xref: /titanic_41/usr/src/lib/libm/common/complex/csqrtl.c (revision a9d3dcd5820128b4f34bf38f447e47aa95c004e8)
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 __csqrtl = csqrtl
31 
32 #include "libm.h"		/* fabsl/isinfl/sqrtl */
33 #include "complex_wrapper.h"
34 #include "longdouble.h"
35 
36 /* INDENT OFF */
37 static const long double
38 	twom9001 = 2.6854002716003034957421765100615693043656e-2710L,
39 	twom4500 = 2.3174987687592429423263242862381544149252e-1355L,
40 	two8999 = 9.3095991180122343502582347372163290310934e+2708L,
41 	two4500 = 4.3149968987270974283777803545571722250806e+1354L,
42 	zero = 0.0L,
43 	half = 0.5L,
44 	two = 2.0L;
45 /* INDENT ON */
46 
47 ldcomplex
csqrtl(ldcomplex z)48 csqrtl(ldcomplex z) {
49 	ldcomplex ans;
50 	long double x, y, t, ax, ay;
51 	int n, ix, iy, hx, hy;
52 
53 	x = LD_RE(z);
54 	y = LD_IM(z);
55 	hx = HI_XWORD(x);
56 	hy = HI_XWORD(y);
57 	ix = hx & 0x7fffffff;
58 	iy = hy & 0x7fffffff;
59 	ay = fabsl(y);
60 	ax = fabsl(x);
61 	if (ix >= 0x7fff0000 || iy >= 0x7fff0000) {
62 		/* x or y is Inf or NaN */
63 		if (isinfl(y))
64 			LD_IM(ans) = LD_RE(ans) = ay;
65 		else if (isinfl(x)) {
66 			if (hx > 0) {
67 				LD_RE(ans) = ax;
68 				LD_IM(ans) = ay * zero;
69 			} else {
70 				LD_RE(ans) = ay * zero;
71 				LD_IM(ans) = ax;
72 			}
73 		} else
74 			LD_IM(ans) = LD_RE(ans) = ax + ay;
75 	} else if (y == zero) {
76 		if (hx >= 0) {
77 			LD_RE(ans) = sqrtl(ax);
78 			LD_IM(ans) = zero;
79 		} else {
80 			LD_IM(ans) = sqrtl(ax);
81 			LD_RE(ans) = zero;
82 		}
83 	} else if (ix >= iy) {
84 		n = (ix - iy) >> 16;
85 #if defined(__x86)		/* 64 significant bits */
86 		if (n >= 35)
87 #else				/* 113 significant bits  */
88 		if (n >= 60)
89 #endif
90 			t = sqrtl(ax);
91 		else if (ix >= 0x5f3f0000) {	/* x > 2**8000 */
92 			ax *= twom9001;
93 			y *= twom9001;
94 			t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
95 		} else if (iy <= 0x20bf0000) {	/* y < 2**-8000 */
96 			ax *= two8999;
97 			y *= two8999;
98 			t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
99 		} else
100 			t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
101 
102 		if (hx >= 0) {
103 			LD_RE(ans) = t;
104 			LD_IM(ans) = ay / (t + t);
105 		} else {
106 			LD_IM(ans) = t;
107 			LD_RE(ans) = ay / (t + t);
108 		}
109 	} else {
110 		n = (iy - ix) >> 16;
111 #if defined(__x86)		/* 64 significant bits */
112 		if (n >= 35) {	/* } */
113 #else				/* 113 significant bits  */
114 		if (n >= 60) {
115 #endif
116 			if (n >= 120)
117 				t = sqrtl(half * ay);
118 			else if (iy >= 0x7ffe0000)
119 				t = sqrtl(half * ay + half * ax);
120 			else if (ix <= 0x00010000)
121 				t = half * (sqrtl(two * (ax + ay)));
122 			else
123 				t = sqrtl(half * (ax + ay));
124 		} else if (iy >= 0x5f3f0000) {	/* y > 2**8000 */
125 			ax *= twom9001;
126 			y *= twom9001;
127 			t = two4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
128 		} else if (ix <= 0x20bf0000) {
129 			ax *= two8999;
130 			y *= two8999;
131 			t = twom4500 * sqrtl(ax + sqrtl(ax * ax + y * y));
132 		} else
133 			t = sqrtl(half * (ax + sqrtl(ax * ax + y * y)));
134 
135 		if (hx >= 0) {
136 			LD_RE(ans) = t;
137 			LD_IM(ans) = ay / (t + t);
138 		} else {
139 			LD_IM(ans) = t;
140 			LD_RE(ans) = ay / (t + t);
141 		}
142 	}
143 	if (hy < 0)
144 		LD_IM(ans) = -LD_IM(ans);
145 	return (ans);
146 }
147