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5261 libm should stop using synonyms.h
5298 fabs is 0-sized, confuses dis(1) and others
Reviewed by: Josef 'Jeff' Sipek <jeffpc@josefsipek.net>
Approved by: Gordon Ross <gwr@nexenta.com>
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--- old/usr/src/lib/libm/common/complex/cpowl.c
+++ new/usr/src/lib/libm/common/complex/cpowl.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
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20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 25 /*
26 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 27 * Use is subject to license terms.
28 28 */
29 29
30 -#pragma weak cpowl = __cpowl
30 +#pragma weak __cpowl = cpowl
31 31
32 32 #include "libm.h" /* __k_clog_rl/__k_atan2l */
33 33 /* atan2l/atan2pil/exp2l/expl/fabsl/hypotl/isinfl/logl/powl/sincosl/sincospil */
34 34 #include "complex_wrapper.h"
35 -#include "longdouble.h"
35 +#include "longdouble.h"
36 36
37 37 #if defined(__sparc)
38 38 #define HALF(x) ((int *) &x)[3] = 0; ((int *) &x)[2] &= 0xfe000000
39 39 #define LAST(x) ((int *) &x)[3]
40 40 #elif defined(__x86)
41 41 #define HALF(x) ((int *) &x)[0] = 0
42 42 #define LAST(x) ((int *) &x)[0]
43 43 #endif
44 44
45 45 /* INDENT OFF */
46 46 static const int hiinf = 0x7fff0000;
47 47 static const long double
48 48 tiny = 1.0e-4000L,
49 49 huge = 1.0e4000L,
50 50 #if defined(__x86)
51 51 /* 43 significant bits, 21 trailing zeros */
52 52 ln2hil = 0.693147180559890330187045037746429443359375L,
53 53 ln2lol = 5.497923018708371174712471612513436025525412068e-14L,
54 54 #else /* sparc */
55 55 /* 0x3FF962E4 2FEFA39E F35793C7 00000000 */
56 56 ln2hil = 0.693147180559945309417231592858066493070671489074L,
57 57 ln2lol = 5.28600110075004828645286235820646730106802446566153e-25L,
58 58 #endif
59 59 invln2 = 1.442695040888963407359924681001892137427e+0000L,
60 60 one = 1.0L,
61 61 zero = 0.0L;
62 62 /* INDENT ON */
63 63
64 64 /*
65 65 * Assuming |t[0]| > |t[1]| and |t[2]| > |t[3]|, sum4fpl subroutine
66 66 * compute t[0] + t[1] + t[2] + t[3] into two long double fp numbers.
67 67 */
68 68 static long double sum4fpl(long double ta[], long double *w)
69 69 {
70 70 long double t1, t2, t3, t4, w1, w2, t;
71 71 t1 = ta[0]; t2 = ta[1]; t3 = ta[2]; t4 = ta[3];
72 72 /*
73 73 * Rearrange ti so that |t1| >= |t2| >= |t3| >= |t4|
74 74 */
75 75 if (fabsl(t4) > fabsl(t1)) {
76 76 t = t1; t1 = t3; t3 = t;
77 77 t = t2; t2 = t4; t4 = t;
78 78 } else if (fabsl(t3) > fabsl(t1)) {
79 79 t = t1; t1 = t3;
80 80 if (fabsl(t4) > fabsl(t2)) {
81 81 t3 = t4; t4 = t2; t2 = t;
82 82 } else {
83 83 t3 = t2; t2 = t;
84 84 }
85 85 } else if (fabsl(t3) > fabsl(t2)) {
86 86 t = t2; t2 = t3;
87 87 if (fabsl(t4) > fabsl(t2)) {
88 88 t3 = t4; t4 = t;
89 89 } else
90 90 t3 = t;
91 91 }
92 92 /* summing r = t1 + t2 + t3 + t4 to w1 + w2 */
93 93 w1 = t3 + t4;
94 94 w2 = t4 - (w1 - t3);
95 95 t = t2 + w1;
