1 /* Compute complex natural logarithm.
2 Copyright (C) 1997-2012 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>
26 __clogf (__complex__ float x)
28 __complex__ float result;
29 int rcls = fpclassify (__real__ x);
30 int icls = fpclassify (__imag__ x);
32 if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
34 /* Real and imaginary part are 0.0. */
35 __imag__ result = signbit (__real__ x) ? M_PI : 0.0;
36 __imag__ result = __copysignf (__imag__ result, __imag__ x);
37 /* Yes, the following line raises an exception. */
38 __real__ result = -1.0 / fabsf (__real__ x);
40 else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
42 /* Neither real nor imaginary part is NaN. */
43 float absx = fabsf (__real__ x), absy = fabsf (__imag__ x);
53 if (absx > FLT_MAX / 2.0f)
56 absx = __scalbnf (absx, scale);
57 absy = (absy >= FLT_MIN * 2.0f ? __scalbnf (absy, scale) : 0.0f);
59 else if (absx < FLT_MIN && absy < FLT_MIN)
62 absx = __scalbnf (absx, scale);
63 absy = __scalbnf (absy, scale);
66 if (absx == 1.0f && scale == 0)
68 float absy2 = absy * absy;
69 if (absy2 <= FLT_MIN * 2.0f)
71 #if __FLT_EVAL_METHOD__ == 0
72 __real__ result = absy2 / 2.0f - absy2 * absy2 / 4.0f;
74 volatile float force_underflow = absy2 * absy2 / 4.0f;
75 __real__ result = absy2 / 2.0f - force_underflow;
79 __real__ result = __log1pf (absy2) / 2.0f;
81 else if (absx > 1.0f && absx < 2.0f && absy < 1.0f && scale == 0)
83 float d2m1 = (absx - 1.0f) * (absx + 1.0f);
84 if (absy >= FLT_EPSILON)
86 __real__ result = __log1pf (d2m1) / 2.0f;
90 && absy < FLT_EPSILON / 2.0f
93 float d2m1 = (absx - 1.0f) * (absx + 1.0f);
94 __real__ result = __log1pf (d2m1) / 2.0f;
96 else if (absx < 1.0f && (absx >= 0.75f || absy >= 0.5f) && scale == 0)
98 float d2m1 = __x2y2m1f (absx, absy);
99 __real__ result = __log1pf (d2m1) / 2.0f;
103 float d = __ieee754_hypotf (absx, absy);
104 __real__ result = __ieee754_logf (d) - scale * (float) M_LN2;
107 __imag__ result = __ieee754_atan2f (__imag__ x, __real__ x);
111 __imag__ result = __nanf ("");
112 if (rcls == FP_INFINITE || icls == FP_INFINITE)
113 /* Real or imaginary part is infinite. */
114 __real__ result = HUGE_VALF;
116 __real__ result = __nanf ("");
122 weak_alias (__clogf, clogf)