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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/casinl.c
+++ new/usr/src/lib/libm/common/complex/casinl.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 casinl = __casinl
30 +#pragma weak __casinl = casinl
31 31
32 32 #include "libm.h" /* asinl/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_4 = 0.7853981633974483095739921312272713294078130L,
48 48 pi_4_l = 4.1668714592604391641479322342670193036704898e-20L,
49 49 pi_2 = 1.5707963267948966191479842624545426588156260L,
50 50 pi_2_l = 8.3337429185208783282958644685340386073409796e-20L;
51 51
52 52 #else
53 53 E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */
54 54 pi_4 = 0.7853981633974483096156608458198756993697670L,
55 55 pi_4_l = 2.1679525325309452561992610065108379921905808e-35L,
56 56 pi_2 = 1.5707963267948966192313216916397513987395340L,
57 57 pi_2_l = 4.3359050650618905123985220130216759843811616e-35L;
58 58
59 59 #endif
60 60 /* INDENT ON */
61 61
62 62 #if defined(__x86)
63 63 static const int ip1 = 0x40400000; /* 2**65 */
64 64 #else
65 65 static const int ip1 = 0x40710000; /* 2**114 */
66 66 #endif
67 67
68 68 ldcomplex
69 69 casinl(ldcomplex z) {
70 70 long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
71 71 int ix, iy, hx, hy;
72 72 ldcomplex ans;
73 73
74 74 x = LD_RE(z);
75 75 y = LD_IM(z);
76 76 hx = HI_XWORD(x);
77 77 hy = HI_XWORD(y);
78 78 ix = hx & 0x7fffffff;
79 79 iy = hy & 0x7fffffff;
80 80 x = fabsl(x);
81 81 y = fabsl(y);
82 82
83 83 /* special cases */
84 84
85 85 /* x is inf or NaN */
86 86 if (ix >= 0x7fff0000) { /* x is inf or NaN */
87 87 if (isinfl(x)) { /* x is INF */
88 88 LD_IM(ans) = x;
89 89 if (iy >= 0x7fff0000) {
90 90 if (isinfl(y))
91 91 /* casin(inf + i inf) = pi/4 + i inf */
92 92 LD_RE(ans) = pi_4 + pi_4_l;
93 93 else /* casin(inf + i NaN) = NaN + i inf */
94 94 LD_RE(ans) = y + y;
95 95 } else /* casin(inf + iy) = pi/2 + i inf */
96 96 LD_RE(ans) = pi_2 + pi_2_l;
97 97 } else { /* x is NaN */
98 98 if (iy >= 0x7fff0000) {
99 99 /* INDENT OFF */
100 100 /*
101 101 * casin(NaN + i inf) = NaN + i inf
102 102 * casin(NaN + i NaN) = NaN + i NaN
103 103 */
104 104 /* INDENT ON */
105 105 LD_IM(ans) = y + y;
106 106 LD_RE(ans) = x + x;
107 107 } else {
108 108 /* INDENT OFF */
109 109 /* casin(NaN + i y ) = NaN + i NaN */
110 110 /* INDENT ON */
111 111 LD_IM(ans) = LD_RE(ans) = x + y;
112 112 }
113 113 }
114 114 if (hx < 0)
115 115 LD_RE(ans) = -LD_RE(ans);
116 116 if (hy < 0)
117 117 LD_IM(ans) = -LD_IM(ans);
118 118 return (ans);
119 119 }
120 120
121 121 /* casin(+0 + i 0) = 0 + i 0. */
122 122 if (x == zero && y == zero)
123 123 return (z);
124 124
125 125 if (iy >= 0x7fff0000) { /* y is inf or NaN */
126 126 if (isinfl(y)) { /* casin(x + i inf) = 0 + i inf */
127 127 LD_IM(ans) = y;
128 128 LD_RE(ans) = zero;
129 129 } else { /* casin(x + i NaN) = NaN + i NaN */
130 130 LD_IM(ans) = x + y;
131 131 if (x == zero)
132 132 LD_RE(ans) = x;
133 133 else
134 134 LD_RE(ans) = y;
135 135 }
136 136 if (hx < 0)
137 137 LD_RE(ans) = -LD_RE(ans);
138 138 if (hy < 0)
139 139 LD_IM(ans) = -LD_IM(ans);
140 140 return (ans);
141 141 }
142 142
143 143 if (y == zero) { /* region 1: y=0 */
