mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
66 lines
2 KiB
C
66 lines
2 KiB
C
/*
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Copyright (C) 2017 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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void
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acb_expm1(acb_t res, const acb_t z, slong prec)
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{
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if (acb_is_real(z))
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{
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arb_expm1(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 (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -3) <= 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -3) <= 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -3) <= 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -3) <= 0)
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{
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arf_srcptr midmax;
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slong extra;
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if (arf_cmpabs(arb_midref(acb_realref(z)), arb_midref(acb_imagref(z))) >= 0)
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midmax = arb_midref(acb_realref(z));
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else
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midmax = arb_midref(acb_imagref(z));
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if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -prec - 100) > 0)
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{
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extra = -ARF_EXP(midmax);
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extra = FLINT_MIN(extra, prec + 100);
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extra = FLINT_MAX(extra, 0);
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acb_exp(res, z, prec + extra + 4);
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acb_sub_ui(res, res, 1, prec);
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}
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else
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{
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/* lazy solution: e^z-1 = 4 (sinh(z/4)+cosh(z/4))^2 sinh(z/4) cosh(z/4) */
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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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acb_mul_2exp_si(t, z, -2);
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acb_sinh_cosh(t, u, t, prec + 4);
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acb_add(res, t, u, prec + 4);
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acb_mul(res, res, res, prec + 4);
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acb_mul(t, t, u, prec + 4);
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acb_mul(res, res, t, prec);
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acb_mul_2exp_si(res, res, 2);
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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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else
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{
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acb_exp(res, z, prec + 4);
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acb_sub_ui(res, res, 1, prec);
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}
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}
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