libiberty/floatformat.c

   1 /* IEEE floating point support routines, for GDB, the GNU Debugger.
   2    Copyright 1991, 1994, 1999, 2000, 2003, 2005, 2006
   3    Free Software Foundation, Inc.
   4
   5 This file is part of GDB.
   6
   7 This program is free software; you can redistribute it and/or modify
   8 it under the terms of the GNU General Public License as published by
   9 the Free Software Foundation; either version 2 of the License, or
  10 (at your option) any later version.
  11
  12 This program is distributed in the hope that it will be useful,
  13 but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 GNU General Public License for more details.
  16
  17 You should have received a copy of the GNU General Public License
  18 along with this program; if not, write to the Free Software
  19 Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.  */
  20
  21 /* This is needed to pick up the NAN macro on some systems.  */
  22 #define _GNU_SOURCE
  23
  24 #ifdef HAVE_CONFIG_H
  25 #include "config.h"
  26 #endif
  27
  28 #include <math.h>
  29
  30 #ifdef HAVE_STRING_H
  31 #include <string.h>
  32 #endif
  33
  34 /* On some platforms, <float.h> provides DBL_QNAN.  */
  35 #ifdef STDC_HEADERS
  36 #include <float.h>
  37 #endif
  38
  39 #include "ansidecl.h"
  40 #include "libiberty.h"
  41 #include "floatformat.h"
  42
  43 #ifndef INFINITY
  44 #ifdef HUGE_VAL
  45 #define INFINITY HUGE_VAL
  46 #else
  47 #define INFINITY (1.0 / 0.0)
  48 #endif
  49 #endif
  50
  51 #ifndef NAN
  52 #ifdef DBL_QNAN
  53 #define NAN DBL_QNAN
  54 #else
  55 #define NAN (0.0 / 0.0)
  56 #endif
  57 #endif
  58
  59 static unsigned long get_field (const unsigned char *,
  60                                 enum floatformat_byteorders,
  61                                 unsigned int,
  62                                 unsigned int,
  63                                 unsigned int);
  64 static int floatformat_always_valid (const struct floatformat *fmt,
  65                                      const void *from);
  66
  67 static int
  68 floatformat_always_valid (const struct floatformat *fmt ATTRIBUTE_UNUSED,
  69                           const void *from ATTRIBUTE_UNUSED)
  70 {
  71   return 1;
  72 }
  73
  74 /* The odds that CHAR_BIT will be anything but 8 are low enough that I'm not
  75    going to bother with trying to muck around with whether it is defined in
  76    a system header, what we do if not, etc.  */
  77 #define FLOATFORMAT_CHAR_BIT 8
  78
  79 /* floatformats for IEEE single and double, big and little endian.  */
  80 const struct floatformat floatformat_ieee_single_big =
  81 {
  82   floatformat_big, 32, 0, 1, 8, 127, 255, 9, 23,
  83   floatformat_intbit_no,
  84   "floatformat_ieee_single_big",
  85   floatformat_always_valid
  86 };
  87 const struct floatformat floatformat_ieee_single_little =
  88 {
  89   floatformat_little, 32, 0, 1, 8, 127, 255, 9, 23,
  90   floatformat_intbit_no,
  91   "floatformat_ieee_single_little",
  92   floatformat_always_valid
  93 };
  94 const struct floatformat floatformat_ieee_double_big =
  95 {
  96   floatformat_big, 64, 0, 1, 11, 1023, 2047, 12, 52,
  97   floatformat_intbit_no,
  98   "floatformat_ieee_double_big",
  99   floatformat_always_valid
 100 };
 101 const struct floatformat floatformat_ieee_double_little =
 102 {
 103   floatformat_little, 64, 0, 1, 11, 1023, 2047, 12, 52,
