/* Test file for mpfr_atan.

Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
Contributed by the Arenaire and Caramel 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 3 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.LESSER.  If not, see
http://www.gnu.org/licenses/ or 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, MPFR_RNDN);
  if (mpfr_cmp (y, z))
    {
      printf ("Error in mpfr_atan for prec=53, rnd=MPFR_RNDN\n");
      printf ("x=");
      mpfr_out_str (stdout, 2, 0, x, MPFR_RNDN);
      printf ("\nexpected ");
      mpfr_out_str (stdout, 2, 0, y, MPFR_RNDN);
      printf ("\ngot      ");
      mpfr_out_str (stdout, 2, 0, z, MPFR_RNDN);
      printf ("\n");
      exit (1);
    }

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

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

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

  /* atan(+/-0) = +/-0 */
  mpfr_set_ui (x, 0, MPFR_RNDN);
  MPFR_SET_NEG (y);
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_ui (y, 0) || MPFR_IS_NEG (y))
    {
      printf ("Error: mpfr_atan (+0) <> +0\n");
      exit (1);
    }
  mpfr_atan (x, x, MPFR_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, MPFR_RNDN);
  MPFR_SET_POS (y);
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_ui (y, 0) || MPFR_IS_POS (y))
    {
      printf ("Error: mpfr_atan (-0) <> -0\n");
      exit (1);
    }
  mpfr_atan (x, x, MPFR_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, MPFR_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, MPFR_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, MPFR_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, MPFR_RNDN);
  if (mpfr_cmp_str (y,
   "1.01100100000101111111001110011001010110100100000000e-12", 2, MPFR_RNDN)
      || i >= 0)
    {
      printf ("Wrong Regression test (%d)\n", i);
      mpfr_dump (y);
      exit (1);
    }

  mpfr_set_si (x, -1, MPFR_RNDN);
  mpfr_atan (x, x, MPFR_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, MPFR_RNDD);
  if (mpfr_cmp_str (y, "0.111001110010000011111100000001111111110000010011E-18", 2, MPFR_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), MPFR_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;
  mpfr_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, MPFR_RNDN);
  if (mpfr_cmp_str (y, "0.100111011001100111000010111101000111010101011110E0",
                    2, MPFR_RNDN))
    {
      printf("Special Overflow error.\n");
      mpfr_dump (y);
      exit (1);
    }

  /* intermediate Pi overflows while atan(+Inf) = Pi/2 is representable */
  set_emax (1);
  mpfr_set_inf (x, +1);
  mpfr_clear_flags ();
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_str (y, "C90FDAA22169p-47", 16, MPFR_RNDN)
      || mpfr_overflow_p ())
    {
      printf("atan(+Inf) = Pi/2 should not overflow when emax = %ld\n",
             (long int) mpfr_get_emax ());
      mpfr_dump (y);
      exit (1);
    }

  /* atan(+Inf) = Pi/2 underflows */
  set_emax (128);
  set_emin (3);
  mpfr_clear_flags ();
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_ui (y, 0) || !mpfr_underflow_p ())
    {
      printf("atan(+Inf) = Pi/2 should underflow when emin = %ld\n",
             (long int) mpfr_get_emin ());
      mpfr_dump (y);
      exit (1);
    }

  /* intermediate Pi overflows while atan(+1) = Pi/4 is representable */
  set_emax (1);
  set_emin (-128);
  mpfr_set_ui (x, 1, MPFR_RNDN);
  mpfr_clear_flags ();
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_str (y, "C90FDAA22169p-48", 16, MPFR_RNDN)
      || mpfr_overflow_p ())
    {
      printf("atan(+1) = Pi/4 should not overflow when emax = %ld\n",
             (long int) mpfr_get_emax ());
      mpfr_dump (y);
      exit (1);
    }

  /* atan(+1) = Pi/4 underflows and is rounded up to 1 */
  set_emax (128);
  set_emin (1);
  mpfr_set_prec (y, 2);
  mpfr_clear_flags ();
  mpfr_atan (y, x, MPFR_RNDN);
  if (mpfr_cmp_ui (y, 1) || !mpfr_underflow_p ())
    {
      printf("atan(+1) = Pi/4 should underflow when emin = %+ld\n",
             (long int) mpfr_get_emin ());
      mpfr_dump (y);
      exit (1);
    }

