mirror of
https://github.com/vale981/arb
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128 lines
3.5 KiB
C
128 lines
3.5 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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmprb_poly.h"
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#include "gamma.h"
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#include "zeta.h"
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static __inline__ void
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_log_rising_ui_series(fmprb_ptr t, const fmprb_t x, long r, long len, long prec)
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{
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fmprb_struct f[2];
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long rflen;
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fmprb_init(f);
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fmprb_init(f + 1);
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fmprb_set(f, x);
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fmprb_one(f + 1);
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rflen = FLINT_MIN(len, r + 1);
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_fmprb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, prec);
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_fmprb_poly_log_series(t, t, rflen, len, prec);
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fmprb_clear(f);
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fmprb_clear(f + 1);
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}
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void
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_fmprb_poly_lgamma_series(fmprb_ptr res, fmprb_srcptr h, long hlen, long len, long prec)
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{
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int reflect;
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long r, n, wp;
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fmprb_t zr;
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fmprb_ptr t, u;
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hlen = FLINT_MIN(hlen, len);
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wp = prec + FLINT_BIT_COUNT(prec);
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t = _fmprb_vec_init(len);
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u = _fmprb_vec_init(len);
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fmprb_init(zr);
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/* use zeta values at small integers */
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if (fmprb_is_int(h) && (fmpr_cmpabs_ui(fmprb_midref(h), prec / 2) < 0))
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{
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r = fmpr_get_si(fmprb_midref(h), FMPR_RND_DOWN);
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if (r <= 0)
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{
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_fmprb_vec_indeterminate(res, len);
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}
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else
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{
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gamma_lgamma_series_at_one(u, len, wp);
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if (r != 1)
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{
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fmprb_one(zr);
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_log_rising_ui_series(t, zr, r - 1, len, wp);
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_fmprb_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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fmprb_lgamma(u, h, wp);
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if (len == 2)
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fmprb_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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gamma_stirling_choose_param_fmprb(&reflect, &r, &n, h, 0, 0, wp);
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fmprb_add_ui(zr, h, r, wp);
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gamma_stirling_eval_fmprb_series(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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_fmprb_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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fmprb_zero(t);
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_fmprb_vec_set(t + 1, h + 1, hlen - 1);
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_fmprb_poly_compose_series(res, u, len, t, hlen, len, prec);
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fmprb_clear(zr);
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_fmprb_vec_clear(t, len);
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_fmprb_vec_clear(u, len);
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}
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void
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fmprb_poly_lgamma_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec)
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{
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fmprb_poly_fit_length(res, n);
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if (f->length == 0 || n == 0)
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_fmprb_vec_indeterminate(res->coeffs, n);
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else
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_fmprb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec);
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_fmprb_poly_set_length(res, n);
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_fmprb_poly_normalise(res);
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}
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