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/*
Copyright (C) 2016 Fredrik Johansson
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"
#include "acb_poly.h"
void
acb_dirichlet_hurwitz_precomp_init(acb_dirichlet_hurwitz_precomp_t pre,
const acb_t s, int deflate, slong A, slong K, slong N, slong prec)
{
slong i, k;
pre->deflate = deflate;
pre->A = A;
pre->K = K;
pre->N = N;
acb_init(&pre->s);
acb_set(&pre->s, s);
if (A == 0)
return;
if (A < 1 || K < 1 || N < 1)
{
flint_printf("hurwitz_precomp_init: require A, K, N >= 1 (unless A == 0)\n");
flint_abort();
}
pre->coeffs = _acb_vec_init(N * K);
mag_init(&pre->err);
acb_dirichlet_hurwitz_precomp_bound(&pre->err, s, A, K, N);
if (mag_is_finite(&pre->err))
{
acb_t t, a;
acb_init(t);
acb_init(a);
/* (-1)^k (s)_k / k! */
acb_one(pre->coeffs + 0);
for (k = 1; k < K; k++)
{
acb_add_ui(pre->coeffs + k, s, k - 1, prec);
acb_mul(pre->coeffs + k, pre->coeffs + k, pre->coeffs + k - 1, prec);
acb_div_ui(pre->coeffs + k, pre->coeffs + k, k, prec);
acb_neg(pre->coeffs + k, pre->coeffs + k);
}
for (i = 1; i < N; i++)
_acb_vec_set(pre->coeffs + i * K, pre->coeffs, K);
/* zeta(s+k,a) where a = A + (2*i+1)/(2*N) */
for (i = 0; i < N; i++)
{
acb_set_ui(a, 2 * i + 1);
acb_div_ui(a, a, 2 * N, prec);
acb_add_ui(a, a, A, prec);
for (k = 0; k < K; k++)
{
acb_add_ui(t, s, k, prec);
if (deflate && k == 0)
_acb_poly_zeta_cpx_series(t, t, a, 1, 1, prec);
else
acb_hurwitz_zeta(t, t, a, prec);
acb_mul(pre->coeffs + i * K + k,
pre->coeffs + i * K + k, t, prec);
}
}
acb_clear(t);
acb_clear(a);
}
}
void
acb_dirichlet_hurwitz_precomp_init_num(acb_dirichlet_hurwitz_precomp_t pre,
const acb_t s, int deflate, double num_eval, slong prec)
{
ulong A, K, N;
acb_dirichlet_hurwitz_precomp_choose_param(&A, &K, &N, s, num_eval, prec);
acb_dirichlet_hurwitz_precomp_init(pre, s, deflate, A, K, N, prec);
}
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