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 2004 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_mul(z, w) returns z * w with infinities handled according 31 * to C99. 32 * 33 * If z and w are both finite, _D_cplx_mul(z, w) delivers the complex 34 * product according to the usual formula: let a = Re(z), b = Im(z), 35 * c = Re(w), and d = Im(w); then _D_cplx_mul(z, w) delivers x + I * y 36 * where x = a * c - b * d and y = a * d + b * c. This implementation 37 * uses extended precision to form these expressions, so none of the 38 * intermediate products can overflow. 39 * 40 * If one of z or w is infinite and the other is either finite nonzero 41 * or infinite, _D_cplx_mul delivers an infinite result. If one factor 42 * is infinite and the other is zero, _D_cplx_mul delivers NaN + I * NaN. 43 * C99 doesn't specify the latter case. 44 * 45 * C99 also doesn't specify what should happen if either z or w is a 46 * complex NaN (i.e., neither finite nor infinite). This implementation 47 * delivers NaN + I * NaN in this case. 48 * 49 * This implementation can raise spurious invalid operation and inexact 50 * exceptions. C99 allows this. 51 */ 52 53 #if !defined(i386) && !defined(__i386) && !defined(__amd64) 54 #error This code is for x86 only 55 #endif 56 57 static union { 58 int i; 59 float f; 60 } inf = { 61 0x7f800000 62 }; 63 64 /* 65 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise 66 */ 67 static int 68 testinf(double x) 69 { 70 union { 71 int i[2]; 72 double d; 73 } xx; 74 75 xx.d = x; 76 return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)? 77 (1 | (xx.i[1] >> 31)) : 0); 78 } 79 80 double _Complex 81 _D_cplx_mul(double _Complex z, double _Complex w) 82 { 83 double _Complex v; 84 double a, b, c, d; 85 long double x, y; 86 int recalc, i, j; 87 88 /* 89 * The following is equivalent to 90 * 91 * a = creal(z); b = cimag(z); 92 * c = creal(w); d = cimag(w); 93 */ 94 /* LINTED alignment */ 95 a = ((double *)&z)[0]; 96 /* LINTED alignment */ 97 b = ((double *)&z)[1]; 98 /* LINTED alignment */ 99 c = ((double *)&w)[0]; 100 /* LINTED alignment */ 101 d = ((double *)&w)[1]; 102 103 x = (long double)a * c - (long double)b * d; 104 y = (long double)a * d + (long double)b * c; 105 106 if (x != x && y != y) { 107 /* 108 * Both x and y are NaN, so z and w can't both be finite. 109 * If at least one of z or w is a complex NaN, and neither 110 * is infinite, then we might as well deliver NaN + I * NaN. 111 * So the only cases to check are when one of z or w is 112 * infinite. 113 */ 114 recalc = 0; 115 i = testinf(a); 116 j = testinf(b); 117 if (i | j) { /* z is infinite */ 118 /* "factor out" infinity */ 119 a = i; 120 b = j; 121 recalc = 1; 122 } 123 i = testinf(c); 124 j = testinf(d); 125 if (i | j) { /* w is infinite */ 126 /* "factor out" infinity */ 127 c = i; 128 d = j; 129 recalc = 1; 130 } 131 if (recalc) { 132 x = inf.f * ((long double)a * c - (long double)b * d); 133 y = inf.f * ((long double)a * d + (long double)b * c); 134 } 135 } 136 137 /* 138 * The following is equivalent to 139 * 140 * return x + I * y; 141 */ 142 /* LINTED alignment */ 143 ((double *)&v)[0] = (double)x; 144 /* LINTED alignment */ 145 ((double *)&v)[1] = (double)y; 146 return (v); 147 } 148