mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
112 lines
2.7 KiB
C
112 lines
2.7 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_chebyshev_u(acb_t res, const acb_t n, const acb_t z, slong prec)
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{
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acb_t t, u;
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if (acb_is_int(n) &&
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arf_cmpabs_2exp_si(arb_midref(acb_realref(n)), FLINT_BITS - 1) < 0)
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{
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slong k = arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN);
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if (k >= 0)
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{
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acb_chebyshev_u_ui(res, k, z, prec);
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}
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else if (k == -1)
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{
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acb_zero(res);
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}
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else
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{
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acb_chebyshev_u_ui(res, -2-k, z, prec);
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acb_neg(res, res);
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}
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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_mul_2exp_si(res, n, -1);
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acb_cos_pi(res, res, prec);
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return;
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}
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if (acb_is_one(z))
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{
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acb_add_ui(res, n, 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_add_ui(u, n, 1, prec);
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acb_sub_ui(t, z, 1, prec);
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if (arf_cmpabs_2exp_si(arb_midref(acb_realref(t)), -2 - prec / 10) < 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_imagref(t)), -2 - prec / 10) < 0)
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{
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acb_t a, b, c;
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acb_init(a);
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acb_init(b);
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acb_init(c);
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acb_neg(a, n);
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acb_add_ui(b, n, 2, prec);
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acb_set_ui(c, 3);
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acb_mul_2exp_si(c, c, -1);
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acb_neg(t, t);
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acb_mul_2exp_si(t, t, -1);
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acb_hypgeom_2f1(t, a, b, c, t, 0, prec);
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acb_mul(res, t, u, prec);
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acb_clear(a);
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acb_clear(b);
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acb_clear(c);
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}
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else
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{
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if (arb_is_positive(acb_realref(t)))
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{
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/* sinh((n+1) acosh(z)) / (sqrt(z-1) sqrt(z+1));
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can use one square root when strictly in the right half plane */
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acb_mul(t, z, z, prec);
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acb_sub_ui(t, t, 1, prec);
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acb_acosh(res, z, prec);
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acb_mul(res, res, u, prec);
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acb_sinh(res, res, prec);
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acb_rsqrt(t, t, prec);
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acb_mul(res, res, t, prec);
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}
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else
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{
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acb_mul(t, z, z, prec);
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acb_sub_ui(t, t, 1, prec);
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acb_acos(res, z, prec);
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acb_mul(res, res, u, prec);
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acb_sin(res, res, prec);
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acb_neg(t, t);
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acb_rsqrt(t, t, prec);
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acb_mul(res, res, t, prec);
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}
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}
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acb_clear(t);
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acb_clear(u);
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}
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