mirror of
https://github.com/vale981/arb
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113 lines
3.2 KiB
C
113 lines
3.2 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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void
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_fmprb_poly_lgamma_cpx_series(fmprb_ptr res, const fmprb_t z, long len, long prec)
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{
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int reflect;
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long r, n, rflen, wp;
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fmprb_t zr;
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fmprb_ptr t, u, f;
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wp = prec + FLINT_BIT_COUNT(prec);
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gamma_stirling_choose_param_fmprb(&reflect, &r, &n, z, 0, 0, wp);
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t = _fmprb_vec_init(len);
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u = _fmprb_vec_init(len);
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f = _fmprb_vec_init(2);
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fmprb_init(zr);
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/* log(gamma(z)) = log(gamma(z+r)) - log(rf(z,r)) */
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fmprb_add_ui(zr, z, r, wp);
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/* u = log(gamma(z+r)) */
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gamma_stirling_eval_fmprb_series(u, zr, n, len, wp);
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/* t = rising factorial */
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fmprb_set(f, z);
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fmprb_one(f + 1);
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rflen = FLINT_MIN(len, r + 1);
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_fmprb_poly_rfac_series_ui(t, f, FLINT_MIN(2, len), r, rflen, prec);
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_fmprb_poly_log_series(t, t, rflen, len, wp);
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_fmprb_vec_sub(res, u, t, 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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_fmprb_vec_clear(f, 2);
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}
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void
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fmprb_poly_lgamma_cpx_series(fmprb_poly_t res, const fmprb_t z, long num, long prec)
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{
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fmprb_poly_fit_length(res, num);
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_fmprb_poly_lgamma_cpx_series(res->coeffs, z, num, prec);
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_fmprb_poly_set_length(res, num);
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_fmprb_poly_normalise(res);
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}
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void
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_fmprb_poly_lgamma_series(fmprb_ptr res, fmprb_ptr h, long hlen, long len, long prec)
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{
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fmprb_ptr t, u;
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fmprb_t z;
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hlen = FLINT_MIN(hlen, len);
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t = _fmprb_vec_init(hlen);
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u = _fmprb_vec_init(len);
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fmprb_init(z);
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fmprb_set(z, h);
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_fmprb_vec_set(t + 1, h + 1, hlen - 1);
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_fmprb_poly_lgamma_cpx_series(u, z, len, prec);
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_fmprb_poly_compose_series(res, u, len, t, hlen, len, prec);
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fmprb_clear(z);
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_fmprb_vec_clear(t, hlen);
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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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if (f->length == 0 || n == 0)
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{
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printf("fmprb_poly_lgamma_series: require n > 0 and nonzero input\n");
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abort();
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}
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fmprb_poly_fit_length(res, n);
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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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