1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21 /*
22 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak cpowf = __cpowf
30
31 #include "libm.h"
32 #include "complex_wrapper.h"
33
34 extern void sincospi(double, double *, double *);
35 extern void sincospif(float, float *, float *);
36 extern double atan2pi(double, double);
37 extern float atan2pif(float, float);
38
39 #if defined(__i386) && !defined(__amd64)
40 extern int __swapRP(int);
41 #endif
42
43 static const double
44 dpi = 3.1415926535897931160E0, /* Hex 2^ 1 * 1.921FB54442D18 */
45 dhalf = 0.5,
46 dsqrt2 = 1.41421356237309514547, /* 3FF6A09E 667F3BCD */
47 dinvpi = 0.3183098861837906715377675;
48
49 static const float one = 1.0F, zero = 0.0F;
50
51 #define hiinf 0x7f800000
52
53 fcomplex
54 cpowf(fcomplex z, fcomplex w) {
55 fcomplex ans;
56 float x, y, u, v, t, c, s;
57 double dx, dy, du, dv, dt, dc, ds, dp, dq, dr;
58 int ix, iy, hx, hy, hv, hu, iu, iv, j;
59
60 x = F_RE(z);
61 y = F_IM(z);
62 u = F_RE(w);
63 v = F_IM(w);
64 hx = THE_WORD(x);
65 hy = THE_WORD(y);
66 hu = THE_WORD(u);
67 hv = THE_WORD(v);
68 ix = hx & 0x7fffffff;
69 iy = hy & 0x7fffffff;
70 iu = hu & 0x7fffffff;
71 iv = hv & 0x7fffffff;
72
73 j = 0;
74 if (iv == 0) { /* z**(real) */
75 if (hu == 0x3f800000) { /* (anything) ** 1 is itself */
76 F_RE(ans) = x;
77 F_IM(ans) = y;
78 } else if (iu == 0) { /* (anything) ** 0 is 1 */
79 F_RE(ans) = one;
80 F_IM(ans) = zero;
81 } else if (iy == 0) { /* (real)**(real) */
82 F_IM(ans) = zero;
83 if (hx < 0 && ix < hiinf && iu < hiinf) {
84 /* -x ** u is exp(i*pi*u)*pow(x,u) */
85 t = powf(-x, u);
86 sincospif(u, &s, &c);
87 F_RE(ans) = (c == zero)? c: c * t;
88 F_IM(ans) = (s == zero)? s: s * t;
89 } else {
90 F_RE(ans) = powf(x, u);
91 }
92 } else if (ix == 0 || ix >= hiinf || iy >= hiinf) {
93 if (ix > hiinf || iy > hiinf || iu > hiinf) {
94 F_RE(ans) = F_IM(ans) = x + y + u;
95 } else {
96 v = fabsf(y);
97 if (ix != 0)
98 v += fabsf(x);
99 t = atan2pif(y, x);
100 sincospif(t * u, &s, &c);
101 F_RE(ans) = (c == zero)? c: c * v;
102 F_IM(ans) = (s == zero)? s: s * v;
103 }
104 } else if (ix == iy) { /* if |x| == |y| */
105 #if defined(__i386) && !defined(__amd64)
106 int rp = __swapRP(fp_extended);
107 #endif
108 dx = (double)x;
109 du = (double)u;
110 dt = (hx >= 0)? 0.25 : 0.75;
111 if (hy < 0)
112 dt = -dt;
113 dr = pow(dsqrt2 * dx, du);
114 sincospi(dt * du, &ds, &dc);
115 F_RE(ans) = (float)(dr * dc);
116 F_IM(ans) = (float)(dr * ds);
117 #if defined(__i386) && !defined(__amd64)
118 if (rp != fp_extended)
119 (void) __swapRP(rp);
120 #endif
121 } else {
122 j = 1;
123 }
124 if (j == 0)
125 return (ans);
126 }
127 if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
128 /*
129 * non-zero imaginery part(s) with inf component(s) yields NaN
130 */
131 t = fabsf(x) + fabsf(y) + fabsf(u) + fabsf(v);
132 F_RE(ans) = F_IM(ans) = t - t;
133 } else {
134 #if defined(__i386) && !defined(__amd64)
135 int rp = __swapRP(fp_extended);
136 #endif
137 /* INDENT OFF */
138 /*
139 * r = u*log(hypot(x,y))-v*atan2(y,x),
140 * q = u*atan2(y,x)+v*log(hypot(x,y))
141 * or
142 * r = u*log(hypot(x,y))-v*pi*atan2pi(y,x),
143 * q/pi = u*atan2pi(y,x)+v*log(hypot(x,y))/pi
144 * ans = exp(r)*(cospi(q/pi) + i sinpi(q/pi))
145 */
146 /* INDENT ON */
147 dx = (double)x;
148 dy = (double)y;
149 du = (double)u;
150 dv = (double)v;
151 if (ix > 0x3f000000 && ix < 0x40000000) /* .5 < |x| < 2 */
152 dt = dhalf * log1p((dx - 1.0) * (dx + 1.0) + dy * dy);
153 else if (iy > 0x3f000000 && iy < 0x40000000) /* .5 < |y| < 2 */
154 dt = dhalf * log1p((dy - 1.0) * (dy + 1.0) + dx * dx);
155 else
156 dt = dhalf * log(dx * dx + dy * dy);
157 dp = atan2pi(dy, dx);
158 if (iv == 0) { /* dv = 0 */
159 dr = exp(du * dt);
160 dq = du * dp;
161 } else {
162 dr = exp(du * dt - dv * dp * dpi);
163 dq = du * dp + dv * dt * dinvpi;
164 }
165 sincospi(dq, &ds, &dc);
166 F_RE(ans) = (float)(dr * dc);
167 F_IM(ans) = (float)(dr * ds);
168 #if defined(__i386) && !defined(__amd64)
169 if (rp != fp_extended)
170 (void) __swapRP(rp);
171 #endif
172 }
173 return (ans);
174 }