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 * _D_cplx_div(z, w) returns z / w with infinities handled according
31 * to C99.
32 *
33 * If z and w are both finite and w is nonzero, _D_cplx_div(z, w)
34 * delivers the complex quotient q according to the usual formula:
35 * let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
36 * I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
37 * with r = c * c + d * d.  This implementation scales to avoid
38 * premature underflow or overflow.
39 *
40 * If z is neither NaN nor zero and w is zero, or if z is infinite
41 * and w is finite and nonzero, _D_cplx_div delivers an infinite
42 * result.  If z is finite and w is infinite, _D_cplx_div delivers
43 * a zero result.
44 *
45 * If z and w are both zero or both infinite, or if either z or w is
46 * a complex NaN, _D_cplx_div delivers NaN + I * NaN.  C99 doesn't
47 * specify these cases.
48 *
49 * This implementation can raise spurious underflow, overflow, in-
50 * valid operation, inexact, and division-by-zero exceptions.  C99
51 * allows this.
52 *
53 * Warning: Do not attempt to "optimize" this code by removing multi-
54 * plications by zero.
55 */
56
57#if !defined(sparc) && !defined(__sparc)
58#error This code is for SPARC only
59#endif
60
61static union {
62	int	i[2];
63	double	d;
64} inf = {
65	0x7ff00000, 0
66};
67
68/*
69 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
70 */
71static int
72testinf(double x)
73{
74	union {
75		int	i[2];
76		double	d;
77	} xx;
78
79	xx.d = x;
80	return (((((xx.i[0] << 1) - 0xffe00000) | xx.i[1]) == 0)?
81		(1 | (xx.i[0] >> 31)) : 0);
82}
83
84double _Complex
85_D_cplx_div(double _Complex z, double _Complex w)
86{
87	double _Complex	v;
88	union {
89		int	i[2];
90		double	d;
91	} aa, bb, cc, dd, ss;
92	double		a, b, c, d, r;
93	int		ha, hb, hc, hd, hz, hw, hs, i, j;
94
95	/*
96	 * The following is equivalent to
97	 *
98	 *  a = creal(z); b = cimag(z);
99	 *  c = creal(w); d = cimag(w);
100	 */
101	a = ((double *)&z)[0];
102	b = ((double *)&z)[1];
103	c = ((double *)&w)[0];
104	d = ((double *)&w)[1];
105
106	/* extract high-order words to estimate |z| and |w| */
107	aa.d = a;
108	bb.d = b;
109	ha = aa.i[0] & ~0x80000000;
110	hb = bb.i[0] & ~0x80000000;
111	hz = (ha > hb)? ha : hb;
112
113	cc.d = c;
114	dd.d = d;
115	hc = cc.i[0] & ~0x80000000;
116	hd = dd.i[0] & ~0x80000000;
117	hw = (hc > hd)? hc : hd;
118
119	/* check for special cases */
120	if (hw >= 0x7ff00000) { /* w is inf or nan */
121		r = 0.0;
122		i = testinf(c);
123		j = testinf(d);
124		if (i | j) { /* w is infinite */
125			/*
126			 * "factor out" infinity, being careful to preserve
127			 * signs of finite values
128			 */
129			c = i? i : ((cc.i[0] < 0)? -0.0 : 0.0);
130			d = j? j : ((dd.i[0] < 0)? -0.0 : 0.0);
131			if (hz >= 0x7fe00000) {
132				/* scale to avoid overflow below */
133				c *= 0.5;
134				d *= 0.5;
135			}
136		}
137		((double *)&v)[0] = (a * c + b * d) * r;
138		((double *)&v)[1] = (b * c - a * d) * r;
139		return (v);
140	}
141
142	if (hw < 0x00100000) {
143		/*
144		 * This nonsense is needed to work around some SPARC
145		 * implementations of nonstandard mode; if both parts
146		 * of w are subnormal, multiply them by one to force
147		 * them to be flushed to zero when nonstandard mode
148		 * is enabled.  Sheesh.
