===================================================================
RCS file: /home/cvs/OpenXM_contrib2/asir2018/engine/Q.c,v
retrieving revision 1.3
retrieving revision 1.21
diff -u -p -r1.3 -r1.21
--- OpenXM_contrib2/asir2018/engine/Q.c	2018/09/24 22:26:43	1.3
+++ OpenXM_contrib2/asir2018/engine/Q.c	2021/10/08 07:27:05	1.21
@@ -1,17 +1,26 @@
+/* $OpenXM: OpenXM_contrib2/asir2018/engine/Q.c,v 1.20 2020/12/04 08:09:33 noro Exp $ */
 #include "ca.h"
 #include "gmp.h"
 #include "base.h"
 #include "inline.h"
 
 mpz_t ONEMPZ;
-Z ONE;
+extern Z ONE;
 int lf_lazy;
 Z current_mod_lf;
 int current_mod_lf_size;
 gmp_randstate_t GMP_RAND;
 
+#define F4_INTRAT_PERIOD 4 
+
+extern int DP_Print;
+
 void isqrtz(Z a,Z *r);
 void bshiftz(Z a,int n,Z *r);
+int mpz_inttorat(mpz_t c,mpz_t m,mpz_t b,mpz_t nm,mpz_t dn);
+int generic_gauss_elim_hensel64(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp,DP *mb);
+int find_lhs_and_lu_mod64(mp_limb_t **a,int row,int col,mp_limb_t md,int **rinfo,int **cinfo);
+void solve_by_lu_mod64(mp_limb_t **a,int n,mp_limb_t md,mp_limb_signed_t **b,int l,int normalize);
 
 void *gc_realloc(void *p,size_t osize,size_t nsize)
 {
@@ -25,19 +34,21 @@ void gc_free(void *p,size_t size)
 
 void init_gmpq()
 {
-  mp_set_memory_functions(Risa_GC_malloc_atomic,gc_realloc,gc_free);
+  mp_set_memory_functions(Risa_GC_malloc,gc_realloc,gc_free);
 
   mpz_init(ONEMPZ); mpz_set_ui(ONEMPZ,1); MPZTOZ(ONEMPZ,ONE);
   gmp_randinit_default(GMP_RAND);
 }
 
+void printexpr(VL,Obj);
+
 void pmat(Z **a,int row,int col)
 {
   int i,j;
 
   for ( i = 0; i < row; i++, printf("\n") )
     for ( j = 0; j < col; j++, printf(" ") )
-      printexpr(CO,a[i][j]);
+      printexpr(CO,(Obj)a[i][j]);
   printf("\n");
 }
 
@@ -86,8 +97,11 @@ void dnq(Q q,Z *r)
 int sgnq(Q q)
 {
   if ( !q ) return 0;
-  else if ( q->z ) return mpz_sgn(BDY((Z)q));
-  else return mpz_sgn(mpq_numref(BDY(q)));
+  else if ( q->z ) {
+   int sgn;
+   sgn = mpz_sgn(BDY((Z)q));
+   return sgn;
+  } else return mpz_sgn(mpq_numref(BDY(q)));
 }
 
 Q mpqtozq(mpq_t a)
@@ -353,7 +367,7 @@ void pwrz(Z n1,Z n,Z *nr)
   } else if ( !smallz(n) ) {
     error("exponent too big."); *nr = 0;
   } else if ( n1->z && mpz_sgn(BDY((Z)n))>0 ) {
-    mpz_init(z); mpz_pow_ui(z,BDY(n1),QTOS(n)); MPZTOZ(z,*nr);
+    mpz_init(z); mpz_pow_ui(z,BDY(n1),ZTOS(n)); MPZTOZ(z,*nr);
   } else {
     MPZTOMPQ(BDY(n1),q); MPQTOQ(q,r);
     pwrq(r,(Q)n,&p); *nr = (Z)p;
@@ -381,6 +395,8 @@ int cmpz(Z q1,Z q2)
     else if ( sgn < 0 ) return -1;
     else return 0;
   }
+  /* XXX */
+  return 0;
 }
 
 void gcdz(Z n1,Z n2,Z *nq)
@@ -453,7 +469,7 @@ void gcdvz_estimate(VECT v,Z *q)
     else addz(s,b[i],&u);
     s = u;
   }
-  for ( i = 0, t = 0; i < n; i++ ) {
+  for ( t = 0; i < n; i++ ) {
     if ( b[i] && mpz_sgn(BDY(b[i]))<0 ) subz(t,b[i],&u);
     else addz(t,b[i],&u);
     t = u;
@@ -461,11 +477,54 @@ void gcdvz_estimate(VECT v,Z *q)
   gcdz(s,t,q);
 }
 
