mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
75 lines
1.9 KiB
C
75 lines
1.9 KiB
C
/*
|
|
Copyright (C) 2021 Fredrik Johansson
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb is free software: you can redistribute it and/or modify it under
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "arb_hypgeom.h"
|
|
|
|
void arb_hypgeom_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec);
|
|
int arb_hypgeom_gamma_exact(arb_t res, const arb_t x, int reciprocal, slong prec);
|
|
void arb_hypgeom_gamma_stirling_inner(arb_t s, const arb_t z, slong N, slong prec);
|
|
|
|
void
|
|
arb_hypgeom_lgamma_stirling(arb_t y, const arb_t x, slong prec)
|
|
{
|
|
int reflect;
|
|
slong r, n, wp;
|
|
arb_t t, u;
|
|
double acc;
|
|
|
|
/* todo: for large x (if exact or accurate enough), increase precision */
|
|
acc = arb_rel_accuracy_bits(x);
|
|
acc = FLINT_MAX(acc, 0);
|
|
wp = FLINT_MIN(prec, acc + 20);
|
|
wp = FLINT_MAX(wp, 2);
|
|
wp = wp + FLINT_BIT_COUNT(wp);
|
|
|
|
arb_hypgeom_gamma_stirling_choose_param(&reflect, &r, &n, x, 0, 0, wp);
|
|
|
|
arb_init(t);
|
|
arb_init(u);
|
|
|
|
/* log(gamma(x)) = log(gamma(x+r)) - log(rf(x,r)) */
|
|
arb_init(t);
|
|
arb_init(u);
|
|
|
|
arb_add_ui(t, x, r, wp);
|
|
arb_hypgeom_gamma_stirling_inner(u, t, n, wp);
|
|
arb_hypgeom_rising_ui_rec(t, x, r, wp);
|
|
arb_log(t, t, wp);
|
|
arb_sub(y, u, t, prec);
|
|
|
|
arb_clear(t);
|
|
arb_clear(u);
|
|
}
|
|
|
|
void
|
|
arb_hypgeom_lgamma(arb_t res, const arb_t x, slong prec)
|
|
{
|
|
if (!arb_is_positive(x) || !arb_is_finite(x))
|
|
{
|
|
arb_indeterminate(res);
|
|
return;
|
|
}
|
|
|
|
if (arb_hypgeom_gamma_exact(res, x, 0, prec))
|
|
{
|
|
arb_log(res, res, prec);
|
|
return;
|
|
}
|
|
|
|
if (arb_hypgeom_gamma_taylor(res, x, 0, prec))
|
|
{
|
|
arb_log(res, res, prec);
|
|
return;
|
|
}
|
|
|
|
arb_hypgeom_lgamma_stirling(res, x, prec);
|
|
}
|
|
|