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https://github.com/vale981/arb
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71 lines
1.6 KiB
C
71 lines
1.6 KiB
C
/*
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Copyright (C) 2014 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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const int mag_bernoulli_div_fac_ui_tab[32] =
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{
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1, 536870912,
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-3, 715827883,
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-9, 763549742,
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-14, 581752185,
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-20, 930803495,
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-25, 752164440,
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-30, 609225645,
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-36, 987456906,
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-41, 800365631,
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-46, 648744507,
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-52, 1051701970,
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-57, 852476898,
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-62, 690991623,
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-67, 560096688,
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-73, 907994540,
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-78, 735992650,
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};
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/* computes upper bound for B_n / n! */
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void
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mag_bernoulli_div_fac_ui(mag_t z, ulong n)
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{
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if (n % 2 == 1)
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{
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if (n == 1)
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{
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mag_one(z);
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mag_mul_2exp_si(z, z, -1);
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}
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else
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{
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mag_zero(z);
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}
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}
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else if (n < 32)
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{
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_fmpz_demote(MAG_EXPREF(z));
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MAG_EXP(z) = mag_bernoulli_div_fac_ui_tab[n];
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MAG_MAN(z) = mag_bernoulli_div_fac_ui_tab[n + 1];
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}
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else
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{
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/* upper bound for 1/(2pi) */
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mag_set_ui_2exp_si(z, 683565276, -32);
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/* 2 (1/(2pi))^n */
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mag_pow_ui(z, z, n);
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mag_mul_2exp_si(z, z, 1);
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/* we should multiply by an upper bound for zeta(n),
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but the error in the upper bound for 1/(2pi)
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used above is already larger than this factor
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when n >= 32, so there is no need */
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}
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}
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