/* tzeta -- test file for the Riemann Zeta function

Copyright 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC 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
test1 (void)
{
  mpfr_t x, y;

  mpfr_init2 (x, 32);
  mpfr_init2 (y, 42);

  mpfr_set_str_binary (x, "1.1111111101000111011010010010100e-1");
  mpfr_zeta (y, x, MPFR_RNDN); /* shouldn't crash */

  mpfr_set_prec (x, 40);
  mpfr_set_prec (y, 50);
  mpfr_set_str_binary (x, "1.001101001101000010011010110100110000101e-1");
  mpfr_zeta (y, x, MPFR_RNDU);
  mpfr_set_prec (x, 50);
  mpfr_set_str_binary (x, "-0.11111100011100111111101111100011110111001111111111E1");
  if (mpfr_cmp (x, y))
    {
      printf ("Error for input on 40 bits, output on 50 bits\n");
      printf ("Expected "); mpfr_print_binary (x); puts ("");
      printf ("Got      "); mpfr_print_binary (y); puts ("");
      mpfr_set_str_binary (x, "1.001101001101000010011010110100110000101e-1");
      mpfr_zeta (y, x, MPFR_RNDU);
      mpfr_print_binary (x); puts ("");
      mpfr_print_binary (y); puts ("");
      exit (1);
    }

  mpfr_set_prec (x, 2);
  mpfr_set_prec (y, 55);
  mpfr_set_str_binary (x, "0.11e3");
  mpfr_zeta (y, x, MPFR_RNDN);
  mpfr_set_prec (x, 55);
  mpfr_set_str_binary (x, "0.1000001000111000010011000010011000000100100100100010010E1");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_zeta (1)\n");
      printf ("Expected "); mpfr_print_binary (x); puts ("");
      printf ("Got      "); mpfr_print_binary (y); puts ("");
      exit (1);
    }

  mpfr_set_prec (x, 3);
  mpfr_set_prec (y, 47);
  mpfr_set_str_binary (x, "0.111e4");
  mpfr_zeta (y, x, MPFR_RNDN);
  mpfr_set_prec (x, 47);
  mpfr_set_str_binary (x, "1.0000000000000100000000111001001010111100101011");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_zeta (2)\n");
      exit (1);
    }

  /* coverage test */
  mpfr_set_prec (x, 7);
  mpfr_set_str_binary (x, "1.000001");
  mpfr_set_prec (y, 2);
  mpfr_zeta (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_cmp_ui (y, 64) == 0);

  /* another coverage test */
  mpfr_set_prec (x, 24);
  mpfr_set_ui (x, 2, MPFR_RNDN);
  mpfr_set_prec (y, 2);
  mpfr_zeta (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_cmp_ui_2exp (y, 3, -1) == 0);

  mpfr_set_nan (x);
  mpfr_zeta (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_nan_p (y));

  mpfr_set_inf (x, 1);
  mpfr_zeta (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_cmp_ui (y, 1) == 0);

  mpfr_set_inf (x, -1);
  mpfr_zeta (y, x, MPFR_RNDN);
  MPFR_ASSERTN(mpfr_nan_p (y));

