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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __casinl = casinl
32
33 #include "libm.h" /* asinl/atanl/fabsl/isinfl/log1pl/logl/sqrtl */
34 #include "complex_wrapper.h"
35 #include "longdouble.h"
36
37 /* BEGIN CSTYLED */
38 static const long double zero = 0.0L,
39 one = 1.0L,
40 Acrossover = 1.5L,
41 Bcrossover = 0.6417L,
42 half = 0.5L,
43 ln2 = 6.931471805599453094172321214581765680755e-0001L,
44 Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L, /* 2**-8189 */
45 #if defined(__x86)
46 E = 5.4210108624275221700372640043497085571289e-20L, /* 2**-64 */
47 pi_4 = 0.7853981633974483095739921312272713294078130L,
48 pi_4_l = 4.1668714592604391641479322342670193036704898e-20L,
49 pi_2 = 1.5707963267948966191479842624545426588156260L,
50 pi_2_l = 8.3337429185208783282958644685340386073409796e-20L;
51 #else
52 E = 9.6296497219361792652798897129246365926905e-35L, /* 2**-113 */
53 pi_4 = 0.7853981633974483096156608458198756993697670L,
54 pi_4_l = 2.1679525325309452561992610065108379921905808e-35L,
55 pi_2 = 1.5707963267948966192313216916397513987395340L,
56 pi_2_l = 4.3359050650618905123985220130216759843811616e-35L;
57 #endif
58 /* END CSTYLED */
59
60 #if defined(__x86)
61 static const int ip1 = 0x40400000; /* 2**65 */
62 #else
63 static const int ip1 = 0x40710000; /* 2**114 */
64 #endif
65
66 ldcomplex
67 casinl(ldcomplex z)
68 {
69 long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
70 int ix, iy, hx, hy;
71 ldcomplex ans;
72
73 x = LD_RE(z);
74 y = LD_IM(z);
75 hx = HI_XWORD(x);
76 hy = HI_XWORD(y);
77 ix = hx & 0x7fffffff;
78 iy = hy & 0x7fffffff;
79 x = fabsl(x);
80 y = fabsl(y);
81
82 /* special cases */
83
84 /* x is inf or NaN */
85 if (ix >= 0x7fff0000) { /* x is inf or NaN */
86 if (isinfl(x)) { /* x is INF */
87 LD_IM(ans) = x;
88
89 if (iy >= 0x7fff0000) {
90 if (isinfl(y))
91 /* casin(inf + i inf) = pi/4 + i inf */
92 LD_RE(ans) = pi_4 + pi_4_l;
93 else /* casin(inf + i NaN) = NaN + i inf */
94 LD_RE(ans) = y + y;
95 } else { /* casin(inf + iy) = pi/2 + i inf */
96 LD_RE(ans) = pi_2 + pi_2_l;
97 }
98 } else { /* x is NaN */
99 if (iy >= 0x7fff0000) {
100
101 /*
102 * casin(NaN + i inf) = NaN + i inf
103 * casin(NaN + i NaN) = NaN + i NaN
104 */
105 LD_IM(ans) = y + y;
106 LD_RE(ans) = x + x;
107 } else {
108 /*
109 * casin(NaN + i y ) = NaN + i NaN
110 */
111 LD_IM(ans) = LD_RE(ans) = x + y;
112 }
113 }
114
115 if (hx < 0)
116 LD_RE(ans) = -LD_RE(ans);
117
118 if (hy < 0)
119 LD_IM(ans) = -LD_IM(ans);
120
121 return (ans);
122 }
123
124 /* casin(+0 + i 0) = 0 + i 0. */
125 if (x == zero && y == zero)
126 return (z);
127
128 if (iy >= 0x7fff0000) { /* y is inf or NaN */
129 if (isinfl(y)) { /* casin(x + i inf) = 0 + i inf */
130 LD_IM(ans) = y;
131 LD_RE(ans) = zero;
132 } else { /* casin(x + i NaN) = NaN + i NaN */
133 LD_IM(ans) = x + y;
134
135 if (x == zero)
136 LD_RE(ans) = x;
137 else
138 LD_RE(ans) = y;
139 }
