1 /*- 2 * Copyright (c) 2004 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 <inttypes.h> 32 #include <limits.h> 33 #include <math.h> 34 #include <stdlib.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_BIAS (DBL_MAX_EXP - 1) 43 #define LDBL_BIAS (LDBL_MAX_EXP - 1) 44 45 #ifdef LDBL_IMPLICIT_NBIT 46 #define LDBL_NBIT_ADJ 0 47 #else 48 #define LDBL_NBIT_ADJ 1 49 #endif 50 51 /* 52 * Efficiently compute the log2 of an integer. Uses a combination of 53 * arcane tricks found in fortune and arcane tricks not (yet) in 54 * fortune. This routine behaves similarly to fls(9). 55 */ 56 static int 57 log2_32(uint32_t n) 58 { 59 60 n |= (n >> 1); 61 n |= (n >> 2); 62 n |= (n >> 4); 63 n |= (n >> 8); 64 n |= (n >> 16); 65 66 n = (n & 0x55555555) + ((n & 0xaaaaaaaa) >> 1); 67 n = (n & 0x33333333) + ((n & 0xcccccccc) >> 2); 68 n = (n & 0x0f0f0f0f) + ((n & 0xf0f0f0f0) >> 4); 69 n = (n & 0x00ff00ff) + ((n & 0xff00ff00) >> 8); 70 n = (n & 0x0000ffff) + ((n & 0xffff0000) >> 16); 71 return (n - 1); 72 } 73 74 #if (LDBL_MANH_SIZE > 32 || LDBL_MANL_SIZE > 32) 75 76 static int 77 log2_64(uint64_t n) 78 { 79 80 if (n >> 32 != 0) 81 return (log2_32((uint32_t)(n >> 32)) + 32); 82 else 83 return (log2_32((uint32_t)n)); 84 } 85 86 #endif /* (LDBL_MANH_SIZE > 32 || LDBL_MANL_SIZE > 32) */ 87 88 /* 89 * Round up the given digit string. If the digit string is fff...f, 90 * this procedure sets it to 100...0 and returns 1 to indicate that 91 * the exponent needs to be bumped. Otherwise, 0 is returned. 92 */ 93 static int 94 roundup(char *s0, int ndigits) 95 { 96 char *s; 97 98 for (s = s0 + ndigits - 1; *s == 0xf; s--) { 99 if (s == s0) { 100 *s = 1; 101 return (1); 102 } 103 ++*s; 104 } 105 ++*s; 106 return (0); 107 } 108 109 /* 110 * Round the given digit string to ndigits digits according to the 111 * current rounding mode. Note that this could produce a string whose 112 * value is not representable in the corresponding floating-point 113 * type. The exponent pointed to by decpt is adjusted if necessary. 114 */ 115 static void 116 dorounding(char *s0, int ndigits, int sign, int *decpt) 117 { 118 int adjust = 0; /* do we need to adjust the exponent? */ 119 120 switch (FLT_ROUNDS) { 121 case 0: /* toward zero */ 122 default: /* implementation-defined */ 123 break; 124 case 1: /* to nearest, halfway rounds to even */ 125 if ((s0[ndigits] > 8) || 126 (s0[ndigits] == 8 && s0[ndigits - 1] & 1)) 127 adjust = roundup(s0, ndigits); 128 break; 129 case 2: /* toward +inf */ 130 if (sign == 0) 131 adjust = roundup(s0, ndigits); 132 break; 133 case 3: /* toward -inf */ 134 if (sign != 0) 135 adjust = roundup(s0, ndigits); 136 break; 137 } 138 139 if (adjust) 140 *decpt += 4; 141 } 142 143 /* 144 * This procedure converts a double-precision number in IEEE format 145 * into a string of hexadecimal digits and an exponent of 2. Its 146 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the 147 * following exceptions: 148 * 149 * - An ndigits < 0 causes it to use as many digits as necessary to 150 * represent the number exactly. 151 * - The additional xdigs argument should point to either the string 152 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on 153 * which case is desired. 154 * - This routine does not repeat dtoa's mistake of setting decpt 155 * to 9999 in the case of an infinity or NaN. INT_MAX is used 156 * for this purpose instead. 157 * 158 * Note that the C99 standard does not specify what the leading digit 159 * should be for non-zero numbers. For instance, 0x1.3p3 is the same 160 * as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the 161 * first digit so that subsequent digits are aligned on nibble 162 * boundaries (before rounding). 