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 * _X_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, _X_cplx_div delivers
32 * the complex quotient q according to the usual formula: let a =
33 * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
34 * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
35 * r = c * c + d * d. This implementation scales to avoid premature
36 * underflow or overflow.
37 *
38 * If z is neither NaN nor zero and w is zero, or if z is infinite
39 * and w is finite and nonzero, _X_cplx_div delivers an infinite
40 * result. If z is finite and w is infinite, _X_cplx_div delivers
41 * a zero result.
42 *
43 * If z and w are both zero or both infinite, or if either z or w is
44 * a complex NaN, _X_cplx_div delivers NaN + I * NaN. C99 doesn't
45 * specify these cases.
46 *
47 * This implementation can raise spurious underflow, overflow, in-
48 * valid operation, inexact, and division-by-zero exceptions. C99
49 * allows this.
50 */
51
52 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
53 #error This code is for x86 only
54 #endif
55
56 static union {
57 int i;
58 float f;
59 } inf = {
60 0x7f800000
61 };
62
63 /*
64 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
65 */
66 static int
testinfl(long double x)67 testinfl(long double x)
68 {
69 union {
70 int i[3];
71 long double e;
72 } xx;
73
74 xx.e = x;
75 if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
76 return (0);
77 return (1 | ((xx.i[2] << 16) >> 31));
78 }
79
80 long double _Complex
_X_cplx_div(long double _Complex z,long double _Complex w)81 _X_cplx_div(long double _Complex z, long double _Complex w)
82 {
83 long double _Complex v;
84 union {
85 int i[3];
86 long double e;
87 } aa, bb, cc, dd, ss;
88 long double a, b, c, d, r;
89 int ea, eb, ec, ed, ez, ew, es, i, j;
90
91 /*
92 * The following is equivalent to
93 *
94 * a = creall(*z); b = cimagl(*z);
95 * c = creall(*w); d = cimagl(*w);
96 */
97 a = ((long double *)&z)[0];
98 b = ((long double *)&z)[1];
99 c = ((long double *)&w)[0];
100 d = ((long double *)&w)[1];
101
102 /* extract exponents to estimate |z| and |w| */
103 aa.e = a;
104 bb.e = b;
105 ea = aa.i[2] & 0x7fff;
106 eb = bb.i[2] & 0x7fff;
107 ez = (ea > eb)? ea : eb;
108
109 cc.e = c;
110 dd.e = d;
111 ec = cc.i[2] & 0x7fff;
112 ed = dd.i[2] & 0x7fff;
113 ew = (ec > ed)? ec : ed;
114
115 /* check for special cases */
116 if (ew >= 0x7fff) { /* w is inf or nan */
117 r = 0.0f;
118 i = testinfl(c);
119 j = testinfl(d);
120 if (i | j) { /* w is infinite */
121 /*
122 * "factor out" infinity, being careful to preserve
123 * signs of finite values
124 */
125 c = i? i : (((cc.i[2] << 16) < 0)? -0.0f : 0.0f);
126 d = j? j : (((dd.i[2] << 16) < 0)? -0.0f : 0.0f);
127 if (ez >= 0x7ffe) {
128 /* scale to avoid overflow below */
129 c *= 0.5f;
130 d *= 0.5f;
131 }
132 }
133 ((long double *)&v)[0] = (a * c + b * d) * r;
134 ((long double *)&v)[1] = (b * c - a * d) * r;
135 return (v);
136 }
137
138 if (ew == 0 && (cc.i[1] | cc.i[0] | dd.i[1] | dd.i[0]) == 0) {
139 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
140 c = 1.0f / c;
141 i = testinfl(a);
142 j = testinfl(b);
143 if (i | j) { /* z is infinite */
144 a = i;
145 b = j;
146 }
147 ((long double *)&v)[0] = a * c + b * d;
148 ((long double *)&v)[1] = b * c - a * d;
149 return (v);
150 }
151
152 if (ez >= 0x7fff) { /* z is inf or nan */
153 i = testinfl(a);
154 j = testinfl(b);
155 if (i | j) { /* z is infinite */
156 a = i;
157 b = j;
158 r = inf.f;
159 }
160 ((long double *)&v)[0] = a * c + b * d;
161 ((long double *)&v)[1] = b * c - a * d;
162 return (v);
163 }
164
165 /*
166 * Scale c and d to compute 1/|w|^2 and the real and imaginary
167 * parts of the quotient.
168 */
169 es = ((ew >> 2) - ew) + 0x6ffd;
170 if (ez < 0x0086) { /* |z| < 2^-16249 */
171 if (((ew - 0x3efe) | (0x4083 - ew)) >= 0)
172 es = ((0x4083 - ew) >> 1) + 0x3fff;
173 }
174 ss.i[2] = es;
175 ss.i[1] = 0x80000000;
176 ss.i[0] = 0;
177
178 c *= ss.e;
179 d *= ss.e;
180 r = 1.0f / (c * c + d * d);
181
182 c *= ss.e;
183 d *= ss.e;
184
185 ((long double *)&v)[0] = (a * c + b * d) * r;
186 ((long double *)&v)[1] = (b * c - a * d) * r;
187 return (v);
188 }
189