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