 104   floatformat_intbit_no,
 105   "floatformat_ieee_double_little",
 106   floatformat_always_valid
 107 };
 108
 109 /* floatformat for IEEE double, little endian byte order, with big endian word
 110    ordering, as on the ARM.  */
 111
 112 const struct floatformat floatformat_ieee_double_littlebyte_bigword =
 113 {
 114   floatformat_littlebyte_bigword, 64, 0, 1, 11, 1023, 2047, 12, 52,
 115   floatformat_intbit_no,
 116   "floatformat_ieee_double_littlebyte_bigword",
 117   floatformat_always_valid
 118 };
 119
 120 /* floatformat for VAX.  Not quite IEEE, but close enough.  */
 121
 122 const struct floatformat floatformat_vax_f =
 123 {
 124   floatformat_vax, 32, 0, 1, 8, 129, 0, 9, 23,
 125   floatformat_intbit_no,
 126   "floatformat_vax_f",
 127   floatformat_always_valid
 128 };
 129 const struct floatformat floatformat_vax_d =
 130 {
 131   floatformat_vax, 64, 0, 1, 8, 129, 0, 9, 55,
 132   floatformat_intbit_no,
 133   "floatformat_vax_d",
 134   floatformat_always_valid
 135 };
 136 const struct floatformat floatformat_vax_g =
 137 {
 138   floatformat_vax, 64, 0, 1, 11, 1025, 0, 12, 52,
 139   floatformat_intbit_no,
 140   "floatformat_vax_g",
 141   floatformat_always_valid
 142 };
 143
 144 static int floatformat_i387_ext_is_valid (const struct floatformat *fmt,
 145                                           const void *from);
 146
 147 static int
 148 floatformat_i387_ext_is_valid (const struct floatformat *fmt, const void *from)
 149 {
 150   /* In the i387 double-extended format, if the exponent is all ones,
 151      then the integer bit must be set.  If the exponent is neither 0
 152      nor ~0, the intbit must also be set.  Only if the exponent is
 153      zero can it be zero, and then it must be zero.  */
 154   unsigned long exponent, int_bit;
 155   const unsigned char *ufrom = (const unsigned char *) from;
 156
 157   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 158                         fmt->exp_start, fmt->exp_len);
 159   int_bit = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 160                        fmt->man_start, 1);
 161
 162   if ((exponent == 0) != (int_bit == 0))
 163     return 0;
 164   else
 165     return 1;
 166 }
 167
 168 const struct floatformat floatformat_i387_ext =
 169 {
 170   floatformat_little, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 171   floatformat_intbit_yes,
 172   "floatformat_i387_ext",
 173   floatformat_i387_ext_is_valid
 174 };
 175 const struct floatformat floatformat_m68881_ext =
 176 {
 177   /* Note that the bits from 16 to 31 are unused.  */
 178   floatformat_big, 96, 0, 1, 15, 0x3fff, 0x7fff, 32, 64,
 179   floatformat_intbit_yes,
 180   "floatformat_m68881_ext",
 181   floatformat_always_valid
 182 };
 183 const struct floatformat floatformat_i960_ext =
 184 {
 185   /* Note that the bits from 0 to 15 are unused.  */
 186   floatformat_little, 96, 16, 17, 15, 0x3fff, 0x7fff, 32, 64,
 187   floatformat_intbit_yes,
 188   "floatformat_i960_ext",
 189   floatformat_always_valid
 190 };
 191 const struct floatformat floatformat_m88110_ext =
 192 {
 193   floatformat_big, 80, 0, 1, 15, 0x3fff, 0x7fff, 16, 64,
 194   floatformat_intbit_yes,
 195   "floatformat_m88110_ext",
 196   floatformat_always_valid
 197 };
 198 const struct floatformat floatformat_m88110_harris_ext =
 199 {
 200   /* Harris uses raw format 128 bytes long, but the number is just an ieee
