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/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <math.h>
#include "arith.h"
void arith_landau_function_vec(fmpz * res, slong len)
{
mp_limb_t p, pmax;
mp_limb_t pk, pkhi;
fmpz_t a;
ulong k, n;
if (len < 1)
return;
for (k = 0; k < len; k++)
fmpz_one(res + k);
pmax = 1.328 * sqrt(len*log(len) + 1);
fmpz_init(a);
for (p = UWORD(2); p <= pmax; p = n_nextprime(p, 0))
{
for (n = len - 1; n >= p; n--)
{
pk = p;
pkhi = UWORD(0);
for (k = 1; k <= len; k++)
{
if (pk > n || pkhi)
break;
fmpz_mul_ui(a, res + n - pk, pk);
if (fmpz_cmp(res + n, a) < 0)
fmpz_set(res + n, a);
umul_ppmm(pkhi, pk, pk, p);
}
}
}
fmpz_clear(a);
}
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