gcc/mpfr/tests/tatan.c

/* Test file for mpfr_atan.

Copyright 2001, 2002, 2003, 2004, 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"

static void
special (void)
{
  mpfr_t x, y, z;
  int r;
  int i;

  mpfr_init2 (x, 53);
  mpfr_init2 (y, 53);
  mpfr_init2 (z, 53);

  mpfr_set_str_binary (x, "1.0000100110000001100111100011001110101110100111011101");
  mpfr_set_str_binary (y, "1.1001101101110100101100110011011101101000011010111110e-1");
  mpfr_atan (z, x, GMP_RNDN);
  if (mpfr_cmp (y, z))
    {
      printf ("Error in mpfr_atan for prec=53, rnd=GMP_RNDN\n");
      printf ("x=");
      mpfr_out_str (stdout, 2, 0, x, GMP_RNDN);
      printf ("\nexpected ");
      mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
      printf ("\ngot      ");
      mpfr_out_str (stdout, 2, 0, z, GMP_RNDN);
      printf ("\n");
      exit (1);
    }

  /* atan(+Inf) = Pi/2 */
  for (r = 0; r < GMP_RND_MAX ; r++)
    {
      mpfr_set_inf (x, 1);
      mpfr_atan (y, x, (mp_rnd_t) r);
      mpfr_const_pi (x, (mp_rnd_t) r);
      mpfr_div_2exp (x, x, 1, (mp_rnd_t) r);
      if (mpfr_cmp (x, y))
        {
          printf ("Error: mpfr_atan(+Inf), rnd=%s\n",
                  mpfr_print_rnd_mode ((mp_rnd_t) r));
          exit (1);
        }
    }

  /* atan(-Inf) = - Pi/2 */
  for (r = 0; r < GMP_RND_MAX ; r++)
    {
      mpfr_set_inf (x, -1);
      mpfr_atan (y, x, (mp_rnd_t) r);
      mpfr_const_pi (x, MPFR_INVERT_RND((mp_rnd_t) r));
      mpfr_neg (x, x, (mp_rnd_t) r);
      mpfr_div_2exp (x, x, 1, (mp_rnd_t) r);
      if (mpfr_cmp (x, y))
        {
          printf ("Error: mpfr_atan(-Inf), rnd=%s\n",
                  mpfr_print_rnd_mode ((mp_rnd_t) r));
          exit (1);
        }
    }

  /* atan(NaN) = NaN */
  mpfr_set_nan (x);
  mpfr_atan (y, x, GMP_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_atan(NaN) <> NaN\n");
      exit (1);
    }

  /* atan(+/-0) = +/-0 */
  mpfr_set_ui (x, 0, GMP_RNDN);
  MPFR_SET_NEG (y);
  mpfr_atan (y, x, GMP_RNDN);
  if (mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
    {
      printf ("Error: mpfr_atan (+0) <> +0\n");
      exit (1);
    }
  mpfr_atan (x, x, GMP_RNDN);
  if (mpfr_cmp_ui (x, 0) || MPFR_IS_NEG (x))
    {
      printf ("Error: mpfr_atan (+0) <> +0 (in place)\n");
      exit (1);
    }
  mpfr_neg (x, x, GMP_RNDN);
  MPFR_SET_POS (y);
  mpfr_atan (y, x, GMP_RNDN);
  if (mpfr_cmp_ui (y, 0) || MPFR_IS_POS (y))
    {
      printf ("Error: mpfr_atan (-0) <> -0\n");
      exit (1);
    }
  mpfr_atan (x, x, GMP_RNDN);
  if (mpfr_cmp_ui (x, 0) || MPFR_IS_POS (x))
    {
      printf ("Error: mpfr_atan (-0) <> -0 (in place)\n");
      exit (1);
    }

  mpfr_set_prec (x, 32);
  mpfr_set_prec (y, 32);

  /* test one random positive argument */
  mpfr_set_str_binary (x, "0.10000100001100101001001001011001");
  mpfr_atan (x, x, GMP_RNDN);
  mpfr_set_str_binary (y, "0.1111010000001111001111000000011E-1");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_atan (1)\n");
      exit (1);
    }

  /* test one random negative argument */
  mpfr_set_str_binary (x, "-0.1100001110110000010101011001011");
  mpfr_atan (x, x, GMP_RNDN);
  mpfr_set_str_binary (y, "-0.101001110001010010110001110001");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_atan (2)\n");
      mpfr_print_binary (x); printf ("\n");
      mpfr_print_binary (y); printf ("\n");
      exit (1);
    }

  mpfr_set_prec (x, 3);
  mpfr_set_prec (y, 192);
  mpfr_set_prec (z, 192);
  mpfr_set_str_binary (x, "-0.100e1");
  mpfr_atan (z, x, GMP_RNDD);
  mpfr_set_str_binary (y, "-0.110010010000111111011010101000100010000101101000110000100011010011000100110001100110001010001011100000001101110000011100110100010010100100000010010011100000100010001010011001111100110001110101");
  if (mpfr_cmp (z, y))
    {
      printf ("Error in mpfr_atan (3)\n");
      printf ("Expected "); mpfr_print_binary (y); printf ("\n");
      printf ("Got      "); mpfr_print_binary (z); printf ("\n");
      exit (1);
    }

