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 * On SPARC V8, _Q_cplx_div(v, z, w) sets *v = *z / *w with infin-
31 * ities handling according to C99.
32 *
33 * On SPARC V9, _Q_cplx_div(z, w) returns *z / *w with infinities
34 * handled according to C99.
35 *
36 * If z and w are both finite and w is nonzero, _Q_cplx_div delivers
37 * the complex quotient q according to the usual formula: let a =
38 * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
39 * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
40 * r = c * c + d * d. This implementation scales to avoid premature
41 * underflow or overflow.
42 *
43 * If z is neither NaN nor zero and w is zero, or if z is infinite
44 * and w is finite and nonzero, _Q_cplx_div delivers an infinite
45 * result. If z is finite and w is infinite, _Q_cplx_div delivers
46 * a zero result.
47 *
48 * If z and w are both zero or both infinite, or if either z or w is
49 * a complex NaN, _Q_cplx_div delivers NaN + I * NaN. C99 doesn't
50 * specify these cases.
51 *
52 * This implementation can raise spurious underflow, overflow, in-
53 * valid operation, inexact, and division-by-zero exceptions. C99
54 * allows this.
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[4];
63 long double q;
64 } inf = {
65 0x7fff0000, 0, 0, 0
66 };
67
68 /*
69 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
70 */
71 static int
testinfl(long double x)72 testinfl(long double x)
73 {
74 union {
75 int i[4];
76 long double q;
77 } xx;
78
79 xx.q = x;
80 return (((((xx.i[0] << 1) - 0xfffe0000) | xx.i[1] | xx.i[2] | xx.i[3])
81 == 0)? (1 | (xx.i[0] >> 31)) : 0);
82 }
83
84 #ifdef __sparcv9
85 long double _Complex
_Q_cplx_div(const long double _Complex * z,const long double _Complex * w)86 _Q_cplx_div(const long double _Complex *z, const long double _Complex *w)
87 {
88 long double _Complex v;
89 #else
90 void
91 _Q_cplx_div(long double _Complex *v, const long double _Complex *z,
92 const long double _Complex *w)
93 {
94 #endif
95 union {
96 int i[4];
97 long double q;
98 } aa, bb, cc, dd, ss;
99 long double a, b, c, d, r;
100 int ha, hb, hc, hd, hz, hw, hs, i, j;
101
102 /*
103 * The following is equivalent to
104 *
105 * a = creall(*z); b = cimagl(*z);
106 * c = creall(*w); d = cimagl(*w);
107 */
108 a = ((long double *)z)[0];
109 b = ((long double *)z)[1];
110 c = ((long double *)w)[0];
111 d = ((long double *)w)[1];
112
113 /* extract high-order words to estimate |z| and |w| */
114 aa.q = a;
115 bb.q = b;
116 ha = aa.i[0] & ~0x80000000;
117 hb = bb.i[0] & ~0x80000000;
118 hz = (ha > hb)? ha : hb;
119
120 cc.q = c;
121 dd.q = d;
122 hc = cc.i[0] & ~0x80000000;
123 hd = dd.i[0] & ~0x80000000;
124 hw = (hc > hd)? hc : hd;
125
126 /* check for special cases */
127 if (hw >= 0x7fff0000) { /* w is inf or nan */
128 r = 0.0l;
129 i = testinfl(c);
130 j = testinfl(d);
131 if (i | j) { /* w is infinite */
132 /*
133 * "factor out" infinity, being careful to preserve
134 * signs of finite values
135 */
136 c = i? i : ((cc.i[0] < 0)? -0.0l : 0.0l);
137 d = j? j : ((dd.i[0] < 0)? -0.0l : 0.0l);
138 if (hz >= 0x7ffe0000) {
139 /* scale to avoid overflow below */
140 c *= 0.5l;
141 d *= 0.5l;
142 }
143 }
144 goto done;
145 }
146
147 if (hw == 0 && (cc.i[1] | cc.i[2] | cc.i[3] |
148 dd.i[1] | dd.i[2] | dd.i[3]) == 0) {
149 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
150 r = 1.0l;
151 c = 1.0l / c;
152 i = testinfl(a);
153 j = testinfl(b);
154 if (i | j) { /* z is infinite */
155 a = i;
156 b = j;
157 }
158 goto done;
159 }
160
161 if (hz >= 0x7fff0000) { /* z is inf or nan */
162 r = 1.0l;
163 i = testinfl(a);
164 j = testinfl(b);
165 if (i | j) { /* z is infinite */
166 a = i;
167 b = j;
168 r = inf.q;
169 }
170 goto done;
171 }
172
173 /*
174 * Scale c and d to compute 1/|w|^2 and the real and imaginary
175 * parts of the quotient.
176 */
177 hs = (((hw >> 2) - hw) + 0x6ffd7fff) & 0xffff0000;
178 if (hz < 0x00ea0000) { /* |z| < 2^-16149 */
179 if (((hw - 0x3e380000) | (0x40e90000 - hw)) >= 0)
180 hs = (((0x40e90000 - hw) >> 1) & 0xffff0000)
181 + 0x3fff0000;
182 }
183 ss.i[0] = hs;
184 ss.i[1] = ss.i[2] = ss.i[3] = 0;
185
186 c *= ss.q;
187 d *= ss.q;
188 r = 1.0l / (c * c + d * d);
189
190 c *= ss.q;
191 d *= ss.q;
192
193 done:
194 #ifdef __sparcv9
195 ((long double *)&v)[0] = (a * c + b * d) * r;
196 ((long double *)&v)[1] = (b * c - a * d) * r;
197 return (v);
198 #else
199 ((long double *)v)[0] = (a * c + b * d) * r;
200 ((long double *)v)[1] = (b * c - a * d) * r;
201 #endif
202 }
203