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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/cacosl.c
+++ new/usr/src/lib/libm/common/complex/cacosl.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 cacosl = __cacosl
30 +#pragma weak __cacosl = cacosl
31 31
32 32 #include "libm.h" /* acosl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
33 33 #include "complex_wrapper.h"
34 34 #include "longdouble.h"
35 35
36 36 /* INDENT OFF */
37 37 static const long double
38 38 zero = 0.0L,
39 39 one = 1.0L,
40 40 Acrossover = 1.5L,
41 41 Bcrossover = 0.6417L,
42 42 half = 0.5L,
43 43 ln2 = 6.931471805599453094172321214581765680755e-0001L,
44 44 Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L, /* 2**-8189 */
45 45 #if defined(__x86)
46 46 E = 5.4210108624275221700372640043497085571289e-20L, /* 2**-64 */
47 47 pi = 3.141592653589793238295968524909085317631252110004425048828125L,
48 48 pi_l = 1.666748583704175665659172893706807721468195923078e-19L,
49 49 pi_2 = 1.5707963267948966191479842624545426588156260L,
50 50 pi_2_l = 8.3337429185208783282958644685340386073409796e-20L,
51 51 pi_4 = 0.78539816339744830957399213122727132940781302750110626220703125L,
52 52 pi_4_l = 4.166871459260439164147932234267019303670489807695410e-20L,
53 53 pi3_4 = 2.35619449019234492872197639368181398822343908250331878662109375L,
54 54 pi3_4_l = 1.250061437778131749244379670280105791101146942308e-19L;
55 55 #else
56 56 E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */
57 57 pi = 3.1415926535897932384626433832795027974790680981372955730045043318L,
58 58 pi_l = 8.6718101301237810247970440260433519687623233462565303417759356862e-35L,
59 59 pi_2 = 1.5707963267948966192313216916397513987395340L,
60 60 pi_2_l = 4.3359050650618905123985220130216759843811616e-35L,
61 61 pi_4 = 0.785398163397448309615660845819875699369767024534323893251126L,
62 62 pi_4_l = 2.167952532530945256199261006510837992190580836564132585443e-35L,
63 63 pi3_4 = 2.35619449019234492884698253745962709810930107360297167975337824L,
64 64 pi3_4_l = 6.503857597592835768597783019532513976571742509692397756331e-35L;
65 65 #endif
66 66 /* INDENT ON */
67 67
68 68 #if defined(__x86)
69 69 static const int ip1 = 0x40400000; /* 2**65 */
70 70 #else
71 71 static const int ip1 = 0x40710000; /* 2**114 */
72 72 #endif
73 73
74 74 ldcomplex
75 75 cacosl(ldcomplex z) {
76 76 long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
77 77 int ix, iy, hx, hy;
78 78 ldcomplex ans;
79 79
80 80 x = LD_RE(z);
81 81 y = LD_IM(z);
82 82 hx = HI_XWORD(x);
83 83 hy = HI_XWORD(y);
84 84 ix = hx & 0x7fffffff;
85 85 iy = hy & 0x7fffffff;
86 86
87 87 /* x is 0 */
88 88 if (x == zero) {
89 89 if (y == zero || (iy >= 0x7fff0000)) {
90 90 LD_RE(ans) = pi_2 + pi_2_l;
91 91 LD_IM(ans) = -y;
92 92 return (ans);
93 93 }
94 94 }
95 95
96 96 /* |y| is inf or NaN */
97 97 if (iy >= 0x7fff0000) {
98 98 if (isinfl(y)) { /* cacos(x + i inf) = pi/2 - i inf */
99 99 LD_IM(ans) = -y;
100 100 if (ix < 0x7fff0000) {
101 101 LD_RE(ans) = pi_2 + pi_2_l;
102 102 } else if (isinfl(x)) {
103 103 if (hx >= 0)
104 104 LD_RE(ans) = pi_4 + pi_4_l;
105 105 else
106 106 LD_RE(ans) = pi3_4 + pi3_4_l;
107 107 } else {
108 108 LD_RE(ans) = x;
109 109 }
110 110 } else { /* cacos(x + i NaN) = NaN + i NaN */
111 111 LD_RE(ans) = y + x;
112 112 if (isinfl(x))
113 113 LD_IM(ans) = -fabsl(x);
114 114 else
115 115 LD_IM(ans) = y;
116 116 }
117 117 return (ans);
118 118 }
119 119
120 120 y = fabsl(y);
121 121
122 122 if (ix >= 0x7fff0000) { /* x is inf or NaN */
123 123 if (isinfl(x)) { /* x is INF */
124 124 LD_IM(ans) = -fabsl(x);
125 125 if (iy >= 0x7fff0000) {
126 126 if (isinfl(y)) {
127 127 /* INDENT OFF */
128 128 /* cacos(inf + i inf) = pi/4 - i inf */
129 129 /* cacos(-inf+ i inf) =3pi/4 - i inf */
130 130 /* INDENT ON */
131 131 if (hx >= 0)
132 132 LD_RE(ans) = pi_4 + pi_4_l;
133 133 else
134 134 LD_RE(ans) = pi3_4 + pi3_4_l;
135 135 } else
136 136 /* INDENT OFF */
137 137 /* cacos(inf + i NaN) = NaN - i inf */
138 138 /* INDENT ON */
139 139 LD_RE(ans) = y + y;
140 140 } else {
141 141 /* INDENT OFF */
142 142 /* cacos(inf + iy ) = 0 - i inf */
