mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
104 lines
2.6 KiB
C
104 lines
2.6 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) 2016 Fredrik Johansson
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******************************************************************************/
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#include "acb.h"
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void
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acb_bernoulli_poly_ui(acb_t res, ulong n, const acb_t x, slong prec)
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{
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acb_t s, x2;
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arb_t t, c;
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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_mul_2exp_si(res, x, 1);
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acb_sub_ui(res, res, 1, prec);
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acb_mul_2exp_si(res, res, -1);
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return;
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}
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if (acb_is_real(x))
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{
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arb_bernoulli_poly_ui(acb_realref(res), n, acb_realref(x), prec);
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arb_zero(acb_imagref(res));
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return;
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}
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/* assuming small n simplifies the code that follows */
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if (n >> (FLINT_BITS / 2) || !acb_is_finite(x))
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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(s);
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acb_init(x2);
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arb_init(t);
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arb_init(c);
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acb_mul(x2, x, x, prec);
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/* s = x^2 - x n / 2 */
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acb_mul_ui(s, x, n, prec);
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acb_mul_2exp_si(s, s, -1);
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acb_sub(s, x2, s, prec);
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/* c = n (n-1) / 2; s = s + c / 6 */
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arb_set_ui(c, n * (n - 1));
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arb_mul_2exp_si(c, c, -1);
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arb_div_ui(t, c, 6, prec);
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acb_add_arb(s, s, t, prec);
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for (k = 4; k <= n; k += 2)
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{
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/* c = binomial(n,k) */
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arb_mul_ui(c, c, (n + 1 - k) * (n + 2 - k), prec);
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arb_div_ui(c, c, k * (k - 1), prec);
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/* s = s x^2 + b_k c */
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acb_mul(s, s, x2, prec);
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arb_bernoulli_ui(t, k, prec);
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arb_mul(t, t, c, prec);
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acb_add_arb(s, s, t, prec);
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}
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if (n >= 3 && n % 2)
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acb_mul(s, s, x, prec);
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acb_swap(res, s);
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acb_clear(s);
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acb_clear(x2);
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arb_clear(t);
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arb_clear(c);
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}
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