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 __cacosl = cacosl
32
33 #include "libm.h" /* acosl/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 = 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 /* END CSTYLED */
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 {
77 long double x, y, t, R, S, A, Am1, B, y2, xm1, xp1, Apx;
78 int ix, iy, hx, hy;
79 ldcomplex ans;
80
81 x = LD_RE(z);
82 y = LD_IM(z);
83 hx = HI_XWORD(x);
84 hy = HI_XWORD(y);
85 ix = hx & 0x7fffffff;
86 iy = hy & 0x7fffffff;
87
88 /* x is 0 */
89 if (x == zero) {
90 if (y == zero || (iy >= 0x7fff0000)) {
91 LD_RE(ans) = pi_2 + pi_2_l;
92 LD_IM(ans) = -y;
93 return (ans);
94 }
95 }
96
97 /* |y| is inf or NaN */
98 if (iy >= 0x7fff0000) {
99 if (isinfl(y)) { /* cacos(x + i inf) = pi/2 - i inf */
100 LD_IM(ans) = -y;
101
102 if (ix < 0x7fff0000) {
103 LD_RE(ans) = pi_2 + pi_2_l;
104 } else if (isinfl(x)) {
105 if (hx >= 0)
106 LD_RE(ans) = pi_4 + pi_4_l;
107 else
108 LD_RE(ans) = pi3_4 + pi3_4_l;
109 } else {
110 LD_RE(ans) = x;
111 }
112 } else { /* cacos(x + i NaN) = NaN + i NaN */
113 LD_RE(ans) = y + x;
114
115 if (isinfl(x))
116 LD_IM(ans) = -fabsl(x);
117 else
118 LD_IM(ans) = y;
119 }
120
121 return (ans);
122 }
123
124 y = fabsl(y);
125
126 if (ix >= 0x7fff0000) { /* x is inf or NaN */
127 if (isinfl(x)) { /* x is INF */
128 LD_IM(ans) = -fabsl(x);
129
130 if (iy >= 0x7fff0000) {
131 if (isinfl(y)) {
132 /*
133 * cacos(inf + i inf) = pi/4 - i inf
134 * cacos(-inf+ i inf) =3pi/4 - i inf
135 */
136 if (hx >= 0)
137 LD_RE(ans) = pi_4 + pi_4_l;
138 else
139 LD_RE(ans) = pi3_4 + pi3_4_l;
140 } else {
141 /*
142 * cacos(inf + i NaN) = NaN - i inf
143 */
144 LD_RE(ans) = y + y;
145 }
146 } else {
147 /*
148 * cacos(inf + iy ) = 0 - i inf
149 * cacos(-inf+ iy ) = pi - i inf
150 */
151 if (hx >= 0)
152 LD_RE(ans) = zero;
153 else
154 LD_RE(ans) = pi + pi_l;
155 }
156 } else { /* x is NaN */
157
158 /*
159 * cacos(NaN + i inf) = NaN - i inf
160 * cacos(NaN + i y ) = NaN + i NaN
161 * cacos(NaN + i NaN) = NaN + i NaN
162 */
163 LD_RE(ans) = x + y;
164
165 if (iy >= 0x7fff0000)
166 LD_IM(ans) = -y;
167 else
168 LD_IM(ans) = x;
169 }
170
171 if (hy < 0)
172 LD_IM(ans) = -LD_IM(ans);
173
174 return (ans);
175 }
176
177 if (y == zero) { /* region 1: y=0 */
178 if (ix < 0x3fff0000) { /* |x| < 1 */
179 LD_RE(ans) = acosl(x);
180 LD_IM(ans) = zero;
181 } else {
182 LD_RE(ans) = zero;
183 x = fabsl(x);
184
185 if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
186 LD_IM(ans) = ln2 + logl(x);
187 } else if (ix >= 0x3fff8000) { /* x > Acrossover */
188 LD_IM(ans) = logl(x + sqrtl((x - one) * (x +
189 one)));