 201      double, and the last 64 bits are wasted. */
 202   floatformat_big,128, 0, 1, 11,  0x3ff,  0x7ff, 12, 52,
 203   floatformat_intbit_no,
 204   "floatformat_m88110_ext_harris",
 205   floatformat_always_valid
 206 };
 207 const struct floatformat floatformat_arm_ext_big =
 208 {
 209   /* Bits 1 to 16 are unused.  */
 210   floatformat_big, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 211   floatformat_intbit_yes,
 212   "floatformat_arm_ext_big",
 213   floatformat_always_valid
 214 };
 215 const struct floatformat floatformat_arm_ext_littlebyte_bigword =
 216 {
 217   /* Bits 1 to 16 are unused.  */
 218   floatformat_littlebyte_bigword, 96, 0, 17, 15, 0x3fff, 0x7fff, 32, 64,
 219   floatformat_intbit_yes,
 220   "floatformat_arm_ext_littlebyte_bigword",
 221   floatformat_always_valid
 222 };
 223 const struct floatformat floatformat_ia64_spill_big =
 224 {
 225   floatformat_big, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 226   floatformat_intbit_yes,
 227   "floatformat_ia64_spill_big",
 228   floatformat_always_valid
 229 };
 230 const struct floatformat floatformat_ia64_spill_little =
 231 {
 232   floatformat_little, 128, 0, 1, 17, 65535, 0x1ffff, 18, 64,
 233   floatformat_intbit_yes,
 234   "floatformat_ia64_spill_little",
 235   floatformat_always_valid
 236 };
 237 const struct floatformat floatformat_ia64_quad_big =
 238 {
 239   floatformat_big, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 240   floatformat_intbit_no,
 241   "floatformat_ia64_quad_big",
 242   floatformat_always_valid
 243 };
 244 const struct floatformat floatformat_ia64_quad_little =
 245 {
 246   floatformat_little, 128, 0, 1, 15, 16383, 0x7fff, 16, 112,
 247   floatformat_intbit_no,
 248   "floatformat_ia64_quad_little",
 249   floatformat_always_valid
 250 };
 251 \f
 252
 253 #ifndef min
 254 #define min(a, b) ((a) < (b) ? (a) : (b))
 255 #endif
 256
 257 /* Extract a field which starts at START and is LEN bits long.  DATA and
 258    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 259 static unsigned long
 260 get_field (const unsigned char *data, enum floatformat_byteorders order,
 261            unsigned int total_len, unsigned int start, unsigned int len)
 262 {
 263   unsigned long result = 0;
 264   unsigned int cur_byte;
 265   int lo_bit, hi_bit, cur_bitshift = 0;
 266   int nextbyte = (order == floatformat_little) ? 1 : -1;
 267
 268   /* Start is in big-endian bit order!  Fix that first.  */
 269   start = total_len - (start + len);
 270
 271   /* Start at the least significant part of the field.  */
 272   if (order == floatformat_little)
 273     cur_byte = start / FLOATFORMAT_CHAR_BIT;
 274   else
 275     cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT;
 276
 277   lo_bit = start % FLOATFORMAT_CHAR_BIT;
 278   hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT);
 279
 280   do
 281     {
 282       unsigned int shifted = *(data + cur_byte) >> lo_bit;
 283       unsigned int bits = hi_bit - lo_bit;
 284       unsigned int mask = (1 << bits) - 1;
 285       result |= (shifted & mask) << cur_bitshift;
 286       len -= bits;
 287       cur_bitshift += bits;
 288       cur_byte += nextbyte;
 289       lo_bit = 0;
 290       hi_bit = min (len, FLOATFORMAT_CHAR_BIT);
 291     }
 292   while (len != 0);
 293
 294   return result;
 295 }
 296
 297 /* Convert from FMT to a double.