+void gcdv_mpz_estimate(mpz_t g,mpz_t *b,int n)
+{
+  int m,m2,i,j;
+  mpz_t s,t;
+
+  mpz_init(g);
+  for ( i = 0, m = 0; i < n; i++ )
+    if ( mpz_sgn(b[i]) ) m++;
+  if ( !m ) {
+    mpz_set_ui(g,0);
+    return;
+  }
+  if ( m == 1 ) {
+    for ( i = 0, m = 0; i < n; i++ )
+      if ( mpz_sgn(b[i]) ) break;
+    if ( mpz_sgn(b[i])<0 ) mpz_neg(g,b[i]);
+    else mpz_set(g,b[i]);
+    return ;
+  }
+  m2 = m/2;
+  mpz_init_set_ui(s,0);
+  for ( i = j = 0; j < m2; i++ ) {
+    if ( mpz_sgn(b[i]) ) {
+      if ( mpz_sgn(b[i])<0 ) 
+        mpz_sub(s,s,b[i]);
+      else
+        mpz_add(s,s,b[i]);
+      j++;
+    }
+  }
+  mpz_init_set_ui(t,0);
+  for ( ; i < n; i++ ) {
+    if ( mpz_sgn(b[i]) ) {
+      if ( mpz_sgn(b[i])<0 ) 
+        mpz_sub(t,t,b[i]);
+      else
+        mpz_add(t,t,b[i]);
+    }
+  }
+  mpz_gcd(g,s,t);
+}
+
+
 void factorialz(unsigned int n,Z *nr)
 {
   mpz_t a;
   mpz_init(a);
-  mpz_fac_ui(a,n);
+  mpz_fac_ui(a,(unsigned long)n);
   MPZTOZ(a,*nr);
 }
 
@@ -508,7 +567,7 @@ void subq(Q n1,Q n2,Q *nr)
 
   if ( !n1 ) {
     if ( !n2 ) *nr = 0;
-    else if ( n1->z ) chsgnz((Z)n1,(Z *)nr);
+    else if ( n2->z ) chsgnz((Z)n2,(Z *)nr);
     else {
         mpq_init(t); mpq_neg(t,BDY(n2)); MPQTOQ(t,*nr);
       }
@@ -605,7 +664,7 @@ void pwrq(Q n1,Q n,Q *nr)
   } else if ( !smallz((Z)n) ) {
     error("exponent too big."); *nr = 0;
   } else {
-    e = QTOS(n);
+    e = ZTOS(n);
     if ( e < 0 ) {
       e = -e;
       if ( n1->z ) {
@@ -615,6 +674,10 @@ void pwrq(Q n1,Q n,Q *nr)
         nm[0] = mpq_denref(BDY(n1))[0];
         dn[0] = mpq_numref(BDY(n1))[0];
       }
+      if ( mpz_sgn(dn)<0 ) {
+        mpz_neg(nm,nm);
+        mpz_neg(dn,dn);
+      }      
     } else {
       if ( n1->z ) {
         nm[0] = BDY((Z)n1)[0];
@@ -662,8 +725,8 @@ void mkbc(int n,Z *t)
   Z c,d,iq;
 
   for ( t[0] = ONE, i = 1; i <= n/2; i++ ) {
-    STOQ(n-i+1,c); mulz(t[i-1],c,&d); 
-    STOQ(i,iq); divsz(d,iq,&t[i]);
+    STOZ(n-i+1,c); mulz(t[i-1],c,&d); 
+    STOZ(i,iq); divsz(d,iq,&t[i]);
   }
   for ( ; i <= n; i++ )
     t[i] = t[n-i];
@@ -712,12 +775,15 @@ void lgp(P p,Z *g,Z *l);
 
 void ptozp(P p,int sgn,Q *c,P *pr)
 {
-  Z nm,dn;
+  Z nm,dn,nm1;
 
   if ( !p ) {
     *c = 0; *pr = 0;
   } else {
     lgp(p,&nm,&dn);
+    if ( sgn < 0 ) {
+      chsgnz(nm,&nm1); nm = nm1;
+    }
     divz(nm,dn,(Z *)c);
     divsp(CO,p,(P)*c,pr);
   }
@@ -730,10 +796,10 @@ void lgp(P p,Z *g,Z *l)
 
