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_ix(b, w) returns (I * b) / w with infinities handled
31  * according to C99.
32  *
33  * If b and w are both finite and w is nonzero, _D_cplx_div_ix(b, w)
34  * delivers the complex quotient q according to the usual formula:
35  * let c = Re(w), and d = Im(w); then q = x + I * y where x = (b * d)
36  * / r and y = (b * c) / r with r = c * c + d * d.  This implementa-
37  * tion scales to avoid premature underflow or overflow.
38  *
39  * If b is neither NaN nor zero and w is zero, or if b is infinite
40  * and w is finite and nonzero, _D_cplx_div_ix delivers an infinite
41  * result.  If b is finite and w is infinite, _D_cplx_div_ix delivers
42  * a zero result.
43  *
44  * If b and w are both zero or both infinite, or if either b or w is
45  * NaN, _D_cplx_div_ix delivers NaN + I * NaN.  C99 doesn't specify
46  * these cases.
47  *
48  * This implementation can raise spurious underflow, overflow, in-
49  * valid operation, inexact, and division-by-zero exceptions.  C99
50  * allows this.
51  *
52  * Warning: Do not attempt to "optimize" this code by removing multi-
53  * plications by zero.
54  */
55 
56 #if !defined(sparc) && !defined(__sparc)
57 #error This code is for SPARC only
58 #endif
59 
60 /*
61  * scl[i].d = 2^(250*(4-i)) for i = 0, ..., 9
62  */
63 static const union {
64 	int	i[2];
65 	double	d;
66 } scl[9] = {
67 	{ 0x7e700000, 0 },
68 	{ 0x6ed00000, 0 },
69 	{ 0x5f300000, 0 },
70 	{ 0x4f900000, 0 },
71 	{ 0x3ff00000, 0 },
72 	{ 0x30500000, 0 },
73 	{ 0x20b00000, 0 },
74 	{ 0x11100000, 0 },
75 	{ 0x01700000, 0 }
76 };
77 
78 /*
79  * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
80  */
81 static int
testinf(double x)82 testinf(double x)
83 {
84 	union {
85 		int	i[2];
86 		double	d;
87 	} xx;
88 
89 	xx.d = x;
90 	return (((((xx.i[0] << 1) - 0xffe00000) | xx.i[1]) == 0)?
91 		(1 | (xx.i[0] >> 31)) : 0);
92 }
93 
94 double _Complex
_D_cplx_div_ix(double b,double _Complex w)95 _D_cplx_div_ix(double b, double _Complex w)
96 {
97 	double _Complex	v;
98 	union {
99 		int	i[2];
100 		double	d;
101 	} bb, cc, dd;
102 	double		c, d, sc, sd, r;
103 	int		hb, hc, hd, hw, i, j;
104 
105 	/*
106 	 * The following is equivalent to
107 	 *
108 	 *  c = creal(w); d = cimag(w);
109 	 */
110 	c = ((double *)&w)[0];
111 	d = ((double *)&w)[1];
112 
113 	/* extract high-order words to estimate |b| and |w| */
114 	bb.d = b;
115 	hb = bb.i[0] & ~0x80000000;
116 
117 	cc.d = c;
118 	dd.d = d;
119 	hc = cc.i[0] & ~0x80000000;
120 	hd = dd.i[0] & ~0x80000000;
121 	hw = (hc > hd)? hc : hd;
122 
123 	/* check for special cases */
124 	if (hw >= 0x7ff00000) { /* w is inf or nan */
125 		i = testinf(c);
126 		j = testinf(d);
127 		if (i | j) { /* w is infinite */
128 			c = (cc.i[0] < 0)? -0.0 : 0.0;
129 			d = (dd.i[0] < 0)? -0.0 : 0.0;
130 		} else /* w is nan */
131 			b *= c * d;
132 		((double *)&v)[0] = b * d;
133 		((double *)&v)[1] = b * c;
134 		return (v);
135 	}
136 
137 	if (hw < 0x00100000) {
138 		/*
139 		 * This nonsense is needed to work around some SPARC
140 		 * implementations of nonstandard mode; if both parts
141 		 * of w are subnormal, multiply them by one to force
142 		 * them to be flushed to zero when nonstandard mode
143 		 * is enabled.  Sheesh.
144 		 */
145 		cc.d = c = c * 1.0;
146 		dd.d = d = d * 1.0;
147 		hc = cc.i[0] & ~0x80000000;
148 		hd = dd.i[0] & ~0x80000000;
149 		hw = (hc > hd)? hc : hd;
150 	}
151 
152 	if (hw == 0 && (cc.i[1] | dd.i[1]) == 0) {
153 		/* w is zero; multiply b by 1/Re(w) - I * Im(w) */
154 		c = 1.0 / c;
155 		j = testinf(b);
156 		if (j) { /* b is infinite */
157 			b = j;
158 		}
159 		((double *)&v)[0] = (b == 0.0)? b * c : b * d;
160 		((double *)&v)[1] = b * c;
161 		return (v);
162 	}
163 
164 	if (hb >= 0x7ff00000) { /* a is inf or nan */
165 		((double *)&v)[0] = b * d;
166 		((double *)&v)[1] = b * c;
167 		return (v);
168 	}
169 
170 	/*
171 	 * Compute the real and imaginary parts of the quotient,
172 	 * scaling to avoid overflow or underflow.
173 	 */
174 	hw = (hw - 0x38000000) >> 28;
175 	sc = c * scl[hw + 4].d;
176 	sd = d * scl[hw + 4].d;
177 	r = sc * sc + sd * sd;
178 
179 	hb = (hb - 0x38000000) >> 28;
180 	b = (b * scl[hb + 4].d) / r;
181 	hb -= (hw + hw);
182 
183 	hc = (hc - 0x38000000) >> 28;
184 	c = (c * scl[hc + 4].d) * b;
185 	hc += hb;
186 
187 	hd = (hd - 0x38000000) >> 28;
188 	d = (d * scl[hd + 4].d) * b;
189 	hd += hb;
190 
191 	/* compensate for scaling */
192 	sc = scl[3].d; /* 2^250 */
193 	if (hc < 0) {
194 		hc = -hc;
195 		sc = scl[5].d; /* 2^-250 */
196 	}
197 	while (hc--)
198 		c *= sc;
199 
200 	sd = scl[3].d;
201 	if (hd < 0) {
202 		hd = -hd;
203 		sd = scl[5].d;
204 	}
205 	while (hd--)
206 		d *= sd;
207 
208 	((double *)&v)[0] = d;
209 	((double *)&v)[1] = c;
210 	return (v);
211 }
212