144 144 if (ix < 0x3fff0000) { /* |x| < 1 */
145 145 LD_RE(ans) = asinl(x);
146 146 LD_IM(ans) = zero;
147 147 } else {
148 148 LD_RE(ans) = pi_2 + pi_2_l;
149 149 if (ix >= ip1) /* |x| >= i386 ? 2**65 : 2**114 */
150 150 LD_IM(ans) = ln2 + logl(x);
151 151 else if (ix >= 0x3fff8000) /* x > Acrossover */
152 152 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
153 153 one)));
154 154 else {
155 155 xm1 = x - one;
156 156 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
157 157 one)));
158 158 }
159 159 }
160 160 } else if (y <= E * fabsl(x - one)) { /* region 2: y < tiny*|x-1| */
161 161 if (ix < 0x3fff0000) { /* x < 1 */
162 162 LD_RE(ans) = asinl(x);
163 163 LD_IM(ans) = y / sqrtl((one + x) * (one - x));
164 164 } else {
165 165 LD_RE(ans) = pi_2 + pi_2_l;
166 166 if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
167 167 LD_IM(ans) = ln2 + logl(x);
168 168 else if (ix >= 0x3fff8000) /* x > Acrossover */
169 169 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
170 170 one)));
171 171 else
172 172 LD_IM(ans) = log1pl((x - one) + sqrtl((x -
173 173 one) * (x + one)));
174 174 }
175 175 } else if (y < Foursqrtu) { /* region 3 */
176 176 t = sqrtl(y);
177 177 LD_RE(ans) = pi_2 - (t - pi_2_l);
178 178 LD_IM(ans) = t;
179 179 } else if (E * y - one >= x) { /* region 4 */
180 180 LD_RE(ans) = x / y; /* need to fix underflow cases */
181 181 LD_IM(ans) = ln2 + logl(y);
182 182 } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
183 183 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
184 184 t = x / y;
185 185 LD_RE(ans) = atanl(t);
186 186 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
187 187 } else if (x < Foursqrtu) {
188 188 /* region 6: x is very small, < 4sqrt(min) */
189 189 A = sqrtl(one + y * y);
190 190 LD_RE(ans) = x / A; /* may underflow */
191 191 if (iy >= 0x3fff8000) /* if y > Acrossover */
192 192 LD_IM(ans) = logl(y + A);
193 193 else
194 194 LD_IM(ans) = half * log1pl((y + y) * (y + A));
195 195 } else { /* safe region */
196 196 y2 = y * y;
197 197 xp1 = x + one;
198 198 xm1 = x - one;
199 199 R = sqrtl(xp1 * xp1 + y2);
200 200 S = sqrtl(xm1 * xm1 + y2);
201 201 A = half * (R + S);
202 202 B = x / A;
203 203 if (B <= Bcrossover)
204 204 LD_RE(ans) = asinl(B);
205 205 else { /* use atan and an accurate approx to a-x */
206 206 Apx = A + x;
207 207 if (x <= one)
208 208 LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
209 209 (R + xp1) + (S - xm1))));
210 210 else
211 211 LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
212 212 (R + xp1) + Apx / (S + xm1)))));
213 213 }
214 214 if (A <= Acrossover) {
215 215 /* use log1p and an accurate approx to A-1 */
216 216 if (x < one)
217 217 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
218 218 else
219 219 Am1 = half * (y2 / (R + xp1) + (S + xm1));
220 220 LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
221 221 } else {
222 222 LD_IM(ans) = logl(A + sqrtl(A * A - one));
223 223 }
224 224 }
225 225
226 226 if (hx < 0)
227 227 LD_RE(ans) = -LD_RE(ans);
228 228 if (hy < 0)
229 229 LD_IM(ans) = -LD_IM(ans);
230 230
231 231 return (ans);
232 232 }
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