mirror of
https://github.com/vale981/arb
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102 lines
2.5 KiB
C
102 lines
2.5 KiB
C
/*
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Copyright (C) 2017 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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#include "bernoulli.h"
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/* todo: use log(1-z) when this is better? would also need to
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adjust strategy in the main function */
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void
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acb_hypgeom_dilog_bernoulli(acb_t res, const acb_t z, slong prec)
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{
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acb_t s, w, w2;
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slong n, k;
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fmpz_t c, d;
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mag_t m, err;
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double lm;
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int real;
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acb_init(s);
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acb_init(w);
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acb_init(w2);
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fmpz_init(c);
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fmpz_init(d);
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mag_init(m);
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mag_init(err);
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real = 0;
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if (acb_is_real(z))
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{
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arb_sub_ui(acb_realref(w), acb_realref(z), 1, 30);
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real = arb_is_nonpositive(acb_realref(w));
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}
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acb_log(w, z, prec);
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acb_get_mag(m, w);
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/* for k >= 4, the terms are bounded by (|w| / (2 pi))^k */
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mag_set_ui_2exp_si(err, 2670177, -24); /* upper bound for 1/(2pi) */
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mag_mul(err, err, m);
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lm = mag_get_d_log2_approx(err);
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if (lm < -0.25)
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{
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n = prec / (-lm) + 1;
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n = FLINT_MAX(n, 4);
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mag_geom_series(err, err, n);
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BERNOULLI_ENSURE_CACHED(n)
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acb_mul(w2, w, w, prec);
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for (k = n - (n % 2 == 0); k >= 3; k -= 2)
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{
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fmpz_mul_ui(c, fmpq_denref(bernoulli_cache + k - 1), k - 1);
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fmpz_mul_ui(d, c, (k + 1) * (k + 2));
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acb_mul(s, s, w2, prec);
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acb_mul_fmpz(s, s, c, prec);
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fmpz_mul_ui(c, fmpq_numref(bernoulli_cache + k - 1), (k + 1) * (k + 2));
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acb_sub_fmpz(s, s, c, prec);
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acb_div_fmpz(s, s, d, prec);
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}
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acb_mul(s, s, w, prec);
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acb_mul_2exp_si(s, s, 1);
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acb_sub_ui(s, s, 3, prec);
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acb_mul(s, s, w2, prec);
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acb_mul_2exp_si(s, s, -1);
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acb_const_pi(w2, prec);
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acb_addmul(s, w2, w2, prec);
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acb_div_ui(s, s, 6, prec);
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acb_neg(w2, w);
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acb_log(w2, w2, prec);
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acb_submul(s, w2, w, prec);
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acb_add(res, s, w, prec);
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acb_add_error_mag(res, err);
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if (real)
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arb_zero(acb_imagref(res));
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}
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else
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{
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acb_indeterminate(res);
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}
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acb_clear(s);
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acb_clear(w);
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acb_clear(w2);
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fmpz_clear(c);
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fmpz_clear(d);
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mag_clear(m);
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mag_clear(err);
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}
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