88 lines
2.4 KiB
C
88 lines
2.4 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 "arith.h"
|
|
|
|
void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n)
|
|
{
|
|
mpz_t r;
|
|
mpfr_t t, u, z, pi;
|
|
mp_bitcnt_t prec, pi_prec;
|
|
|
|
arith_bernoulli_number_denom(den, n);
|
|
|
|
if (n % 2)
|
|
{
|
|
fmpz_set_si(num, -(n == 1));
|
|
return;
|
|
}
|
|
|
|
if (n < BERNOULLI_SMALL_NUMER_LIMIT)
|
|
{
|
|
fmpz_set_si(num, _bernoulli_numer_small[n / 2]);
|
|
return;
|
|
}
|
|
|
|
prec = arith_bernoulli_number_size(n) + fmpz_bits(den);
|
|
prec += 10 + 2*FLINT_BIT_COUNT(n);
|
|
pi_prec = prec;
|
|
|
|
mpz_init(r);
|
|
mpfr_init2(t, prec);
|
|
mpfr_init2(u, prec);
|
|
mpfr_init2(z, prec);
|
|
mpfr_init2(pi, pi_prec);
|
|
|
|
/* t = 2 * n! / (2*pi)^n */
|
|
flint_mpz_fac_ui(r, n);
|
|
mpfr_set_z(t, r, GMP_RNDN);
|
|
mpfr_mul_2exp(t, t, 1, GMP_RNDN);
|
|
mpfr_const_pi(pi, GMP_RNDN);
|
|
mpfr_mul_2exp(pi, pi, 1, GMP_RNDN);
|
|
mpfr_pow_ui(pi, pi, n, GMP_RNDN);
|
|
mpfr_div(t, t, pi, GMP_RNDN);
|
|
|
|
/* t = t / zeta(n) */
|
|
mpfr_zeta_inv_euler_product(z, n, 0);
|
|
mpfr_div(t, t, z, GMP_RNDN);
|
|
|
|
/* round numerator */
|
|
fmpz_get_mpz(r, den);
|
|
mpfr_mul_z(t, t, r, GMP_RNDN);
|
|
mpfr_round(t, t);
|
|
mpfr_get_z(r, t, GMP_RNDN);
|
|
fmpz_set_mpz(num, r);
|
|
|
|
if (n % 4 == 0)
|
|
fmpz_neg(num, num);
|
|
|
|
mpz_clear(r);
|
|
mpfr_clear(t);
|
|
mpfr_clear(u);
|
|
mpfr_clear(z);
|
|
mpfr_clear(pi);
|
|
}
|
|
|