   if ( NUM(p) ) {
     if ( ((Q)p)->z ) {
-      MPZTOZ(BDY((Z)p),*g);
+      absz((Z)p,g);
       *l = ONE;
     } else {
-      MPZTOZ(mpq_numref(BDY((Q)p)),*g);
+      MPZTOZ(mpq_numref(BDY((Q)p)),g1); absz(g1,g);
       MPZTOZ(mpq_denref(BDY((Q)p)),*l);
     }
   } else {
@@ -841,10 +907,6 @@ unsigned int remqi(Q a,unsigned int mod)
   return c;
 }
 
-extern int DP_Print;
-
-#define F4_INTRAT_PERIOD 8 
-
 int generic_gauss_elim(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
 {
   int **wmat;
@@ -854,7 +916,15 @@ int generic_gauss_elim(MAT mat,MAT *nm,Z *dn,int **rin
   int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
   MAT r,crmat;
   int ret;
+  MAT mat2,nm2;
+  Z dn2;
+  int *rind2,*cind2;
+  int ret2;
 
+#if SIZEOF_LONG == 8
+  ret = generic_gauss_elim64(mat,nm,dn,rindp,cindp);
+  return ret;
+#endif
   bmat = (Z **)mat->body;
   row = mat->row; col = mat->col;
   wmat = (int **)almat(row,col);
@@ -1131,6 +1201,40 @@ int generic_gauss_elim_direct(MAT mat,MAT *nm,Z *dn,in
   return rank;
 }
 
+int mpz_intmtoratm(mpz_t **mat,int row,int col,mpz_t md,mpz_t **nm,mpz_t dn)
+{
+  mpz_t t,s,b,u,nm1,dn1;
+  int i,j,k,l,ret;
+  mpz_t *mi,*nmk;
+
+  if ( UNIMPZ(md) )
+    return 0;
+  mpz_init(t); mpz_init(s); mpz_init(b); mpz_init(u);
+  mpz_init(nm1); mpz_init(dn1);
+  mpz_fdiv_q_2exp(t,md,1); mpz_sqrt(s,t); mpz_fdiv_q_2exp(b,s,64);
+  if ( !mpz_sgn(b) ) mpz_set_ui(b,1);
+  mpz_set_ui(dn,1);
+  for ( i = 0; i < row; i++ )
+    for ( j = 0, mi = mat[i]; j < col; j++ )
+      if ( mpz_sgn(mi[j]) ) {
+        mpz_mul(s,mi[j],dn);
+        mpz_mod(u,s,md);
+        ret = mpz_inttorat(u,md,b,nm1,dn1);
+        if ( !ret ) 
+          return 0;
+        else {
+          if ( !UNIMPZ(dn1) ) {
+            for ( k = 0; k < i; k++ )
+              for ( l = 0, nmk = nm[k]; l < col; l++ ) mpz_mul(nmk[l],nmk[l],dn1);
+            for ( l = 0, nmk = nm[i]; l < j; l++ ) mpz_mul(nmk[l],nmk[l],dn1);
+          }
+          mpz_set(nm[i][j],nm1);
+          mpz_mul(dn,dn,dn1);
+        }
+      }
+  return 1;
+}
+
 int intmtoratm(MAT mat,Z md,MAT nm,Z *dn)
 {
   Z t,s,b,dn0,dn1,nm1,q,u,unm,udn,dmy;
@@ -1231,9 +1335,45 @@ int intvtoratv(Z *v,int n,Z md,Z b,Z *nm,Z *dn)
 
