mirror of
https://github.com/vale981/arb
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73 lines
1.9 KiB
C
73 lines
1.9 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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "bernoulli.h"
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#include "zeta.h"
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void zeta_inv_ui_euler_product(fmprb_t z, ulong s, long prec);
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void
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bernoulli_fmprb_ui_zeta(fmprb_t b, ulong n, long prec)
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{
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long wp, piwp;
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fmprb_t t, u;
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if (n < 10 || n % 2 != 0)
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abort();
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wp = prec + 8;
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piwp = wp + 2*FLINT_BIT_COUNT(n);
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fmprb_init(t);
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fmprb_init(u);
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/* |B_n| = 2 * n! / (2*pi)^n * zeta(n) */
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fmprb_fac_ui(b, n, piwp);
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fmprb_const_pi(t, piwp);
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fmprb_mul_2exp_si(t, t, 1);
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fmprb_pow_ui(t, t, n, piwp);
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if (n > 0.7 * wp)
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{
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zeta_ui_asymp(u, n, wp);
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fmprb_mul(b, b, u, wp);
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}
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else
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{
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zeta_inv_ui_euler_product(u, n, wp);
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fmprb_mul(t, t, u, wp);
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}
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fmprb_div(b, b, t, prec);
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fmprb_mul_2exp_si(b, b, 1);
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if (n % 4 == 0)
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fmprb_neg(b, b);
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fmprb_clear(t);
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fmprb_clear(u);
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}
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