lib/libc/gdtoa/hdtoa.c

   1 /*      $NetBSD: hdtoa.c,v 1.6 2008/03/21 23:13:48 christos Exp $       */
   2
   3 /*-
   4  * Copyright (c) 2004, 2005 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 #if 0
  31 __FBSDID("$FreeBSD: src/lib/libc/gdtoa/_hdtoa.c,v 1.4 2007/01/03 04:57:58 das Exp $");
  32 #else
  33 __RCSID("$NetBSD: hdtoa.c,v 1.6 2008/03/21 23:13:48 christos Exp $");
  34 #endif
  35
  36 #include <float.h>
  37 #include <limits.h>
  38 #include <math.h>
  39 #ifndef __vax__
  40 #include <machine/ieee.h>
  41 #else
  42 #include <machine/vaxfp.h>
  43 #define ieee_double_u vax_dfloating_u
  44 #define dblu_d dfltu_d
  45 #define dblu_dbl dfltu_dflt
  46 #define dbl_sign dflt_sign
  47 #define dbl_exp dflt_exp
  48 #define dbl_frach dflt_frach
  49 #define dbl_fracm dflt_fracm
  50 #define dbl_fracl dflt_fracl
  51 #define DBL_FRACHBITS   DFLT_FRACHBITS
  52 #define DBL_FRACMBITS   DFLT_FRACMBITS
  53 #define DBL_FRACLBITS   DFLT_FRACLBITS
  54 #define DBL_EXPBITS     DFLT_EXPBITS
  55 #endif
  56 #include "gdtoaimp.h"
  57
  58 /* Strings values used by dtoa() */
  59 #define INFSTR  "Infinity"
  60 #define NANSTR  "NaN"
  61
  62 #define DBL_ADJ         (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
  63 #define LDBL_ADJ        (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
  64
  65 /*
  66  * Round up the given digit string.  If the digit string is fff...f,
  67  * this procedure sets it to 100...0 and returns 1 to indicate that
  68  * the exponent needs to be bumped.  Otherwise, 0 is returned.
  69  */
  70 static int
  71 roundup(char *s0, int ndigits)
  72 {
  73         char *s;
  74
  75         for (s = s0 + ndigits - 1; *s == 0xf; s--) {
  76                 if (s == s0) {
  77                         *s = 1;
  78                         return (1);
  79                 }
  80                 *s = 0;
  81         }
  82         ++*s;
  83         return (0);
  84 }
  85
  86 /*
  87  * Round the given digit string to ndigits digits according to the
  88  * current rounding mode.  Note that this could produce a string whose
  89  * value is not representable in the corresponding floating-point
  90  * type.  The exponent pointed to by decpt is adjusted if necessary.
  91  */
  92 static void
  93 dorounding(char *s0, int ndigits, int sign, int *decpt)
  94 {
  95         int adjust = 0; /* do we need to adjust the exponent? */
  96
  97         switch (FLT_ROUNDS) {
  98         case 0:         /* toward zero */
  99         default:        /* implementation-defined */
 100                 break;
 101         case 1:         /* to nearest, halfway rounds to even */
 102                 if ((s0[ndigits] > 8) ||
 103                     (s0[ndigits] == 8 && s0[ndigits - 1] & 1))
 104                         adjust = roundup(s0, ndigits);
 105                 break;
 106         case 2:         /* toward +inf */
 107                 if (sign == 0)
 108                         adjust = roundup(s0, ndigits);
 109                 break;
 110         case 3:         /* toward -inf */
 111                 if (sign != 0)
 112                         adjust = roundup(s0, ndigits);
 113                 break;
 114         }
 115
 116         if (adjust)
 117                 *decpt += 4;
 118 }
 119
 120 /*
 121  * This procedure converts a double-precision number in IEEE format
 122  * into a string of hexadecimal digits and an exponent of 2.  Its
 123  * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
 124  * following exceptions:
 125  *
 126  * - An ndigits < 0 causes it to use as many digits as necessary to
 127  *   represent the number exactly.
 128  * - The additional xdigs argument should point to either the string
 129  *   "0123456789ABCDEF" or the string "0123456789abcdef", depending on
 130  *   which case is desired.