 /* assuming 0 < c < m */
 
+int mpz_inttorat(mpz_t c,mpz_t m,mpz_t b,mpz_t nm,mpz_t dn)
+{
+  mpz_t u1,v1,u2,v2,r1,r2;
+  mpz_t q,t;
+
+  mpz_init_set_ui(u1,0); mpz_init_set_ui(v1,1);
+  mpz_init_set(u2,m); mpz_init_set(v2,c);
+  mpz_init(q); mpz_init(t); mpz_init(r1); mpz_init(r2);
+  while ( mpz_cmp(v2,b) >= 0 ) {
+    /* r2 = u2-q*v2 */
+    mpz_fdiv_qr(q,r2,u2,v2);
+    mpz_set(u2,v2); mpz_set(v2,r2);
+    /* r1 = u1-q*v1 */
+    mpz_mul(t,q,v1); mpz_sub(r1,u1,t);
+    mpz_set(u1,v1); mpz_set(v1,r1);
+  }
+  if ( mpz_cmp(v1,b) >= 0 ) return 0;
+  else {
+    mpz_gcd(t,v1,v2);
+    if ( UNIMPZ(t) ) 
+      mpz_set_ui(r1,0); 
+    else {
+      /* v1 /= t, v2 /= t, t=c*v1-v2, r1=t%m */
+      mpz_divexact(v1,v1,t); mpz_divexact(v2,v2,t);
+      mpz_mul(t,c,v1); mpz_sub(t,t,v2); mpz_mod(r1,t,m);
+    }
+    if ( mpz_sgn(r1) ) return 0;
+    if ( mpz_sgn(v1)<0  ) {
+      mpz_neg(dn,v1); mpz_neg(nm,v2);
+    } else {
+      mpz_set(dn,v1); mpz_set(nm,v2);
+    }
+    return 1;
+  }
+}
+
 int inttorat(Z c,Z m,Z b,Z *nmp,Z *dnp)
 {
-  Z qq,t,u1,v1,r1;
+  Z qq,t,s,r,u1,v1,r1;
   Z q,u2,v2,r2;
 
   u1 = 0; v1 = ONE; u2 = m; v2 = c;
@@ -1243,17 +1383,59 @@ int inttorat(Z c,Z m,Z b,Z *nmp,Z *dnp)
   }
   if ( cmpz(v1,b) >= 0 ) return 0;
   else {
-    if ( mpz_sgn(BDY(v1))<0  ) {
-      chsgnz(v1,dnp); chsgnz(v2,nmp);
+    /* reduction and check */
+    /* v2/v1 = u2/u1, c*u1-u2 = 0 mod m? */
+    gcdz(v1,v2,&t);
+    if ( UNIZ(t) ) {
+      u1 = v1; u2 = v2; r = 0;
     } else {
-      *dnp = v1; *nmp = v2;
+      divsz(v1,t,&u1); divsz(v2,t,&u2);
+      mulz(c,u1,&t); subz(t,u2,&s); remz(s,m,&r);
     }
+    if ( r ) return 0;
+    if ( mpz_sgn(BDY(u1))<0  ) {
+      chsgnz(u1,dnp); chsgnz(u2,nmp);
+    } else {
+      *dnp = u1; *nmp = u2;
+    }
     return 1;
   }
 }
 
 extern int f4_nocheck;
 
+int mpz_gensolve_check(MAT mat,mpz_t **nm,mpz_t dn,int rank,int clen,int *rind,int *cind)
+{
+  int row,col,i,j,k,l;
+  mpz_t t;
+  mpz_t *w;
+  Z *mati;
+  mpz_t *nmk;
+
+  if ( f4_nocheck ) return 1;
+  row = mat->row; col = mat->col;
+  w = (mpz_t *)MALLOC(clen*sizeof(mpz_t));
+  mpz_init(t);
+  for ( i = 0; i < clen; i++ ) mpz_init(w[i]);
+  for ( i = 0; i < row; i++ ) {
+    mati = (Z *)mat->body[i];
+    for ( l = 0; l < clen; l++ ) mpz_set_ui(w[l],0);
+    for ( k = 0; k < rank; k++ )
+      for ( l = 0, nmk = (mpz_t *)nm[k]; l < clen; l++ ) {
+        /* w[l] += mati[rind[k]]*nmk[k] */
+        if ( mati[rind[k]] ) mpz_addmul(w[l],BDY(mati[rind[k]]),nmk[l]);
+      }
+    for ( j = 0; j < clen; j++ ) {
+      if ( mati[cind[j]] ) mpz_mul(t,dn,BDY(mati[cind[j]]));
+      else mpz_set_ui(t,0);
+      if ( mpz_cmp(w[j],t) ) break;
+    }
+    if ( j != clen ) break;
+  }
+  if ( i != row ) return 0;
+  else return 1;
+}
+
 int gensolve_check(MAT mat,MAT nm,Z dn,int *rind,int *cind)
 {
   int row,col,rank,clen,i,j,k,l;
@@ -1322,11 +1504,11 @@ void isqrtz(Z a,Z *r)
   Z two;
 
   if ( !a ) *r = 0;
-  else if ( UNIQ(a) ) *r = ONE;
+  else if ( UNIZ(a) ) *r = ONE;
   else {
     k = z_bits((Q)a); /* a <= 2^k-1 */
     bshiftz(ONE,-((k>>1)+(k&1)),&x); /* a <= x^2 */
-    STOQ(2,two);
+    STOZ(2,two);
     while ( 1 ) {
       pwrz(x,two,&t);
       if ( cmpz(t,a) <= 0 ) {
@@ -1444,13 +1626,16 @@ int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Z *dn
   Z wn;
   Z wq;
 
