pqc/external/flint-2.4.3/arith/dedekind_sum_coprime_large.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"
void
arith_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k)
{
fmpz_t sigma, p, pp, hh, kk, a, t;
int sign;
if (fmpz_cmp_ui(k, UWORD(2)) <= 0)
{
fmpq_zero(s);
return;
}
sign = 1;
fmpz_init(sigma);
fmpz_init(hh);
fmpz_init(kk);
fmpz_init(p);
fmpz_init(pp);
fmpz_init(a);
fmpz_init(t);
fmpz_set_ui(p, UWORD(1));
fmpz_set(hh, h);
fmpz_set(kk, k);
while (!fmpz_is_zero(hh))
{
fmpz_fdiv_qr(a, t, kk, hh);
if (sign == 1)
fmpz_add(sigma, sigma, a);
else
fmpz_sub(sigma, sigma, a);
sign = -sign;
/* kk, hh = hh, kk mod hh */
fmpz_swap(kk, hh);
fmpz_swap(hh, t);
/* p, pp = a*p + pp, p */
fmpz_addmul(pp, a, p);
fmpz_swap(p, pp);
}
if (sign < 0)
fmpz_sub_ui(sigma, sigma, UWORD(3));
/* s = (sigma + (h - p*s) / p) / 12 */
if (sign < 0)
fmpz_add(fmpq_numref(s), h, pp);
else
fmpz_sub(fmpq_numref(s), h, pp);
fmpz_addmul(fmpq_numref(s), sigma, p);
fmpz_mul_ui(fmpq_denref(s), p, UWORD(12));
_fmpq_canonicalise(fmpq_numref(s), fmpq_denref(s));
fmpz_clear(sigma);
fmpz_clear(hh);
fmpz_clear(kk);
fmpz_clear(p);
fmpz_clear(pp);
fmpz_clear(a);
fmpz_clear(t);
}