mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
76 lines
1.7 KiB
C
76 lines
1.7 KiB
C
/*
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Copyright (C) 2021 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 "arb_hypgeom.h"
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#include "acb_hypgeom.h"
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void arb_gamma_stirling_coeff(acb_t b, ulong k, int digamma, slong prec);
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void
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acb_hypgeom_gamma_stirling_sum_horner(acb_t s, const acb_t z, slong N, slong prec)
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{
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acb_t b, t, zinv, w;
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mag_t zinv_mag;
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slong n, term_mag, term_prec;
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slong * term_mags;
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if (N <= 1)
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{
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acb_zero(s);
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return;
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}
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acb_init(b);
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acb_init(t);
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acb_init(zinv);
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acb_init(w);
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mag_init(zinv_mag);
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acb_inv(zinv, z, prec);
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acb_mul(w, zinv, zinv, prec);
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acb_get_mag(zinv_mag, zinv);
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term_mags = flint_malloc(sizeof(ulong) * N);
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_arb_hypgeom_gamma_stirling_term_bounds(term_mags, zinv_mag, N);
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acb_zero(s);
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for (n = N - 1; n >= 1; n--)
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{
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term_mag = term_mags[n];
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term_prec = prec + term_mag;
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term_prec = FLINT_MIN(term_prec, prec);
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term_prec = FLINT_MAX(term_prec, 10);
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if (prec - term_prec > 200)
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{
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acb_set_round(t, w, term_prec);
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acb_mul(s, s, t, term_prec);
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}
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else
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acb_mul(s, s, w, term_prec);
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arb_gamma_stirling_coeff(b, n, 0, term_prec);
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acb_add(s, s, b, term_prec);
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}
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acb_mul(s, s, zinv, prec);
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flint_free(term_mags);
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acb_clear(t);
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acb_clear(b);
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acb_clear(zinv);
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acb_clear(w);
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mag_clear(zinv_mag);
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}
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