Use flint-3 for the subproduct trees in the trial division step.

* lib/cm-impl.h (cm_flint_tree_gcd): Declare new function.
* lib/flint.c (cm_flint_tree_gcd): New function.
* lib/nt.c (tree_gcd): Drop function when flint-3 is available.
  (cm_nt_mpz_tree_gcd): Use new function when flint-3 is available.

lib/cm-impl.h

@@ -132,6 +132,8 @@ extern char* cm_pari_sprintf_hfactor (int_cl_t d);
 #ifdef HAVE_FLINT3
 extern void cm_flint_mpz_powm (mpz_ptr z, mpz_srcptr a, mpz_srcptr e,
    mpz_srcptr p);
+extern void cm_flint_tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m,
+   int no_m);
 #endif
 extern void cm_flint_mpzx_xplusa_pow_modmod (mpzx_ptr g, unsigned long int a,
    mpz_srcptr e, mpzx_srcptr m, mpz_srcptr p);

lib/flint.c

@@ -146,6 +146,82 @@ void cm_flint_mpz_powm (mpz_ptr z, mpz_srcptr a, mpz_srcptr e, mpz_srcptr p)
 }
 #endif
 
+/*****************************************************************************/
+/*                                                                           */
+/* Function for product tree relying on FLINT.                               */
+/*                                                                           */
+/*****************************************************************************/
+
+#ifdef HAVE_FLINT3
+void cm_flint_tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m, int no_m)
+   /* This is a copy-paste of the static function tree_gcd from nt.c
+      with fmpz types. */
+{
+   fmpz_t np;
+   mpz_t tmp;
+   fmpz_t **tree;
+   int *width;
+   int levels;
+   int i, j;
+
+   fmpz_init (np);
+   fmpz_set_mpz (np, n);
+   mpz_init (tmp);
+
+   /* Compute the height of the subproduct tree of the m in levels. */
+   for (i = no_m, levels = 1; i > 1; i = (i+1) / 2, levels++);
+
+   /* Compute bottom-up a subproduct tree with m on the leaves. */
+   tree = (fmpz_t **) malloc (levels * sizeof (fmpz_t *));
+   width = (int *) malloc (levels * sizeof (int));
+   width [0] = no_m;
+   tree [0] = (fmpz_t *) malloc (no_m * sizeof (fmpz_t));
+   for (j = 0; j < no_m; j++) {
+      fmpz_init (tree [0][j]);
+      fmpz_set_mpz (tree [0][j], m [j]);
+   }
+   for (i = 1; i < levels; i++) {
+      width [i] = (width [i-1] + 1) / 2;
+      tree [i] = (fmpz_t *) malloc (width [i] * sizeof (fmpz_t));
+      for (j = 0; j < width [i-1] / 2; j++) {
+         fmpz_init (tree [i][j]);
+         fmpz_mul (tree [i][j], tree [i-1][2*j], tree [i-1][2*j+1]);
+      }
+      if (width [i-1] % 2 != 0)
+         fmpz_init_set (tree [i][j], tree [i-1][2*j]);
+   }
+
+   /* Replace the tree tops by n modulo the entry. */
+   for (j = 0; j < width [levels-1]; j++)
+      fmpz_mod (tree [levels-1][j], np, tree [levels-1][j]);
+
+   /* Replace top-down the tree entries by n modulo the entry. */
+   for (i = levels - 2; i >= 0; i--) {
+      for (j = 0; j < (width [i] / 2) * 2; j++)
+         fmpz_mod (tree [i][j], tree [i+1][j/2], tree [i][j]);
+      if (width [i] % 2 != 0)
+         fmpz_set (tree [i][j], tree [i+1][j/2]);
+   }
+
+   /* Compute the gcd of n mod m [j] and m [j]. */
+   for (j = 0; j < no_m; j++) {
+      fmpz_get_mpz (tmp, tree [0][j]);
+      mpz_gcd (gcd [j], tmp, m [j]);
+   }
+
+   /* Clear the tree. */
+   for (i = 0; i < levels; i++) {
+      for (j = 0; j < width [i]; j++)
+         fmpz_clear (tree [i][j]);
+      free (tree [i]);
+   }
+   free (tree);
+   free (width);
+   fmpz_clear (np);
+   mpz_clear (tmp);
+}
+#endif
+
 /*****************************************************************************/
 /*                                                                           */
 /* Functions for mpzx modulo p relying on FLINT.                             */

lib/nt.c

@@ -24,7 +24,9 @@ Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 #include "cm-impl.h"
 
 static void cm_mpz_powm (mpz_ptr z, mpz_srcptr a, mpz_srcptr e, mpz_srcptr p);
+#ifndef HAVE_FLINT3
 static void tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m, int no_m);
+#endif
 static int miller_rabin (mpz_srcptr n);
 static void cm_nt_mpz_tonelli_with_generator (mpz_ptr root, mpz_srcptr a,
    mpz_srcptr p, unsigned int e, mpz_srcptr q, mpz_srcptr z);
@@ -455,6 +457,7 @@ void cm_nt_mpz_tonelli_si (mpz_ptr root, const long int a, mpz_srcptr p)
 
 /*****************************************************************************/
 
+#ifndef HAVE_FLINT3
 static void tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m, int no_m)
    /* This is the workhorse behind the cm_nt_mpz_tree_gcd function; it
       assumes that the total size of the no_m entries of m is less than
@@ -513,6 +516,7 @@ static void tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m, int no_m)
    free (tree);
    free (width);
 }
+#endif
 
 /*****************************************************************************/
 
@@ -538,7 +542,11 @@ void cm_nt_mpz_tree_gcd (mpz_t *gcd, mpz_srcptr n, mpz_t *m, int no_m)
               && size_m + mpz_sizeinbase (m [offset + no_batch], 2)
                  < size_n / 2;
            size_m += mpz_sizeinbase (m [offset + no_batch], 2), no_batch++);
+#ifdef HAVE_FLINT3
+      cm_flint_tree_gcd (gcd + offset, n, m + offset, no_batch);
+#else
       tree_gcd (gcd + offset, n, m + offset, no_batch);
+#endif
    }
 }