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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak cabs = __cabs
30
31 #include "libm_synonyms.h"
32 #include <math.h>
33 #include "complex_wrapper.h"
34
35 /*
36 * If C were the only standard we cared about, cabs could just call
37 * hypot. Unfortunately, various other standards say that hypot must
38 * call matherr and/or set errno to ERANGE when the result overflows.
39 * Since cabs should do neither of these things, we have to either
40 * make hypot a wrapper on another internal function or duplicate
41 * the hypot implementation here. I've chosen to do the latter.
42 */
43
44 static const double
45 zero = 0.0,
46 onep1u = 1.00000000000000022204e+00, /* 0x3ff00000 1 = 1+2**-52 */
47 twom53 = 1.11022302462515654042e-16, /* 0x3ca00000 0 = 2**-53 */
48 twom768 = 6.441148769597133308e-232, /* 2^-768 */
49 two768 = 1.552518092300708935e+231; /* 2^768 */
50
51 double
52 cabs(dcomplex z)
53 {
54 double x, y, xh, yh, w, ax, ay;
55 int i, j, nx, ny, ix, iy, iscale = 0;
56 unsigned lx, ly;
57
58 x = D_RE(z);
59 y = D_IM(z);
60
61 ix = ((int *)&x)[HIWORD] & ~0x80000000;
62 lx = ((int *)&x)[LOWORD];
63 iy = ((int *)&y)[HIWORD] & ~0x80000000;
64 ly = ((int *)&y)[LOWORD];
65
66 /* force ax = |x| ~>~ ay = |y| */
67 if (iy > ix) {
68 ax = fabs(y);
69 ay = fabs(x);
70 i = ix;
71 ix = iy;
72 iy = i;
73 i = lx;
74 lx = ly;
75 ly = i;
76 } else {
77 ax = fabs(x);
78 ay = fabs(y);
79 }
80 nx = ix >> 20;
81 ny = iy >> 20;
82 j = nx - ny;
83
84 if (nx >= 0x5f3) {
85 /* x >= 2^500 (x*x or y*y may overflow) */
86 if (nx == 0x7ff) {
87 /* inf or NaN, signal of sNaN */
88 if (((ix - 0x7ff00000) | lx) == 0)
89 return ((ax == ay)? ay : ax);
90 else if (((iy - 0x7ff00000) | ly) == 0)
91 return ((ay == ax)? ax : ay);
92 else
93 return (ax * ay);
94 } else if (j > 32) {
95 /* x >> y */
96 if (j <= 53)
97 ay *= twom53;
98 ax += ay;
99 return (ax);
100 }
101 ax *= twom768;
102 ay *= twom768;
103 iscale = 2;
104 ix -= 768 << 20;
105 iy -= 768 << 20;
106 } else if (ny < 0x23d) {
107 /* y < 2^-450 (x*x or y*y may underflow) */
108 if ((ix | lx) == 0)
109 return (ay);
110 if ((iy | ly) == 0)
111 return (ax);
112 if (j > 53) /* x >> y */
113 return (ax + ay);
114 iscale = 1;
115 ax *= two768;
116 ay *= two768;
117 if (nx == 0) {
118 if (ax == zero) /* guard subnormal flush to zero */
119 return (ax);
120 ix = ((int *)&ax)[HIWORD];
121 } else {
122 ix += 768 << 20;
123 }
124 if (ny == 0) {
125 if (ay == zero) /* guard subnormal flush to zero */
126 return (ax * twom768);
127 iy = ((int *)&ay)[HIWORD];
128 } else {
129 iy += 768 << 20;
130 }
131 j = (ix >> 20) - (iy >> 20);
132 if (j > 32) {
133 /* x >> y */
134 if (j <= 53)
135 ay *= twom53;
136 return ((ax + ay) * twom768);
137 }
138 } else if (j > 32) {
139 /* x >> y */
140 if (j <= 53)
141 ay *= twom53;
142 return (ax + ay);
143 }
144
145 /*
146 * Medium range ax and ay with max{|ax/ay|,|ay/ax|} bounded by 2^32.
147 * First check rounding mode by comparing onep1u*onep1u with onep1u
148 * + twom53. Make sure the computation is done at run-time.
149 */
150 if (((lx | ly) << 5) == 0) {
151 ay = ay * ay;
152 ax += ay / (ax + sqrt(ax * ax + ay));
153 } else if (onep1u * onep1u != onep1u + twom53) {
154 /* round-to-zero, positive, negative mode */
155 /* magic formula with less than an ulp error */
156 w = sqrt(ax * ax + ay * ay);
157 ax += ay / ((ax + w) / ay);
158 } else {
159 /* round-to-nearest mode */
160 w = ax - ay;
161 if (w > ay) {
162 ((int *)&xh)[HIWORD] = ix;
163 ((int *)&xh)[LOWORD] = 0;
164 ay = ay * ay + (ax - xh) * (ax + xh);
165 ax = sqrt(xh * xh + ay);
166 } else {
167 ax = ax + ax;
168 ((int *)&xh)[HIWORD] = ix + 0x00100000;
169 ((int *)&xh)[LOWORD] = 0;
170 ((int *)&yh)[HIWORD] = iy;
171 ((int *)&yh)[LOWORD] = 0;
172 ay = w * w + ((ax - xh) * yh + (ay - yh) * ax);
173 ax = sqrt(xh * yh + ay);
174 }
175 }
176 if (iscale > 0) {
177 if (iscale == 1)
178 ax *= twom768;
179 else
180 ax *= two768; /* must generate side effect here */
181 }
182 return (ax);
183 }