mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
101 lines
2.7 KiB
C
101 lines
2.7 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_hypgeom.h"
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static void
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phase(acb_t res, const arb_t re, const arb_t im)
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{
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if (arb_is_nonnegative(re) || arb_is_negative(im))
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{
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acb_one(res);
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}
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else if (arb_is_negative(re) && arb_is_nonnegative(im))
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{
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acb_set_si(res, -3);
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}
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else
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{
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arb_zero(acb_imagref(res));
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/* -1 +/- 2 */
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arf_set_si(arb_midref(acb_realref(res)), -1);
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mag_one(arb_radref(acb_realref(res)));
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mag_mul_2exp_si(arb_radref(acb_realref(res)), arb_radref(acb_realref(res)), 1);
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}
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}
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void
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acb_hypgeom_bessel_y(acb_t res, const acb_t nu, const acb_t z, slong prec)
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{
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acb_t t, u, v;
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acb_init(t);
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acb_init(u);
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acb_init(v);
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if (acb_is_int(nu))
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{
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int is_real = acb_is_real(nu) && acb_is_real(z)
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&& arb_is_positive(acb_realref(z));
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acb_mul_onei(t, z);
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acb_hypgeom_bessel_k(t, nu, t, prec);
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acb_onei(u);
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acb_pow(u, u, nu, prec);
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acb_mul(t, t, u, prec);
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acb_const_pi(u, prec);
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acb_div(t, t, u, prec);
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acb_mul_2exp_si(t, t, 1);
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acb_neg(t, t);
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acb_hypgeom_bessel_j(u, nu, z, prec);
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phase(v, acb_realref(z), acb_imagref(z));
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acb_mul(u, u, v, prec);
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acb_mul_onei(u, u);
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acb_sub(res, t, u, prec);
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if (is_real)
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arb_zero(acb_imagref(res));
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}
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else
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{
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acb_sin_cos_pi(t, u, nu, prec);
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acb_hypgeom_bessel_j(v, nu, z, prec);
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acb_mul(v, v, u, prec);
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acb_neg(u, nu);
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acb_hypgeom_bessel_j(u, u, z, prec);
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acb_sub(v, v, u, prec);
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acb_div(res, v, t, prec);
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}
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acb_clear(t);
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acb_clear(u);
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acb_clear(v);
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}
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