0]; dn[0] = mpq_numref(BDY(n1))[0];
			}
		} else {
			if ( NID(n1)==N_GZ ) {
				nm[0] = BDY((GZ)n1)[0]; dn[0] = ONEMPZ[0];
			} else {
				nm[0] = mpq_numref(BDY(n1))[0]; dn[0] = mpq_denref(BDY(n1))[0];
			}
		}
		mpq_init(t);
		mpz_pow_ui(mpq_numref(t),nm,e); mpz_pow_ui(mpq_denref(t),dn,e);
		*nr = mpqtogzq(t);
	}
}

int cmpgq(GQ n1,GQ n2)
{
	mpq_t q1,q2;
	int sgn;

	if ( !n1 ) 
		if ( !n2 ) return 0;
		else return (NID(n2)==N_GZ) ? -mpz_sgn(BDY((GZ)n2)) : -mpq_sgn(BDY(n2));
	if ( !n2 ) return (NID(n1)==N_GZ) ? mpz_sgn(BDY((GZ)n1)) : mpq_sgn(BDY(n1));
	else if ( (sgn = mpq_sgn(BDY(n1))) != mpq_sgn(BDY(n2)) ) return sgn;
	else {
		if ( NID(n1) == N_GZ ) MPZTOMPQ(BDY((GZ)n1),q1);
		else q1[0] = BDY(n1)[0];
		if ( NID(n2) == N_GZ ) MPZTOMPQ(BDY((GZ)n2),q2);
		else q2[0] = BDY(n2)[0];
		sgn = mpq_cmp(q1,q2);
		if ( sgn > 0 ) return 1;
		else if ( sgn < 0 ) return -1;
		else return 0;
	}
}

void mkgwc(int k,int l,GZ *t)
{
	mpz_t a,b,q,nm,z,u;
	int i,n;

	n = MIN(k,l);
	mpz_init_set_ui(z,1);
	mpz_init(u); mpz_set(u,z); MPZTOGZ(u,t[0]);
	mpz_init(a); mpz_init(b); mpz_init(nm);
	for ( i = 1; i <= n; i++ ) {
		mpz_set_ui(a,k-i+1); mpz_set_ui(b,l-i+1); mpz_mul(nm,a,b);
		mpz_mul(z,BDY(t[i-1]),nm); mpz_fdiv_q_ui(z,z,i);
		mpz_init(u); mpz_set(u,z); MPZTOGZ(u,t[i]);
	}
}

void gz_lgp(P p,GZ *g,GZ *l);

void gz_ptozp(P p,int sgn,GQ *c,P *pr)
{
	GZ nm,dn;

	if ( !p ) {
		*c = 0; *pr = 0;
	} else {
		gz_lgp(p,&nm,&dn);
		divgz(nm,dn,(GZ *)c);
		divsp(CO,p,(P)*c,pr);
	}
}

void gz_lgp(P p,GZ *g,GZ *l)
{
	DCP dc;
	GZ g1,g2,l1,l2,l3,l4;

	if ( NUM(p) ) {
		if ( NID((GZ)p)==N_GZ ) {
			MPZTOGZ(BDY((GZ)p),*g);
			*l = ONEGZ;
		} else {
			MPZTOGZ(mpq_numref(BDY((GQ)p)),*g);
			MPZTOGZ(mpq_denref(BDY((GQ)p)),*l);
		}
	} else {
		dc = DC(p); gz_lgp(COEF(dc),g,l);
		for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
			gz_lgp(COEF(dc),&g1,&l1); gcdgz(*g,g1,&g2); *g = g2;
			gcdgz(*l,l1,&l2); mulgz(*l,l1,&l3); divgz(l3,l2,l);
		}
	} 
}

void gz_qltozl(GQ *w,int n,GZ *dvr)
{
	GZ nm,dn;
	GZ g,g1,l1,l2,l3;
	GQ c;
	int i;
	struct oVECT v;