  /* Test regression */
  mpfr_set_prec (x, 51);
  mpfr_set_prec (y, 51);
  mpfr_set_str_binary (x,
           "0.101100100000101111111010001111111000001000000000000E-11");
  i = mpfr_atan (y, x, GMP_RNDN);
  if (mpfr_cmp_str (y,
   "1.01100100000101111111001110011001010110100100000000e-12", 2, GMP_RNDN)
      || i >= 0)
    {
      printf ("Wrong Regression test (%d)\n", i);
      mpfr_dump (y);
      exit (1);
    }

  mpfr_set_si (x, -1, GMP_RNDN);
  mpfr_atan (x, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_NEG (x));

  /* Test regression */
  mpfr_set_prec (x, 48);
  mpfr_set_prec (y, 48);
  mpfr_set_str_binary (x, "1.11001110010000011111100000010000000000000000000e-19");
  mpfr_atan (y, x, GMP_RNDD);
  if (mpfr_cmp_str (y, "0.111001110010000011111100000001111111110000010011E-18", 2, GMP_RNDN))
    {
      printf ("Error in mpfr_atan (4)\n");
      printf ("Input    1.11001110010000011111100000010000000000000000000e-19 [prec=48]\n");
      printf ("Expected 0.111001110010000011111100000001111111110000010011E-18\n");
      printf ("Got      "); mpfr_dump (y);
      exit (1);
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
}

#define TEST_FUNCTION mpfr_atan
#define test_generic test_generic_atan
#define RAND_FUNCTION(x) (mpfr_urandomb (x, RANDS), mpfr_mul_2si (x, x, (randlimb () %1000-500), GMP_RNDN))
#include "tgeneric.c"

#define TEST_FUNCTION mpfr_atan2
#define TWO_ARGS
#define test_generic test_generic_atan2
#include "tgeneric.c"

#define TEST_FUNCTION mpfr_atan2
#define TWO_ARGS
#define RAND_FUNCTION(x) (mpfr_urandomb (x, RANDS), MPFR_SET_NEG (x))
#define test_generic test_generic_atan2_neg
#include "tgeneric.c"

static void
special_overflow (void)
{
  mpfr_t x, y;
  mp_exp_t emin, emax;

  emin = mpfr_get_emin ();
  emax = mpfr_get_emax ();

  set_emin (-125);
  set_emax (128);
  mpfr_init2 (x, 24);
  mpfr_init2 (y, 48);
  mpfr_set_str_binary (x, "0.101101010001001101111010E0");
  mpfr_atan (y, x, GMP_RNDN);
  if (mpfr_cmp_str (y, "0.100111011001100111000010111101000111010101011110E0",
                    2, GMP_RNDN))
    {
      printf("Special Overflow error.\n");
      mpfr_dump (y);
      exit (1);
    }
  mpfr_clear (y);
  mpfr_clear (x);
  set_emin (emin);
  set_emax (emax);
}

static void
special_atan2 (void)
{
  mpfr_t x, y, z;

  mpfr_inits2 (4, x, y, z, (mpfr_ptr) 0);

  /* Anything with NAN should be set to NAN */
  mpfr_set_ui (y, 0, GMP_RNDN);
  mpfr_set_nan (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_NAN (z));
  mpfr_swap (x, y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_NAN (z));

  /* 0+ 0+ --> 0+ */
  mpfr_set_ui (y, 0, GMP_RNDN);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
  /* 0- 0+ --> 0- */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
  /* 0- 0- --> -PI */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, GMP_RNDN) == 0);
  /* 0+ 0- --> +PI */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, GMP_RNDN) == 0);
  /* 0+ -1 --> PI */
  mpfr_set_si (x, -1, GMP_RNDN);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, GMP_RNDN) == 0);
  /* 0- -1 --> -PI */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, GMP_RNDN) == 0);
  /* 0- +1 --> 0- */
  mpfr_set_ui (x, 1, GMP_RNDN);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
  /* 0+ +1 --> 0+ */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
  /* +1 0+ --> PI/2 */
  mpfr_swap (x, y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, GMP_RNDN) == 0);
  /* +1 0- --> PI/2 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, GMP_RNDN) == 0);
  /* -1 0- --> -PI/2 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, GMP_RNDN) == 0);
  /* -1 0+ --> -PI/2 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, GMP_RNDN) == 0);

