pqc/external/flint-2.4.3/arith/dedekind_sum_naive.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_naive(fmpq_t s, const fmpz_t h, const fmpz_t k)
{
fmpz_t i, j, q1, r1, q2, r2;
if (fmpz_is_zero(k))
{
fmpq_zero(s);
return;
}
fmpz_init(i);
fmpz_init(j);
fmpz_init(q1);
fmpz_init(r1);
fmpz_init(q2);
fmpz_init(r2);
fmpz_zero(fmpq_numref(s));
for (fmpz_one(i); fmpz_cmp(i, k) < 0; fmpz_add_ui(i, i, 1))
{
fmpz_fdiv_qr(q1, r1, i, k);
if (fmpz_is_zero(r1))
continue;
fmpz_mul(j, h, i);
fmpz_fdiv_qr(q2, r2, j, k);
if (fmpz_is_zero(r2))
continue;
fmpz_mul(q1, q1, k);
fmpz_sub(q1, i, q1);
fmpz_mul_ui(q1, q1, 2);
fmpz_sub(q1, q1, k);
fmpz_mul(q2, q2, k);
fmpz_sub(q2, j, q2);
fmpz_mul_ui(q2, q2, 2);
fmpz_sub(q2, q2, k);
fmpz_addmul(fmpq_numref(s), q1, q2);
}
fmpz_mul(fmpq_denref(s), k, k);
fmpz_mul_ui(fmpq_denref(s), fmpq_denref(s), 4);
fmpq_canonicalise(s);
fmpz_clear(i);
fmpz_clear(j);
fmpz_clear(q1);
fmpz_clear(r1);
fmpz_clear(q2);
fmpz_clear(r2);
}