mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
75 lines
1.7 KiB
C
75 lines
1.7 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_gamma_stirling_coeff(arb_t b, ulong k, int digamma, slong prec);
|
|
|
|
void
|
|
arb_hypgeom_gamma_stirling_sum_horner(arb_t s, const arb_t z, slong N, slong prec)
|
|
{
|
|
arb_t b, t, zinv, w;
|
|
mag_t zinv_mag;
|
|
slong n, term_mag, term_prec;
|
|
slong * term_mags;
|
|
|
|
if (N <= 1)
|
|
{
|
|
arb_zero(s);
|
|
return;
|
|
}
|
|
|
|
arb_init(b);
|
|
arb_init(t);
|
|
arb_init(zinv);
|
|
arb_init(w);
|
|
mag_init(zinv_mag);
|
|
|
|
arb_inv(zinv, z, prec);
|
|
arb_mul(w, zinv, zinv, prec);
|
|
|
|
arb_get_mag(zinv_mag, zinv);
|
|
term_mags = flint_malloc(sizeof(ulong) * N);
|
|
|
|
_arb_hypgeom_gamma_stirling_term_bounds(term_mags, zinv_mag, N);
|
|
|
|
arb_zero(s);
|
|
|
|
for (n = N - 1; n >= 1; n--)
|
|
{
|
|
term_mag = term_mags[n];
|
|
term_prec = prec + term_mag;
|
|
term_prec = FLINT_MIN(term_prec, prec);
|
|
term_prec = FLINT_MAX(term_prec, 10);
|
|
|
|
if (prec - term_prec > 200)
|
|
{
|
|
arb_set_round(t, w, term_prec);
|
|
arb_mul(s, s, t, term_prec);
|
|
}
|
|
else
|
|
arb_mul(s, s, w, term_prec);
|
|
|
|
arb_gamma_stirling_coeff(b, n, 0, term_prec);
|
|
arb_add(s, s, b, term_prec);
|
|
}
|
|
|
|
arb_mul(s, s, zinv, prec);
|
|
|
|
flint_free(term_mags);
|
|
|
|
arb_clear(t);
|
|
arb_clear(b);
|
|
arb_clear(zinv);
|
|
arb_clear(w);
|
|
mag_clear(zinv_mag);
|
|
}
|
|
|