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

74 lines
2.2 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_polynomial(fmpq_poly_t poly, ulong n)
{
fmpz_t t;
fmpz * den;
slong k;
if (n == 0)
{
fmpq_poly_set_ui(poly, UWORD(1));
return;
}
fmpq_poly_fit_length(poly, n + 1);
fmpz_init(t);
den = _fmpz_vec_init(n + 1);
_arith_bernoulli_number_vec(poly->coeffs, den, n + 1);
/* Multiply the odd term by binomial(n,1) = n */
fmpz_mul_ui(poly->coeffs + 1, poly->coeffs + 1, n);
/* Multiply even terms by binomial coefficients */
fmpz_one(t);
for (k = 2; k <= n; k += 2)
{
fmpz_mul2_uiui(t, t, n-k+1, n-k+2);
fmpz_divexact2_uiui(t, t, k, k-1);
fmpz_mul(poly->coeffs + k, poly->coeffs + k, t);
}
/* Convert to common denominator */
arith_primorial(poly->den, n + 2);
for (k = 0; k <= n; k++)
{
fmpz_mul(poly->coeffs + k, poly->coeffs+k, poly->den);
fmpz_divexact(poly->coeffs + k, poly->coeffs + k, den + k);
}
_fmpz_poly_reverse(poly->coeffs, poly->coeffs, n + 1, n + 1);
_fmpq_poly_set_length(poly, n + 1);
fmpq_poly_canonicalise(poly);
_fmpz_vec_clear(den, n + 1);
fmpz_clear(t);
}