1 /*
2 Copyright (C) 2014 Fredrik Johansson
3
4 This file is part of Arb.
5
6 Arb is free software: you can redistribute it and/or modify it under
7 the terms of the GNU Lesser General Public License (LGPL) as published
8 by the Free Software Foundation; either version 2.1 of the License, or
9 (at your option) any later version. See <http://www.gnu.org/licenses/>.
10 */
11
12 #include "flint/double_extras.h"
13 #include "mag.h"
14
15 void
mag_log1p(mag_t z,const mag_t x)16 mag_log1p(mag_t z, const mag_t x)
17 {
18 if (mag_is_special(x))
19 {
20 if (mag_is_zero(x))
21 mag_zero(z);
22 else
23 mag_inf(z);
24 }
25 else
26 {
27 double t;
28 fmpz exp = MAG_EXP(x);
29
30 if (!COEFF_IS_MPZ(exp))
31 {
32 /* Quick bound by x */
33 if (exp < -10)
34 {
35 mag_set(z, x);
36 }
37 else if (exp < 1000)
38 {
39 t = ldexp(MAG_MAN(x), exp - MAG_BITS);
40 t = (1.0 + t) * (1 + 1e-14);
41 t = mag_d_log_upper_bound(t);
42 mag_set_d(z, t);
43 }
44 else
45 {
46 /* log(2^(exp-1) * (2*v)) = exp*log(2) + log(2*v), 1 <= 2v < 2 */
47 t = (MAG_MAN(x) + 1) * ldexp(1.0, 1 - MAG_BITS);
48 t = mag_d_log_upper_bound(t);
49 t += (exp - 1) * 0.69314718055994530942;
50 t *= (1 + 1e-13);
51 mag_set_d(z, t);
52 }
53 }
54 else if (fmpz_sgn(MAG_EXPREF(x)) < 0)
55 {
56 /* Quick bound by x */
57 mag_set(z, x);
58 }
59 else
60 {
61 mag_add_ui(z, x, 1);
62 mag_log(z, z);
63 }
64 }
65 }
66
67