File: [local] / OpenXM_contrib2 / asir2000 / engine / gmpq.c (download)
Revision 1.3, Tue Aug 19 06:35:01 2014 UTC (10 years, 1 month ago) by noro
Branch: MAIN
CVS Tags: RELEASE_1_3_1_13b Changes since 1.2: +10 -0
lines
dp_set_top_weight() now accepts a matrix with non-negative integer elements.
(experimental)
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#include "ca.h"
#include "gmp.h"
#include "base.h"
#include "inline.h"
mpz_t ONEMPZ;
GZ ONEGZ;
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_atomic,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;
}
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;
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);
else {
mpz_init(t); mpz_mul(t,BDY(n1),BDY(n2)); MPZTOGZ(t,*nr);
}
}
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 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 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);
}
}