mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
70 lines
1.4 KiB
C
70 lines
1.4 KiB
C
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/*
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Copyright (C) 2017 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 "mag.h"
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void
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mag_bin_uiui(mag_t res, ulong n, ulong k)
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{
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mag_t t;
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if (k > n)
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{
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mag_zero(res);
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return;
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}
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if (k > n / 2)
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k = n - k;
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if (k == 0)
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{
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mag_one(res);
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return;
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}
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if (k == 1)
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{
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mag_set_ui(res, n);
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return;
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}
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mag_init(t);
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if (n < 256 && k < 256)
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{
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/* using accurate (lookup table) factorials */
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mag_fac_ui(res, n);
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mag_rfac_ui(t, k);
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mag_mul(res, res, t);
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mag_rfac_ui(t, n - k);
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mag_mul(res, res, t);
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}
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else
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{
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/* binary entropy bound (n/(n-k))^(n-k) (n/k)^k = n^n / (k^k (n-k)^(n-k)) */
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mag_set_ui(res, n);
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mag_div_ui(res, res, n - k);
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mag_pow_ui(res, res, n - k);
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/* (n/(n-k))^(n-k) is also bounded by exp(k) */
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mag_set_ui(t, k);
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mag_exp(t, t);
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mag_min(res, res, t);
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mag_set_ui(t, n);
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mag_div_ui(t, t, k);
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mag_pow_ui(t, t, k);
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mag_mul(res, res, t);
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}
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mag_clear(t);
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}
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