  /* -1 +INF --> -0 */
  MPFR_SET_INF (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
  /* +1 +INF --> +0 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
  /* +1 -INF --> +PI */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, GMP_RNDN) == 0);
  /* -1 -INF --> -PI */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, GMP_RNDN) == 0);
  /* -INF -1 --> -PI/2 */
  mpfr_swap (x, y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, GMP_RNDN) == 0);
  /* +INF -1  --> PI/2 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, GMP_RNDN) == 0);
  /* +INF -INF --> 3*PI/4 */
  MPFR_SET_INF (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "2.356194490192344928", 10, GMP_RNDN) == 0);
  /* +INF +INF --> PI/4 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "0.785375", 10, GMP_RNDN) == 0);
  /* -INF +INF --> -PI/4 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-0.785375", 10, GMP_RNDN) == 0);
  /* -INF -INF --> -3*PI/4 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-2.356194490192344928", 10, GMP_RNDN) == 0);

  mpfr_clears (x, y, z, (mpfr_ptr) 0);
}

/* from Christopher Creutzig, 18 Jul 2007 */
static void
smallvals_atan2 (void)
{
  mpfr_t a, x, y;
  mp_exp_t old_emin;

  mpfr_inits (a, x, y, (mpfr_ptr) 0);
  mpfr_set_ui (y, 0, GMP_RNDN);
  mpfr_nextbelow (y);
  mpfr_set_ui (x, 1, GMP_RNDN);
  /* y=-2^(-emin-1), x=1 */

  mpfr_atan2 (a, y, x, GMP_RNDD);
  MPFR_ASSERTN (mpfr_equal_p (a, y));

  mpfr_atan2 (a, y, x, GMP_RNDU);
  MPFR_ASSERTN (mpfr_zero_p (a) && MPFR_IS_NEG(a));

  mpfr_set_prec (x, 8);
  mpfr_set_prec (y, 8);
  mpfr_set_prec (a, 8);
  old_emin = mpfr_get_emin ();
  mpfr_set_emin (MPFR_EMIN_MIN);

  mpfr_set_si (y, 3, GMP_RNDN);
  mpfr_set_exp (y, mpfr_get_emin ());
  mpfr_set_str_binary (x, "1.1");
  mpfr_atan2 (a, y, x, GMP_RNDU);
  mpfr_set_si (y, 1, GMP_RNDN);
  mpfr_set_exp (y, mpfr_get_emin ());
  MPFR_ASSERTN (mpfr_equal_p (a, y));

  /* From a bug reported by Christopher Creutzig on 2007-08-28.
     Added test in each rounding mode.
     Segmentation fault or assertion failure due to an infinite Ziv loop. */
  mpfr_set_si (y, 1, GMP_RNDN);
  mpfr_set_exp (y, mpfr_get_emin ());
  mpfr_set_str_binary (x, "1.01");
  mpfr_atan2 (a, y, x, GMP_RNDZ);
  MPFR_ASSERTN (mpfr_zero_p (a));
  mpfr_atan2 (a, y, x, GMP_RNDD);
  MPFR_ASSERTN (mpfr_zero_p (a));
  mpfr_atan2 (a, y, x, GMP_RNDU);
  MPFR_ASSERTN (mpfr_equal_p (a, y));
  mpfr_atan2 (a, y, x, GMP_RNDN);
  MPFR_ASSERTN (mpfr_equal_p (a, y));

  mpfr_set_emin (old_emin);

  mpfr_clears (a, x, y, (mpfr_ptr) 0);
}

/* Bug found by Robert Bajema (regression in MPFR 2.3.0).
   The cause is the underflow flag set before the mpfr_atan2 call. */
static void
atan2_bug_20071003 (void)
{
  mpfr_t a, x, y, z;

  mpfr_inits (a, x, y, z, (mpfr_ptr) 0);

  mpfr_set_underflow ();
  mpfr_set_str_binary (y,
    "-0.10100110110100110111010110111111100110100010001110110E2");
  mpfr_set_str_binary (x,
    "0.10100101010110010100010010111000110110011110001011110E3");
  mpfr_set_str_binary (z,
    "-0.11101111001101101100111011001101000010010111101110110E-1");
  mpfr_atan2 (a, y, x, GMP_RNDN);
  if (! mpfr_equal_p (a, z))
    {
      printf ("mpfr_atan2 fails on:\n");
      printf ("  y = ");
      mpfr_dump (y);
      printf ("  x = ");
      mpfr_dump (x);
      printf ("Expected ");
      mpfr_dump (z);
      printf ("Got      ");
      mpfr_dump (a);
      exit (1);
    }

  mpfr_clears (a, x, y, z, (mpfr_ptr) 0);
}

int
main (int argc, char *argv[])
{
  tests_start_mpfr ();

  special_overflow ();
  special ();
  special_atan2 ();
  smallvals_atan2 ();
  atan2_bug_20071003 ();

  test_generic_atan  (2, 200, 17);
  test_generic_atan2 (2, 200, 17);
  test_generic_atan2_neg (2, 200, 17);

  data_check ("data/atan", mpfr_atan, "mpfr_atan");
  bad_cases (mpfr_atan, mpfr_tan, "mpfr_atan", 256, -40, 1, 4, 128, 800, 40);

  tests_end_mpfr ();
  return 0;
}