 298    FROM is the address of the extended float.
 299    Store the double in *TO.  */
 300
 301 void
 302 floatformat_to_double (const struct floatformat *fmt,
 303                        const void *from, double *to)
 304 {
 305   const unsigned char *ufrom = (const unsigned char *) from;
 306   double dto;
 307   long exponent;
 308   unsigned long mant;
 309   unsigned int mant_bits, mant_off;
 310   int mant_bits_left;
 311   int special_exponent;         /* It's a NaN, denorm or zero */
 312
 313   exponent = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 314                         fmt->exp_start, fmt->exp_len);
 315
 316   /* If the exponent indicates a NaN, we don't have information to
 317      decide what to do.  So we handle it like IEEE, except that we
 318      don't try to preserve the type of NaN.  FIXME.  */
 319   if ((unsigned long) exponent == fmt->exp_nan)
 320     {
 321       int nan;
 322
 323       mant_off = fmt->man_start;
 324       mant_bits_left = fmt->man_len;
 325       nan = 0;
 326       while (mant_bits_left > 0)
 327         {
 328           mant_bits = min (mant_bits_left, 32);
 329
 330           if (get_field (ufrom, fmt->byteorder, fmt->totalsize,
 331                          mant_off, mant_bits) != 0)
 332             {
 333               /* This is a NaN.  */
 334               nan = 1;
 335               break;
 336             }
 337
 338           mant_off += mant_bits;
 339           mant_bits_left -= mant_bits;
 340         }
 341
 342       /* On certain systems (such as GNU/Linux), the use of the
 343          INFINITY macro below may generate a warning that can not be
 344          silenced due to a bug in GCC (PR preprocessor/11931).  The
 345          preprocessor fails to recognise the __extension__ keyword in
 346          conjunction with the GNU/C99 extension for hexadecimal
 347          floating point constants and will issue a warning when
 348          compiling with -pedantic.  */
 349       if (nan)
 350         dto = NAN;
 351       else
 352         dto = INFINITY;
 353
 354       if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 355         dto = -dto;
 356
 357       *to = dto;
 358
 359       return;
 360     }
 361
 362   mant_bits_left = fmt->man_len;
 363   mant_off = fmt->man_start;
 364   dto = 0.0;
 365
 366   special_exponent = exponent == 0 || (unsigned long) exponent == fmt->exp_nan;
 367
 368   /* Don't bias zero's, denorms or NaNs.  */
 369   if (!special_exponent)
 370     exponent -= fmt->exp_bias;
 371
 372   /* Build the result algebraically.  Might go infinite, underflow, etc;
 373      who cares. */
 374
 375   /* If this format uses a hidden bit, explicitly add it in now.  Otherwise,
 376      increment the exponent by one to account for the integer bit.  */
 377
 378   if (!special_exponent)
 379     {
 380       if (fmt->intbit == floatformat_intbit_no)
 381         dto = ldexp (1.0, exponent);
 382       else
 383         exponent++;
 384     }
 385
 386   while (mant_bits_left > 0)
 387     {
 388       mant_bits = min (mant_bits_left, 32);
 389
 390       mant = get_field (ufrom, fmt->byteorder, fmt->totalsize,
 391                          mant_off, mant_bits);
 392
 393       /* Handle denormalized numbers.  FIXME: What should we do for
 394          non-IEEE formats?  */
 395       if (special_exponent && exponent == 0 && mant != 0)
 396         dto += ldexp ((double)mant,
 397                       (- fmt->exp_bias
 398                        - mant_bits
 399                        - (mant_off - fmt->man_start)
 400                        + 1));
 401       else
 402         dto += ldexp ((double)mant, exponent - mant_bits);
 403       if (exponent != 0)
