hiro/arb
1
0
Fork 0
mirror of https://github.com/vale981/arb synced 2025-03-05 17:31:38 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

complete zeta_ui

Browse source
This commit is contained in:
Fredrik Johansson 2012-09-07 13:38:59 +02:00
parent 849e713207
commit 2d57bab3a4
2 changed files with 75 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

1
fmprb.h
View file

@ -192,6 +192,7 @@ void fmprb_const_zeta3_bsplit(fmprb_t x, long prec);
void fmprb_zeta_ui_bsplit(fmprb_t x, ulong s, long prec);
void fmprb_zeta_ui_euler_product(fmprb_t z, ulong s, long prec);
void fmprb_zeta_ui_bernoulli(fmprb_t x, ulong n, long prec);
void fmprb_zeta_ui(fmprb_t x, ulong n, long prec);
static __inline__ void
fmprb_add_error_2exp_si(fmprb_t x, long err)

74
fmprb/zeta_ui.c Normal file
View file

@ -0,0 +1,74 @@
/*=============================================================================
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 <math.h>
#include "arith.h"
#include "fmprb.h"
static void
fmprb_zeta_ui_mpfr(fmprb_t x, ulong n, long prec)
{
mpfr_t t;
mpfr_init2(t, prec);
mpfr_zeta_ui(t, n, MPFR_RNDD);
fmprb_zero(x);
fmpr_set_mpfr(fmprb_midref(x), t);
fmprb_add_error_2exp_si(x, mpfr_get_exp(t)-prec);
mpfr_clear(t);
}
void
fmprb_zeta_ui(fmprb_t x, ulong n, long prec)
{
/* asymptotic case */
if (n == 0 || n > 0.7 * prec)
{
fmprb_zeta_ui_mpfr(x, n, prec);
}
else if (n == 3)
{
fmprb_const_zeta3_bsplit(x, prec);
}
/* small even n */
else if ((n % 2 == 0) && (n < 40 + 0.11*prec))
{
fmprb_zeta_ui_bernoulli(x, n, prec);
}
/* small odd n, extremely high precision */
else if (n < prec * 0.0006)
{
fmprb_zeta_ui_bsplit(x, n, prec);
}
/* large n */
else if (prec > 20 && n > 0.4 * pow(prec, 0.8))
{
fmprb_zeta_ui_euler_product(x, n, prec);
}
/* fallback */
else
{
fmprb_zeta_ui_mpfr(x, n, prec);
}
}