1 /*
2 Copyright (C) 2015 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 "acb.h"
13
14 static void
acb_log1p_tiny(acb_t r,const acb_t z,slong prec)15 acb_log1p_tiny(acb_t r, const acb_t z, slong prec)
16 {
17 mag_t b, c;
18 acb_t t;
19 int real;
20
21 mag_init(b);
22 mag_init(c);
23 acb_init(t);
24
25 real = acb_is_real(z);
26
27 /* if |z| < 1, then |log(1+z) - [z - z^2/2]| <= |z|^3/(1-|z|) */
28 acb_get_mag(b, z);
29 mag_one(c);
30 mag_sub_lower(c, c, b);
31 mag_pow_ui(b, b, 3);
32 mag_div(b, b, c);
33
34 acb_mul(t, z, z, prec);
35 acb_mul_2exp_si(t, t, -1);
36 acb_sub(r, z, t, prec);
37
38 if (real && mag_is_finite(b))
39 arb_add_error_mag(acb_realref(r), b);
40 else
41 acb_add_error_mag(r, b);
42
43 mag_clear(b);
44 mag_clear(c);
45 acb_clear(t);
46 }
47
48 void
acb_log1p(acb_t r,const acb_t z,slong prec)49 acb_log1p(acb_t r, const acb_t z, slong prec)
50 {
51 slong magz, magx, magy;
52
53 if (acb_is_zero(z))
54 {
55 acb_zero(r);
56 return;
57 }
58
59 magx = arf_abs_bound_lt_2exp_si(arb_midref(acb_realref(z)));
60 magy = arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(z)));
61 magz = FLINT_MAX(magx, magy);
62
63 if (magz < -prec)
64 {
65 acb_log1p_tiny(r, z, prec);
66 }
67 else
68 {
69 if (magz < 0)
70 acb_add_ui(r, z, 1, prec + (-magz) + 4);
71 else
72 acb_add_ui(r, z, 1, prec + 4);
73
74 acb_log(r, r, prec);
75 }
76 }
77
78