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 2003 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 * On SPARC V8, _Q_cplx_div(v, z, w) sets *v = *z / *w with infin-
31*0Sstevel@tonic-gate * ities handling according to C99.
32*0Sstevel@tonic-gate *
33*0Sstevel@tonic-gate * On SPARC V9, _Q_cplx_div(z, w) returns *z / *w with infinities
34*0Sstevel@tonic-gate * handled according to C99.
35*0Sstevel@tonic-gate *
36*0Sstevel@tonic-gate * If z and w are both finite and w is nonzero, _Q_cplx_div delivers
37*0Sstevel@tonic-gate * the complex quotient q according to the usual formula: let a =
38*0Sstevel@tonic-gate * Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x + I * y
39*0Sstevel@tonic-gate * where x = (a * c + b * d) / r and y = (b * c - a * d) / r with
40*0Sstevel@tonic-gate * r = c * c + d * d. This implementation scales to avoid premature
41*0Sstevel@tonic-gate * underflow or overflow.
42*0Sstevel@tonic-gate *
43*0Sstevel@tonic-gate * If z is neither NaN nor zero and w is zero, or if z is infinite
44*0Sstevel@tonic-gate * and w is finite and nonzero, _Q_cplx_div delivers an infinite
45*0Sstevel@tonic-gate * result. If z is finite and w is infinite, _Q_cplx_div delivers
46*0Sstevel@tonic-gate * a zero result.
47*0Sstevel@tonic-gate *
48*0Sstevel@tonic-gate * If z and w are both zero or both infinite, or if either z or w is
49*0Sstevel@tonic-gate * a complex NaN, _Q_cplx_div delivers NaN + I * NaN. C99 doesn't
50*0Sstevel@tonic-gate * specify these cases.
51*0Sstevel@tonic-gate *
52*0Sstevel@tonic-gate * This implementation can raise spurious underflow, overflow, in-
53*0Sstevel@tonic-gate * valid operation, inexact, and division-by-zero exceptions. C99
54*0Sstevel@tonic-gate * allows this.
55*0Sstevel@tonic-gate */
56*0Sstevel@tonic-gate
57*0Sstevel@tonic-gate #if !defined(sparc) && !defined(__sparc)
58*0Sstevel@tonic-gate #error This code is for SPARC only
59*0Sstevel@tonic-gate #endif
60*0Sstevel@tonic-gate
61*0Sstevel@tonic-gate static union {
62*0Sstevel@tonic-gate int i[4];
63*0Sstevel@tonic-gate long double q;
64*0Sstevel@tonic-gate } inf = {
65*0Sstevel@tonic-gate 0x7fff0000, 0, 0, 0
66*0Sstevel@tonic-gate };
67*0Sstevel@tonic-gate
68*0Sstevel@tonic-gate /*
69*0Sstevel@tonic-gate * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
70*0Sstevel@tonic-gate */
71*0Sstevel@tonic-gate static int
testinfl(long double x)72*0Sstevel@tonic-gate testinfl(long double x)
73*0Sstevel@tonic-gate {
74*0Sstevel@tonic-gate union {
75*0Sstevel@tonic-gate int i[4];
76*0Sstevel@tonic-gate long double q;
77*0Sstevel@tonic-gate } xx;
78*0Sstevel@tonic-gate
79*0Sstevel@tonic-gate xx.q = x;
80*0Sstevel@tonic-gate return (((((xx.i[0] << 1) - 0xfffe0000) | xx.i[1] | xx.i[2] | xx.i[3])
81*0Sstevel@tonic-gate == 0)? (1 | (xx.i[0] >> 31)) : 0);
82*0Sstevel@tonic-gate }
83*0Sstevel@tonic-gate
84*0Sstevel@tonic-gate #ifdef __sparcv9
85*0Sstevel@tonic-gate long double _Complex
_Q_cplx_div(const long double _Complex * z,const long double _Complex * w)86*0Sstevel@tonic-gate _Q_cplx_div(const long double _Complex *z, const long double _Complex *w)
87*0Sstevel@tonic-gate {
88*0Sstevel@tonic-gate long double _Complex v;
89*0Sstevel@tonic-gate #else
90*0Sstevel@tonic-gate void
91*0Sstevel@tonic-gate _Q_cplx_div(long double _Complex *v, const long double _Complex *z,
92*0Sstevel@tonic-gate const long double _Complex *w)
93*0Sstevel@tonic-gate {
94*0Sstevel@tonic-gate #endif
95*0Sstevel@tonic-gate union {
96*0Sstevel@tonic-gate int i[4];
97*0Sstevel@tonic-gate long double q;
98*0Sstevel@tonic-gate } aa, bb, cc, dd, ss;
99*0Sstevel@tonic-gate long double a, b, c, d, r;
100*0Sstevel@tonic-gate int ha, hb, hc, hd, hz, hw, hs, i, j;
101*0Sstevel@tonic-gate
102*0Sstevel@tonic-gate /*
103*0Sstevel@tonic-gate * The following is equivalent to
104*0Sstevel@tonic-gate *
105*0Sstevel@tonic-gate * a = creall(*z); b = cimagl(*z);
106*0Sstevel@tonic-gate * c = creall(*w); d = cimagl(*w);
107*0Sstevel@tonic-gate */
108*0Sstevel@tonic-gate a = ((long double *)z)[0];
109*0Sstevel@tonic-gate b = ((long double *)z)[1];