  /* atan(+1) = Pi/4 underflows and is rounded down to 0 */
  mpfr_clear_flags ();
  mpfr_atan (y, x, MPFR_RNDD);
  if (mpfr_cmp_ui (y, 0) || !mpfr_underflow_p ())
    {
      printf("atan(+1) = Pi/4 should underflow when emin = %+ld\n",
             (long int) mpfr_get_emin ());
      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, MPFR_RNDN);
  mpfr_set_nan (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (MPFR_IS_NAN (z));
  mpfr_swap (x, y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (MPFR_IS_NAN (z));

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

  /* -1 +INF --> -0 */
  MPFR_SET_INF (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_NEG (z));
  /* +1 +INF --> +0 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
  /* +1 -INF --> +PI */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "3.1415", 10, MPFR_RNDN) == 0);
  /* -1 -INF --> -PI */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-3.1415", 10, MPFR_RNDN) == 0);
  /* -INF -1 --> -PI/2 */
  mpfr_swap (x, y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-1.57075", 10, MPFR_RNDN) == 0);
  /* +INF -1  --> PI/2 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "1.57075", 10, MPFR_RNDN) == 0);
  /* +INF -INF --> 3*PI/4 */
  MPFR_SET_INF (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "2.356194490192344928", 10, MPFR_RNDN) == 0);
  /* +INF +INF --> PI/4 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "0.785375", 10, MPFR_RNDN) == 0);
  /* -INF +INF --> -PI/4 */
  MPFR_CHANGE_SIGN (y);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-0.785375", 10, MPFR_RNDN) == 0);
  /* -INF -INF --> -3*PI/4 */
  MPFR_CHANGE_SIGN (x);
  mpfr_atan2 (z, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-2.356194490192344928", 10, MPFR_RNDN) == 0);
  mpfr_set_prec (z, 905); /* exercises Ziv's loop */
  mpfr_atan2 (z, y, x, MPFR_RNDZ);
  MPFR_ASSERTN (mpfr_cmp_str (z, "-2.35619449019234492884698253745962716314787704953132936573120844423086230471465674897102611900658780098661106488496172998532038345716293667379401955609636083808771307702645389082916973346721171619778647332160823174945008459635673617534008737395340143185923642519259526145784", 10, MPFR_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;
  mpfr_exp_t old_emin;

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

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

  mpfr_atan2 (a, y, x, MPFR_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, MPFR_RNDN);
  mpfr_set_exp (y, mpfr_get_emin ());
  mpfr_set_str_binary (x, "1.1");
  mpfr_atan2 (a, y, x, MPFR_RNDU);
  mpfr_set_si (y, 1, MPFR_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, MPFR_RNDN);
  mpfr_set_exp (y, mpfr_get_emin ());
  mpfr_set_str_binary (x, "1.01");
  mpfr_atan2 (a, y, x, MPFR_RNDZ);
  MPFR_ASSERTN (mpfr_zero_p (a));
  mpfr_atan2 (a, y, x, MPFR_RNDD);
  MPFR_ASSERTN (mpfr_zero_p (a));
  mpfr_atan2 (a, y, x, MPFR_RNDU);
  MPFR_ASSERTN (mpfr_equal_p (a, y));
  mpfr_atan2 (a, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_equal_p (a, y));

  /* trigger underflow with rounding to nearest */
  mpfr_set_ui (x, 4, MPFR_RNDN);
  mpfr_atan2 (a, y, x, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_zero_p (a));

  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, MPFR_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);
}

/* Bug found on 2009-04-29 by Christopher Creutzig.
 * With r6179: atan.c:62: MPFR assertion failed: r > n
 */
static void
atan2_different_prec (void)
{
  mpfr_t a, x, y;

  mpfr_init2 (a, 59);
  mpfr_init2 (x, 59);
  mpfr_init2 (y, 86);

  mpfr_set_ui (x, 1, MPFR_RNDN);
  mpfr_set_ui (y, 1, MPFR_RNDN);
  mpfr_nextbelow (y);
  mpfr_atan2 (a, y, x, MPFR_RNDN);

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

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

  special_overflow ();
  special ();
  special_atan2 ();
  smallvals_atan2 ();
  atan2_bug_20071003 ();
  atan2_different_prec ();

  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;
}