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 #pragma ident "%Z%%M% %I% %E% SMI"
28
29 /*
30 * _F_cplx_div(z, w) returns z / w with infinities handled according
31 * to C99.
32 *
33 * If z and w are both finite and w is nonzero, _F_cplx_div(z, w)
34 * delivers the complex quotient q according to the usual formula:
35 * let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
36 * I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
37 * with r = c * c + d * d. This implementation computes intermediate
38 * results in double precision to avoid premature underflow or over-
39 * flow.
40 *
41 * If z is neither NaN nor zero and w is zero, or if z is infinite
42 * and w is finite and nonzero, _F_cplx_div delivers an infinite
43 * result. If z is finite and w is infinite, _F_cplx_div delivers
44 * a zero result.
45 *
46 * If z and w are both zero or both infinite, or if either z or w is
47 * a complex NaN, _F_cplx_div delivers NaN + I * NaN. C99 doesn't
48 * specify these cases.
49 *
50 * This implementation can raise spurious invalid operation, inexact,
51 * and division-by-zero exceptions. C99 allows this.
52 *
53 * Warning: Do not attempt to "optimize" this code by removing multi-
54 * plications by zero.
55 */
56
57 #if !defined(sparc) && !defined(__sparc)
58 #error This code is for SPARC only
59 #endif
60
61 static union {
62 int i[2];
63 double d;
64 } inf = {
65 0x7ff00000, 0
66 };
67
68 /*
69 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
70 */
71 static int
testinff(float x)72 testinff(float x)
73 {
74 union {
75 int i;
76 float f;
77 } xx;
78
79 xx.f = x;
80 return ((((xx.i << 1) - 0xff000000) == 0)? (1 | (xx.i >> 31)) : 0);
81 }
82
83 float _Complex
_F_cplx_div(float _Complex z,float _Complex w)84 _F_cplx_div(float _Complex z, float _Complex w)
85 {
86 float _Complex v;
87 union {
88 int i;
89 float f;
90 } cc, dd;
91 float a, b, c, d;
92 double r, x, y;
93 int i, j, recalc;
94
95 /*
96 * The following is equivalent to
97 *
98 * a = crealf(z); b = cimagf(z);
99 * c = crealf(w); d = cimagf(w);
100 */
101 a = ((float *)&z)[0];
102 b = ((float *)&z)[1];
103 c = ((float *)&w)[0];
104 d = ((float *)&w)[1];
105
106 r = (double)c * c + (double)d * d;
107
108 if (r == 0.0) {
109 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
110 c = 1.0f / c;
111 i = testinff(a);
112 j = testinff(b);
113 if (i | j) { /* z is infinite */
114 a = i;
115 b = j;
116 }
117 ((float *)&v)[0] = a * c + b * d;
118 ((float *)&v)[1] = b * c - a * d;
119 return (v);
120 }
121
122 r = 1.0 / r;
123 x = ((double)a * c + (double)b * d) * r;
124 y = ((double)b * c - (double)a * d) * r;
125
126 if (x != x && y != y) {
127 /*
128 * Both x and y are NaN, so z and w can't both be finite
129 * and nonzero. Since we handled the case w = 0 above,
130 * the only cases to check here are when one of z or w
131 * is infinite.
132 */
133 r = 1.0;
134 recalc = 0;
135 i = testinff(a);
136 j = testinff(b);
137 if (i | j) { /* z is infinite */
138 /* "factor out" infinity */
139 a = i;
140 b = j;
141 r = inf.d;
142 recalc = 1;
143 }
144 i = testinff(c);
145 j = testinff(d);
146 if (i | j) { /* w is infinite */
147 /*
148 * "factor out" infinity, being careful to preserve
149 * signs of finite values
150 */
151 cc.f = c;
152 dd.f = d;
153 c = i? i : ((cc.i < 0)? -0.0f : 0.0f);
154 d = j? j : ((dd.i < 0)? -0.0f : 0.0f);
155 r *= 0.0;
156 recalc = 1;
157 }
158 if (recalc) {
159 x = ((double)a * c + (double)b * d) * r;
160 y = ((double)b * c - (double)a * d) * r;
161 }
162 }
163
164 /*
165 * The following is equivalent to
166 *
167 * return x + I * y;
168 */
169 ((float *)&v)[0] = (float)x;
170 ((float *)&v)[1] = (float)y;
171 return (v);
172 }
173