1 | /* Compute complex natural logarithm. |
2 | Copyright (C) 1997-2016 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. |
5 | |
6 | The GNU C Library is free software; you can redistribute it and/or |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either |
9 | version 2.1 of the License, or (at your option) any later version. |
10 | |
11 | The GNU C Library is distributed in the hope that it will be useful, |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ |
19 | |
20 | #include <complex.h> |
21 | #include <math.h> |
22 | #include <math_private.h> |
23 | #include <float.h> |
24 | |
25 | /* To avoid spurious underflows, use this definition to treat IBM long |
26 | double as approximating an IEEE-style format. */ |
27 | #if LDBL_MANT_DIG == 106 |
28 | # undef LDBL_EPSILON |
29 | # define LDBL_EPSILON 0x1p-106L |
30 | #endif |
31 | |
32 | __complex__ long double |
33 | __clogl (__complex__ long double x) |
34 | { |
35 | __complex__ long double result; |
36 | int rcls = fpclassify (__real__ x); |
37 | int icls = fpclassify (__imag__ x); |
38 | |
39 | if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
40 | { |
41 | /* Real and imaginary part are 0.0. */ |
42 | __imag__ result = signbit (__real__ x) ? M_PIl : 0.0; |
43 | __imag__ result = __copysignl (__imag__ result, __imag__ x); |
44 | /* Yes, the following line raises an exception. */ |
45 | __real__ result = -1.0 / fabsl (__real__ x); |
46 | } |
47 | else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN)) |
48 | { |
49 | /* Neither real nor imaginary part is NaN. */ |
50 | long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x); |
51 | int scale = 0; |
52 | |
53 | if (absx < absy) |
54 | { |
55 | long double t = absx; |
56 | absx = absy; |
57 | absy = t; |
58 | } |
59 | |
60 | if (absx > LDBL_MAX / 2.0L) |
61 | { |
62 | scale = -1; |
63 | absx = __scalbnl (absx, scale); |
64 | absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L); |
65 | } |
66 | else if (absx < LDBL_MIN && absy < LDBL_MIN) |
67 | { |
68 | scale = LDBL_MANT_DIG; |
69 | absx = __scalbnl (absx, scale); |
70 | absy = __scalbnl (absy, scale); |
71 | } |
72 | |
73 | if (absx == 1.0L && scale == 0) |
74 | { |
75 | __real__ result = __log1pl (absy * absy) / 2.0L; |
76 | math_check_force_underflow_nonneg (__real__ result); |
77 | } |
78 | else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0) |
79 | { |
80 | long double d2m1 = (absx - 1.0L) * (absx + 1.0L); |
81 | if (absy >= LDBL_EPSILON) |
82 | d2m1 += absy * absy; |
83 | __real__ result = __log1pl (d2m1) / 2.0L; |
84 | } |
85 | else if (absx < 1.0L |
86 | && absx >= 0.5L |
87 | && absy < LDBL_EPSILON / 2.0L |
88 | && scale == 0) |
89 | { |
90 | long double d2m1 = (absx - 1.0L) * (absx + 1.0L); |
91 | __real__ result = __log1pl (d2m1) / 2.0L; |
92 | } |
93 | else if (absx < 1.0L |
94 | && absx >= 0.5L |
95 | && scale == 0 |
96 | && absx * absx + absy * absy >= 0.5L) |
97 | { |
98 | long double d2m1 = __x2y2m1l (absx, absy); |
99 | __real__ result = __log1pl (d2m1) / 2.0L; |
100 | } |
101 | else |
102 | { |
103 | long double d = __ieee754_hypotl (absx, absy); |
104 | __real__ result = __ieee754_logl (d) - scale * M_LN2l; |
105 | } |
106 | |
107 | __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x); |
108 | } |
109 | else |
110 | { |
111 | __imag__ result = __nanl ("" ); |
112 | if (rcls == FP_INFINITE || icls == FP_INFINITE) |
113 | /* Real or imaginary part is infinite. */ |
114 | __real__ result = HUGE_VALL; |
115 | else |
116 | __real__ result = __nanl ("" ); |
117 | } |
118 | |
119 | return result; |
120 | } |
121 | weak_alias (__clogl, clogl) |
122 | |