mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
99 lines
2.5 KiB
C
99 lines
2.5 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_hypgeom.h"
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void
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acb_hypgeom_erfc(acb_t res, const acb_t z, slong prec)
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{
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double x, y, abs_z2, log_z, log_erfc_z_asymp;
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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 (acb_is_zero(z))
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{
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acb_one(res);
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return;
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}
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if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -64) < 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -64) < 0) ||
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arf_sgn(arb_midref(acb_realref(z))) < 0)
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{
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acb_hypgeom_erf(res, z, prec);
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acb_sub_ui(res, res, 1, prec);
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acb_neg(res, res);
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return;
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}
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if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 64) > 0 ||
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arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 64) > 0))
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{
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acb_hypgeom_erf_asymp(res, z, 1, prec, prec);
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return;
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}
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x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN);
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y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN);
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abs_z2 = x * x + y * y;
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if (abs_z2 > (prec + 8) * 0.69314718055994530942)
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{
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acb_hypgeom_erf_asymp(res, z, 1, prec, prec);
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}
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else
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{
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slong wp;
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log_z = 0.5 * log(abs_z2);
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log_erfc_z_asymp = y * y - x * x - log_z;
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wp = prec + 2;
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if (log_erfc_z_asymp < 0.0)
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wp += (-log_erfc_z_asymp) * 1.4426950408889634074;
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if (acb_rel_accuracy_bits(z) >= wp)
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{
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acb_hypgeom_erf(res, z, wp);
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}
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else
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{
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acb_t zmid;
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mag_t re_err, im_err;
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acb_init(zmid);
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mag_init(re_err);
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mag_init(im_err);
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acb_hypgeom_erf_propagated_error(re_err, im_err, z);
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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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acb_hypgeom_erf(res, zmid, wp);
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arb_add_error_mag(acb_realref(res), re_err);
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arb_add_error_mag(acb_imagref(res), im_err);
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acb_clear(zmid);
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mag_clear(re_err);
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mag_clear(im_err);
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}
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acb_sub_ui(res, res, 1, prec);
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acb_neg(res, res);
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}
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}
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