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