mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
76 lines
1.8 KiB
C
76 lines
1.8 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb.h"
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#include "partitions.h"
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/* defined in flint*/
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FLINT_DLL extern const unsigned int partitions_lookup[128];
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/* we get log2(p(n))/2 bits with the leading term */
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static int
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use_exact(const fmpz_t n, slong prec)
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{
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if (fmpz_size(n) >= 3)
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return 0;
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return (prec + 20.0) * (prec + 20.0) > 3.42 * fmpz_get_d(n);
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}
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void
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arb_partitions_fmpz(arb_t res, const fmpz_t n, slong prec)
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{
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if (fmpz_cmp_ui(n, 128) < 0)
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{
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arb_set_ui(res, fmpz_sgn(n) >= 0 ? partitions_lookup[*n] : 0);
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arb_set_round(res, res, prec);
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}
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else if (use_exact(n, prec))
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{
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fmpz_t t;
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fmpz_init(t);
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partitions_fmpz_fmpz(t, n, 0);
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arb_set_round_fmpz(res, t, prec);
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fmpz_clear(t);
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}
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else
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{
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mag_t err;
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mag_init(err);
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partitions_leading_fmpz(res, n, prec + 10);
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/* n >= 128; it is easy to check that the error is bounded
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by the square root of the leading approximation */
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arb_get_mag(err, res);
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mag_sqrt(err, err);
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arb_add_error_mag(res, err);
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arb_set_round(res, res, prec);
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mag_clear(err);
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}
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}
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void
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arb_partitions_ui(arb_t res, ulong n, slong prec)
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{
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if (n < 128)
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{
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arb_set_ui(res, partitions_lookup[n]);
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arb_set_round(res, res, prec);
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}
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else
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{
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fmpz_t t;
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fmpz_init_set_ui(t, n);
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arb_partitions_fmpz(res, t, prec);
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fmpz_clear(t);
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}
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}
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