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 * _X_cplx_mul(z, w) returns z * w with infinities handled according 31 * to C99. 32 * 33 * If z and w are both finite, _X_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 _X_cplx_mul(z, w) delivers x + I * y 36 * where x = a * c - b * d and y = a * d + b * c. Note that if both 37 * ac and bd overflow, then at least one of ad or bc must also over- 38 * flow, and vice versa, so that if one component of the product is 39 * NaN, the other is infinite. (Such a value is considered infinite 40 * according to C99.) 41 * 42 * If one of z or w is infinite and the other is either finite nonzero 43 * or infinite, _X_cplx_mul delivers an infinite result. If one factor 44 * is infinite and the other is zero, _X_cplx_mul delivers NaN + I * NaN. 45 * C99 doesn't specify the latter case. 46 * 47 * C99 also doesn't specify what should happen if either z or w is a 48 * complex NaN (i.e., neither finite nor infinite). This implementation 49 * delivers NaN + I * NaN in this case. 50 * 51 * This implementation can raise spurious underflow, overflow, invalid 52 * operation, and inexact exceptions. C99 allows this. 53 */ 54 55 #if !defined(i386) && !defined(__i386) && !defined(__amd64) 56 #error This code is for x86 only 57 #endif 58 59 static union { 60 int i; 61 float f; 62 } inf = { 63 0x7f800000 64 }; 65 66 /* 67 * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise 68 */ 69 static int 70 testinfl(long double x) 71 { 72 union { 73 int i[3]; 74 long double e; 75 } xx; 76 77 xx.e = x; 78 if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0) 79 return (0); 80 return (1 | ((xx.i[2] << 16) >> 31)); 81 } 82 83 long double _Complex 84 _X_cplx_mul(long double _Complex z, long double _Complex w) 85 { 86 long double _Complex v; 87 long double a, b, c, d, x, y; 88 int recalc, i, j; 89 90 /* 91 * The following is equivalent to 92 * 93 * a = creall(z); b = cimagl(z); 94 * c = creall(w); d = cimagl(w); 95 */ 96 a = ((long double *)&z)[0]; 97 b = ((long double *)&z)[1]; 98 c = ((long double *)&w)[0]; 99 d = ((long double *)&w)[1]; 100 101 x = a * c - b * d; 102 y = a * d + 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 = testinfl(a); 114 j = testinfl(b); 115 if (i | j) { /* z is infinite */ 116 /* "factor out" infinity */ 117 a = i; 118 b = j; 119 recalc = 1; 120 } 121 i = testinfl(c); 122 j = testinfl(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 * (a * c - b * d); 131 y = inf.f * (a * d + b * c); 132 } 133 } 134 135 /* 136 * The following is equivalent to 137 * 138 * return x + I * y; 139 */ 140 ((long double *)&v)[0] = x; 141 ((long double *)&v)[1] = y; 142 return (v); 143 } 144