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: src/lib/libc/gdtoa/_hdtoa.c,v 1.5 2007/05/08 02:59:37 das Exp $"); 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 */ 48static int 49roundup(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 */ 70static void 71dorounding(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 */ 122char * 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, f; 130 131 u.d = d; 132 *sign = u.bits.sign; 133 134 switch (f = fpclassify(d)) { 135 case FP_NORMAL: 136 *decpt = u.bits.exp - DBL_ADJ; 137 break; 138 case FP_ZERO: 139return_zero: 140 *decpt = 1; 141 return (nrv_alloc("0", rve, 1)); 142 case FP_SUBNORMAL: 143 /* 144 * For processors that treat subnormals as zero, comparison 145 * with zero will be equal, so we jump to the FP_ZERO case. 146 */ 147 if(u.d == 0.0) goto return_zero; 148 u.d *= 0x1p514; 149 *decpt = u.bits.exp - (514 + DBL_ADJ); 150 break; 151 case FP_INFINITE: 152 *decpt = INT_MAX; 153 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 154 case FP_NAN: 155 *decpt = INT_MAX; 156 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 157 default: 158 LIBC_ABORT("fpclassify returned %d", f); 159 } 160 161 /* FP_NORMAL or FP_SUBNORMAL */ 162 163 if (ndigits == 0) /* dtoa() compatibility */ 164 ndigits = 1; 165 166 /* 167 * For simplicity, we generate all the digits even if the 168 * caller has requested fewer. 169 */ 170 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 171 s0 = rv_alloc(bufsize); 172 173 /* 174 * We work from right to left, first adding any requested zero 175 * padding, then the least significant portion of the 176 * mantissa, followed by the most significant. The buffer is 177 * filled with the byte values 0x0 through 0xf, which are 178 * converted to xdigs[0x0] through xdigs[0xf] after the 179 * rounding phase. 180 */ 181 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 182 *s = 0; 183 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 184 *s = u.bits.manl & 0xf; 185 u.bits.manl >>= 4; 186 } 187 for (; s > s0; s--) { 188 *s = u.bits.manh & 0xf; 189 u.bits.manh >>= 4; 190 } 191 192 /* 193 * At this point, we have snarfed all the bits in the 194 * mantissa, with the possible exception of the highest-order 195 * (partial) nibble, which is dealt with by the next 196 * statement. We also tack on the implicit normalization bit. 197 */ 198 *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4)); 199 200 /* If ndigits < 0, we are expected to auto-size the precision. */ 201 if (ndigits < 0) { 202 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 203 ; 204 } 205 206 if (sigfigs > ndigits && s0[ndigits] != 0) 207 dorounding(s0, ndigits, u.bits.sign, decpt); 208 209 s = s0 + ndigits; 210 if (rve != NULL) 211 *rve = s; 212 *s-- = '\0'; 213 for (; s >= s0; s--) 214 *s = xdigs[(unsigned int)*s]; 215 216 return (s0); 217} 218 219#if (LDBL_MANT_DIG > DBL_MANT_DIG) 220 221/* 222 * This is the long double version of __hdtoa(). 223 */ 224char * 225__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 226 char **rve) 227{ 228 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4; 229 union IEEEl2bits u; 230 char *s, *s0; 231 int bufsize, f; 232 233 u.e = e; 234 *sign = u.bits.sign; 235 236 switch (f = fpclassify(e)) { 237 case FP_NORMAL: 238 case FP_SUPERNORMAL: 239 *decpt = u.bits.exp - LDBL_ADJ; 240 break; 241 case FP_ZERO: 242 *decpt = 1; 243 return (nrv_alloc("0", rve, 1)); 244 case FP_SUBNORMAL: 245 u.e *= 0x1p514L; 246 *decpt = u.bits.exp - (514 + LDBL_ADJ); 247 break; 248 case FP_INFINITE: 249 *decpt = INT_MAX; 250 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 251 case FP_NAN: 252 *decpt = INT_MAX; 253 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 254 default: 255 LIBC_ABORT("fpclassify returned %d", f); 256 } 257 258 /* FP_NORMAL or FP_SUBNORMAL */ 259 260 if (ndigits == 0) /* dtoa() compatibility */ 261 ndigits = 1; 262 263 /* 264 * For simplicity, we generate all the digits even if the 265 * caller has requested fewer. 266 */ 267 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 268 s0 = rv_alloc(bufsize); 269 270 /* 271 * We work from right to left, first adding any requested zero 272 * padding, then the least significant portion of the 273 * mantissa, followed by the most significant. The buffer is 274 * filled with the byte values 0x0 through 0xf, which are 275 * converted to xdigs[0x0] through xdigs[0xf] after the 276 * rounding phase. 277 */ 278 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 279 *s = 0; 280 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 281 *s = u.bits.manl & 0xf; 282 u.bits.manl >>= 4; 283 } 284 for (; s > s0; s--) { 285 *s = u.bits.manh & 0xf; 286 u.bits.manh >>= 4; 287 } 288 289 /* 290 * At this point, we have snarfed all the bits in the 291 * mantissa, with the possible exception of the highest-order 292 * (partial) nibble, which is dealt with by the next 293 * statement. We also tack on the implicit normalization bit. 294 */ 295 *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4)); 296 297 /* If ndigits < 0, we are expected to auto-size the precision. */ 298 if (ndigits < 0) { 299 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 300 ; 301 } 302 303 if (sigfigs > ndigits && s0[ndigits] != 0) 304 dorounding(s0, ndigits, u.bits.sign, decpt); 305 306 s = s0 + ndigits; 307 if (rve != NULL) 308 *rve = s; 309 *s-- = '\0'; 310 for (; s >= s0; s--) 311 *s = xdigs[(unsigned int)*s]; 312 313 return (s0); 314} 315 316#else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 317 318char * 319__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 320 char **rve) 321{ 322 323 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve)); 324} 325 326#endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 327