108 lines
2.8 KiB
C
108 lines
2.8 KiB
C
/*=============================================================================
|
|
|
|
This file is part of FLINT.
|
|
|
|
FLINT 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.
|
|
|
|
FLINT 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 FLINT; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2011 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include <math.h>
|
|
#include "arith.h"
|
|
|
|
void mpfr_zeta_inv_euler_product(mpfr_t res, ulong s, int char_4)
|
|
{
|
|
mpz_t z, x, y, r;
|
|
mp_limb_t p;
|
|
slong prec, powprec, yexp, shift;
|
|
|
|
mpz_init(x);
|
|
mpz_init(y);
|
|
mpz_init(z);
|
|
mpz_init(r);
|
|
|
|
prec = mpfr_get_prec(res) + 32 + 2*FLINT_BIT_COUNT(s);
|
|
|
|
flint_mpz_set_ui(z, UWORD(1));
|
|
mpz_mul_2exp(z, z, prec);
|
|
|
|
if (!char_4)
|
|
{
|
|
flint_mpz_set_ui(r, UWORD(1));
|
|
mpz_mul_2exp(r, r, prec - s);
|
|
mpz_sub(z, z, r);
|
|
}
|
|
|
|
p = UWORD(3);
|
|
|
|
while (1)
|
|
{
|
|
slong i;
|
|
powprec = prec - s*log(p)*1.4426950408889634 + 1;
|
|
|
|
/* flint_printf("prime %wu, powprec %wd\n", p, powprec); */
|
|
|
|
if (powprec < 5)
|
|
break;
|
|
|
|
flint_mpz_set_ui(x, p);
|
|
flint_mpz_set_ui(y, UWORD(1));
|
|
yexp = 0;
|
|
|
|
/* Slow equivalent: flint_mpz_pow_ui(y, x, s) */
|
|
flint_mpz_set_ui(y, p);
|
|
for (i = FLINT_BIT_COUNT(s) - 2; i >= 0; i--)
|
|
{
|
|
mpz_mul(y, y, y);
|
|
yexp += yexp;
|
|
shift = mpz_sizeinbase(y, 2) - powprec - 4;
|
|
if (shift >= 0)
|
|
{
|
|
mpz_tdiv_q_2exp(y, y, shift);
|
|
yexp += shift;
|
|
}
|
|
|
|
if (s & (UWORD(1)<<i))
|
|
flint_mpz_mul_ui(y, y, p);
|
|
}
|
|
|
|
shift = yexp;
|
|
if (shift >= 0)
|
|
mpz_tdiv_q_2exp(r, z, shift);
|
|
else
|
|
mpz_mul_2exp(r, z, -shift);
|
|
|
|
mpz_tdiv_q(r, r, y);
|
|
|
|
if (char_4 && (p % 4 == 3))
|
|
mpz_add(z, z, r);
|
|
else
|
|
mpz_sub(z, z, r);
|
|
|
|
p = n_nextprime(p, 0);
|
|
}
|
|
|
|
mpfr_set_z_2exp(res, z, -prec, GMP_RNDN);
|
|
|
|
mpz_clear(x);
|
|
mpz_clear(y);
|
|
mpz_clear(z);
|
|
mpz_clear(r);
|
|
}
|