1*0Sstevel@tonic-gate /*
2*0Sstevel@tonic-gate * CDDL HEADER START
3*0Sstevel@tonic-gate *
4*0Sstevel@tonic-gate * The contents of this file are subject to the terms of the
5*0Sstevel@tonic-gate * Common Development and Distribution License, Version 1.0 only
6*0Sstevel@tonic-gate * (the "License"). You may not use this file except in compliance
7*0Sstevel@tonic-gate * with the License.
8*0Sstevel@tonic-gate *
9*0Sstevel@tonic-gate * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
10*0Sstevel@tonic-gate * or http://www.opensolaris.org/os/licensing.
11*0Sstevel@tonic-gate * See the License for the specific language governing permissions
12*0Sstevel@tonic-gate * and limitations under the License.
13*0Sstevel@tonic-gate *
14*0Sstevel@tonic-gate * When distributing Covered Code, include this CDDL HEADER in each
15*0Sstevel@tonic-gate * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
16*0Sstevel@tonic-gate * If applicable, add the following below this CDDL HEADER, with the
17*0Sstevel@tonic-gate * fields enclosed by brackets "[]" replaced with your own identifying
18*0Sstevel@tonic-gate * information: Portions Copyright [yyyy] [name of copyright owner]
19*0Sstevel@tonic-gate *
20*0Sstevel@tonic-gate * CDDL HEADER END
21*0Sstevel@tonic-gate */
22*0Sstevel@tonic-gate /*
23*0Sstevel@tonic-gate * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
24*0Sstevel@tonic-gate * Use is subject to license terms.
25*0Sstevel@tonic-gate */
26*0Sstevel@tonic-gate
27*0Sstevel@tonic-gate #pragma ident "%Z%%M% %I% %E% SMI"
28*0Sstevel@tonic-gate
29*0Sstevel@tonic-gate /*
30*0Sstevel@tonic-gate * _X_cplx_div(z, w) returns z / w with infinities handled according
31*0Sstevel@tonic-gate * to C99.
32*0Sstevel@tonic-gate *
33*0Sstevel@tonic-gate * If z and w are both finite and w is nonzero, _X_cplx_div delivers
34*0Sstevel@tonic-gate * the complex quotient q according to the usual formula: let a =
35*0Sstevel@tonic-gate * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
36*0Sstevel@tonic-gate * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
37*0Sstevel@tonic-gate * r = c * c + d * d. This implementation scales to avoid premature
38*0Sstevel@tonic-gate * underflow or overflow.
39*0Sstevel@tonic-gate *
40*0Sstevel@tonic-gate * If z is neither NaN nor zero and w is zero, or if z is infinite
41*0Sstevel@tonic-gate * and w is finite and nonzero, _X_cplx_div delivers an infinite
42*0Sstevel@tonic-gate * result. If z is finite and w is infinite, _X_cplx_div delivers
43*0Sstevel@tonic-gate * a zero result.
44*0Sstevel@tonic-gate *
45*0Sstevel@tonic-gate * If z and w are both zero or both infinite, or if either z or w is
46*0Sstevel@tonic-gate * a complex NaN, _X_cplx_div delivers NaN + I * NaN. C99 doesn't
47*0Sstevel@tonic-gate * specify these cases.
48*0Sstevel@tonic-gate *
49*0Sstevel@tonic-gate * This implementation can raise spurious underflow, overflow, in-
50*0Sstevel@tonic-gate * valid operation, inexact, and division-by-zero exceptions. C99
51*0Sstevel@tonic-gate * allows this.