190 } else {
191 xm1 = x - one;
192 LD_IM(ans) = log1pl(xm1 + sqrtl(xm1 * (x +
193 one)));
194 }
195 }
196 } else if (y <= E * fabsl(fabsl(x) - one)) {
197 /* region 2: y < tiny*||x|-1| */
198 if (ix < 0x3fff0000) { /* x < 1 */
199 LD_RE(ans) = acosl(x);
200 x = fabsl(x);
201 LD_IM(ans) = y / sqrtl((one + x) * (one - x));
202 } else if (ix >= ip1) { /* i386 ? 2**65 : 2**114 */
203 if (hx >= 0) {
204 LD_RE(ans) = y / x;
205 } else {
206 if (ix >= ip1 + 0x00040000) {
207 LD_RE(ans) = pi + pi_l;
208 } else {
209 t = pi_l + y / x;
210 LD_RE(ans) = pi + t;
211 }
212 }
213
214 LD_IM(ans) = ln2 + logl(fabsl(x));
215 } else {
216 x = fabsl(x);
217 t = sqrtl((x - one) * (x + one));
218 LD_RE(ans) = (hx >= 0) ? y / t : pi - (y / t - pi_l);
219
220 if (ix >= 0x3fff8000) /* x > Acrossover */
221 LD_IM(ans) = logl(x + t);
222 else
223 LD_IM(ans) = log1pl(t - (one - x));
224 }
225 } else if (y < Foursqrtu) { /* region 3 */
226 t = sqrtl(y);
227 LD_RE(ans) = (hx >= 0) ? t : pi + pi_l;
228 LD_IM(ans) = t;
229 } else if (E * y - one >= fabsl(x)) { /* region 4 */
230 LD_RE(ans) = pi_2 + pi_2_l;
231 LD_IM(ans) = ln2 + logl(y);
232 } else if (ix >= 0x5ffb0000 || iy >= 0x5ffb0000) {
233 /* region 5: x+1 and y are both (>= sqrt(max)/8) i.e. 2**8188 */
234 t = x / y;
235 LD_RE(ans) = atan2l(y, x);
236 LD_IM(ans) = ln2 + logl(y) + half * log1pl(t * t);
237 } else if (fabsl(x) < Foursqrtu) {
238 /* region 6: x is very small, < 4sqrt(min) */
239 LD_RE(ans) = pi_2 + pi_2_l;
240 A = sqrtl(one + y * y);
241
242 if (iy >= 0x3fff8000) /* if y > Acrossover */
243 LD_IM(ans) = logl(y + A);
244 else
245 LD_IM(ans) = half * log1pl((y + y) * (y + A));
246 } else { /* safe region */
247 t = fabsl(x);
248 y2 = y * y;
249 xp1 = t + one;
250 xm1 = t - one;
251 R = sqrtl(xp1 * xp1 + y2);
252 S = sqrtl(xm1 * xm1 + y2);
253 A = half * (R + S);
254 B = t / A;
255
256 if (B <= Bcrossover) {
257 LD_RE(ans) = (hx >= 0) ? acosl(B) : acosl(-B);
258 } else { /* use atan and an accurate approx to a-x */
259 Apx = A + t;
260
261 if (t <= one)
262 LD_RE(ans) = atan2l(sqrtl(half * Apx * (y2 /
263 (R + xp1) + (S - xm1))), x);
264 else
265 LD_RE(ans) = atan2l((y * sqrtl(half * (Apx /
266 (R + xp1) + Apx / (S + xm1)))), x);
267 }
268
269 if (A <= Acrossover) {
270 /* use log1p and an accurate approx to A-1 */
271 if (ix < 0x3fff0000)
272 Am1 = half * (y2 / (R + xp1) + y2 / (S - xm1));
273 else
274 Am1 = half * (y2 / (R + xp1) + (S + xm1));
275
276 LD_IM(ans) = log1pl(Am1 + sqrtl(Am1 * (A + one)));
277 } else {
278 LD_IM(ans) = logl(A + sqrtl(A * A - one));
279 }
280 }
281
282 if (hy >= 0)
283 LD_IM(ans) = -LD_IM(ans);
284
285 return (ans);
286 }