	for ( i = 0; i < n; i++ )
		if ( w[i] && NID(w[i])==N_GQ )
			break;
	if ( i == n ) {
		v.id = O_VECT; v.len = n; v.body = (pointer *)w;
		gcdvgz(&v,dvr); return;
	}
	for ( i = 0; !w[i]; i++ );
	c = w[i]; 
	if ( NID(c)==N_GQ ) {
		MPZTOGZ(mpq_numref(BDY(c)),nm); MPZTOGZ(mpq_denref(BDY(c)),dn);
	} else {
		MPZTOGZ(BDY((GZ)c),nm); dn = ONEGZ;
	}
	for ( i++; i < n; i++ ) {
		c = w[i]; 
		if ( !c ) continue;
		if ( NID(c)==N_GQ ) {
			MPZTOGZ(mpq_numref(BDY(c)),g1); MPZTOGZ(mpq_denref(BDY(c)),l1);
		} else {
			MPZTOGZ(BDY((GZ)c),g1); l1 = ONEGZ;
		}
		gcdgz(nm,g1,&g); nm = g;
		gcdgz(dn,l1,&l2); mulgz(dn,l1,&l3); divgz(l3,l2,&dn);
	}
	divgz(nm,dn,dvr);
}

int gz_bits(GQ q)
{
	if ( !q ) return 0;
	else if ( NID(q)==N_Q ) 
		return n_bits(NM((Q)q))+(INT((Q)q)?0:n_bits(DN((Q)q)));
	else if ( NID(q)==N_GZ ) return mpz_sizeinbase(BDY((GZ)q),2);
	else
		return mpz_sizeinbase(mpq_numref(BDY(q)),2)
			+ mpz_sizeinbase(mpq_denref(BDY(q)),2);
}

int gzp_mag(P p)
{
	int s;
	DCP dc;
	
	if ( !p ) return 0;
	else if ( OID(p) == O_N ) return gz_bits((GQ)p);
	else {
		for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) s += gzp_mag(COEF(dc));
		return s;
	}
}

void makesubstgz(VL v,NODE *s)
{
	NODE r,r0;
	GZ q;	
	unsigned int n;

	for ( r0 = 0; v; v = NEXT(v) ) {
		NEXTNODE(r0,r); BDY(r) = (pointer)v->v;
#if defined(_PA_RISC1_1)
		n = mrand48()&BMASK; q = utogz(n);
#else
		n = random(); q = utogz(n);
#endif
		NEXTNODE(r0,r); BDY(r) = (pointer)q;
	}
	if ( r0 ) NEXT(r) = 0;
	*s = r0;
}

unsigned int remgq(GQ a,unsigned int mod)
{
	unsigned int c,nm,dn;
	mpz_t r;

	if ( !a ) return 0;
	else if ( NID(a)==N_GZ ) {
		mpz_init(r);
		c = mpz_fdiv_r_ui(r,BDY((GZ)a),mod);
	} else {
		mpz_init(r);
		nm = mpz_fdiv_r_ui(r,mpq_numref(BDY(a)),mod);
		dn = mpz_fdiv_r_ui(r,mpq_denref(BDY(a)),mod);
		dn = invm(dn,mod);		
		DMAR(nm,dn,0,mod,c);
	}
	return c;
}

extern int DP_Print;

#define GZ_F4_INTRAT_PERIOD 8 

int gz_generic_gauss_elim(MAT mat,MAT *nm,GZ *dn,int **rindp,int **cindp)
{
	int **wmat;
	GZ **bmat,**tmat,*bmi,*tmi;
	GZ q,m1,m2,m3,s,u;
	int *wmi,*colstat,*wcolstat,*rind,*cind;
	int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
	MAT r,crmat;
	int ret;

