mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
95 lines
2.4 KiB
C
95 lines
2.4 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2015 Fredrik Johansson
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******************************************************************************/
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#include "acb.h"
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/* branch cuts are on (+/-i)*[1,inf] */
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int
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acb_atan_on_branch_cut(const acb_t z)
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{
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arb_t unit;
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int result;
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if (!acb_is_finite(z))
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return 1;
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if (arb_is_nonzero(acb_realref(z)))
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return 0;
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if (arb_contains_si(acb_imagref(z), 1) || arb_contains_si(acb_imagref(z), -1))
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return 1;
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arb_init(unit);
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mag_one(arb_radref(unit));
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result = !arb_contains(unit, acb_imagref(z));
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arb_clear(unit);
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return result;
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}
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void
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acb_atan(acb_t r, const acb_t z, slong prec)
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{
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if (arb_is_zero(acb_imagref(z)))
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{
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arb_atan(acb_realref(r), acb_realref(z), prec);
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arb_zero(acb_imagref(r));
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}
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else if (!acb_is_finite(z))
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{
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acb_indeterminate(r);
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}
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else
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{
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acb_t t, u;
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acb_init(t);
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acb_init(u);
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if (acb_atan_on_branch_cut(z))
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{
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acb_mul_onei(u, z);
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acb_neg(t, u);
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acb_log1p(t, t, prec);
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acb_log1p(u, u, prec);
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acb_sub(t, t, u, prec);
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}
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else
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{
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acb_onei(t);
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acb_sub(t, t, z, prec);
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acb_div(t, z, t, prec);
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acb_mul_2exp_si(t, t, 1);
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acb_log1p(t, t, prec);
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}
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acb_mul_onei(t, t);
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acb_mul_2exp_si(r, t, -1);
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acb_clear(t);
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acb_clear(u);
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}
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}
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