1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG> 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 #include <sys/cdefs.h> 30 __FBSDID("$FreeBSD$"); 31 32 #include <float.h> 33 #include <limits.h> 34 #include <math.h> 35 36 #include "../stdio/floatio.h" 37 #include "fpmath.h" 38 #include "gdtoaimp.h" 39 40 /* Strings values used by dtoa() */ 41 #define INFSTR "Infinity" 42 #define NANSTR "NaN" 43 44 #define DBL_ADJ (DBL_MAX_EXP - 2) 45 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1) 46 47 static const float one[] = { 1.0f, -1.0f }; 48 49 /* 50 * This procedure converts a double-precision number in IEEE format 51 * into a string of hexadecimal digits and an exponent of 2. Its 52 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the 53 * following exceptions: 54 * 55 * - An ndigits < 0 causes it to use as many digits as necessary to 56 * represent the number exactly. 57 * - The additional xdigs argument should point to either the string 58 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on 59 * which case is desired. 60 * - This routine does not repeat dtoa's mistake of setting decpt 61 * to 9999 in the case of an infinity or NaN. INT_MAX is used 62 * for this purpose instead. 63 * 64 * Note that the C99 standard does not specify what the leading digit 65 * should be for non-zero numbers. For instance, 0x1.3p3 is the same 66 * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes 67 * the leading digit a 1. This ensures that the exponent printed is the 68 * actual base-2 exponent, i.e., ilogb(d). 69 * 70 * Inputs: d, xdigs, ndigits 71 * Outputs: decpt, sign, rve 72 */ 73 char * 74 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, 75 char **rve) 76 { 77 union IEEEd2bits u; 78 char *s, *s0; 79 int bufsize; 80 uint32_t manh, manl; 81 82 u.d = d; 83 *sign = u.bits.sign; 84 85 switch (fpclassify(d)) { 86 case FP_NORMAL: 87 *decpt = u.bits.exp - DBL_ADJ; 88 break; 89 case FP_ZERO: 90 *decpt = 1; 91 return (nrv_alloc("0", rve, 1)); 92 case FP_SUBNORMAL: 93 u.d *= 0x1p514; 94 *decpt = u.bits.exp - (514 + DBL_ADJ); 95 break; 96 case FP_INFINITE: 97 *decpt = INT_MAX; 98 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 99 default: /* FP_NAN or unrecognized */ 100 *decpt = INT_MAX; 101 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 102 } 103 104 /* FP_NORMAL or FP_SUBNORMAL */ 105 106 if (ndigits == 0) /* dtoa() compatibility */ 107 ndigits = 1; 108 109 /* 110 * If ndigits < 0, we are expected to auto-size, so we allocate 111 * enough space for all the digits. 112 */ 113 bufsize = (ndigits > 0) ? ndigits : SIGFIGS; 114 s0 = rv_alloc(bufsize); 115 116 /* Round to the desired number of digits. */ 117 if (SIGFIGS > ndigits && ndigits > 0) { 118 float redux = one[u.bits.sign]; 119 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG; 120 u.bits.exp = offset; 121 u.d += redux; 122 u.d -= redux; 123 *decpt += u.bits.exp - offset; 124 } 125 126 manh = u.bits.manh; 127 manl = u.bits.manl; 128 *s0 = '1'; 129 for (s = s0 + 1; s < s0 + bufsize; s++) { 130 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf]; 131 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4)); 132 manl <<= 4; 133 } 134 135 /* If ndigits < 0, we are expected to auto-size the precision. */ 136 if (ndigits < 0) { 137 for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--) 138 ; 139 } 140 141 s = s0 + ndigits; 142 *s = '\0'; 143 if (rve != NULL) 144 *rve = s; 145 return (s0); 146 } 147