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 * _X_cplx_div_ix(b, w) returns (I * b) / w with infinities handled
31 * according to C99.
32 *
33 * If b and w are both finite and w is nonzero, _X_cplx_div_ix de-
34 * livers the complex quotient q according to the usual formula: let
35 * c = Re(w), and d = Im(w); then q = x + I * y where x = (b * d) / r
36 * and y = (b * c) / r with r = c * c + d * d. This implementation
37 * scales to avoid premature underflow or overflow.
38 *
39 * If b is neither NaN nor zero and w is zero, or if b is infinite
40 * and w is finite and nonzero, _X_cplx_div_ix delivers an infinite
41 * result. If b is finite and w is infinite, _X_cplx_div_ix delivers
42 * a zero result.
43 *
44 * If b and w are both zero or both infinite, or if either b or w is
45 * NaN, _X_cplx_div_ix delivers NaN + I * NaN. C99 doesn't specify
46 * these cases.
47 *
48 * This implementation can raise spurious underflow, overflow, in-
49 * valid operation, inexact, and division-by-zero exceptions. C99
50 * allows this.
51 */
52
53 #if !defined(i386) && !defined(__i386) && !defined(__amd64)
54 #error This code is for x86 only
55 #endif
56
57 /*
58 * scl[i].e = 2^(4080*(4-i)) for i = 0, ..., 9
59 */
60 static const union {
61 unsigned int i[3];
62 long double e;
63 } scl[9] = {
64 { 0, 0x80000000, 0x7fbf },
65 { 0, 0x80000000, 0x6fcf },
66 { 0, 0x80000000, 0x5fdf },
67 { 0, 0x80000000, 0x4fef },
68 { 0, 0x80000000, 0x3fff },
69 { 0, 0x80000000, 0x300f },
70 { 0, 0x80000000, 0x201f },
71 { 0, 0x80000000, 0x102f },
72 { 0, 0x80000000, 0x003f }
73 };
74
75 /*
76 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
77 */
78 static int
testinfl(long double x)79 testinfl(long double x)
80 {
81 union {
82 int i[3];
83 long double e;
84 } xx;
85
86 xx.e = x;
87 if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
88 return (0);
89 return (1 | ((xx.i[2] << 16) >> 31));
90 }
91
92 long double _Complex
_X_cplx_div_ix(long double b,long double _Complex w)93 _X_cplx_div_ix(long double b, long double _Complex w)
94 {
95 long double _Complex v;
96 union {
97 int i[3];
98 long double e;
99 } bb, cc, dd;
100 long double c, d, sc, sd, r;
101 int eb, ec, ed, ew, i, j;
102
103 /*
104 * The following is equivalent to
105 *
106 * c = creall(*w); d = cimagl(*w);
107 */
108 c = ((long double *)&w)[0];
109 d = ((long double *)&w)[1];
110
111 /* extract exponents to estimate |z| and |w| */
112 bb.e = b;
113 eb = bb.i[2] & 0x7fff;
114
115 cc.e = c;
116 dd.e = d;
117 ec = cc.i[2] & 0x7fff;
118 ed = dd.i[2] & 0x7fff;
119 ew = (ec > ed)? ec : ed;
120
121 /* check for special cases */
122 if (ew >= 0x7fff) { /* w is inf or nan */
123 i = testinfl(c);
124 j = testinfl(d);
125 if (i | j) { /* w is infinite */
126 c = ((cc.i[2] << 16) < 0)? -0.0f : 0.0f;
127 d = ((dd.i[2] << 16) < 0)? -0.0f : 0.0f;
128 } else /* w is nan */
129 b += c + d;
130 ((long double *)&v)[0] = b * d;
131 ((long double *)&v)[1] = b * c;
132 return (v);
133 }
134
135 if (ew == 0 && (cc.i[1] | cc.i[0] | dd.i[1] | dd.i[0]) == 0) {
136 /* w is zero; multiply b by 1/Re(w) - I * Im(w) */
137 c = 1.0f / c;
138 j = testinfl(b);
139 if (j) { /* b is infinite */
140 b = j;
141 }
142 ((long double *)&v)[0] = (b == 0.0f)? b * c : b * d;
143 ((long double *)&v)[1] = b * c;
144 return (v);
145 }
146
147 if (eb >= 0x7fff) { /* a is inf or nan */
148 ((long double *)&v)[0] = b * d;
149 ((long double *)&v)[1] = b * c;
150 return (v);
151 }
152
153 /*
154 * Compute the real and imaginary parts of the quotient,
155 * scaling to avoid overflow or underflow.
156 */
157 ew = (ew - 0x3800) >> 12;
158 sc = c * scl[ew + 4].e;
159 sd = d * scl[ew + 4].e;
160 r = sc * sc + sd * sd;
161
162 eb = (eb - 0x3800) >> 12;
163 b = (b * scl[eb + 4].e) / r;
164 eb -= (ew + ew);
165
166 ec = (ec - 0x3800) >> 12;
167 c = (c * scl[ec + 4].e) * b;
168 ec += eb;
169
170 ed = (ed - 0x3800) >> 12;
171 d = (d * scl[ed + 4].e) * b;
172 ed += eb;
173
174 /* compensate for scaling */
175 sc = scl[3].e; /* 2^4080 */
176 if (ec < 0) {
177 ec = -ec;
178 sc = scl[5].e; /* 2^-4080 */
179 }
180 while (ec--)
181 c *= sc;
182
183 sd = scl[3].e;
184 if (ed < 0) {
185 ed = -ed;
186 sd = scl[5].e;
187 }
188 while (ed--)
189 d *= sd;
190
191 ((long double *)&v)[0] = d;
192 ((long double *)&v)[1] = c;
193 return (v);
194 }
195