mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
130 lines
2.8 KiB
C
130 lines
2.8 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_ei_asymp(acb_t res, const acb_t z, slong prec)
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{
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acb_t t, u;
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acb_init(t);
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acb_init(u);
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acb_one(t);
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acb_neg(u, z);
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acb_hypgeom_u_asymp(u, t, t, u, -1, prec);
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acb_div(u, u, z, prec);
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acb_exp(t, z, prec);
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acb_mul(u, u, t, prec);
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if (arb_is_zero(acb_imagref(z)))
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{
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arb_zero(acb_imagref(u));
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}
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else if (arb_is_positive(acb_imagref(z)))
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{
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acb_const_pi(t, prec);
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arb_add(acb_imagref(u), acb_imagref(u), acb_realref(t), prec);
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}
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else if (arb_is_negative(acb_imagref(z)))
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{
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acb_const_pi(t, prec);
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arb_sub(acb_imagref(u), acb_imagref(u), acb_realref(t), prec);
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}
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else
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{
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/* add [-pi,pi] i */
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acb_const_pi(t, prec);
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arb_add_error(acb_imagref(u), acb_realref(t));
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}
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acb_swap(res, u);
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acb_clear(t);
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acb_clear(u);
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}
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/*
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Ei(z) = z 2F2(1,1,2,2,z) + 0.5[log(z)-log(1/z)] + gamma
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*/
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void
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acb_hypgeom_ei_2f2(acb_t res, const acb_t z, slong prec)
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{
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acb_t a, t;
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acb_struct b[2];
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acb_init(a);
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acb_init(b);
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acb_init(b + 1);
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acb_init(t);
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acb_one(a);
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acb_set_ui(b, 2);
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acb_set_ui(b + 1, 2);
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acb_hypgeom_pfq_direct(t, a, 1, b, 2, z, -1, prec);
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acb_mul(t, t, z, prec);
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arb_const_euler(acb_realref(a), prec);
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arb_add(acb_realref(t), acb_realref(t), acb_realref(a), prec);
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if (arb_is_zero(acb_imagref(z)))
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{
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if (arb_is_positive(acb_realref(z)))
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{
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acb_log(a, z, prec);
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}
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else
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{
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/* ok if overlapping zero -- will be indeterminate either way */
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acb_neg(a, z);
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acb_log(a, a, prec);
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arb_zero(acb_imagref(a));
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}
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acb_add(t, t, a, prec);
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}
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else if (arb_is_nonzero(acb_imagref(z))
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|| arb_is_nonnegative(acb_realref(z))) /* not overlapping (-inf,0] */
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{
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acb_log(a, z, prec);
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acb_add(t, t, a, prec);
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}
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else
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{
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acb_log(a, z, prec);
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arb_zero(acb_imagref(a));
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acb_const_pi(b, prec);
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arb_add_error(acb_imagref(a), acb_realref(b));
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acb_add(t, t, a, prec);
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}
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acb_swap(res, t);
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acb_clear(a);
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acb_clear(b);
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acb_clear(b + 1);
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acb_clear(t);
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}
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void
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acb_hypgeom_ei(acb_t res, const acb_t z, slong prec)
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{
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if (acb_hypgeom_u_use_asymp(z, prec))
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acb_hypgeom_ei_asymp(res, z, prec);
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else
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acb_hypgeom_ei_2f2(res, z, prec);
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}
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