mirror of
https://github.com/vale981/arb
synced 2025-03-05 17:31:38 -05:00
85 lines
2.6 KiB
C
85 lines
2.6 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) 2012 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "bernoulli.h"
|
|
|
|
void
|
|
bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax)
|
|
{
|
|
long j;
|
|
fmpz_t t;
|
|
fmprb_t x;
|
|
int round1, round2;
|
|
long wp;
|
|
|
|
nmax -= (nmax % 2);
|
|
iter->n = nmax;
|
|
|
|
iter->alloc = 0;
|
|
if (nmax < bernoulli_rev_MIN)
|
|
return;
|
|
|
|
iter->prec = wp = global_prec(nmax);
|
|
|
|
iter->max_power = zeta_terms(nmax, iter->prec);
|
|
iter->alloc = iter->max_power + 1;
|
|
iter->powers = _fmpz_vec_init(iter->alloc);
|
|
fmpz_init(iter->pow_error);
|
|
fmprb_init(iter->prefactor);
|
|
fmprb_init(iter->two_pi_squared);
|
|
|
|
fmprb_init(x);
|
|
fmpz_init(t);
|
|
|
|
/* precompute powers */
|
|
for (j = 3; j <= iter->max_power; j += 2)
|
|
{
|
|
fmprb_ui_pow_ui(x, j, nmax, power_prec(j, nmax, wp));
|
|
fmprb_ui_div(x, 1UL, x, power_prec(j, nmax, wp));
|
|
round1 = fmpr_get_fmpz_fixed_si(t, fmprb_midref(x), -wp);
|
|
fmpz_set(iter->powers + j, t);
|
|
|
|
/* error: the radius, plus two roundings */
|
|
round2 = fmpr_get_fmpz_fixed_si(t, fmprb_radref(x), -wp);
|
|
fmpz_add_ui(t, t, (round1 != 0) + (round2 != 0));
|
|
if (fmpz_cmp(iter->pow_error, t) < 0)
|
|
fmpz_set(iter->pow_error, t);
|
|
}
|
|
|
|
/* precompute (2pi)^2 and 2*(n!)/(2pi)^n */
|
|
fmprb_fac_ui(iter->prefactor, nmax, wp);
|
|
fmprb_mul_2exp_si(iter->prefactor, iter->prefactor, 1);
|
|
|
|
fmprb_const_pi(x, wp);
|
|
fmprb_mul_2exp_si(x, x, 1);
|
|
fmprb_mul(iter->two_pi_squared, x, x, wp);
|
|
|
|
fmprb_pow_ui(x, iter->two_pi_squared, nmax / 2, wp);
|
|
fmprb_div(iter->prefactor, iter->prefactor, x, wp);
|
|
|
|
fmpz_clear(t);
|
|
fmprb_clear(x);
|
|
}
|
|
|