149		 */
150		cc.d = c = c * 1.0;
151		dd.d = d = d * 1.0;
152		hc = cc.i[0] & ~0x80000000;
153		hd = dd.i[0] & ~0x80000000;
154		hw = (hc > hd)? hc : hd;
155	}
156
157	if (hw == 0 && (cc.i[1] | dd.i[1]) == 0) {
158		/* w is zero; multiply z by 1/Re(w) - I * Im(w) */
159		c = 1.0 / c;
160		i = testinf(a);
161		j = testinf(b);
162		if (i | j) { /* z is infinite */
163			a = i;
164			b = j;
165		}
166		((double *)&v)[0] = a * c + b * d;
167		((double *)&v)[1] = b * c - a * d;
168		return (v);
169	}
170
171	if (hz >= 0x7ff00000) { /* z is inf or nan */
172		r = 1.0;
173		i = testinf(a);
174		j = testinf(b);
175		if (i | j) { /* z is infinite */
176			a = i;
177			b = j;
178			r = inf.d;
179		}
180		((double *)&v)[0] = (a * c + b * d) * r;
181		((double *)&v)[1] = (b * c - a * d) * r;
182		return (v);
183	}
184
185	/*
186	 * Scale c and d to compute 1/|w|^2 and the real and imaginary
187	 * parts of the quotient.
188	 *
189	 * Note that for any s, if we let c' = sc, d' = sd, c'' = sc',
190	 * and d'' = sd', then
191	 *
192	 *  (ac'' + bd'') / (c'^2 + d'^2) = (ac + bd) / (c^2 + d^2)
193	 *
194	 * and similarly for the imaginary part of the quotient.  We want
195	 * to choose s such that (i) r := 1/(c'^2 + d'^2) can be computed
196	 * without overflow or harmful underflow, and (ii) (ac'' + bd'')
197	 * and (bc'' - ad'') can be computed without spurious overflow or
198	 * harmful underflow.  To avoid unnecessary rounding, we restrict
199	 * s to a power of two.
200	 *
201	 * To satisfy (i), we need to choose s such that max(|c'|,|d'|)
202	 * is not too far from one.  To satisfy (ii), we need to choose
203	 * s such that max(|c''|,|d''|) is also not too far from one.
204	 * There is some leeway in our choice, but to keep the logic
205	 * from getting overly complicated, we simply attempt to roughly
206	 * balance these constraints by choosing s so as to make r about
207	 * the same size as max(|c''|,|d''|).  This corresponds to choos-
208	 * ing s to be a power of two near |w|^(-3/4).
209	 *
210	 * Regarding overflow, observe that if max(|c''|,|d''|) <= 1/2,
211	 * then the computation of (ac'' + bd'') and (bc'' - ad'') can-
212	 * not overflow; otherwise, the computation of either of these
213	 * values can only incur overflow if the true result would be
214	 * within a factor of two of the overflow threshold.  In other
215	 * words, if we bias the choice of s such that at least one of
216	 *
217	 *  max(|c''|,|d''|) <= 1/2   or   r >= 2
218	 *
219	 * always holds, then no undeserved overflow can occur.
220	 *
221	 * To cope with underflow, note that if r < 2^-53, then any
222	 * intermediate results that underflow are insignificant; either
223	 * they will be added to normal results, rendering the under-
224	 * flow no worse than ordinary roundoff, or they will contribute
225	 * to a final result that is smaller than the smallest subnormal
226	 * number.  Therefore, we need only modify the preceding logic
227	 * when z is very small and w is not too far from one.  In that
228	 * case, we can reduce the effect of any intermediate underflow
229	 * to no worse than ordinary roundoff error by choosing s so as
230	 * to make max(|c''|,|d''|) large enough that at least one of
231	 * (ac'' + bd'') or (bc'' - ad'') is normal.
232	 */
233	hs = (((hw >> 2) - hw) + 0x6fd7ffff) & 0xfff00000;
234	if (hz < 0x07200000) { /* |z| < 2^-909 */
235		if (((hw - 0x32800000) | (0x47100000 - hw)) >= 0)
236			hs = (((0x47100000 - hw) >> 1) & 0xfff00000)
237				+ 0x3ff00000;
238	}
239	ss.i[0] = hs;
240	ss.i[1] = 0;
241
242	c *= ss.d;
243	d *= ss.d;
244	r = 1.0 / (c * c + d * d);
245
246	c *= ss.d;
247	d *= ss.d;
248	((double *)&v)[0] = (a * c + b * d) * r;
249	((double *)&v)[1] = (b * c - a * d) * r;
250	return (v);
251}
252