gdtoa/FreeBSD/_hdtoa.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 1.5 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  */
  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 return_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  */
 224 char *
 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
 318 char *
 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) */