17c478bd9Sstevel@tonic-gate /*
27c478bd9Sstevel@tonic-gate * CDDL HEADER START
37c478bd9Sstevel@tonic-gate *
47c478bd9Sstevel@tonic-gate * The contents of this file are subject to the terms of the
57c478bd9Sstevel@tonic-gate * Common Development and Distribution License, Version 1.0 only
67c478bd9Sstevel@tonic-gate * (the "License"). You may not use this file except in compliance
77c478bd9Sstevel@tonic-gate * with the License.
87c478bd9Sstevel@tonic-gate *
97c478bd9Sstevel@tonic-gate * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
107c478bd9Sstevel@tonic-gate * or http://www.opensolaris.org/os/licensing.
117c478bd9Sstevel@tonic-gate * See the License for the specific language governing permissions
127c478bd9Sstevel@tonic-gate * and limitations under the License.
137c478bd9Sstevel@tonic-gate *
147c478bd9Sstevel@tonic-gate * When distributing Covered Code, include this CDDL HEADER in each
157c478bd9Sstevel@tonic-gate * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
167c478bd9Sstevel@tonic-gate * If applicable, add the following below this CDDL HEADER, with the
177c478bd9Sstevel@tonic-gate * fields enclosed by brackets "[]" replaced with your own identifying
187c478bd9Sstevel@tonic-gate * information: Portions Copyright [yyyy] [name of copyright owner]
197c478bd9Sstevel@tonic-gate *
207c478bd9Sstevel@tonic-gate * CDDL HEADER END
217c478bd9Sstevel@tonic-gate */
227c478bd9Sstevel@tonic-gate /*
237c478bd9Sstevel@tonic-gate * Copyright 2004 Sun Microsystems, Inc. All rights reserved.
247c478bd9Sstevel@tonic-gate * Use is subject to license terms.
257c478bd9Sstevel@tonic-gate */
267c478bd9Sstevel@tonic-gate
277c478bd9Sstevel@tonic-gate /*
287c478bd9Sstevel@tonic-gate * _X_cplx_mul(z, w) returns z * w with infinities handled according
297c478bd9Sstevel@tonic-gate * to C99.
307c478bd9Sstevel@tonic-gate *
317c478bd9Sstevel@tonic-gate * If z and w are both finite, _X_cplx_mul(z, w) delivers the complex
327c478bd9Sstevel@tonic-gate * product according to the usual formula: let a = Re(z), b = Im(z),
337c478bd9Sstevel@tonic-gate * c = Re(w), and d = Im(w); then _X_cplx_mul(z, w) delivers x + I * y
347c478bd9Sstevel@tonic-gate * where x = a * c - b * d and y = a * d + b * c. Note that if both
357c478bd9Sstevel@tonic-gate * ac and bd overflow, then at least one of ad or bc must also over-
367c478bd9Sstevel@tonic-gate * flow, and vice versa, so that if one component of the product is
377c478bd9Sstevel@tonic-gate * NaN, the other is infinite. (Such a value is considered infinite
387c478bd9Sstevel@tonic-gate * according to C99.)
397c478bd9Sstevel@tonic-gate *
407c478bd9Sstevel@tonic-gate * If one of z or w is infinite and the other is either finite nonzero
417c478bd9Sstevel@tonic-gate * or infinite, _X_cplx_mul delivers an infinite result. If one factor
427c478bd9Sstevel@tonic-gate * is infinite and the other is zero, _X_cplx_mul delivers NaN + I * NaN.
437c478bd9Sstevel@tonic-gate * C99 doesn't specify the latter case.
447c478bd9Sstevel@tonic-gate *
457c478bd9Sstevel@tonic-gate * C99 also doesn't specify what should happen if either z or w is a
467c478bd9Sstevel@tonic-gate * complex NaN (i.e., neither finite nor infinite). This implementation
477c478bd9Sstevel@tonic-gate * delivers NaN + I * NaN in this case.
487c478bd9Sstevel@tonic-gate *
497c478bd9Sstevel@tonic-gate * This implementation can raise spurious underflow, overflow, invalid
507c478bd9Sstevel@tonic-gate * operation, and inexact exceptions. C99 allows this.