 404         exponent -= mant_bits;
 405       mant_off += mant_bits;
 406       mant_bits_left -= mant_bits;
 407     }
 408
 409   /* Negate it if negative.  */
 410   if (get_field (ufrom, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1))
 411     dto = -dto;
 412   *to = dto;
 413 }
 414 \f
 415 static void put_field (unsigned char *, enum floatformat_byteorders,
 416                        unsigned int,
 417                        unsigned int,
 418                        unsigned int,
 419                        unsigned long);
 420
 421 /* Set a field which starts at START and is LEN bits long.  DATA and
 422    TOTAL_LEN are the thing we are extracting it from, in byteorder ORDER.  */
 423 static void
 424 put_field (unsigned char *data, enum floatformat_byteorders order,
 425            unsigned int total_len, unsigned int start, unsigned int len,
 426            unsigned long stuff_to_put)
 427 {
 428   unsigned int cur_byte;
 429   int lo_bit, hi_bit;
 430   int nextbyte = (order == floatformat_little) ? 1 : -1;
 431
 432   /* Start is in big-endian bit order!  Fix that first.  */
 433   start = total_len - (start + len);
 434
 435   /* Start at the least significant part of the field.  */
 436   if (order == floatformat_little)
 437     cur_byte = start / FLOATFORMAT_CHAR_BIT;
 438   else
 439     cur_byte = (total_len - start - 1) / FLOATFORMAT_CHAR_BIT;
 440
 441   lo_bit = start % FLOATFORMAT_CHAR_BIT;
 442   hi_bit = min (lo_bit + len, FLOATFORMAT_CHAR_BIT);
 443
 444   do
 445     {
 446       unsigned char *byte_ptr = data + cur_byte;
 447       unsigned int bits = hi_bit - lo_bit;
 448       unsigned int mask = ((1 << bits) - 1) << lo_bit;
 449       *byte_ptr = (*byte_ptr & ~mask) | ((stuff_to_put << lo_bit) & mask);
 450       stuff_to_put >>= bits;
 451       len -= bits;
 452       cur_byte += nextbyte;
 453       lo_bit = 0;
 454       hi_bit = min (len, FLOATFORMAT_CHAR_BIT);
 455     }
 456   while (len != 0);
 457 }
 458
 459 /* The converse: convert the double *FROM to an extended float
 460    and store where TO points.  Neither FROM nor TO have any alignment
 461    restrictions.  */
 462
 463 void
 464 floatformat_from_double (const struct floatformat *fmt,
 465                          const double *from, void *to)
 466 {
 467   double dfrom;
 468   int exponent;
 469   double mant;
 470   unsigned int mant_bits, mant_off;
 471   int mant_bits_left;
 472   unsigned char *uto = (unsigned char *) to;
 473
 474   dfrom = *from;
 475   memset (uto, 0, fmt->totalsize / FLOATFORMAT_CHAR_BIT);
 476
 477   /* If negative, set the sign bit.  */
 478   if (dfrom < 0)
 479     {
 480       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->sign_start, 1, 1);
 481       dfrom = -dfrom;
 482     }
 483
 484   if (dfrom == 0)
 485     {
 486       /* 0.0.  */
 487       return;
 488     }
 489
 490   if (dfrom != dfrom)
 491     {
 492       /* NaN.  */
 493       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 494                  fmt->exp_len, fmt->exp_nan);
 495       /* Be sure it's not infinity, but NaN value is irrelevant.  */
 496       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->man_start,
 497                  32, 1);
 498       return;
 499     }
 500
 501   if (dfrom + dfrom == dfrom)
 502     {
 503       /* This can only happen for an infinite value (or zero, which we
 504          already handled above).  */
 505       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 506                  fmt->exp_len, fmt->exp_nan);
 507       return;
 508     }
 509
 510   mant = frexp (dfrom, &exponent);
 511   if (exponent + fmt->exp_bias - 1 > 0)
 512     put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 513                fmt->exp_len, exponent + fmt->exp_bias - 1);