 131  * - This routine does not repeat dtoa's mistake of setting decpt
 132  *   to 9999 in the case of an infinity or NaN.  INT_MAX is used
 133  *   for this purpose instead.
 134  *
 135  * Note that the C99 standard does not specify what the leading digit
 136  * should be for non-zero numbers.  For instance, 0x1.3p3 is the same
 137  * as 0x2.6p2 is the same as 0x4.cp3.  This implementation chooses the
 138  * first digit so that subsequent digits are aligned on nibble
 139  * boundaries (before rounding).
 140  *
 141  * Inputs:      d, xdigs, ndigits
 142  * Outputs:     decpt, sign, rve
 143  */
 144 char *
 145 hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
 146     char **rve)
 147 {
 148         static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
 149         union ieee_double_u u;
 150         char *s, *s0;
 151         size_t bufsize;
 152
 153         u.dblu_d = d;
 154         *sign = u.dblu_dbl.dbl_sign;
 155
 156         switch (fpclassify(d)) {
 157         case FP_NORMAL:
 158                 *decpt = u.dblu_dbl.dbl_exp - DBL_ADJ;
 159                 break;
 160         case FP_ZERO:
 161                 *decpt = 1;
 162                 return (nrv_alloc("0", rve, 1));
 163         case FP_SUBNORMAL:
 164                 u.dblu_d *= 0x1p514;
 165                 *decpt = u.dblu_dbl.dbl_exp - (514 + DBL_ADJ);
 166                 break;
 167         case FP_INFINITE:
 168                 *decpt = INT_MAX;
 169                 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
 170         case FP_NAN:
 171                 *decpt = INT_MAX;
 172                 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
 173         default:
 174                 abort();
 175         }
 176
 177         /* FP_NORMAL or FP_SUBNORMAL */
 178
 179         if (ndigits == 0)               /* dtoa() compatibility */
 180                 ndigits = 1;
 181
 182         /*
 183          * For simplicity, we generate all the digits even if the
 184          * caller has requested fewer.
 185          */
 186         bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
 187         s0 = rv_alloc(bufsize);
 188         if (s0 == NULL)
 189                 return NULL;
 190
 191         /*
 192          * We work from right to left, first adding any requested zero
 193          * padding, then the least significant portion of the
 194          * mantissa, followed by the most significant.  The buffer is
 195          * filled with the byte values 0x0 through 0xf, which are
 196          * converted to xdigs[0x0] through xdigs[0xf] after the
 197          * rounding phase.
 198          */
 199         for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
 200                 *s = 0;
 201         for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) {
 202                 *s = u.dblu_dbl.dbl_fracl & 0xf;
 203                 u.dblu_dbl.dbl_fracl >>= 4;
 204         }
 205 #ifdef DBL_FRACMBITS
 206         for (; s > s0; s--) {
 207                 *s = u.dblu_dbl.dbl_fracm & 0xf;
 208                 u.dblu_dbl.dbl_fracm >>= 4;
 209         }
 210 #endif
 211         for (; s > s0; s--) {
 212                 *s = u.dblu_dbl.dbl_frach & 0xf;
 213                 u.dblu_dbl.dbl_frach >>= 4;
 214         }
 215
 216         /*
 217          * At this point, we have snarfed all the bits in the
 218          * mantissa, with the possible exception of the highest-order
 219          * (partial) nibble, which is dealt with by the next
 220          * statement.  We also tack on the implicit normalization bit.
 221          */
 222         *s = u.dblu_dbl.dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4));
 223
 224         /* If ndigits < 0, we are expected to auto-size the precision. */
 225         if (ndigits < 0) {
 226                 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
 227                         continue;
 228         }
 229
 230         if (sigfigs > ndigits && s0[ndigits] != 0)
 231                 dorounding(s0, ndigits, u.dblu_dbl.dbl_sign, decpt);
 232
 233         s = s0 + ndigits;
 234         if (rve != NULL)
 235                 *rve = s;
 236         *s-- = '\0';
 237         for (; s >= s0; s--)
 238                 *s = xdigs[(unsigned int)*s];
 239
 240         return (s0);
 241 }
 242
 243 #if (LDBL_MANT_DIG > DBL_MANT_DIG)
 244
 245 /*
 246  * This is the long double version of hdtoa().
