mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
78 lines
2.1 KiB
C
78 lines
2.1 KiB
C
/*=============================================================================
|
|
|
|
This file is part of ARB.
|
|
|
|
ARB is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
ARB is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with ARB; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2012 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "fmprb.h"
|
|
|
|
|
|
|
|
/* TODO: fix/optimize for n > prec */
|
|
void
|
|
fmprb_div_2expm1_ui(fmprb_t y, const fmprb_t x, ulong n, long prec)
|
|
{
|
|
if (n < FLINT_BITS)
|
|
{
|
|
fmprb_div_ui(y, x, (1UL << n) - 1, prec);
|
|
}
|
|
else if (n < 1024 + prec / 32)
|
|
{
|
|
fmprb_t t;
|
|
fmprb_init(t);
|
|
fmprb_one(t);
|
|
fmpz_set_ui(fmpr_expref(fmprb_midref(t)), n);
|
|
fmprb_sub_ui(t, t, 1, prec);
|
|
fmprb_div(y, x, t, prec);
|
|
fmprb_clear(t);
|
|
}
|
|
else
|
|
{
|
|
fmprb_t s, t;
|
|
long i, b;
|
|
|
|
fmprb_init(s);
|
|
fmprb_init(t);
|
|
|
|
/* x / (2^n - 1) = sum_{k>=1} x * 2^(-k*n)*/
|
|
|
|
fmprb_mul_2exp_si(s, x, -n);
|
|
fmprb_set(t, s);
|
|
b = 1;
|
|
|
|
for (i = 2; i <= prec / n; i++)
|
|
{
|
|
fmprb_mul_2exp_si(t, t, -n);
|
|
fmprb_add(s, s, t, prec);
|
|
b = i;
|
|
}
|
|
|
|
/* error bound: sum_{k>b} x * 2^(-k*n) <= x * 2^(-b*n - (n-1)) */
|
|
fmprb_mul_2exp_si(t, x, -b*n - (n-1));
|
|
fmprb_add_error(s, t);
|
|
|
|
fmprb_set(y, s);
|
|
|
|
fmprb_clear(s);
|
|
fmprb_clear(t);
|
|
}
|
|
}
|