Add mpc_tan function.

git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@122 211d60ee-9f03-0410-a15a-8952a2c7a4e4

1 files changed, 426 insertions, 0 deletions

diff --git a/tests/ttan.c b/tests/ttan.c
new file mode 100644
index 0000000..1247afe
--- /dev/null
+++ b/tests/ttan.c
@@ -0,0 +1,426 @@
+/* test file for mpc_tan.
+
+Copyright (C) 2008 Philippe Th\'eveny.
+
+This file is part of the MPC Library.
+
+The MPC 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 MPC 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 MPC Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "gmp.h"
+#include "mpfr.h"
+#include "mpc.h"
+#include "mpc-impl.h"
+
+#define TEST_FUNCTION mpc_tan
+#include "tgeneric.c"
+
+static void
+test_failed (mpc_t op, mpc_t get, mpc_t expected)
+{
+  printf ("mpc_tan(op) failed with ");
+  OUT (op);
+  printf ("     ");
+  OUT (get);
+  OUT (expected);
+  exit (1);
+}
+
+/* check special values as defined in C99 standard */
+static void
+special ()
+{
+  mpc_t z;
+  mpc_t t;
+  mpc_t c99;
+
+  mpc_init (z);
+  mpc_init (t);
+  mpc_init (c99);
+
+  /* tan(+Inf +i*Inf) = +/-0 +i */
+  mpfr_set_inf (MPC_RE (z), +1);
+  mpfr_set_inf (MPC_IM (z), +1);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_cmp_si (MPC_IM (t), +1) != 0)
+    {
+      mpfr_set_ui (MPC_RE(c99), 0, GMP_RNDN);
+      mpfr_set_ui (MPC_IM(c99), 1, GMP_RNDN);
+      test_failed (z, t, c99);
+    }
+
+  /* tan(+Inf -i*Inf) = +/-0 -i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_cmp_si (MPC_IM (t), -1) != 0)
+    {
+      mpfr_set_ui (MPC_RE(c99), 0, GMP_RNDN);
+      mpfr_set_si (MPC_IM(c99), -1, GMP_RNDN);
+      test_failed (z, t, c99);
+    }
+
+  /* tan(-Inf +i*Inf) = -/+0 +i */
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_cmp_si (MPC_IM (t), +1) != 0)
+    {
+      mpfr_set_ui (MPC_RE(c99), 0, GMP_RNDN);
+      mpfr_set_si (MPC_IM(c99), -1, GMP_RNDN);
+      mpc_neg (c99, c99, MPC_RNDNN);
+      test_failed (z, t, c99);
+    }
+
+  /* tan(-Inf -i*Inf) = -/+0 -i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_cmp_si (MPC_IM (t), -1) != 0)
+    {
+      mpfr_set_ui (MPC_RE(c99), 0, GMP_RNDN);
+      mpfr_set_ui (MPC_IM(c99), 1, GMP_RNDN);
+      mpc_neg (c99, c99, MPC_RNDNN);
+      test_failed (z, t, c99);
+    }
+
+  /* tan(-Inf +i*y) = NaN+i*NaN, when y is finite */
+  /* tan(+Inf +i*y) = NaN+i*NaN, when y is finite */
+  mpfr_set_si (MPC_IM (z), -1, GMP_RNDN);
+  mpfr_set_nan (MPC_RE (c99));
+  mpfr_set_nan (MPC_IM (c99));
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpfr_set_ui (MPC_IM (z), 0, GMP_RNDN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  /* tan(x +i*NaN) = NaN +i*NaN, when x is non zero */
+  mpfr_set_inf (MPC_RE (z), +1);
+  mpfr_set_nan (MPC_IM (z));
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpfr_set_ui (MPC_RE (z), 1, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_nan_p (MPC_RE (t)) || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, c99);
