mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
70 lines
2 KiB
C
70 lines
2 KiB
C
/*
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Copyright (C) 2015 Fredrik Johansson
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Copyright (C) 2020 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.h"
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void
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acb_csc_pi(acb_t res, const acb_t z, slong prec)
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{
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if (acb_contains_zero(z) || !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 (arb_is_zero(acb_imagref(z)))
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{
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arb_csc_pi(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 (arb_is_zero(acb_realref(z)))
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{
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arb_const_pi(acb_realref(res), prec);
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arb_mul(acb_imagref(res), acb_imagref(z), acb_realref(res), prec);
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arb_csch(acb_imagref(res), acb_imagref(res), prec);
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arb_neg(acb_imagref(res), acb_imagref(res));
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arb_zero(acb_realref(res));
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}
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else
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{
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if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) > 0)
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{
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acb_t t;
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acb_init(t);
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if (arf_sgn(arb_midref(acb_imagref(z))) < 0)
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{
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acb_neg(t, z);
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acb_exp_pi_i(t, t, prec + 4);
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acb_mul(res, t, t, prec + 4);
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acb_sub_ui(res, res, 1, prec + 4);
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acb_div(res, t, res, prec);
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acb_neg(res, res);
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}
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else
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{
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acb_exp_pi_i(t, z, prec + 4);
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acb_mul(res, t, t, prec + 4);
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acb_sub_ui(res, res, 1, prec + 4);
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acb_div(res, t, res, prec);
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}
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acb_mul_2exp_si(res, res, 1);
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acb_mul_onei(res, res);
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acb_clear(t);
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}
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else
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{
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acb_sin_pi(res, z, prec + 4);
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acb_inv(res, res, prec);
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}
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}
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}
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