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 * On SPARC V8, _Q_cplx_div(v, z, w) sets *v = *z / *w with infin-
29 * ities handling according to C99.
30 *
31 * On SPARC V9, _Q_cplx_div(z, w) returns *z / *w with infinities
32 * handled according to C99.
33 *
34 * If z and w are both finite and w is nonzero, _Q_cplx_div delivers
35 * the complex quotient q according to the usual formula: let a =
36 * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
37 * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
38 * r = c * c + d * d. This implementation scales to avoid premature
39 * underflow or overflow.
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, _Q_cplx_div delivers an infinite
43 * result. If z is finite and w is infinite, _Q_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, _Q_cplx_div delivers NaN + I * NaN. C99 doesn't
48 * specify these cases.
49 *
50 * This implementation can raise spurious underflow, overflow, in-
51 * valid operation, inexact, and division-by-zero exceptions. C99
52 * allows this.
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[4];
61 long double q;
62 } inf = {
63 0x7fff0000, 0, 0, 0
64 };
65
66 /*
67 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
68 */
69 static int
testinfl(long double x)70 testinfl(long double x)
71 {
72 union {
73 int i[4];
74 long double q;
75 } xx;
76
77 xx.q = x;
78 return (((((xx.i[0] << 1) - 0xfffe0000) | xx.i[1] | xx.i[2] | xx.i[3])
79 == 0)? (1 | (xx.i[0] >> 31)) : 0);
80 }
81
82 #ifdef __sparcv9
83 long double _Complex
_Q_cplx_div(const long double _Complex * z,const long double _Complex * w)84 _Q_cplx_div(const long double _Complex *z, const long double _Complex *w)
85 {
86 long double _Complex v = 0;
87 #else
88 void
89 _Q_cplx_div(long double _Complex *v, const long double _Complex *z,
90 const long double _Complex *w)
91 {
92 #endif
93 union {
94 int i[4];
95 long double q;
96 } aa, bb, cc, dd, ss;
97 long double a, b, c, d, r;
98 int ha, hb, hc, hd, hz, hw, hs, i, j;
99
100 /*
101 * The following is equivalent to
102 *
103 * a = creall(*z); b = cimagl(*z);
104 * c = creall(*w); d = cimagl(*w);
105 */
106 a = ((long double *)z)[0];
107 b = ((long double *)z)[1];
108 c = ((long double *)w)[0];
109 d = ((long double *)w)[1];
110
111 /* extract high-order words to estimate |z| and |w| */
112 aa.q = a;
113 bb.q = b;
114 ha = aa.i[0] & ~0x80000000;
115 hb = bb.i[0] & ~0x80000000;
116 hz = (ha > hb)? ha : hb;
117
118 cc.q = c;
119 dd.q = d;
120 hc = cc.i[0] & ~0x80000000;
121 hd = dd.i[0] & ~0x80000000;
122 hw = (hc > hd)? hc : hd;
123
124 /* check for special cases */
125 if (hw >= 0x7fff0000) { /* w is inf or nan */
126 r = 0.0l;
127 i = testinfl(c);
128 j = testinfl(d);
129 if (i | j) { /* w is infinite */
130 /*
131 * "factor out" infinity, being careful to preserve
132 * signs of finite values
133 */
134 c = i? i : ((cc.i[0] < 0)? -0.0l : 0.0l);
135 d = j? j : ((dd.i[0] < 0)? -0.0l : 0.0l);
136 if (hz >= 0x7ffe0000) {
137 /* scale to avoid overflow below */
138 c *= 0.5l;
139 d *= 0.5l;
140 }
141 }
142 goto done;
143 }
144
145 if (hw == 0 && (cc.i[1] | cc.i[2] | cc.i[3] |
146 dd.i[1] | dd.i[2] | dd.i[3]) == 0) {
147 /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
148 r = 1.0l;
149 c = 1.0l / c;
150 i = testinfl(a);
151 j = testinfl(b);
152 if (i | j) { /* z is infinite */
153 a = i;
154 b = j;
155 }
156 goto done;
157 }
158
159 if (hz >= 0x7fff0000) { /* z is inf or nan */
160 r = 1.0l;
161 i = testinfl(a);
162 j = testinfl(b);
163 if (i | j) { /* z is infinite */
164 a = i;
165 b = j;
166 r = inf.q;
167 }
168 goto done;
169 }
170
171 /*
172 * Scale c and d to compute 1/|w|^2 and the real and imaginary
173 * parts of the quotient.
174 */
175 hs = (((hw >> 2) - hw) + 0x6ffd7fff) & 0xffff0000;
176 if (hz < 0x00ea0000) { /* |z| < 2^-16149 */
177 if (((hw - 0x3e380000) | (0x40e90000 - hw)) >= 0)
178 hs = (((0x40e90000 - hw) >> 1) & 0xffff0000)
179 + 0x3fff0000;
180 }
181 ss.i[0] = hs;
182 ss.i[1] = ss.i[2] = ss.i[3] = 0;
183
184 c *= ss.q;
185 d *= ss.q;
186 r = 1.0l / (c * c + d * d);
187
188 c *= ss.q;
189 d *= ss.q;
190
191 done:
192 #ifdef __sparcv9
193 ((long double *)&v)[0] = (a * c + b * d) * r;
194 ((long double *)&v)[1] = (b * c - a * d) * r;
195 return (v);
196 #else
197 ((long double *)v)[0] = (a * c + b * d) * r;
198 ((long double *)v)[1] = (b * c - a * d) * r;
199 #endif
200 }
201