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

139 lines
3.8 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
Inspired by a Sage implementation written by William Stein.
******************************************************************************/
#include <math.h>
#include "arith.h"
/* Bound coefficients using (x + u)^(2^n) and the binomial
coefficients. TODO: this is about 2x too large... */
static slong __bound_prec(ulong n)
{
slong i;
double u, N;
N = UWORD(1) << n;
/* u = (sum of square roots)^(2^n) */
u = 0;
for (i = 0; i < n; i++)
u += sqrt(n_nth_prime(1 + i));
u = N * log(u) * 1.44269504088897;
/* Central binomial coefficient C(N,N/2) < 2^N / sqrt(3*N/2) */
u += N - 0.5*(n-1) - 0.792481250360578; /* log(sqrt(3)) */
return u;
}
void arith_swinnerton_dyer_polynomial(fmpz_poly_t poly, ulong n)
{
fmpz *square_roots, *T, *tmp1, *tmp2, *tmp3;
fmpz_t one;
slong i, j, k, N;
slong prec;
if (n == 0)
{
fmpz_poly_zero(poly);
fmpz_poly_set_coeff_ui(poly, 1, UWORD(1));
return;
}
N = WORD(1) << n;
prec = __bound_prec(n);
/* flint_printf("prec: %wd\n", prec); */
fmpz_poly_fit_length(poly, N + 1);
T = poly->coeffs;
fmpz_init(one);
fmpz_one(one);
fmpz_mul_2exp(one, one, prec);
square_roots = _fmpz_vec_init(n);
tmp1 = flint_malloc((N/2 + 1) * sizeof(fmpz));
tmp2 = flint_malloc((N/2 + 1) * sizeof(fmpz));
tmp3 = _fmpz_vec_init(N);
for (i = 0; i < n; i++)
{
fmpz_set_ui(square_roots + i, n_nth_prime(i + 1));
fmpz_mul_2exp(square_roots + i, square_roots + i, 2 * prec);
fmpz_sqrt(square_roots + i, square_roots + i);
}
/* Build linear factors */
for (i = 0; i < N; i++)
{
fmpz_zero(T + i);
for (j = 0; j < n; j++)
{
if ((i >> j) & 1)
fmpz_add(T + i, T + i, square_roots + j);
else
fmpz_sub(T + i, T + i, square_roots + j);
}
}
/* For each level... */
for (i = 0; i < n; i++)
{
slong stride = UWORD(1) << i;
for (j = 0; j < N; j += 2*stride)
{
for (k = 0; k < stride; k++)
{
tmp1[k] = T[j + k];
tmp2[k] = T[j + stride + k];
}
tmp1[stride] = *one;
tmp2[stride] = *one;
_fmpz_poly_mullow(tmp3, tmp1, stride + 1, tmp2, stride + 1, 2*stride);
_fmpz_vec_scalar_fdiv_q_2exp(T + j, tmp3, 2*stride, prec);
}
}
/* Round */
fmpz_fdiv_q_2exp(one, one, 1);
for (i = 0; i < N; i++)
fmpz_add(T + i, T + i, one);
_fmpz_vec_scalar_fdiv_q_2exp(T, T, N, prec);
fmpz_one(T + (UWORD(1) << n));
_fmpz_poly_set_length(poly, N + 1);
_fmpz_vec_clear(square_roots, n);
flint_free(tmp1);
flint_free(tmp2);
_fmpz_vec_clear(tmp3, UWORD(1) << n);
fmpz_clear(one);
}