 247  */
 248 char *
 249 hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
 250     char **rve)
 251 {
 252         static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
 253         union ieee_ext_u u;
 254         char *s, *s0;
 255         size_t bufsize;
 256
 257         u.extu_ld = e;
 258         *sign = u.extu_ext.ext_sign;
 259
 260         switch (fpclassify(e)) {
 261         case FP_NORMAL:
 262                 *decpt = u.extu_ext.ext_exp - LDBL_ADJ;
 263                 break;
 264         case FP_ZERO:
 265                 *decpt = 1;
 266                 return (nrv_alloc("0", rve, 1));
 267         case FP_SUBNORMAL:
 268                 u.extu_ld *= 0x1p514L;
 269                 *decpt = u.extu_ext.ext_exp - (514 + LDBL_ADJ);
 270                 break;
 271         case FP_INFINITE:
 272                 *decpt = INT_MAX;
 273                 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
 274         case FP_NAN:
 275                 *decpt = INT_MAX;
 276                 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
 277         default:
 278                 abort();
 279         }
 280
 281         /* FP_NORMAL or FP_SUBNORMAL */
 282
 283         if (ndigits == 0)               /* dtoa() compatibility */
 284                 ndigits = 1;
 285
 286         /*
 287          * For simplicity, we generate all the digits even if the
 288          * caller has requested fewer.
 289          */
 290         bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
 291         s0 = rv_alloc(bufsize);
 292         if (s0 == NULL)
 293                 return NULL;
 294
 295         /*
 296          * We work from right to left, first adding any requested zero
 297          * padding, then the least significant portion of the
 298          * mantissa, followed by the most significant.  The buffer is
 299          * filled with the byte values 0x0 through 0xf, which are
 300          * converted to xdigs[0x0] through xdigs[0xf] after the
 301          * rounding phase.
 302          */
 303         for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
 304                 *s = 0;
 305         for (; s > s0 + sigfigs - (EXT_FRACLBITS / 4) - 1 && s > s0; s--) {
 306                 *s = u.extu_ext.ext_fracl & 0xf;
 307                 u.extu_ext.ext_fracl >>= 4;
 308         }
 309 #ifdef EXT_FRACHMBITS
 310         for (; s > s0; s--) {
 311                 *s = u.extu_ext.ext_frachm & 0xf;
 312                 u.extu_ext.ext_frachm >>= 4;
 313         }
 314 #endif
 315 #ifdef EXT_FRACLMBITS
 316         for (; s > s0; s--) {
 317                 *s = u.extu_ext.ext_fraclm & 0xf;
 318                 u.extu_ext.ext_fraclm >>= 4;
 319         }
 320 #endif
 321         for (; s > s0; s--) {
 322                 *s = u.extu_ext.ext_frach & 0xf;
 323                 u.extu_ext.ext_frach >>= 4;
 324         }
 325
 326         /*
 327          * At this point, we have snarfed all the bits in the
 328          * mantissa, with the possible exception of the highest-order
 329          * (partial) nibble, which is dealt with by the next
 330          * statement.  We also tack on the implicit normalization bit.
 331          */
 332         *s = u.extu_ext.ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4));
 333
 334         /* If ndigits < 0, we are expected to auto-size the precision. */
 335         if (ndigits < 0) {
 336                 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
 337                         continue;
 338         }
 339
 340         if (sigfigs > ndigits && s0[ndigits] != 0)
 341                 dorounding(s0, ndigits, u.extu_ext.ext_sign, decpt);
 342
 343         s = s0 + ndigits;
 344         if (rve != NULL)
 345                 *rve = s;
 346         *s-- = '\0';
 347         for (; s >= s0; s--)
 348                 *s = xdigs[(unsigned int)*s];
 349
 350         return (s0);
 351 }
 352
 353 #else   /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
 354
 355 char *
 356 hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
 357     char **rve)
 358 {
 359
 360         return (hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
 361 }
 362
 363 #endif  /* (LDBL_MANT_DIG == DBL_MANT_DIG) */