mirror of
https://github.com/vale981/arb
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76 lines
2.1 KiB
C
76 lines
2.1 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) 2016 Fredrik Johansson
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******************************************************************************/
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#include "arb.h"
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void
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arb_euler_number_fmpz(arb_t res, const fmpz_t n, slong prec)
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{
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if (fmpz_cmp_ui(n, UWORD_MAX) <= 0)
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{
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if (fmpz_sgn(n) >= 0)
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arb_euler_number_ui(res, fmpz_get_ui(n), prec);
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else
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arb_zero(res);
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}
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else if (fmpz_is_odd(n))
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{
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arb_zero(res);
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}
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else
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{
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arb_t t;
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fmpz_t m;
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slong wp;
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arb_init(t);
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fmpz_init(m);
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wp = prec + 2 * fmpz_bits(n);
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/* beta(n) ~= 1 */
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arf_one(arb_midref(res));
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mag_one(arb_radref(res));
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mag_mul_2exp_si(arb_radref(res), arb_radref(res), WORD_MIN);
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/* |E_n| = 2 n! beta(n+1) / (pi/2)^(n+1) */
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fmpz_add_ui(m, n, 1);
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arb_gamma_fmpz(t, m, wp);
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arb_mul(res, res, t, wp);
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arb_const_pi(t, wp);
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arb_mul_2exp_si(t, t, -1);
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arb_pow_fmpz(t, t, m, wp);
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arb_div(res, res, t, prec);
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arb_mul_2exp_si(res, res, 1);
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if (fmpz_fdiv_ui(n, 4) == 2)
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arb_neg(res, res);
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arb_clear(t);
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fmpz_clear(m);
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}
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}
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