mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
131 lines
3.1 KiB
C
131 lines
3.1 KiB
C
/*
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Copyright (C) 2015 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 void
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acb_log_sin_pi_half(acb_t res, const acb_t z, slong prec, int upper)
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{
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acb_t t, u, zmid;
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arf_t n;
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arb_t pi;
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acb_init(t);
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acb_init(u);
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acb_init(zmid);
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arf_init(n);
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arb_init(pi);
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arf_set(arb_midref(acb_realref(zmid)), arb_midref(acb_realref(z)));
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arf_set(arb_midref(acb_imagref(zmid)), arb_midref(acb_imagref(z)));
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arf_floor(n, arb_midref(acb_realref(zmid)));
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arb_sub_arf(acb_realref(zmid), acb_realref(zmid), n, prec);
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arb_const_pi(pi, prec);
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if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(zmid)), 2) < 1)
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{
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acb_sin_pi(t, zmid, prec);
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acb_log(t, t, prec);
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}
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else /* i*pi*(z-0.5) + log((1-exp(-2i*pi*z))/2) */
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{
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acb_mul_2exp_si(t, zmid, 1);
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acb_neg(t, t);
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if (upper)
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acb_conj(t, t);
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acb_exp_pi_i(t, t, prec);
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acb_sub_ui(t, t, 1, prec);
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acb_neg(t, t);
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acb_mul_2exp_si(t, t, -1);
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acb_log(t, t, prec);
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acb_one(u);
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acb_mul_2exp_si(u, u, -1);
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acb_sub(u, zmid, u, prec);
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if (upper)
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acb_conj(u, u);
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acb_mul_onei(u, u);
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acb_addmul_arb(t, u, pi, prec);
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if (upper)
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acb_conj(t, t);
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}
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if (upper)
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arb_submul_arf(acb_imagref(t), pi, n, prec);
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else
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arb_addmul_arf(acb_imagref(t), pi, n, prec);
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/* propagated error bound from the derivative pi cot(pi z) */
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if (!acb_is_exact(z))
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{
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mag_t zm, um;
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mag_init(zm);
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mag_init(um);
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acb_cot_pi(u, z, prec);
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acb_mul_arb(u, u, pi, prec);
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mag_hypot(zm, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z)));
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acb_get_mag(um, u);
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mag_mul(um, um, zm);
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acb_add_error_mag(t, um);
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mag_clear(zm);
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mag_clear(um);
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}
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acb_set(res, t);
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acb_clear(t);
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acb_clear(u);
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acb_clear(zmid);
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arf_clear(n);
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arb_clear(pi);
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}
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void
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acb_log_sin_pi(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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return;
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}
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if (arb_is_positive(acb_imagref(z)) ||
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(arb_is_zero(acb_imagref(z)) && arb_is_negative(acb_realref(z))))
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{
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acb_log_sin_pi_half(res, z, prec, 1);
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}
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else if (arb_is_negative(acb_imagref(z)) ||
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(arb_is_zero(acb_imagref(z)) && arb_is_positive(acb_realref(z))))
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{
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acb_log_sin_pi_half(res, z, prec, 0);
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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_log_sin_pi_half(t, z, prec, 1);
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acb_log_sin_pi_half(res, z, prec, 0);
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arb_union(acb_realref(res), acb_realref(res), acb_realref(t), prec);
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arb_union(acb_imagref(res), acb_imagref(res), acb_imagref(t), prec);
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acb_clear(t);
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}
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}
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