52*0Sstevel@tonic-gate */
53*0Sstevel@tonic-gate
54*0Sstevel@tonic-gate #if !defined(i386) && !defined(__i386) && !defined(__amd64)
55*0Sstevel@tonic-gate #error This code is for x86 only
56*0Sstevel@tonic-gate #endif
57*0Sstevel@tonic-gate
58*0Sstevel@tonic-gate static union {
59*0Sstevel@tonic-gate int i;
60*0Sstevel@tonic-gate float f;
61*0Sstevel@tonic-gate } inf = {
62*0Sstevel@tonic-gate 0x7f800000
63*0Sstevel@tonic-gate };
64*0Sstevel@tonic-gate
65*0Sstevel@tonic-gate /*
66*0Sstevel@tonic-gate * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
67*0Sstevel@tonic-gate */
68*0Sstevel@tonic-gate static int
testinfl(long double x)69*0Sstevel@tonic-gate testinfl(long double x)
70*0Sstevel@tonic-gate {
71*0Sstevel@tonic-gate union {
72*0Sstevel@tonic-gate int i[3];
73*0Sstevel@tonic-gate long double e;
74*0Sstevel@tonic-gate } xx;
75*0Sstevel@tonic-gate
76*0Sstevel@tonic-gate xx.e = x;
77*0Sstevel@tonic-gate if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
78*0Sstevel@tonic-gate return (0);
79*0Sstevel@tonic-gate return (1 | ((xx.i[2] << 16) >> 31));
80*0Sstevel@tonic-gate }
81*0Sstevel@tonic-gate
82*0Sstevel@tonic-gate long double _Complex
_X_cplx_div(long double _Complex z,long double _Complex w)83*0Sstevel@tonic-gate _X_cplx_div(long double _Complex z, long double _Complex w)
84*0Sstevel@tonic-gate {
85*0Sstevel@tonic-gate long double _Complex v;
86*0Sstevel@tonic-gate union {
87*0Sstevel@tonic-gate int i[3];
88*0Sstevel@tonic-gate long double e;
89*0Sstevel@tonic-gate } aa, bb, cc, dd, ss;
90*0Sstevel@tonic-gate long double a, b, c, d, r;
91*0Sstevel@tonic-gate int ea, eb, ec, ed, ez, ew, es, i, j;
92*0Sstevel@tonic-gate
93*0Sstevel@tonic-gate /*
94*0Sstevel@tonic-gate * The following is equivalent to
95*0Sstevel@tonic-gate *
96*0Sstevel@tonic-gate * a = creall(*z); b = cimagl(*z);
97*0Sstevel@tonic-gate * c = creall(*w); d = cimagl(*w);
98*0Sstevel@tonic-gate */
99*0Sstevel@tonic-gate a = ((long double *)&z)[0];
100*0Sstevel@tonic-gate b = ((long double *)&z)[1];
101*0Sstevel@tonic-gate c = ((long double *)&w)[0];
102*0Sstevel@tonic-gate d = ((long double *)&w)[1];
103*0Sstevel@tonic-gate
104*0Sstevel@tonic-gate /* extract exponents to estimate |z| and |w| */
105*0Sstevel@tonic-gate aa.e = a;
106*0Sstevel@tonic-gate bb.e = b;
107*0Sstevel@tonic-gate ea = aa.i[2] & 0x7fff;
108*0Sstevel@tonic-gate eb = bb.i[2] & 0x7fff;
109*0Sstevel@tonic-gate ez = (ea > eb)? ea : eb;
110*0Sstevel@tonic-gate
111*0Sstevel@tonic-gate cc.e = c;
112*0Sstevel@tonic-gate dd.e = d;
113*0Sstevel@tonic-gate ec = cc.i[2] & 0x7fff;
114*0Sstevel@tonic-gate ed = dd.i[2] & 0x7fff;
115*0Sstevel@tonic-gate ew = (ec > ed)? ec : ed;
116*0Sstevel@tonic-gate
117*0Sstevel@tonic-gate /* check for special cases */
118*0Sstevel@tonic-gate if (ew >= 0x7fff) { /* w is inf or nan */
119*0Sstevel@tonic-gate r = 0.0f;
120*0Sstevel@tonic-gate i = testinfl(c);
121*0Sstevel@tonic-gate j = testinfl(d);
122*0Sstevel@tonic-gate if (i | j) { /* w is infinite */
123*0Sstevel@tonic-gate /*
