121 lines
3.3 KiB
C
121 lines
3.3 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 Fredrik Johansson
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******************************************************************************/
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#include "fmpz.h"
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#include "arith.h"
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void arith_ramanujan_tau_series(fmpz_poly_t res, slong n)
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{
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slong j, k, jv, kv;
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fmpz_t tmp;
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fmpz_poly_fit_length(res, n);
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_fmpz_vec_zero(res->coeffs, n);
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_fmpz_poly_set_length(res, n);
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fmpz_init(tmp);
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for (j = jv = 0; jv < n; jv += ++j)
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{
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fmpz_set_ui(tmp, 2*j+1);
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for (k = kv = 0; jv + kv < n; kv += ++k)
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{
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if ((j+k) & 1)
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fmpz_submul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
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else
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fmpz_addmul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
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}
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}
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fmpz_poly_sqrlow(res, res, n-1);
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fmpz_poly_sqrlow(res, res, n-1);
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fmpz_poly_shift_left(res, res, 1);
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fmpz_clear(tmp);
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}
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void _arith_ramanujan_tau(fmpz_t res, fmpz_factor_t factors)
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{
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fmpz_poly_t poly;
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fmpz_t tau_p, p_11, next, this, prev;
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slong k, r;
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ulong max_prime;
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max_prime = UWORD(1);
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for (k = 0; k < factors->num; k++)
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{
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/* TODO: handle overflow properly */
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max_prime = FLINT_MAX(max_prime, fmpz_get_ui(factors->p + k));
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}
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fmpz_poly_init(poly);
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arith_ramanujan_tau_series(poly, max_prime + 1);
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fmpz_one(res);
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fmpz_init(tau_p);
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fmpz_init(p_11);
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fmpz_init(next);
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fmpz_init(this);
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fmpz_init(prev);
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for (k = 0; k < factors->num; k++)
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{
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ulong p = fmpz_get_ui(factors->p + k);
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fmpz_set(tau_p, poly->coeffs + p);
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fmpz_set_ui(p_11, p);
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fmpz_pow_ui(p_11, p_11, 11);
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fmpz_one(prev);
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fmpz_set(this, tau_p);
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for (r = 1; r < factors->exp[k]; r++)
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{
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fmpz_mul(next, tau_p, this);
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fmpz_submul(next, p_11, prev);
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fmpz_set(prev, this);
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fmpz_set(this, next);
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}
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fmpz_mul(res, res, this);
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}
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fmpz_clear(tau_p);
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fmpz_clear(p_11);
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fmpz_clear(next);
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fmpz_clear(this);
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fmpz_clear(prev);
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fmpz_poly_clear(poly);
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}
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void arith_ramanujan_tau(fmpz_t res, const fmpz_t n)
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{
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fmpz_factor_t factors;
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if (fmpz_sgn(n) <= 0)
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{
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fmpz_zero(res);
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return;
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}
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fmpz_factor_init(factors);
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fmpz_factor(factors, n);
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_arith_ramanujan_tau(res, factors);
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fmpz_factor_clear(factors);
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}
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