mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
114 lines
2.4 KiB
C
114 lines
2.4 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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/* this can be improved */
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static int
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use_recurrence(const acb_t n, const acb_t m, slong prec)
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{
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if (!acb_is_int(n) || !arb_is_nonnegative(acb_realref(n)))
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return 0;
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if (arf_cmpabs_ui(arb_midref(acb_realref(n)), prec) > 0)
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return 0;
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if (arf_cmpabs(arb_midref(acb_realref(n)), arb_midref(acb_realref(m))) >= 0)
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return 0;
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return 1;
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}
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void
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acb_hypgeom_laguerre_l_ui_recurrence(acb_t res, ulong n, const acb_t m,
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const acb_t z, slong prec)
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{
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acb_t t, u, v;
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ulong k;
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if (n == 0)
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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 (n == 1)
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{
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acb_sub(res, m, z, prec);
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acb_add_ui(res, res, 1, prec);
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return;
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}
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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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acb_one(t);
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acb_sub(u, m, z, prec);
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acb_add_ui(u, u, 1, prec);
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for (k = 2; k <= n; k++)
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{
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acb_add_ui(v, m, k - 1, prec);
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acb_mul(t, t, v, prec);
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acb_add_ui(v, m, 2 * k - 1, prec);
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acb_sub(v, v, z, prec);
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acb_mul(v, v, u, prec);
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acb_sub(t, v, t, prec);
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acb_div_ui(t, t, k, prec);
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acb_swap(t, u);
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}
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acb_set(res, u);
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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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void
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acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec)
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{
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acb_t t, u, v;
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if (use_recurrence(n, m, prec))
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{
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acb_hypgeom_laguerre_l_ui_recurrence(res,
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arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), m, z, prec);
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return;
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}
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/* todo: should be a test of whether n contains any negative integer */
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if (acb_contains_int(n) && !arb_is_nonnegative(acb_realref(n)))
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{
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acb_indeterminate(res);
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return;
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}
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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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acb_neg(t, n);
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acb_add_ui(u, m, 1, prec);
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acb_hypgeom_m(t, t, u, z, 1, prec);
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acb_add_ui(u, n, 1, prec);
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acb_rising(u, u, m, prec);
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acb_mul(res, t, u, prec);
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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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