 514   else
 515     {
 516       /* Handle a denormalized number.  FIXME: What should we do for
 517          non-IEEE formats?  */
 518       put_field (uto, fmt->byteorder, fmt->totalsize, fmt->exp_start,
 519                  fmt->exp_len, 0);
 520       mant = ldexp (mant, exponent + fmt->exp_bias - 1);
 521     }
 522
 523   mant_bits_left = fmt->man_len;
 524   mant_off = fmt->man_start;
 525   while (mant_bits_left > 0)
 526     {
 527       unsigned long mant_long;
 528       mant_bits = mant_bits_left < 32 ? mant_bits_left : 32;
 529
 530       mant *= 4294967296.0;
 531       mant_long = (unsigned long)mant;
 532       mant -= mant_long;
 533
 534       /* If the integer bit is implicit, and we are not creating a
 535          denormalized number, then we need to discard it.  */
 536       if ((unsigned int) mant_bits_left == fmt->man_len
 537           && fmt->intbit == floatformat_intbit_no
 538           && exponent + fmt->exp_bias - 1 > 0)
 539         {
 540           mant_long &= 0x7fffffff;
 541           mant_bits -= 1;
 542         }
 543       else if (mant_bits < 32)
 544         {
 545           /* The bits we want are in the most significant MANT_BITS bits of
 546              mant_long.  Move them to the least significant.  */
 547           mant_long >>= 32 - mant_bits;
 548         }
 549
 550       put_field (uto, fmt->byteorder, fmt->totalsize,
 551                  mant_off, mant_bits, mant_long);
 552       mant_off += mant_bits;
 553       mant_bits_left -= mant_bits;
 554     }
 555 }
 556
 557 /* Return non-zero iff the data at FROM is a valid number in format FMT.  */
 558
 559 int
 560 floatformat_is_valid (const struct floatformat *fmt, const void *from)
 561 {
 562   return fmt->is_valid (fmt, from);
 563 }
 564
 565
 566 #ifdef IEEE_DEBUG
 567
 568 #include <stdio.h>
 569
 570 /* This is to be run on a host which uses IEEE floating point.  */
 571
 572 void
 573 ieee_test (double n)
 574 {
 575   double result;
 576
 577   floatformat_to_double (&floatformat_ieee_double_little, &n, &result);
 578   if ((n != result && (! isnan (n) || ! isnan (result)))
 579       || (n < 0 && result >= 0)
 580       || (n >= 0 && result < 0))
 581     printf ("Differ(to): %.20g -> %.20g\n", n, result);
 582
 583   floatformat_from_double (&floatformat_ieee_double_little, &n, &result);
 584   if ((n != result && (! isnan (n) || ! isnan (result)))
 585       || (n < 0 && result >= 0)
 586       || (n >= 0 && result < 0))
 587     printf ("Differ(from): %.20g -> %.20g\n", n, result);
 588
 589 #if 0
 590   {
 591     char exten[16];
 592
 593     floatformat_from_double (&floatformat_m68881_ext, &n, exten);
 594     floatformat_to_double (&floatformat_m68881_ext, exten, &result);
 595     if (n != result)
 596       printf ("Differ(to+from): %.20g -> %.20g\n", n, result);
 597   }
 598 #endif
 599
 600 #if IEEE_DEBUG > 1
 601   /* This is to be run on a host which uses 68881 format.  */
 602   {
 603     long double ex = *(long double *)exten;
 604     if (ex != n)
 605       printf ("Differ(from vs. extended): %.20g\n", n);
 606   }
 607 #endif
 608 }
 609
 610 int
 611 main (void)
 612 {
 613   ieee_test (0.0);
 614   ieee_test (0.5);
 615   ieee_test (256.0);
 616   ieee_test (0.12345);
 617   ieee_test (234235.78907234);
 618   ieee_test (-512.0);
 619   ieee_test (-0.004321);
 620   ieee_test (1.2E-70);
 621   ieee_test (1.2E-316);
 622   ieee_test (4.9406564584124654E-324);
 623   ieee_test (- 4.9406564584124654E-324);
 624   ieee_test (- 0.0);
 625   ieee_test (- INFINITY);
 626   ieee_test (- NAN);
 627   ieee_test (INFINITY);
 628   ieee_test (NAN);
 629   return 0;
 630 }
 631 #endif