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https://github.com/vale981/arb
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39 lines
1,005 B
C
39 lines
1,005 B
C
/*
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Copyright (C) 2016 Pascal Molin
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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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#include <math.h>
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#define PI 3.14159265358
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#define LOG2 0.69314718055
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ulong
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acb_dirichlet_theta_length_d(ulong q, double t, slong prec)
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{
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double a, la;
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a = PI / (double)q * t * t;
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la = (a < .3) ? -log(2*a*(1-a)) : .8;
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la = ((double)prec * LOG2 + la) / a;
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return ceil(sqrt(la)+.5);
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}
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ulong
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acb_dirichlet_theta_length(ulong q, const arb_t t, slong prec)
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{
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double dt;
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ulong len;
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arf_t at;
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arf_init(at);
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arb_get_lbound_arf(at, t, 53);
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dt = arf_get_d(at, ARF_RND_DOWN);
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len = acb_dirichlet_theta_length_d(q, dt, prec);
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arf_clear(at);
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return len;
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}
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