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 * _F_cplx_mul(z, w) returns z * w with infinities handled according
29 * to C99.
30 *
31 * If z and w are both finite, _F_cplx_mul(z, w) delivers the complex
32 * product according to the usual formula: let a = Re(z), b = Im(z),
33 * c = Re(w), and d = Im(w); then _F_cplx_mul(z, w) delivers x + I * y
34 * where x = a * c - b * d and y = a * d + b * c. This implementation
35 * uses extended precision to form these expressions, so none of the
36 * intermediate products can overflow.
37 *
38 * If one of z or w is infinite and the other is either finite nonzero
39 * or infinite, _F_cplx_mul delivers an infinite result. If one factor
40 * is infinite and the other is zero, _F_cplx_mul delivers NaN + I * NaN.
41 * C99 doesn't specify the latter case.
42 *
43 * C99 also doesn't specify what should happen if either z or w is a
44 * complex NaN (i.e., neither finite nor infinite). This implementation
45 * delivers NaN + I * NaN in this case.
46 *
47 * This implementation can raise spurious invalid operation and inexact
48 * exceptions. C99 allows this.
49 */
50
51 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
52 #error This code is for x86 only
53 #endif
54
55 static union {
56 int i;
57 float f;
58 } inf = {
59 0x7f800000
60 };
61
62 /*
63 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
64 */
65 static int
testinff(float x)66 testinff(float x)
67 {
68 union {
69 int i;
70 float f;
71 } xx;
72
73 xx.f = x;
74 return ((((xx.i << 1) - 0xff000000) == 0)? (1 | (xx.i >> 31)) : 0);
75 }
76
77 float _Complex
_F_cplx_mul(float _Complex z,float _Complex w)78 _F_cplx_mul(float _Complex z, float _Complex w)
79 {
80 float _Complex v = 0;
81 float a, b, c, d;
82 long double x, y;
83 int recalc, i, j;
84
85 /*
86 * The following is equivalent to
87 *
88 * a = crealf(z); b = cimagf(z);
89 * c = crealf(w); d = cimagf(w);
90 */
91 a = ((float *)&z)[0];
92 b = ((float *)&z)[1];
93 c = ((float *)&w)[0];
94 d = ((float *)&w)[1];
95
96 x = (long double)a * c - (long double)b * d;
97 y = (long double)a * d + (long double)b * c;
98
99 if (x != x && y != y) {
100 /*
101 * Both x and y are NaN, so z and w can't both be finite.
102 * If at least one of z or w is a complex NaN, and neither
103 * is infinite, then we might as well deliver NaN + I * NaN.
104 * So the only cases to check are when one of z or w is
105 * infinite.
106 */
107 recalc = 0;
108 i = testinff(a);
109 j = testinff(b);
110 if (i | j) { /* z is infinite */
111 /* "factor out" infinity */
112 a = i;
113 b = j;
114 recalc = 1;
115 }
116 i = testinff(c);
117 j = testinff(d);
118 if (i | j) { /* w is infinite */
119 /* "factor out" infinity */
120 c = i;
121 d = j;
122 recalc = 1;
123 }
124 if (recalc) {
125 x = inf.f * ((long double)a * c - (long double)b * d);
126 y = inf.f * ((long double)a * d + (long double)b * c);
127 }
128 }
129
130 /*
131 * The following is equivalent to
132 *
133 * return x + I * y;
134 */
135 ((float *)&v)[0] = (float)x;
136 ((float *)&v)[1] = (float)y;
137 return (v);
138 }
139