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 * _X_cplx_mul(z, w) returns z * w with infinities handled according 29 * to C99. 30 * 31 * If z and w are both finite, _X_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 _X_cplx_mul(z, w) delivers x + I * y 34 * where x = a * c - b * d and y = a * d + b * c. Note that if both 35 * ac and bd overflow, then at least one of ad or bc must also over- 36 * flow, and vice versa, so that if one component of the product is 37 * NaN, the other is infinite. (Such a value is considered infinite 38 * according to C99.) 39 * 40 * If one of z or w is infinite and the other is either finite nonzero 41 * or infinite, _X_cplx_mul delivers an infinite result. If one factor 42 * is infinite and the other is zero, _X_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 underflow, overflow, invalid 50 * operation, and inexact 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 testinfl(long double x) 69 { 70 union { 71 int i[3]; 72 long double e; 73 } xx; 74 75 xx.e = x; 76 if ((xx.i[2] & 0x7fff) != 0x7fff || ((xx.i[1] << 1) | xx.i[0]) != 0) 77 return (0); 78 return (1 | ((xx.i[2] << 16) >> 31)); 79 } 80 81 long double _Complex 82 _X_cplx_mul(long double _Complex z, long double _Complex w) 83 { 84 long double _Complex v = 0; 85 long double a, b, c, d, x, y; 86 int recalc, i, j; 87 88 /* 89 * The following is equivalent to 90 * 91 * a = creall(z); b = cimagl(z); 92 * c = creall(w); d = cimagl(w); 93 */ 94 a = ((long double *)&z)[0]; 95 b = ((long double *)&z)[1]; 96 c = ((long double *)&w)[0]; 97 d = ((long double *)&w)[1]; 98 99 x = a * c - b * d; 100 y = a * d + b * c; 101 102 if (x != x && y != y) { 103 /* 104 * Both x and y are NaN, so z and w can't both be finite. 105 * If at least one of z or w is a complex NaN, and neither 106 * is infinite, then we might as well deliver NaN + I * NaN. 107 * So the only cases to check are when one of z or w is 108 * infinite. 109 */ 110 recalc = 0; 111 i = testinfl(a); 112 j = testinfl(b); 113 if (i | j) { /* z is infinite */ 114 /* "factor out" infinity */ 115 a = i; 116 b = j; 117 recalc = 1; 118 } 119 i = testinfl(c); 120 j = testinfl(d); 121 if (i | j) { /* w is infinite */ 122 /* "factor out" infinity */ 123 c = i; 124 d = j; 125 recalc = 1; 126 } 127 if (recalc) { 128 x = inf.f * (a * c - b * d); 129 y = inf.f * (a * d + b * c); 130 } 131 } 132 133 /* 134 * The following is equivalent to 135 * 136 * return x + I * y; 137 */ 138 ((long double *)&v)[0] = x; 139 ((long double *)&v)[1] = y; 140 return (v); 141 } 142