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