110*0Sstevel@tonic-gate c = ((long double *)w)[0];
111*0Sstevel@tonic-gate d = ((long double *)w)[1];
112*0Sstevel@tonic-gate
113*0Sstevel@tonic-gate /* extract high-order words to estimate |z| and |w| */
114*0Sstevel@tonic-gate aa.q = a;
115*0Sstevel@tonic-gate bb.q = b;
116*0Sstevel@tonic-gate ha = aa.i[0] & ~0x80000000;
117*0Sstevel@tonic-gate hb = bb.i[0] & ~0x80000000;
118*0Sstevel@tonic-gate hz = (ha > hb)? ha : hb;
119*0Sstevel@tonic-gate
120*0Sstevel@tonic-gate cc.q = c;
121*0Sstevel@tonic-gate dd.q = d;
122*0Sstevel@tonic-gate hc = cc.i[0] & ~0x80000000;
123*0Sstevel@tonic-gate hd = dd.i[0] & ~0x80000000;
124*0Sstevel@tonic-gate hw = (hc > hd)? hc : hd;
125*0Sstevel@tonic-gate
126*0Sstevel@tonic-gate /* check for special cases */
127*0Sstevel@tonic-gate if (hw >= 0x7fff0000) { /* w is inf or nan */
128*0Sstevel@tonic-gate r = 0.0l;
129*0Sstevel@tonic-gate i = testinfl(c);
130*0Sstevel@tonic-gate j = testinfl(d);
131*0Sstevel@tonic-gate if (i | j) { /* w is infinite */
132*0Sstevel@tonic-gate /*
133*0Sstevel@tonic-gate * "factor out" infinity, being careful to preserve
134*0Sstevel@tonic-gate * signs of finite values
135*0Sstevel@tonic-gate */
136*0Sstevel@tonic-gate c = i? i : ((cc.i[0] < 0)? -0.0l : 0.0l);
137*0Sstevel@tonic-gate d = j? j : ((dd.i[0] < 0)? -0.0l : 0.0l);
138*0Sstevel@tonic-gate if (hz >= 0x7ffe0000) {
139*0Sstevel@tonic-gate /* scale to avoid overflow below */
140*0Sstevel@tonic-gate c *= 0.5l;
141*0Sstevel@tonic-gate d *= 0.5l;
142*0Sstevel@tonic-gate }
143*0Sstevel@tonic-gate }
144*0Sstevel@tonic-gate goto done;
145*0Sstevel@tonic-gate }
146*0Sstevel@tonic-gate
147*0Sstevel@tonic-gate if (hw == 0 && (cc.i[1] | cc.i[2] | cc.i[3] |
148*0Sstevel@tonic-gate dd.i[1] | dd.i[2] | dd.i[3]) == 0) {
149*0Sstevel@tonic-gate /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
150*0Sstevel@tonic-gate r = 1.0l;
151*0Sstevel@tonic-gate c = 1.0l / c;
152*0Sstevel@tonic-gate i = testinfl(a);
153*0Sstevel@tonic-gate j = testinfl(b);
154*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
155*0Sstevel@tonic-gate a = i;
156*0Sstevel@tonic-gate b = j;
157*0Sstevel@tonic-gate }
158*0Sstevel@tonic-gate goto done;
159*0Sstevel@tonic-gate }
160*0Sstevel@tonic-gate
161*0Sstevel@tonic-gate if (hz >= 0x7fff0000) { /* z is inf or nan */
162*0Sstevel@tonic-gate r = 1.0l;
163*0Sstevel@tonic-gate i = testinfl(a);
164*0Sstevel@tonic-gate j = testinfl(b);
165*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
166*0Sstevel@tonic-gate a = i;
167*0Sstevel@tonic-gate b = j;
168*0Sstevel@tonic-gate r = inf.q;
169*0Sstevel@tonic-gate }
170*0Sstevel@tonic-gate goto done;
171*0Sstevel@tonic-gate }
172*0Sstevel@tonic-gate
173*0Sstevel@tonic-gate /*
174*0Sstevel@tonic-gate * Scale c and d to compute 1/|w|^2 and the real and imaginary
175*0Sstevel@tonic-gate * parts of the quotient.
176*0Sstevel@tonic-gate */
177*0Sstevel@tonic-gate hs = (((hw >> 2) - hw) + 0x6ffd7fff) & 0xffff0000;
178*0Sstevel@tonic-gate if (hz < 0x00ea0000) { /* |z| < 2^-16149 */
179*0Sstevel@tonic-gate if (((hw - 0x3e380000) | (0x40e90000 - hw)) >= 0)
180*0Sstevel@tonic-gate hs = (((0x40e90000 - hw) >> 1) & 0xffff0000)
181*0Sstevel@tonic-gate + 0x3fff0000;
182*0Sstevel@tonic-gate }
183*0Sstevel@tonic-gate ss.i[0] = hs;
184*0Sstevel@tonic-gate ss.i[1] = ss.i[2] = ss.i[3] = 0;
185*0Sstevel@tonic-gate
186*0Sstevel@tonic-gate c *= ss.q;
187*0Sstevel@tonic-gate d *= ss.q;
188*0Sstevel@tonic-gate r = 1.0l / (c * c + d * d);
189*0Sstevel@tonic-gate
190*0Sstevel@tonic-gate c *= ss.q;
191*0Sstevel@tonic-gate d *= ss.q;
192*0Sstevel@tonic-gate
193*0Sstevel@tonic-gate done:
194*0Sstevel@tonic-gate #ifdef __sparcv9
195*0Sstevel@tonic-gate ((long double *)&v)[0] = (a * c + b * d) * r;
196*0Sstevel@tonic-gate ((long double *)&v)[1] = (b * c - a * d) * r;
197*0Sstevel@tonic-gate return (v);
198*0Sstevel@tonic-gate #else
199*0Sstevel@tonic-gate ((long double *)v)[0] = (a * c + b * d) * r;
200*0Sstevel@tonic-gate ((long double *)v)[1] = (b * c - a * d) * r;
201*0Sstevel@tonic-gate #endif
202*0Sstevel@tonic-gate }
203