517c478bd9Sstevel@tonic-gate */
527c478bd9Sstevel@tonic-gate
537c478bd9Sstevel@tonic-gate #if !defined(i386) && !defined(__i386) && !defined(__amd64)
547c478bd9Sstevel@tonic-gate #error This code is for x86 only
557c478bd9Sstevel@tonic-gate #endif
567c478bd9Sstevel@tonic-gate
577c478bd9Sstevel@tonic-gate static union {
587c478bd9Sstevel@tonic-gate int i;
597c478bd9Sstevel@tonic-gate float f;
607c478bd9Sstevel@tonic-gate } inf = {
617c478bd9Sstevel@tonic-gate 0x7f800000
627c478bd9Sstevel@tonic-gate };
637c478bd9Sstevel@tonic-gate
647c478bd9Sstevel@tonic-gate /*
657c478bd9Sstevel@tonic-gate * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
667c478bd9Sstevel@tonic-gate */
677c478bd9Sstevel@tonic-gate static int
testinfl(long double x)687c478bd9Sstevel@tonic-gate testinfl(long double x)
697c478bd9Sstevel@tonic-gate {
707c478bd9Sstevel@tonic-gate union {
717c478bd9Sstevel@tonic-gate int i[3];
727c478bd9Sstevel@tonic-gate long double e;
737c478bd9Sstevel@tonic-gate } xx;
747c478bd9Sstevel@tonic-gate
757c478bd9Sstevel@tonic-gate xx.e = x;
767c478bd9Sstevel@tonic-gate if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0)
777c478bd9Sstevel@tonic-gate return (0);
787c478bd9Sstevel@tonic-gate return (1 | ((xx.i[2] << 16) >> 31));
797c478bd9Sstevel@tonic-gate }
807c478bd9Sstevel@tonic-gate
817c478bd9Sstevel@tonic-gate long double _Complex
_X_cplx_mul(long double _Complex z,long double _Complex w)827c478bd9Sstevel@tonic-gate _X_cplx_mul(long double _Complex z, long double _Complex w)
837c478bd9Sstevel@tonic-gate {
84*c764c31dSToomas Soome long double _Complex v = 0;
857c478bd9Sstevel@tonic-gate long double a, b, c, d, x, y;
867c478bd9Sstevel@tonic-gate int recalc, i, j;
877c478bd9Sstevel@tonic-gate
887c478bd9Sstevel@tonic-gate /*
897c478bd9Sstevel@tonic-gate * The following is equivalent to
907c478bd9Sstevel@tonic-gate *
917c478bd9Sstevel@tonic-gate * a = creall(z); b = cimagl(z);
927c478bd9Sstevel@tonic-gate * c = creall(w); d = cimagl(w);
937c478bd9Sstevel@tonic-gate */
947c478bd9Sstevel@tonic-gate a = ((long double *)&z)[0];
957c478bd9Sstevel@tonic-gate b = ((long double *)&z)[1];
967c478bd9Sstevel@tonic-gate c = ((long double *)&w)[0];
977c478bd9Sstevel@tonic-gate d = ((long double *)&w)[1];
987c478bd9Sstevel@tonic-gate
997c478bd9Sstevel@tonic-gate x = a * c - b * d;
1007c478bd9Sstevel@tonic-gate y = a * d + b * c;
1017c478bd9Sstevel@tonic-gate
1027c478bd9Sstevel@tonic-gate if (x != x && y != y) {
1037c478bd9Sstevel@tonic-gate /*
1047c478bd9Sstevel@tonic-gate * Both x and y are NaN, so z and w can't both be finite.
1057c478bd9Sstevel@tonic-gate * If at least one of z or w is a complex NaN, and neither
1067c478bd9Sstevel@tonic-gate * is infinite, then we might as well deliver NaN + I * NaN.
1077c478bd9Sstevel@tonic-gate * So the only cases to check are when one of z or w is
1087c478bd9Sstevel@tonic-gate * infinite.
1097c478bd9Sstevel@tonic-gate */
1107c478bd9Sstevel@tonic-gate recalc = 0;
1117c478bd9Sstevel@tonic-gate i = testinfl(a);
1127c478bd9Sstevel@tonic-gate j = testinfl(b);
1137c478bd9Sstevel@tonic-gate if (i | j) { /* z is infinite */
1147c478bd9Sstevel@tonic-gate /* "factor out" infinity */
1157c478bd9Sstevel@tonic-gate a = i;
1167c478bd9Sstevel@tonic-gate b = j;
1177c478bd9Sstevel@tonic-gate recalc = 1;
1187c478bd9Sstevel@tonic-gate }
1197c478bd9Sstevel@tonic-gate i = testinfl(c);
1207c478bd9Sstevel@tonic-gate j = testinfl(d);
1217c478bd9Sstevel@tonic-gate if (i | j) { /* w is infinite */
1227c478bd9Sstevel@tonic-gate /* "factor out" infinity */
1237c478bd9Sstevel@tonic-gate c = i;
1247c478bd9Sstevel@tonic-gate d = j;
1257c478bd9Sstevel@tonic-gate recalc = 1;
1267c478bd9Sstevel@tonic-gate }
1277c478bd9Sstevel@tonic-gate if (recalc) {
1287c478bd9Sstevel@tonic-gate x = inf.f * (a * c - b * d);
1297c478bd9Sstevel@tonic-gate y = inf.f * (a * d + b * c);
1307c478bd9Sstevel@tonic-gate }
1317c478bd9Sstevel@tonic-gate }
1327c478bd9Sstevel@tonic-gate
1337c478bd9Sstevel@tonic-gate /*
1347c478bd9Sstevel@tonic-gate * The following is equivalent to
1357c478bd9Sstevel@tonic-gate *
1367c478bd9Sstevel@tonic-gate * return x + I * y;
1377c478bd9Sstevel@tonic-gate */
1387c478bd9Sstevel@tonic-gate ((long double *)&v)[0] = x;
1397c478bd9Sstevel@tonic-gate ((long double *)&v)[1] = y;
1407c478bd9Sstevel@tonic-gate return (v);
1417c478bd9Sstevel@tonic-gate }
142