+#if SIZEOF_LONG == 8
+  return generic_gauss_elim_hensel64(mat,nmmat,dn,rindp,cindp,0);
+#endif
 init_eg(&eg_mul1); init_eg(&eg_mul2);
   a0 = (Z **)mat->body;
   row = mat->row; col = mat->col;
   w = (int **)almat(row,col);
   for ( ind = 0; ; ind++ ) {
     md = get_lprime(ind);
-    STOQ(md,mdq);
+    STOZ(md,mdq);
     for ( i = 0; i < row; i++ )
       for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
         wi[j] = remqi((Q)ai[j],md);
@@ -1556,8 +1741,10 @@ get_eg(&tmp2); add_eg(&eg_mul2,&tmp1,&tmp2);
                 if ( !cinfo[j] )
                   cind[k++] = j;
               return rank;
-            }
+            } else
+              goto reset;
           } else {
+reset:
             period = period*3/2;
             count = 0;
           }
@@ -1593,12 +1780,15 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
   Z wq;
   DP m;
 
+#if SIZEOF_LONG == 8
+  return generic_gauss_elim_hensel64(mat,nmmat,dn,rindp,cindp,mb);
+#endif
   a0 = (Z **)mat->body;
   row = mat->row; col = mat->col;
   w = (int **)almat(row,col);
   for ( ind = 0; ; ind++ ) {
     md = get_lprime(ind);
-    STOQ(md,mdq);
+    STOZ(md,mdq);
     for ( i = 0; i < row; i++ )
       for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
         wi[j] = remqi((Q)ai[j],md);
@@ -1624,14 +1814,14 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
     a = (Z **)almat_pointer(rank,rank); /* lhs mat */
     MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
     for ( j = li = ri = 0; j < col; j++ )
-      if ( cinfo[j] ) {
+      if ( cinfo[j] > 0 ) {
         /* the column is in lhs */
         for ( i = 0; i < rank; i++ ) {
           w[i][li] = w[i][j];
           a[i][li] = a0[rinfo[i]][j];
         }
         li++;
-      } else {
+      } else if ( !cinfo[j] ) {
         /* the column is in rhs */
         for ( i = 0; i < rank; i++ )
           b[i][ri] = a0[rinfo[i]][j];
@@ -1665,8 +1855,8 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
         for ( i = 0; i < rank; i++ )
           for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
             wi[j] = remqi((Q)bi[j],md);
-        /* wc = A^(-1)wc; wc is normalized */
-        solve_by_lu_mod(w,rank,md,wc,ri,1);
+        /* wc = A^(-1)wc; wc is not normalized */
+        solve_by_lu_mod(w,rank,md,wc,ri,0);
         /* x += q*wc */
         for ( i = 0; i < rank; i++ )
           for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
@@ -1679,17 +1869,13 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
               mpz_init_set(uz,BDY(b[i][j]));
             else
               mpz_init_set_ui(uz,0);
-            for ( k = 0; k < rank; k++ ) {
-              if ( a[i][k] && wc[k][j] ) {
-                if ( wc[k][j] < 0 )
-                  mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
-                else
+            for ( k = 0; k < rank; k++ )
+              if ( a[i][k] && wc[k][j] )
                   mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
-              }
-            }
             MPZTOZ(uz,u);
             divsz(u,mdq,&b[i][j]);
           }
+
         count++;
         /* q = q*md */
         mulz(q,mdq,&u); q = u;
@@ -1709,8 +1895,439 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
                 if ( !cinfo[j] )
                   cind[k++] = j;
               return rank;
+            } else
+              goto reset;
+          } else {
+reset:
+            period = period*3/2;
+            count = 0;
+          }
+        }
+      }
+  }
+}
+
+#if SIZEOF_LONG == 8
