mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
121 lines
3.1 KiB
C
121 lines
3.1 KiB
C
/*
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Copyright (C) 2013 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_poly.h"
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#include "arb_hypgeom.h"
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slong arf_get_si(const arf_t x, arf_rnd_t rnd);
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void _arb_poly_lgamma_series_at_one(arb_ptr u, slong len, slong prec);
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void arb_hypgeom_gamma_stirling_choose_param(int * reflect, slong * r, slong * n,
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const arb_t x, int use_reflect, int digamma, slong prec);
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void _arb_poly_gamma_stirling_eval(arb_ptr res, const arb_t z, slong n, slong num, slong prec);
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static __inline__ void
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_log_rising_ui_series(arb_ptr t, const arb_t x, slong r, slong len, slong prec)
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{
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slong rflen;
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rflen = FLINT_MIN(len, r + 1);
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arb_hypgeom_rising_ui_jet(t, x, r, rflen, prec);
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_arb_poly_log_series(t, t, rflen, len, prec);
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}
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void
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_arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec)
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{
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int reflect;
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slong r, n, wp;
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arb_t zr;
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arb_ptr t, u;
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if (!arb_is_positive(h))
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{
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_arb_vec_indeterminate(res, len);
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return;
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}
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hlen = FLINT_MIN(hlen, len);
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wp = prec + FLINT_BIT_COUNT(prec);
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t = _arb_vec_init(len);
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u = _arb_vec_init(len);
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arb_init(zr);
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/* use zeta values at small integers */
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if (arb_is_int(h) && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0))
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{
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r = arf_get_si(arb_midref(h), ARF_RND_DOWN);
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if (r <= 0)
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{
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_arb_vec_indeterminate(res, len);
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goto cleanup;
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}
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else
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{
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_arb_poly_lgamma_series_at_one(u, len, wp);
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if (r != 1)
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{
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arb_one(zr);
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_log_rising_ui_series(t, zr, r - 1, len, wp);
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_arb_vec_add(u, u, t, len, wp);
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}
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}
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}
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else if (len <= 2)
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{
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arb_lgamma(u, h, wp);
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if (len == 2)
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arb_digamma(u + 1, h, wp);
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}
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else
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{
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/* otherwise use Stirling series */
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arb_hypgeom_gamma_stirling_choose_param(&reflect, &r, &n, h, 0, 0, wp);
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arb_add_ui(zr, h, r, wp);
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_arb_poly_gamma_stirling_eval(u, zr, n, len, wp);
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if (r != 0)
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{
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_log_rising_ui_series(t, h, r, len, wp);
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_arb_vec_sub(u, u, t, len, wp);
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}
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}
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/* compose with nonconstant part */
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arb_zero(t);
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_arb_vec_set(t + 1, h + 1, hlen - 1);
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_arb_poly_compose_series(res, u, len, t, hlen, len, prec);
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cleanup:
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arb_clear(zr);
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_arb_vec_clear(t, len);
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_arb_vec_clear(u, len);
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}
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void
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arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)
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{
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arb_poly_fit_length(res, n);
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if (f->length == 0 || n == 0)
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_arb_vec_indeterminate(res->coeffs, n);
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else
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_arb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
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_arb_poly_set_length(res, n);
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_arb_poly_normalise(res);
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}
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