143 143 /* cacos(-inf+ iy ) = pi - i inf */
144 144 /* INDENT ON */
145 145 if (hx >= 0)
146 146 LD_RE(ans) = zero;
147 147 else
148 148 LD_RE(ans) = pi + pi_l;
149 149 }
150 150 } else { /* x is NaN */
151 151 /* INDENT OFF */
152 152 /*
153 153 * cacos(NaN + i inf) = NaN - i inf
154 154 * cacos(NaN + i y ) = NaN + i NaN
155 155 * cacos(NaN + i NaN) = NaN + i NaN
156 156 */
157 157 /* INDENT ON */
158 158 LD_RE(ans) = x + y;
159 159 if (iy >= 0x7fff0000) {
160 160 LD_IM(ans) = -y;
161 161 } else {
162 162 LD_IM(ans) = x;
163 163 }
164 164 }
165 165 if (hy < 0)
166 166 LD_IM(ans) = -LD_IM(ans);
167 167 return (ans);
168 168 }
169 169
170 170 if (y == zero) { /* region 1: y=0 */
171 171 if (ix < 0x3fff0000) { /* |x| < 1 */
172 172 LD_RE(ans) = acosl(x);
173 173 LD_IM(ans) = zero;
174 174 } else {
175 175 LD_RE(ans) = zero;
176 176 x = fabsl(x);
177 177 if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
178 178 LD_IM(ans) = ln2 + logl(x);
179 179 else if (ix >= 0x3fff8000) /* x > Acrossover */
180 180 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
181 181 one)));
182 182 else {
183 183 xm1 = x - one;
184 184 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
185 185 one)));
186 186 }
187 187 }
188 188 } else if (y <= E * fabsl(fabsl(x) - one)) {
189 189 /* region 2: y < tiny*||x|-1| */
190 190 if (ix < 0x3fff0000) { /* x < 1 */
191 191 LD_RE(ans) = acosl(x);
192 192 x = fabsl(x);
193 193 LD_IM(ans) = y / sqrtl((one + x) * (one - x));
194 194 } else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
195 195 if (hx >= 0)
196 196 LD_RE(ans) = y / x;
197 197 else {
198 198 if (ix >= ip1 + 0x00040000)
199 199 LD_RE(ans) = pi + pi_l;
200 200 else {
201 201 t = pi_l + y / x;
202 202 LD_RE(ans) = pi + t;
203 203 }
204 204 }
205 205 LD_IM(ans) = ln2 + logl(fabsl(x));
206 206 } else {
207 207 x = fabsl(x);
208 208 t = sqrtl((x - one) * (x + one));
209 209 LD_RE(ans) = (hx >= 0)? y / t : pi - (y / t - pi_l);
210 210 if (ix >= 0x3fff8000) /* x > Acrossover */
211 211 LD_IM(ans) = logl(x + t);
212 212 else
213 213 LD_IM(ans) = log1pl(t - (one - x));
214 214 }
215 215 } else if (y < Foursqrtu) { /* region 3 */
216 216 t = sqrtl(y);
217 217 LD_RE(ans) = (hx >= 0)? t : pi + pi_l;
218 218 LD_IM(ans) = t;
219 219 } else if (E * y - one >= fabsl(x)) { /* region 4 */
220 220 LD_RE(ans) = pi_2 + pi_2_l;
221 221 LD_IM(ans) = ln2 + logl(y);
222 222 } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
223 223 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
224 224 t = x / y;
225 225 LD_RE(ans) = atan2l(y, x);
226 226 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
227 227 } else if (fabsl(x) < Foursqrtu) {
228 228 /* region 6: x is very small, < 4sqrt(min) */
229 229 LD_RE(ans) = pi_2 + pi_2_l;
230 230 A = sqrtl(one + y * y);
231 231 if (iy >= 0x3fff8000) /* if y > Acrossover */
232 232 LD_IM(ans) = logl(y + A);
233 233 else
234 234 LD_IM(ans) = half * log1pl((y + y) * (y + A));
235 235 } else { /* safe region */
236 236 t = fabsl(x);
237 237 y2 = y * y;
238 238 xp1 = t + one;
239 239 xm1 = t - one;
240 240 R = sqrtl(xp1 * xp1 + y2);
241 241 S = sqrtl(xm1 * xm1 + y2);
242 242 A = half * (R + S);
243 243 B = t / A;
244 244
245 245 if (B <= Bcrossover)
246 246 LD_RE(ans) = (hx >= 0)? acosl(B) : acosl(-B);
247 247 else { /* use atan and an accurate approx to a-x */
248 248 Apx = A + t;
249 249 if (t <= one)
250 250 LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
251 251 (R + xp1) + (S - xm1))), x);
252 252 else
253 253 LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
254 254 (R + xp1) + Apx / (S + xm1)))), x);
255 255 }
256 256 if (A <= Acrossover) {
257 257 /* use log1p and an accurate approx to A-1 */
258 258 if (ix < 0x3fff0000)
259 259 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
260 260 else
261 261 Am1 = half * (y2 / (R + xp1) + (S + xm1));
262 262 LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
263 263 } else {
264 264 LD_IM(ans) = logl(A + sqrtl(A * A - one));
265 265 }
266 266 }
267 267
268 268 if (hy >= 0)
269 269 LD_IM(ans) = -LD_IM(ans);
270 270
271 271 return (ans);
272 272 }
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