1 /* Compute complex natural logarithm.
2 Copyright (C) 1997-2022 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19 #include <complex.h>
20 #include <math.h>
21 #include <math_private.h>
22 #include <math-underflow.h>
23 #include <float.h>
24
25 CFLOAT
M_DECL_FUNC(__clog)26 M_DECL_FUNC (__clog) (CFLOAT x)
27 {
28 CFLOAT result;
29 int rcls = fpclassify (__real__ x);
30 int icls = fpclassify (__imag__ x);
31
32 if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
33 {
34 /* Real and imaginary part are 0.0. */
35 __imag__ result = signbit (__real__ x) ? M_MLIT (M_PI) : 0;
36 __imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
37 /* Yes, the following line raises an exception. */
38 __real__ result = -1 / M_FABS (__real__ x);
39 }
40 else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
41 {
42 /* Neither real nor imaginary part is NaN. */
43 FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
44 int scale = 0;
45
46 if (absx < absy)
47 {
48 FLOAT t = absx;
49 absx = absy;
50 absy = t;
51 }
52
53 if (absx > M_MAX / 2)
54 {
55 scale = -1;
56 absx = M_SCALBN (absx, scale);
57 absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
58 }
59 else if (absx < M_MIN && absy < M_MIN)
60 {
61 scale = M_MANT_DIG;
62 absx = M_SCALBN (absx, scale);
63 absy = M_SCALBN (absy, scale);
64 }
65
66 if (absx == 1 && scale == 0)
67 {
68 __real__ result = M_LOG1P (absy * absy) / 2;
69 math_check_force_underflow_nonneg (__real__ result);
70 }
71 else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
72 {
73 FLOAT d2m1 = (absx - 1) * (absx + 1);
74 if (absy >= M_EPSILON)
75 d2m1 += absy * absy;
76 __real__ result = M_LOG1P (d2m1) / 2;
77 }
78 else if (absx < 1
79 && absx >= M_LIT (0.5)
80 && absy < M_EPSILON / 2
81 && scale == 0)
82 {
83 FLOAT d2m1 = (absx - 1) * (absx + 1);
84 __real__ result = M_LOG1P (d2m1) / 2;
85 }
86 else if (absx < 1
87 && absx >= M_LIT (0.5)
88 && scale == 0
89 && absx * absx + absy * absy >= M_LIT (0.5))
90 {
91 FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
92 __real__ result = M_LOG1P (d2m1) / 2;
93 }
94 else
95 {
96 FLOAT d = M_HYPOT (absx, absy);
97 __real__ result = M_LOG (d) - scale * M_MLIT (M_LN2);
98 }
99
100 __imag__ result = M_ATAN2 (__imag__ x, __real__ x);
101 }
102 else
103 {
104 __imag__ result = M_NAN;
105 if (rcls == FP_INFINITE || icls == FP_INFINITE)
106 /* Real or imaginary part is infinite. */
107 __real__ result = M_HUGE_VAL;
108 else
109 __real__ result = M_NAN;
110 }
111
112 return result;
113 }
114
115 declare_mgen_alias (__clog, clog)
116