1 /* Compute complex natural logarithm.
2 Copyright (C) 1997-2015 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/>. */
22 #include <math_private.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
29 # define LDBL_EPSILON 0x1p-106L
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 (__glibc_unlikely (rcls
== FP_ZERO
&& icls
== FP_ZERO
))
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 (__glibc_likely (rcls
!= FP_NAN
&& icls
!= FP_NAN
))
49 /* Neither real nor imaginary part is NaN. */
50 long double absx
= fabsl (__real__ x
), absy
= fabsl (__imag__ x
);
60 if (absx
> LDBL_MAX
/ 2.0L)
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)
78 long double force_underflow
= absy2
* absy2
;
79 __real__ result
= absy2
/ 2.0L;
80 math_force_eval (force_underflow
);
83 __real__ result
= __log1pl (absy2
) / 2.0L;
85 else if (absx
> 1.0L && absx
< 2.0L && absy
< 1.0L && scale
== 0)
87 long double d2m1
= (absx
- 1.0L) * (absx
+ 1.0L);
88 if (absy
>= LDBL_EPSILON
)
90 __real__ result
= __log1pl (d2m1
) / 2.0L;
94 && absy
< LDBL_EPSILON
/ 2.0L
97 long double d2m1
= (absx
- 1.0L) * (absx
+ 1.0L);
98 __real__ result
= __log1pl (d2m1
) / 2.0L;
100 else if (absx
< 1.0L && (absx
>= 0.75L || absy
>= 0.5L) && scale
== 0)
102 long double d2m1
= __x2y2m1l (absx
, absy
);
103 __real__ result
= __log1pl (d2m1
) / 2.0L;
107 long double d
= __ieee754_hypotl (absx
, absy
);
108 __real__ result
= __ieee754_logl (d
) - scale
* M_LN2l
;
111 __imag__ result
= __ieee754_atan2l (__imag__ x
, __real__ x
);
115 __imag__ result
= __nanl ("");
116 if (rcls
== FP_INFINITE
|| icls
== FP_INFINITE
)
117 /* Real or imaginary part is infinite. */
118 __real__ result
= HUGE_VALL
;
120 __real__ result
= __nanl ("");
125 weak_alias (__clogl
, clogl
)