1*627f7eb2Smrg /* Compute complex natural logarithm.
2*627f7eb2Smrg Copyright (C) 1997-2018 Free Software Foundation, Inc.
3*627f7eb2Smrg This file is part of the GNU C Library.
4*627f7eb2Smrg Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
5*627f7eb2Smrg
6*627f7eb2Smrg The GNU C Library is free software; you can redistribute it and/or
7*627f7eb2Smrg modify it under the terms of the GNU Lesser General Public
8*627f7eb2Smrg License as published by the Free Software Foundation; either
9*627f7eb2Smrg version 2.1 of the License, or (at your option) any later version.
10*627f7eb2Smrg
11*627f7eb2Smrg The GNU C Library is distributed in the hope that it will be useful,
12*627f7eb2Smrg but WITHOUT ANY WARRANTY; without even the implied warranty of
13*627f7eb2Smrg MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14*627f7eb2Smrg Lesser General Public License for more details.
15*627f7eb2Smrg
16*627f7eb2Smrg You should have received a copy of the GNU Lesser General Public
17*627f7eb2Smrg License along with the GNU C Library; if not, see
18*627f7eb2Smrg <http://www.gnu.org/licenses/>. */
19*627f7eb2Smrg
20*627f7eb2Smrg #include "quadmath-imp.h"
21*627f7eb2Smrg
22*627f7eb2Smrg __complex128
clogq(__complex128 x)23*627f7eb2Smrg clogq (__complex128 x)
24*627f7eb2Smrg {
25*627f7eb2Smrg __complex128 result;
26*627f7eb2Smrg int rcls = fpclassifyq (__real__ x);
27*627f7eb2Smrg int icls = fpclassifyq (__imag__ x);
28*627f7eb2Smrg
29*627f7eb2Smrg if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
30*627f7eb2Smrg {
31*627f7eb2Smrg /* Real and imaginary part are 0.0. */
32*627f7eb2Smrg __imag__ result = signbitq (__real__ x) ? (__float128) M_PIq : 0;
33*627f7eb2Smrg __imag__ result = copysignq (__imag__ result, __imag__ x);
34*627f7eb2Smrg /* Yes, the following line raises an exception. */
35*627f7eb2Smrg __real__ result = -1 / fabsq (__real__ x);
36*627f7eb2Smrg }
37*627f7eb2Smrg else if (__glibc_likely (rcls != QUADFP_NAN && icls != QUADFP_NAN))
38*627f7eb2Smrg {
39*627f7eb2Smrg /* Neither real nor imaginary part is NaN. */
40*627f7eb2Smrg __float128 absx = fabsq (__real__ x), absy = fabsq (__imag__ x);
41*627f7eb2Smrg int scale = 0;
42*627f7eb2Smrg
43*627f7eb2Smrg if (absx < absy)
44*627f7eb2Smrg {
45*627f7eb2Smrg __float128 t = absx;
46*627f7eb2Smrg absx = absy;
47*627f7eb2Smrg absy = t;
48*627f7eb2Smrg }
49*627f7eb2Smrg
50*627f7eb2Smrg if (absx > FLT128_MAX / 2)
51*627f7eb2Smrg {
52*627f7eb2Smrg scale = -1;
53*627f7eb2Smrg absx = scalbnq (absx, scale);
54*627f7eb2Smrg absy = (absy >= FLT128_MIN * 2 ? scalbnq (absy, scale) : 0);
55*627f7eb2Smrg }
56*627f7eb2Smrg else if (absx < FLT128_MIN && absy < FLT128_MIN)
57*627f7eb2Smrg {
58*627f7eb2Smrg scale = FLT128_MANT_DIG;
59*627f7eb2Smrg absx = scalbnq (absx, scale);
60*627f7eb2Smrg absy = scalbnq (absy, scale);
61*627f7eb2Smrg }
62*627f7eb2Smrg
63*627f7eb2Smrg if (absx == 1 && scale == 0)
64*627f7eb2Smrg {
65*627f7eb2Smrg __real__ result = log1pq (absy * absy) / 2;
66*627f7eb2Smrg math_check_force_underflow_nonneg (__real__ result);
67*627f7eb2Smrg }
68*627f7eb2Smrg else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
69*627f7eb2Smrg {
70*627f7eb2Smrg __float128 d2m1 = (absx - 1) * (absx + 1);
71*627f7eb2Smrg if (absy >= FLT128_EPSILON)
72*627f7eb2Smrg d2m1 += absy * absy;
73*627f7eb2Smrg __real__ result = log1pq (d2m1) / 2;
74*627f7eb2Smrg }
75*627f7eb2Smrg else if (absx < 1
76*627f7eb2Smrg && absx >= 0.5Q
77*627f7eb2Smrg && absy < FLT128_EPSILON / 2
78*627f7eb2Smrg && scale == 0)
79*627f7eb2Smrg {
80*627f7eb2Smrg __float128 d2m1 = (absx - 1) * (absx + 1);
81*627f7eb2Smrg __real__ result = log1pq (d2m1) / 2;
82*627f7eb2Smrg }
83*627f7eb2Smrg else if (absx < 1
84*627f7eb2Smrg && absx >= 0.5Q
85*627f7eb2Smrg && scale == 0
86*627f7eb2Smrg && absx * absx + absy * absy >= 0.5Q)
87*627f7eb2Smrg {
88*627f7eb2Smrg __float128 d2m1 = __quadmath_x2y2m1q (absx, absy);
89*627f7eb2Smrg __real__ result = log1pq (d2m1) / 2;
90*627f7eb2Smrg }
91*627f7eb2Smrg else
92*627f7eb2Smrg {
93*627f7eb2Smrg __float128 d = hypotq (absx, absy);
94*627f7eb2Smrg __real__ result = logq (d) - scale * (__float128) M_LN2q;
95*627f7eb2Smrg }
96*627f7eb2Smrg
97*627f7eb2Smrg __imag__ result = atan2q (__imag__ x, __real__ x);
98*627f7eb2Smrg }
99*627f7eb2Smrg else
100*627f7eb2Smrg {
101*627f7eb2Smrg __imag__ result = nanq ("");
102*627f7eb2Smrg if (rcls == QUADFP_INFINITE || icls == QUADFP_INFINITE)
103*627f7eb2Smrg /* Real or imaginary part is infinite. */
104*627f7eb2Smrg __real__ result = HUGE_VALQ;
105*627f7eb2Smrg else
106*627f7eb2Smrg __real__ result = nanq ("");
107*627f7eb2Smrg }
108*627f7eb2Smrg
109*627f7eb2Smrg return result;
110*627f7eb2Smrg }
111