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 /* 28 * _D_cplx_mul(z, w) returns z * w with infinities handled according 29 * to C99. 30 * 31 * If z and w are both finite, _D_cplx_mul(z, w) delivers the complex 32 * product according to the usual formula: let a = Re(z), b = Im(z), 33 * c = Re(w), and d = Im(w); then _D_cplx_mul(z, w) delivers x + I * y 34 * where x = a * c - b * d and y = a * d + b * c. This implementation 35 * uses extended precision to form these expressions, so none of the 36 * intermediate products can overflow. 37 * 38 * If one of z or w is infinite and the other is either finite nonzero 39 * or infinite, _D_cplx_mul delivers an infinite result. If one factor 40 * is infinite and the other is zero, _D_cplx_mul delivers NaN + I * NaN. 41 * C99 doesn't specify the latter case. 42 * 43 * C99 also doesn't specify what should happen if either z or w is a 44 * complex NaN (i.e., neither finite nor infinite). This implementation 45 * delivers NaN + I * NaN in this case. 46 * 47 * This implementation can raise spurious invalid operation and inexact 48 * exceptions. C99 allows this. 49 */ 50 51 #if !defined(i386) && !defined(__i386) && !defined(__amd64) 52 #error This code is for x86 only 53 #endif 54 55 static union { 56 int i; 57 float f; 58 } inf = { 59 0x7f800000 60 }; 61 62 /* 63 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise 64 */ 65 static int 66 testinf(double x) 67 { 68 union { 69 int i[2]; 70 double d; 71 } xx; 72 73 xx.d = x; 74 return (((((xx.i[1] << 1) - 0xffe00000) | xx.i[0]) == 0)? 75 (1 | (xx.i[1] >> 31)) : 0); 76 } 77 78 double _Complex 79 _D_cplx_mul(double _Complex z, double _Complex w) 80 { 81 double _Complex v = 0; 82 double a, b, c, d; 83 long double x, y; 84 int recalc, i, j; 85 86 /* 87 * The following is equivalent to 88 * 89 * a = creal(z); b = cimag(z); 90 * c = creal(w); d = cimag(w); 91 */ 92 /* LINTED alignment */ 93 a = ((double *)&z)[0]; 94 /* LINTED alignment */ 95 b = ((double *)&z)[1]; 96 /* LINTED alignment */ 97 c = ((double *)&w)[0]; 98 /* LINTED alignment */ 99 d = ((double *)&w)[1]; 100 101 x = (long double)a * c - (long double)b * d; 102 y = (long double)a * d + (long double)b * c; 103 104 if (x != x && y != y) { 105 /* 106 * Both x and y are NaN, so z and w can't both be finite. 107 * If at least one of z or w is a complex NaN, and neither 108 * is infinite, then we might as well deliver NaN + I * NaN. 109 * So the only cases to check are when one of z or w is 110 * infinite. 111 */ 112 recalc = 0; 113 i = testinf(a); 114 j = testinf(b); 115 if (i | j) { /* z is infinite */ 116 /* "factor out" infinity */ 117 a = i; 118 b = j; 119 recalc = 1; 120 } 121 i = testinf(c); 122 j = testinf(d); 123 if (i | j) { /* w is infinite */ 124 /* "factor out" infinity */ 125 c = i; 126 d = j; 127 recalc = 1; 128 } 129 if (recalc) { 130 x = inf.f * ((long double)a * c - (long double)b * d); 131 y = inf.f * ((long double)a * d + (long double)b * c); 132 } 133 } 134 135 /* 136 * The following is equivalent to 137 * 138 * return x + I * y; 139 */ 140 /* LINTED alignment */ 141 ((double *)&v)[0] = (double)x; 142 /* LINTED alignment */ 143 ((double *)&v)[1] = (double)y; 144 return (v); 145 } 146