mirror of
https://github.com/vale981/arb
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91 lines
2.3 KiB
C
91 lines
2.3 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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static void
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acb_log1p_tiny(acb_t r, const acb_t z, slong prec)
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{
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mag_t b, c;
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acb_t t;
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int real;
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mag_init(b);
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mag_init(c);
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acb_init(t);
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real = acb_is_real(z);
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/* if |z| < 1, then |log(1+z) - [z - z^2/2]| <= |z|^3/(1-|z|) */
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acb_get_mag(b, z);
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mag_one(c);
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mag_sub_lower(c, c, b);
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mag_pow_ui(b, b, 3);
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mag_div(b, b, c);
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acb_mul(t, z, z, prec);
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acb_mul_2exp_si(t, t, -1);
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acb_sub(r, z, t, prec);
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if (real && mag_is_finite(b))
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arb_add_error_mag(acb_realref(r), b);
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else
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acb_add_error_mag(r, b);
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mag_clear(b);
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mag_clear(c);
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acb_clear(t);
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}
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void
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acb_log1p(acb_t r, const acb_t z, slong prec)
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{
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slong magz, magx, magy;
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if (acb_is_zero(z))
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{
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acb_zero(r);
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return;
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}
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magx = arf_abs_bound_lt_2exp_si(arb_midref(acb_realref(z)));
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magy = arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(z)));
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magz = FLINT_MAX(magx, magy);
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if (magz < -prec)
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{
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acb_log1p_tiny(r, z, prec);
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}
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else
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{
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if (magz < 0)
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acb_add_ui(r, z, 1, prec + (-magz) + 4);
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else
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acb_add_ui(r, z, 1, prec + 4);
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acb_log(r, r, prec);
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}
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}
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