163 * 164 * Inputs: d, xdigs, ndigits 165 * Outputs: decpt, sign, rve 166 */ 167 char * 168 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, 169 char **rve) 170 { 171 union IEEEd2bits u; 172 char *s, *s0; 173 int bufsize; 174 int impnbit; /* implicit normalization bit */ 175 int pos; 176 int shift; /* for subnormals, # of shifts required to normalize */ 177 int sigfigs; /* number of significant hex figures in result */ 178 179 u.d = d; 180 *sign = u.bits.sign; 181 182 switch (fpclassify(d)) { 183 case FP_NORMAL: 184 sigfigs = (DBL_MANT_DIG + 3) / 4; 185 impnbit = 1 << ((DBL_MANT_DIG - 1) % 4); 186 *decpt = u.bits.exp - DBL_BIAS + 1 - 187 ((DBL_MANT_DIG - 1) % 4); 188 break; 189 case FP_ZERO: 190 *decpt = 1; 191 return (nrv_alloc("0", rve, 1)); 192 case FP_SUBNORMAL: 193 /* 194 * The position of the highest-order bit tells us by 195 * how much to adjust the exponent (decpt). The 196 * adjustment is raised to the next nibble boundary 197 * since we will later choose the leftmost hexadecimal 198 * digit so that all subsequent digits align on nibble 199 * boundaries. 200 */ 201 if (u.bits.manh != 0) { 202 pos = log2_32(u.bits.manh); 203 shift = DBL_MANH_SIZE - pos; 204 } else { 205 pos = log2_32(u.bits.manl); 206 shift = DBL_MANH_SIZE + DBL_MANL_SIZE - pos; 207 } 208 sigfigs = (3 + DBL_MANT_DIG - shift) / 4; 209 impnbit = 0; 210 *decpt = DBL_MIN_EXP - ((shift + 3) & ~(4 - 1)); 211 break; 212 case FP_INFINITE: 213 *decpt = INT_MAX; 214 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 215 case FP_NAN: 216 *decpt = INT_MAX; 217 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 218 default: 219 abort(); 220 } 221 222 /* FP_NORMAL or FP_SUBNORMAL */ 223 224 if (ndigits == 0) /* dtoa() compatibility */ 225 ndigits = 1; 226 227 /* 228 * For simplicity, we generate all the digits even if the 229 * caller has requested fewer. 230 */ 231 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 232 s0 = rv_alloc(bufsize); 233 234 /* 235 * We work from right to left, first adding any requested zero 236 * padding, then the least significant portion of the 237 * mantissa, followed by the most significant. The buffer is 238 * filled with the byte values 0x0 through 0xf, which are 239 * converted to xdigs[0x0] through xdigs[0xf] after the 240 * rounding phase. 241 */ 242 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 243 *s = 0; 244 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 245 *s = u.bits.manl & 0xf; 246 u.bits.manl >>= 4; 247 } 248 for (; s > s0; s--) { 249 *s = u.bits.manh & 0xf; 250 u.bits.manh >>= 4; 251 } 252 253 /* 254 * At this point, we have snarfed all the bits in the 255 * mantissa, with the possible exception of the highest-order 256 * (partial) nibble, which is dealt with by the next 257 * statement. That nibble is usually in manh, but it could be 258 * in manl instead for small subnormals. We also tack on the 259 * implicit normalization bit if appropriate. 260 */ 261 *s = u.bits.manh | u.bits.manl | impnbit; 262 263 /* If ndigits < 0, we are expected to auto-size the precision. */ 264 if (ndigits < 0) { 265 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 266 ; 267 } 268 269 if (sigfigs > ndigits && s0[ndigits] != 0) 270 dorounding(s0, ndigits, u.bits.sign, decpt); 271 272 s = s0 + ndigits; 273 if (rve != NULL) 274 *rve = s; 275 *s-- = '\0'; 276 for (; s >= s0; s--) 277 *s = xdigs[(unsigned int)*s]; 278 279 return (s0); 280 } 281 282 #if (LDBL_MANT_DIG > DBL_MANT_DIG) 283 284 /* 285 * This is the long double version of __hdtoa(). 286 * 287 * On architectures that have an explicit integer bit, unnormals and 288 * pseudo-denormals cause problems in the conversion routine, so they 289 * are ``fixed'' by effectively toggling the integer bit. Although 290 * this is not correct behavior, the hardware will not produce these 291 * formats externally. 