mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
137 lines
2.9 KiB
C
137 lines
2.9 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.h"
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#include "acb_poly.h"
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void
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_arb_const_zeta_minus_one_eval(arb_t y, slong prec)
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{
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acb_struct z[2];
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acb_t s, a;
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acb_init(z + 0);
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acb_init(z + 1);
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acb_init(s);
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acb_init(a);
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acb_set_si(s, -1);
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acb_one(a);
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_acb_poly_zeta_cpx_series(z, s, a, 0, 2, prec + 20);
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arb_set(y, acb_realref(z + 1));
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acb_clear(z + 0);
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acb_clear(z + 1);
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acb_clear(s);
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acb_clear(a);
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}
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ARB_DEF_CACHED_CONSTANT(_arb_const_zeta_minus_one, _arb_const_zeta_minus_one_eval)
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/* LogG(z) = (z-1) LogGamma(z) - zeta'(-1,z) + zeta'(-1)
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LogG'(z) = (1/2)(-2z + 1 + log(2pi)) + (z-1) digamma(z) */
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void
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_acb_log_barnes_g_zeta(acb_t res, const acb_t z, slong prec)
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{
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acb_struct t[3];
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acb_init(t + 0);
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acb_init(t + 1);
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acb_init(t + 2);
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acb_set_si(t + 2, -1);
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_acb_poly_zeta_cpx_series(t, t + 2, z, 0, 2, prec);
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_arb_const_zeta_minus_one(acb_realref(t), prec);
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arb_zero(acb_imagref(t));
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acb_sub(t, t, t + 1, prec);
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acb_lgamma(t + 1, z, prec);
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acb_sub_ui(t + 2, z, 1, prec);
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acb_addmul(t, t + 1, t + 2, prec);
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acb_set(res, t);
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acb_clear(t + 0);
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acb_clear(t + 1);
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acb_clear(t + 2);
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}
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void
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_acb_barnes_g_ui_rec(acb_t res, ulong n, slong prec)
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{
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acb_t t;
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ulong k;
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acb_init(t);
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acb_one(res);
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acb_one(t);
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for (k = 3; k < n; k++)
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{
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acb_mul_ui(t, t, k - 1, prec);
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acb_mul(res, res, t, prec);
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}
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acb_clear(t);
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}
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void
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acb_log_barnes_g(acb_t res, const acb_t z, slong prec)
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{
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if (acb_is_int(z))
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{
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if (arb_is_nonpositive(acb_realref(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 (arf_cmpabs_ui(arb_midref(acb_realref(z)), prec) < 0)
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{
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_acb_barnes_g_ui_rec(res,
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arf_get_si(arb_midref(acb_realref(z)), ARF_RND_DOWN), prec);
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acb_log(res, res, prec);
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return;
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}
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}
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_acb_log_barnes_g_zeta(res, z, prec);
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}
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void
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acb_barnes_g(acb_t res, const acb_t z, slong prec)
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{
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int real;
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real = acb_is_real(z);
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if (acb_is_int(z))
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{
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if (arb_is_nonpositive(acb_realref(z)))
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{
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acb_zero(res);
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return;
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}
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if (arf_cmpabs_ui(arb_midref(acb_realref(z)), prec) < 0)
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{
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_acb_barnes_g_ui_rec(res,
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arf_get_si(arb_midref(acb_realref(z)), ARF_RND_DOWN), prec);
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return;
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}
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}
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_acb_log_barnes_g_zeta(res, z, prec);
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acb_exp(res, res, prec);
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if (real)
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arb_zero(acb_imagref(res));
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}
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