/* tzeta -- test file for the Riemann Zeta function
Copyright 2003-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba 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);
/* bug reported by Fredrik Johansson on 19 Jan 2016 */
mpfr_set_prec (s, 536);
mpfr_set_ui_2exp (s, 1, -424, MPFR_RNDN);
mpfr_sub_ui (s, s, 128, MPFR_RNDN); /* -128 + 2^(-424) */
for (prec = 6; prec <= 536; prec += 8) /* should go through 318 */
{
mpfr_set_prec (z, prec);
mpfr_zeta (z, s, MPFR_RNDD);
mpfr_set_prec (y, prec + 10);
mpfr_zeta (y, s, MPFR_RNDD);
mpfr_prec_round (y, prec, MPFR_RNDD);
if (! mpfr_equal_p (z, y))
{
printf ("mpfr_zeta fails near -128 for inprec=%lu outprec=%lu\n",
(unsigned long) mpfr_get_prec (s), (unsigned long) prec);
printf ("expected "); mpfr_dump (y);
printf ("got "); mpfr_dump (z);
exit (1);
}
}
mpfr_clear (s);
mpfr_clear (y);
mpfr_clear (z);
/* FIXME: change the last argument back to 5 once the working precision
in the mpfr_zeta implementation no longer depends on the precision of
the input. */
test_generic (MPFR_PREC_MIN, 70, 1);
test2 ();
tests_end_mpfr ();
return 0;
}