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 2003 Sun Microsystems, Inc. All rights reserved.
24 * Use is subject to license terms.
25 */
26
27 /*
28 * _F_cplx_div(z, w) returns z / w with infinities handled according
29 * to C99.
30 *
31 * If z and w are both finite and w is nonzero, _F_cplx_div(z, w)
32 * delivers the complex quotient q according to the usual formula:
33 * let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
34 * I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
35 * with r = c * c + d * d. This implementation computes intermediate
36 * results in double precision to avoid premature underflow or over-
37 * flow.
38 *
39 * If z is neither NaN nor zero and w is zero, or if z is infinite
40 * and w is finite and nonzero, _F_cplx_div delivers an infinite
41 * result. If z is finite and w is infinite, _F_cplx_div delivers
42 * a zero result.
43 *
44 * If z and w are both zero or both infinite, or if either z or w is
45 * a complex NaN, _F_cplx_div delivers NaN + I * NaN. C99 doesn't
46 * specify these cases.
47 *
48 * This implementation can raise spurious invalid operation, inexact,
49 * and division-by-zero exceptions. C99 allows this.
50 *
51 * Warning: Do not attempt to "optimize" this code by removing multi-
52 * plications by zero.
53 */
54
55 #if !defined(sparc) && !defined(__sparc)
56 #error This code is for SPARC only
57 #endif
58
59 static union {
60 int i[2];
61 double d;
62 } inf = {
63 0x7ff00000, 0
64 };
65
66 /*
67 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
68 */
69 static int
testinff(float x)70 testinff(float x)
71 {
72 union {
73 int i;
74 float f;
75 } xx;
76
77 xx.f = x;
78 return ((((xx.i << 1) - 0xff000000) == 0)? (1 | (xx.i >> 31)) : 0);
79 }
80
81 float _Complex
_F_cplx_div(float _Complex z,float _Complex w)82 _F_cplx_div(float _Complex z, float _Complex w)
83 {
84 float _Complex v;
85 union {
86 int i;
87 float f;
88 } cc, dd;
89 float a, b, c, d;
90 double r, x, y;
91 int i, j, recalc;
92
93 /*
94 * The following is equivalent to
95 *
96 * a = crealf(z); b = cimagf(z);
97 * c = crealf(w); d = cimagf(w);
98 */
99 a = ((float *)&z)[0];
100 b = ((float *)&z)[1];
101 c = ((float *)&w)[0];
102 d = ((float *)&w)[1];
103
104 r = (double)c * c + (double)d * d;
105
106 if (r == 0.0) {
107 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
108 c = 1.0f / c;
109 i = testinff(a);
110 j = testinff(b);
111 if (i | j) { /* z is infinite */
112 a = i;
113 b = j;
114 }
115 ((float *)&v)[0] = a * c + b * d;
116 ((float *)&v)[1] = b * c - a * d;
117 return (v);
118 }
119
120 r = 1.0 / r;
121 x = ((double)a * c + (double)b * d) * r;
122 y = ((double)b * c - (double)a * d) * r;
123
124 if (x != x && y != y) {
125 /*
126 * Both x and y are NaN, so z and w can't both be finite
127 * and nonzero. Since we handled the case w = 0 above,
128 * the only cases to check here are when one of z or w
129 * is infinite.
130 */
131 r = 1.0;
132 recalc = 0;
133 i = testinff(a);
134 j = testinff(b);
135 if (i | j) { /* z is infinite */
136 /* "factor out" infinity */
137 a = i;
138 b = j;
139 r = inf.d;
140 recalc = 1;
141 }
142 i = testinff(c);
143 j = testinff(d);
144 if (i | j) { /* w is infinite */
145 /*
146 * "factor out" infinity, being careful to preserve
147 * signs of finite values
148 */
149 cc.f = c;
150 dd.f = d;
151 c = i? i : ((cc.i < 0)? -0.0f : 0.0f);
152 d = j? j : ((dd.i < 0)? -0.0f : 0.0f);
153 r *= 0.0;
154 recalc = 1;
155 }
156 if (recalc) {
157 x = ((double)a * c + (double)b * d) * r;
158 y = ((double)b * c - (double)a * d) * r;
159 }
160 }
161
162 /*
163 * The following is equivalent to
164 *
165 * return x + I * y;
166 */
167 ((float *)&v)[0] = (float)x;
168 ((float *)&v)[1] = (float)y;
169 return (v);
170 }
171