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[glibc.git] / math / s_clogl.c
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1 /* Compute complex natural logarithm.
2 Copyright (C) 1997-2014 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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.
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.
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/>. */
20 #include <complex.h>
21 #include <math.h>
22 #include <math_private.h>
23 #include <float.h>
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
32 __complex__ long double
33 __clogl (__complex__ long double x)
35 __complex__ long double result;
36 int rcls = fpclassify (__real__ x);
37 int icls = fpclassify (__imag__ x);
39 if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
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);
47 else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
49 /* Neither real nor imaginary part is NaN. */
50 long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
51 int scale = 0;
53 if (absx < absy)
55 long double t = absx;
56 absx = absy;
57 absy = t;
60 if (absx > LDBL_MAX / 2.0L)
62 scale = -1;
63 absx = __scalbnl (absx, scale);
64 absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
66 else if (absx < LDBL_MIN && absy < LDBL_MIN)
68 scale = LDBL_MANT_DIG;
69 absx = __scalbnl (absx, scale);
70 absy = __scalbnl (absy, scale);
73 if (absx == 1.0L && scale == 0)
75 long double absy2 = absy * absy;
76 if (absy2 <= LDBL_MIN * 2.0L)
77 __real__ result = absy2 / 2.0L - absy2 * absy2 / 4.0L;
78 else
79 __real__ result = __log1pl (absy2) / 2.0L;
81 else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
83 long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
84 if (absy >= LDBL_EPSILON)
85 d2m1 += absy * absy;
86 __real__ result = __log1pl (d2m1) / 2.0L;
88 else if (absx < 1.0L
89 && absx >= 0.75L
90 && absy < LDBL_EPSILON / 2.0L
91 && scale == 0)
93 long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
94 __real__ result = __log1pl (d2m1) / 2.0L;
96 else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0)
98 long double d2m1 = __x2y2m1l (absx, absy);
99 __real__ result = __log1pl (d2m1) / 2.0L;
101 else
103 long double d = __ieee754_hypotl (absx, absy);
104 __real__ result = __ieee754_logl (d) - scale * M_LN2l;
107 __imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
109 else
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 ("");
119 return result;
121 weak_alias (__clogl, clogl)