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}
121weak_alias (__clogl, clogl)
122