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/*
Copyright (C) 2016 Pascal Molin
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"
typedef void (*do_f) (acb_ptr w, acb_srcptr v, slong len, slong prec);
void
check_vec_eq_prec(acb_srcptr w1, acb_srcptr w2, slong len, slong prec, slong digits, ulong q, char f1[], char f2[])
{
slong i;
for (i = 0; i < len; i++)
{
if (!acb_overlaps(w1 + i, w2 + i))
{
flint_printf("FAIL\n\n");
flint_printf("q = %wu, size = %wd\n", q, len);
flint_printf("\nDFT differ from index %wd / %wd \n", i, len);
flint_printf("\n%s =\n", f1);
acb_vec_printd(w1, len, digits);
flint_printf("\n%s =\n", f2);
acb_vec_printd(w2, len, digits);
flint_printf("\n\n");
abort();
}
else if (acb_rel_accuracy_bits(w1 + i) < 30
|| acb_rel_accuracy_bits(w2 + i) < 30)
{
flint_printf("FAIL\n\n");
flint_printf("q = %wu\n", q);
flint_printf("\nDFT inaccurate from index %wd / %wd \n", i, len);
flint_printf("\nnaive =\n");
acb_printd(w1 + i, digits);
flint_printf("\nfast =\n");
acb_printd(w2 + i, digits);
flint_printf("\nerrors %wd & %wd [prec = %wd]\n",
acb_rel_accuracy_bits(w1 + i),
acb_rel_accuracy_bits(w2 + i), prec);
abort();
}
}
}
int main()
{
slong k;
slong prec = 100, digits = 30;
slong nq = 13;
ulong q[13] = { 2, 3, 4, 5, 6, 23, 10, 15, 30, 59, 308, 335, 961};
flint_rand_t state;
flint_printf("dft....");
fflush(stdout);
flint_randinit(state);
/* Dirichlet group DFT */
for (k = 0; k < nq; k++)
{
slong i, j, len;
dirichlet_group_t G;
dirichlet_char_t x, y;
acb_dirichlet_roots_t roots;
acb_t chiy;
acb_ptr v, w1, w2;
dirichlet_group_init(G, q[k]);
len = G->phi_q;
v = _acb_vec_init(len);
w1 = _acb_vec_init(len);
w2 = _acb_vec_init(len);
acb_init(chiy);
acb_dirichlet_roots_init(roots, G->expo, len, prec);
dirichlet_char_init(x, G);
dirichlet_char_init(y, G);
for (i = 0; i < len; i++)
acb_randtest_precise(v + i, state, prec, 0);
/* naive */
dirichlet_char_one(x, G);
for (i = 0; i < len; i++)
{
acb_zero(w1 + i);
dirichlet_char_one(y, G);
for (j = 0; j < len; j++)
{
acb_dirichlet_root(chiy, roots, dirichlet_pairing_char(G, x, y), prec);
acb_conj(chiy, chiy);
acb_addmul(w1 + i, chiy, v + j, prec);
dirichlet_char_next(y, G);
}
dirichlet_char_next(x, G);
}
/* dft */
acb_dirichlet_dft_index(w2, v, G, prec);
check_vec_eq_prec(w1, w2, len, prec, digits, q[k], "naive", "group");
_acb_vec_clear(v, len);
_acb_vec_clear(w1, len);
_acb_vec_clear(w2, len);
acb_dirichlet_roots_clear(roots);
dirichlet_char_clear(x);
dirichlet_char_clear(y);
dirichlet_group_clear(G);
acb_clear(chiy);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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