1 /*- 2 * Copyright (c) 2004, 2005 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 #include "fpmath.h" 34 #include "gdtoaimp.h" 35 36 /* Strings values used by dtoa() */ 37 #define INFSTR "Infinity" 38 #define NANSTR "NaN" 39 40 #define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4)) 41 #define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4)) 42 43 /* 44 * Round up the given digit string. If the digit string is fff...f, 45 * this procedure sets it to 100...0 and returns 1 to indicate that 46 * the exponent needs to be bumped. Otherwise, 0 is returned. 47 */ 48 static int 49 roundup(char *s0, int ndigits) 50 { 51 char *s; 52 53 for (s = s0 + ndigits - 1; *s == 0xf; s--) { 54 if (s == s0) { 55 *s = 1; 56 return (1); 57 } 58 *s = 0; 59 } 60 ++*s; 61 return (0); 62 } 63 64 /* 65 * Round the given digit string to ndigits digits according to the 66 * current rounding mode. Note that this could produce a string whose 67 * value is not representable in the corresponding floating-point 68 * type. The exponent pointed to by decpt is adjusted if necessary. 69 */ 70 static void 71 dorounding(char *s0, int ndigits, int sign, int *decpt) 72 { 73 int adjust = 0; /* do we need to adjust the exponent? */ 74 75 switch (FLT_ROUNDS) { 76 case 0: /* toward zero */ 77 default: /* implementation-defined */ 78 break; 79 case 1: /* to nearest, halfway rounds to even */ 80 if ((s0[ndigits] > 8) || 81 (s0[ndigits] == 8 && s0[ndigits + 1] & 1)) 82 adjust = roundup(s0, ndigits); 83 break; 84 case 2: /* toward +inf */ 85 if (sign == 0) 86 adjust = roundup(s0, ndigits); 87 break; 88 case 3: /* toward -inf */ 89 if (sign != 0) 90 adjust = roundup(s0, ndigits); 91 break; 92 } 93 94 if (adjust) 95 *decpt += 4; 96 } 97 98 /* 99 * This procedure converts a double-precision number in IEEE format 100 * into a string of hexadecimal digits and an exponent of 2. Its 101 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the 102 * following exceptions: 103 * 104 * - An ndigits < 0 causes it to use as many digits as necessary to 105 * represent the number exactly. 106 * - The additional xdigs argument should point to either the string 107 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on 108 * which case is desired. 109 * - This routine does not repeat dtoa's mistake of setting decpt 110 * to 9999 in the case of an infinity or NaN. INT_MAX is used 111 * for this purpose instead. 112 * 113 * Note that the C99 standard does not specify what the leading digit 114 * should be for non-zero numbers. For instance, 0x1.3p3 is the same 115 * as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the 116 * first digit so that subsequent digits are aligned on nibble 117 * boundaries (before rounding). 118 * 119 * Inputs: d, xdigs, ndigits 120 * Outputs: decpt, sign, rve 121 */ 122 char * 123 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, 124 char **rve) 125 { 126 static const int sigfigs = (DBL_MANT_DIG + 3) / 4; 127 union IEEEd2bits u; 128 char *s, *s0; 129 int bufsize; 130 131 u.d = d; 132 *sign = u.bits.sign; 133 134 switch (fpclassify(d)) { 135 case FP_NORMAL: 136 *decpt = u.bits.exp - DBL_ADJ; 137 break; 138 case FP_ZERO: 139 *decpt = 1; 140 return (nrv_alloc("0", rve, 1)); 141 case FP_SUBNORMAL: 142 u.d *= 0x1p514; 143 *decpt = u.bits.exp - (514 + DBL_ADJ); 144 break; 145 case FP_INFINITE: 146 *decpt = INT_MAX; 147 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 148 case FP_NAN: 149 *decpt = INT_MAX; 150 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 151 default: 152 abort(); 153 } 154 155 /* FP_NORMAL or FP_SUBNORMAL */ 156 157 if (ndigits == 0) /* dtoa() compatibility */ 158 ndigits = 1; 159 160 /* 161 * For simplicity, we generate all the digits even if the 162 * caller has requested fewer. 163 */ 164 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 165 s0 = rv_alloc(bufsize); 166 167 /* 168 * We work from right to left, first adding any requested zero 169 * padding, then the least significant portion of the 170 * mantissa, followed by the most significant. The buffer is 171 * filled with the byte values 0x0 through 0xf, which are 172 * converted to xdigs[0x0] through xdigs[0xf] after the 173 * rounding phase. 