mirror of
https://github.com/vale981/arb
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97 lines
2.1 KiB
C
97 lines
2.1 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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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.h"
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static int
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_acb_is_large(const acb_t z)
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{
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int res;
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mag_t t;
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mag_init(t);
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acb_get_mag_lower(t, z);
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res = mag_cmp_2exp_si(t, 0) >= 0;
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mag_clear(t);
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return res;
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}
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static void
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_acb_sinc_direct(acb_t res, const acb_t z, slong prec)
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{
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if (acb_is_zero(z))
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{
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acb_one(res);
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}
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else
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{
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acb_t t;
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acb_init(t);
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acb_sin(t, z, prec + 2);
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acb_div(res, t, z, prec);
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acb_clear(t);
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}
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}
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static void
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_acb_sinc_diffbound(acb_t res, const acb_t z, slong prec)
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{
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mag_t u, v;
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int isreal;
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mag_init(u);
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mag_init(v);
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isreal = arb_is_zero(acb_realref(z));
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/* exp(|im(z)|) is a crude bound for |sinc'(z)| */
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arb_get_mag(u, acb_imagref(z));
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mag_hypot(v, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z)));
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mag_exp(u, u);
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mag_mul(u, u, v);
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arf_set(arb_midref(acb_realref(res)), arb_midref(acb_realref(z)));
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arf_set(arb_midref(acb_imagref(res)), arb_midref(acb_imagref(z)));
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mag_zero(arb_radref(acb_realref(res)));
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mag_zero(arb_radref(acb_imagref(res)));
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_acb_sinc_direct(res, res, prec);
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if (isreal)
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arb_add_error_mag(acb_realref(res), u);
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else
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acb_add_error_mag(res, u);
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mag_clear(u);
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mag_clear(v);
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}
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void
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acb_sinc(acb_t res, const acb_t z, slong prec)
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{
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if (!acb_is_finite(z))
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{
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acb_indeterminate(res);
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}
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else if (acb_is_real(z))
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{
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arb_sinc(acb_realref(res), acb_realref(z), prec);
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arb_zero(acb_imagref(res));
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}
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else if (acb_is_exact(z) || _acb_is_large(z))
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{
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_acb_sinc_direct(res, z, prec);
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}
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else
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{
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_acb_sinc_diffbound(res, z, prec);
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}
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}
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