mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
95 lines
2.7 KiB
C
95 lines
2.7 KiB
C
/*
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Copyright (C) 2014 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_poly.h"
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#include "bernoulli.h"
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void _acb_poly_mullow_cpx(acb_ptr res, acb_srcptr src, slong len, const acb_t c, slong trunc, slong prec);
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void
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_acb_poly_zeta_em_tail_naive(acb_ptr sum, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong d, slong prec)
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{
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acb_ptr u, term;
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acb_t Na2, splus, rec;
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arb_t x;
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fmpz_t c;
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int aint;
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slong r;
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BERNOULLI_ENSURE_CACHED(2 * M);
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u = _acb_vec_init(d);
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term = _acb_vec_init(d);
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acb_init(splus);
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acb_init(rec);
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acb_init(Na2);
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arb_init(x);
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fmpz_init(c);
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_acb_vec_zero(sum, d);
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/* u = 1/2 * Nasx */
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_acb_vec_scalar_mul_2exp_si(u, Nasx, d, -WORD(1));
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/* term = u * (s+x) / (N+a) */
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_acb_poly_mullow_cpx(u, u, d, s, d, prec);
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_acb_vec_scalar_div(term, u, d, Na, prec);
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/* (N+a)^2 or 1/(N+a)^2 */
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acb_mul(Na2, Na, Na, prec);
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aint = acb_is_int(Na2);
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if (!aint)
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acb_inv(Na2, Na2, prec);
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for (r = 1; r <= M; r++)
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{
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/* flint_printf("sum 2: %wd %wd\n", r, M); */
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/* sum += bernoulli number * term */
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arb_set_round_fmpz(x, fmpq_numref(bernoulli_cache + 2 * r), prec);
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arb_div_fmpz(x, x, fmpq_denref(bernoulli_cache + 2 * r), prec);
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_acb_vec_scalar_mul_arb(u, term, d, x, prec);
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_acb_vec_add(sum, sum, u, d, prec);
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/* multiply term by ((s+x)+2r-1)((s+x)+2r) / ((N+a)^2 * (2*r+1)*(2*r+2)) */
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acb_set(splus, s);
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arb_add_ui(acb_realref(splus), acb_realref(splus), 2*r-1, prec);
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_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
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arb_add_ui(acb_realref(splus), acb_realref(splus), 1, prec);
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_acb_poly_mullow_cpx(term, term, d, splus, d, prec);
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/* TODO: combine with previous multiplication? */
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if (aint)
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{
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arb_mul_ui(x, acb_realref(Na2), 2*r+1, prec);
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arb_mul_ui(x, x, 2*r+2, prec);
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_acb_vec_scalar_div_arb(term, term, d, x, prec);
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}
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else
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{
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fmpz_set_ui(c, 2*r+1);
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fmpz_mul_ui(c, c, 2*r+2);
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acb_div_fmpz(rec, Na2, c, prec);
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_acb_vec_scalar_mul(term, term, d, rec, prec);
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}
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}
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_acb_vec_clear(u, d);
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_acb_vec_clear(term, d);
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acb_clear(splus);
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acb_clear(rec);
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acb_clear(Na2);
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arb_clear(x);
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fmpz_clear(c);
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}
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