292 */ 293 char * 294 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 295 char **rve) 296 { 297 union IEEEl2bits u; 298 char *s, *s0; 299 int bufsize; 300 int impnbit; /* implicit normalization bit */ 301 int pos; 302 int shift; /* for subnormals, # of shifts required to normalize */ 303 int sigfigs; /* number of significant hex figures in result */ 304 305 u.e = e; 306 *sign = u.bits.sign; 307 308 switch (fpclassify(e)) { 309 case FP_NORMAL: 310 sigfigs = (LDBL_MANT_DIG + 3) / 4; 311 impnbit = 1 << ((LDBL_MANT_DIG - 1) % 4); 312 *decpt = u.bits.exp - LDBL_BIAS + 1 - 313 ((LDBL_MANT_DIG - 1) % 4); 314 break; 315 case FP_ZERO: 316 *decpt = 1; 317 return (nrv_alloc("0", rve, 1)); 318 case FP_SUBNORMAL: 319 /* 320 * The position of the highest-order bit tells us by 321 * how much to adjust the exponent (decpt). The 322 * adjustment is raised to the next nibble boundary 323 * since we will later choose the leftmost hexadecimal 324 * digit so that all subsequent digits align on nibble 325 * boundaries. 326 */ 327 #ifdef LDBL_IMPLICIT_NBIT 328 /* Don't trust the normalization bit to be off. */ 329 u.bits.manh &= ~(~0ULL << (LDBL_MANH_SIZE - 1)); 330 #endif 331 if (u.bits.manh != 0) { 332 #if LDBL_MANH_SIZE > 32 333 pos = log2_64(u.bits.manh); 334 #else 335 pos = log2_32(u.bits.manh); 336 #endif 337 shift = LDBL_MANH_SIZE - LDBL_NBIT_ADJ - pos; 338 } else { 339 #if LDBL_MANL_SIZE > 32 340 pos = log2_64(u.bits.manl); 341 #else 342 pos = log2_32(u.bits.manl); 343 #endif 344 shift = LDBL_MANH_SIZE + LDBL_MANL_SIZE - 345 LDBL_NBIT_ADJ - pos; 346 } 347 sigfigs = (3 + LDBL_MANT_DIG - LDBL_NBIT_ADJ - shift) / 4; 348 *decpt = LDBL_MIN_EXP + LDBL_NBIT_ADJ - 349 ((shift + 3) & ~(4 - 1)); 350 impnbit = 0; 351 break; 352 case FP_INFINITE: 353 *decpt = INT_MAX; 354 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); 355 case FP_NAN: 356 *decpt = INT_MAX; 357 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); 358 default: 359 abort(); 360 } 361 362 /* FP_NORMAL or FP_SUBNORMAL */ 363 364 if (ndigits == 0) /* dtoa() compatibility */ 365 ndigits = 1; 366 367 /* 368 * For simplicity, we generate all the digits even if the 369 * caller has requested fewer. 370 */ 371 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; 372 s0 = rv_alloc(bufsize); 373 374 /* 375 * We work from right to left, first adding any requested zero 376 * padding, then the least significant portion of the 377 * mantissa, followed by the most significant. The buffer is 378 * filled with the byte values 0x0 through 0xf, which are 379 * converted to xdigs[0x0] through xdigs[0xf] after the 380 * rounding phase. 381 */ 382 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) 383 *s = 0; 384 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) { 385 *s = u.bits.manl & 0xf; 386 u.bits.manl >>= 4; 387 } 388 for (; s > s0; s--) { 389 *s = u.bits.manh & 0xf; 390 u.bits.manh >>= 4; 391 } 392 393 /* 394 * At this point, we have snarfed all the bits in the 395 * mantissa, with the possible exception of the highest-order 396 * (partial) nibble, which is dealt with by the next 397 * statement. That nibble is usually in manh, but it could be 398 * in manl instead for small subnormals. We also tack on the 399 * implicit normalization bit if appropriate. 400 */ 401 *s = u.bits.manh | u.bits.manl | impnbit; 402 403 /* If ndigits < 0, we are expected to auto-size the precision. */ 404 if (ndigits < 0) { 405 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) 406 ; 407 } 408 409 if (sigfigs > ndigits && s0[ndigits] != 0) 410 dorounding(s0, ndigits, u.bits.sign, decpt); 411 412 s = s0 + ndigits; 413 if (rve != NULL) 414 *rve = s; 415 *s-- = '\0'; 416 for (; s >= s0; s--) 417 *s = xdigs[(unsigned int)*s]; 418 419 return (s0); 420 } 421 422 #else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 423 424 char * 425 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, 426 char **rve) 427 { 428 429 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve)); 430 } 431 432 #endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ 433