arb/fmpcb/gamma.c

88 lines
2.4 KiB
C

/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "fmpcb.h"
#include "gamma.h"
static void
_fmpcb_gamma(fmpcb_t y, const fmpcb_t x, long prec, int inverse)
{
int reflect;
long r, n, wp;
fmpcb_t t, u, v;
wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmpcb(&reflect, &r, &n, x, 1, 0, wp);
fmpcb_init(t);
fmpcb_init(u);
fmpcb_init(v);
if (reflect)
{
/* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */
fmpcb_sub_ui(t, x, 1, wp);
fmpcb_neg(t, t);
gamma_rising_fmpcb_ui_bsplit(u, t, r, wp);
fmprb_const_pi(fmpcb_realref(v), wp);
fmpcb_mul_fmprb(u, u, fmpcb_realref(v), wp);
fmpcb_add_ui(t, t, r, wp);
gamma_stirling_eval_fmpcb(v, t, n, 0, wp);
fmpcb_exp(v, v, wp);
fmpcb_sin_pi(t, x, wp);
fmpcb_mul(v, v, t, wp);
}
else
{
/* gamma(x) = gamma(x+r) / rf(x,r) */
fmpcb_add_ui(t, x, r, wp);
gamma_stirling_eval_fmpcb(u, t, n, 0, wp);
fmpcb_exp(u, u, prec);
gamma_rising_fmpcb_ui_bsplit(v, x, r, wp);
}
if (inverse)
fmpcb_div(y, v, u, prec);
else
fmpcb_div(y, u, v, prec);
fmpcb_clear(t);
fmpcb_clear(u);
fmpcb_clear(v);
}
void
fmpcb_gamma(fmpcb_t y, const fmpcb_t x, long prec)
{
_fmpcb_gamma(y, x, prec, 0);
}
void
fmpcb_rgamma(fmpcb_t y, const fmpcb_t x, long prec)
{
_fmpcb_gamma(y, x, prec, 1);
}