1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
/*
Copyright (C) 2011 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include <math.h>
#include "ulong_extras.h"
#include "fmpz.h"
#include "arith.h"
void arith_landau_function_vec(fmpz * res, slong len)
{
ulong p, pmax;
ulong 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);
}