mirror of
https://github.com/vale981/arb
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113 lines
3 KiB
C
113 lines
3 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) 2012, 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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#include "gamma.h"
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static void
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_fmprb_gamma(fmprb_t y, const fmprb_t x, long prec, int inverse)
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{
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int reflect;
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long r, n, wp;
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fmprb_t t, u, v;
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wp = prec + FLINT_BIT_COUNT(prec);
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gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 1, 0, wp);
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fmprb_init(t);
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fmprb_init(u);
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fmprb_init(v);
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if (reflect)
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{
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/* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */
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fmprb_sub_ui(t, x, 1, wp);
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fmprb_neg(t, t);
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gamma_rising_fmprb_ui_bsplit(u, t, r, wp);
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fmprb_const_pi(v, wp);
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fmprb_mul(u, u, v, wp);
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fmprb_add_ui(t, t, r, wp);
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gamma_stirling_eval_series_fmprb(v, t, n, 0, wp);
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fmprb_exp(v, v, wp);
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fmprb_sin_pi(t, x, wp);
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fmprb_mul(v, v, t, wp);
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}
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else
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{
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/* gamma(x) = gamma(x+r) / rf(x,r) */
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fmprb_add_ui(t, x, r, wp);
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gamma_stirling_eval_series_fmprb(u, t, n, 0, wp);
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fmprb_exp(u, u, prec);
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gamma_rising_fmprb_ui_bsplit(v, x, r, wp);
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}
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if (inverse)
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fmprb_div(y, v, u, prec);
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else
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fmprb_div(y, u, v, prec);
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fmprb_clear(t);
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fmprb_clear(u);
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fmprb_clear(v);
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}
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void
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fmprb_gamma(fmprb_t y, const fmprb_t x, long prec)
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{
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_fmprb_gamma(y, x, prec, 0);
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}
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void
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fmprb_rgamma(fmprb_t y, const fmprb_t x, long prec)
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{
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_fmprb_gamma(y, x, prec, 1);
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}
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void
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fmprb_lgamma(fmprb_t y, const fmprb_t x, 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 t, u;
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wp = prec + FLINT_BIT_COUNT(prec);
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gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 0, 0, wp);
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/* log(gamma(x)) = log(gamma(x+r)) - log(rf(x,r)) */
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fmprb_init(t);
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fmprb_init(u);
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fmprb_add_ui(t, x, r, wp);
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gamma_stirling_eval_series_fmprb(u, t, n, 0, wp);
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gamma_rising_fmprb_ui_bsplit(t, x, r, wp);
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fmprb_log(t, t, wp);
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fmprb_sub(y, u, t, prec);
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fmprb_clear(t);
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fmprb_clear(u);
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}
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