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
61static 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 */
71static int
72testinfl(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
85long double _Complex
86_Q_cplx_div(const long double _Complex *z, const long double _Complex *w)
87{
88	long double _Complex	v;
89#else
90void
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
193done:
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