  mpfr_clear (x);
  mpfr_clear (y);
}

static const char *const val[] = {
  "-2000", "0.0",
  "-2.0", "0.0",
  "-1.0", "-0.000101010101010101010101010101010101010101010101010101010101010",
  "-0.9", "-0.000110011110011111010001010001100010111101001010100110001110110",
  /*  "-0.8", "-0.000111110011101010001011100011010010000001010011110100010001110",
  "-0.7", "-0.00100101011011111100110011110011111010111111000110110100010110",
  "-0.6", "-0.00101100101100100100110111111000110010111010110010111000001100",
  "-0.5", "-0.00110101001110000000100000011001100100010000111100010001111100",
  "-0.4", "-0.00111111010001100011110001010010111110010001010101111101110001",
  "-0.3", "-0.0100101100110111010101010100111011000001001010111010110101010",
  "-0.2", "-0.0101100110000011101110101011011110101111000010000010110101111",
  "-0.1", "-0.0110101011001111011101001111011000010001111010110011011111011",
  "-0.0", "-0.100000000000000000000000000000000000000000000000000000000000",
  "0.1", "-0.100110100110000010101010101110100000101100100011011001000101",
  "0.2", "-0.10111011111000100011110111100010010001111010010010010100010110",
  "0.3", "-0.11100111100100010011001000001011001100110010110101101110110110",
  "0.4", "-1.0010001010000010000110111000100101001000001011101010110101011",
  "0.5", "-1.0111010111011001110010110000011111100111001111111110111000110",
  "0.6", "-1.1111001111100001100111101110010001001000001101100110110000100",
  "0.7", "-10.110001110100010001110111000101010011110011000110010100101000",
  "0.8", "-100.01110000000000101000010010000011000000111101100101100011010",
  "0.9", "-1001.0110111000011011111100111100111011100010001111111010000100",
  "0.99","-0.11000110110110001101011010110001011010011000110001011100101110E7",
  "0.997", "-0.10100110011000001100111110011111100011110000111011101110001010E9",
  "0.9995", "-0.11111001111011011000011110111111010111101001000110001111110010E11",
  "0.99998", "-0.11000011010011110110110000111011101100001000101101011001110100E16",
  "1.00001", "0.11000011010100000100100111100010001110100000110101110011111011E17",
  "1.0002", "0.10011100010001001001111000101010111000011011011111110010110100E13",
  "1.003","0.10100110111101001001010000000110101101110100001010100000110000E9",
  "1.04", "11001.100101001000001011000111010110011010000001000010111101101",
  "1.1", "1010.1001010110011110011010100010001100101001001111111101100001",
  "1.2", "101.10010111011100011111001001100101101111110000110001101100010",
  "1.3", "11.111011101001010000111001001110100100000101000101101011010100",
  "1.4", "11.000110110000010100100101011110110001100001110100100100111111",
  "1.5", "10.100111001100010010100001011111110111101100010011101011011100",
  "1.6", "10.010010010010011111110000010011000110101001110011101010100110",
  "1.7", "10.000011011110010111011110001100110010100010011100011111110010",
  "1.8", "1.1110000111011001110011001101110101010000011011101100010111001",
  "1.9", "1.1011111111101111011000011110001100100111100110111101101000101",
  "2.0", "1.1010010100011010011001100010010100110000011111010011001000110",
  "42.17", "1.0000000000000000000000000000000000000000001110001110001011001",
  "-17.42", "-11.101110101010101000000001001000001111111101000100001100101100",
  "-24.17", "-0.10001111010010011111000010001011111010010111101011000010010011E13"*/
};

static void
test2 (void)
{
  mpfr_t x, y;
  int i, n = numberof(val);

  mpfr_inits2 (55, x, y, (mpfr_ptr) 0);

  for(i = 0 ; i < n ; i+=2)
    {
      mpfr_set_str1 (x, val[i]);
      mpfr_zeta(y, x, MPFR_RNDZ);
      if (mpfr_cmp_str (y, val[i+1] , 2, MPFR_RNDZ))
        {
          printf("Wrong result for zeta(%s=", val[i]);
          mpfr_print_binary (x);
          printf (").\nGot     : ");
          mpfr_print_binary(y); putchar('\n');
          printf("Expected: ");
          mpfr_set_str (y, val[i+1], 2, MPFR_RNDZ);
          mpfr_print_binary(y); putchar('\n');
          mpfr_set_prec(y, 65);
          mpfr_zeta(y, x, MPFR_RNDZ);
          printf("+ Prec  : ");
          mpfr_print_binary(y); putchar('\n');
          exit(1);
        }
    }
  mpfr_clears (x, y, (mpfr_ptr) 0);
}

#define TEST_FUNCTION mpfr_zeta
#define TEST_RANDOM_EMIN -48
#define TEST_RANDOM_EMAX 31
#include "tgeneric.c"

/* Usage: tzeta - generic tests
          tzeta s prec rnd_mode - compute zeta(s) with precision 'prec'
                                  and rounding mode 'mode' */
int
main (int argc, char *argv[])
{
  mpfr_t s, y, z;
  mpfr_prec_t prec;
  mpfr_rnd_t rnd_mode;
  int inex;

  tests_start_mpfr ();

  if (argc != 1 && argc != 4)
    {
      printf ("Usage: tzeta\n"
              "    or tzeta s prec rnd_mode\n");
      exit (1);
    }

  if (argc == 4)
    {
      prec = atoi(argv[2]);
      mpfr_init2 (s, prec);
      mpfr_init2 (z, prec);
      mpfr_set_str (s, argv[1], 10, MPFR_RNDN);
      rnd_mode = (mpfr_rnd_t) atoi(argv[3]);

      mpfr_zeta (z, s, rnd_mode);
      mpfr_out_str (stdout, 10, 0, z, MPFR_RNDN);
      printf ("\n");

      mpfr_clear (s);
      mpfr_clear (z);

      return 0;
    }

  test1();

  mpfr_init2 (s, MPFR_PREC_MIN);
  mpfr_init2 (y, MPFR_PREC_MIN);
  mpfr_init2 (z, MPFR_PREC_MIN);


