mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
64 lines
1.6 KiB
C
64 lines
1.6 KiB
C
/*
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Copyright (C) 2019 D.H.J Polymath
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_dirichlet.h"
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static void
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_mag_div_ui_ui(mag_t res, ulong a, ulong b)
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{
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mag_set_ui(res, a);
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mag_div_ui(res, res, b);
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}
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void
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acb_dirichlet_backlund_s_bound(mag_t res, const arb_t t)
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{
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if (!arb_is_nonnegative(t))
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{
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mag_inf(res);
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}
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else
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{
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mag_t m;
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mag_init(m);
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arb_get_mag(m, t);
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if (mag_cmp_2exp_si(m, 8) < 0) /* 2^8 < 280 */
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{
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mag_one(res);
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}
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else if (mag_cmp_2exp_si(m, 22) < 0) /* 2^22 < 6.8*10^6 */
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{
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mag_set_ui(res, 2);
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}
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else if (mag_cmp_2exp_si(m, 29) < 0) /* 2^29 < 5.45*10^8 */
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{
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_mag_div_ui_ui(res, 231366, 100000);
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}
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else
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{
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/* |S(t)| <= 0.112*log(t) + 0.278*log(log(t)) + 2.51 */
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mag_t c, logm;
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mag_init(c);
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mag_init(logm);
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mag_log(logm, m);
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_mag_div_ui_ui(c, 278, 1000);
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mag_log(res, logm);
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mag_mul(res, res, c);
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_mag_div_ui_ui(c, 112, 1000);
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mag_addmul(res, c, logm);
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_mag_div_ui_ui(c, 251, 100);
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mag_add(res, res, c);
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mag_clear(c);
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mag_clear(logm);
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}
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mag_clear(m);
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}
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}
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