97 lines
2.4 KiB
C
97 lines
2.4 KiB
C
/*=============================================================================
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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_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k)
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{
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fmpz_t sigma, p, pp, hh, kk, a, t;
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int sign;
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if (fmpz_cmp_ui(k, UWORD(2)) <= 0)
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{
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fmpq_zero(s);
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return;
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}
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sign = 1;
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fmpz_init(sigma);
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fmpz_init(hh);
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fmpz_init(kk);
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fmpz_init(p);
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fmpz_init(pp);
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fmpz_init(a);
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fmpz_init(t);
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fmpz_set_ui(p, UWORD(1));
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fmpz_set(hh, h);
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fmpz_set(kk, k);
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while (!fmpz_is_zero(hh))
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{
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fmpz_fdiv_qr(a, t, kk, hh);
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if (sign == 1)
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fmpz_add(sigma, sigma, a);
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else
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fmpz_sub(sigma, sigma, a);
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sign = -sign;
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/* kk, hh = hh, kk mod hh */
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fmpz_swap(kk, hh);
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fmpz_swap(hh, t);
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/* p, pp = a*p + pp, p */
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fmpz_addmul(pp, a, p);
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fmpz_swap(p, pp);
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}
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if (sign < 0)
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fmpz_sub_ui(sigma, sigma, UWORD(3));
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/* s = (sigma + (h - p*s) / p) / 12 */
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if (sign < 0)
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fmpz_add(fmpq_numref(s), h, pp);
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else
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fmpz_sub(fmpq_numref(s), h, pp);
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fmpz_addmul(fmpq_numref(s), sigma, p);
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fmpz_mul_ui(fmpq_denref(s), p, UWORD(12));
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_fmpq_canonicalise(fmpq_numref(s), fmpq_denref(s));
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fmpz_clear(sigma);
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fmpz_clear(hh);
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fmpz_clear(kk);
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fmpz_clear(p);
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fmpz_clear(pp);
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fmpz_clear(a);
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fmpz_clear(t);
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}
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