+
+  /* tan(+0 +i*NaN) = +0 +i*NaN */
+  mpfr_set_ui (MPC_RE (z), 0, GMP_RNDN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_signbit (MPC_RE (t))
+      || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, z);
+
+  /* tan(-0 +i*NaN) = -0 +i*NaN */
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (!mpfr_zero_p (MPC_RE (t)) || mpfr_signbit (MPC_RE (t)) == 0
+      || !mpfr_nan_p (MPC_IM (t)))
+    test_failed (z, t, z);
+
+  /* tan(x -i*Inf) = 0*sin(2*x)-i */
+  /*  tan(0.5 -i*Inf) = +0 -i */
+  mpfr_set_ui_2exp (MPC_RE (z), 1, -1, GMP_RNDN);
+  mpfr_set_inf (MPC_IM (z), -1);
+  mpc_set_si_si (c99, 0, -1, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(0.5 +i*Inf) = +0 +i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_conj (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(-0.5 -i*Inf) = -0 -i */
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_neg (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(-0.5 +i*Inf) = -0 +i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_conj (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(+0 -i*Inf) = +0 -i */
+  mpfr_set_ui (MPC_RE (z), 0, GMP_RNDN);
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_neg (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(+0 +i*Inf) = +0 +i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_conj (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(-0 -i*Inf) = -0 -i */
+  mpc_neg (z, z, MPC_RNDNN);
+  mpc_neg (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  /*  tan(-0 +i*Inf) = -0 +i */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_conj (c99, c99, MPC_RNDNN);
+  mpc_tan (t, z, MPC_RNDNN);
+  if (mpc_cmp (t, c99))
+    test_failed (z, t, c99);
+
+  mpc_clear (c99);
+  mpc_clear (t);
+  mpc_clear (z);
+}
+
+static void
+pure_real_argument ()
+{
+  /* tan(x -i*0) = tan(x) -i*0 */
+  /* tan(x +i*0) = tan(x) +i*0 */
+  mpfr_t x;
+  mpfr_t tan_x;
+  mpc_t z;
+  mpc_t tan_z;
+
+  mpfr_init (x);
+  mpfr_init (tan_x);
+  mpc_init (z);
+  mpc_init (tan_z);
+
+  /* tan(1 +i*0) = tan(1) +i*0 */
+  mpc_set_ui_ui (z, 1, 0, MPC_RNDNN);
+  mpfr_set_ui (x, 1, GMP_RNDN);
+  mpfr_tan (tan_x, x, GMP_RNDN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(1 + i * 0) failed\n");
+      exit (1);
+    }
+
+  /* tan(1 -i*0) = tan(1) -i*0 */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || !mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(1 - i * 0) failed\n");
+      exit (1);
+    }
+
+  /* tan(Pi/2 +i*0) = +Inf +i*0 */
+  mpfr_const_pi (x, GMP_RNDN);
+  mpfr_div_2ui (x, x, 1, GMP_RNDN);
+  mpfr_set (MPC_RE (z), x, GMP_RNDN);
+  mpfr_set_ui (MPC_IM (z), 0, GMP_RNDN);
+  mpfr_tan (tan_x, x, GMP_RNDN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(Pi/2 + i * 0) failed\n");
+      exit (1);
+    }
+
