xref: /illumos-gate/usr/src/lib/libm/common/complex/cpowf.c (revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8)
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 }
175