pqc/external/flint-2.4.3/arith/zeta_inv_euler_product.c
2014-05-24 23:16:06 +02:00

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);
}