+  /* tan(Pi/2 -i*0) = +Inf -i*0 */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || !mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(Pi/2 - i * 0) failed\n");
+      exit (1);
+    }
+
+  /* tan(-Pi/2 +i*0) = -Inf +i*0 */
+  mpfr_neg (x, x, GMP_RNDN);
+  mpc_neg (z, z, MPC_RNDNN);
+  mpfr_tan (tan_x, x, GMP_RNDN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(-Pi/2 + i * 0) failed\n");
+      exit (1);
+    }
+
+  /* tan(-Pi/2 -i*0) = -Inf -i*0 */
+  mpc_conj (z, z, MPC_RNDNN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_RE (tan_z), tan_x) != 0
+      || !mpfr_zero_p (MPC_IM (tan_z)) || !mpfr_signbit (MPC_IM (tan_z)))
+    {
+      printf ("mpc_tan(-Pi/2 - i * 0) failed\n");
+      exit (1);
+    }
+
+  mpc_clear (tan_z);
+  mpc_clear (z);
+  mpfr_clear (tan_x);
+  mpfr_clear (x);
+}
+
+static void
+pure_imaginary_argument ()
+{
+  /* tan(-0 +i*y) = -0 +i*tanh(y) */
+  /* tan(+0 +i*y) = +0 +i*tanh(y) */
+  mpfr_t y;
+  mpfr_t tanh_y;
+  mpc_t z;
+  mpc_t tan_z;
+
+  mpfr_init (y);
+  mpfr_init (tanh_y);
+  mpc_init (z);
+  mpc_init (tan_z);
+
+  /* tan(0 +i) = +0 +i*tanh(1) */
+  mpc_set_ui_ui (z, 0, 1, MPC_RNDNN);
+  mpfr_set_ui (y, 1, GMP_RNDN);
+  mpfr_tanh (tanh_y, y, GMP_RNDN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_IM (tan_z), tanh_y) != 0
+      || !mpfr_zero_p (MPC_RE (tan_z)) || mpfr_signbit (MPC_RE (tan_z)))
+    {
+      printf ("mpc_tan(+0 + i) failed\n");
+      exit (1);
+    }
+
+  /* tan(-0 -i) = -0 +i*tan(-1) */
+  mpc_neg (z, z, MPC_RNDNN);
+  mpfr_neg (tanh_y, tanh_y, GMP_RNDN);
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  if (mpfr_cmp (MPC_IM (tan_z), tanh_y) != 0
+      || !mpfr_zero_p (MPC_RE (tan_z)) || !mpfr_signbit (MPC_RE (tan_z)))
+    {
+      printf ("mpc_tan(-0 - i) failed\n");
+      exit (1);
+    }
+
+  mpc_clear (tan_z);
+  mpc_clear (z);
+  mpfr_clear (tanh_y);
+  mpfr_clear (y);
+}
+
+static void
+check_53()
+{
+  mpfr_t hpi;
+  mpc_t z;
+  mpc_t tan_z;
+  mpc_t t;
+
+  mpfr_init2 (hpi, 53);
+  mpc_init2 (z, 53);
+  mpc_init2 (tan_z, 53);
+  mpc_init2 (t, 53);
+
+  /* hpi = Pi/2 rounded to nearest to 53-bits precision. */
+  mpfr_const_pi (hpi, GMP_RNDN);
+  mpfr_div_2ui (hpi, hpi, 1, GMP_RNDN);
+
+  /* Im(z) = 2^{-52} */
+  mpfr_set_si_2exp (MPC_IM (z), 1, -52, GMP_RNDN);
+
+  /* Re(z) = Pi/2 - 2^{-52} rounded to nearest to 53-bits precision */
+  if (mpfr_sub (MPC_RE (z), hpi, MPC_IM (z), GMP_RNDN) != 0)
+    {
+      printf ("Error: N(Pi/2)-2^{-53} should equal N(Pi/2 - 2^{-53})\n");
+      exit (1);
+    }
+
+  mpc_tan (tan_z, z, MPC_RNDNN);
+  mpfr_set_str (MPC_RE (t), "1F12E8A6080473P-2", 16, GMP_RNDN);
+  mpfr_set_str (MPC_IM (t), "C2DB2FB340F81P-1", 16, GMP_RNDN);
+  if (mpc_cmp (tan_z, t) != 0)
+    test_failed (z, tan_z, t);
+
+  mpc_clear (t);
+  mpc_clear (tan_z);
+  mpc_clear (z);
+  mpfr_clear (hpi);
+}
+
+int
+main()
+{
+  special ();
+  pure_real_argument ();
+  pure_imaginary_argument ();
+
+  tgeneric ();
+
+  check_53 ();
+
+  return 0;
+}