mirror of
https://github.com/vale981/arb
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63 lines
1.8 KiB
C
63 lines
1.8 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB 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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ARB 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 ARB; 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) 2016 Fredrik Johansson
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******************************************************************************/
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#include "partitions.h"
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void
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partitions_leading_fmpz(arb_t res, const fmpz_t n, slong prec)
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{
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arb_t t;
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fmpz_t c;
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slong eprec;
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arb_init(t);
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fmpz_init(c);
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eprec = prec + fmpz_bits(n) / 2;
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/* c = 24n-1 */
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fmpz_mul_ui(c, n, 24);
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fmpz_sub_ui(c, c, 1);
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/* t = pi sqrt(24n-1) / 6 */
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arb_sqrt_fmpz(t, c, eprec);
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arb_const_pi(res, eprec);
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arb_mul(t, t, res, eprec);
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arb_div_ui(t, t, 6, eprec);
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/* res = exp(t) - exp(t) / t */
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/* todo: eprec only needed for argument reduction */
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arb_exp(res, t, eprec);
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arb_div(t, res, t, prec);
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arb_sub(res, res, t, prec);
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arb_sqrt_ui(t, 12, prec);
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arb_mul(res, res, t, prec);
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arb_div_fmpz(res, res, c, prec);
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arb_clear(t);
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fmpz_clear(c);
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}
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