mirror of
https://github.com/vale981/arb
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82 lines
2.2 KiB
C
82 lines
2.2 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmpcb.h"
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#include "zeta.h"
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void
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fmpcb_hurwitz_zeta(fmpcb_t z, const fmpcb_t s, const fmpcb_t a, long prec)
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{
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zeta_series(z, s, a, 0, 1, prec);
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}
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void
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fmpcb_zeta(fmpcb_t z, const fmpcb_t s, long prec)
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{
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fmpcb_t a;
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fmpcb_init(a);
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fmpcb_one(a);
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if (fmpr_sgn(fmprb_midref(fmpcb_realref(s))) < 0)
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{
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fmpcb_t t, u, v;
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long wp = prec + 6;
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fmpcb_init(t);
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fmpcb_init(u);
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fmpcb_init(v);
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fmpcb_sub_ui(t, s, 1, wp);
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/* 2 * (2pi)^(s-1) */
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fmprb_const_pi(fmpcb_realref(u), wp);
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fmpcb_mul_2exp_si(u, u, 1);
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fmpcb_pow(u, u, t, wp);
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fmpcb_mul_2exp_si(u, u, 1);
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/* sin(pi*s/2) */
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fmpcb_mul_2exp_si(v, s, -1);
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fmpcb_sin_pi(v, v, wp);
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fmpcb_mul(u, u, v, wp);
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/* gamma(1-s) zeta(1-s) */
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fmpcb_neg(t, t);
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fmpcb_gamma(v, t, wp);
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fmpcb_mul(u, u, v, wp);
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fmpcb_hurwitz_zeta(v, t, a, wp);
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fmpcb_mul(z, u, v, prec);
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fmpcb_clear(t);
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fmpcb_clear(u);
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fmpcb_clear(v);
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}
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else
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{
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fmpcb_hurwitz_zeta(z, s, a, prec);
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}
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fmpcb_clear(a);
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}
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