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 */
37static const long double
38zero = 0.0L,
39one = 1.0L,
40Acrossover = 1.5L,
41Bcrossover = 0.6417L,
42half = 0.5L,
43ln2 = 6.931471805599453094172321214581765680755e-0001L,
44Foursqrtu = 7.3344154702193886624856495681939326638255e-2466L,	/* 2**-8189 */
45#if defined(__x86)
46E = 5.4210108624275221700372640043497085571289e-20L,		/* 2**-64 */
47pi = 3.141592653589793238295968524909085317631252110004425048828125L,
48pi_l = 1.666748583704175665659172893706807721468195923078e-19L,
49pi_2 = 1.5707963267948966191479842624545426588156260L,
50pi_2_l = 8.3337429185208783282958644685340386073409796e-20L,
51pi_4 = 0.78539816339744830957399213122727132940781302750110626220703125L,
52pi_4_l = 4.166871459260439164147932234267019303670489807695410e-20L,
53pi3_4 = 2.35619449019234492872197639368181398822343908250331878662109375L,
54pi3_4_l = 1.250061437778131749244379670280105791101146942308e-19L;
55#else
56E = 9.6296497219361792652798897129246365926905e-35L,		/* 2**-113 */
57pi = 3.1415926535897932384626433832795027974790680981372955730045043318L,
58pi_l = 8.6718101301237810247970440260433519687623233462565303417759356862e-35L,
59pi_2 = 1.5707963267948966192313216916397513987395340L,
60pi_2_l = 4.3359050650618905123985220130216759843811616e-35L,
61pi_4 = 0.785398163397448309615660845819875699369767024534323893251126L,
62pi_4_l = 2.167952532530945256199261006510837992190580836564132585443e-35L,
63pi3_4 = 2.35619449019234492884698253745962709810930107360297167975337824L,
64pi3_4_l = 6.503857597592835768597783019532513976571742509692397756331e-35L;
65#endif
66/* INDENT ON */
67
68#if defined(__x86)
69static const int ip1 = 0x40400000;	/* 2**65 */
70#else
71static const int ip1 = 0x40710000;	/* 2**114 */
72#endif
73
74ldcomplex
75cacosl(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}
273