mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
112 lines
2.7 KiB
C
112 lines
2.7 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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/* 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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acb_mul_onei(t, t);
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acb_mul_2exp_si(r, t, -1);
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}
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else if (acb_is_exact(z))
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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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acb_mul_onei(t, t);
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acb_mul_2exp_si(r, t, -1);
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}
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else
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{
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mag_t err, err2;
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mag_init(err);
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mag_init(err2);
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/* atan'(z) = 1/(1+z^2) = 1/((z+i)(z-i)) */
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acb_onei(t);
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acb_add(t, z, t, prec);
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acb_get_mag_lower(err, t);
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acb_onei(t);
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acb_sub(t, z, t, prec);
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acb_get_mag_lower(err2, t);
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mag_mul_lower(err, err, err2);
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mag_hypot(err2, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z)));
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mag_div(err, err2, err);
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arf_set(arb_midref(acb_realref(t)), arb_midref(acb_realref(z)));
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arf_set(arb_midref(acb_imagref(t)), arb_midref(acb_imagref(z)));
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mag_zero(arb_radref(acb_realref(t)));
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mag_zero(arb_radref(acb_imagref(t)));
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acb_atan(r, t, prec);
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acb_add_error_mag(r, err);
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mag_clear(err);
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mag_clear(err2);
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}
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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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