	bmat = (GZ **)mat->body;
	row = mat->row; col = mat->col;
	wmat = (int **)almat(row,col);
	colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	for ( ind = 0; ; ind++ ) {
		if ( DP_Print ) {
			fprintf(asir_out,"."); fflush(asir_out);
		}
		md = get_lprime(ind);
		for ( i = 0; i < row; i++ )
			for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
				wmi[j] = remgq((GQ)bmi[j],md);
		rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
		if ( !ind ) {
RESET:
			m1 = utogz(md);
			rank0 = rank;
			bcopy(wcolstat,colstat,col*sizeof(int));
			MKMAT(crmat,rank,col-rank);
			MKMAT(r,rank,col-rank); *nm = r;
			tmat = (GZ **)crmat->body;
			for ( i = 0; i < rank; i++ )
				for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
					if ( !colstat[j] ) tmi[k++] = utogz(wmi[j]);
		} else {
			if ( rank < rank0 ) {
				if ( DP_Print ) {
					fprintf(asir_out,"lower rank matrix; continuing...\n");
					fflush(asir_out);
				}
				continue;
			} else if ( rank > rank0 ) {
				if ( DP_Print ) {
					fprintf(asir_out,"higher rank matrix; resetting...\n");
					fflush(asir_out);
				}
				goto RESET;
			} else {
				for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
				if ( j < col ) {
					if ( DP_Print ) {
						fprintf(asir_out,"inconsitent colstat; resetting...\n");
						fflush(asir_out);
					}
					goto RESET;
				}
			}

			inv = invm(remgq((GQ)m1,md),md);
			m2 = utogz(md); mulgz(m1,m2,&m3);
			for ( i = 0; i < rank; i++ )			
				for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
					if ( !colstat[j] ) {
						if ( tmi[k] ) {
						/* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
							t = remgq((GQ)tmi[k],md);
							if ( wmi[j] >= t ) t = wmi[j]-t;
							else t = md-(t-wmi[j]);
							DMAR(t,inv,0,md,t1) 
							u = utogz(t1); mulgz(m1,u,&s); 
							addgz(tmi[k],s,&u); tmi[k] = u;
						} else if ( wmi[j] ) {
						/* f3 = m1*(m1 mod m2)^(-1)*f2 */
							DMAR(wmi[j],inv,0,md,t)
							u = utogz(t); mulgz(m1,u,&s); tmi[k] = s;
						}
						k++;
					}
			m1 = m3;
			if ( ind % GZ_F4_INTRAT_PERIOD ) 
				ret = 0;
			else 
				ret = gz_intmtoratm(crmat,m1,*nm,dn);
			if ( ret ) {
				*rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
				*cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
				for ( j = k = l = 0; j < col; j++ )
					if ( colstat[j] ) rind[k++] = j;	
					else cind[l++] = j;
				if ( gz_gensolve_check(mat,*nm,*dn,rind,cind) )
					return rank;
			}
		}
	}
}

int gz_generic_gauss_elim2(MAT mat,MAT *nm,GZ *dn,int **rindp,int **cindp)
{

	MAT full;
	GZ **bmat,**b;
	GZ *bmi;
	GZ dn0;
	int row,col,md,i,j,rank,ret;
	int **wmat;
	int *wmi;
	int *colstat,*rowstat;

	bmat = (GZ **)mat->body;
	row = mat->row; col = mat->col;
	wmat = (int **)almat(row,col);
	colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	rowstat = (int *)MALLOC_ATOMIC(row*sizeof(int));
	/* XXX */
	md = get_lprime(0);
	for ( i = 0; i < row; i++ )
		for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
			wmi[j] = remgq((GQ)bmi[j],md);
	rank = generic_gauss_elim_mod2(wmat,row,col,md,colstat,rowstat);
	b = (GZ **)MALLOC(rank*sizeof(GZ));
	for ( i = 0; i < rank; i++ ) b[i] = bmat[rowstat[i]];
	NEWMAT(full); full->row = rank; full->col = col; full->body = (pointer **)b;
	ret = gz_generic_gauss_elim_full(full,nm,dn,rindp,cindp);
	if ( !ret ) {
		rank = gz_generic_gauss_elim(mat,nm,&dn0,rindp,cindp);
		for ( i = 0; i < rank; i++ ) dn[i] = dn0;
	}
	return rank;
}

int gz_generic_gauss_elim_full(MAT mat,MAT *nm,GZ *dn,int **rindp,int **cindp)
{
	int **wmat;
	int *stat;
	GZ **bmat,**tmat,*bmi,*tmi,*ri;
	GZ q,m1,m2,m3,s,u;
	int *wmi,*colstat,*wcolstat,*rind,*cind;
	int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv,h;
	MAT r,crmat;
	int ret,initialized,done;