+mp_limb_t remqi64(Q a,mp_limb_t mod)
+{
+  mp_limb_t c,nm,dn;
+  mpz_t r;
+
+  if ( !a ) return 0;
+  else if ( a->z ) {
+    mpz_init(r);
+    c = mpz_fdiv_r_ui(r,BDY((Z)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 = invmod64(dn,mod);    
+    c = mulmod64(nm,dn,mod);
+  }
+  return c;
+}
+
+int generic_gauss_elim_mod64(mp_limb_t **mat,int row,int col,mp_limb_t md,int *colstat);
+mp_limb_t get_lprime64(int ind);
+
+void mpz_print(mpz_t a)
+{
+  mpz_out_str(stdout,10,a); printf("\n");
+}
+
+void mpz_printmat(mpz_t **a,int row,int col)
+{
+  int i,j;
+  for ( i = 0; i < row; i++ ) {
+    for ( j = 0; j < col; j++ ) {
+      mpz_out_str(stdout,10,a[i][j]); printf(" ");
+    }
+    printf("\n");
+  }
+}
+
+mpz_t **mpz_allocmat(int row,int col)
+{
+  mpz_t **p;
+  int i,j;
+
+  p = (mpz_t **)MALLOC(row*sizeof(mpz_t *));
+  for ( i = 0; i < row; i++ ) {
+    p[i] = (mpz_t *)MALLOC(col*sizeof(mpz_t));
+    for ( j = 0; j < col; j++ ) mpz_init(p[i][j]);
+  }
+  return p;
+}
+
+#if 1
+int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
+{
+  mp_limb_t **wmat;
+  mp_limb_t *wmi;
+  mp_limb_t md,inv,t,t1;
+  Z z;
+  Z **bmat,*bmi;
+  mpz_t **tmat,**num;
+  mpz_t *tmi;
+  mpz_t den;
+  mpz_t q,m1,m3,s,u;
+  int *colstat,*wcolstat,*rind,*cind;
+  int row,col,ind,i,j,k,l,rank,rank0;
+  MAT r;
+  int ret;
+
+  bmat = (Z **)mat->body;
+  row = mat->row; col = mat->col;
+  wmat = (mp_limb_t **)almat64(row,col);
+  colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
+  wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
+  mpz_init(m1); mpz_init(m3); mpz_init(den);
+  for ( ind = 0; ; ind++ ) {
+    if ( DP_Print ) {
+      fprintf(asir_out,"."); fflush(asir_out);
+    }
+    md = get_lprime64(ind);
+    for ( i = 0; i < row; i++ )
+      for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
+        wmi[j] = bmi[j]==0?0:mpz_fdiv_ui(BDY(bmi[j]),md);
+    rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
+    if ( !ind ) {
+RESET:
+      mpz_set_ui(m1,md);
+      rank0 = rank;
+      bcopy(wcolstat,colstat,col*sizeof(int));
+      // crmat
+      tmat = mpz_allocmat(rank,col-rank);
+      // 
+      num = mpz_allocmat(rank,col-rank);
+      for ( i = 0; i < rank; i++ )
+        for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
+          if ( !colstat[j] ) { mpz_set_ui(tmi[k],wmi[j]); k++; }
+    } 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 = invmod64(mpz_fdiv_ui(m1,md),md);
+      mpz_mul_ui(m3,m1,md);
+      for ( i = 0; i < rank; i++ )      
+        for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
+          if ( !colstat[j] ) {
+            if ( mpz_sgn(tmi[k]) ) {
+            /* f3 = f1+m1*(m1 mod md)^(-1)*(f2 - f1 mod md) */
+              t = mpz_fdiv_ui(tmi[k],md);
+              if ( wmi[j] >= t ) t = wmi[j]-t;
+              else t = md-(t-wmi[j]);
+              mpz_addmul_ui(tmi[k],m1,mulmod64(t,inv,md));
+            } else if ( wmi[j] ) {
+            /* f3 = m1*(m1 mod m2)^(-1)*f2 */
+              mpz_mul_ui(tmi[k],m1,mulmod64(wmi[j],inv,md));
             }
+            k++;
+          }
+      mpz_set(m1,m3);
+      if ( ind % F4_INTRAT_PERIOD ) 
+        ret = 0;
+      else 
+        ret = mpz_intmtoratm(tmat,rank,col-rank,m1,num,den);
+      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 ( mpz_gensolve_check(mat,num,den,rank,col-rank,rind,cind) ) {
+          MKMAT(r,rank,col-rank); *nm = r;
+          for ( i = 0; i < rank; i++ )
+            for ( j = 0; j < col-rank; j++ ) {
+              MPZTOZ(num[i][j],z); BDY(r)[i][j] = z;
