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/*
23 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24 */
25/*
26 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27 * Use is subject to license terms.
28 */
29
30#pragma weak __cpowl = cpowl
31
32#include "libm.h"				/* __k_clog_rl/__k_atan2l */
33/* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */
34#include "complex_wrapper.h"
35#include "longdouble.h"
36
37#if defined(__sparc)
38#define	HALF(x)  ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000
39#define	LAST(x)  ((int *) &x)[3]
40#elif defined(__x86)
41#define	HALF(x)  ((int *) &x)[0] = 0
42#define	LAST(x)  ((int *) &x)[0]
43#endif
44
45/* INDENT OFF */
46static const int hiinf = 0x7fff0000;
47static const long double
48	tiny = 1.0e-4000L,
49	huge = 1.0e4000L,
50#if defined(__x86)
51		/* 43 significant bits, 21 trailing zeros */
52	ln2hil = 0.693147180559890330187045037746429443359375L,
53	ln2lol = 5.497923018708371174712471612513436025525412068e-14L,
54#else   /* sparc */
55		/* 0x3FF962E4 2FEFA39E F35793C7 00000000 */
56	ln2hil = 0.693147180559945309417231592858066493070671489074L,
57	ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L,
58#endif
59	invln2  = 1.442695040888963407359924681001892137427e+0000L,
60	one = 1.0L,
61	zero = 0.0L;
62/* INDENT ON */
63
64/*
65 * Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine
66 * compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers.
67 */
68static long double sum4fpl(long double ta[], long double *w)
69{
70	long double t1, t2, t3, t4, w1, w2, t;
71	t1 = ta[0]; t2 = ta[1]; t3 = ta[2]; t4 = ta[3];
72	/*
73	 * Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4|
74	 */
75	if (fabsl(t4) > fabsl(t1)) {
76		t = t1; t1 = t3; t3 = t;
77		t = t2; t2 = t4; t4 = t;
78	} else if (fabsl(t3) > fabsl(t1)) {
79		t = t1; t1 = t3;
80		if (fabsl(t4) > fabsl(t2)) {
81			t3 = t4; t4 = t2; t2 = t;
82		} else {
83			t3 = t2; t2 = t;
84		}
85	} else if (fabsl(t3) > fabsl(t2)) {
86		t = t2; t2 = t3;
87		if (fabsl(t4) > fabsl(t2)) {
88			t3 = t4; t4 = t;
89		} else
90			t3 = t;
91	}
92	/* summing r = t1 + t2 + t3 + t4 to w1 + w2 */
93	w1 = t3 + t4;
94	w2 = t4 - (w1 - t3);
95	t  = t2 + w1;
96	w2 += w1 - (t - t2);
97	w1 = t + w2;
98	w2 += t - w1;
99	t  = t1 + w1;
100	w2 += w1 - (t - t1);
101	w1 = t + w2;
102	*w = w2 - (w1 - t);
103	return (w1);
104}
105
106ldcomplex
107cpowl(ldcomplex z, ldcomplex w) {
108	ldcomplex ans;
109	long double x, y, u, v, t, c, s, r;
110	long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
111	int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
112
113	x = LD_RE(z);
114	y = LD_IM(z);
115	u = LD_RE(w);
116	v = LD_IM(w);
117	hx = HI_XWORD(x);
118	hy = HI_XWORD(y);
119	hu = HI_XWORD(u);
120	hv = HI_XWORD(v);
121	ix = hx & 0x7fffffff;
122	iy = hy & 0x7fffffff;
123	iu = hu & 0x7fffffff;
124	iv = hv & 0x7fffffff;
125
126	j = 0;
127	if (v == zero) {	/* z**(real) */
128		if (u == one) {	/* (anything) ** 1  is itself */
129			LD_RE(ans) = x;
130			LD_IM(ans) = y;
131		} else if (u == zero) {	/* (anything) ** 0  is 1 */
132			LD_RE(ans) = one;
133			LD_IM(ans) = zero;
134		} else if (y == zero) {	/* real ** real */
135			LD_IM(ans) = zero;
136			if (hx < 0 && ix < hiinf && iu < hiinf) {
137			/* -x ** u  is exp(i*pi*u)*pow(x,u) */
138				r = powl(-x, u);
139				sincospil(u, &s, &c);
140				LD_RE(ans) = (c == zero)? c: c * r;
141				LD_IM(ans) = (s == zero)? s: s * r;
142			} else
143				LD_RE(ans) = powl(x, u);
144		} else if (x == zero || ix >= hiinf || iy >= hiinf) {
145			if (isnanl(x) || isnanl(y) || isnanl(u))
146				LD_RE(ans) = LD_IM(ans) = x + y + u;
147			else {
148				if (x == zero)
149					r = fabsl(y);
150				else
151					r = fabsl(x) + fabsl(y);
152				t = atan2pil(y, x);
153				sincospil(t * u, &s, &c);