	initialized = 0;
	bmat = (GZ **)mat->body;
	row = mat->row; col = mat->col;
	wmat = (int **)almat(row,col);
	stat = (int *)MALLOC_ATOMIC(row*sizeof(int));
	for ( i = 0; i < row; i++ ) stat[i] = 0;
	colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	for ( ind = 0; ; ind++ ) {
		if ( DP_Print ) {
			fprintf(asir_out,"."); fflush(asir_out);
		}
		md = get_lprime(ind);
		for ( i = 0; i < row; i++ )
			for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
				wmi[j] = remgq((GQ)bmi[j],md);
		rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
		if ( rank < row ) continue;
		if ( !initialized ) {
			m1 = utogz(md);
			bcopy(wcolstat,colstat,col*sizeof(int));
			MKMAT(crmat,row,col-row);
			MKMAT(r,row,col-row); *nm = r;
			tmat = (GZ **)crmat->body;
			for ( i = 0; i < row; i++ )
				for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
					if ( !colstat[j] ) tmi[k++] = utogz(wmi[j]);
			initialized = 1;
		} else {
			for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
			if ( j < col ) continue;

			inv = invm(remgq((GQ)m1,md),md);
			m2 = utogz(md); mulgz(m1,m2,&m3);
			for ( i = 0; i < row; i++ )
				switch ( stat[i] ) {
					case 1: 
						/* consistency check */
						ri = (GZ *)BDY(r)[i]; wmi = wmat[i];
						for ( j = 0; j < col; j++ ) if ( colstat[j] ) break;
						h = md-remgq((GQ)dn[i],md);
						for ( j++, k = 0; j < col; j++ )
							if ( !colstat[j] ) {
								t = remgq((GQ)ri[k],md);
								DMAR(wmi[i],h,t,md,t1);
								if ( t1 ) break;
							}
						if ( j == col ) { stat[i]++; break; }
						else {
							/* fall to the case 0 */
							stat[i] = 0;
						}
					case 0:
						tmi = tmat[i]; wmi = wmat[i];
						for ( j = k = 0; j < col; j++ )
							if ( !colstat[j] ) {
								if ( tmi[k] ) {
								/* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
									t = remgq((GQ)tmi[k],md);
									if ( wmi[j] >= t ) t = wmi[j]-t;
									else t = md-(t-wmi[j]);
									DMAR(t,inv,0,md,t1) 
									u = utogz(t1); mulgz(m1,u,&s); 
									addgz(tmi[k],s,&u); tmi[k] = u;
								} else if ( wmi[j] ) {
								/* f3 = m1*(m1 mod m2)^(-1)*f2 */
									DMAR(wmi[j],inv,0,md,t)
									u = utogz(t); mulgz(m1,u,&s); tmi[k] = s;
								}
								k++;
							}
						break;
					case 2: default:
						break;
				}
			m1 = m3;
			if ( ind % 4 )
				ret = 0;
			else 
				ret = gz_intmtoratm2(crmat,m1,*nm,dn,stat);
			if ( ret ) {
				*rindp = rind = (int *)MALLOC_ATOMIC(row*sizeof(int));
				*cindp = cind = (int *)MALLOC_ATOMIC((col-row)*sizeof(int));
				for ( j = k = l = 0; j < col; j++ )
					if ( colstat[j] ) rind[k++] = j;	
					else cind[l++] = j;
				return gz_gensolve_check2(mat,*nm,dn,rind,cind);
			}
		}
	}
}

int gz_generic_gauss_elim_direct(MAT mat,MAT *nm,GZ *dn,int **rindp,int **cindp){
	GZ **bmat,*s;
	GZ u,v,w,x,d,t,y;
	int row,col,i,j,k,l,m,rank;
	int *colstat,*colpos,*cind;
	MAT r,in;

