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, Version 1.0 only
6 * (the "License"). You may not use this file except in compliance
7 * with the License.
8 *
9 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
10 * or http://www.opensolaris.org/os/licensing.
11 * See the License for the specific language governing permissions
12 * and limitations under the License.
13 *
14 * When distributing Covered Code, include this CDDL HEADER in each
15 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
16 * If applicable, add the following below this CDDL HEADER, with the
17 * fields enclosed by brackets "[]" replaced with your own identifying
18 * information: Portions Copyright [yyyy] [name of copyright owner]
19 *
20 * CDDL HEADER END
21 */
22 /*
23 * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
24 * Use is subject to license terms.
25 */
26
27 #pragma ident "%Z%%M% %I% %E% SMI"
28
29 /*
30 * _D_cplx_div_ix(b, w) returns (I * b) / w with infinities handled
31 * according to C99.
32 *
33 * If b and w are both finite and w is nonzero, _D_cplx_div_ix(b, w)
34 * delivers the complex quotient q according to the usual formula:
35 * let c = Re(w), and d = Im(w); then q = x + I * y where x = (b * d)
36 * / r and y = (b * c) / r with r = c * c + d * d. This implementa-
37 * tion computes intermediate results in extended precision to avoid
38 * premature underflow or overflow.
39 *
40 * If b is neither NaN nor zero and w is zero, or if b is infinite
41 * and w is finite and nonzero, _D_cplx_div_ix delivers an infinite
42 * result. If b is finite and w is infinite, _D_cplx_div_ix delivers
43 * a zero result.
44 *
45 * If b and w are both zero or both infinite, or if either b or w is
46 * NaN, _D_cplx_div_ix delivers NaN + I * NaN. C99 doesn't specify
47 * these cases.
48 *
49 * This implementation can raise spurious invalid operation, inexact,
50 * and division-by-zero exceptions. C99 allows this.
51 *
52 * Warning: Do not attempt to "optimize" this code by removing multi-
53 * plications by zero.
54 */
55
56 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
57 #error This code is for x86 only
58 #endif
59
60 /*
61 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
62 */
63 static int
testinf(double x)64 testinf(double x)
65 {
66 union {
67 int i[2];
68 double d;
69 } xx;
70
71 xx.d = x;
72 return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)?
73 (1 | (xx.i[1] >> 31)) : 0);
74 }
75
76 double _Complex
_D_cplx_div_ix(double b,double _Complex w)77 _D_cplx_div_ix(double b, double _Complex w)
78 {
79 double _Complex v;
80 union {
81 int i[2];
82 double d;
83 } cc, dd;
84 double c, d;
85 long double r, x, y;
86 int i, j;
87
88 /*
89 * The following is equivalent to
90 *
91 * c = creal(w); d = cimag(w);
92 */
93 /* LINTED alignment */
94 c = ((double *)&w)[0];
95 /* LINTED alignment */
96 d = ((double *)&w)[1];
97
98 r = (long double)c * c + (long double)d * d;
99
100 if (r == 0.0f) {
101 /* w is zero; multiply b by 1/Re(w) - I * Im(w) */
102 c = 1.0f / c;
103 j = testinf(b);
104 if (j) { /* b is infinite */
105 b = j;
106 }
107 /* LINTED alignment */
108 ((double *)&v)[0] = (b == 0.0f)? b * c : b * d;
109 /* LINTED alignment */
110 ((double *)&v)[1] = b * c;
111 return (v);
112 }
113
114 r = (long double)b / r;
115 x = (long double)d * r;
116 y = (long double)c * r;
117
118 if (x != x || y != y) {
119 /*
120 * x or y is NaN, so b and w can't both be finite and
121 * nonzero. Since we handled the case w = 0 above, the
122 * only case to check here is when w is infinite.
123 */
124 i = testinf(c);
125 j = testinf(d);
126 if (i | j) { /* w is infinite */
127 cc.d = c;
128 dd.d = d;
129 c = (cc.i[1] < 0)? -0.0f : 0.0f;
130 d = (dd.i[1] < 0)? -0.0f : 0.0f;
131 x = (long double)d * b;
132 y = (long double)c * b;
133 }
134 }
135
136 /*
137 * The following is equivalent to
138 *
139 * return x + I * y;
140 */
141 /* LINTED alignment */
142 ((double *)&v)[0] = (double)x;
143 /* LINTED alignment */
144 ((double *)&v)[1] = (double)y;
145 return (v);
146 }
147