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diff --git a/mpfr/tests/tzeta_ui.c b/mpfr/tests/tzeta_ui.c
new file mode 100644
index 00000000..6fb20f0d
--- /dev/null
+++ b/mpfr/tests/tzeta_ui.c
@@ -0,0 +1,112 @@
+/* Test file for mpfr_zeta_ui.
+
+Copyright 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The GNU MPFR Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "mpfr-test.h"
+
+#define TEST_FUNCTION mpfr_zeta_ui
+
+int
+main (int argc, char *argv[])
+{
+#if MPFR_VERSION >= MPFR_VERSION_NUM(2,3,0)
+  unsigned int prec, yprec;
+  int rnd;
+  mpfr_t x, y, z, t;
+  int inexact;
+  unsigned long n;
+
+  tests_start_mpfr ();
+
+  mpfr_init (x);
+  mpfr_init (y);
+  mpfr_init (z);
+  mpfr_init (t);
+
+  if (argc >= 3) /* tzeta_ui n prec [rnd] */
+    {
+      mpfr_set_prec (x, atoi (argv[2]));
+      mpfr_zeta_ui (x, atoi (argv[1]),
+                    argc > 3 ? (mp_rnd_t) atoi (argv[3]) : GMP_RNDN);
+      mpfr_out_str (stdout, 10, 0, x, GMP_RNDN);
+      printf ("\n");
+      goto clear_and_exit;
+    }
+
+  mpfr_set_prec (x, 33);
+  mpfr_set_prec (y, 33);
+  mpfr_zeta_ui (x, 3, GMP_RNDZ);
+  mpfr_set_str_binary (y, "0.100110011101110100000000001001111E1");
+  if (mpfr_cmp (x, y))
+    {
+      printf ("Error for zeta(3), prec=33, GMP_RNDZ\n");
+      printf ("expected "); mpfr_dump (y);
+      printf ("got      "); mpfr_dump (x);
+      exit (1);
+    }
+
+  for (prec = MPFR_PREC_MIN; prec <= 100; prec++)
+    {
+      mpfr_set_prec (x, prec);
+      mpfr_set_prec (z, prec);
+      mpfr_set_prec (t, prec);
+      yprec = prec + 10;
+      mpfr_set_prec (y, yprec);
+
+      for (n = 0; n < 50; n++)
+        for (rnd = 0; rnd < GMP_RND_MAX; rnd++)
+          {
+            inexact = mpfr_zeta_ui (y, n, GMP_RNDN);
+            if (mpfr_can_round (y, yprec, GMP_RNDN, GMP_RNDZ, prec
+                                + (rnd == GMP_RNDN)))
+              {
+                mpfr_set (t, y, (mp_rnd_t) rnd);
+                inexact = mpfr_zeta_ui (z, n, (mp_rnd_t) rnd);
+                if (mpfr_cmp (t, z))
+                  {
+                    printf ("results differ for n=%lu", n);
+                    printf (" prec=%u rnd_mode=%s\n", prec,
+                            mpfr_print_rnd_mode ((mp_rnd_t) rnd));
+                    printf ("   got      ");
+                    mpfr_dump (z);
+                    printf ("   expected ");
+                    mpfr_dump (t);
+                    printf ("   approx   ");
+                    mpfr_dump (y);
+                    exit (1);
+                  }
+              }
+          }
+    }
+
+ clear_and_exit:
+  mpfr_clear (x);
+  mpfr_clear (y);
+  mpfr_clear (z);
+  mpfr_clear (t);
+
+  tests_end_mpfr ();
+#endif
+  return 0;
+}