mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
109 lines
3 KiB
C
109 lines
3 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 "zeta.h"
|
|
|
|
/* With parameter n, the error is bounded by 3/(3+sqrt(8))^n */
|
|
#define ERROR_A 1.5849625007211561815 /* log2(3) */
|
|
#define ERROR_B 2.5431066063272239453 /* log2(3+sqrt(8)) */
|
|
|
|
void borwein_error(fmpr_t err, long n);
|
|
|
|
void
|
|
zeta_ui_vec_borwein(fmprb_ptr z, ulong start, long num, ulong step, long prec)
|
|
{
|
|
long j, k, s, n, wp;
|
|
fmpz_t c, d, t, u;
|
|
fmpz * zeta;
|
|
fmpr_t err;
|
|
|
|
if (num < 1)
|
|
return;
|
|
|
|
wp = prec + FLINT_BIT_COUNT(prec);
|
|
n = wp / 2.5431066063272239453 + 1;
|
|
|
|
fmpz_init(c);
|
|
fmpz_init(d);
|
|
fmpz_init(t);
|
|
fmpz_init(u);
|
|
zeta = _fmpz_vec_init(num);
|
|
|
|
fmpz_set_ui(c, 1);
|
|
fmpz_mul_2exp(c, c, 2 * n - 1);
|
|
fmpz_set(d, c);
|
|
|
|
for (k = n; k > 0; k--)
|
|
{
|
|
/* divide by first k^s */
|
|
fmpz_ui_pow_ui(u, k, start);
|
|
fmpz_tdiv_q(t, d, u);
|
|
if (k % 2 == 0)
|
|
fmpz_neg(t, t);
|
|
fmpz_add(zeta, zeta, t);
|
|
|
|
/* remaining k^s */
|
|
fmpz_ui_pow_ui(u, k, step);
|
|
for (j = 1; j < num; j++)
|
|
{
|
|
fmpz_tdiv_q(t, t, u);
|
|
fmpz_add(zeta + j, zeta + j, t);
|
|
}
|
|
|
|
/* hypergeometric recurrence */
|
|
fmpz_mul2_uiui(c, c, k, 2 * k - 1);
|
|
fmpz_divexact2_uiui(c, c, 2 * (n - k + 1), n + k - 1);
|
|
fmpz_add(d, d, c);
|
|
}
|
|
|
|
fmpr_init(err);
|
|
borwein_error(err, n);
|
|
|
|
for (k = 0; k < num; k++)
|
|
{
|
|
fmprb_ptr x = z + k;
|
|
s = start + step * k;
|
|
|
|
fmprb_set_fmpz(x, zeta + k);
|
|
/* the error in each term in the main loop is < 2 */
|
|
fmpr_set_ui(fmprb_radref(x), 2 * n);
|
|
fmprb_div_fmpz(x, x, d, wp);
|
|
|
|
/* mathematical error for eta(s), bounded by 3/(3+sqrt(8))^n */
|
|
fmprb_add_error_fmpr(x, err);
|
|
|
|
/* convert from eta(s) to zeta(s) */
|
|
fmprb_div_2expm1_ui(x, x, s - 1, wp);
|
|
fmprb_mul_2exp_si(x, x, s - 1);
|
|
}
|
|
|
|
fmpr_clear(err);
|
|
|
|
fmpz_clear(c);
|
|
fmpz_clear(d);
|
|
fmpz_clear(t);
|
|
fmpz_clear(u);
|
|
_fmpz_vec_clear(zeta, num);
|
|
}
|