	row = mat->row; col = mat->col;
	MKMAT(in,row,col);
	for ( i = 0; i < row; i++ )
		for ( j = 0; j < col; j++ ) in->body[i][j] = mat->body[i][j];
	bmat = (GZ **)in->body;
	colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
	*rindp = colpos = (int *)MALLOC_ATOMIC(row*sizeof(int));
	for ( j = 0, rank = 0, d = ONEGZ; j < col; j++ ) {
		for ( i = rank; i < row && !bmat[i][j]; i++  );
		if ( i == row ) { colstat[j] = 0; continue; }
		else { colstat[j] = 1; colpos[rank] = j; }
		if ( i != rank )
			for ( k = j; k < col; k++ ) {
				t = bmat[i][k]; bmat[i][k] = bmat[rank][k]; bmat[rank][k] = t;
			}
		for ( i = rank+1, v = bmat[rank][j]; i < row; i++ )
			for ( k = j, u = bmat[i][j]; k < col; k++ ) {
				mulgz(bmat[i][k],v,&w); mulgz(bmat[rank][k],u,&x);
				subgz(w,x,&y); divsgz(y,d,&bmat[i][k]);
			}
		d = v; rank++;
	}
	*dn = d;
	s = (GZ *)MALLOC(col*sizeof(GZ));
	for ( i = rank-1; i >= 0; i-- ) {
		for ( k = colpos[i]; k < col; k++ ) mulgz(bmat[i][k],d,&s[k]); 
		for ( m = rank-1; m > i; m-- ) {
			for ( k = colpos[m], u = bmat[i][k]; k < col; k++ ) {
				mulgz(bmat[m][k],u,&w); subgz(s[k],w,&x); s[k] = x;
			}
		}
		for ( k = colpos[i], u = bmat[i][k]; k < col; k++ )
			divgz(s[k],u,&bmat[i][k]);
	}
	*cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
	MKMAT(r,rank,col-rank); *nm = r;
	for ( j = 0, k = 0; j < col; j++ )
		if ( !colstat[j] ) {
			cind[k] = j;
			for ( i = 0; i < rank; i++ ) r->body[i][k] = bmat[i][j];
			k++;
		}
	return rank;
}

int gz_intmtoratm(MAT mat,GZ md,MAT nm,GZ *dn)
{
	GZ t,s,b,dn0,dn1,nm1,q,u,unm,udn,dmy;
	int i,j,k,l,row,col,sgn,ret;
	GZ **rmat,**tmat,*tmi,*nmk;

	if ( UNIGZ(md) )
		return 0;
	row = mat->row; col = mat->col;
	bshiftgz(md,1,&t);
	isqrtgz(t,&s);
	bshiftgz(s,64,&b);
	if ( !b ) b = ONEGZ;
	dn0 = ONEGZ;
	tmat = (GZ **)mat->body;
	rmat = (GZ **)nm->body;
	for ( i = 0; i < row; i++ )
		for ( j = 0, tmi = tmat[i]; j < col; j++ )
			if ( tmi[j] ) {
				mulgz(tmi[j],dn0,&s);
				divqrgz(s,md,&dmy,&u);
				ret = gz_inttorat(u,md,b,&sgn,&unm,&udn);
				if ( !ret ) return 0;
				else {
					if ( sgn < 0 ) chsgngz(unm,&nm1);
					else nm1 = unm;
					dn1 = udn;
					if ( !UNIGZ(dn1) ) {
						for ( k = 0; k < i; k++ )
							for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
								mulgz(nmk[l],dn1,&q); nmk[l] = q;
							}
						for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
							mulgz(nmk[l],dn1,&q); nmk[l] = q;
						}
					}
					rmat[i][j] = nm1;
					mulgz(dn0,dn1,&q); dn0 = q;
				}
			}
	*dn = dn0;
	return 1;
}

int gz_intmtoratm2(MAT mat,GZ md,MAT nm,GZ *dn,int *stat)
{
	int row,col,i,j,ret;
	GZ dn0,dn1,t,s,b;
	GZ *w,*tmi;
	GZ **tmat;

