83 lines
2.2 KiB
C
83 lines
2.2 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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void
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arith_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k)
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{
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fmpz_t i, j, q1, r1, q2, r2;
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if (fmpz_is_zero(k))
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{
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fmpq_zero(s);
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return;
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}
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fmpz_init(i);
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fmpz_init(j);
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fmpz_init(q1);
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fmpz_init(r1);
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fmpz_init(q2);
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fmpz_init(r2);
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fmpz_zero(fmpq_numref(s));
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for (fmpz_one(i); fmpz_cmp(i, k) < 0; fmpz_add_ui(i, i, 1))
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{
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fmpz_fdiv_qr(q1, r1, i, k);
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if (fmpz_is_zero(r1))
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continue;
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fmpz_mul(j, h, i);
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fmpz_fdiv_qr(q2, r2, j, k);
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if (fmpz_is_zero(r2))
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continue;
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fmpz_mul(q1, q1, k);
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fmpz_sub(q1, i, q1);
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fmpz_mul_ui(q1, q1, 2);
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fmpz_sub(q1, q1, k);
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fmpz_mul(q2, q2, k);
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fmpz_sub(q2, j, q2);
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fmpz_mul_ui(q2, q2, 2);
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fmpz_sub(q2, q2, k);
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fmpz_addmul(fmpq_numref(s), q1, q2);
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}
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fmpz_mul(fmpq_denref(s), k, k);
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fmpz_mul_ui(fmpq_denref(s), fmpq_denref(s), 4);
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fmpq_canonicalise(s);
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fmpz_clear(i);
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fmpz_clear(j);
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fmpz_clear(q1);
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fmpz_clear(r1);
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fmpz_clear(q2);
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fmpz_clear(r2);
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}
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