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
34extern void sincospi(double, double *, double *);
35extern void sincospif(float, float *, float *);
36extern double atan2pi(double, double);
37extern float atan2pif(float, float);
38
39#if defined(__i386) && !defined(__amd64)
40extern int __swapRP(int);
41#endif
42
43static 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
49static const float one = 1.0F, zero = 0.0F;
50
51#define	hiinf	0x7f800000
52
53fcomplex
54cpowf(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