	bshiftgz(md,1,&t);
	isqrtgz(t,&s);
	bshiftgz(s,64,&b);
	tmat = (GZ **)mat->body;
	if ( UNIGZ(md) ) return 0;
	row = mat->row; col = mat->col;
	dn0 = ONEGZ;
	for ( i = 0; i < row; i++ )
		if ( cmpgz(dn[i],dn0) > 0 ) dn0 = dn[i];
	w = (GZ *)MALLOC(col*sizeof(GZ));
	for ( i = 0; i < row; i++ )
		if ( stat[i] == 0 ) {
			for ( j = 0, tmi = tmat[i]; j < col; j++ )
					mulgz(tmi[j],dn0,&w[j]);
			ret = gz_intvtoratv(w,col,md,b,BDY(nm)[i],&dn[i]);
			if ( ret ) {
				stat[i] = 1;
				mulgz(dn0,dn[i],&t); dn[i] = t; dn0 = t;
			}
		}
	for ( i = 0; i < row; i++ ) if ( !stat[i] ) break;
	if ( i == row ) return 1;
	else return 0;
}

int gz_intvtoratv(GZ *v,int n,GZ md,GZ b,GZ *nm,GZ *dn)
{
	GZ dn0,dn1,q,s,u,nm1,unm,udn,dmy;
	GZ *nmk;
	int j,l,col,ret,sgn;

	for ( j = 0; j < n; j++ ) nm[j] = 0;
	dn0 = ONEGZ;
	for ( j = 0; j < n; j++ ) {
		if ( !v[j] ) continue;
		mulgz(v[j],dn0,&s);
		divqrgz(s,md,&dmy,&u);
		ret = gz_inttorat(u,md,b,&sgn,&unm,&udn);
		if ( !ret ) return 0;
		if ( sgn < 0 ) chsgngz(unm,&nm1);
		else nm1 = unm;
		dn1 = udn;
		if ( !UNIGZ(dn1) )
			for ( l = 0; l < j; l++ ) {
				mulgz(nm[l],dn1,&q); nm[l] = q;
			}
		nm[j] = nm1;
		mulgz(dn0,dn1,&q); dn0 = q;
	}
	*dn = dn0;
	return 1;
}

/* assuming 0 < c < m */

int gz_inttorat(GZ c,GZ m,GZ b,int *sgnp,GZ *nmp,GZ *dnp)
{
	GZ qq,t,u1,v1,r1;
	GZ q,u2,v2,r2;

	u1 = 0; v1 = ONEGZ; u2 = m; v2 = c;
	while ( cmpgz(v2,b) >= 0 ) {
		divqrgz(u2,v2,&q,&r2); u2 = v2; v2 = r2;
		mulgz(q,v1,&t); subgz(u1,t,&r1); u1 = v1; v1 = r1; 
	}
	if ( cmpgz(v1,b) >= 0 ) return 0;
	else {
		*nmp = v2;
		if ( mpz_sgn(BDY(v1))<0  ) {
			*sgnp = -1; chsgngz(v1,dnp);
		} else {
			*sgnp = 1; *dnp = v1;
		}
		return 1;
	}
}

extern int f4_nocheck;

int gz_gensolve_check(MAT mat,MAT nm,GZ dn,int *rind,int *cind)
{
	int row,col,rank,clen,i,j,k,l;
	GZ s,t;
	GZ *w;
	GZ *mati,*nmk;

	if ( f4_nocheck ) return 1;
	row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;	
	w = (GZ *)MALLOC(clen*sizeof(GZ));
	for ( i = 0; i < row; i++ ) {
		mati = (GZ *)mat->body[i];
		bzero(w,clen*sizeof(GZ));
		for ( k = 0; k < rank; k++ )
			for ( l = 0, nmk = (GZ *)nm->body[k]; l < clen; l++ ) {
				mulgz(mati[rind[k]],nmk[l],&t); addgz(w[l],t,&s); w[l] = s;
			}
		for ( j = 0; j < clen; j++ ) {
			mulgz(dn,mati[cind[j]],&t);
			if ( cmpgz(w[j],t) ) break;
		}
		if ( j != clen ) break;
	}
	if ( i != row ) return 0;
	else return 1;
}

int gz_gensolve_check2(MAT mat,MAT nm,GZ *dn,int *rind,int *cind)
{
	int row,col,rank,clen,i,j,k,l;
	GZ s,t,u,d;
	GZ *w,*m;
	GZ *mati,*nmk;

