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 * _D_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, _D_cplx_div(z, w)
34*0Sstevel@tonic-gate * delivers the complex quotient q according to the usual formula:
35*0Sstevel@tonic-gate * let a = Re(z), b = Im(z), c = Re(w), and d = Im(w); then q = x +
36*0Sstevel@tonic-gate * I * y where x = (a * c + b * d) / r and y = (b * c - a * d) / r
37*0Sstevel@tonic-gate * with r = c * c + d * d. This implementation computes intermediate
38*0Sstevel@tonic-gate * results in extended precision to avoid premature underflow or over-
39*0Sstevel@tonic-gate * flow.
40*0Sstevel@tonic-gate *
41*0Sstevel@tonic-gate * If z is neither NaN nor zero and w is zero, or if z is infinite
42*0Sstevel@tonic-gate * and w is finite and nonzero, _D_cplx_div delivers an infinite
43*0Sstevel@tonic-gate * result. If z is finite and w is infinite, _D_cplx_div delivers
44*0Sstevel@tonic-gate * a zero result.
45*0Sstevel@tonic-gate *
46*0Sstevel@tonic-gate * If z and w are both zero or both infinite, or if either z or w is
47*0Sstevel@tonic-gate * a complex NaN, _D_cplx_div delivers NaN + I * NaN. C99 doesn't
48*0Sstevel@tonic-gate * specify these cases.
49*0Sstevel@tonic-gate *
50*0Sstevel@tonic-gate * This implementation can raise spurious invalid operation, inexact,
51*0Sstevel@tonic-gate * and division-by-zero exceptions. C99 allows this.
52*0Sstevel@tonic-gate *
53*0Sstevel@tonic-gate * Warning: Do not attempt to "optimize" this code by removing multi-
54*0Sstevel@tonic-gate * plications by zero.
55*0Sstevel@tonic-gate */
56*0Sstevel@tonic-gate
57*0Sstevel@tonic-gate #if !defined(i386) && !defined(__i386) && !defined(__amd64)
58*0Sstevel@tonic-gate #error This code is for x86 only
59*0Sstevel@tonic-gate #endif
60*0Sstevel@tonic-gate
61*0Sstevel@tonic-gate static union {
62*0Sstevel@tonic-gate int i;
63*0Sstevel@tonic-gate float f;
64*0Sstevel@tonic-gate } inf = {
65*0Sstevel@tonic-gate 0x7f800000
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
testinf(double x)72*0Sstevel@tonic-gate testinf(double x)
73*0Sstevel@tonic-gate {
74*0Sstevel@tonic-gate union {
75*0Sstevel@tonic-gate int i[2];
76*0Sstevel@tonic-gate double d;
77*0Sstevel@tonic-gate } xx;
78*0Sstevel@tonic-gate
79*0Sstevel@tonic-gate xx.d = x;
80*0Sstevel@tonic-gate return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)?
81*0Sstevel@tonic-gate (1 | (xx.i[1] >> 31)) : 0);
82*0Sstevel@tonic-gate }
83*0Sstevel@tonic-gate
84*0Sstevel@tonic-gate double _Complex
_D_cplx_div(double _Complex z,double _Complex w)85*0Sstevel@tonic-gate _D_cplx_div(double _Complex z, double _Complex w)
86*0Sstevel@tonic-gate {
87*0Sstevel@tonic-gate double _Complex v;
88*0Sstevel@tonic-gate union {
89*0Sstevel@tonic-gate int i[2];
90*0Sstevel@tonic-gate double d;
91*0Sstevel@tonic-gate } cc, dd;
92*0Sstevel@tonic-gate double a, b, c, d;
93*0Sstevel@tonic-gate long double r, x, y;
94*0Sstevel@tonic-gate int i, j, recalc;
95*0Sstevel@tonic-gate
96*0Sstevel@tonic-gate /*
97*0Sstevel@tonic-gate * The following is equivalent to
98*0Sstevel@tonic-gate *
99*0Sstevel@tonic-gate * a = creal(z); b = cimag(z);
100*0Sstevel@tonic-gate * c = creal(w); d = cimag(w);
101*0Sstevel@tonic-gate */
102*0Sstevel@tonic-gate /* LINTED alignment */
103*0Sstevel@tonic-gate a = ((double *)&z)[0];
104*0Sstevel@tonic-gate /* LINTED alignment */