  /* the following seems to loop */
  mpfr_set_prec (s, 6);
  mpfr_set_prec (z, 6);
  mpfr_set_str_binary (s, "1.10010e4");
  mpfr_zeta (z, s, MPFR_RNDZ);


  mpfr_set_prec (s, 53);
  mpfr_set_prec (y, 53);
  mpfr_set_prec (z, 53);

  mpfr_set_ui (s, 1, MPFR_RNDN);
  mpfr_clear_divby0();
  mpfr_zeta (z, s, MPFR_RNDN);
  if (!mpfr_inf_p (z) || MPFR_SIGN (z) < 0 || !mpfr_divby0_p())
    {
      printf ("Error in mpfr_zeta for s = 1 (should be +inf) with divby0 flag\n");
      exit (1);
    }

  mpfr_set_str_binary (s, "0.1100011101110111111111111010000110010111001011001011");
  mpfr_set_str_binary (y, "-0.11111101111011001001001111111000101010000100000100100E2");
  mpfr_zeta (z, s, MPFR_RNDN);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (1,RNDN)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDZ);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (1,RNDZ)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDU);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (1,RNDU)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDD);
  mpfr_nexttoinf (y);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (1,RNDD)\n");
      exit (1);
    }

  mpfr_set_str_binary (s, "0.10001011010011100110010001100100001011000010011001011");
  mpfr_set_str_binary (y, "-0.11010011010010101101110111011010011101111101111010110E1");
  mpfr_zeta (z, s, MPFR_RNDN);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (2,RNDN)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDZ);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (2,RNDZ)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDU);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (2,RNDU)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDD);
  mpfr_nexttoinf (y);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (2,RNDD)\n");
      exit (1);
    }

  mpfr_set_str_binary (s, "0.1100111110100001111110111000110101111001011101000101");
  mpfr_set_str_binary (y, "-0.10010111010110000111011111001101100001111011000001010E3");
  mpfr_zeta (z, s, MPFR_RNDN);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (3,RNDN)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDD);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (3,RNDD)\n");
      exit (1);
    }
  mpfr_nexttozero (y);
  mpfr_zeta (z, s, MPFR_RNDZ);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (3,RNDZ)\n");
      exit (1);
    }
  mpfr_zeta (z, s, MPFR_RNDU);
  if (mpfr_cmp (z, y) != 0)
    {
      printf ("Error in mpfr_zeta (3,RNDU)\n");
      exit (1);
    }

  mpfr_set_str (s, "-400000001", 10, MPFR_RNDZ);
  mpfr_zeta (z, s, MPFR_RNDN);
  if (!(mpfr_inf_p (z) && MPFR_SIGN(z) < 0))
    {
      printf ("Error in mpfr_zeta (-400000001)\n");
      exit (1);
    }
  mpfr_set_str (s, "-400000003", 10, MPFR_RNDZ);
  mpfr_zeta (z, s, MPFR_RNDN);
  if (!(mpfr_inf_p (z) && MPFR_SIGN(z) > 0))
    {
      printf ("Error in mpfr_zeta (-400000003)\n");
      exit (1);
    }

  mpfr_set_prec (s, 34);
  mpfr_set_prec (z, 34);
  mpfr_set_str_binary (s, "-1.111111100001011110000010001010000e-35");
  mpfr_zeta (z, s, MPFR_RNDD);
  mpfr_set_str_binary (s, "-1.111111111111111111111111111111111e-2");
  if (mpfr_cmp (s, z))
    {
      printf ("Error in mpfr_zeta, prec=34, MPFR_RNDD\n");
      mpfr_dump (z);
      exit (1);
    }

  /* bug found by nightly tests on June 7, 2007 */
  mpfr_set_prec (s, 23);
  mpfr_set_prec (z, 25);
  mpfr_set_str_binary (s, "-1.0110110110001000000000e-27");
  mpfr_zeta (z, s, MPFR_RNDN);
  mpfr_set_prec (s, 25);
  mpfr_set_str_binary (s, "-1.111111111111111111111111e-2");
  if (mpfr_cmp (s, z))
    {
      printf ("Error in mpfr_zeta, prec=25, MPFR_RNDN\n");
      printf ("expected "); mpfr_dump (s);
      printf ("got      "); mpfr_dump (z);
      exit (1);
    }

  /* bug reported by Kevin Rauch on 26 Oct 2007 */
  mpfr_set_prec (s, 128);
  mpfr_set_prec (z, 128);
  mpfr_set_str_binary (s, "-0.1000000000000000000000000000000000000000000000000000000000000001E64");
  inex = mpfr_zeta (z, s, MPFR_RNDN);
  MPFR_ASSERTN (mpfr_inf_p (z) && MPFR_SIGN (z) < 0 && inex < 0);
  inex = mpfr_zeta (z, s, MPFR_RNDU);
  mpfr_set_inf (s, -1);
  mpfr_nextabove (s);
  MPFR_ASSERTN (mpfr_equal_p (z, s) && inex > 0);

  mpfr_clear (s);
  mpfr_clear (y);
  mpfr_clear (z);

  test_generic (2, 70, 5);
  test2 ();

  tests_end_mpfr ();
  return 0;
}