gdtoa/_hdtoa-fbsd.c

   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 1.3 2005/01/18 18:44:07 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  */
  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, 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:
 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                 LIBC_ABORT("fpclassify returned %d", f);
 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 #ifndef LDBL_COMPAT
 214 #if (LDBL_MANT_DIG > DBL_MANT_DIG)
 215
 216 /*
 217  * This is the long double version of __hdtoa().
 218  */
 219 char *
 220 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
 221     char **rve)
 222 {
 223         static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
 224         union IEEEl2bits u;
 225         char *s, *s0;
 226         int bufsize, f;
 227 #ifdef LDBL_HEAD_TAIL_PAIR
 228         uint32_t bits[4];
 229         int i, pos;
 230 #endif /* LDBL_HEAD_TAIL_PAIR */
 231
 232         u.e = e;
 233         *sign = u.bits.sign;
 234
 235         switch (f = fpclassify(e)) {
 236         case FP_NORMAL:
 237         case FP_SUPERNORMAL:
 238                 *decpt = u.bits.exp - LDBL_ADJ;
 239                 break;
 240         case FP_ZERO:
 241                 *decpt = 1;
 242                 return (nrv_alloc("0", rve, 1));
 243         case FP_SUBNORMAL:
 244                 u.e *= 0x1p514L;
 245                 *decpt = u.bits.exp - (514 + LDBL_ADJ);
 246                 break;
 247         case FP_INFINITE:
 248                 *decpt = INT_MAX;
 249                 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
 250         case FP_NAN:
 251                 *decpt = INT_MAX;
 252                 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
 253         default:
 254                 LIBC_ABORT("fpclassify returned %d", f);
 255         }
 256
 257         /* FP_NORMAL or FP_SUBNORMAL */
 258
 259         if (ndigits == 0)               /* dtoa() compatibility */
 260                 ndigits = 1;
 261
 262         /*
 263          * For simplicity, we generate all the digits even if the
 264          * caller has requested fewer.
 265          */
 266         bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
 267         s0 = rv_alloc(bufsize);
 268
 269         /*
 270          * We work from right to left, first adding any requested zero
 271          * padding, then the least significant portion of the
 272          * mantissa, followed by the most significant.  The buffer is
 273          * filled with the byte values 0x0 through 0xf, which are
 274          * converted to xdigs[0x0] through xdigs[0xf] after the
 275          * rounding phase.
 276          */
 277         for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
 278                 *s = 0;
 279 #ifdef LDBL_HEAD_TAIL_PAIR
 280         *decpt -= _ldbl2array32dd(u, bits);
 281         i = 0;
 282         pos = 8;
 283         for (; s > s0; s--) {
 284                 *s = bits[i] & 0xf;
 285                 bits[i] >>= 4;
 286                 if (--pos <= 0) {
 287                         i++;
 288                         pos = 8;
 289                 }
 290         }
 291 #else /* LDBL_HEAD_TAIL_PAIR */
 292         for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
 293                 *s = u.bits.manl & 0xf;
 294                 u.bits.manl >>= 4;
 295         }
 296         for (; s > s0; s--) {
 297                 *s = u.bits.manh & 0xf;
 298                 u.bits.manh >>= 4;
 299         }
 300 #endif /* LDBL_HEAD_TAIL_PAIR */
 301
 302         /*
 303          * At this point, we have snarfed all the bits in the
 304          * mantissa, with the possible exception of the highest-order
 305          * (partial) nibble, which is dealt with by the next
 306          * statement.  We also tack on the implicit normalization bit.
 307          */
 308 #ifdef LDBL_HEAD_TAIL_PAIR
 309         *s = bits[i];
 310 #else /* LDBL_HEAD_TAIL_PAIR */
 311         *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
 312 #endif /* LDBL_HEAD_TAIL_PAIR */
 313
 314         /* If ndigits < 0, we are expected to auto-size the precision. */
 315         if (ndigits < 0) {
 316                 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
 317                         ;
 318         }
 319
 320         if (sigfigs > ndigits && s0[ndigits] != 0)
 321                 dorounding(s0, ndigits, u.bits.sign, decpt);
 322
 323         s = s0 + ndigits;
 324         if (rve != NULL)
 325                 *rve = s;
 326         *s-- = '\0';
 327         for (; s >= s0; s--)
 328                 *s = xdigs[(unsigned int)*s];
 329
 330         return (s0);
 331 }
 332
 333 #else   /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
 334
 335 char *
 336 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
 337     char **rve)
 338 {
 339
 340         return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
 341 }
 342
 343 #endif  /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
 344 #endif  /* !LDBL_COMPAT */