154				LD_RE(ans) = (c == zero)? c: c * r;
155				LD_IM(ans) = (s == zero)? s: s * r;
156			}
157		} else if (fabsl(x) == fabsl(y)) {    /* |x| = |y| */
158			if (hx >= 0) {
159				t = (hy >= 0)? 0.25L : -0.25L;
160				sincospil(t * u, &s, &c);
161			} else if ((LAST(u) & 3) == 0) {
162				t = (hy >= 0)? 0.75L : -0.75L;
163				sincospil(t * u, &s, &c);
164			} else {
165				r = (hy >= 0)? u : -u;
166				t = -0.25L * r;
167				w1 = r + t;
168				w2 = t - (w1 - r);
169				sincospil(w1, &t1, &t2);
170				sincospil(w2, &t3, &t4);
171				s = t1 * t4 + t3 * t2;
172				c = t2 * t4 - t1 * t3;
173			}
174			if (ix < 0x3ffe0000)	/* |x| < 1/2 */
175				r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
176			else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
177				/* |x| >= 1 or |u| < 16383 */
178				r = powl(fabsl(x), u) * exp2l(0.5L * u);
179			else   /* special treatment */
180				j = 2;
181			if (j == 0) {
182				LD_RE(ans) = (c == zero)? c: c * r;
183				LD_IM(ans) = (s == zero)? s: s * r;
184			}
185		} else
186			j = 1;
187		if (j == 0)
188			return (ans);
189	}
190	if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
191		/*
192		 * non-zero imag part(s) with inf component(s) yields NaN
193		 */
194		t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
195		LD_RE(ans) = LD_IM(ans) = t - t;
196	} else {
197		k = 0;	/* no scaling */
198		if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
199			u *= 1.52587890625000000000e-05L;
200			v *= 1.52587890625000000000e-05L;
201			k = 1;	/* scale u and v by 2**-16 */
202		}
203		/*
204		 * Use similated higher precision arithmetic to compute:
205		 * r = u * log(hypot(x, y)) - v * atan2(y, x)
206		 * q = u * atan2(y, x) + v * log(hypot(x, y))
207		 */
208
209		t1 = __k_clog_rl(x, y, &t2);
210		t3 = __k_atan2l(y, x, &t4);
211		x1 = t1; HALF(x1);
212		y1 = t3; HALF(y1);
213		u1 = u; HALF(u1);
214		v1 = v; HALF(v1);
215		x2 = t2 - (x1 - t1);    /* log(hypot(x,y)) = x1 + x2 */
216		y2 = t4 - (y1 - t3);    /* atan2(y,x) = y1 + y2 */
217		/* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
218		if (j != 2) {
219			b[0] = u1 * y1;
220			b[1] = (u - u1) * y1 + u * y2;
221			if (j == 1) {	/* v = 0 */
222				w1 = b[0] + b[1];
223				w2 = b[1] - (w1 - b[0]);
224			} else {
225				b[2] = v1 * x1;
226				b[3] = (v - v1) * x1 + v * x2;
227				w1 = sum4fpl(b, &w2);
228			}
229			sincosl(w1, &t1, &t2);
230			sincosl(w2, &t3, &t4);
231			s = t1 * t4 + t3 * t2;
232			c = t2 * t4 - t1 * t3;
233			if (k == 1)	/* square j times */
234				for (i = 0; i < 10; i++) {
235					t1 = s * c;
236					c = (c + s) * (c - s);
237					s = t1 + t1;
238				}
239		}
240		/* compute r = u * (t1, t2) - v * (t3, t4) */
241		b[0] = u1 * x1;
242		b[1] = (u - u1) * x1 + u * x2;
243		if (j == 1) {   /* v = 0 */
244			w1 = b[0] + b[1];
245			w2 = b[1] - (w1 - b[0]);
246		} else {
247			b[2] = -v1 * y1;
248			b[3] = (v1 - v) * y1 - v * y2;
249			w1 = sum4fpl(b, &w2);
250		}
251		/* scale back unless w1 is large enough to cause exception */
252		if (k != 0 && fabsl(w1) < 20000.0L) {
253			w1 *= 65536.0L; w2 *= 65536.0L;
254		}
255		hx = HI_XWORD(w1);
256		ix = hx & 0x7fffffff;
257		/* compute exp(w1 + w2) */
258		k = 0;
259		if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */
260			r = one;
261		else if (ix >= 0x400c6760) /* overflow/underflow */
262			r = (hx < 0)? tiny * tiny : huge * huge;
263		else {  /* compute exp(w1 + w2) */
264			k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L));
265			t1 = (long double) k;
266			t2 = w1 - t1 * ln2hil;
267			t3 = w2 - t1 * ln2lol;
268			r = expl(t2 + t3);
269		}
270		if (c != zero) c *= r;
271		if (s != zero) s *= r;
272		if (k != 0) {
273			c = scalbnl(c, k);
274			s = scalbnl(s, k);
275		}
276		LD_RE(ans) = c;
277		LD_IM(ans) = s;
278	}
279	return (ans);
280}
281