mirror of
https://github.com/vale981/arb
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79 lines
2.2 KiB
C
79 lines
2.2 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) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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/* TODO: fix/optimize for n > prec */
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void
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fmprb_div_2expm1_ui(fmprb_t y, const fmprb_t x, ulong n, long prec)
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{
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if (n < FLINT_BITS)
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{
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fmprb_div_ui(y, x, (1UL << n) - 1, prec);
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}
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else if (n < 1024 + prec / 32 || n > LONG_MAX / 2)
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{
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fmprb_t t;
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fmprb_init(t);
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fmprb_one(t);
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fmpz_set_ui(fmpr_expref(fmprb_midref(t)), n);
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fmprb_sub_ui(t, t, 1, prec);
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fmprb_div(y, x, t, prec);
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fmprb_clear(t);
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}
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else
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{
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fmprb_t s, t;
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long i, b;
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fmprb_init(s);
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fmprb_init(t);
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/* x / (2^n - 1) = sum_{k>=1} x * 2^(-k*n)*/
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fmprb_mul_2exp_si(s, x, -n);
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fmprb_set(t, s);
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b = 1;
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for (i = 2; i <= prec / n + 1; i++)
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{
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fmprb_mul_2exp_si(t, t, -n);
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fmprb_add(s, s, t, prec);
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b = i;
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}
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/* error bound: sum_{k>b} x * 2^(-k*n) <= x * 2^(-b*n - (n-1)) */
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fmprb_mul_2exp_si(t, x, -b*n - (n-1));
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fmprb_abs(t, t);
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fmprb_add_error(s, t);
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fmprb_set(y, s);
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fmprb_clear(s);
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fmprb_clear(t);
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}
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}
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