105*0Sstevel@tonic-gate b = ((double *)&z)[1];
106*0Sstevel@tonic-gate /* LINTED alignment */
107*0Sstevel@tonic-gate c = ((double *)&w)[0];
108*0Sstevel@tonic-gate /* LINTED alignment */
109*0Sstevel@tonic-gate d = ((double *)&w)[1];
110*0Sstevel@tonic-gate
111*0Sstevel@tonic-gate r = (long double)c * c + (long double)d * d;
112*0Sstevel@tonic-gate
113*0Sstevel@tonic-gate if (r == 0.0f) {
114*0Sstevel@tonic-gate /* w is zero; multiply z by 1/Re(w) - I * Im(w) */
115*0Sstevel@tonic-gate c = 1.0f / c;
116*0Sstevel@tonic-gate i = testinf(a);
117*0Sstevel@tonic-gate j = testinf(b);
118*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
119*0Sstevel@tonic-gate a = i;
120*0Sstevel@tonic-gate b = j;
121*0Sstevel@tonic-gate }
122*0Sstevel@tonic-gate /* LINTED alignment */
123*0Sstevel@tonic-gate ((double *)&v)[0] = a * c + b * d;
124*0Sstevel@tonic-gate /* LINTED alignment */
125*0Sstevel@tonic-gate ((double *)&v)[1] = b * c - a * d;
126*0Sstevel@tonic-gate return (v);
127*0Sstevel@tonic-gate }
128*0Sstevel@tonic-gate
129*0Sstevel@tonic-gate r = 1.0f / r;
130*0Sstevel@tonic-gate x = ((long double)a * c + (long double)b * d) * r;
131*0Sstevel@tonic-gate y = ((long double)b * c - (long double)a * d) * r;
132*0Sstevel@tonic-gate
133*0Sstevel@tonic-gate if (x != x && y != y) {
134*0Sstevel@tonic-gate /*
135*0Sstevel@tonic-gate * Both x and y are NaN, so z and w can't both be finite
136*0Sstevel@tonic-gate * and nonzero. Since we handled the case w = 0 above,
137*0Sstevel@tonic-gate * the only cases to check here are when one of z or w
138*0Sstevel@tonic-gate * is infinite.
139*0Sstevel@tonic-gate */
140*0Sstevel@tonic-gate r = 1.0f;
141*0Sstevel@tonic-gate recalc = 0;
142*0Sstevel@tonic-gate i = testinf(a);
143*0Sstevel@tonic-gate j = testinf(b);
144*0Sstevel@tonic-gate if (i | j) { /* z is infinite */
145*0Sstevel@tonic-gate /* "factor out" infinity */
146*0Sstevel@tonic-gate a = i;
147*0Sstevel@tonic-gate b = j;
148*0Sstevel@tonic-gate r = inf.f;
149*0Sstevel@tonic-gate recalc = 1;
150*0Sstevel@tonic-gate }
151*0Sstevel@tonic-gate i = testinf(c);
152*0Sstevel@tonic-gate j = testinf(d);
153*0Sstevel@tonic-gate if (i | j) { /* w is infinite */
154*0Sstevel@tonic-gate /*
155*0Sstevel@tonic-gate * "factor out" infinity, being careful to preserve
156*0Sstevel@tonic-gate * signs of finite values
157*0Sstevel@tonic-gate */
158*0Sstevel@tonic-gate cc.d = c;
159*0Sstevel@tonic-gate dd.d = d;
160*0Sstevel@tonic-gate c = i? i : ((cc.i[1] < 0)? -0.0f : 0.0f);
161*0Sstevel@tonic-gate d = j? j : ((dd.i[1] < 0)? -0.0f : 0.0f);
162*0Sstevel@tonic-gate r *= 0.0f;
163*0Sstevel@tonic-gate recalc = 1;
164*0Sstevel@tonic-gate }
165*0Sstevel@tonic-gate if (recalc) {
166*0Sstevel@tonic-gate x = ((long double)a * c + (long double)b * d) * r;
167*0Sstevel@tonic-gate y = ((long double)b * c - (long double)a * d) * r;
168*0Sstevel@tonic-gate }
169*0Sstevel@tonic-gate }
170*0Sstevel@tonic-gate
171*0Sstevel@tonic-gate /*
172*0Sstevel@tonic-gate * The following is equivalent to
173*0Sstevel@tonic-gate *
174*0Sstevel@tonic-gate * return x + I * y;
175*0Sstevel@tonic-gate */
176*0Sstevel@tonic-gate /* LINTED alignment */
177*0Sstevel@tonic-gate ((double *)&v)[0] = (double)x;
178*0Sstevel@tonic-gate /* LINTED alignment */
179*0Sstevel@tonic-gate ((double *)&v)[1] = (double)y;
180*0Sstevel@tonic-gate return (v);
181*0Sstevel@tonic-gate }
182