+            }
+          MPZTOZ(den,*dn);
+          return rank;
+        }
+      }
+    }
+  }
+}
+#else
+int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
+{
+  mp_limb_t **wmat;
+  mp_limb_t *wmi;
+  mp_limb_t md,inv,t,t1;
+  Z **bmat,**tmat,*bmi,*tmi;
+  Z q,m1,m2,m3,s,u;
+  int *colstat,*wcolstat,*rind,*cind;
+  int row,col,ind,i,j,k,l,rank,rank0;
+  MAT r,crmat;
+  int ret;
+
+  bmat = (Z **)mat->body;
+  row = mat->row; col = mat->col;
+  wmat = (mp_limb_t **)almat64(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_lprime64(ind);
+    for ( i = 0; i < row; i++ )
+      for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
+        wmi[j] = remqi64((Q)bmi[j],md);
+    rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
+    if ( !ind ) {
+RESET:
+      UTOZ(md,m1);
+      rank0 = rank;
+      bcopy(wcolstat,colstat,col*sizeof(int));
+      MKMAT(crmat,rank,col-rank);
+      MKMAT(r,rank,col-rank); *nm = r;
+      tmat = (Z **)crmat->body;
+      for ( i = 0; i < rank; i++ )
+        for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
+          if ( !colstat[j] ) { UTOZ(wmi[j],tmi[k]); k++; }
+    } 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 = invmod64(remqi64((Q)m1,md),md);
+      UTOZ(md,m2); mulz(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 = remqi64((Q)tmi[k],md);
+              if ( wmi[j] >= t ) t = wmi[j]-t;
+              else t = md-(t-wmi[j]);
+              t1 = mulmod64(t,inv,md);
+              UTOZ(t1,u); mulz(m1,u,&s); 
+              addz(tmi[k],s,&u); tmi[k] = u;
+            } else if ( wmi[j] ) {
+            /* f3 = m1*(m1 mod m2)^(-1)*f2 */
+              t = mulmod64(wmi[j],inv,md);
+              UTOZ(t,u); mulz(m1,u,&s); tmi[k] = s;
+            }
+            k++;
+          }
+      m1 = m3;
+      if ( ind % F4_INTRAT_PERIOD ) 
+        ret = 0;
+      else 
+        ret = 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 ( gensolve_check(mat,*nm,*dn,rind,cind) )
+          return rank;
+      }
+    }
+  }
+}
+#endif
+
+int generic_gauss_elim_hensel64(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp,DP *mb)
+{
+  MAT r;
+  Z z;
+  Z **a0;
+  Z *ai;
+  mpz_t **a,**b,**x,**nm;
+  mpz_t *bi,*xi;
+  mpz_t q,u,den;
+  mp_limb_t **w;
+  mp_limb_t *wi;
+  mp_limb_t **wc;
+  mp_limb_t md;
+  int row,col;
+  int ind,i,j,k,l,li,ri,rank;
+  int *cinfo,*rinfo;
+  int *rind,*cind;
+  int count;
+  int ret;
+  int period;
+  DP m;
+
+  a0 = (Z **)mat->body;
+  row = mat->row; col = mat->col;
+  w = (mp_limb_t **)almat64(row,col);
+  for ( ind = 0; ; ind++ ) {
+    md = get_lprime64(ind);
+    for ( i = 0; i < row; i++ )
+      for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
+        wi[j] = remqi64((Q)ai[j],md);
+
+    if ( DP_Print > 3 ) {
+      fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
+    }
+    rank = find_lhs_and_lu_mod64(w,row,col,md,&rinfo,&cinfo);
+    if ( DP_Print > 3 ) {
+      fprintf(asir_out,"done.\n"); fflush(asir_out);
+    }
+
+    if ( mb ) {
+      /* this part is added for inv_or_split_dalg */
+      for ( i = 0; i < col-1; i++ ) {
+        if ( !cinfo[i] ) {
+          m = mb[i];
+          for ( j = i+1; j < col-1; j++ )
+            if ( dp_redble(mb[j],m) )
+              cinfo[j] = -1;
+        }
+      }
+    }
+  
+    a = (mpz_t **)mpz_allocmat(rank,rank); /* lhs mat */
+    b = (mpz_t **)mpz_allocmat(rank,col-rank);
+    for ( j = li = ri = 0; j < col; j++ )
+      if ( cinfo[j] > 0 ) {
+        /* the column is in lhs */
+        for ( i = 0; i < rank; i++ ) {
