1 /* $NetBSD: compat_ldexp_ieee754.c,v 1.8 2020/05/21 05:56:31 riastradh Exp $ */ 2 3 /*- 4 * Copyright (c) 1999 The NetBSD Foundation, Inc. 5 * All rights reserved. 6 * 7 * This code is derived from software contributed to The NetBSD Foundation 8 * by Charles M. Hannum. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS 20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS 23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 29 * POSSIBILITY OF SUCH DAMAGE. 30 */ 31 32 #include <sys/cdefs.h> 33 #if defined(LIBC_SCCS) && !defined(lint) 34 __RCSID("$NetBSD: compat_ldexp_ieee754.c,v 1.8 2020/05/21 05:56:31 riastradh Exp $"); 35 #endif /* LIBC_SCCS and not lint */ 36 37 #include <sys/types.h> 38 39 #include <machine/ieee.h> 40 41 #include <errno.h> 42 #include <float.h> 43 #include <math.h> 44 45 static volatile const double tiny = DBL_MIN, huge = DBL_MAX; 46 47 static double 48 underflow(double val) 49 { 50 51 errno = ERANGE; 52 return (val < 0 ? -tiny*tiny : tiny*tiny); 53 } 54 55 static double 56 overflow(double val) 57 { 58 59 errno = ERANGE; 60 return (val < 0 ? -huge*huge : huge*huge); 61 } 62 63 /* 64 * Multiply the given value by 2^expon. 65 */ 66 double 67 ldexp(double val, int expon) 68 { 69 int oldexp, newexp; 70 union ieee_double_u u, mul; 71 72 u.dblu_d = val; 73 oldexp = u.dblu_dbl.dbl_exp; 74 75 /* 76 * If input is zero, Inf or NaN, just return it, but raise 77 * invalid exception if it is a signalling NaN: adding any of 78 * these inputs to itself gives itself as output; arithmetic on 79 * a signalling NaN additionally raises invalid-operation. 80 */ 81 if (u.dblu_d == 0.0 || oldexp == DBL_EXP_INFNAN) 82 return (val + val); 83 84 if (oldexp == 0) { 85 /* 86 * u.v is denormal. We must adjust it so that the exponent 87 * arithmetic below will work. 88 */ 89 if (expon <= DBL_EXP_BIAS) { 90 /* 91 * Optimization: if the scaling can be done in a single 92 * multiply, or underflows, just do it now. 93 */ 94 if (expon <= -DBL_FRACBITS) 95 return underflow(val); 96 mul.dblu_d = 0.0; 97 mul.dblu_dbl.dbl_exp = expon + DBL_EXP_BIAS; 98 u.dblu_d *= mul.dblu_d; 99 if (u.dblu_d == 0.0) 100 return underflow(val); 101 return (u.dblu_d); 102 } else { 103 /* 104 * We know that expon is very large, and therefore the 105 * result cannot be denormal (though it may be Inf). 106 * Shift u.v by just enough to make it normal. 107 */ 108 mul.dblu_d = 0.0; 109 mul.dblu_dbl.dbl_exp = DBL_FRACBITS + DBL_EXP_BIAS; 110 u.dblu_d *= mul.dblu_d; 111 expon -= DBL_FRACBITS; 112 oldexp = u.dblu_dbl.dbl_exp; 113 } 114 } 115 116 /* 117 * u.v is now normalized and oldexp has been adjusted if necessary. 118 * Calculate the new exponent and check for underflow and overflow. 119 */ 120 newexp = oldexp + expon; 121 122 if (newexp >= DBL_EXP_INFNAN || 123 (oldexp >= 0 && expon >= DBL_EXP_INFNAN)) { 124 /* 125 * The result overflowed; return +/-Inf. 126 */ 127 return overflow(val); 128 } else if (newexp <= 0) { 129 /* 130 * The output number is either denormal or underflows (see 131 * comments in machine/ieee.h). 132 */ 133 if (newexp <= -DBL_FRACBITS) 134 return underflow(val); 135 /* 136 * Denormalize the result. We do this with a multiply. If 137 * expon is very large, it won't fit in a double, so we have 138 * to adjust the exponent first. This is safe because we know 139 * that u.v is normal at this point. 140 */ 141 if (expon <= -DBL_EXP_BIAS) { 142 u.dblu_dbl.dbl_exp = 1; 143 expon += oldexp - 1; 144 } 145 mul.dblu_d = 0.0; 146 mul.dblu_dbl.dbl_exp = expon + DBL_EXP_BIAS; 147 u.dblu_d *= mul.dblu_d; 148 return (u.dblu_d); 149 } else { 150 /* 151 * The result is normal; just replace the old exponent with the 152 * new one. 153 */ 154 u.dblu_dbl.dbl_exp = newexp; 155 return (u.dblu_d); 156 } 157 } 158