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_mul(z, w) returns z * w with infinities handled according
31 * to C99.
32 *
33 * If z and w are both finite, _D_cplx_mul(z, w) delivers the complex
34 * product according to the usual formula: let a = Re(z), b = Im(z),
35 * c = Re(w), and d = Im(w); then _D_cplx_mul(z, w) delivers x + I * y
36 * where x = a * c - b * d and y = a * d + b * c. This implementation
37 * uses extended precision to form these expressions, so none of the
38 * intermediate products can overflow.
39 *
40 * If one of z or w is infinite and the other is either finite nonzero
41 * or infinite, _D_cplx_mul delivers an infinite result. If one factor
42 * is infinite and the other is zero, _D_cplx_mul delivers NaN + I * NaN.
43 * C99 doesn't specify the latter case.
44 *
45 * C99 also doesn't specify what should happen if either z or w is a
46 * complex NaN (i.e., neither finite nor infinite). This implementation
47 * delivers NaN + I * NaN in this case.
48 *
49 * This implementation can raise spurious invalid operation and inexact
50 * exceptions. C99 allows this.
51 */
52
53 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
54 #error This code is for x86 only
55 #endif
56
57 static union {
58 int i;
59 float f;
60 } inf = {
61 0x7f800000
62 };
63
64 /*
65 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
66 */
67 static int
testinf(double x)68 testinf(double x)
69 {
70 union {
71 int i[2];
72 double d;
73 } xx;
74
75 xx.d = x;
76 return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)?
77 (1 | (xx.i[1] >> 31)) : 0);
78 }
79
80 double _Complex
_D_cplx_mul(double _Complex z,double _Complex w)81 _D_cplx_mul(double _Complex z, double _Complex w)
82 {
83 double _Complex v;
84 double a, b, c, d;
85 long double x, y;
86 int recalc, i, j;
87
88 /*
89 * The following is equivalent to
90 *
91 * a = creal(z); b = cimag(z);
92 * c = creal(w); d = cimag(w);
93 */
94 /* LINTED alignment */
95 a = ((double *)&z)[0];
96 /* LINTED alignment */
97 b = ((double *)&z)[1];
98 /* LINTED alignment */
99 c = ((double *)&w)[0];
100 /* LINTED alignment */
101 d = ((double *)&w)[1];
102
103 x = (long double)a * c - (long double)b * d;
104 y = (long double)a * d + (long double)b * c;
105
106 if (x != x && y != y) {
107 /*
108 * Both x and y are NaN, so z and w can't both be finite.
109 * If at least one of z or w is a complex NaN, and neither
110 * is infinite, then we might as well deliver NaN + I * NaN.
111 * So the only cases to check are when one of z or w is
112 * infinite.
113 */
114 recalc = 0;
115 i = testinf(a);
116 j = testinf(b);
117 if (i | j) { /* z is infinite */
118 /* "factor out" infinity */
119 a = i;
120 b = j;
121 recalc = 1;
122 }
123 i = testinf(c);
124 j = testinf(d);
125 if (i | j) { /* w is infinite */
126 /* "factor out" infinity */
127 c = i;
128 d = j;
129 recalc = 1;
130 }
131 if (recalc) {
132 x = inf.f * ((long double)a * c - (long double)b * d);
133 y = inf.f * ((long double)a * d + (long double)b * c);
134 }
135 }
136
137 /*
138 * The following is equivalent to
139 *
140 * return x + I * y;
141 */
142 /* LINTED alignment */
143 ((double *)&v)[0] = (double)x;
144 /* LINTED alignment */
145 ((double *)&v)[1] = (double)y;
146 return (v);
147 }
148