96 96 w2 += w1 - (t - t2);
97 97 w1 = t + w2;
98 98 w2 += t - w1;
99 99 t = t1 + w1;
100 100 w2 += w1 - (t - t1);
101 101 w1 = t + w2;
102 102 *w = w2 - (w1 - t);
103 103 return (w1);
104 104 }
105 105
106 106 ldcomplex
107 107 cpowl(ldcomplex z, ldcomplex w) {
108 108 ldcomplex ans;
109 109 long double x, y, u, v, t, c, s, r;
110 110 long double t1, t2, t3, t4, x1, x2, y1, y2, u1, v1, b[4], w1, w2;
111 111 int ix, iy, hx, hy, hv, hu, iu, iv, i, j, k;
112 112
113 113 x = LD_RE(z);
114 114 y = LD_IM(z);
115 115 u = LD_RE(w);
116 116 v = LD_IM(w);
117 117 hx = HI_XWORD(x);
118 118 hy = HI_XWORD(y);
119 119 hu = HI_XWORD(u);
120 120 hv = HI_XWORD(v);
121 121 ix = hx & 0x7fffffff;
122 122 iy = hy & 0x7fffffff;
123 123 iu = hu & 0x7fffffff;
124 124 iv = hv & 0x7fffffff;
125 125
126 126 j = 0;
127 127 if (v == zero) { /* z**(real) */
128 128 if (u == one) { /* (anything) ** 1 is itself */
129 129 LD_RE(ans) = x;
130 130 LD_IM(ans) = y;
131 131 } else if (u == zero) { /* (anything) ** 0 is 1 */
132 132 LD_RE(ans) = one;
133 133 LD_IM(ans) = zero;
134 134 } else if (y == zero) { /* real ** real */
135 135 LD_IM(ans) = zero;
136 136 if (hx < 0 && ix < hiinf && iu < hiinf) {
137 137 /* -x ** u is exp(i*pi*u)*pow(x,u) */
138 138 r = powl(-x, u);
139 139 sincospil(u, &s, &c);
140 140 LD_RE(ans) = (c == zero)? c: c * r;
141 141 LD_IM(ans) = (s == zero)? s: s * r;
142 142 } else
143 143 LD_RE(ans) = powl(x, u);
144 144 } else if (x == zero || ix >= hiinf || iy >= hiinf) {
145 145 if (isnanl(x) || isnanl(y) || isnanl(u))
146 146 LD_RE(ans) = LD_IM(ans) = x + y + u;
147 147 else {
148 148 if (x == zero)
149 149 r = fabsl(y);
150 150 else
151 151 r = fabsl(x) + fabsl(y);
152 152 t = atan2pil(y, x);
153 153 sincospil(t * u, &s, &c);
154 154 LD_RE(ans) = (c == zero)? c: c * r;
155 155 LD_IM(ans) = (s == zero)? s: s * r;
156 156 }
157 157 } else if (fabsl(x) == fabsl(y)) { /* |x| = |y| */
158 158 if (hx >= 0) {
159 159 t = (hy >= 0)? 0.25L : -0.25L;
160 160 sincospil(t * u, &s, &c);
161 161 } else if ((LAST(u) & 3) == 0) {
162 162 t = (hy >= 0)? 0.75L : -0.75L;
163 163 sincospil(t * u, &s, &c);
164 164 } else {
165 165 r = (hy >= 0)? u : -u;
166 166 t = -0.25L * r;
167 167 w1 = r + t;
168 168 w2 = t - (w1 - r);
169 169 sincospil(w1, &t1, &t2);
170 170 sincospil(w2, &t3, &t4);
171 171 s = t1 * t4 + t3 * t2;
172 172 c = t2 * t4 - t1 * t3;
173 173 }
174 174 if (ix < 0x3ffe0000) /* |x| < 1/2 */
175 175 r = powl(fabsl(x + x), u) * exp2l(-0.5L * u);
176 176 else if (ix >= 0x3fff0000 || iu < 0x400cfff8)
177 177 /* |x| >= 1 or |u| < 16383 */
178 178 r = powl(fabsl(x), u) * exp2l(0.5L * u);
179 179 else /* special treatment */
180 180 j = 2;
181 181 if (j == 0) {
182 182 LD_RE(ans) = (c == zero)? c: c * r;
183 183 LD_IM(ans) = (s == zero)? s: s * r;
184 184 }
185 185 } else
186 186 j = 1;
187 187 if (j == 0)
188 188 return (ans);
189 189 }
190 190 if (iu >= hiinf || iv >= hiinf || ix >= hiinf || iy >= hiinf) {