174 */ 175 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 176 *s = 0; 177 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 178 *s = u.bits.manl & 0xf; 179 u.bits.manl >>= 4; 180 } 181 for (; s > s0; s--) { 182 *s = u.bits.manh & 0xf; 183 u.bits.manh >>= 4; 184 } 185 186 /* 187 * At this point, we have snarfed all the bits in the 188 * mantissa, with the possible exception of the highest-order 189 * (partial) nibble, which is dealt with by the next 190 * statement. We also tack on the implicit normalization bit. 191 */ 192 *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4)); 193 194 /* If ndigits < 0, we are expected to auto-size the precision. */ 195 if (ndigits < 0) { 196 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 197 ; 198 } 199 200 if (sigfigs > ndigits && s0[ndigits] != 0) 201 dorounding(s0, ndigits, u.bits.sign, decpt); 202 203 s = s0 + ndigits; 204 if (rve != NULL) 205 *rve = s; 206 *s-- = '\0'; 207 for (; s >= s0; s--) 208 *s = xdigs[(unsigned int)*s]; 209 210 return (s0); 211 } 212 213 #if (LDBL_MANT_DIG > DBL_MANT_DIG) 214 215 /* 216 * This is the long double version of __hdtoa(). 217 */ 218 char * 219 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 220 char **rve) 221 { 222 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4; 223 union IEEEl2bits u; 224 char *s, *s0; 225 int bufsize; 226 227 u.e = e; 228 *sign = u.bits.sign; 229 230 switch (fpclassify(e)) { 231 case FP_NORMAL: 232 *decpt = u.bits.exp - LDBL_ADJ; 233 break; 234 case FP_ZERO: 235 *decpt = 1; 236 return (nrv_alloc("0", rve, 1)); 237 case FP_SUBNORMAL: 238 u.e *= 0x1p514L; 239 *decpt = u.bits.exp - (514 + LDBL_ADJ); 240 break; 241 case FP_INFINITE: 242 *decpt = INT_MAX; 243 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 244 case FP_NAN: 245 *decpt = INT_MAX; 246 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 247 default: 248 abort(); 249 } 250 251 /* FP_NORMAL or FP_SUBNORMAL */ 252 253 if (ndigits == 0) /* dtoa() compatibility */ 254 ndigits = 1; 255 256 /* 257 * For simplicity, we generate all the digits even if the 258 * caller has requested fewer. 259 */ 260 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 261 s0 = rv_alloc(bufsize); 262 263 /* 264 * We work from right to left, first adding any requested zero 265 * padding, then the least significant portion of the 266 * mantissa, followed by the most significant. The buffer is 267 * filled with the byte values 0x0 through 0xf, which are 268 * converted to xdigs[0x0] through xdigs[0xf] after the 269 * rounding phase. 270 */ 271 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 272 *s = 0; 273 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 274 *s = u.bits.manl & 0xf; 275 u.bits.manl >>= 4; 276 } 277 for (; s > s0; s--) { 278 *s = u.bits.manh & 0xf; 279 u.bits.manh >>= 4; 280 } 281 282 /* 283 * At this point, we have snarfed all the bits in the 284 * mantissa, with the possible exception of the highest-order 285 * (partial) nibble, which is dealt with by the next 286 * statement. We also tack on the implicit normalization bit. 287 */ 288 *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4)); 289 290 /* If ndigits < 0, we are expected to auto-size the precision. */ 291 if (ndigits < 0) { 292 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 293 ; 294 } 295 296 if (sigfigs > ndigits && s0[ndigits] != 0) 297 dorounding(s0, ndigits, u.bits.sign, decpt); 298 299 s = s0 + ndigits; 300 if (rve != NULL) 301 *rve = s; 302 *s-- = '\0'; 303 for (; s >= s0; s--) 304 *s = xdigs[(unsigned int)*s]; 305 306 return (s0); 307 } 308 309 #else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 310 311 char * 312 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 313 char **rve) 314 { 315 316 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve)); 317 } 318 319 #endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 320