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 slong
acb_rel_error_bits(const acb_t x)15 acb_rel_error_bits(const acb_t x)
16 {
17 int am, ar, bm, br;
18 slong result;
19 const fmpz * radmag;
20 const fmpz * midmag;
21 fmpz_t t;
22
23 am = !arf_is_zero(arb_midref(acb_realref(x)));
24 ar = !mag_is_zero(arb_radref(acb_realref(x)));
25
26 bm = !arf_is_zero(arb_midref(acb_imagref(x)));
27 br = !mag_is_zero(arb_radref(acb_imagref(x)));
28
29 /* no radius -- exact */
30 if (!ar && !br)
31 return -ARF_PREC_EXACT;
32
33 /* no midpoint -- infinite relative error */
34 if (!am && !bm)
35 return ARF_PREC_EXACT;
36
37 if (!acb_is_finite(x))
38 return ARF_PREC_EXACT;
39
40 #define ame ARF_EXPREF(arb_midref(acb_realref(x)))
41 #define are MAG_EXPREF(arb_radref(acb_realref(x)))
42 #define bme ARF_EXPREF(arb_midref(acb_imagref(x)))
43 #define bre MAG_EXPREF(arb_radref(acb_imagref(x)))
44
45 if (am && bm)
46 midmag = fmpz_cmp(ame, bme) >= 0 ? ame : bme;
47 else if (am)
48 midmag = ame;
49 else
50 midmag = bme;
51
52 if (ar && br)
53 radmag = fmpz_cmp(are, bre) >= 0 ? are : bre;
54 else if (ar)
55 radmag = are;
56 else
57 radmag = bre;
58
59 fmpz_init(t);
60 fmpz_add_ui(t, radmag, 1);
61 result = _fmpz_sub_small(t, midmag);
62 fmpz_clear(t);
63
64 return result;
65 }
66
acb_rel_one_accuracy_bits(const acb_t z)67 slong acb_rel_one_accuracy_bits(const acb_t z)
68 {
69 if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -1) < 0 &&
70 arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -1) < 0)
71 {
72 acb_t t;
73 arf_init(arb_midref(acb_realref(t)));
74 arf_one(arb_midref(acb_realref(t)));
75 arf_init(arb_midref(acb_imagref(t)));
76 *arb_radref(acb_realref(t)) = *arb_radref(acb_realref(z));
77 *arb_radref(acb_imagref(t)) = *arb_radref(acb_imagref(z));
78 return acb_rel_accuracy_bits(t);
79 }
80 else
81 {
82 return acb_rel_accuracy_bits(z);
83 }
84 }
85
86