	if ( f4_nocheck ) return 1;
	row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;	
	w = (GZ *)MALLOC(clen*sizeof(GZ));
	m = (GZ *)MALLOC(clen*sizeof(GZ));
	for ( d = dn[0], i = 1; i < rank; i++ ) {
		lcmgz(d,dn[i],&t); d = t;
	}
	for ( i = 0; i < rank; i++ ) divsgz(d,dn[i],&m[i]);
	for ( i = 0; i < row; i++ ) {
		mati = (GZ *)mat->body[i];
		bzero(w,clen*sizeof(GZ));
		for ( k = 0; k < rank; k++ ) {
			mulgz(mati[rind[k]],m[k],&u);
			for ( l = 0, nmk = (GZ *)nm->body[k]; l < clen; l++ ) {
				mulgz(u,nmk[l],&t); addgz(w[l],t,&s); w[l] = s;
			}
		}
		for ( j = 0; j < clen; j++ ) {
			mulgz(d,mati[cind[j]],&t);
			if ( cmpgz(w[j],t) ) break;
		}
		if ( j != clen ) break;
	}
	if ( i != row ) return 0;
	else return 1;
}

void isqrtgz(GZ a,GZ *r)
{
	int k;
	GZ x,t,x2,xh,quo,rem;
	Q two;

	if ( !a ) *r = 0;
	else if ( UNIGZ(a) ) *r = ONEGZ;
	else {
		k = gz_bits((GQ)a); /* a <= 2^k-1 */
		bshiftgz(ONEGZ,-((k>>1)+(k&1)),&x); /* a <= x^2 */
		STOQ(2,two);
		while ( 1 ) {
			pwrgz(x,two,&t);
			if ( cmpgz(t,a) <= 0 ) {
				*r = x; return;
			} else {
				if ( mpz_tstbit(BDY(x),0) ) addgz(x,a,&t);
				else t = a;
				bshiftgz(x,-1,&x2); divqrgz(t,x2,&quo,&rem);
				bshiftgz(x,1,&xh); addgz(quo,xh,&x);
			}
		}
	}
}

void bshiftgz(GZ a,int n,GZ *r)
{
	mpz_t t;

	if ( !a ) *r = 0;
	else if ( n == 0 ) *r = a;
	else if ( n < 0 ) {
		mpz_init(t); mpz_mul_2exp(t,BDY(a),-n); MPZTOGZ(t,*r);
	} else { 
		mpz_init(t); mpz_fdiv_q_2exp(t,BDY(a),n);
		if ( !mpz_sgn(t) ) *r = 0;
		else MPZTOGZ(t,*r);
	}
}

void addlf(GZ a,GZ b,GZ *c)
{
  GZ t;

  addgz(a,b,c);
  if ( !lf_lazy ) {
    remgz(*c,current_mod_lf,&t); *c = t;
  }
}

void sublf(GZ a,GZ b,GZ *c)
{
  GZ t;

  subgz(a,b,c);
  if ( !lf_lazy ) {
    remgz(*c,current_mod_lf,&t); *c = t;
  }
}

void mullf(GZ a,GZ b,GZ *c)
{
  GZ t;

  mulgz(a,b,c);
  if ( !lf_lazy ) {
    remgz(*c,current_mod_lf,&t); *c = t;
  }
}

void divlf(GZ a,GZ b,GZ *c)
{
  GZ t,inv;

  invgz(b,&inv);
  mulgz(a,inv,c);
  if ( !lf_lazy ) {
    remgz(*c,current_mod_lf,&t); *c = t;
  }
}

void chsgnlf(GZ a,GZ *c)
{
  GZ t;

  chsgngz(a,c);
  if ( !lf_lazy ) {
    remgz(*c,current_mod_lf,&t); *c = t;
  }
}

void lmtolf(LM a,GZ *b)
{
  Q q;

  if ( !a ) *b = 0;
  else {
    NTOQ(BDY(a),1,q); *b = ztogz(q);
  }
}

void setmod_lf(N p)
{
    Q q;

    NTOQ(p,1,q); current_mod_lf = ztogz(q);
    current_mod_lf_size = mpz_size(BDY(current_mod_lf))+1;
}

void simplf_force(GZ a,GZ *b)
{
    GZ t;

    remgz(a,current_mod_lf,&t); *b = t;
}