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c131718c | 1 | /* Compute complex natural logarithm. |
b168057a | 2 | Copyright (C) 1997-2015 Free Software Foundation, Inc. |
c131718c UD |
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 | |
41bdb6e2 AJ |
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. | |
c131718c UD |
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 | |
41bdb6e2 | 14 | Lesser General Public License for more details. |
c131718c | 15 | |
41bdb6e2 | 16 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
c131718c UD |
19 | |
20 | #include <complex.h> | |
21 | #include <math.h> | |
9277c064 | 22 | #include <math_private.h> |
1897ad44 | 23 | #include <float.h> |
c131718c UD |
24 | |
25 | __complex__ double | |
26 | __clog (__complex__ double x) | |
27 | { | |
28 | __complex__ double result; | |
63551311 UD |
29 | int rcls = fpclassify (__real__ x); |
30 | int icls = fpclassify (__imag__ x); | |
c131718c | 31 | |
a1ffb40e | 32 | if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
c131718c | 33 | { |
63551311 | 34 | /* Real and imaginary part are 0.0. */ |
c131718c | 35 | __imag__ result = signbit (__real__ x) ? M_PI : 0.0; |
63551311 | 36 | __imag__ result = __copysign (__imag__ result, __imag__ x); |
c131718c UD |
37 | /* Yes, the following line raises an exception. */ |
38 | __real__ result = -1.0 / fabs (__real__ x); | |
39 | } | |
a1ffb40e | 40 | else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN)) |
c131718c | 41 | { |
63551311 | 42 | /* Neither real nor imaginary part is NaN. */ |
638a572e | 43 | double absx = fabs (__real__ x), absy = fabs (__imag__ x); |
1897ad44 JM |
44 | int scale = 0; |
45 | ||
da865e95 JM |
46 | if (absx < absy) |
47 | { | |
48 | double t = absx; | |
49 | absx = absy; | |
50 | absy = t; | |
51 | } | |
52 | ||
638a572e | 53 | if (absx > DBL_MAX / 2.0) |
1897ad44 JM |
54 | { |
55 | scale = -1; | |
638a572e JM |
56 | absx = __scalbn (absx, scale); |
57 | absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0); | |
1897ad44 | 58 | } |
638a572e | 59 | else if (absx < DBL_MIN && absy < DBL_MIN) |
1897ad44 JM |
60 | { |
61 | scale = DBL_MANT_DIG; | |
638a572e JM |
62 | absx = __scalbn (absx, scale); |
63 | absy = __scalbn (absy, scale); | |
1897ad44 JM |
64 | } |
65 | ||
da865e95 JM |
66 | if (absx == 1.0 && scale == 0) |
67 | { | |
68 | double absy2 = absy * absy; | |
69 | if (absy2 <= DBL_MIN * 2.0) | |
70 | { | |
6f05bafe JM |
71 | double force_underflow = absy2 * absy2; |
72 | __real__ result = absy2 / 2.0; | |
73 | math_force_eval (force_underflow); | |
da865e95 JM |
74 | } |
75 | else | |
76 | __real__ result = __log1p (absy2) / 2.0; | |
77 | } | |
d0419dbf JM |
78 | else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0) |
79 | { | |
80 | double d2m1 = (absx - 1.0) * (absx + 1.0); | |
81 | if (absy >= DBL_EPSILON) | |
82 | d2m1 += absy * absy; | |
83 | __real__ result = __log1p (d2m1) / 2.0; | |
84 | } | |
d032e0d2 JM |
85 | else if (absx < 1.0 |
86 | && absx >= 0.75 | |
87 | && absy < DBL_EPSILON / 2.0 | |
88 | && scale == 0) | |
89 | { | |
90 | double d2m1 = (absx - 1.0) * (absx + 1.0); | |
91 | __real__ result = __log1p (d2m1) / 2.0; | |
92 | } | |
93 | else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0) | |
94 | { | |
95 | double d2m1 = __x2y2m1 (absx, absy); | |
96 | __real__ result = __log1p (d2m1) / 2.0; | |
97 | } | |
da865e95 JM |
98 | else |
99 | { | |
100 | double d = __ieee754_hypot (absx, absy); | |
101 | __real__ result = __ieee754_log (d) - scale * M_LN2; | |
102 | } | |
1897ad44 | 103 | |
c131718c UD |
104 | __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x); |
105 | } | |
106 | else | |
107 | { | |
108 | __imag__ result = __nan (""); | |
63551311 UD |
109 | if (rcls == FP_INFINITE || icls == FP_INFINITE) |
110 | /* Real or imaginary part is infinite. */ | |
c131718c UD |
111 | __real__ result = HUGE_VAL; |
112 | else | |
113 | __real__ result = __nan (""); | |
114 | } | |
115 | ||
116 | return result; | |
117 | } | |
118 | weak_alias (__clog, clog) | |
119 | #ifdef NO_LONG_DOUBLE | |
120 | strong_alias (__clog, __clogl) | |
121 | weak_alias (__clog, clogl) | |
122 | #endif |