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 /*
28 * _D_cplx_div_rx(a, w) returns a / w with infinities handled according
29 * to C99.
30 *
31 * If a and w are both finite and w is nonzero, _D_cplx_div_rx(a, w)
32 * delivers the complex quotient q according to the usual formula:
33 * let c = Re(w), and d = Im(w); then q = x + I * y where x = (a * c)
34 * / r and y = (-a * d) / r with r = c * c + d * d. This implementa-
35 * tion computes intermediate results in extended precision to avoid
36 * premature underflow or overflow.
37 *
38 * If a is neither NaN nor zero and w is zero, or if a is infinite
39 * and w is finite and nonzero, _D_cplx_div_rx delivers an infinite
40 * result. If a is finite and w is infinite, _D_cplx_div_rx delivers
41 * a zero result.
42 *
43 * If a and w are both zero or both infinite, or if either a or w is
44 * NaN, _D_cplx_div_rx delivers NaN + I * NaN. C99 doesn't specify
45 * these cases.
46 *
47 * This implementation can raise spurious invalid operation, inexact,
48 * and division-by-zero exceptions. C99 allows this.
49 *
50 * Warning: Do not attempt to "optimize" this code by removing multi-
51 * plications by zero.
52 */
53
54 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
55 #error This code is for x86 only
56 #endif
57
58 /*
59 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
60 */
61 static int
testinf(double x)62 testinf(double x)
63 {
64 union {
65 int i[2];
66 double d;
67 } xx;
68
69 xx.d = x;
70 return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)?
71 (1 | (xx.i[1] >> 31)) : 0);
72 }
73
74 double _Complex
_D_cplx_div_rx(double a,double _Complex w)75 _D_cplx_div_rx(double a, double _Complex w)
76 {
77 double _Complex v;
78 union {
79 int i[2];
80 double d;
81 } cc, dd;
82 double c, d;
83 long double r, x, y;
84 int i, j;
85
86 /*
87 * The following is equivalent to
88 *
89 * c = creal(w); d = cimag(w);
90 */
91 /* LINTED alignment */
92 c = ((double *)&w)[0];
93 /* LINTED alignment */
94 d = ((double *)&w)[1];
95
96 r = (long double)c * c + (long double)d * d;
97
98 if (r == 0.0f) {
99 /* w is zero; multiply a by 1/Re(w) - I * Im(w) */
100 c = 1.0f / c;
101 i = testinf(a);
102 if (i) { /* a is infinite */
103 a = i;
104 }
105 /* LINTED alignment */
106 ((double *)&v)[0] = a * c;
107 /* LINTED alignment */
108 ((double *)&v)[1] = (a == 0.0f)? a * c : -a * d;
109 return (v);
110 }
111
112 r = (long double)a / r;
113 x = (long double)c * r;
114 y = (long double)-d * r;
115
116 if (x != x || y != y) {
117 /*
118 * x or y is NaN, so a and w can't both be finite and
119 * nonzero. Since we handled the case w = 0 above, the
120 * only case to check here is when w is infinite.
121 */
122 i = testinf(c);
123 j = testinf(d);
124 if (i | j) { /* w is infinite */
125 cc.d = c;
126 dd.d = d;
127 c = (cc.i[1] < 0)? -0.0f : 0.0f;
128 d = (dd.i[1] < 0)? -0.0f : 0.0f;
129 x = (long double)c * a;
130 y = (long double)-d * a;
131 }
132 }
133
134 /*
135 * The following is equivalent to
136 *
137 * return x + I * y;
138 */
139 /* LINTED alignment */
140 ((double *)&v)[0] = (double)x;
141 /* LINTED alignment */
142 ((double *)&v)[1] = (double)y;
143 return (v);
144 }
145