+          w[i][li] = w[i][j];
+          if ( a0[rinfo[i]][j] )
+            mpz_set(a[i][li],BDY(a0[rinfo[i]][j]));
+          else
+            mpz_set_ui(a[i][li],0);
+        }
+        li++;
+      } else if ( !cinfo[j] ) {
+        /* the column is in rhs */
+        for ( i = 0; i < rank; i++ ) {
+          if ( a0[rinfo[i]][j] )
+            mpz_set(b[i][ri],BDY(a0[rinfo[i]][j]));
+          else
+            mpz_set_ui(b[i][ri],0);
+        }
+        ri++;
+      }
+
+      /* solve Ax=B; A: rank x rank, B: rank x ri */
+      /* algorithm
+         c <- B
+         x <- 0
+         q <- 1
+         do 
+           t <- A^(-1)c mod p
+           x <- x+qt
+           c <- (c-At)/p
+           q <- qp
+         end do
+         then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
+      */
+      x = (mpz_t **)mpz_allocmat(rank,ri);
+      nm = (mpz_t **)mpz_allocmat(rank,ri);
+      wc = (mp_limb_t **)almat64(rank,ri);
+      *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
+      *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
+
+      period = F4_INTRAT_PERIOD;
+      mpz_init_set_ui(q,1);
+      mpz_init(u);
+      mpz_init(den);
+      for ( count = 0; ; ) {
+        /* check Ax=B mod q */
+        if ( DP_Print > 3 )
+          fprintf(stderr,"o");
+        /* wc = b mod md */
+        for ( i = 0; i < rank; i++ )
+          for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
+            wi[j] = mpz_fdiv_ui(bi[j],md);
+        /* wc = A^(-1)wc; wc is not normalized */
+        solve_by_lu_mod64(w,rank,md,(mp_limb_signed_t **)wc,ri,0);
+        /* x += q*wc */
+        for ( i = 0; i < rank; i++ )
+          for ( j = 0, wi = wc[i]; j < ri; j++ )
+            if ( wi[j] > 0 )
+              mpz_addmul_ui(x[i][j],q,wi[j]);
+            else if ( wi[j] < 0 )
+              mpz_submul_ui(x[i][j],q,-wi[j]);
+        /* b =(b-A*wc)/md */
+        for ( i = 0; i < rank; i++ )
+          for ( j = 0; j < ri; j++ ) {
+            mpz_set(u,b[i][j]);
+            for ( k = 0; k < rank; k++ ) {
+              if ( a[i][k] && wc[k][j] ) {
+                if ( wc[k][j] < 0 )
+                  mpz_addmul_ui(u,a[i][k],-wc[k][j]);
+                else
+                  mpz_submul_ui(u,a[i][k],wc[k][j]);
+              }
+            }
+            mpz_divexact_ui(b[i][j],u,md);
+          }
+        count++;
+        /* q = q*md */
+        mpz_mul_ui(q,q,md);
+        if ( count == period ) {
+          ret = mpz_intmtoratm(x,rank,ri,q,nm,den);
+          if ( ret ) {
+            for ( j = k = l = 0; j < col; j++ )
+              if ( cinfo[j] > 0 )
+                rind[k++] = j;  
+              else if ( !cinfo[j] )
+                cind[l++] = j;
+            ret = mpz_gensolve_check(mat,nm,den,rank,ri,rind,cind);
+            if ( ret ) {
+              *rindp = rind;
+              *cindp = cind;
+              for ( j = k = 0; j < col; j++ )
+                if ( !cinfo[j] )
+                  cind[k++] = j;
+              MKMAT(r,rank,ri); *nmmat = r;
+              for ( i = 0; i < rank; i++ )
+                for ( j = 0; j < ri; j++ ) {
+                  MPZTOZ(nm[i][j],z); BDY(r)[i][j] = z;
+                }
+              MPZTOZ(den,*dn);
+              return rank;
+            } else
+              goto reset;
           } else {
+reset:
+            fprintf(stderr,"F");
             period = period*3/2;
             count = 0;
           }
@@ -1718,3 +2335,5 @@ int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT 
       }
   }
 }
+
+#endif