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

121 lines
3.3 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) 2010 Fredrik Johansson
******************************************************************************/
#include "fmpz.h"
#include "arith.h"
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)
{
slong j, k, jv, kv;
fmpz_t tmp;
fmpz_poly_fit_length(res, n);
_fmpz_vec_zero(res->coeffs, n);
_fmpz_poly_set_length(res, n);
fmpz_init(tmp);
for (j = jv = 0; jv < n; jv += ++j)
{
fmpz_set_ui(tmp, 2*j+1);
for (k = kv = 0; jv + kv < n; kv += ++k)
{
if ((j+k) & 1)
fmpz_submul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
else
fmpz_addmul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
}
}
fmpz_poly_sqrlow(res, res, n-1);
fmpz_poly_sqrlow(res, res, n-1);
fmpz_poly_shift_left(res, res, 1);
fmpz_clear(tmp);
}
void _arith_ramanujan_tau(fmpz_t res, fmpz_factor_t factors)
{
fmpz_poly_t poly;
fmpz_t tau_p, p_11, next, this, prev;
slong k, r;
ulong max_prime;
max_prime = UWORD(1);
for (k = 0; k < factors->num; k++)
{
/* TODO: handle overflow properly */
max_prime = FLINT_MAX(max_prime, fmpz_get_ui(factors->p + k));
}
fmpz_poly_init(poly);
arith_ramanujan_tau_series(poly, max_prime + 1);
fmpz_one(res);
fmpz_init(tau_p);
fmpz_init(p_11);
fmpz_init(next);
fmpz_init(this);
fmpz_init(prev);
for (k = 0; k < factors->num; k++)
{
ulong p = fmpz_get_ui(factors->p + k);
fmpz_set(tau_p, poly->coeffs + p);
fmpz_set_ui(p_11, p);
fmpz_pow_ui(p_11, p_11, 11);
fmpz_one(prev);
fmpz_set(this, tau_p);
for (r = 1; r < factors->exp[k]; r++)
{
fmpz_mul(next, tau_p, this);
fmpz_submul(next, p_11, prev);
fmpz_set(prev, this);
fmpz_set(this, next);
}
fmpz_mul(res, res, this);
}
fmpz_clear(tau_p);
fmpz_clear(p_11);
fmpz_clear(next);
fmpz_clear(this);
fmpz_clear(prev);
fmpz_poly_clear(poly);
}
void arith_ramanujan_tau(fmpz_t res, const fmpz_t n)
{
fmpz_factor_t factors;
if (fmpz_sgn(n) <= 0)
{
fmpz_zero(res);
return;
}
fmpz_factor_init(factors);
fmpz_factor(factors, n);
_arith_ramanujan_tau(res, factors);
fmpz_factor_clear(factors);
}