191 191 /*
192 192 * non-zero imag part(s) with inf component(s) yields NaN
193 193 */
194 194 t = fabsl(x) + fabsl(y) + fabsl(u) + fabsl(v);
195 195 LD_RE(ans) = LD_IM(ans) = t - t;
196 196 } else {
197 197 k = 0; /* no scaling */
198 198 if (iu > 0x7ffe0000 || iv > 0x7ffe0000) {
199 199 u *= 1.52587890625000000000e-05L;
200 200 v *= 1.52587890625000000000e-05L;
201 201 k = 1; /* scale u and v by 2**-16 */
202 202 }
203 203 /*
204 204 * Use similated higher precision arithmetic to compute:
205 205 * r = u * log(hypot(x, y)) - v * atan2(y, x)
206 206 * q = u * atan2(y, x) + v * log(hypot(x, y))
207 207 */
208 208
209 209 t1 = __k_clog_rl(x, y, &t2);
210 210 t3 = __k_atan2l(y, x, &t4);
211 211 x1 = t1; HALF(x1);
212 212 y1 = t3; HALF(y1);
213 213 u1 = u; HALF(u1);
214 214 v1 = v; HALF(v1);
215 215 x2 = t2 - (x1 - t1); /* log(hypot(x,y)) = x1 + x2 */
216 216 y2 = t4 - (y1 - t3); /* atan2(y,x) = y1 + y2 */
217 217 /* compute q = u * atan2(y, x) + v * log(hypot(x, y)) */
218 218 if (j != 2) {
219 219 b[0] = u1 * y1;
220 220 b[1] = (u - u1) * y1 + u * y2;
221 221 if (j == 1) { /* v = 0 */
222 222 w1 = b[0] + b[1];
223 223 w2 = b[1] - (w1 - b[0]);
224 224 } else {
225 225 b[2] = v1 * x1;
226 226 b[3] = (v - v1) * x1 + v * x2;
227 227 w1 = sum4fpl(b, &w2);
228 228 }
229 229 sincosl(w1, &t1, &t2);
230 230 sincosl(w2, &t3, &t4);
231 231 s = t1 * t4 + t3 * t2;
232 232 c = t2 * t4 - t1 * t3;
233 233 if (k == 1) /* square j times */
234 234 for (i = 0; i < 10; i++) {
235 235 t1 = s * c;
236 236 c = (c + s) * (c - s);
237 237 s = t1 + t1;
238 238 }
239 239 }
240 240 /* compute r = u * (t1, t2) - v * (t3, t4) */
241 241 b[0] = u1 * x1;
242 242 b[1] = (u - u1) * x1 + u * x2;
243 243 if (j == 1) { /* v = 0 */
244 244 w1 = b[0] + b[1];
245 245 w2 = b[1] - (w1 - b[0]);
246 246 } else {
247 247 b[2] = -v1 * y1;
248 248 b[3] = (v1 - v) * y1 - v * y2;
249 249 w1 = sum4fpl(b, &w2);
250 250 }
251 251 /* scale back unless w1 is large enough to cause exception */
252 252 if (k != 0 && fabsl(w1) < 20000.0L) {
253 253 w1 *= 65536.0L; w2 *= 65536.0L;
254 254 }
255 255 hx = HI_XWORD(w1);
256 256 ix = hx & 0x7fffffff;
257 257 /* compute exp(w1 + w2) */
258 258 k = 0;
259 259 if (ix < 0x3f8c0000) /* exp(tiny < 2**-115) = 1 */
260 260 r = one;
261 261 else if (ix >= 0x400c6760) /* overflow/underflow */
262 262 r = (hx < 0)? tiny * tiny : huge * huge;
263 263 else { /* compute exp(w1 + w2) */
264 264 k = (int) (invln2 * w1 + ((hx >= 0)? 0.5L : -0.5L));
265 265 t1 = (long double) k;
266 266 t2 = w1 - t1 * ln2hil;
267 267 t3 = w2 - t1 * ln2lol;
268 268 r = expl(t2 + t3);
269 269 }
270 270 if (c != zero) c *= r;
271 271 if (s != zero) s *= r;
272 272 if (k != 0) {
273 273 c = scalbnl(c, k);
274 274 s = scalbnl(s, k);
275 275 }
276 276 LD_RE(ans) = c;
277 277 LD_IM(ans) = s;
278 278 }
279 279 return (ans);
280 280 }
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