arb/gamma/taylor_bound_mag.c

66 lines
1.9 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 "gamma.h"
long
gamma_taylor_bound_mag(long n)
{
fmprb_t t, u;
long v;
fmprb_init(t);
fmprb_init(u);
/* (pi-1) n */
fmprb_const_pi(t, FMPRB_RAD_PREC);
fmprb_sub_ui(t, t, 1, FMPRB_RAD_PREC);
fmprb_mul_ui(t, t, n, FMPRB_RAD_PREC);
/* (3-5n) log(n/6) */
fmprb_set_ui(u, n);
fmprb_div_ui(u, u, 6, FMPRB_RAD_PREC);
fmprb_log(u, u, FMPRB_RAD_PREC);
fmprb_mul_si(u, u, 3 - 5*n, FMPRB_RAD_PREC);
fmprb_add(t, t, u, FMPRB_RAD_PREC);
/* divide by 6 log(2) */
fmprb_log_ui(u, 2, FMPRB_RAD_PREC);
fmprb_mul_ui(u, u, 6, FMPRB_RAD_PREC);
fmprb_div(t, t, u, FMPRB_RAD_PREC);
/* upper bound */
fmpr_add(fmprb_midref(t), fmprb_midref(t), fmprb_radref(t),
FMPRB_RAD_PREC, FMPR_RND_CEIL);
v = fmpr_get_si(fmprb_midref(t), FMPR_RND_CEIL);
fmprb_clear(t);
fmprb_clear(u);
return v;
}