124*0Sstevel@tonic-gate * "factor out" infinity, being careful to preserve
125*0Sstevel@tonic-gate * signs of finite values
126*0Sstevel@tonic-gate */
127*0Sstevel@tonic-gate c = i? i : (((cc.i[2] << 16) < 0)? -0.0f : 0.0f);
128*0Sstevel@tonic-gate d = j? j : (((dd.i[2] << 16) < 0)? -0.0f : 0.0f);
129*0Sstevel@tonic-gate if (ez >= 0x7ffe) {
130*0Sstevel@tonic-gate /* scale to avoid overflow below */
131*0Sstevel@tonic-gate c *= 0.5f;
132*0Sstevel@tonic-gate d *= 0.5f;
133*0Sstevel@tonic-gate }
134*0Sstevel@tonic-gate }
135*0Sstevel@tonic-gate ((long double *)&v)[0] = (a * c + b * d) * r;
136*0Sstevel@tonic-gate ((long double *)&v)[1] = (b * c - a * d) * r;
137*0Sstevel@tonic-gate return (v);
138*0Sstevel@tonic-gate }
139*0Sstevel@tonic-gate
140*0Sstevel@tonic-gate if (ew == 0 && (cc.i[1] | cc.i[0] | dd.i[1] | dd.i[0]) == 0) {
141*0Sstevel@tonic-gate /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
142*0Sstevel@tonic-gate c = 1.0f / c;
143*0Sstevel@tonic-gate i = testinfl(a);
144*0Sstevel@tonic-gate j = testinfl(b);
145*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
146*0Sstevel@tonic-gate a = i;
147*0Sstevel@tonic-gate b = j;
148*0Sstevel@tonic-gate }
149*0Sstevel@tonic-gate ((long double *)&v)[0] = a * c + b * d;
150*0Sstevel@tonic-gate ((long double *)&v)[1] = b * c - a * d;
151*0Sstevel@tonic-gate return (v);
152*0Sstevel@tonic-gate }
153*0Sstevel@tonic-gate
154*0Sstevel@tonic-gate if (ez >= 0x7fff) { /* z is inf or nan */
155*0Sstevel@tonic-gate i = testinfl(a);
156*0Sstevel@tonic-gate j = testinfl(b);
157*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
158*0Sstevel@tonic-gate a = i;
159*0Sstevel@tonic-gate b = j;
160*0Sstevel@tonic-gate r = inf.f;
161*0Sstevel@tonic-gate }
162*0Sstevel@tonic-gate ((long double *)&v)[0] = a * c + b * d;
163*0Sstevel@tonic-gate ((long double *)&v)[1] = b * c - a * d;
164*0Sstevel@tonic-gate return (v);
165*0Sstevel@tonic-gate }
166*0Sstevel@tonic-gate
167*0Sstevel@tonic-gate /*
168*0Sstevel@tonic-gate * Scale c and d to compute 1/|w|^2 and the real and imaginary
169*0Sstevel@tonic-gate * parts of the quotient.
170*0Sstevel@tonic-gate */
171*0Sstevel@tonic-gate es = ((ew >> 2) - ew) + 0x6ffd;
172*0Sstevel@tonic-gate if (ez < 0x0086) { /* |z| < 2^-16249 */
173*0Sstevel@tonic-gate if (((ew - 0x3efe) | (0x4083 - ew)) >= 0)
174*0Sstevel@tonic-gate es = ((0x4083 - ew) >> 1) + 0x3fff;
175*0Sstevel@tonic-gate }
176*0Sstevel@tonic-gate ss.i[2] = es;
177*0Sstevel@tonic-gate ss.i[1] = 0x80000000;
178*0Sstevel@tonic-gate ss.i[0] = 0;
179*0Sstevel@tonic-gate
180*0Sstevel@tonic-gate c *= ss.e;
181*0Sstevel@tonic-gate d *= ss.e;
182*0Sstevel@tonic-gate r = 1.0f / (c * c + d * d);
183*0Sstevel@tonic-gate
184*0Sstevel@tonic-gate c *= ss.e;
185*0Sstevel@tonic-gate d *= ss.e;
186*0Sstevel@tonic-gate
187*0Sstevel@tonic-gate ((long double *)&v)[0] = (a * c + b * d) * r;
188*0Sstevel@tonic-gate ((long double *)&v)[1] = (b * c - a * d) * r;
189*0Sstevel@tonic-gate return (v);
190*0Sstevel@tonic-gate }
191