xref: /titanic_41/usr/src/lib/libm/common/complex/cpowl.c (revision 8d62b2231107e557adb17ea75579d9c49511457b)
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 */
46 static const int hiinf = 0x7fff0000;
47 static 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  */
68 static 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 
106 ldcomplex
107 cpowl(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