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