140
141 if (hx < 0)
142 LD_RE(ans) = -LD_RE(ans);
143
144 if (hy < 0)
145 LD_IM(ans) = -LD_IM(ans);
146
147 return (ans);
148 }
149
150 if (y == zero) { /* region 1: y=0 */
151 if (ix < 0x3fff0000) { /* |x| < 1 */
152 LD_RE(ans) = asinl(x);
153 LD_IM(ans) = zero;
154 } else {
155 LD_RE(ans) = pi_2 + pi_2_l;
156
157 if (ix >= ip1) { /* |x| >= i386 ? 2**65 : 2**114 */
158 LD_IM(ans) = ln2 + logl(x);
159 } else if (ix >= 0x3fff8000) { /* x > Acrossover */
160 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
161 one)));
162 } else {
163 xm1 = x - one;
164 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
165 one)));
166 }
167 }
168 } else if (y <= E * fabsl(x - one)) { /* region 2: y < tiny*|x-1| */
169 if (ix < 0x3fff0000) { /* x < 1 */
170 LD_RE(ans) = asinl(x);
171 LD_IM(ans) = y / sqrtl((one + x) * (one - x));
172 } else {
173 LD_RE(ans) = pi_2 + pi_2_l;
174
175 if (ix >= ip1) /* i386 ? 2**65 : 2**114 */
176 LD_IM(ans) = ln2 + logl(x);
177 else if (ix >= 0x3fff8000) /* x > Acrossover */
178 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
179 one)));
180 else
181 LD_IM(ans) = log1pl((x - one) + sqrtl((x -
182 one) * (x + one)));
183 }
184 } else if (y < Foursqrtu) { /* region 3 */
185 t = sqrtl(y);
186 LD_RE(ans) = pi_2 - (t - pi_2_l);
187 LD_IM(ans) = t;
188 } else if (E * y - one >= x) { /* region 4 */
189 LD_RE(ans) = x / y; /* need to fix underflow cases */
190 LD_IM(ans) = ln2 + logl(y);
191 } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
192 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
193 t = x / y;
194 LD_RE(ans) = atanl(t);
195 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
196 } else if (x < Foursqrtu) {
197 /* region 6: x is very small, < 4sqrt(min) */
198 A = sqrtl(one + y * y);
199 LD_RE(ans) = x / A; /* may underflow */
200
201 if (iy >= 0x3fff8000) /* if y > Acrossover */
202 LD_IM(ans) = logl(y + A);
203 else
204 LD_IM(ans) = half * log1pl((y + y) * (y + A));
205 } else { /* safe region */
206 y2 = y * y;
207 xp1 = x + one;
208 xm1 = x - one;
209 R = sqrtl(xp1 * xp1 + y2);
210 S = sqrtl(xm1 * xm1 + y2);
211 A = half * (R + S);
212 B = x / A;
213
214 if (B <= Bcrossover) {
215 LD_RE(ans) = asinl(B);
216 } else { /* use atan and an accurate approx to a-x */
217 Apx = A + x;
218
219 if (x <= one)
220 LD_RE(ans) = atanl(x / sqrtl(half * Apx * (y2 /
221 (R + xp1) + (S - xm1))));
222 else
223 LD_RE(ans) = atanl(x / (y * sqrtl(half * (Apx /
224 (R + xp1) + Apx / (S + xm1)))));
225 }
226
227 if (A <= Acrossover) {
228 /* use log1p and an accurate approx to A-1 */
229 if (x < one)
230 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
231 else
232 Am1 = half * (y2 / (R + xp1) + (S + xm1));
233
234 LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
235 } else {
236 LD_IM(ans) = logl(A + sqrtl(A * A - one));
237 }
238 }
239
240 if (hx < 0)
241 LD_RE(ans) = -LD_RE(ans);
242
243 if (hy < 0)
244 LD_IM(ans) = -LD_IM(ans);
245
246 return (ans);
247 }