pqc/external/flint-2.4.3/arith/legendre_polynomial.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
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"
static __inline__ void __legendre_denom(fmpz_t den, ulong n)
{
ulong d, k;
d = k = n >> 1;
while (k)
{
k >>= 1;
d += k;
}
fmpz_one(den);
fmpz_mul_2exp(den, den, d);
}
void _arith_legendre_polynomial(fmpz * coeffs, fmpz_t den, ulong n)
{
fmpz * r;
int odd;
slong k;
ulong L;
L = n / 2;
odd = n % 2;
r = coeffs + odd;
__legendre_denom(den, n);
fmpz_bin_uiui(r, n, L);
fmpz_mul(r, r, den);
if (odd)
fmpz_mul_ui(r, r, L + 1);
fmpz_fdiv_q_2exp(r, r, 2*L);
if (L % 2)
fmpz_neg(r, r);
for (k = 1; k <= L; k++)
{
fmpz_mul2_uiui(r + 2, r, L + 1 - k, 2*k + 2*L - 1 + 2*odd);
fmpz_divexact2_uiui(r + 2, r + 2, k, 2*k - 1 + 2*odd);
fmpz_neg(r + 2, r + 2);
r += 2;
}
for (k = 1 - odd; k < n; k += 2)
fmpz_zero(coeffs + k);
}
void arith_legendre_polynomial(fmpq_poly_t poly, ulong n)
{
if (n == 0)
{
fmpq_poly_set_ui(poly, UWORD(1));
return;
}
fmpq_poly_fit_length(poly, n + 1);
if (n == 1)
{
fmpz_zero(poly->coeffs);
fmpz_one(poly->coeffs + 1);
fmpz_one(poly->den);
}
else
_arith_legendre_polynomial(poly->coeffs, poly->den, n);
_fmpq_poly_set_length(poly, n + 1);
}