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/*
Copyright (C) 2019 D.H.J. Polymath
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_nzeros....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 130 + 20 * arb_test_multiplier(); iter++)
{
arb_t x, y, t;
arf_t f1, f2;
fmpz_t n, m, k1, k2;
acb_t z;
slong prec1, prec2;
arb_init(x);
arb_init(y);
arb_init(t);
acb_init(z);
arf_init(f1);
arf_init(f2);
fmpz_init(n);
fmpz_init(m);
fmpz_init(k1);
fmpz_init(k2);
if (iter < 130)
{
fmpz_set_si(n, iter + 1);
}
else
{
fmpz_randtest_unsigned(n, state, 20);
fmpz_add_ui(n, n, 131);
}
prec1 = 2 + n_randtest(state) % 50;
prec2 = 2 + n_randtest(state) % 200;
acb_dirichlet_hardy_z_zero(t, n, prec1);
acb_dirichlet_zeta_nzeros(x, t, prec2);
fmpz_sub_ui(m, n, 1);
if (!arb_contains_fmpz(x, n) || !arb_contains_fmpz(x, m))
{
flint_printf("FAIL: zero containment\n\n");
flint_printf("n = "); fmpz_print(n);
flint_printf(" prec1 = %wd prec2 = %wd\n\n", prec1, prec2);
flint_printf("t = "); arb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("x = "); arb_printn(x, 100, 0); flint_printf("\n\n");
flint_abort();
}
arb_get_lbound_arf(f1, t, prec1);
arb_get_ubound_arf(f2, t, prec1);
_acb_dirichlet_exact_zeta_nzeros(k1, f1);
_acb_dirichlet_exact_zeta_nzeros(k2, f2);
if (!(fmpz_cmp(k1, n) < 0 && fmpz_cmp(k2, n) >= 0))
{
flint_printf("FAIL: near a zero\n\n");
flint_printf("n = "); fmpz_print(n); flint_printf("\n\n");
flint_printf("t = "); arb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n");
flint_printf("k1 = "); fmpz_print(k1); flint_printf("\n\n");
flint_printf("k2 = "); fmpz_print(k2); flint_printf("\n\n");
flint_abort();
}
fmpz_sub_ui(m, n, 2);
acb_dirichlet_gram_point(t, m, NULL, NULL, prec1);
arb_get_lbound_arf(f1, t, prec1);
arb_get_ubound_arf(f2, t, prec1);
arb_set_interval_arf(t, f1, f2, prec1);
acb_set_arb(z, t);
acb_dirichlet_hardy_z(z, z, NULL, NULL, 1, prec1);
if (!acb_contains_zero(z))
{
_acb_dirichlet_exact_zeta_nzeros(k1, f1);
_acb_dirichlet_exact_zeta_nzeros(k2, f2);
if (!fmpz_equal(k1, k2))
{
flint_printf("FAIL: near a gram point\n\n");
flint_printf("m = "); fmpz_print(m); flint_printf("\n\n");
flint_printf("t = "); arb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n");
flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n");
flint_printf("k1 = "); fmpz_print(k1); flint_printf("\n\n");
flint_printf("k2 = "); fmpz_print(k2); flint_printf("\n\n");
flint_abort();
}
}
arb_clear(x);
arb_clear(y);
arb_clear(t);
acb_clear(z);
arf_clear(f1);
arf_clear(f2);
fmpz_clear(n);
fmpz_clear(m);
fmpz_clear(k1);
fmpz_clear(k2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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